the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 20 Jun 2022
Validation of a fully-coupled radiative transfer model for sea ice with albedo and transmittance measurements
Abstract. A rigorous treatment of the sea ice medium has been incorporated in the advanced Coupled Ocean-Atmosphere Radiative Transfer (COART) model. The inherent optical properties (IOPs) of brine pockets and air bubbles over the 0.25–4.0 µm spectral region are parameterized as a function of the vertical profile of the sea ice physical properties (temperature, salinity and density). We test the model performance using available albedo and transmittance measurements collected during the Impacts of Climate on the Ecosystems and Chemistry of the Arctic Pacific Environment (ICESCAPE) and the Surface Heat Budget of the Arctic Ocean (SHEBA) field campaigns. The observations are adequately simulated when at least three layers are used to represent bare (first-year and multi-year) ice, including a thin top layer characterized by low density and high scattering. Two layers can be sufficient to model isolated cases of multi-year ice, and apply well to ponded ice except for shallow ponds over thick ice. The albedo and transmittance of ponded ice in the visible are mainly determined by the optical properties of the ice underlying the water layer used to model the pond. Sensitivity results indicate that the air volume or ice density has the largest impact on the simulated fluxes. Possible contamination from light-absorbing impurities, such as black carbon or ice algae, is also implemented in the model and is able to effectively reduce the albedo and transmittance in the visible spectrum to further improve the model-observation agreement. The agreement between the observed and modeled spectra validates the parameterization of the sea ice IOPs, and endorses COART as an accurate tool for radiation studies in the cryosphere.
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RC1: 'Comment on tc-2022-106', Anonymous Referee #1, 22 Jul 2022
General comments:
The authors have extended a coupled ocean-atmosphere radiative transfer (COART) model to the radiative transfer model (RTM) in the atmosphere-sea ice-ocean system (hereafter, the extended COART model). They compared the simulation results with measurement data of spectral albedo and transmittance collected at SHEBA and ICESCAPE stations to validate the extended COART model, and showed the agreement with previous studies that the model representations were improved by considering the vertical structure of sea ice such as SSL, DL and IL. They also showed the effect of contamination (LAPs and ice algae) of spectral albedo and transmittance of sea ice. The effectiveness of the extended COART model was emphasized through the series of analysis.
The result of albedo and transmittance comparisons between measurement and model looks good, but there are some questions on the results. In particular, following major comment (1) is critical issue. This paper’s main purpose is to validate the extended COART model. However, because there are few in-situ measurement data required for the validation of RTM, most of the simulated results are based on guesswork. Therefore, this paper is a qualitative discussion and is insufficient to validate the accuracy of the extended COART model. The authors should reconsider how to validate the RTM, so that a major revision would be needed.
Major comments:
1. Most of snow and sea ice physical parameters (sea ice density, ice temperature, salinity, ice thickness Chl. a concentration, snow grain size, LAPs, snow density, snow depth), which are input parameters used for the radiative transfer calculations, are not based on in-situ measurement data, but on the guess due to the lack of the information about snow and sea ice. Although the result of albedo and transmittance comparisons between measurement and model looks good, it is no exaggeration to say that the input variables are adjusted to match the calculation results with the observation ones. In general, since we simulate spectral albedo and transmittance based on the measurement data, we can validate a proposed model and can also find the physical processes that cannot be considered yet. In order to achieve the purpose of this paper, sufficient data must be prepared. The authors need to review the data used for the validation work again. If it is difficult to prepare the data, an alternative method is to confirm the reproducibility of your model by comparing it with a well-validated model.
2. Regarding the extended COART model, (a) why is it necessary to add the surface roughness scheme in the sea ice surface? Please add the reason by referring to Lamare et al. [2022; TCD]. In addition, the surface roughness is related to the specular reflection, and the magnitude of the surface roughness differs depending on the value of σ in the Gaussian normal distribution. The authors need to explain how the value of σ was determined. Furthermore, did authors apply this scheme to the boundary between the atmosphere and the melt pond where there is a large difference in refractive index between two medias? Please describe the explanation in detail. (b) There are various sizes of melt pond in the horizontal scale. The authors should describe the applicability of the extended COART model which is a plane-parallel RTM.
Technical comments:
L31-33: “The interaction between … surface temperature” this sentence is not clear. Explain the details about climate models mentioned in the text and cite references.
L48-: The last two paragraphs were well documented, but they do not mention the specific focus and the motivation for this manuscript. The authors need to describe it more clearly.
L78-: There is no mention about the ice algae in the section 2 which is a crucial for the transmittance of the sea ice though authors mentioned it in Fig. 6. Provide more details about the treatment of absorption/scattering properties of the ice algae.
L143: What does “AOPs” stand for?
The comments in the section 3 and below are omitted because they overlap with the major comment 1.
Citation: https://doi.org/10.5194/tc-2022-106-RC1 -
AC1: 'Reply on RC1', Matteo Ottaviani, 09 Aug 2022
We thank the reviewer for the comments. We address them one by one below.
General comments:
The authors have extended a coupled ocean-atmosphere radiative transfer (COART) model to the radiative transfer model (RTM) in the atmosphere-sea ice-ocean system (hereafter, the extended COART model). They compared the simulation results with measurement data of spectral albedo and transmittance collected at SHEBA and ICESCAPE stations to validate the extended COART model, and showed the agreement with previous studies that the model representations were improved by considering the vertical structure of sea ice such as SSL, DL and IL. They also showed the effect of contamination (LAPs and ice algae) of spectral albedo and transmittance of sea ice. The effectiveness of the extended COART model was emphasized through the series of analysis.
The result of albedo and transmittance comparisons between measurement and model looks good, but there are some questions on the results. In particular, following major comment (1) is critical issue. This paper’s main purpose is to validate the extended COART model. However, because there are few in-situ measurement data required for the validation of RTM, most of the simulated results are based on guesswork. Therefore, this paper is a qualitative discussion and is insufficient to validate the accuracy of the extended COART model. The authors should reconsider how to validate the RTM, so that a major revision would be needed.
This study validates a physically-consistent parameterization of bare sea ice IOPs as a function of its physical properties that can be directly measured (temperature, salinity, density and thickness). It is certainly true that a comprehensive set of in-situ measurements, required for a rigorous validation of RTM in sea ice in all conditions, is presently lacking. Therefore, we focused on bare and ponded ice cases (as defined observationally), for which we could source the most critical input parameters. In contrast, many alternative sea-ice RTMs employ as input parameters directly the IOPs (extinction coefficient, single scattering albedo and asymmetry factor), which are very challenging to measure in-situ or even in the laboratory. For example, the RTM used by Lamare et al. (2022) (referred to in a reviewer’s comment) uses a constant, wavelength-independent scattering asymmetry factor of 0.98 and constant scattering coefficients. Similarly, L08 and L15 use a constant scattering asymmetry factor of 0.94 and tuned scattering coefficients. Using the ice IOPs directly bypasses the complex relationships between the sea ice physical structure and its optical behavior, while in our case each physical parameter affects the IOPs at all wavelengths as it should be. Therefore, if the parameterization is not correct, obtaining model-observation agreement in both albedo and transmittance (again, simultaneously and at all wavelengths) is extremely unlikely even if a few unknown input properties were adjusted. For these reasons, we have full confidence that our approach is legitimate to validate radiative transfer processes in sea ice. Further details are provided in the following.
Major comments:
- Most of snow and sea ice physical parameters (sea ice density, ice temperature, salinity, ice thickness Chl. a concentration, snow grain size, LAPs, snow density, snow depth), which are input parameters used for the radiative transfer calculations, are not based on in-situ measurement data, but on the guess due to the lack of the information about snow and sea ice. Although the result of albedo and transmittance comparisons between measurement and model looks good, it is no exaggeration to say that the input variables are adjusted to match the calculation results with the observation ones. In general, since we simulate spectral albedo and transmittance based on the measurement data, we can validate a proposed model and can also find the physical processes that cannot be considered yet. In order to achieve the purpose of this paper, sufficient data must be prepared. The authors need to review the data used for the validation work again. If it is difficult to prepare the data, an alternative method is to confirm the reproducibility of your model by comparing it with a well-validated model.
We recognize a fundamental misunderstanding regarding this point. The reviewer puts forth a complete list of input parameters as if they all had the same relevance in the study. We are not focusing on the modeling of the albedo and transmittance of snow-covered ice. The main objective of this paper is to evaluate our IOP parametrization for bare ice and the relative RT processes. Within our approach, the bare-ice IOPs are parameterized exclusively as a function of the fundamental ice physical properties: salinity, density, and temperature. Such parameters, together with the ice total thickness, are based on real measurements, obtained after a thorough search for the best available datasets. The ICESCAPE and SHEBA data proved to be the most suitable for our study. We have made several attempts at including at least a preliminary version of MOSAiC data, but constantly hit the embargo that will last until January 2023. On the other hand, it was demonstrated in L08 that SHEBA and ICESCAPE data, albeit collected 20 years apart, show remarkable consistency. Furthermore, the appendix completes the study by highlighting the insensitivity to small variations in a lot of these parameters (especially temperature). The properties of the SSL have instead to be estimated (because no reliable measurement sets exist) based on the measured albedo in the near IR spectrum, as already done in L08.
The vertical profiles we use are documented by Polashenski et al (2015) and partially in L15, and we have used their exact values. We were even able to use density measurements for the 19 July 2011 case, based on the uppermost 80 cm of the annotated core (see L15, Fig. 7). Effectively, we adjusted the ice density in the other simulations only when forced by the lack of in-situ observations, but the adjustments ranged within commonly accepted values which also include those found in L08. The fact that these measurements are scarce (and we advocate for extensive collections of vertical profiles as one of the final messages) cannot be held as a flaw in our approach. Note that the manuscript highlights the use of such observations in several places, e.g.:
- Lines 147-148: “We strived to use all available observational data to determine the input to the model, focusing on two common ice types: bare and ponded ice.”
- Lines 156-157: “The Solar Zenith Angle (SZA) is calculated based on the reported observational time and location latitude and longitude.”
- Lines 166-168: This paragraph has been slightly corrected to: “We were able to exploit one of the few density measurements collected during ICESCAPE, although the density was only measured in the uppermost 80 cm where it varied between 0.625 and 0.909 g/cm3. When such measurements are not available, we assume typical FYI densities as reported by Timco and Frederking (1995): between 0.84 and 0.91 g/cm3 for the ice above the waterline, and between 0.90 and 0.94 g/cm3 for the ice below the waterline.”
- Lines 185-188: “For the salinity, we use the profiles reported from the core analysis of Polashenski et al. (2015), averaging the available data points in each model layer. Since measurements are not reported for the SSL (which normally gets destroyed when collecting the core) and the bottom of the ice, we assume the shallowest and deepest value extend to these remaining portions.”
- Line 306: (slightly modified): “The vertical profiles of salinity are also from cores, and vary between ⁓0.5 and 3.0 ppt (Polashenski et al., 2015).”
The misunderstanding regarding the snow layer concerns the treatment of the SSL. We think the reviewer was misled to believe that we were required to use in-situ measurements of snow properties. Instead, we correctly consider the ice SSL as a low-density ice layer, and the thin snow layer used to produce Fig. 3 and relative discussion is merely used to mimic the method used by L08, in which a snow layer with assumed physical and optical properties is used to represent the ice. We thought it was very informative to include this comparison with this flawed modeling of the SSL as snow, which inevitably leads to assuming meaningless “snow” properties (grain size, density, depth). These comparisons reinforce the advantages of considering a physically consistent model versus an ad-hoc approach that directly acts on the scattering coefficients and makes unjustified assumptions.
Next, we found that the simulated albedo and transmittance of bare ice are often higher than observation in the visible spectrum in most of the cases. We then tested the effects of possible LAPs: in these sensitivity tests, the Chl-a concentration and particulate amount are based on climatologies that are referred to in the manuscript. These are merely sensitivity tests aimed at illustrating how the inclusion of these contaminants could further improve the model-observation agreement.
We appreciate the reviewer’s suggestion of “comparing the code with a well-validated model”, but all available RT models for sea ice are approximated to some level. According to the reviewer’s standard on validation, we argue that such a model does not yet exist. We think the most intensively validated model is the 4-stream code used by Dr. Light’s group at the University of Washington. As detailed in the paper, this model was developed by Grenfell (1991), used in L08 and several other studies, and used the same discrete-ordinate method as the extended COART model, but in a simplified 4-stream version. The extended COART model is more advanced and can adopt any number of streams, in addition to the coupling feature and the treatment of ice roughness.
Finally, we note that the core point of the reviewer is contradicting: “the input variables are adjusted to match the calculation results with the observation ones”. Isn’t this the definition of a fit? Also, the point raised in the following sentence is obscure: “since we simulate spectral albedo and transmittance based on the measurement data, we can validate a proposed model and can also find the physical processes that cannot be considered yet”.
For all the reasons listed above, and since we strive to provide the best possible study, we kindly ask the reviewer to elaborate further on the raised points if he/she thinks we haven’t been clear enough.
- Regarding the extended COART model, (a) why is it necessary to add the surface roughness scheme in the sea ice surface? Please add the reason by referring to Lamare et al. [2022; TCD]. In addition, the surface roughness is related to the specular reflection, and the magnitude of the surface roughness differs depending on the value of σ in the Gaussian normal distribution. The authors need to explain how the value of σ was determined. Furthermore, did authors apply this scheme to the boundary between the atmosphere and the melt pond where there is a large difference in refractive index between two medias? Please describe the explanation in detail. (b) There are various sizes of melt pond in the horizontal scale. The authors should describe the applicability of the extended COART model which is a plane-parallel RTM.
The reason to implement a scheme accounting for the ice surface roughness is that the ice surface is naturally rough, especially for melting MYI, and the surface roughness affects the ice albedo and transmission. While surface roughness affects both the direct and diffuse light components (and therefore the surface BRDF as shown in Lamare et al. (2022), its effect on albedo and transmittance is small, as demonstrated in the figure attached as a supplement.
Lacking surface roughness measurement, we simply used σ=0.5 and σ=0.1 for the ice and pond surface, respectively. Based on the Cox-Munk formulation, σ=0.1 represents a minimal ocean surface roughness (wind speed=1.4 m/s). For the ice cases in this study, a coarse-grained ice surface layer was observed. Because the SSL appears granular, many surface facets must have large tilt angles. A value of σ=0.5 implies that 95% of the facet normals are <45o and 99.7% of them are within 56o from the local vertical. No observational data exist to constrain the roughness value, but again (differently from the radiance) its effect on fluxes is small. What is more important is that the extended COART model offers full flexibility in the treatment of roughness.
The applicability of a 1-D plane-parallel RTM depends on the relative dimension of the horizontal and the vertical scales. In the presence of a melt pond, the radiation field in the atmosphere calculated by a 1-D RTM is of course not valid. However, the atmosphere in our case only provides an approximate direct and diffuse partition for the incident solar spectral irradiance on sea ice surface. Since we model the RT in pond water and the ice beneath against “point” measurements provided by spectroradiometers, the use of a 1-D RTM to calculate radiative fluxes in the ice is totally justified as long as the pond horizontal extent is significantly larger than the ice thickness.
Technical comments:
L31-33: “The interaction between … surface temperature” this sentence is not clear. Explain the details about climate models mentioned in the text and cite references.
The reviewer is right, this sentence was left too “lonely”. We have replaced it with:
“Many sea ice models employ simplistic albedo parameterizations for the albedo, resulting in large uncertainties in both present-day simulations climate and future climate projections in the Arctic (Notz et al., 2016; Koenigk et al., 2014)”
L48-: The last two paragraphs were well documented, but they do not mention the specific focus and the motivation for this manuscript. The authors need to describe it more clearly.
We agree. We have modified and expanded lines 74-ff to:
“Many sea ice radiative transfer models require the Inherent Optical Properties (IOPs) at input, which constitutes a major limitation since the IOPs are very challenging to measure in-situ and even in laboratory. As a consequence, the IOPs more or less always suffer from very significant approximations. For example, Briegleb and Light (2007), L08 and L15 use a constant, spectrally-flat scattering asymmetry factor of 0.94 and tuned scattering coefficients, while Lamare et al. (2022) use a scattering asymmetry factor of 0.98 and constant scattering coefficients.
As described in the next section, Jin et al. (2006) developed a Coupled Ocean-Atmospheric Radiative Transfer (COART) model with high spectral resolution (up to 0.1 cm-1) to finely resolve atmospheric absorption, and accurate treatment of surface roughness. Here, we extend this previously validated (Jin et al., 2002; 2005) model to include the sea ice medium, in order to rigorously calculate the radiative distribution in the atmosphere-sea ice-ocean system. As part of the extension, the sea ice optical properties are directly parameterized as a function of its measurable physical properties (i.e., temperature, salinity, and density), so as to eliminate the need to provide the IOPs (extinction, single scattering albedo, and asymmetry factor) at input. This physically-based strategy also enables a direct connection with the physical ice properties simulated in climate models. In developing such a GCM-oriented version of COART, the objective of this study is to validate said parametrization against observations of albedo and transmittance by constraining the physical properties with available measurements of their vertical profiles.”
There is no mention about the ice algae in the section 2 which is a crucial for the transmittance of the sea ice though authors mentioned it in Fig. 6. Provide more details about the treatment of absorption/scattering properties of the ice algae.
We totally agree that the text around Line 100:
“The presence of other possible inclusions (BC and phytoplankton) is also considered.”
Is insufficient. We have modified it to read:
“Beside brine pockets and air bubbles, the model can easily consider the presence of any other inclusion with a vertical distribution throughout the ice column. We have currently included a black-carbon-type of aerosol (Hess et al., 1998) and ice algal pigments (Arrigo, Pers. Comm.).”
L143: What does “AOPs” stand for?
Apparent Optical Properties (as opposed to Inherent Optical Properties). Thanks for catching the lack of the spell out (now added)!
The comments in the section 3 and below are omitted because they overlap with the major comment 1.
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AC1: 'Reply on RC1', Matteo Ottaviani, 09 Aug 2022
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RC2: 'Comment on tc-2022-106', Anonymous Referee #2, 20 Oct 2022
General Comments
This manuscript aims to validate the implementation of a sea ice radiative transfer model into the advanced COART. The model inputs are vertically resolved salinity, temperature and density. These inputs together with the phase-equilibrium relationship developed by Cox and Weeks 1983 are used to predict brine and air total volume. Using these latters, an empirical mathematical equation developed by Light 2003 calculates gases and brine channels size distributions assuming inclusions to be spherical. Mie theory is used to predict the inherent optical properties (IOPs) of the different layers representing sea ice. A radiative transfer model based on the discrete ordinates method is finally used to calculate the output apparent optical properties (AOPs).
Modelled AOPs based on structural measurements are validated by comparison with measured AOPS obtained during the SHEBA and ICESCAPE campaigns. Three scenarios were considered: first-year ice bare ice, multi-year bare ice and ponded ice. The effect of soot impurities and algae are also assessed for these scenarios.
A model incorporating Mie theory and using physical structure to calculate AOPs would be a valuable tool as mentioned by the authors. However, the fact that the model as to be tuned in order to obtain agreements undermines the validity of this model. Two aspects (1) and (2) would have to be addressed in order to demonstrate the validity of the model.
Major Comments
- The inclusions distributions described by Light 2003 are valid for columnar (interior) ice. These distributions of inclusions size and shape are probably significantly different in the drained layer (DL) and surface scattering layer (SSL ) because of several processes (e.g., surface melting/refreezing, channel drainage, air bubble inclusion under dynamic growth, surface ablation by sunlight, etc.). The induction of inclusions distributions describing interior layer to drained and surface scattering layer might explain the mismatch between the untuned model and measurements. The author should suggest a different approach in order to predict inclusions distributions for these two layers. Microstructural observations of the SSL obtained during the MOSAiC expedition could be a start for such a model (when they will be available).
- The density, temperature and salinity measurements as well as absorbing particles concentrations used as inputs are often guessed by the authors because they were not measured on the field at the location of AOPS measurements. Without these reference measurements, the system is undetermined. Unfortunately, it is difficult to demonstrate the validity of the model without having the actual measurements or justifying the choice of the input with strong evidence. A solution could be to change the scope of the paper in order to study the sensitivity of AOPS to the tuning of the different inputs. Another suggestion would be to validate the model by comparison with another model. However, point (1) would need to be addressed first.
Specific Comments
28 Morphological changes and thinning of sea ice along with sea ice cover reduction are responsible for lower albedo and shortwave absorption in the ocean (Arndt and Nicolaus 2014 ).
46 The range is probably wider than that, especially for SSL. Would that be the range for columnar sea ice?
86 What is the value of the refractive index used for ice? Please provide a number or a range for this value.
88 The explanation of how the surface is implemented is insufficient. Water and ice have different roughness, therefore the parameters of the Gaussian equation describing its roughness should be different. From an optical perspective, it would be helpful to have a description of how it translates into the distribution of diffuse reflection. It would also be useful to describe the importance of purely specular reflection at the ice surface in the model.
99 Is absorption coefficient based on volume fraction? More details should be provided.
126 This explanation mixes a few concepts. The scattering efficiency Q (ratio of scattering surface area to geometrical surface area) in the Mie regime is close to 2 no matter the phase function. The reduced scattering coefficient or similarity variable b’=b*(1-g) which describes the mixed effect of scattering coefficient and phase function will indeed go down as the phase function represented by the asymmetry parameter g goes up. This concept should be addressed in this explanation. It is not that obvious that the reduced scattering coefficient goes down significantly for big inclusions. One would need to prove that claim quantitatively using the similarity principle (where b could be calculated from cross section area and g from Mie Theory).
131 Mirabilite crystals precipitates under -8 C (Light 2004).
137 As stated in (1), the approach described in this section is based on a description of columnar (interior ice). Since the processes dictating the bubbles and brine channels size distributions and refractive index are different in drained and surface scattering ice, we cannot consider the treatment described here as complete.
159 Cloud optical thickness of 10 is too low for an upper bound. 100 would be recommended.
201 The finality of L08 and L15 is to determine the IOPs of sea ice. The use of tuning in this case is justified because it is needed to find what the IOPs should be in order to meet measured AOPs. Furthermore, an explanation of the bias which they are rectifying by tuning is also provided. In the case of this study, density is an input and not a value that is being determined. Therefore, it is illogical to modify the input density in order to meet the correct answer. Unless these density tunings are justified with an explanation.
203 Following the similarity principle b’=b*(1-g), in the diffusion regime , it does not truly matter if g is kept constant or not. As long as the reduced scattering coefficient b’ is consistent.
216 Why change DL density and snow depth? These choices needs to be justified.
228 Indicate figure number.
236 It needs to be kept in mind that absorption coefficient of suits in air and in ice are not the same.
250-257 if temperature, salinity, SSL thickness, SSL density are not measured, the system is strongly under-determined. Furthermore, the manuscript needs to clarify if the density of 0.915 g/cm3 and salinity of 3 ppt used for interior ice are measured or guessed.
254 Granular ice and surface scattering layer are not equivalent. The word SSL should be kept in this case.
268-274 The manuscript needs to clarify if these inputs are assumptions or measurements.
275 The systematic bias could also come from guesses on ice physical parameters.
276 What is meant by ‘’other species’’ ? At this point in the manuscript, there has been no mention about any biological specie.
279 Please verify the claim that algal pigments are more concentrated at the top layer.
289 The explanation is unclear. The sentence seems to contain 3 ideas : (1) Melt pond occurs when sun irradiance is the largest, (2) Melt Pond water as a lower reflection and higher transmission than ice, (3) these two effects combined impact energy distribution.
304 Is temperature measured or guessed?
311 The manuscript should justify why thicker ice as a three-layer model while thinner ice only has a two-layer model.
312 Missing units after 0.83.
313 The use of tables to summarize inputs and to clarify how many total layers are used to represent ponds +ice would make the manuscript easier to read.To indicate whether the inputs are measured or assumed could also clarify the context.
325-326 The conclusion that transmittance decreases with increasing pond depth is counter-intuitive, since melt water contained in ponds scatters significantly less than interior sea ice. How would that be explained? Is it because of the high absorption of the melt water? This trend is in opposition with measurements from L15 fig 5b.
343 Light_2015 used observation of the albedo to invert SSL IOPs. They used single diameter spheres approximation, as it is used for snow, only to provide an initial guess.
348 A complete analysis of the sensitivity of AOPs to salinity was never presented. This notion was only mentioned qualitatively in the text of section 3.2.
351 There are two ideas mixed in the same sentence. (1) Depending on pond depths and (2) the albedo (transmittance) is significantly lower (higher) than that of bare ice
352 The claim on the relation between pond depth and transmission is in opposition with what was stated at line 325.
Figure 2 The scenario using measured density should be specified on the caption or legend. Name of the layers should be specified.
Figure 3 As a comparison, having a scenario with SSL modeled using the reference model would be useful. Name of the layers should be specified.
Figure 4 Name of layers should be specified.
Figure 5 The difference between the dotted and full black lines representing measurements should be specified. Name of layers should be specified.
Figure 6 Same as fig. 5
Reference
Arndt, S. and Nicolaus, M.: Seasonal cycle and long-term trend of 75 solar energy fluxes through Arctic sea ice, The Cryosphere, 8, 2219–2233, https://doi.org/10.5194/tc-8-2219-2014, 2014.
Light, B., Maykut, G., and Grenfell, T.: A temperature-dependent, structural-optical model of first-year sea ice, J. Geophys. Res.- Oceans, 109, C06013, https://doi.org/10.1029/2003JC002164, 2004.
Citation: https://doi.org/10.5194/tc-2022-106-RC2 -
AC2: 'Reply on RC2', Matteo Ottaviani, 17 Nov 2022
General Comments
This manuscript aims to validate the implementation of a sea ice radiative transfer model into the advanced COART. The model inputs are vertically resolved salinity, temperature and density. These inputs together with the phase-equilibrium relationship developed by Cox and Weeks 1983 are used to predict brine and air total volume. Using these latters, an empirical mathematical equation developed by Light 2003 calculates gases and brine channels size distributions assuming inclusions to be spherical. Mie theory is used to predict the inherent optical properties (IOPs) of the different layers representing sea ice. A radiative transfer model based on the discrete ordinates method is finally used to calculate the output apparent optical properties (AOPs).
Modelled AOPs based on structural measurements are validated by comparison with measured AOPS obtained during the SHEBA and ICESCAPE campaigns. Three scenarios were considered: first-year ice bare ice, multi-year bare ice and ponded ice. The effect of soot impurities and algae are also assessed for these scenarios.
A model incorporating Mie theory and using physical structure to calculate AOPs would be a valuable tool as mentioned by the authors. However, the fact that the model as to be tuned in order to obtain agreements undermines the validity of this model. Two aspects (1) and (2) would have to be addressed in order to demonstrate the validity of the model.
We thank the Reviewer for the feedback. Before proceeding to the point-to-point response, we’d like to briefly address this general comment. We believe a major misunderstanding generated most of the questions below, and it has to do with the choice of using the word “tuning”. The main objective of this paper is to evaluate our IOP parametrization for bare ice and the relative RT processes. Within our approach, the bare-ice IOPs are parameterized exclusively as a function of the fundamental ice physical properties: salinity, density, and temperature. Such parameters, together with the ice total thickness, are based on real measurements, obtained after a thorough search for the best available datasets (see below for more explanations). We simply invert for the density needed to best fit the measurements. The density values are within reported typical ranges for each of the SSL, DL or IL. In one case (19 July), we were even able to use the density measured in a core extracted next to the location of the optical measurements.
Major Comments
1. The inclusions distributions described by Light 2003 are valid for columnar (interior) ice. These distributions of inclusions size and shape are probably significantly different in the drained layer (DL) and surface scattering layer (SSL ) because of several processes (e.g., surface melting/refreezing, channel drainage, air bubble inclusion under dynamic growth, surface ablation by sunlight, etc.). The induction of inclusions distributions describing interior layer to drained and surface scattering layer might explain the mismatch between the untuned model and measurements. The author should suggest a different approach in order to predict inclusions distributions for these two layers. Microstructural observations of the SSL obtained during the MOSAiC expedition could be a start for such a model (when they will be available).
We understand that the size distributions for the inclusions described in L03 are sampled from the interior ice. We extended it to the SSL and DL because there are no such measurements specifically for these top layers. In fact, this assumption is no different from the assumption of a constant scattering asymmetry factor in all ice layers used in other studies (e.g., Briegleb and Light, 2007, L08, L15, and Lamare et al., 2022). Since the scattering asymmetry factor is solely dependent on the size distribution for a given wavelength, using the same asymmetry factor in different ice layers implies a constant size distribution profile. Actually, in contrast to the studies mentioned above, our assumption is less severe (more physical), because the asymmetry factor in our approach depends on wavelength and also on the ice physical properties (i.e., it is layer-dependent). Some assumptions are obviously inevitable whenever measurements are not exhaustive. However, the good model-observation agreement in the spectral albedo indicates that using the size distributions of the IL also for the SSL and DL is acceptable, particularly in the NIR where the modeled albedo is more sensitive to the optical properties of the SSL and the DL. The agreement might be partially attributed to the (generally) much thinner dimensions of the SSL and DL, and to error compensation between size distribution and ice density, similar to the error compensation between the asymmetry factor and the adjusted scattering coefficients in the studies referred to above.
We have made several attempts at including at least a preliminary version of MOSAiC data, but constantly hit the embargo that will last until January 2023. Requests to PIs for preliminary versions failed as well. On the other hand, it was demonstrated in L08 that SHEBA and ICESCAPE data, albeit collected 20 years apart, show remarkable consistency (see response to your point 2 for more details). In addition, we are not sure how reliable the inclusion distributions obtained in the loose, fast-changing SSL of a few centimeters are, and if it is possible to measure them at all. Can the reviewer advise on how to promptly obtain such data? Notwithstanding the fact that we’ll always strive to implement the most recent advances in the model, the fate of the paper cannot depend on potential availability of future datasets.
Regarding the suggestion of “a different approach in order to predict inclusions distributions”, the development of new techniques to obtain size distributions is out of the scope of this paper. The model can accommodate any size distribution, but in absence of reliable measurements it makes little sense to privilege one or the other if the fit to the measurements are satisfactory.
2. The density, temperature and salinity measurements as well as absorbing particles concentrations used as inputs are often guessed by the authors because they were not measured on the field at the location of AOPS measurements. Without these reference measurements, the system is undetermined. Unfortunately, it is difficult to demonstrate the validity of the model without having the actual measurements or justifying the choice of the input with strong evidence. A solution could be to change the scope of the paper in order to study the sensitivity of AOPS to the tuning of the different inputs. Another suggestion would be to validate the model by comparison with another model. However, point (1) would need to be addressed first.
Again, this is a misunderstanding. For the modeling, we use every available observational data for input. The ICESCAPE and SHEBA data proved to be the most suitable for our study. Furthermore, the appendix completes the study by highlighting the insensitivity to small variations in a lot of these parameters. The properties of the SSL have instead to be estimated (because exhaustive measurement sets are not yet available) based on the measured albedo in the near IR spectrum, as already done in L08.
The vertical profiles we use are documented by Polashenski et al (2015) and partially in L15, and we have used their exact values. We were even able to use density measurements for the 19 July 2011 case, based on the uppermost 80 cm of the annotated core (see L15, Fig. 7). Effectively, we adjusted the ice density in the other simulations only when forced by the lack of in-situ observations, but the adjustments ranged within commonly accepted values which also include those found in L08. The fact that these measurements are scarce (and we advocate for extensive collections of vertical profiles as one of the final messages) cannot be held as a flaw in our approach. Note that the manuscript highlights the use of such observations in several places, e.g.:
- Lines 147-148: “We strived to use all available observational data to determine the input to the model, focusing on two common ice types: bare and ponded ice.”
- Lines 156-157: “The Solar Zenith Angle (SZA) is calculated based on the reported observational time and location latitude and longitude.”
- Lines 166-168: This paragraph has been slightly corrected to: “We were able to exploit one of the few density measurements collected during ICESCAPE, although the density was only measured in the uppermost 80 cm where it varied between 0.625 and 0.909 g/cm3. When such measurements are not available, we assume typical FYI densities as reported by Timco and Frederking (1995): between 0.84 and 0.91 g/cm3 for the ice above the waterline, and between 0.90 and 0.94 g/cm3 for the ice below the waterline.”
- Lines 185-188: “For the salinity, we use the profiles reported from the core analysis of Polashenski et al. (2015), averaging the available data points in each model layer. Since measurements are not reported for the SSL (which normally gets destroyed when collecting the core) and the bottom of the ice, we assume the shallowest and deepest value extend to these remaining portions.”
- Line 306: (slightly modified): “The vertical profiles of salinity are also from cores, and vary between ⁓0.5 and 3.0 ppt (Polashenski et al., 2015).”
When not measured in situ, we use data based on pertinent observations reported in the literature. As for "absorbing particles concentrations used as inputs are often guessed": please note that the particle concentration is NOT an input variable and is not guessed but determined by the ice density, temperature, and salinity through the Cox-Weeks equation for the given size distributions (see Eqs 1-3). Among the three ice properties, salinity is the one most available for the examined cases. To avoid large temperature uncertainties, we chose melting ice and ponded ice cases, for which the top temperature can be set to a very good approximation to 0°. Because the ice base (ice-water interface) can be fixed at -2°C and the temperature profile in the ice is generally very close to linear (based on observations), the temperature in each layer is easily estimated. In addition, our sensitivity test shows small dependence on temperature (see Appendix). The density is the most scarcely measured variable, and we therefore use reported observational values (L15; Timco and Frederking, 1995). One of our goals is to improve the radiative transfer in sea ice in the NASA climate model (ModelE), which simulates the ice temperature and salinity profiles in sea ice but not the density. Therefore, the ice density is an adjustable parameter in ModelE. Accordingly, we present a physically-consistent parameterization of bare sea ice IOPs as a function of its physical properties that can be directly measured or modeled in climate models. In contrast, many alternative sea-ice RTMs employ as input parameters directly the IOPs (extinction and scattering coefficients, and asymmetry factor), which are very challenging to measure in-situ or even in the laboratory. It is certainly true that a comprehensive set of in-situ measurements, required for a rigorous validation of RTM in sea ice in all conditions, is presently lacking. Because in our physically-based parameterization the IOPs are linked to the ice properties, changing the ice density changes all the IOPs consistently and differentially in different spectral bands: band-by-band adjustments as in the studies referred to above are not needed. If the parameterization is not correct, obtaining model-observation agreement in both albedo and transmittance (again, simultaneously and at all wavelengths) is extremely unlikely even if a few unknown input properties are “adjusted”. For all these reasons, we have full confidence that our approach is legitimate to validate radiative transfer processes in sea ice. Should more complete suites of input parameters become available in the future, the focus can shift towards the betterment of the IOP parametrization.
“However, point (1) would need to be addressed first”: This size distribution issue has already been addressed in the response to point (1) above.
The detailed explanation above has been condensed in a new paragraph added to the beginning of Sec. 3:
“The ICESCAPE and SHEBA data proved to be the most suitable for our study. Of all the physical variables needed at input and measured in situ, the total ice thickness and the vertical profiles of salinity within the ice column are the most available. For ICESCAPE, we use the exact values of layer-resolved salinity documented by Polashenski et al. (2015) and partially in L15. For SHEBA, density profiles from cores are generally very scarce. We were able to use density measurements for the 19 July 2011 case, based on the uppermost 80 cm of the annotated core (see L15, Fig. 7). When forced by the lack of in-situ observations the values were varied within commonly accepted ranges, which also include those found in L08. Temperature profiles are also sporadic, but estimates based on straight physics can be used that do not substantially affect the quality of the fit, as shown in the Appendix. For example, the top temperature of ponded ice can be set at 0°C because this is the water-ice coexisting temperature of water and ice. The bottom ice temperature of -2°C is based on the freezing temperature of sea water.”
Finally, all available RT models for sea ice are approximated to some level. As for the comparison with other models, it was indeed done in Light et al. (2003), which compared DISORTB (an earlier version of our RT solver used in COART) and found that the modeled sea ice albedo and transmittance are consistent with their 4-stream results as should be (see Figs 4-6 in L03). Their model is most commonly used for applications to sea ice RT. The extended COART model is more advanced and can adopt any number of streams (not just 4), in addition to the coupling feature and the treatment of ice roughness.
Reference: Light, B., G. A. Maykut, and T. C. Grenfell (2003), A two-dimensional Monte Carlo model of radiative transfer in sea ice, J. Geophys. Res., 108(C7), 3219.
Specific Comments
28 Morphological changes and thinning of sea ice along with sea ice cover reduction are responsible for lower albedo and shortwave absorption in the ocean (Arndt and Nicolaus 2014).
Yes, thinning of sea ice (and some morphological changes, not all) also contribute to ice albedo reduction, but to a much smaller extent. We have modified the text to read: “A reduction in sea ice cover and its thinning lower the albedo and increases shortwave absorption in the ocean, causing more melting in a mechanism known as ice-albedo feedback (Curry et al., 29 1995; Hall, 2004; Déry and Brown, 2007, Arndt and Nicolaus 2014)
46 The range is probably wider than that, especially for SSL. Would that be the range for columnar sea ice?
This is a very good point! The density of the SSL is largely unknown, although some descriptions are contained in very recent publications (https://www.osti.gov/servlets/purl/1844399). Since this point is made in the introduction, we prefer to specify that this is a general range for bulk sea ice. According to Timco and Frederking (1996) “the in situ density of sea ice may be quite different above and below the waterline. In the upper part of the ice sheet, there may be a wide variation in the ice density, with realistic values in the range 0.84 to 0.91 Mg m -3 for first-year ice, and 0.72 to 0.91 Mg m -3 for multi-year ice. However, below the waterline, the density values are much more consistent and range from 0.90 Mg m -3 to 0.94 Mg m -3 for both types of ice.”
86 What is the value of the refractive index used for ice? Please provide a number or a range for this value.
As specified in the manuscript, the spectral refractive index of ice is taken from Warren and Brandt (2008). A plot of it is has been uploaded as a supplement (see figure "S1_rev2"). We have added “spectral” to the sentence in the text. We think that reporting specific values makes the text unnecessarily heavy, without being particularly useful.
88 The explanation of how the surface implemented is insufficient. Water and ice have different roughness, therefore the parameters of the Gaussian equation describing its roughness should be different. From an optical perspective, it would be helpful to have a description of how it translates into the distribution of diffuse reflection. It would also be useful to describe the importance of purely specular reflection at the ice surface in the model.
We have added the following section to the Appendix:
“Ice surfaces are naturally rough, and the extended COART model offers full flexibility in the treatment of roughness (Jin et al., 2006). . A Gaussian equation is used to describe the statistical distribution of the surface facets, in a similar fashion as the Cox-Munk model used to parameterize the distribution of ocean waves. The extension to any other distribution is trivial, should observational evidence indicate the need. Since no sunglint has been reported on ice surfaces and granular features are observed, the sea ice surface is likely rougher than a calm ocean surface. Lacking appropriate measurements of surface roughness statistics, we simply used σ=0.5 and σ=0.1 for the ice and pond surface, respectively. Based on the Cox-Munk formulation, σ=0.1 represents a minimal ocean surface roughness (wind speed=1.4 m/s). For the ice cases in this study, a coarse-grained surface layer was observed. Because the SSL appears granular, many surface facets must have large tilt angles. A value of σ=0.5 implies that 95% (99.7%) of the facet normals are <45°(<56°) from the local vertical. No observational data exist to constrain the roughness value, but again (differently from its impact on the radiance) the effect on the irradiance is small. In any case, while surface roughness affects both the direct and diffuse light components (and therefore the surface BRDF as shown in Lamare et al. (2022)), its effect on albedo and transmittance is small, as demonstrated in Fig. A5.”
For more information on surface roughness, please refer to:
Jin et al., 2006: An analytical solution of radiative transfer in the coupled atmosphere-ocean system with a rough surface. Applied Optics, 45, 7443-7455.
99 Is absorption coefficient based on volume fraction? More details should be provided.
Yes, it is based on the volume fractions of ice and brine. To clarify, we have added: “The total ice layer absorption is the average of ice and brine water weighted by volume fractions.”.
126 This explanation mixes a few concepts. The scattering efficiency Q (ratio of scattering surface area to geometrical surface area) in the Mie regime is close to 2 no matter the phase function. The reduced scattering coefficient or similarity variable b’=b*(1-g) which describes the mixed effect of scattering coefficient and phase function will indeed go down as the phase function represented by the asymmetry parameter g goes up. This concept should be addressed in this explanation. It is not that obvious that the reduced scattering coefficient goes down significantly for big inclusions. One would need to prove that claim quantitatively using the similarity principle (where b could be calculated from cross section area and g from Mie Theory).
The reviewer is mistaken on this point and we attempt to clarify in what follows. For large particle scattering (like brine pockets in sea ice), more than half of the scattered light is due to diffraction which goes nearly straight forward. Another fraction of the incident light is refracted and transmitted in and near the forward direction. This forward scattering contribution increases with particle size and as the relative refractive index approaches 1. Because brine pockets are large compared to the wavelength and the refractive index difference between brine water and ice is small, more than 90% of the scattered photons are concentrated in a very small cone around the forward direction. In IOP calculation, we modified the Mie code and didn’t account for this forward scattered energy in the scattering phase function and accordingly in the scattering efficiency. In radiative transfer calculations, this forward scattering component can be considered as not being scattered, and can be added back to the incident beam after the scattering. Therefore, the scattering coefficient is drastically reduced (by over 90% and so we consider it significant). This treatment goes beyond the simplistic similarity concept the reviewer pointed out. A final remark: COART can also accept the phase function as a direct input. This is useful when accurate radiance calculations are performed, and it is not important for the irradiance computations contained in this study.
131 Mirabilite crystals precipitates under -8 C (Light 2004).
The focus here is on the temperature at which precipitated salts start to significantly affect radiative transfer, not the temperature at which salts start to precipitate.
137 As stated in (1), the approach described in this section is based on a description of columnar (interior ice). Since the processes dictating the bubbles and brine channels size distributions and refractive index are different in drained and surface scattering ice, we cannot consider the treatment described here as complete.
As addressed in the response to (1), our size distribution assumption is analogous to assuming a constant g in all ice layers adopted in previous studies (L08, L15, and Lamare et al., 2022). Lacking observational data, this assumption is necessary. However, in our approach g changes with wavelength as physically expected. We have adjusted the relative sentence to “This physically-based approach provides a sophisticated and complete treatment of radiative transfer in sea ice. The extension to novel discoveries on, e.g., size distributions for the inclusion can trivially be extended to any size distribution obtained from observational evidence.“
159 Cloud optical thickness of 10 is too low for an upper bound. 100 would be recommended.
See figure in the appendix, where it is seen that the results have already “converged” using tau=10, especially for the typical low-sun conditions in the Arctic, so there is no need to use Tau=100. For the reviewer’s benefit, in the supplemental figure "FigS2_rev2.pdf" we have specifically isolated the differences obtained using tau=10 or tau=100.
201 The finality of L08 and L15 is to determine the IOPs of sea ice. The use of tuning in this case is justified because it is needed to find what the IOPs should be in order to meet measured AOPs. Furthermore, an explanation of the bias which they are rectifying by tuning is also provided. In the case of this study, density is an input and not a value that is being determined. Therefore, it is illogical to modify the input density in order to meet the correct answer. Unless these density tunings are justified with an explanation.
L08 and L15 directly use ice IOPs as an input to calculate the AOPs (albedo and transmittance). We agree that “it is needed to find what the IOPs should be in order to meet measured AOPs”, but such adjusted IOPs are unlikely to represent the real IOPs because they are based on a constant particle size assumption. As expressed in the reviewer’s major comment (1), the particle size (i.e., the asymmetry factor) should be different in different ice layers. In our approach, the ice IOPs are physically linked to the ice physical properties. As the density changes, the IOPs vary simultaneously across all wavelengths. L08 and L15 directly tune the IOP (scattering) band by band, with a fixed g (which is not logical). As a consequence, it is relatively easier to match the AOPs. One way or another, assumptions are necessary whenever complete measurements are not available. We understand the necessary IOP adjustments in L08 and L15, because it is impossible to derive all the IOPs (extinction, scattering coefficient and phase function) only using irradiance measurements. Even the extinction derived from the measurements may not represent the real IOP extinction, because of measurement limitations (e.g., angular coverage) and ice property inhomogeneity, which could result in different extinction values for upward and downward irradiances (real extinction is direction independent). In summary, we and L08 and L15 all determined some set of IOPs that best fits the measurements. The difference is in directly tuning the IOPs or letting them be driven (as it should be) by the ice physical properties. In other words, L15 retrieve IOPs from measured albedo, whereas we retrieve ice density (because of the scarcity of in situ measurements). To avoid the confusion, we have provided more details on how the density is obtained in the revision:
“Because of the lack of in-situ density measurement, we consider the density adjustable and invert it using the measured spectral albedo. Based on previous observations, we first set the density ranges for the IL and DL as 0.90-0.94 g/cm3 and 0.82-9.925 g/cm3, respectively. Because no density has been reported for the thin top SSL, we simply use either 0.55 or 0.60 g/cm3 for this layer. For a SSL density, we loop the density in DL and IL in step of 0.001 g/cm3 and compare the modeled spectral albedo with the measured albedo in each step. When the averaged difference reaches the threshold of 5% or less, the iterating stops and densities are considered retrieved. Otherwise, the densities giving the minimum difference are used. This process is similar to the process used to obtain the scattering in L08 and L15 but not band by band.”.
203 Following the similarity principle b’=b*(1-g), in the diffusion regime , it does not truly matter if g is kept constant or not. As long as the reduced scattering coefficient b’ is consistent.
It may not matter in the visible spectrum where absorption is small but it does matter in the NIR, especially for transmittance. The error of this approximation depends on absorption and solar zenith angle. This similarity principle goes back to the time before the delta-M, which offers a more rigorous treatment. Is it possible to obtain the real scattering coefficient and phase function from merely the irradiance measurements?
216 Why change DL density and snow depth? These choices needs to be justified.
As hopefully made clear by the many explanations given above, starting from the optimal fit (black line) in Fig. 3, we show and discuss the sensitivity to the key parameters, as
advocated also by the reviewer. In comparing the approach of L15 (who modeled the SSL using properties of a snow layer) to our 3-layer model, we provide examples of the effect of assuming different snow properties.
228 Indicate figure number.
We replaced “in the previous figures” with “in Figs. 1-3”.
236 It needs to be kept in mind that absorption coefficient of suits in air and in ice are not the same.
Understood. It is considered.
250-257 if temperature, salinity, SSL thickness, SSL density are not measured, the system is strongly under-determined. Furthermore, the manuscript needs to clarify if the density of 0.915 g/cm3 and salinity of 3 ppt used for interior ice are measured or guessed.
For melting ice, using a temperature of 0°C at the top is a good approximation. RTMs used in other studies (Briegleb and Light, 2007, Light et al., 2008, 2015) treated this low ice density SSL as a layer of “snow” and with all guessed “snow” properties (grain size and density). We did similarly for this top SSL but treated it as a low density ice layer in the RT calculations. Density and salinity for the interior ice for this case are from observed typical values.
254 Granular ice and surface scattering layer are not equivalent. The word SSL should be kept in this case.
Smith et al. (“Sensitivity of the Arctic Sea Ice Cover to the Summer Surface Scattering Layer”, 2022) define the SSL as a “highly-scattering, coarse-grained ice layer”, a definition that seems to be consistent with the rest of the literature. “Granular layer” was verbatim found in the field notes for the relative measurement. Rather than removing “granular layer”, we prefer to substitute “SSL” with “top layer”, although we do not think this is needed.
268-274 The manuscript needs to clarify if these inputs are assumptions or measurements.
This recurring comment is now addressed by the new paragraph added at the beginning of Sec. 3, and reported in the last paragraph of the response to major comment 2.
275 The systematic bias could also come from guesses on ice physical parameters.
It could be, but the bias exists only in the visible spectrum and is small. If a “guess” (to use the reviewer’s words) yields a match in AOPs simultaneously and at all wavelengths, it is likely a very good guess, since our approach avoids the unphysical wavelength-by-wavelength adjustment of the IOPs.
276 What is meant by ‘’other species’’ ? At this point in the manuscript, there has been no mention about any biological specie.
For example, dust aerosol deposition, sediments, CDOM. In any case, the reviewer is correct. We changed the sentence to: “Several species”.
279 Please verify the claim that algal pigments are more concentrated at the top layer.
Higher concentrations in the bottom layer are common. In the discussion of the cited reference (Perovich et al., 1998), it is reported that “ for both seasons, particle concentrations were high at the snow-ice interface. Algal cells transported by brine wicking in the spring are left behind after drainage occurs. These particles undergo growth, increasing in concentration and resulting in increased absorption of shortwave radiation at the interface during the melting season”.
289 The explanation is unclear. The sentence seems to contain 3 ideas : (1) Melt pond occurs when sun irradiance is the largest, (2) Melt Pond water as a lower reflection and higher transmission than ice, (3) these two effects combined impact energy distribution.
Agree. We have reworded this sentence: “Melt ponds occur in late spring and summer when solar irradiance is large. Because water has much lower reflection and higher transmission than ice, melt ponds over the ice could significantly alter the solar energy distribution in the atmosphere-sea ice-ocean system.”.
304 Is temperature measured or guessed?
The two temperatures are estimated based on straight physics. The top temperature of the ponded ice is set at 0°C because this is the coexisting temperature of water and ice (neglecting salinity in the pond water). The bottom ice temperature of -2°C is based on the freezing temperature of sea water.
311 The manuscript should justify why thicker ice as a three-layer model while thinner ice only has a two-layer model.
This paragraph relates to ponded ice, not to thicker vs thinner ice. It results from our simulations that two layers are generally sufficient to obtain as good agreement as using three layers for ponded ice, so we are not sure what “justification” should be provided. Did the reviewer mean to suggest a sentence like “Given the presence of the pond water above, the vertical resolution of the ice layers is less important than for bare ice”?
312 Missing units after 0.83.
Added “g/cm3”.
313 The use of tables to summarize inputs and to clarify how many total layers are used to represent ponds +ice would make the manuscript easier to read.To indicate whether the inputs are measured or assumed could also clarify the context.
This is now addressed by the new text added to the beginning Sec. 3.
325-326 The conclusion that transmittance decreases with increasing pond depth is counter-intuitive, since melt water contained in ponds scatters significantly less than interior sea ice. How would that be explained? Is it because of the high absorption of the melt water? This trend is in opposition with measurements from L15 fig 5b.
Although it might appear counter-intuitive, this is what the data say. The explanation might reside in the density change below the melt pond. When pond water fills the voids in ice, the ice scattering could be reduced significantly and therefore transmission increases. The significantly higher transmission of the ponded ice than the bare ice with similar thickness seems to further validate this hypothesis. For clarity, we have added a sentence at the end of this paragraph: “This probably results from the reduced scattering due that the pond water fills the voids in ice as indicated by the higher retrieved ice density.”.
The data in L15 Fig 5b covers ponded ice thickness from 50 cm to 150 cm, whereas the ice thicknesses for our selected cases are between 70 cm and 120 cm. If the linear fitting is applied to the same thickness range (70-120cm) in L15 fig 5b, you would get exactly the same as we described here (i.e., transmittance decreases as ice thickness increases).
343 Light_2015 used observation of the albedo to invert SSL IOPs. They used single diameter spheres approximation, as it is used for snow, only to provide an initial guess.
We are not sure of the point the reviewer is trying to raise here. Based on L15 paper, there is no measurement for the SSL and “these surface layers were typically not preserved in the core samples.”. To obtain the absorption required for RT, the density must be provided. How was the density obtained in L15 if not by guess? The scattering asymmetry factor of 0.94 is apparently a guess too. Using these two guessed model inputs, the scattering (not measured either) is obtained by matching the measured albedo band by band, as explicitly quoted: “Scattering coefficients are thus assigned to the uppermost layers such that modeled albedos agree with observation, starting with near-infrared wavelengths and working progressively toward shorter wavelengths.”. The adjusted scattering is in turn used as RT input to model the albedo. In addition, L08 and L15 treat the SSL as a layer of “snow”, but the snow grain size was not and could not (because it is not snow) be measured. While the grain size can be inverted by matching with the albedo, such inverted grain size is different for different spectral bands. Thus, some guessing in the grain size is also required. Please note that we are not criticizing the “guessing” (to put it in the reviewer’s words) used in L08 and L16. We understand the necessity of some tuning processes, but we don’t understand why the reviewer prefers one guess (or inverting) to another.
348 A complete analysis of the sensitivity of AOPs to salinity was never presented. This notion was only mentioned qualitatively in the text of section 3.2.
That is not entirely correct, as a partial sensitivity test is contained in Fig. 5. In any case, we completely agree that it is useful to add one more specific figure to the Appendix (see attached supplemental figure "FigS3_rev2"), with the following text:
“Figure A3 shows the optical effect of different salinity profiles. The maximum value (10 ppt) is a rare occurrence anywhere in the ice column, but was deemed a good maximum value in order to capture the full range of potential variability. Detectable changes are present up to the NIR, and are significant in the visible. In most situations, it is observed that the model predicts maximum differences in both albedo and transmittance of up to 0.05, in correspondence of their peaks in the visible.”
351 There are two ideas mixed in the same sentence. (1) Depending on pond depths and (2) the albedo (transmittance) is significantly lower (higher) than that of bare ice
For clarity, we deleted the second half of this sentence.
352 The claim on the relation between pond depth and transmission is in opposition with what was stated at line 325.
The reviewer is absolutely right, this was a typo. Changed to “...transmittance decreases with pond depth for 352 similar ice thicknesses below”.
Figure 2 The scenario using measured density should be specified on the caption or legend. Name of the layers should be specified.
The caption was certainly not optimal. Changed to: “Fig. 2: Effect of different ice density profiles (colored curves, values in g/cm3 for the SSL, DL and IL) on modeled albedo and transmittance. The black lines are the optimal fits to the measurements (gray areas) for the 3 July 2010 bare, FYI ice site (see top row of Fig. 1). ”
Figure 3 As a comparison, having a scenario with SSL modeled using the reference model would be useful. Name of the layers should be specified.
We will include the reference line (black line in Fig. 1). Caption changed to: “Figure 3: As in Fig. 2, but for a SSL consisting of spherical snow grains of the indicated thickness and effective radius Rs (in μm).”. The reference to the DL and IL is not needed since the caption refers to Fig. 2.
Figure 4 Name of layers should be specified.
Captain changed to: “Figure 4: As in Fig. 2, but considering added contamination from sootlike, BC particulate in the top 10 cm of the ice column.” The reference to the DL and IL is not needed since the caption refers to Fig. 2.
Figure 5 The difference between the dotted and full black lines representing measurements should be specified. Name of layers should be specified.
We will change the two experimental lines to solid gray, and modify accordingly the explanation already provided at lines 246-ff, “The gray lines are albedo and transmittance measurements collected during SHEBA with two different spectroradiometers: a Spectron Engineering SE-590 and Analytical Spectral Devices Ice-1.”
Figure 6 Same as fig. 5
Same as above.
Reference
Arndt, S. and Nicolaus, M.: Seasonal cycle and long-term trend of 75 solar energy fluxes through Arctic sea ice, The Cryosphere, 8, 2219–2233, https://doi.org/10.5194/tc-8-2219-2014, 2014.
Light, B., Maykut, G., and Grenfell, T.: A temperature-dependent, structural-optical model of first-year sea ice, J. Geophys. Res.- Oceans, 109, C06013, https://doi.org/10.1029/2003JC002164, 2004.
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RC3: 'Comment on tc-2022-106', Anonymous Referee #3, 24 Oct 2022
General Comments
This manuscript aims to validate an implementation of a radiative transfer model in sea ice into in the advanced coupled-atmosphere radiative transfer (COART) model. The influence of several environmental factors (number of the ice layer, density profile, presence of black carbon or phytoplankton…) on the simulated albedo and transmittance are studied using in situ optical measurements led in sea ice during the SHEBA and the ICESCAPE field campaigns. The authors show that the simulated albedo and transmittance are closer to the observation when at least three layers (for bare ice) and two layers (for ponded ice) are considered which is in line with previous studies. They also show that the ice density profile has a large influence on the representation of both optical properties.
The analyses suggested in this manuscript confirm results from previous studies and bring new material for a better understanding and representation of the radiative transfer in sea ice. However important elements are missing to (1) validate the model as the scope of the manuscript suggests it and to (2) well understand the methodology used here.
Major Comments
- A validation of the radiative transfer in the ice is suggested in this paper nevertheless, by the adjustment of the physical parameter ( ice density, temperature profile, BC amount ... ) used as model inputs to match the observed optical parameters as well as the too-small data set, it does not seem possible to conclude on the robustness of the model presented here. A solution would be to change the focus of the paper to better highlight the sensitivity analyses that are led in the manuscript.
- Methodological information is hard to find in the paper due to the lack of a proper methodology section. Some information needed for a good understanding of the manuscript is missing or is diluted in the “validation study” section :
- A description of the in-situ observations used in this manuscript should be added and gathered. Information such as the region of both campaigns, the number of observations for each section (FYI, MYI and Ponded ice), the physical parameters that have been measured, and how each parameter (optical and physical) has been recorded should be gathered in a same paragraph or section.
- A paragraph or section about the evaluation protocol is also missing. How are the simulated transmittance and albedo calculated based on the IOP retrieved in the look-up tables? What are the inputs of the model? Among these inputs which ones come from observations, and which ones have been adjusted?
Specific Comments
P1 lines 31-35: “The interactions between snow, sea ice and solar radiation in most climate models are based on empirical parameterizations that are often just a function of snow depth, sea ice thickness and surface temperature.” References to these models should appear here.
P2 line 59: “to complement the observations from SHEBA and ICESCAPE”. Previously in the paragraph, the FIRE ACE project is mentioned. Why is it not mentioned anymore here? and why is it not used in the present analysis?
P2 lines 72-74: This part of the introduction could benefit from a better description of the focus of the present study.
P3 lines 100-101: “The presence of other possible inclusions (BC and phytoplankton) is also considered.” The part of the model that considers these inclusions should be described.
P3 line 126: What do the authors mean by "the actual scattering coefficient"?
P3 lines 132-133: "the cases studied here pertain to sea ice surveyed in the warm, summer season". This should be specified much earlier in the paper (maybe in the introduction section with the focus of the study). The fact that snow is not considered in the model should also be specified earlier.
P4 lines 144-145: Can the authors precise what they mean by “standard subarctic atmospheric profile” and by “open-ocean water properties”, or give references here?
P4 lines 147-148: “We strived to use all available observational data to determine the input to the model, focusing on two common ice types: bare and ponded ice.” As said in the major comment, this requires more explanations. What are the inputs of the model here? And what is done in case the observational data does not exist?
P4 lines 152-153: Why only these two dates have been retained from the ICESCAPE campaign? Are these the only bare ice stations led during the ICESCAPE campaign in 2010 and 2011?
P4 lines 163-165: “The strong spectral dependence of the absorption coefficients for brine, ice, water and organic or other inclusions (Grenfell and Mayakut, 1977; Perovich and Gow, 1996) is responsible for the nearly constant albedo in the visible region and the significant decrease in the near infrared region”. Are the authors still describing Fig. 1 here? Also, there is a mistake in the reference: Grenfell and Maykut, 1977.
P4-5 lines 180-182: Are these densities measured?
P5 lines 189-190: “Our tests show negligible sensitivity of the AOPs to small variations in temperature.” I assume the authors are referring to the analysis they performed in the appendix. It should be specified.
P5 lines 193-194: “It is clear that a single layer is insufficient to adequately reproduce both the albedo and transmittance.” Is this result shown in figure 1? If so, it should be specified.
P5 line 201: “We adjusted the ice density”. I am confused here. The authors said earlier that the AOPs are more sensitive to density than to salinity or temperature. This explains why they choose to simplify the temperature profile. But if they now adjust the density (the only parameter that has a real impact on the AOP) of the observations to match better with the optics parameters, how can the radiative transfer model can then be validated with this adjusted “observation”? If the simulated parameters do not match the observation with the measured physical parameters as inputs, this should mean that the radiative transfer model misses something. Changing the physics won’t fix the optics.
P5 line 210: “in the absence of completely measured density profiles”. Here is an illustration of the second major comment. Since there is no previous description of what inputs are measured and what inputs are not, it is difficult to understand the results here.
P5 line 211: “These results demonstrate how the augmented COART model enables a fine tuning of the AOPs.” I don’t understand why the authors referring to the tuning of the AOPs when it seems that only the physics were tuned.
P5 lines 213-214: “The snow is composed of spherical grains, whose size determines the albedo at absorbing wavelengths (Warren 2019).” How the albedo and transmittance through the snow are calculated by the model should be better described.
P5 lines 214-215: “300 μm to represent new snow, and 1000 μm to represent aged, melting snow.” Where do these values come from?
P6 line 234: “The SHEBA observations show." Why are the authors giving SHEBA’s value while it is only ICESCAPE data that are treated in this section?
P6 line 250: “The salinity profile were assumed”. Here again, the manuscript would benefit from a better description of inputs that are measured and those that are assumed or adjusted.
P6 line 268: “In our modeling, 5 mm of snow with grain size of 200 μm were considered”. Again, how the albedo and transmittance through the snow are calculated by the model should be better described. And where do these values come from?
P7 lines 289-290: The sentence should be cut after “solar irradiance is largest”.
P7 lines 290: “A series of observations”. Again the number of observations used should be specified.
P7 line 293: “It is reasonable to expect that the accumulation of water on top of ice should annihilate the SSL." Why? This should be justified with references.
P7 line 311-313: “For the thick ice with shallow pond (top row) observed on 19 July, a 3- layer ice model is required for satisfactory model-observation agreement.” What could explain this third layer for this particular pond?
P7 line 318: “(3-layer for thick ice)”, how do we know that this is only the ice thickness under the pond that justify the number of optical layers?
P7 lines 320-321: “If the albedo measurements in the near-infrared are accurate”. Why this sentence? Is there anything that suggests the opposite?
P8 line 348: “Sensitivity tests show that lower salinity values”. The sensitivity tests for the salinity are missing from the main text or appendices.
P8 line 352-353: “and transmittance increases with pond depth for similar ice thicknesses below” this is the opposite of what is said in line 325.
P8 line 363-364: “An accurate and efficient radiative transfer model is also required for climate models, which use simple AOP parametrizations for sea ice.” This sentence is not true since some ESM already use the Delta Eddington approach of Briegleb & Light (2007) which is not a “simple AOP parameterization for sea ice”.
P9 line 370: “the density is used as a tunable parameter since in situ measurements are not 370 always available”. As an input parameter of the model, the density should not be treated as a tunable parameter.
Figure 1: Lime text in the legend is hard to read. Also, the authors should consider to better explaining the legend (by naming each layer and explaining what letters refer to).
Figure 2: Albedo and transmittance curves should be differentiated by something (dashed line as it is already done in figure A1). Numbers given in the figure should be explained in the caption.Why are only the results for July 3rd are given and not those for the 19th? Are the results for July 19th similar the those for the 3rd?
Figure 3: Same comment as figure 2.
Figure 4: The caption should better describe the figure here. It is not as Fig.2 as the density profile is not changing. Describing the physics (number of layers, density profile) in the caption and just giving the amount of BC for each line in the legend could help for clarity.
Figure 5: Same comment that for the other figures: the legend should be better explained in the caption. What the dotted line refers to should also be specified.
Figure 6: What the dotted line refers to should be specified.
Figure 7: Considering the number of panels here, adding a letter to call each panel could improve the clarity of the main text and the caption.
Citation: https://doi.org/10.5194/tc-2022-106-RC3 -
AC3: 'Reply on RC3', Matteo Ottaviani, 24 Nov 2022
We thank the reviewer for his detailed perusal of the manuscript. We have worked intensively to address each point, as explained in the point-to-point response below.
Major Comments
- A validation of the radiative transfer in the ice is suggested in this paper nevertheless, by the adjustment of the physical parameter ( ice density, temperature profile, BC amount ... ) used as model inputs to match the observed optical parameters as well as the too-small data set, it does not seem possible to conclude on the robustness of the model presented here. A solution would be to change the focus of the paper to better highlight the sensitivity analyses that are led in the manuscript.
There is some misunderstanding here. Except for the density, which is inverted from the spectral measurements, other input parameters are from in-situ observations, including temperature, salinity and ice thickness. The BC and chlorophyll concentration, as well as the snow properties, are not from in-situ measurements, because they are only used for sensitivity tests. A new subsection (3.1) has been added for clarity (see response to point 2 below).
This exercise aims at assessing the capabilities of COART through comparison with experimental data. Additionally, we have provided relevant sensitivity tests in the Appendix, which now contains two more figures (see also response to Rev. #2). The model accurately accounts for all relevant radiative transfer processes in the atmosphere, ice and ocean. The sensitivity tests highlight the flexibility of COART in representing variations in the observed signals. Sensitivity tests do not require experimental data. On the other hand, every validation effort includes a “sensitivity tests'' component. Since we sourced all possible in-situ measurements to constrain the input parameters (ice density, temperature, salinity profiles, and thickness), restraining the focus of the manuscript to “sensitivity tests” would be deceiving.
2. Methodological information is hard to find in the paper due to the lack of a proper methodology section. Some information needed for a good understanding of the manuscript is missing or is diluted in the “validation study” section :
- A description of the in-situ observations used in this manuscript should be added and gathered. Information such as the region of both campaigns, the number of observations for each section (FYI, MYI and Ponded ice), the physical parameters that have been measured, and how each parameter (optical and physical) has been recorded should be gathered in a same paragraph or section.
- A paragraph or section about the evaluation protocol is also missing. How are the simulated transmittance and albedo calculated based on the IOP retrieved in the look-up tables? What are the inputs of the model? Among these inputs which ones come from observations, and which ones have been adjusted?
A detailed description of the in-situ observations and the region is provided in L15 (and Polashenski et al., 2015) for ICESCAPE and in Perovich et al., 2002, for SHEBA observations, as referenced at lines 55-56 of the original manuscript. The papers we referred to also detailed “how each parameter (optical and physical) has been recorded”. A new subsection (3.1) now summarizes general information on the region and the observations used in the simulations:
“3.1 Data and Methodology
Because the ice IOPs are linked to the ice physical properties through the parametrization described in Sec. 2, the input parameters required by the radiative transfer model become simply the ice salinity, density and temperature in the ice layers. Together with the physical properties in atmospheric and ocean layers, COART derives the IOPs in all layers from the input physical properties in the coupled system and then calculates the irradiances at any desired level. The irradiances at the ice surface and base are used to calculate the albedo and transmittance of sea ice for comparison with observations.
The ICESCAPE and SHEBA campaigns proved to be the most suitable data sources for our study. Both campaigns were conducted in the Arctic Ocean, between the Chukchi Sea and the Beaufort Sea regions. Of all the physical variables needed at the input and measured in situ, the total ice thickness and the vertical profiles of salinity within the ice column are the most available. For ICESCAPE, we use the exact values of layer-resolved salinity documented by Polashenski et al. (2015) and partially in L15. For SHEBA, density profiles from cores are generally very scarce. We were able to use density measurements for the 19 July 2011 case, based on the uppermost 80 cm of the annotated core (see L15, Fig. 7). When forced by the lack of in-situ observations, the values were varied within commonly accepted ranges (Timco and Frederking, 1995), which also include those found in L08: 0.90-0.94 g/cm3 for the IL and 0.82-9.925 g/cm3 for the DL. Because no density has been reported for the thin top SSL, we use either 0.55 or 0.60 g/cm3 for this layer. For each SSL density, we looped the DL and IL densities in steps of 0.001 g/cm3 and compared the modeled spectral albedo with the measured albedo in each step. When the mean square difference falls below 0.02 (~5%), the densities are considered retrieved. Otherwise, the densities (within the given ranges) giving the minimum difference are used. This process is similar to the method used to obtain the scattering in L08 and L15 but not band by band. Temperature profiles are also sporadic, so we choose melting or ponded ice cases for which the temperature can be estimated based on straight physics. For example, for ponded ice cases, the top temperature can be set at 0°C because this is the coexisting temperature of water and ice. The bottom ice temperature of -2°C is based on the freezing temperature of seawater, and then the temperature in any depth of the interior ice is obtained by linear interpolation. Note that the sensitivity to temperature in this narrow range (0°C to -2°C) is small and does not substantially affect the quality of the fit, as shown in the Appendix. The total ice thickness and solar zenith angle (which are generally measured) are also required to calculate the albedo and transmittance. The melt pond depth required for ponded ice is generally available from observation. Snow properties, chlorophyll concentration, and black carbon, are used for sensitivity tests and to demonstrate that the fit can be improved should information on these constituents be available.”
Note that more detailed information on each case was already provided in the subsections: for first-year bare ice, see lines 185-191 in the old Sec. 3.1.1 (now 3.2.1); for multi-year bare ice see Sec. 3.1.2 (now 3.2.2); for ponded ice see Sec. 3.2 (now 3.3). Moreover, we have added a new paragraph and a figure in the Appendix to describe the treatment of ice surface roughness, and edited the sentence at Line 188 to read: “Our tests show negligible sensitivity of the AOPs to small variations in temperature within the chosen ranges”.
Specific Comments
P1 lines 31-35: "The interactions between snow, sea ice and solar radiation in most climate models are based on empirical parameterizations that are often just a function of snow depth, sea ice thickness and surface temperature." References to these models should appear here.
This sentence was already adjusted in response to a comment from Rev. #1:
“Many sea ice models employ simplistic parameterizations for the albedo, resulting in large uncertainties in both present-day simulations and future climate projections in the Arctic (Solomon et al., 2021; Notz et al., 2016; Koenigk et al., 2014; Solomon et al., 2007).”
Now we added two more references:
Solomon, S., D. Qin, M. Manning,M. Marquis, K. Averyt,M.M. B. Tignor, H. L. Miller Jr., and Z. Chen, Eds., 2007: Climate Change 2007: The Physical Science Basis. Cambridge University Press, 996 pp.
Keen, A., Blockley, E., Bailey, D. A., Boldingh Debernard, J., Bushuk, M., Delhaye, S., Docquier, D., Feltham, D., Massonnet, F., O'Farrell, S., Ponsoni, L., Rodriguez, J. M., Schroeder, D., Swart, N., Toyoda, T., Tsujino, H., Vancoppenolle, M., and Wyser, K.: An inter-comparison of the mass budget of the Arctic sea ice in CMIP6 models, The Cryosphere, 15, 951–982, https://doi.org/10.5194/tc-15-951-2021, 2021.
P2 line 59: "to complement the observations from SHEBA and ICESCAPE". Previously in the paragraph, the FIRE ACE project is mentioned. Why is it not mentioned anymore here? and why is it not used in the present analysis?
Because FIRE-ACE provided measurements of (only) albedo and BRDF from airborne instrumentation, which is not the kind of measurements we focus on in this study.
P2 lines 72-74: This part of the introduction could benefit from a better description of the focus of the present study.
We have edited the entire paragraph as:
“Meeting the modeling needs described above requires a tool capable of rigorously calculating the radiative distribution in the atmosphere-sea ice-ocean system. As described in the next section, Jin et al. (2006) developed a Coupled Ocean-Atmospheric Radiative Transfer (COART) model. Here, this previously validated (Jin et al., 2002; 2005) COART model is extended to include the sea ice medium. The sea ice optical properties are directly parameterized as a function of its measurable physical properties, so as to eliminate the need to provide at input the Inherent Optical Properties (IOPs), whose direct measurements are more challenging. The rest of the ocean/atmospheric column can accommodate any species whose IOPs are known. This physically-based strategy also enables a direct connection with the physical ice properties simulated in climate models. In developing such a GCM-oriented version of COART, the objective of this study is to validate said parametrization against observations of albedo and transmittance by constraining the physical properties with available measurements of their vertical profiles. The augmented COART model is described in Sec. 2, and its performance is evaluated against ICESCAPE and SHEBA measurements of spectral albedo and transmittance in Sec. 3, including sensitivity studies with respect to light-absorbing impurities. The ice types vary between bare and ponded sea ice in the melting season. The presence of snow is not a focus of the present study, although it can be accounted for by the model and we included a comparison with a relevant study that used snow grains to model the surface scattering layer (old Sec. 3.1.1, now 3.2.1). The conclusions are presented in Sec. 4. An appendix is also provided to show relevant sensitivity tests.”
P3 lines 100-101: "The presence of other possible inclusions (BC and phytoplankton) is also considered." The part of the model that considers these inclusions should be described.
There’s nothing really to “describe” here, these values are part of the tabulated constants used by the code. We have anyway modified the sentence to read: “In addition to the absorption by pure ice, and scattering and absorption by brine pockets and air bubbles, the presence of other possible inclusions (BC and phytoplankton) can also be considered. The addition of scattering and absorbing particulates is trivial, and achieved via the compilation of tabulated IOPs”.
P3 line 126: What do the authors mean by "the actual scattering coefficient"?
It refers to the scattering coefficient associated with all scattering energy without scaling resulting from the forward scattering truncation. To avoid confusion, we deleted “actual”.
P3 lines 132-133: "the cases studied here pertain to sea ice surveyed in the warm, summer season". This should be specified much earlier in the paper (maybe in the introduction section with the focus of the study). The fact that snow is not considered in the model should also be specified earlier.
Good suggestion! We have implemented it, see response to your comment above (P2 lines 72-74).
P4 lines 144-145: Can the authors precise what they mean by "standard subarctic atmospheric profile” and by “open-ocean water properties" or give references here?
It is simply a static atmospheric model of how the pressure, temperature, density, and viscosity of the Earth's atmosphere change over a wide range of altitudes, similar to the “US standard atmosphere” but for subarctic environments. The reference is added (McClatchey et al., 1972). Similarly, the “open-ocean properties” refer to the “standard” ocean model, in which the ocean optical properties are associated with the chlorophyll content. Based on climatological data, the chlorophyll concentration is around 0.1 g/cm3 on average, a typical value for open ocean. We have modified the paragraph to read: “In the model, we use a standard subarctic atmosphere for vertical profiles of pressure, temperature and density to model the Rayleigh background atmosphere. For the ocean layers beneath the ice, the Chl-a concentration is set to 0.1 mg/m3, about the average reported for the arctic ocean (Gordon and Morel, 1983; Morel and Maritorena, 2001; Morel and Gentili, 2004)”.
- A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, Rep. AFCRL–72–0497, (Air Force Cambridge Research Laboratories, Bedford, Mass., 1972).
P4 lines 147-148: "We strived to use all available observational data to determine the input to the model, focusing on two common ice types: bare and ponded ice." As said in the major comment, this requires more explanations. What are the inputs of the model here? And what is done in case the observational data does not exist?
See new Subsec. 3.1, as explained in the response to Major Comment 2 above.
P4 lines 152-153: Why only these two dates have been retained from the ICESCAPE campaign? Are these the only bare ice stations led during the ICESCAPE campaign in 2010 and 2011?
It is explained in the paper that we surveyed all the ICESCAPE (and SHEBA) data, and those particular dates were selected because of optimal observational conditions: clear sky (if possible, otherwise diffuse illumination with SZA=48° which ensures minimal sensitivity), and most consistent set of measurements over best-defined bare sea ice, as per the field notes. We have modified anyway the start of Sec. 3.1.1 (now 3.2.1) to read:
“The gray areas in Fig. 1 show the total range of a series of albedo and transmittance measurements collected at each of two ICESCAPE stations in the Beaufort Sea: the top panels are for the 3 July, 2010, and the bottom panels for the 19 July, 2011, case. These particular dates were selected because of optimal observational conditions and the most consistent set of measurements over best-defined bare sea ice, as per the field notes.”
P4 lines 163-165: “The strong spectral dependence of the absorption coefficients for brine, ice, water and organic or other inclusions (Grenfell and Mayakut, 1977; Perovich and Gow, 1996) is responsible for the nearly constant albedo in the visible region and the significant decrease in the near infrared region". Are the authors still describing Fig. 1 here? Also, there is a mistake in the reference: Grenfell and Maykut, 1977.
Thanks for catching the typo in the reference (now corrected). The listed statement is general, but the paragraph and what follows refer to Fig. 1 in terms of choosing the density values.
P4-5 lines 180-182: Are these densities measured?
Not in situ. They are typical values for the profile reported in the literature for this type of ice.
P5 lines 189-190: “It is clear that a single layer is insufficient to adequately reproduce both the albedo and transmittance". I assume the authors are referring to the analysis they performed in the appendix. It should be specified.
That’s right. Added: “(See Appendix)”.
P5 lines 193-194: “It is clear that a single layer is insufficient to adequately reproduce both the albedo and transmittance.” Is this result shown in figure 1? If so, it should be specified.
We have modified the paragraph to read: “To highlight the importance of using at least three layers, Fig. 1 includes the results for single- and double-layered ice, with densities taken as the combinations of those used in the 3-layer model. It is clear that a single layer is insufficient to adequately reproduce both the albedo and transmittance, as shown by the blue and magenta lines that are far off the range of measured albedo and transmittance.”
P5 line 201: "We adjusted the ice density". I am confused here. The authors said earlier that the AOPs are more sensitive to density than to salinity or temperature. This explains why they choose to simplify the temperature profile. But if they now adjust the density (the only parameter that has a real impact on the AOP) of the observations to match better with the optics parameters, how can the radiative transfer model can then be validated with this adjusted “observation”? If the simulated parameters do not match the observation with the measured physical parameters as inputs, this should mean that the radiative transfer model misses something. Changing the physics won’t fix the optics.
We apologize for the confusion on the word “adjusted”, but density is simply used as one of our input parameters. In situ measurements are used when available. Otherwise, we use typical values obtained from climatologies pertinent to the ice types in question, as described in the new Subsec. 3.1.
We agree that “the AOPs are more sensitive to density than to salinity or temperature”, but salinity and temperature also impact the AOPs, as demonstrated in the sensitivity test results. It is the density, salinity and temperature that all together control the phase equilibrium and the brine and air volumes, which in turn determine the ice IOPs. Because in our physically-based parameterization the IOPs are linked to the ice properties, changing the ice density changes all the IOPs consistently and differentially in different spectral bands. If the parameterization is not physical, obtaining model-observation agreement in both albedo and transmittance (again, simultaneously and at all wavelengths) is extremely unlikely even if a few unknown input properties are “adjusted”. For all these reasons, we have full confidence that our approach is legitimate to validate radiative transfer processes in sea ice. Should more complete suites of input parameters become available in the future, the focus can shift towards the betterment of the IOP parametrization.
P5 line 210: "in the absence of completely measured density profiles". Here is an illustration of the second major comment. Since there is no previous description of what inputs are measured and what inputs are not, it is difficult to understand the results here.
See new Subsec. 3.1, as explained in the response to Major Comment 2 above.
P5 line 211: “These results demonstrate how the augmented COART model enables a fine tuning of the AOPs.” I don’t understand why the authors referring to the tuning of the AOPs when it seems that only the physics were tuned.
It is clear that most of the confusion comes from the use of the word “tuning”. We have rewritten the sentence as: “These results demonstrate how the augmented COART model can capture many of the spectral signatures and their changes in observed albedo and transmittance”.
P5 lines 213-214: “The snow is composed of spherical grains, whose size determines the albedo at absorbing wavelengths (Warren 2019).” How the albedo and transmittance through the snow are calculated by the model should be better described.
This sentence has been modified as: “The module of the radiative transfer model used to calculate the albedo and transmittance of snow is described in Jin et al. (2008). This model can handle different snow particle habits but, to be consistent with L15, the snow here is assumed to be composed of spherical grains, whose size determines the albedo at absorbing wavelengths (Warren 2019; Wiscombe and Warren, 1980).”
Jin, Z., T.P. Charlock, P. Yang, Y. Xie, W. Miller, Snow optical properties for different particle shapes with application to snow grain size retrieval and MODIS/CERES radiance comparison over Antarctica. Remote Sens. Environ., 112, 3563-3581 (2008).
P5 lines 214-215: “300 μm to represent new snow, and 1000 μm to represent aged, melting snow.” Where do these values come from?
These are typical values for newer versus older snow. We have added the reference to the seminal paper: Wiscombe, W. J., & Warren, S. G. (1980). A Model for the Spectral Albedo of Snow. I: Pure Snow, Journal of Atmospheric Sciences, 37(12), 2712-2733.
P6 line 234: “The SHEBA observations show." Why are the authors giving SHEBA’s value while it is only ICESCAPE data that are treated in this section?
Because we harvested every possible information on impurity content to inform our input. In the effort to find climatological values, we listed those available. We used these plausible values to factor in the plausible absorption amount in the ice, and also showed a sensitivity study that captures the full range of plausible values. There were no BC measurements reported in ICESCAPE.
P6 line 250: “The salinity profile were assumed”. Here again, the manuscript would benefit from a better description of inputs that are measured and those that are assumed or adjusted.
See new Subsec. 3.1, as explained in the response to Major Comment 2 above.
P6 line 268: "In our modeling, 5 mm of snow with grain size of 200 μm were considered". Again, how the albedo and transmittance through the snow are calculated by the model should be better described. And where do these values come from?
More description has been provided on “how the albedo and transmittance through the snow are calculated” (see response to your “P5 lines 213-214” comment). The previous sentence says: ““a few mm of new snow on surface” was reported.” These are a few millimeters of a size typical of new snow. If the reviewer has a better guess of what the notes imply, we can regenerate the figure. However, note that we already present sensitivity studies to both snow depth and snow grain size in Fig. 3.
P7 lines 289-290: The sentence should be cut after "solar irradiance is largest".
Absolutely. Fixed.
P7 lines 290: “A series of observations”. Again the number of observations used should be specified.
See new Subsec. 3.1, as explained in the response to Major Comment 2 above.
P7 line 293: "It is reasonable to expect that the accumulation of water on top of ice should annihilate the SSL." Why? This should be justified with references.
We thought it intuitive to think that water accumulating on top of a fragile, granular thin layer would melt it or at least change its properties dramatically. We have contacted Melissa Webster, who recently published a new study based on MOSAiC observations (“Spatiotemporal evolution of melt ponds on Arctic sea ice: MOSAiC observations and model results”; Elementa: Science of the Anthropocene (2022) 10 (1): 000072). However, the discussions in her work mostly focus on subnivean ponds. To keep in line with the spirit of our original sentence, we have modified it to:
“The SSL is composed of coarse, crumbly grains of ice and voids of air. Meltwater infiltration into the SSL is expected to significantly alter its physical and optical properties. Typically, a water-saturated SSL is indeed less reflective and more absorptive, or absent altogether (Light et al., 2008).”
Note that Light et al., 2008, report:
“Ponded ice, on the other hand, generally shows a much more homogeneous structure throughout its depth. Although the ice-water interface in the ponds can be quite irregular, there are fewer isolated inclusions and fewer air-ice interfaces to scatter radiation, and the SSL is typically either absent or flooded.”
P7 line 311-313: “For the thick ice with shallow pond (top row) observed on 19 July, a 3- layer ice model is required for satisfactory model-observation agreement.” What could explain this third layer for this particular pond?
It is likely due to thicker ice requiring more layers to resolve the variations of the properties within the column.
P7 line 318: “(3-layer for thick ice)”, how do we know that this is only the ice thickness under the pond that justify the number of optical layers?
Does the reviewer mean “How do we know that IT is only the ice thickness...”? What we mean is that thicker ice requires one more layer (at least). This doesn’t preclude that in other cases even more layers could be needed, that’s why we specified “in the cases analyzed here” in the previous sentence.
P7 lines 320-321: “If the albedo measurements in the near-infrared are accurate”. Why this sentence? Is there anything that suggests the opposite?
We meant to refer to specific challenges in controlling the measurement accuracy in this wavelength regime, where the energy is very low. We propose to change the sentence to “If the albedo measurements in the near-infrared are accurate (in this regime the energy and the subsequent S/N are very low),...”
P8 line 348: “Sensitivity tests show that lower salinity values”. The sensitivity tests for the salinity are missing from the main text or appendices.
That is not entirely correct, as a partial sensitivity test is contained in Fig. 5. In any case, we completely agree that it is useful to add one more specific figure to the Appendix (see revised manuscript), with the following text:
“Figure A3 shows the optical effect of different salinity profiles. The maximum value (10 ppt) is a rare occurrence anywhere in the ice column, but was deemed a good maximum value in order to capture the full range of potential variability. Detectable changes are present up to the NIR, and are significant in the visible. In most situations, it is observed that the model predicts maximum differences in both albedo and transmittance of up to 0.05, in correspondence of their peaks in the visible.”
The new figure is attached (FigS3_rev2.pdf) as a supplement for the response to reviewer #2.
P8 line 352-353: “and transmittance increases with pond depth for similar ice thicknesses below” this is the opposite of what is said in line 325.
Yes, this was a typo and is now corrected. Thanks!
P8 line 363-364: “An accurate and efficient radiative transfer model is also required for climate models, which use simple AOP parametrizations for sea ice.” This sentence is not true since some ESM already use the Delta Eddington approach of Briegleb & Light (2007) which is not a “simple AOP parameterization for sea ice”.
We referred to Briegleb and Light, 2007, in the Introduction. To our knowledge, their ESM is the only one using interactive RT for sea ice. However, it is a 2-stream model with a number of assumptions on ice IOPs (e.g., constant scattering asymmetry factor of 0.94 in all bands and all ice layers).
P9 line 370: "the density is used as a tunable parameter since in situ measurements are not 370 always available". As an input parameter of the model, the density should not be treated as a tunable parameter.
This point should now be resolved in view of the many earlier responses to this review.
Figure 1: Lime text in the legend is hard to read. Also, the authors should consider to better explaining the legend (by naming each layer and explaining what letters refer to).
We have improved the explanation to the legend explicitly in the caption. Regarding the color readability, we’ll abide by the requirements of the editorial office should the quality be insufficient.
Figure 2: Albedo and transmittance curves should be differentiated by something (dashed line as it is already done in figure A1). Numbers given in the figure should be explained in the caption.Why are only the results for July 3rd are given and not those for the 19th? Are the results for July 19th similar the those for the 3rd?
We have changed the transmittance curves to dashed, as suggested (it makes total sense for consistency with the figures in the Appendix). The explanation of the legend has been improved as per the previous comment. Yes, the results for July 19th are very similar.
Figure 3: Same comment as figure 2.
Corrected accordingly. See response above.
Figure 4: The caption should better describe the figure here. It is not as Fig.2 as the density profile is not changing. Describing the physics (number of layers, density profile) in the caption and just giving the amount of BC for each line in the legend could help for clarity.
We totally agree. The caption now reads: “Sensitivity to albedo and transmittance to the addition of contamination from sootlike, BC particulate spanning amounts typical of the panarctic. The solid black lines are the optimal spectra for the 3-layer profile in the top panels of Fig. 1 (3 July, 2010).”.
Figure 5: Same comment that for the other figures: the legend should be better explained in the caption. What the dotted line refers to should also be specified.
Changed as suggested, as done for Fig. 2 (see your comment above).
Figure 6: What the dotted line refers to should be specified.
Corrected as per the point above.
Figure 7: Considering the number of panels here, adding a letter to call each panel could improve the clarity of the main text and the caption.
Done, and indicated in the caption and text.
Citation: https://doi.org/10.5194/tc-2022-106-AC3
Status: closed
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RC1: 'Comment on tc-2022-106', Anonymous Referee #1, 22 Jul 2022
General comments:
The authors have extended a coupled ocean-atmosphere radiative transfer (COART) model to the radiative transfer model (RTM) in the atmosphere-sea ice-ocean system (hereafter, the extended COART model). They compared the simulation results with measurement data of spectral albedo and transmittance collected at SHEBA and ICESCAPE stations to validate the extended COART model, and showed the agreement with previous studies that the model representations were improved by considering the vertical structure of sea ice such as SSL, DL and IL. They also showed the effect of contamination (LAPs and ice algae) of spectral albedo and transmittance of sea ice. The effectiveness of the extended COART model was emphasized through the series of analysis.
The result of albedo and transmittance comparisons between measurement and model looks good, but there are some questions on the results. In particular, following major comment (1) is critical issue. This paper’s main purpose is to validate the extended COART model. However, because there are few in-situ measurement data required for the validation of RTM, most of the simulated results are based on guesswork. Therefore, this paper is a qualitative discussion and is insufficient to validate the accuracy of the extended COART model. The authors should reconsider how to validate the RTM, so that a major revision would be needed.
Major comments:
1. Most of snow and sea ice physical parameters (sea ice density, ice temperature, salinity, ice thickness Chl. a concentration, snow grain size, LAPs, snow density, snow depth), which are input parameters used for the radiative transfer calculations, are not based on in-situ measurement data, but on the guess due to the lack of the information about snow and sea ice. Although the result of albedo and transmittance comparisons between measurement and model looks good, it is no exaggeration to say that the input variables are adjusted to match the calculation results with the observation ones. In general, since we simulate spectral albedo and transmittance based on the measurement data, we can validate a proposed model and can also find the physical processes that cannot be considered yet. In order to achieve the purpose of this paper, sufficient data must be prepared. The authors need to review the data used for the validation work again. If it is difficult to prepare the data, an alternative method is to confirm the reproducibility of your model by comparing it with a well-validated model.
2. Regarding the extended COART model, (a) why is it necessary to add the surface roughness scheme in the sea ice surface? Please add the reason by referring to Lamare et al. [2022; TCD]. In addition, the surface roughness is related to the specular reflection, and the magnitude of the surface roughness differs depending on the value of σ in the Gaussian normal distribution. The authors need to explain how the value of σ was determined. Furthermore, did authors apply this scheme to the boundary between the atmosphere and the melt pond where there is a large difference in refractive index between two medias? Please describe the explanation in detail. (b) There are various sizes of melt pond in the horizontal scale. The authors should describe the applicability of the extended COART model which is a plane-parallel RTM.
Technical comments:
L31-33: “The interaction between … surface temperature” this sentence is not clear. Explain the details about climate models mentioned in the text and cite references.
L48-: The last two paragraphs were well documented, but they do not mention the specific focus and the motivation for this manuscript. The authors need to describe it more clearly.
L78-: There is no mention about the ice algae in the section 2 which is a crucial for the transmittance of the sea ice though authors mentioned it in Fig. 6. Provide more details about the treatment of absorption/scattering properties of the ice algae.
L143: What does “AOPs” stand for?
The comments in the section 3 and below are omitted because they overlap with the major comment 1.
Citation: https://doi.org/10.5194/tc-2022-106-RC1 -
AC1: 'Reply on RC1', Matteo Ottaviani, 09 Aug 2022
We thank the reviewer for the comments. We address them one by one below.
General comments:
The authors have extended a coupled ocean-atmosphere radiative transfer (COART) model to the radiative transfer model (RTM) in the atmosphere-sea ice-ocean system (hereafter, the extended COART model). They compared the simulation results with measurement data of spectral albedo and transmittance collected at SHEBA and ICESCAPE stations to validate the extended COART model, and showed the agreement with previous studies that the model representations were improved by considering the vertical structure of sea ice such as SSL, DL and IL. They also showed the effect of contamination (LAPs and ice algae) of spectral albedo and transmittance of sea ice. The effectiveness of the extended COART model was emphasized through the series of analysis.
The result of albedo and transmittance comparisons between measurement and model looks good, but there are some questions on the results. In particular, following major comment (1) is critical issue. This paper’s main purpose is to validate the extended COART model. However, because there are few in-situ measurement data required for the validation of RTM, most of the simulated results are based on guesswork. Therefore, this paper is a qualitative discussion and is insufficient to validate the accuracy of the extended COART model. The authors should reconsider how to validate the RTM, so that a major revision would be needed.
This study validates a physically-consistent parameterization of bare sea ice IOPs as a function of its physical properties that can be directly measured (temperature, salinity, density and thickness). It is certainly true that a comprehensive set of in-situ measurements, required for a rigorous validation of RTM in sea ice in all conditions, is presently lacking. Therefore, we focused on bare and ponded ice cases (as defined observationally), for which we could source the most critical input parameters. In contrast, many alternative sea-ice RTMs employ as input parameters directly the IOPs (extinction coefficient, single scattering albedo and asymmetry factor), which are very challenging to measure in-situ or even in the laboratory. For example, the RTM used by Lamare et al. (2022) (referred to in a reviewer’s comment) uses a constant, wavelength-independent scattering asymmetry factor of 0.98 and constant scattering coefficients. Similarly, L08 and L15 use a constant scattering asymmetry factor of 0.94 and tuned scattering coefficients. Using the ice IOPs directly bypasses the complex relationships between the sea ice physical structure and its optical behavior, while in our case each physical parameter affects the IOPs at all wavelengths as it should be. Therefore, if the parameterization is not correct, obtaining model-observation agreement in both albedo and transmittance (again, simultaneously and at all wavelengths) is extremely unlikely even if a few unknown input properties were adjusted. For these reasons, we have full confidence that our approach is legitimate to validate radiative transfer processes in sea ice. Further details are provided in the following.
Major comments:
- Most of snow and sea ice physical parameters (sea ice density, ice temperature, salinity, ice thickness Chl. a concentration, snow grain size, LAPs, snow density, snow depth), which are input parameters used for the radiative transfer calculations, are not based on in-situ measurement data, but on the guess due to the lack of the information about snow and sea ice. Although the result of albedo and transmittance comparisons between measurement and model looks good, it is no exaggeration to say that the input variables are adjusted to match the calculation results with the observation ones. In general, since we simulate spectral albedo and transmittance based on the measurement data, we can validate a proposed model and can also find the physical processes that cannot be considered yet. In order to achieve the purpose of this paper, sufficient data must be prepared. The authors need to review the data used for the validation work again. If it is difficult to prepare the data, an alternative method is to confirm the reproducibility of your model by comparing it with a well-validated model.
We recognize a fundamental misunderstanding regarding this point. The reviewer puts forth a complete list of input parameters as if they all had the same relevance in the study. We are not focusing on the modeling of the albedo and transmittance of snow-covered ice. The main objective of this paper is to evaluate our IOP parametrization for bare ice and the relative RT processes. Within our approach, the bare-ice IOPs are parameterized exclusively as a function of the fundamental ice physical properties: salinity, density, and temperature. Such parameters, together with the ice total thickness, are based on real measurements, obtained after a thorough search for the best available datasets. The ICESCAPE and SHEBA data proved to be the most suitable for our study. We have made several attempts at including at least a preliminary version of MOSAiC data, but constantly hit the embargo that will last until January 2023. On the other hand, it was demonstrated in L08 that SHEBA and ICESCAPE data, albeit collected 20 years apart, show remarkable consistency. Furthermore, the appendix completes the study by highlighting the insensitivity to small variations in a lot of these parameters (especially temperature). The properties of the SSL have instead to be estimated (because no reliable measurement sets exist) based on the measured albedo in the near IR spectrum, as already done in L08.
The vertical profiles we use are documented by Polashenski et al (2015) and partially in L15, and we have used their exact values. We were even able to use density measurements for the 19 July 2011 case, based on the uppermost 80 cm of the annotated core (see L15, Fig. 7). Effectively, we adjusted the ice density in the other simulations only when forced by the lack of in-situ observations, but the adjustments ranged within commonly accepted values which also include those found in L08. The fact that these measurements are scarce (and we advocate for extensive collections of vertical profiles as one of the final messages) cannot be held as a flaw in our approach. Note that the manuscript highlights the use of such observations in several places, e.g.:
- Lines 147-148: “We strived to use all available observational data to determine the input to the model, focusing on two common ice types: bare and ponded ice.”
- Lines 156-157: “The Solar Zenith Angle (SZA) is calculated based on the reported observational time and location latitude and longitude.”
- Lines 166-168: This paragraph has been slightly corrected to: “We were able to exploit one of the few density measurements collected during ICESCAPE, although the density was only measured in the uppermost 80 cm where it varied between 0.625 and 0.909 g/cm3. When such measurements are not available, we assume typical FYI densities as reported by Timco and Frederking (1995): between 0.84 and 0.91 g/cm3 for the ice above the waterline, and between 0.90 and 0.94 g/cm3 for the ice below the waterline.”
- Lines 185-188: “For the salinity, we use the profiles reported from the core analysis of Polashenski et al. (2015), averaging the available data points in each model layer. Since measurements are not reported for the SSL (which normally gets destroyed when collecting the core) and the bottom of the ice, we assume the shallowest and deepest value extend to these remaining portions.”
- Line 306: (slightly modified): “The vertical profiles of salinity are also from cores, and vary between ⁓0.5 and 3.0 ppt (Polashenski et al., 2015).”
The misunderstanding regarding the snow layer concerns the treatment of the SSL. We think the reviewer was misled to believe that we were required to use in-situ measurements of snow properties. Instead, we correctly consider the ice SSL as a low-density ice layer, and the thin snow layer used to produce Fig. 3 and relative discussion is merely used to mimic the method used by L08, in which a snow layer with assumed physical and optical properties is used to represent the ice. We thought it was very informative to include this comparison with this flawed modeling of the SSL as snow, which inevitably leads to assuming meaningless “snow” properties (grain size, density, depth). These comparisons reinforce the advantages of considering a physically consistent model versus an ad-hoc approach that directly acts on the scattering coefficients and makes unjustified assumptions.
Next, we found that the simulated albedo and transmittance of bare ice are often higher than observation in the visible spectrum in most of the cases. We then tested the effects of possible LAPs: in these sensitivity tests, the Chl-a concentration and particulate amount are based on climatologies that are referred to in the manuscript. These are merely sensitivity tests aimed at illustrating how the inclusion of these contaminants could further improve the model-observation agreement.
We appreciate the reviewer’s suggestion of “comparing the code with a well-validated model”, but all available RT models for sea ice are approximated to some level. According to the reviewer’s standard on validation, we argue that such a model does not yet exist. We think the most intensively validated model is the 4-stream code used by Dr. Light’s group at the University of Washington. As detailed in the paper, this model was developed by Grenfell (1991), used in L08 and several other studies, and used the same discrete-ordinate method as the extended COART model, but in a simplified 4-stream version. The extended COART model is more advanced and can adopt any number of streams, in addition to the coupling feature and the treatment of ice roughness.
Finally, we note that the core point of the reviewer is contradicting: “the input variables are adjusted to match the calculation results with the observation ones”. Isn’t this the definition of a fit? Also, the point raised in the following sentence is obscure: “since we simulate spectral albedo and transmittance based on the measurement data, we can validate a proposed model and can also find the physical processes that cannot be considered yet”.
For all the reasons listed above, and since we strive to provide the best possible study, we kindly ask the reviewer to elaborate further on the raised points if he/she thinks we haven’t been clear enough.
- Regarding the extended COART model, (a) why is it necessary to add the surface roughness scheme in the sea ice surface? Please add the reason by referring to Lamare et al. [2022; TCD]. In addition, the surface roughness is related to the specular reflection, and the magnitude of the surface roughness differs depending on the value of σ in the Gaussian normal distribution. The authors need to explain how the value of σ was determined. Furthermore, did authors apply this scheme to the boundary between the atmosphere and the melt pond where there is a large difference in refractive index between two medias? Please describe the explanation in detail. (b) There are various sizes of melt pond in the horizontal scale. The authors should describe the applicability of the extended COART model which is a plane-parallel RTM.
The reason to implement a scheme accounting for the ice surface roughness is that the ice surface is naturally rough, especially for melting MYI, and the surface roughness affects the ice albedo and transmission. While surface roughness affects both the direct and diffuse light components (and therefore the surface BRDF as shown in Lamare et al. (2022), its effect on albedo and transmittance is small, as demonstrated in the figure attached as a supplement.
Lacking surface roughness measurement, we simply used σ=0.5 and σ=0.1 for the ice and pond surface, respectively. Based on the Cox-Munk formulation, σ=0.1 represents a minimal ocean surface roughness (wind speed=1.4 m/s). For the ice cases in this study, a coarse-grained ice surface layer was observed. Because the SSL appears granular, many surface facets must have large tilt angles. A value of σ=0.5 implies that 95% of the facet normals are <45o and 99.7% of them are within 56o from the local vertical. No observational data exist to constrain the roughness value, but again (differently from the radiance) its effect on fluxes is small. What is more important is that the extended COART model offers full flexibility in the treatment of roughness.
The applicability of a 1-D plane-parallel RTM depends on the relative dimension of the horizontal and the vertical scales. In the presence of a melt pond, the radiation field in the atmosphere calculated by a 1-D RTM is of course not valid. However, the atmosphere in our case only provides an approximate direct and diffuse partition for the incident solar spectral irradiance on sea ice surface. Since we model the RT in pond water and the ice beneath against “point” measurements provided by spectroradiometers, the use of a 1-D RTM to calculate radiative fluxes in the ice is totally justified as long as the pond horizontal extent is significantly larger than the ice thickness.
Technical comments:
L31-33: “The interaction between … surface temperature” this sentence is not clear. Explain the details about climate models mentioned in the text and cite references.
The reviewer is right, this sentence was left too “lonely”. We have replaced it with:
“Many sea ice models employ simplistic albedo parameterizations for the albedo, resulting in large uncertainties in both present-day simulations climate and future climate projections in the Arctic (Notz et al., 2016; Koenigk et al., 2014)”
L48-: The last two paragraphs were well documented, but they do not mention the specific focus and the motivation for this manuscript. The authors need to describe it more clearly.
We agree. We have modified and expanded lines 74-ff to:
“Many sea ice radiative transfer models require the Inherent Optical Properties (IOPs) at input, which constitutes a major limitation since the IOPs are very challenging to measure in-situ and even in laboratory. As a consequence, the IOPs more or less always suffer from very significant approximations. For example, Briegleb and Light (2007), L08 and L15 use a constant, spectrally-flat scattering asymmetry factor of 0.94 and tuned scattering coefficients, while Lamare et al. (2022) use a scattering asymmetry factor of 0.98 and constant scattering coefficients.
As described in the next section, Jin et al. (2006) developed a Coupled Ocean-Atmospheric Radiative Transfer (COART) model with high spectral resolution (up to 0.1 cm-1) to finely resolve atmospheric absorption, and accurate treatment of surface roughness. Here, we extend this previously validated (Jin et al., 2002; 2005) model to include the sea ice medium, in order to rigorously calculate the radiative distribution in the atmosphere-sea ice-ocean system. As part of the extension, the sea ice optical properties are directly parameterized as a function of its measurable physical properties (i.e., temperature, salinity, and density), so as to eliminate the need to provide the IOPs (extinction, single scattering albedo, and asymmetry factor) at input. This physically-based strategy also enables a direct connection with the physical ice properties simulated in climate models. In developing such a GCM-oriented version of COART, the objective of this study is to validate said parametrization against observations of albedo and transmittance by constraining the physical properties with available measurements of their vertical profiles.”
There is no mention about the ice algae in the section 2 which is a crucial for the transmittance of the sea ice though authors mentioned it in Fig. 6. Provide more details about the treatment of absorption/scattering properties of the ice algae.
We totally agree that the text around Line 100:
“The presence of other possible inclusions (BC and phytoplankton) is also considered.”
Is insufficient. We have modified it to read:
“Beside brine pockets and air bubbles, the model can easily consider the presence of any other inclusion with a vertical distribution throughout the ice column. We have currently included a black-carbon-type of aerosol (Hess et al., 1998) and ice algal pigments (Arrigo, Pers. Comm.).”
L143: What does “AOPs” stand for?
Apparent Optical Properties (as opposed to Inherent Optical Properties). Thanks for catching the lack of the spell out (now added)!
The comments in the section 3 and below are omitted because they overlap with the major comment 1.
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AC1: 'Reply on RC1', Matteo Ottaviani, 09 Aug 2022
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RC2: 'Comment on tc-2022-106', Anonymous Referee #2, 20 Oct 2022
General Comments
This manuscript aims to validate the implementation of a sea ice radiative transfer model into the advanced COART. The model inputs are vertically resolved salinity, temperature and density. These inputs together with the phase-equilibrium relationship developed by Cox and Weeks 1983 are used to predict brine and air total volume. Using these latters, an empirical mathematical equation developed by Light 2003 calculates gases and brine channels size distributions assuming inclusions to be spherical. Mie theory is used to predict the inherent optical properties (IOPs) of the different layers representing sea ice. A radiative transfer model based on the discrete ordinates method is finally used to calculate the output apparent optical properties (AOPs).
Modelled AOPs based on structural measurements are validated by comparison with measured AOPS obtained during the SHEBA and ICESCAPE campaigns. Three scenarios were considered: first-year ice bare ice, multi-year bare ice and ponded ice. The effect of soot impurities and algae are also assessed for these scenarios.
A model incorporating Mie theory and using physical structure to calculate AOPs would be a valuable tool as mentioned by the authors. However, the fact that the model as to be tuned in order to obtain agreements undermines the validity of this model. Two aspects (1) and (2) would have to be addressed in order to demonstrate the validity of the model.
Major Comments
- The inclusions distributions described by Light 2003 are valid for columnar (interior) ice. These distributions of inclusions size and shape are probably significantly different in the drained layer (DL) and surface scattering layer (SSL ) because of several processes (e.g., surface melting/refreezing, channel drainage, air bubble inclusion under dynamic growth, surface ablation by sunlight, etc.). The induction of inclusions distributions describing interior layer to drained and surface scattering layer might explain the mismatch between the untuned model and measurements. The author should suggest a different approach in order to predict inclusions distributions for these two layers. Microstructural observations of the SSL obtained during the MOSAiC expedition could be a start for such a model (when they will be available).
- The density, temperature and salinity measurements as well as absorbing particles concentrations used as inputs are often guessed by the authors because they were not measured on the field at the location of AOPS measurements. Without these reference measurements, the system is undetermined. Unfortunately, it is difficult to demonstrate the validity of the model without having the actual measurements or justifying the choice of the input with strong evidence. A solution could be to change the scope of the paper in order to study the sensitivity of AOPS to the tuning of the different inputs. Another suggestion would be to validate the model by comparison with another model. However, point (1) would need to be addressed first.
Specific Comments
28 Morphological changes and thinning of sea ice along with sea ice cover reduction are responsible for lower albedo and shortwave absorption in the ocean (Arndt and Nicolaus 2014 ).
46 The range is probably wider than that, especially for SSL. Would that be the range for columnar sea ice?
86 What is the value of the refractive index used for ice? Please provide a number or a range for this value.
88 The explanation of how the surface is implemented is insufficient. Water and ice have different roughness, therefore the parameters of the Gaussian equation describing its roughness should be different. From an optical perspective, it would be helpful to have a description of how it translates into the distribution of diffuse reflection. It would also be useful to describe the importance of purely specular reflection at the ice surface in the model.
99 Is absorption coefficient based on volume fraction? More details should be provided.
126 This explanation mixes a few concepts. The scattering efficiency Q (ratio of scattering surface area to geometrical surface area) in the Mie regime is close to 2 no matter the phase function. The reduced scattering coefficient or similarity variable b’=b*(1-g) which describes the mixed effect of scattering coefficient and phase function will indeed go down as the phase function represented by the asymmetry parameter g goes up. This concept should be addressed in this explanation. It is not that obvious that the reduced scattering coefficient goes down significantly for big inclusions. One would need to prove that claim quantitatively using the similarity principle (where b could be calculated from cross section area and g from Mie Theory).
131 Mirabilite crystals precipitates under -8 C (Light 2004).
137 As stated in (1), the approach described in this section is based on a description of columnar (interior ice). Since the processes dictating the bubbles and brine channels size distributions and refractive index are different in drained and surface scattering ice, we cannot consider the treatment described here as complete.
159 Cloud optical thickness of 10 is too low for an upper bound. 100 would be recommended.
201 The finality of L08 and L15 is to determine the IOPs of sea ice. The use of tuning in this case is justified because it is needed to find what the IOPs should be in order to meet measured AOPs. Furthermore, an explanation of the bias which they are rectifying by tuning is also provided. In the case of this study, density is an input and not a value that is being determined. Therefore, it is illogical to modify the input density in order to meet the correct answer. Unless these density tunings are justified with an explanation.
203 Following the similarity principle b’=b*(1-g), in the diffusion regime , it does not truly matter if g is kept constant or not. As long as the reduced scattering coefficient b’ is consistent.
216 Why change DL density and snow depth? These choices needs to be justified.
228 Indicate figure number.
236 It needs to be kept in mind that absorption coefficient of suits in air and in ice are not the same.
250-257 if temperature, salinity, SSL thickness, SSL density are not measured, the system is strongly under-determined. Furthermore, the manuscript needs to clarify if the density of 0.915 g/cm3 and salinity of 3 ppt used for interior ice are measured or guessed.
254 Granular ice and surface scattering layer are not equivalent. The word SSL should be kept in this case.
268-274 The manuscript needs to clarify if these inputs are assumptions or measurements.
275 The systematic bias could also come from guesses on ice physical parameters.
276 What is meant by ‘’other species’’ ? At this point in the manuscript, there has been no mention about any biological specie.
279 Please verify the claim that algal pigments are more concentrated at the top layer.
289 The explanation is unclear. The sentence seems to contain 3 ideas : (1) Melt pond occurs when sun irradiance is the largest, (2) Melt Pond water as a lower reflection and higher transmission than ice, (3) these two effects combined impact energy distribution.
304 Is temperature measured or guessed?
311 The manuscript should justify why thicker ice as a three-layer model while thinner ice only has a two-layer model.
312 Missing units after 0.83.
313 The use of tables to summarize inputs and to clarify how many total layers are used to represent ponds +ice would make the manuscript easier to read.To indicate whether the inputs are measured or assumed could also clarify the context.
325-326 The conclusion that transmittance decreases with increasing pond depth is counter-intuitive, since melt water contained in ponds scatters significantly less than interior sea ice. How would that be explained? Is it because of the high absorption of the melt water? This trend is in opposition with measurements from L15 fig 5b.
343 Light_2015 used observation of the albedo to invert SSL IOPs. They used single diameter spheres approximation, as it is used for snow, only to provide an initial guess.
348 A complete analysis of the sensitivity of AOPs to salinity was never presented. This notion was only mentioned qualitatively in the text of section 3.2.
351 There are two ideas mixed in the same sentence. (1) Depending on pond depths and (2) the albedo (transmittance) is significantly lower (higher) than that of bare ice
352 The claim on the relation between pond depth and transmission is in opposition with what was stated at line 325.
Figure 2 The scenario using measured density should be specified on the caption or legend. Name of the layers should be specified.
Figure 3 As a comparison, having a scenario with SSL modeled using the reference model would be useful. Name of the layers should be specified.
Figure 4 Name of layers should be specified.
Figure 5 The difference between the dotted and full black lines representing measurements should be specified. Name of layers should be specified.
Figure 6 Same as fig. 5
Reference
Arndt, S. and Nicolaus, M.: Seasonal cycle and long-term trend of 75 solar energy fluxes through Arctic sea ice, The Cryosphere, 8, 2219–2233, https://doi.org/10.5194/tc-8-2219-2014, 2014.
Light, B., Maykut, G., and Grenfell, T.: A temperature-dependent, structural-optical model of first-year sea ice, J. Geophys. Res.- Oceans, 109, C06013, https://doi.org/10.1029/2003JC002164, 2004.
Citation: https://doi.org/10.5194/tc-2022-106-RC2 -
AC2: 'Reply on RC2', Matteo Ottaviani, 17 Nov 2022
General Comments
This manuscript aims to validate the implementation of a sea ice radiative transfer model into the advanced COART. The model inputs are vertically resolved salinity, temperature and density. These inputs together with the phase-equilibrium relationship developed by Cox and Weeks 1983 are used to predict brine and air total volume. Using these latters, an empirical mathematical equation developed by Light 2003 calculates gases and brine channels size distributions assuming inclusions to be spherical. Mie theory is used to predict the inherent optical properties (IOPs) of the different layers representing sea ice. A radiative transfer model based on the discrete ordinates method is finally used to calculate the output apparent optical properties (AOPs).
Modelled AOPs based on structural measurements are validated by comparison with measured AOPS obtained during the SHEBA and ICESCAPE campaigns. Three scenarios were considered: first-year ice bare ice, multi-year bare ice and ponded ice. The effect of soot impurities and algae are also assessed for these scenarios.
A model incorporating Mie theory and using physical structure to calculate AOPs would be a valuable tool as mentioned by the authors. However, the fact that the model as to be tuned in order to obtain agreements undermines the validity of this model. Two aspects (1) and (2) would have to be addressed in order to demonstrate the validity of the model.
We thank the Reviewer for the feedback. Before proceeding to the point-to-point response, we’d like to briefly address this general comment. We believe a major misunderstanding generated most of the questions below, and it has to do with the choice of using the word “tuning”. The main objective of this paper is to evaluate our IOP parametrization for bare ice and the relative RT processes. Within our approach, the bare-ice IOPs are parameterized exclusively as a function of the fundamental ice physical properties: salinity, density, and temperature. Such parameters, together with the ice total thickness, are based on real measurements, obtained after a thorough search for the best available datasets (see below for more explanations). We simply invert for the density needed to best fit the measurements. The density values are within reported typical ranges for each of the SSL, DL or IL. In one case (19 July), we were even able to use the density measured in a core extracted next to the location of the optical measurements.
Major Comments
1. The inclusions distributions described by Light 2003 are valid for columnar (interior) ice. These distributions of inclusions size and shape are probably significantly different in the drained layer (DL) and surface scattering layer (SSL ) because of several processes (e.g., surface melting/refreezing, channel drainage, air bubble inclusion under dynamic growth, surface ablation by sunlight, etc.). The induction of inclusions distributions describing interior layer to drained and surface scattering layer might explain the mismatch between the untuned model and measurements. The author should suggest a different approach in order to predict inclusions distributions for these two layers. Microstructural observations of the SSL obtained during the MOSAiC expedition could be a start for such a model (when they will be available).
We understand that the size distributions for the inclusions described in L03 are sampled from the interior ice. We extended it to the SSL and DL because there are no such measurements specifically for these top layers. In fact, this assumption is no different from the assumption of a constant scattering asymmetry factor in all ice layers used in other studies (e.g., Briegleb and Light, 2007, L08, L15, and Lamare et al., 2022). Since the scattering asymmetry factor is solely dependent on the size distribution for a given wavelength, using the same asymmetry factor in different ice layers implies a constant size distribution profile. Actually, in contrast to the studies mentioned above, our assumption is less severe (more physical), because the asymmetry factor in our approach depends on wavelength and also on the ice physical properties (i.e., it is layer-dependent). Some assumptions are obviously inevitable whenever measurements are not exhaustive. However, the good model-observation agreement in the spectral albedo indicates that using the size distributions of the IL also for the SSL and DL is acceptable, particularly in the NIR where the modeled albedo is more sensitive to the optical properties of the SSL and the DL. The agreement might be partially attributed to the (generally) much thinner dimensions of the SSL and DL, and to error compensation between size distribution and ice density, similar to the error compensation between the asymmetry factor and the adjusted scattering coefficients in the studies referred to above.
We have made several attempts at including at least a preliminary version of MOSAiC data, but constantly hit the embargo that will last until January 2023. Requests to PIs for preliminary versions failed as well. On the other hand, it was demonstrated in L08 that SHEBA and ICESCAPE data, albeit collected 20 years apart, show remarkable consistency (see response to your point 2 for more details). In addition, we are not sure how reliable the inclusion distributions obtained in the loose, fast-changing SSL of a few centimeters are, and if it is possible to measure them at all. Can the reviewer advise on how to promptly obtain such data? Notwithstanding the fact that we’ll always strive to implement the most recent advances in the model, the fate of the paper cannot depend on potential availability of future datasets.
Regarding the suggestion of “a different approach in order to predict inclusions distributions”, the development of new techniques to obtain size distributions is out of the scope of this paper. The model can accommodate any size distribution, but in absence of reliable measurements it makes little sense to privilege one or the other if the fit to the measurements are satisfactory.
2. The density, temperature and salinity measurements as well as absorbing particles concentrations used as inputs are often guessed by the authors because they were not measured on the field at the location of AOPS measurements. Without these reference measurements, the system is undetermined. Unfortunately, it is difficult to demonstrate the validity of the model without having the actual measurements or justifying the choice of the input with strong evidence. A solution could be to change the scope of the paper in order to study the sensitivity of AOPS to the tuning of the different inputs. Another suggestion would be to validate the model by comparison with another model. However, point (1) would need to be addressed first.
Again, this is a misunderstanding. For the modeling, we use every available observational data for input. The ICESCAPE and SHEBA data proved to be the most suitable for our study. Furthermore, the appendix completes the study by highlighting the insensitivity to small variations in a lot of these parameters. The properties of the SSL have instead to be estimated (because exhaustive measurement sets are not yet available) based on the measured albedo in the near IR spectrum, as already done in L08.
The vertical profiles we use are documented by Polashenski et al (2015) and partially in L15, and we have used their exact values. We were even able to use density measurements for the 19 July 2011 case, based on the uppermost 80 cm of the annotated core (see L15, Fig. 7). Effectively, we adjusted the ice density in the other simulations only when forced by the lack of in-situ observations, but the adjustments ranged within commonly accepted values which also include those found in L08. The fact that these measurements are scarce (and we advocate for extensive collections of vertical profiles as one of the final messages) cannot be held as a flaw in our approach. Note that the manuscript highlights the use of such observations in several places, e.g.:
- Lines 147-148: “We strived to use all available observational data to determine the input to the model, focusing on two common ice types: bare and ponded ice.”
- Lines 156-157: “The Solar Zenith Angle (SZA) is calculated based on the reported observational time and location latitude and longitude.”
- Lines 166-168: This paragraph has been slightly corrected to: “We were able to exploit one of the few density measurements collected during ICESCAPE, although the density was only measured in the uppermost 80 cm where it varied between 0.625 and 0.909 g/cm3. When such measurements are not available, we assume typical FYI densities as reported by Timco and Frederking (1995): between 0.84 and 0.91 g/cm3 for the ice above the waterline, and between 0.90 and 0.94 g/cm3 for the ice below the waterline.”
- Lines 185-188: “For the salinity, we use the profiles reported from the core analysis of Polashenski et al. (2015), averaging the available data points in each model layer. Since measurements are not reported for the SSL (which normally gets destroyed when collecting the core) and the bottom of the ice, we assume the shallowest and deepest value extend to these remaining portions.”
- Line 306: (slightly modified): “The vertical profiles of salinity are also from cores, and vary between ⁓0.5 and 3.0 ppt (Polashenski et al., 2015).”
When not measured in situ, we use data based on pertinent observations reported in the literature. As for "absorbing particles concentrations used as inputs are often guessed": please note that the particle concentration is NOT an input variable and is not guessed but determined by the ice density, temperature, and salinity through the Cox-Weeks equation for the given size distributions (see Eqs 1-3). Among the three ice properties, salinity is the one most available for the examined cases. To avoid large temperature uncertainties, we chose melting ice and ponded ice cases, for which the top temperature can be set to a very good approximation to 0°. Because the ice base (ice-water interface) can be fixed at -2°C and the temperature profile in the ice is generally very close to linear (based on observations), the temperature in each layer is easily estimated. In addition, our sensitivity test shows small dependence on temperature (see Appendix). The density is the most scarcely measured variable, and we therefore use reported observational values (L15; Timco and Frederking, 1995). One of our goals is to improve the radiative transfer in sea ice in the NASA climate model (ModelE), which simulates the ice temperature and salinity profiles in sea ice but not the density. Therefore, the ice density is an adjustable parameter in ModelE. Accordingly, we present a physically-consistent parameterization of bare sea ice IOPs as a function of its physical properties that can be directly measured or modeled in climate models. In contrast, many alternative sea-ice RTMs employ as input parameters directly the IOPs (extinction and scattering coefficients, and asymmetry factor), which are very challenging to measure in-situ or even in the laboratory. It is certainly true that a comprehensive set of in-situ measurements, required for a rigorous validation of RTM in sea ice in all conditions, is presently lacking. Because in our physically-based parameterization the IOPs are linked to the ice properties, changing the ice density changes all the IOPs consistently and differentially in different spectral bands: band-by-band adjustments as in the studies referred to above are not needed. If the parameterization is not correct, obtaining model-observation agreement in both albedo and transmittance (again, simultaneously and at all wavelengths) is extremely unlikely even if a few unknown input properties are “adjusted”. For all these reasons, we have full confidence that our approach is legitimate to validate radiative transfer processes in sea ice. Should more complete suites of input parameters become available in the future, the focus can shift towards the betterment of the IOP parametrization.
“However, point (1) would need to be addressed first”: This size distribution issue has already been addressed in the response to point (1) above.
The detailed explanation above has been condensed in a new paragraph added to the beginning of Sec. 3:
“The ICESCAPE and SHEBA data proved to be the most suitable for our study. Of all the physical variables needed at input and measured in situ, the total ice thickness and the vertical profiles of salinity within the ice column are the most available. For ICESCAPE, we use the exact values of layer-resolved salinity documented by Polashenski et al. (2015) and partially in L15. For SHEBA, density profiles from cores are generally very scarce. We were able to use density measurements for the 19 July 2011 case, based on the uppermost 80 cm of the annotated core (see L15, Fig. 7). When forced by the lack of in-situ observations the values were varied within commonly accepted ranges, which also include those found in L08. Temperature profiles are also sporadic, but estimates based on straight physics can be used that do not substantially affect the quality of the fit, as shown in the Appendix. For example, the top temperature of ponded ice can be set at 0°C because this is the water-ice coexisting temperature of water and ice. The bottom ice temperature of -2°C is based on the freezing temperature of sea water.”
Finally, all available RT models for sea ice are approximated to some level. As for the comparison with other models, it was indeed done in Light et al. (2003), which compared DISORTB (an earlier version of our RT solver used in COART) and found that the modeled sea ice albedo and transmittance are consistent with their 4-stream results as should be (see Figs 4-6 in L03). Their model is most commonly used for applications to sea ice RT. The extended COART model is more advanced and can adopt any number of streams (not just 4), in addition to the coupling feature and the treatment of ice roughness.
Reference: Light, B., G. A. Maykut, and T. C. Grenfell (2003), A two-dimensional Monte Carlo model of radiative transfer in sea ice, J. Geophys. Res., 108(C7), 3219.
Specific Comments
28 Morphological changes and thinning of sea ice along with sea ice cover reduction are responsible for lower albedo and shortwave absorption in the ocean (Arndt and Nicolaus 2014).
Yes, thinning of sea ice (and some morphological changes, not all) also contribute to ice albedo reduction, but to a much smaller extent. We have modified the text to read: “A reduction in sea ice cover and its thinning lower the albedo and increases shortwave absorption in the ocean, causing more melting in a mechanism known as ice-albedo feedback (Curry et al., 29 1995; Hall, 2004; Déry and Brown, 2007, Arndt and Nicolaus 2014)
46 The range is probably wider than that, especially for SSL. Would that be the range for columnar sea ice?
This is a very good point! The density of the SSL is largely unknown, although some descriptions are contained in very recent publications (https://www.osti.gov/servlets/purl/1844399). Since this point is made in the introduction, we prefer to specify that this is a general range for bulk sea ice. According to Timco and Frederking (1996) “the in situ density of sea ice may be quite different above and below the waterline. In the upper part of the ice sheet, there may be a wide variation in the ice density, with realistic values in the range 0.84 to 0.91 Mg m -3 for first-year ice, and 0.72 to 0.91 Mg m -3 for multi-year ice. However, below the waterline, the density values are much more consistent and range from 0.90 Mg m -3 to 0.94 Mg m -3 for both types of ice.”
86 What is the value of the refractive index used for ice? Please provide a number or a range for this value.
As specified in the manuscript, the spectral refractive index of ice is taken from Warren and Brandt (2008). A plot of it is has been uploaded as a supplement (see figure "S1_rev2"). We have added “spectral” to the sentence in the text. We think that reporting specific values makes the text unnecessarily heavy, without being particularly useful.
88 The explanation of how the surface implemented is insufficient. Water and ice have different roughness, therefore the parameters of the Gaussian equation describing its roughness should be different. From an optical perspective, it would be helpful to have a description of how it translates into the distribution of diffuse reflection. It would also be useful to describe the importance of purely specular reflection at the ice surface in the model.
We have added the following section to the Appendix:
“Ice surfaces are naturally rough, and the extended COART model offers full flexibility in the treatment of roughness (Jin et al., 2006). . A Gaussian equation is used to describe the statistical distribution of the surface facets, in a similar fashion as the Cox-Munk model used to parameterize the distribution of ocean waves. The extension to any other distribution is trivial, should observational evidence indicate the need. Since no sunglint has been reported on ice surfaces and granular features are observed, the sea ice surface is likely rougher than a calm ocean surface. Lacking appropriate measurements of surface roughness statistics, we simply used σ=0.5 and σ=0.1 for the ice and pond surface, respectively. Based on the Cox-Munk formulation, σ=0.1 represents a minimal ocean surface roughness (wind speed=1.4 m/s). For the ice cases in this study, a coarse-grained surface layer was observed. Because the SSL appears granular, many surface facets must have large tilt angles. A value of σ=0.5 implies that 95% (99.7%) of the facet normals are <45°(<56°) from the local vertical. No observational data exist to constrain the roughness value, but again (differently from its impact on the radiance) the effect on the irradiance is small. In any case, while surface roughness affects both the direct and diffuse light components (and therefore the surface BRDF as shown in Lamare et al. (2022)), its effect on albedo and transmittance is small, as demonstrated in Fig. A5.”
For more information on surface roughness, please refer to:
Jin et al., 2006: An analytical solution of radiative transfer in the coupled atmosphere-ocean system with a rough surface. Applied Optics, 45, 7443-7455.
99 Is absorption coefficient based on volume fraction? More details should be provided.
Yes, it is based on the volume fractions of ice and brine. To clarify, we have added: “The total ice layer absorption is the average of ice and brine water weighted by volume fractions.”.
126 This explanation mixes a few concepts. The scattering efficiency Q (ratio of scattering surface area to geometrical surface area) in the Mie regime is close to 2 no matter the phase function. The reduced scattering coefficient or similarity variable b’=b*(1-g) which describes the mixed effect of scattering coefficient and phase function will indeed go down as the phase function represented by the asymmetry parameter g goes up. This concept should be addressed in this explanation. It is not that obvious that the reduced scattering coefficient goes down significantly for big inclusions. One would need to prove that claim quantitatively using the similarity principle (where b could be calculated from cross section area and g from Mie Theory).
The reviewer is mistaken on this point and we attempt to clarify in what follows. For large particle scattering (like brine pockets in sea ice), more than half of the scattered light is due to diffraction which goes nearly straight forward. Another fraction of the incident light is refracted and transmitted in and near the forward direction. This forward scattering contribution increases with particle size and as the relative refractive index approaches 1. Because brine pockets are large compared to the wavelength and the refractive index difference between brine water and ice is small, more than 90% of the scattered photons are concentrated in a very small cone around the forward direction. In IOP calculation, we modified the Mie code and didn’t account for this forward scattered energy in the scattering phase function and accordingly in the scattering efficiency. In radiative transfer calculations, this forward scattering component can be considered as not being scattered, and can be added back to the incident beam after the scattering. Therefore, the scattering coefficient is drastically reduced (by over 90% and so we consider it significant). This treatment goes beyond the simplistic similarity concept the reviewer pointed out. A final remark: COART can also accept the phase function as a direct input. This is useful when accurate radiance calculations are performed, and it is not important for the irradiance computations contained in this study.
131 Mirabilite crystals precipitates under -8 C (Light 2004).
The focus here is on the temperature at which precipitated salts start to significantly affect radiative transfer, not the temperature at which salts start to precipitate.
137 As stated in (1), the approach described in this section is based on a description of columnar (interior ice). Since the processes dictating the bubbles and brine channels size distributions and refractive index are different in drained and surface scattering ice, we cannot consider the treatment described here as complete.
As addressed in the response to (1), our size distribution assumption is analogous to assuming a constant g in all ice layers adopted in previous studies (L08, L15, and Lamare et al., 2022). Lacking observational data, this assumption is necessary. However, in our approach g changes with wavelength as physically expected. We have adjusted the relative sentence to “This physically-based approach provides a sophisticated and complete treatment of radiative transfer in sea ice. The extension to novel discoveries on, e.g., size distributions for the inclusion can trivially be extended to any size distribution obtained from observational evidence.“
159 Cloud optical thickness of 10 is too low for an upper bound. 100 would be recommended.
See figure in the appendix, where it is seen that the results have already “converged” using tau=10, especially for the typical low-sun conditions in the Arctic, so there is no need to use Tau=100. For the reviewer’s benefit, in the supplemental figure "FigS2_rev2.pdf" we have specifically isolated the differences obtained using tau=10 or tau=100.
201 The finality of L08 and L15 is to determine the IOPs of sea ice. The use of tuning in this case is justified because it is needed to find what the IOPs should be in order to meet measured AOPs. Furthermore, an explanation of the bias which they are rectifying by tuning is also provided. In the case of this study, density is an input and not a value that is being determined. Therefore, it is illogical to modify the input density in order to meet the correct answer. Unless these density tunings are justified with an explanation.
L08 and L15 directly use ice IOPs as an input to calculate the AOPs (albedo and transmittance). We agree that “it is needed to find what the IOPs should be in order to meet measured AOPs”, but such adjusted IOPs are unlikely to represent the real IOPs because they are based on a constant particle size assumption. As expressed in the reviewer’s major comment (1), the particle size (i.e., the asymmetry factor) should be different in different ice layers. In our approach, the ice IOPs are physically linked to the ice physical properties. As the density changes, the IOPs vary simultaneously across all wavelengths. L08 and L15 directly tune the IOP (scattering) band by band, with a fixed g (which is not logical). As a consequence, it is relatively easier to match the AOPs. One way or another, assumptions are necessary whenever complete measurements are not available. We understand the necessary IOP adjustments in L08 and L15, because it is impossible to derive all the IOPs (extinction, scattering coefficient and phase function) only using irradiance measurements. Even the extinction derived from the measurements may not represent the real IOP extinction, because of measurement limitations (e.g., angular coverage) and ice property inhomogeneity, which could result in different extinction values for upward and downward irradiances (real extinction is direction independent). In summary, we and L08 and L15 all determined some set of IOPs that best fits the measurements. The difference is in directly tuning the IOPs or letting them be driven (as it should be) by the ice physical properties. In other words, L15 retrieve IOPs from measured albedo, whereas we retrieve ice density (because of the scarcity of in situ measurements). To avoid the confusion, we have provided more details on how the density is obtained in the revision:
“Because of the lack of in-situ density measurement, we consider the density adjustable and invert it using the measured spectral albedo. Based on previous observations, we first set the density ranges for the IL and DL as 0.90-0.94 g/cm3 and 0.82-9.925 g/cm3, respectively. Because no density has been reported for the thin top SSL, we simply use either 0.55 or 0.60 g/cm3 for this layer. For a SSL density, we loop the density in DL and IL in step of 0.001 g/cm3 and compare the modeled spectral albedo with the measured albedo in each step. When the averaged difference reaches the threshold of 5% or less, the iterating stops and densities are considered retrieved. Otherwise, the densities giving the minimum difference are used. This process is similar to the process used to obtain the scattering in L08 and L15 but not band by band.”.
203 Following the similarity principle b’=b*(1-g), in the diffusion regime , it does not truly matter if g is kept constant or not. As long as the reduced scattering coefficient b’ is consistent.
It may not matter in the visible spectrum where absorption is small but it does matter in the NIR, especially for transmittance. The error of this approximation depends on absorption and solar zenith angle. This similarity principle goes back to the time before the delta-M, which offers a more rigorous treatment. Is it possible to obtain the real scattering coefficient and phase function from merely the irradiance measurements?
216 Why change DL density and snow depth? These choices needs to be justified.
As hopefully made clear by the many explanations given above, starting from the optimal fit (black line) in Fig. 3, we show and discuss the sensitivity to the key parameters, as
advocated also by the reviewer. In comparing the approach of L15 (who modeled the SSL using properties of a snow layer) to our 3-layer model, we provide examples of the effect of assuming different snow properties.
228 Indicate figure number.
We replaced “in the previous figures” with “in Figs. 1-3”.
236 It needs to be kept in mind that absorption coefficient of suits in air and in ice are not the same.
Understood. It is considered.
250-257 if temperature, salinity, SSL thickness, SSL density are not measured, the system is strongly under-determined. Furthermore, the manuscript needs to clarify if the density of 0.915 g/cm3 and salinity of 3 ppt used for interior ice are measured or guessed.
For melting ice, using a temperature of 0°C at the top is a good approximation. RTMs used in other studies (Briegleb and Light, 2007, Light et al., 2008, 2015) treated this low ice density SSL as a layer of “snow” and with all guessed “snow” properties (grain size and density). We did similarly for this top SSL but treated it as a low density ice layer in the RT calculations. Density and salinity for the interior ice for this case are from observed typical values.
254 Granular ice and surface scattering layer are not equivalent. The word SSL should be kept in this case.
Smith et al. (“Sensitivity of the Arctic Sea Ice Cover to the Summer Surface Scattering Layer”, 2022) define the SSL as a “highly-scattering, coarse-grained ice layer”, a definition that seems to be consistent with the rest of the literature. “Granular layer” was verbatim found in the field notes for the relative measurement. Rather than removing “granular layer”, we prefer to substitute “SSL” with “top layer”, although we do not think this is needed.
268-274 The manuscript needs to clarify if these inputs are assumptions or measurements.
This recurring comment is now addressed by the new paragraph added at the beginning of Sec. 3, and reported in the last paragraph of the response to major comment 2.
275 The systematic bias could also come from guesses on ice physical parameters.
It could be, but the bias exists only in the visible spectrum and is small. If a “guess” (to use the reviewer’s words) yields a match in AOPs simultaneously and at all wavelengths, it is likely a very good guess, since our approach avoids the unphysical wavelength-by-wavelength adjustment of the IOPs.
276 What is meant by ‘’other species’’ ? At this point in the manuscript, there has been no mention about any biological specie.
For example, dust aerosol deposition, sediments, CDOM. In any case, the reviewer is correct. We changed the sentence to: “Several species”.
279 Please verify the claim that algal pigments are more concentrated at the top layer.
Higher concentrations in the bottom layer are common. In the discussion of the cited reference (Perovich et al., 1998), it is reported that “ for both seasons, particle concentrations were high at the snow-ice interface. Algal cells transported by brine wicking in the spring are left behind after drainage occurs. These particles undergo growth, increasing in concentration and resulting in increased absorption of shortwave radiation at the interface during the melting season”.
289 The explanation is unclear. The sentence seems to contain 3 ideas : (1) Melt pond occurs when sun irradiance is the largest, (2) Melt Pond water as a lower reflection and higher transmission than ice, (3) these two effects combined impact energy distribution.
Agree. We have reworded this sentence: “Melt ponds occur in late spring and summer when solar irradiance is large. Because water has much lower reflection and higher transmission than ice, melt ponds over the ice could significantly alter the solar energy distribution in the atmosphere-sea ice-ocean system.”.
304 Is temperature measured or guessed?
The two temperatures are estimated based on straight physics. The top temperature of the ponded ice is set at 0°C because this is the coexisting temperature of water and ice (neglecting salinity in the pond water). The bottom ice temperature of -2°C is based on the freezing temperature of sea water.
311 The manuscript should justify why thicker ice as a three-layer model while thinner ice only has a two-layer model.
This paragraph relates to ponded ice, not to thicker vs thinner ice. It results from our simulations that two layers are generally sufficient to obtain as good agreement as using three layers for ponded ice, so we are not sure what “justification” should be provided. Did the reviewer mean to suggest a sentence like “Given the presence of the pond water above, the vertical resolution of the ice layers is less important than for bare ice”?
312 Missing units after 0.83.
Added “g/cm3”.
313 The use of tables to summarize inputs and to clarify how many total layers are used to represent ponds +ice would make the manuscript easier to read.To indicate whether the inputs are measured or assumed could also clarify the context.
This is now addressed by the new text added to the beginning Sec. 3.
325-326 The conclusion that transmittance decreases with increasing pond depth is counter-intuitive, since melt water contained in ponds scatters significantly less than interior sea ice. How would that be explained? Is it because of the high absorption of the melt water? This trend is in opposition with measurements from L15 fig 5b.
Although it might appear counter-intuitive, this is what the data say. The explanation might reside in the density change below the melt pond. When pond water fills the voids in ice, the ice scattering could be reduced significantly and therefore transmission increases. The significantly higher transmission of the ponded ice than the bare ice with similar thickness seems to further validate this hypothesis. For clarity, we have added a sentence at the end of this paragraph: “This probably results from the reduced scattering due that the pond water fills the voids in ice as indicated by the higher retrieved ice density.”.
The data in L15 Fig 5b covers ponded ice thickness from 50 cm to 150 cm, whereas the ice thicknesses for our selected cases are between 70 cm and 120 cm. If the linear fitting is applied to the same thickness range (70-120cm) in L15 fig 5b, you would get exactly the same as we described here (i.e., transmittance decreases as ice thickness increases).
343 Light_2015 used observation of the albedo to invert SSL IOPs. They used single diameter spheres approximation, as it is used for snow, only to provide an initial guess.
We are not sure of the point the reviewer is trying to raise here. Based on L15 paper, there is no measurement for the SSL and “these surface layers were typically not preserved in the core samples.”. To obtain the absorption required for RT, the density must be provided. How was the density obtained in L15 if not by guess? The scattering asymmetry factor of 0.94 is apparently a guess too. Using these two guessed model inputs, the scattering (not measured either) is obtained by matching the measured albedo band by band, as explicitly quoted: “Scattering coefficients are thus assigned to the uppermost layers such that modeled albedos agree with observation, starting with near-infrared wavelengths and working progressively toward shorter wavelengths.”. The adjusted scattering is in turn used as RT input to model the albedo. In addition, L08 and L15 treat the SSL as a layer of “snow”, but the snow grain size was not and could not (because it is not snow) be measured. While the grain size can be inverted by matching with the albedo, such inverted grain size is different for different spectral bands. Thus, some guessing in the grain size is also required. Please note that we are not criticizing the “guessing” (to put it in the reviewer’s words) used in L08 and L16. We understand the necessity of some tuning processes, but we don’t understand why the reviewer prefers one guess (or inverting) to another.
348 A complete analysis of the sensitivity of AOPs to salinity was never presented. This notion was only mentioned qualitatively in the text of section 3.2.
That is not entirely correct, as a partial sensitivity test is contained in Fig. 5. In any case, we completely agree that it is useful to add one more specific figure to the Appendix (see attached supplemental figure "FigS3_rev2"), with the following text:
“Figure A3 shows the optical effect of different salinity profiles. The maximum value (10 ppt) is a rare occurrence anywhere in the ice column, but was deemed a good maximum value in order to capture the full range of potential variability. Detectable changes are present up to the NIR, and are significant in the visible. In most situations, it is observed that the model predicts maximum differences in both albedo and transmittance of up to 0.05, in correspondence of their peaks in the visible.”
351 There are two ideas mixed in the same sentence. (1) Depending on pond depths and (2) the albedo (transmittance) is significantly lower (higher) than that of bare ice
For clarity, we deleted the second half of this sentence.
352 The claim on the relation between pond depth and transmission is in opposition with what was stated at line 325.
The reviewer is absolutely right, this was a typo. Changed to “...transmittance decreases with pond depth for 352 similar ice thicknesses below”.
Figure 2 The scenario using measured density should be specified on the caption or legend. Name of the layers should be specified.
The caption was certainly not optimal. Changed to: “Fig. 2: Effect of different ice density profiles (colored curves, values in g/cm3 for the SSL, DL and IL) on modeled albedo and transmittance. The black lines are the optimal fits to the measurements (gray areas) for the 3 July 2010 bare, FYI ice site (see top row of Fig. 1). ”
Figure 3 As a comparison, having a scenario with SSL modeled using the reference model would be useful. Name of the layers should be specified.
We will include the reference line (black line in Fig. 1). Caption changed to: “Figure 3: As in Fig. 2, but for a SSL consisting of spherical snow grains of the indicated thickness and effective radius Rs (in μm).”. The reference to the DL and IL is not needed since the caption refers to Fig. 2.
Figure 4 Name of layers should be specified.
Captain changed to: “Figure 4: As in Fig. 2, but considering added contamination from sootlike, BC particulate in the top 10 cm of the ice column.” The reference to the DL and IL is not needed since the caption refers to Fig. 2.
Figure 5 The difference between the dotted and full black lines representing measurements should be specified. Name of layers should be specified.
We will change the two experimental lines to solid gray, and modify accordingly the explanation already provided at lines 246-ff, “The gray lines are albedo and transmittance measurements collected during SHEBA with two different spectroradiometers: a Spectron Engineering SE-590 and Analytical Spectral Devices Ice-1.”
Figure 6 Same as fig. 5
Same as above.
Reference
Arndt, S. and Nicolaus, M.: Seasonal cycle and long-term trend of 75 solar energy fluxes through Arctic sea ice, The Cryosphere, 8, 2219–2233, https://doi.org/10.5194/tc-8-2219-2014, 2014.
Light, B., Maykut, G., and Grenfell, T.: A temperature-dependent, structural-optical model of first-year sea ice, J. Geophys. Res.- Oceans, 109, C06013, https://doi.org/10.1029/2003JC002164, 2004.
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RC3: 'Comment on tc-2022-106', Anonymous Referee #3, 24 Oct 2022
General Comments
This manuscript aims to validate an implementation of a radiative transfer model in sea ice into in the advanced coupled-atmosphere radiative transfer (COART) model. The influence of several environmental factors (number of the ice layer, density profile, presence of black carbon or phytoplankton…) on the simulated albedo and transmittance are studied using in situ optical measurements led in sea ice during the SHEBA and the ICESCAPE field campaigns. The authors show that the simulated albedo and transmittance are closer to the observation when at least three layers (for bare ice) and two layers (for ponded ice) are considered which is in line with previous studies. They also show that the ice density profile has a large influence on the representation of both optical properties.
The analyses suggested in this manuscript confirm results from previous studies and bring new material for a better understanding and representation of the radiative transfer in sea ice. However important elements are missing to (1) validate the model as the scope of the manuscript suggests it and to (2) well understand the methodology used here.
Major Comments
- A validation of the radiative transfer in the ice is suggested in this paper nevertheless, by the adjustment of the physical parameter ( ice density, temperature profile, BC amount ... ) used as model inputs to match the observed optical parameters as well as the too-small data set, it does not seem possible to conclude on the robustness of the model presented here. A solution would be to change the focus of the paper to better highlight the sensitivity analyses that are led in the manuscript.
- Methodological information is hard to find in the paper due to the lack of a proper methodology section. Some information needed for a good understanding of the manuscript is missing or is diluted in the “validation study” section :
- A description of the in-situ observations used in this manuscript should be added and gathered. Information such as the region of both campaigns, the number of observations for each section (FYI, MYI and Ponded ice), the physical parameters that have been measured, and how each parameter (optical and physical) has been recorded should be gathered in a same paragraph or section.
- A paragraph or section about the evaluation protocol is also missing. How are the simulated transmittance and albedo calculated based on the IOP retrieved in the look-up tables? What are the inputs of the model? Among these inputs which ones come from observations, and which ones have been adjusted?
Specific Comments
P1 lines 31-35: “The interactions between snow, sea ice and solar radiation in most climate models are based on empirical parameterizations that are often just a function of snow depth, sea ice thickness and surface temperature.” References to these models should appear here.
P2 line 59: “to complement the observations from SHEBA and ICESCAPE”. Previously in the paragraph, the FIRE ACE project is mentioned. Why is it not mentioned anymore here? and why is it not used in the present analysis?
P2 lines 72-74: This part of the introduction could benefit from a better description of the focus of the present study.
P3 lines 100-101: “The presence of other possible inclusions (BC and phytoplankton) is also considered.” The part of the model that considers these inclusions should be described.
P3 line 126: What do the authors mean by "the actual scattering coefficient"?
P3 lines 132-133: "the cases studied here pertain to sea ice surveyed in the warm, summer season". This should be specified much earlier in the paper (maybe in the introduction section with the focus of the study). The fact that snow is not considered in the model should also be specified earlier.
P4 lines 144-145: Can the authors precise what they mean by “standard subarctic atmospheric profile” and by “open-ocean water properties”, or give references here?
P4 lines 147-148: “We strived to use all available observational data to determine the input to the model, focusing on two common ice types: bare and ponded ice.” As said in the major comment, this requires more explanations. What are the inputs of the model here? And what is done in case the observational data does not exist?
P4 lines 152-153: Why only these two dates have been retained from the ICESCAPE campaign? Are these the only bare ice stations led during the ICESCAPE campaign in 2010 and 2011?
P4 lines 163-165: “The strong spectral dependence of the absorption coefficients for brine, ice, water and organic or other inclusions (Grenfell and Mayakut, 1977; Perovich and Gow, 1996) is responsible for the nearly constant albedo in the visible region and the significant decrease in the near infrared region”. Are the authors still describing Fig. 1 here? Also, there is a mistake in the reference: Grenfell and Maykut, 1977.
P4-5 lines 180-182: Are these densities measured?
P5 lines 189-190: “Our tests show negligible sensitivity of the AOPs to small variations in temperature.” I assume the authors are referring to the analysis they performed in the appendix. It should be specified.
P5 lines 193-194: “It is clear that a single layer is insufficient to adequately reproduce both the albedo and transmittance.” Is this result shown in figure 1? If so, it should be specified.
P5 line 201: “We adjusted the ice density”. I am confused here. The authors said earlier that the AOPs are more sensitive to density than to salinity or temperature. This explains why they choose to simplify the temperature profile. But if they now adjust the density (the only parameter that has a real impact on the AOP) of the observations to match better with the optics parameters, how can the radiative transfer model can then be validated with this adjusted “observation”? If the simulated parameters do not match the observation with the measured physical parameters as inputs, this should mean that the radiative transfer model misses something. Changing the physics won’t fix the optics.
P5 line 210: “in the absence of completely measured density profiles”. Here is an illustration of the second major comment. Since there is no previous description of what inputs are measured and what inputs are not, it is difficult to understand the results here.
P5 line 211: “These results demonstrate how the augmented COART model enables a fine tuning of the AOPs.” I don’t understand why the authors referring to the tuning of the AOPs when it seems that only the physics were tuned.
P5 lines 213-214: “The snow is composed of spherical grains, whose size determines the albedo at absorbing wavelengths (Warren 2019).” How the albedo and transmittance through the snow are calculated by the model should be better described.
P5 lines 214-215: “300 μm to represent new snow, and 1000 μm to represent aged, melting snow.” Where do these values come from?
P6 line 234: “The SHEBA observations show." Why are the authors giving SHEBA’s value while it is only ICESCAPE data that are treated in this section?
P6 line 250: “The salinity profile were assumed”. Here again, the manuscript would benefit from a better description of inputs that are measured and those that are assumed or adjusted.
P6 line 268: “In our modeling, 5 mm of snow with grain size of 200 μm were considered”. Again, how the albedo and transmittance through the snow are calculated by the model should be better described. And where do these values come from?
P7 lines 289-290: The sentence should be cut after “solar irradiance is largest”.
P7 lines 290: “A series of observations”. Again the number of observations used should be specified.
P7 line 293: “It is reasonable to expect that the accumulation of water on top of ice should annihilate the SSL." Why? This should be justified with references.
P7 line 311-313: “For the thick ice with shallow pond (top row) observed on 19 July, a 3- layer ice model is required for satisfactory model-observation agreement.” What could explain this third layer for this particular pond?
P7 line 318: “(3-layer for thick ice)”, how do we know that this is only the ice thickness under the pond that justify the number of optical layers?
P7 lines 320-321: “If the albedo measurements in the near-infrared are accurate”. Why this sentence? Is there anything that suggests the opposite?
P8 line 348: “Sensitivity tests show that lower salinity values”. The sensitivity tests for the salinity are missing from the main text or appendices.
P8 line 352-353: “and transmittance increases with pond depth for similar ice thicknesses below” this is the opposite of what is said in line 325.
P8 line 363-364: “An accurate and efficient radiative transfer model is also required for climate models, which use simple AOP parametrizations for sea ice.” This sentence is not true since some ESM already use the Delta Eddington approach of Briegleb & Light (2007) which is not a “simple AOP parameterization for sea ice”.
P9 line 370: “the density is used as a tunable parameter since in situ measurements are not 370 always available”. As an input parameter of the model, the density should not be treated as a tunable parameter.
Figure 1: Lime text in the legend is hard to read. Also, the authors should consider to better explaining the legend (by naming each layer and explaining what letters refer to).
Figure 2: Albedo and transmittance curves should be differentiated by something (dashed line as it is already done in figure A1). Numbers given in the figure should be explained in the caption.Why are only the results for July 3rd are given and not those for the 19th? Are the results for July 19th similar the those for the 3rd?
Figure 3: Same comment as figure 2.
Figure 4: The caption should better describe the figure here. It is not as Fig.2 as the density profile is not changing. Describing the physics (number of layers, density profile) in the caption and just giving the amount of BC for each line in the legend could help for clarity.
Figure 5: Same comment that for the other figures: the legend should be better explained in the caption. What the dotted line refers to should also be specified.
Figure 6: What the dotted line refers to should be specified.
Figure 7: Considering the number of panels here, adding a letter to call each panel could improve the clarity of the main text and the caption.
Citation: https://doi.org/10.5194/tc-2022-106-RC3 -
AC3: 'Reply on RC3', Matteo Ottaviani, 24 Nov 2022
We thank the reviewer for his detailed perusal of the manuscript. We have worked intensively to address each point, as explained in the point-to-point response below.
Major Comments
- A validation of the radiative transfer in the ice is suggested in this paper nevertheless, by the adjustment of the physical parameter ( ice density, temperature profile, BC amount ... ) used as model inputs to match the observed optical parameters as well as the too-small data set, it does not seem possible to conclude on the robustness of the model presented here. A solution would be to change the focus of the paper to better highlight the sensitivity analyses that are led in the manuscript.
There is some misunderstanding here. Except for the density, which is inverted from the spectral measurements, other input parameters are from in-situ observations, including temperature, salinity and ice thickness. The BC and chlorophyll concentration, as well as the snow properties, are not from in-situ measurements, because they are only used for sensitivity tests. A new subsection (3.1) has been added for clarity (see response to point 2 below).
This exercise aims at assessing the capabilities of COART through comparison with experimental data. Additionally, we have provided relevant sensitivity tests in the Appendix, which now contains two more figures (see also response to Rev. #2). The model accurately accounts for all relevant radiative transfer processes in the atmosphere, ice and ocean. The sensitivity tests highlight the flexibility of COART in representing variations in the observed signals. Sensitivity tests do not require experimental data. On the other hand, every validation effort includes a “sensitivity tests'' component. Since we sourced all possible in-situ measurements to constrain the input parameters (ice density, temperature, salinity profiles, and thickness), restraining the focus of the manuscript to “sensitivity tests” would be deceiving.
2. Methodological information is hard to find in the paper due to the lack of a proper methodology section. Some information needed for a good understanding of the manuscript is missing or is diluted in the “validation study” section :
- A description of the in-situ observations used in this manuscript should be added and gathered. Information such as the region of both campaigns, the number of observations for each section (FYI, MYI and Ponded ice), the physical parameters that have been measured, and how each parameter (optical and physical) has been recorded should be gathered in a same paragraph or section.
- A paragraph or section about the evaluation protocol is also missing. How are the simulated transmittance and albedo calculated based on the IOP retrieved in the look-up tables? What are the inputs of the model? Among these inputs which ones come from observations, and which ones have been adjusted?
A detailed description of the in-situ observations and the region is provided in L15 (and Polashenski et al., 2015) for ICESCAPE and in Perovich et al., 2002, for SHEBA observations, as referenced at lines 55-56 of the original manuscript. The papers we referred to also detailed “how each parameter (optical and physical) has been recorded”. A new subsection (3.1) now summarizes general information on the region and the observations used in the simulations:
“3.1 Data and Methodology
Because the ice IOPs are linked to the ice physical properties through the parametrization described in Sec. 2, the input parameters required by the radiative transfer model become simply the ice salinity, density and temperature in the ice layers. Together with the physical properties in atmospheric and ocean layers, COART derives the IOPs in all layers from the input physical properties in the coupled system and then calculates the irradiances at any desired level. The irradiances at the ice surface and base are used to calculate the albedo and transmittance of sea ice for comparison with observations.
The ICESCAPE and SHEBA campaigns proved to be the most suitable data sources for our study. Both campaigns were conducted in the Arctic Ocean, between the Chukchi Sea and the Beaufort Sea regions. Of all the physical variables needed at the input and measured in situ, the total ice thickness and the vertical profiles of salinity within the ice column are the most available. For ICESCAPE, we use the exact values of layer-resolved salinity documented by Polashenski et al. (2015) and partially in L15. For SHEBA, density profiles from cores are generally very scarce. We were able to use density measurements for the 19 July 2011 case, based on the uppermost 80 cm of the annotated core (see L15, Fig. 7). When forced by the lack of in-situ observations, the values were varied within commonly accepted ranges (Timco and Frederking, 1995), which also include those found in L08: 0.90-0.94 g/cm3 for the IL and 0.82-9.925 g/cm3 for the DL. Because no density has been reported for the thin top SSL, we use either 0.55 or 0.60 g/cm3 for this layer. For each SSL density, we looped the DL and IL densities in steps of 0.001 g/cm3 and compared the modeled spectral albedo with the measured albedo in each step. When the mean square difference falls below 0.02 (~5%), the densities are considered retrieved. Otherwise, the densities (within the given ranges) giving the minimum difference are used. This process is similar to the method used to obtain the scattering in L08 and L15 but not band by band. Temperature profiles are also sporadic, so we choose melting or ponded ice cases for which the temperature can be estimated based on straight physics. For example, for ponded ice cases, the top temperature can be set at 0°C because this is the coexisting temperature of water and ice. The bottom ice temperature of -2°C is based on the freezing temperature of seawater, and then the temperature in any depth of the interior ice is obtained by linear interpolation. Note that the sensitivity to temperature in this narrow range (0°C to -2°C) is small and does not substantially affect the quality of the fit, as shown in the Appendix. The total ice thickness and solar zenith angle (which are generally measured) are also required to calculate the albedo and transmittance. The melt pond depth required for ponded ice is generally available from observation. Snow properties, chlorophyll concentration, and black carbon, are used for sensitivity tests and to demonstrate that the fit can be improved should information on these constituents be available.”
Note that more detailed information on each case was already provided in the subsections: for first-year bare ice, see lines 185-191 in the old Sec. 3.1.1 (now 3.2.1); for multi-year bare ice see Sec. 3.1.2 (now 3.2.2); for ponded ice see Sec. 3.2 (now 3.3). Moreover, we have added a new paragraph and a figure in the Appendix to describe the treatment of ice surface roughness, and edited the sentence at Line 188 to read: “Our tests show negligible sensitivity of the AOPs to small variations in temperature within the chosen ranges”.
Specific Comments
P1 lines 31-35: "The interactions between snow, sea ice and solar radiation in most climate models are based on empirical parameterizations that are often just a function of snow depth, sea ice thickness and surface temperature." References to these models should appear here.
This sentence was already adjusted in response to a comment from Rev. #1:
“Many sea ice models employ simplistic parameterizations for the albedo, resulting in large uncertainties in both present-day simulations and future climate projections in the Arctic (Solomon et al., 2021; Notz et al., 2016; Koenigk et al., 2014; Solomon et al., 2007).”
Now we added two more references:
Solomon, S., D. Qin, M. Manning,M. Marquis, K. Averyt,M.M. B. Tignor, H. L. Miller Jr., and Z. Chen, Eds., 2007: Climate Change 2007: The Physical Science Basis. Cambridge University Press, 996 pp.
Keen, A., Blockley, E., Bailey, D. A., Boldingh Debernard, J., Bushuk, M., Delhaye, S., Docquier, D., Feltham, D., Massonnet, F., O'Farrell, S., Ponsoni, L., Rodriguez, J. M., Schroeder, D., Swart, N., Toyoda, T., Tsujino, H., Vancoppenolle, M., and Wyser, K.: An inter-comparison of the mass budget of the Arctic sea ice in CMIP6 models, The Cryosphere, 15, 951–982, https://doi.org/10.5194/tc-15-951-2021, 2021.
P2 line 59: "to complement the observations from SHEBA and ICESCAPE". Previously in the paragraph, the FIRE ACE project is mentioned. Why is it not mentioned anymore here? and why is it not used in the present analysis?
Because FIRE-ACE provided measurements of (only) albedo and BRDF from airborne instrumentation, which is not the kind of measurements we focus on in this study.
P2 lines 72-74: This part of the introduction could benefit from a better description of the focus of the present study.
We have edited the entire paragraph as:
“Meeting the modeling needs described above requires a tool capable of rigorously calculating the radiative distribution in the atmosphere-sea ice-ocean system. As described in the next section, Jin et al. (2006) developed a Coupled Ocean-Atmospheric Radiative Transfer (COART) model. Here, this previously validated (Jin et al., 2002; 2005) COART model is extended to include the sea ice medium. The sea ice optical properties are directly parameterized as a function of its measurable physical properties, so as to eliminate the need to provide at input the Inherent Optical Properties (IOPs), whose direct measurements are more challenging. The rest of the ocean/atmospheric column can accommodate any species whose IOPs are known. This physically-based strategy also enables a direct connection with the physical ice properties simulated in climate models. In developing such a GCM-oriented version of COART, the objective of this study is to validate said parametrization against observations of albedo and transmittance by constraining the physical properties with available measurements of their vertical profiles. The augmented COART model is described in Sec. 2, and its performance is evaluated against ICESCAPE and SHEBA measurements of spectral albedo and transmittance in Sec. 3, including sensitivity studies with respect to light-absorbing impurities. The ice types vary between bare and ponded sea ice in the melting season. The presence of snow is not a focus of the present study, although it can be accounted for by the model and we included a comparison with a relevant study that used snow grains to model the surface scattering layer (old Sec. 3.1.1, now 3.2.1). The conclusions are presented in Sec. 4. An appendix is also provided to show relevant sensitivity tests.”
P3 lines 100-101: "The presence of other possible inclusions (BC and phytoplankton) is also considered." The part of the model that considers these inclusions should be described.
There’s nothing really to “describe” here, these values are part of the tabulated constants used by the code. We have anyway modified the sentence to read: “In addition to the absorption by pure ice, and scattering and absorption by brine pockets and air bubbles, the presence of other possible inclusions (BC and phytoplankton) can also be considered. The addition of scattering and absorbing particulates is trivial, and achieved via the compilation of tabulated IOPs”.
P3 line 126: What do the authors mean by "the actual scattering coefficient"?
It refers to the scattering coefficient associated with all scattering energy without scaling resulting from the forward scattering truncation. To avoid confusion, we deleted “actual”.
P3 lines 132-133: "the cases studied here pertain to sea ice surveyed in the warm, summer season". This should be specified much earlier in the paper (maybe in the introduction section with the focus of the study). The fact that snow is not considered in the model should also be specified earlier.
Good suggestion! We have implemented it, see response to your comment above (P2 lines 72-74).
P4 lines 144-145: Can the authors precise what they mean by "standard subarctic atmospheric profile” and by “open-ocean water properties" or give references here?
It is simply a static atmospheric model of how the pressure, temperature, density, and viscosity of the Earth's atmosphere change over a wide range of altitudes, similar to the “US standard atmosphere” but for subarctic environments. The reference is added (McClatchey et al., 1972). Similarly, the “open-ocean properties” refer to the “standard” ocean model, in which the ocean optical properties are associated with the chlorophyll content. Based on climatological data, the chlorophyll concentration is around 0.1 g/cm3 on average, a typical value for open ocean. We have modified the paragraph to read: “In the model, we use a standard subarctic atmosphere for vertical profiles of pressure, temperature and density to model the Rayleigh background atmosphere. For the ocean layers beneath the ice, the Chl-a concentration is set to 0.1 mg/m3, about the average reported for the arctic ocean (Gordon and Morel, 1983; Morel and Maritorena, 2001; Morel and Gentili, 2004)”.
- A. McClatchey, R. W. Fenn, J. E. A. Selby, F. E. Volz, J. S. Garing, Rep. AFCRL–72–0497, (Air Force Cambridge Research Laboratories, Bedford, Mass., 1972).
P4 lines 147-148: "We strived to use all available observational data to determine the input to the model, focusing on two common ice types: bare and ponded ice." As said in the major comment, this requires more explanations. What are the inputs of the model here? And what is done in case the observational data does not exist?
See new Subsec. 3.1, as explained in the response to Major Comment 2 above.
P4 lines 152-153: Why only these two dates have been retained from the ICESCAPE campaign? Are these the only bare ice stations led during the ICESCAPE campaign in 2010 and 2011?
It is explained in the paper that we surveyed all the ICESCAPE (and SHEBA) data, and those particular dates were selected because of optimal observational conditions: clear sky (if possible, otherwise diffuse illumination with SZA=48° which ensures minimal sensitivity), and most consistent set of measurements over best-defined bare sea ice, as per the field notes. We have modified anyway the start of Sec. 3.1.1 (now 3.2.1) to read:
“The gray areas in Fig. 1 show the total range of a series of albedo and transmittance measurements collected at each of two ICESCAPE stations in the Beaufort Sea: the top panels are for the 3 July, 2010, and the bottom panels for the 19 July, 2011, case. These particular dates were selected because of optimal observational conditions and the most consistent set of measurements over best-defined bare sea ice, as per the field notes.”
P4 lines 163-165: “The strong spectral dependence of the absorption coefficients for brine, ice, water and organic or other inclusions (Grenfell and Mayakut, 1977; Perovich and Gow, 1996) is responsible for the nearly constant albedo in the visible region and the significant decrease in the near infrared region". Are the authors still describing Fig. 1 here? Also, there is a mistake in the reference: Grenfell and Maykut, 1977.
Thanks for catching the typo in the reference (now corrected). The listed statement is general, but the paragraph and what follows refer to Fig. 1 in terms of choosing the density values.
P4-5 lines 180-182: Are these densities measured?
Not in situ. They are typical values for the profile reported in the literature for this type of ice.
P5 lines 189-190: “It is clear that a single layer is insufficient to adequately reproduce both the albedo and transmittance". I assume the authors are referring to the analysis they performed in the appendix. It should be specified.
That’s right. Added: “(See Appendix)”.
P5 lines 193-194: “It is clear that a single layer is insufficient to adequately reproduce both the albedo and transmittance.” Is this result shown in figure 1? If so, it should be specified.
We have modified the paragraph to read: “To highlight the importance of using at least three layers, Fig. 1 includes the results for single- and double-layered ice, with densities taken as the combinations of those used in the 3-layer model. It is clear that a single layer is insufficient to adequately reproduce both the albedo and transmittance, as shown by the blue and magenta lines that are far off the range of measured albedo and transmittance.”
P5 line 201: "We adjusted the ice density". I am confused here. The authors said earlier that the AOPs are more sensitive to density than to salinity or temperature. This explains why they choose to simplify the temperature profile. But if they now adjust the density (the only parameter that has a real impact on the AOP) of the observations to match better with the optics parameters, how can the radiative transfer model can then be validated with this adjusted “observation”? If the simulated parameters do not match the observation with the measured physical parameters as inputs, this should mean that the radiative transfer model misses something. Changing the physics won’t fix the optics.
We apologize for the confusion on the word “adjusted”, but density is simply used as one of our input parameters. In situ measurements are used when available. Otherwise, we use typical values obtained from climatologies pertinent to the ice types in question, as described in the new Subsec. 3.1.
We agree that “the AOPs are more sensitive to density than to salinity or temperature”, but salinity and temperature also impact the AOPs, as demonstrated in the sensitivity test results. It is the density, salinity and temperature that all together control the phase equilibrium and the brine and air volumes, which in turn determine the ice IOPs. Because in our physically-based parameterization the IOPs are linked to the ice properties, changing the ice density changes all the IOPs consistently and differentially in different spectral bands. If the parameterization is not physical, obtaining model-observation agreement in both albedo and transmittance (again, simultaneously and at all wavelengths) is extremely unlikely even if a few unknown input properties are “adjusted”. For all these reasons, we have full confidence that our approach is legitimate to validate radiative transfer processes in sea ice. Should more complete suites of input parameters become available in the future, the focus can shift towards the betterment of the IOP parametrization.
P5 line 210: "in the absence of completely measured density profiles". Here is an illustration of the second major comment. Since there is no previous description of what inputs are measured and what inputs are not, it is difficult to understand the results here.
See new Subsec. 3.1, as explained in the response to Major Comment 2 above.
P5 line 211: “These results demonstrate how the augmented COART model enables a fine tuning of the AOPs.” I don’t understand why the authors referring to the tuning of the AOPs when it seems that only the physics were tuned.
It is clear that most of the confusion comes from the use of the word “tuning”. We have rewritten the sentence as: “These results demonstrate how the augmented COART model can capture many of the spectral signatures and their changes in observed albedo and transmittance”.
P5 lines 213-214: “The snow is composed of spherical grains, whose size determines the albedo at absorbing wavelengths (Warren 2019).” How the albedo and transmittance through the snow are calculated by the model should be better described.
This sentence has been modified as: “The module of the radiative transfer model used to calculate the albedo and transmittance of snow is described in Jin et al. (2008). This model can handle different snow particle habits but, to be consistent with L15, the snow here is assumed to be composed of spherical grains, whose size determines the albedo at absorbing wavelengths (Warren 2019; Wiscombe and Warren, 1980).”
Jin, Z., T.P. Charlock, P. Yang, Y. Xie, W. Miller, Snow optical properties for different particle shapes with application to snow grain size retrieval and MODIS/CERES radiance comparison over Antarctica. Remote Sens. Environ., 112, 3563-3581 (2008).
P5 lines 214-215: “300 μm to represent new snow, and 1000 μm to represent aged, melting snow.” Where do these values come from?
These are typical values for newer versus older snow. We have added the reference to the seminal paper: Wiscombe, W. J., & Warren, S. G. (1980). A Model for the Spectral Albedo of Snow. I: Pure Snow, Journal of Atmospheric Sciences, 37(12), 2712-2733.
P6 line 234: “The SHEBA observations show." Why are the authors giving SHEBA’s value while it is only ICESCAPE data that are treated in this section?
Because we harvested every possible information on impurity content to inform our input. In the effort to find climatological values, we listed those available. We used these plausible values to factor in the plausible absorption amount in the ice, and also showed a sensitivity study that captures the full range of plausible values. There were no BC measurements reported in ICESCAPE.
P6 line 250: “The salinity profile were assumed”. Here again, the manuscript would benefit from a better description of inputs that are measured and those that are assumed or adjusted.
See new Subsec. 3.1, as explained in the response to Major Comment 2 above.
P6 line 268: "In our modeling, 5 mm of snow with grain size of 200 μm were considered". Again, how the albedo and transmittance through the snow are calculated by the model should be better described. And where do these values come from?
More description has been provided on “how the albedo and transmittance through the snow are calculated” (see response to your “P5 lines 213-214” comment). The previous sentence says: ““a few mm of new snow on surface” was reported.” These are a few millimeters of a size typical of new snow. If the reviewer has a better guess of what the notes imply, we can regenerate the figure. However, note that we already present sensitivity studies to both snow depth and snow grain size in Fig. 3.
P7 lines 289-290: The sentence should be cut after "solar irradiance is largest".
Absolutely. Fixed.
P7 lines 290: “A series of observations”. Again the number of observations used should be specified.
See new Subsec. 3.1, as explained in the response to Major Comment 2 above.
P7 line 293: "It is reasonable to expect that the accumulation of water on top of ice should annihilate the SSL." Why? This should be justified with references.
We thought it intuitive to think that water accumulating on top of a fragile, granular thin layer would melt it or at least change its properties dramatically. We have contacted Melissa Webster, who recently published a new study based on MOSAiC observations (“Spatiotemporal evolution of melt ponds on Arctic sea ice: MOSAiC observations and model results”; Elementa: Science of the Anthropocene (2022) 10 (1): 000072). However, the discussions in her work mostly focus on subnivean ponds. To keep in line with the spirit of our original sentence, we have modified it to:
“The SSL is composed of coarse, crumbly grains of ice and voids of air. Meltwater infiltration into the SSL is expected to significantly alter its physical and optical properties. Typically, a water-saturated SSL is indeed less reflective and more absorptive, or absent altogether (Light et al., 2008).”
Note that Light et al., 2008, report:
“Ponded ice, on the other hand, generally shows a much more homogeneous structure throughout its depth. Although the ice-water interface in the ponds can be quite irregular, there are fewer isolated inclusions and fewer air-ice interfaces to scatter radiation, and the SSL is typically either absent or flooded.”
P7 line 311-313: “For the thick ice with shallow pond (top row) observed on 19 July, a 3- layer ice model is required for satisfactory model-observation agreement.” What could explain this third layer for this particular pond?
It is likely due to thicker ice requiring more layers to resolve the variations of the properties within the column.
P7 line 318: “(3-layer for thick ice)”, how do we know that this is only the ice thickness under the pond that justify the number of optical layers?
Does the reviewer mean “How do we know that IT is only the ice thickness...”? What we mean is that thicker ice requires one more layer (at least). This doesn’t preclude that in other cases even more layers could be needed, that’s why we specified “in the cases analyzed here” in the previous sentence.
P7 lines 320-321: “If the albedo measurements in the near-infrared are accurate”. Why this sentence? Is there anything that suggests the opposite?
We meant to refer to specific challenges in controlling the measurement accuracy in this wavelength regime, where the energy is very low. We propose to change the sentence to “If the albedo measurements in the near-infrared are accurate (in this regime the energy and the subsequent S/N are very low),...”
P8 line 348: “Sensitivity tests show that lower salinity values”. The sensitivity tests for the salinity are missing from the main text or appendices.
That is not entirely correct, as a partial sensitivity test is contained in Fig. 5. In any case, we completely agree that it is useful to add one more specific figure to the Appendix (see revised manuscript), with the following text:
“Figure A3 shows the optical effect of different salinity profiles. The maximum value (10 ppt) is a rare occurrence anywhere in the ice column, but was deemed a good maximum value in order to capture the full range of potential variability. Detectable changes are present up to the NIR, and are significant in the visible. In most situations, it is observed that the model predicts maximum differences in both albedo and transmittance of up to 0.05, in correspondence of their peaks in the visible.”
The new figure is attached (FigS3_rev2.pdf) as a supplement for the response to reviewer #2.
P8 line 352-353: “and transmittance increases with pond depth for similar ice thicknesses below” this is the opposite of what is said in line 325.
Yes, this was a typo and is now corrected. Thanks!
P8 line 363-364: “An accurate and efficient radiative transfer model is also required for climate models, which use simple AOP parametrizations for sea ice.” This sentence is not true since some ESM already use the Delta Eddington approach of Briegleb & Light (2007) which is not a “simple AOP parameterization for sea ice”.
We referred to Briegleb and Light, 2007, in the Introduction. To our knowledge, their ESM is the only one using interactive RT for sea ice. However, it is a 2-stream model with a number of assumptions on ice IOPs (e.g., constant scattering asymmetry factor of 0.94 in all bands and all ice layers).
P9 line 370: "the density is used as a tunable parameter since in situ measurements are not 370 always available". As an input parameter of the model, the density should not be treated as a tunable parameter.
This point should now be resolved in view of the many earlier responses to this review.
Figure 1: Lime text in the legend is hard to read. Also, the authors should consider to better explaining the legend (by naming each layer and explaining what letters refer to).
We have improved the explanation to the legend explicitly in the caption. Regarding the color readability, we’ll abide by the requirements of the editorial office should the quality be insufficient.
Figure 2: Albedo and transmittance curves should be differentiated by something (dashed line as it is already done in figure A1). Numbers given in the figure should be explained in the caption.Why are only the results for July 3rd are given and not those for the 19th? Are the results for July 19th similar the those for the 3rd?
We have changed the transmittance curves to dashed, as suggested (it makes total sense for consistency with the figures in the Appendix). The explanation of the legend has been improved as per the previous comment. Yes, the results for July 19th are very similar.
Figure 3: Same comment as figure 2.
Corrected accordingly. See response above.
Figure 4: The caption should better describe the figure here. It is not as Fig.2 as the density profile is not changing. Describing the physics (number of layers, density profile) in the caption and just giving the amount of BC for each line in the legend could help for clarity.
We totally agree. The caption now reads: “Sensitivity to albedo and transmittance to the addition of contamination from sootlike, BC particulate spanning amounts typical of the panarctic. The solid black lines are the optimal spectra for the 3-layer profile in the top panels of Fig. 1 (3 July, 2010).”.
Figure 5: Same comment that for the other figures: the legend should be better explained in the caption. What the dotted line refers to should also be specified.
Changed as suggested, as done for Fig. 2 (see your comment above).
Figure 6: What the dotted line refers to should be specified.
Corrected as per the point above.
Figure 7: Considering the number of panels here, adding a letter to call each panel could improve the clarity of the main text and the caption.
Done, and indicated in the caption and text.
Citation: https://doi.org/10.5194/tc-2022-106-AC3
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