Sea ice thickness is an essential climate variable. Current L-Band sea ice thickness retrieval methods do not account for sea ice surface roughness that is hypothesised to be not relevant to the process. This study attempts to validate this hypothesis that has not been tested yet. To test this hypothesis, we created a physical model of sea ice roughness based on geometrical optics and merged it into the L-band emissivity model of sea ice that is similar to the one used in the operational sea ice thickness retrieval algorithm. The facet description of sea ice surface used in geometrical optics is derived from 2-D surface elevation measurements. Subsequently the new model was tested with

The L-band brightness temperature (

Here, we investigate the effects of surface roughness on the L-band

At small end of the roughness spectrum i.e. when the change of surface elevation over sampling distance (

In this study, we focus on the other side of the roughness spectrum, i.e. the large-scale surface roughness of sea ice (

GO approximation describes the surface as a set of facets

In this paper, we address the knowledge gap regarding the influence of large-scale surface roughness on L-band

Section

Section

The three key results of this study, namely that (a) surface roughness reduces the polarisation difference, this change being most pronounced at incidence angles greater than 50

Section

In this section we present the SMOSice 2014 campaign that is the key dataset of this study (Sect.

The region of the SMOSice 2014 campaign.

The SMOSice 2014 campaign took place between 21 and 27 March 2014 in the area between Edgeøya and Kong Karls Land, east of Svalbard.

In the period preceding the experiment from late January until early March the meteorological conditions in the region deviated strongly from the climatological means. The air temperature measured at Hopen Island meteorological station was on average 9 to 12

The EMIRAD-2 L-band radiometer (developed by DTUSpace) is a fully polarimetric system with advanced radio frequency interference (RFI) detection features

In this study, the ALS (Riegel VQ-580 laser scanner) has two purposes: (1) to measure the surface elevation for subsequent estimation of the ice thickness and (2) to characterise the surface topography. The ALS near-infrared laser (wavelength 1064 nm) measures snow and ice elevation with the accuracy and precision of 0.0025 m. Across-track and along-track elevation measurements were obtained every 0.25 and 0.50 m, respectively. These sampling characteristics resulted from the combination of the flight altitude (70 m) and the setup of the ALS (pulse repetition rate of 50 kHz, cross-track range of

The estimate of sea ice thickness was built on the hydro-static equilibrium assumption. The data required to estimate sea ice thickness consists of (a) the densities of water and ice, (b) the snow load classically described by snow density and snow thickness, and (c) ALS's freeboard data.

The water, ice, and snow densities retained are 1027 kg m

Snow thickness was meant to be provided by the onboard snow radar; however the equipment was still in the test phase at the time of the experiment. As a workaround, we followed

In this subsection we will analyse the data from the airborne laser scanner (ALS) that we presented in Sect.

In the context of radiation transfer, the surface roughness is characterised in relation to incident wavelength. The ALS along-track spatial sampling of 0.5 m is a few times larger than the L-band wavelength in sea ice (

In the first step, we identify the ice with different degree of surface roughness. For that purpose we divide the flight tracks into 1 s sections (approximately 70 m long), large enough to cover the entire nadir radiometer footprint, and we build a histogram of the standard deviations of surface heights computed for these sections. The number of bins in the histogram is set according to the formula

Histogram of the standard deviation of surface heights computed from 70 m flight strips; bins define the roughness classes of sea ice. Examples for the three roughness classes “smooth”, “medium rough”, and “rough” are marked in the colours blue, green, and red, respectively.

The

In the second step, we interpolate the ALS elevation measurements to a regular 0.5 m grid in order to form a digital elevation model (DEM) of the sea ice surface. The sea ice surface in the DEM is represented as a set of triangular facets. Each facet orientation in the 3-D Cartesian space (for simplicity we assume the base vectors

In the third step, we compute the normal vectors and their orientations for the individual facets. This is done for all roughness classes. We found that the azimuthal orientation angle

In the previous section we used the DEM to calculate the vectors normal to the surface facets. In this subsection we analyse the orientations of facet azimuths.
In order to evaluate the distribution of the facet azimuths, we define parameter

To evaluate

Section

We decide to approximate the PDF of surface slopes with an exponential curve:

Figure

Density of probability of surface slopes on a logarithmic scale for three roughness classes: smooth 0.05 m

Surface roughness parameter

In this subsection we present the emission model for simulating the sea ice brightness temperature (

Brightness temperature simulation setup of the MIcrowave L-band LAyered Sea ice emission model (MILLAS).

In the previous sections, we described the sea ice surface as composed of facets with an orientation described by two angles: the slope

In this section, we describe how we integrate the probability description of faceted sea ice surface with the MILLAS emission model. We will start by describing the coordinate system that we used in the

We consider the Cartesian coordinate system (

We are interested in finding a relationship between the radiation originating from a tilted facet and from a flat one. For that purpose we must consider the tilted coordinate system associated with the

The emissions from the facet at an angle

We model the sea ice surface as a set of facets. Therefore the brightness temperature registered at the antenna aperture is a sum of contributions from

The formula summing the contributions from

At this stage of our study, we aim at modelling the effect of surface roughness on the

This is the formula that we implement in the geometrical roughness model.
Figure

Flow chart showing the processing chain within the geometrical roughness model. The model consists of two principal blocks: the emission model and the inverse transport sampling ITS module responsible for generating the facet orientation. The input parameters surface temperature

Effects of the large-scale surface roughness on the brightness temperature of sea ice, simulated with the geometrical roughness model. Vertical polarisation is in red, and horizontal polarisation is in blue. The black dashed lines mark the

The number of facets

The three main results of this study are as follows. (a) Surface roughness reduces the polarisation difference; this change is most pronounced at incidence angle greater than 50

In Sect.

In Sect.

In our simulation

The effect of increasing surface roughness is two-fold. First, the overall near-nadir intensity is lowered by 2.6 K. Second, the polarisation difference decreases. For the highest value of the roughness parameter, at Brewster's angle the vertical polarisation decreases by 8 K and horizontal polarisation experiences a 4 K increase. The effect of roughness is more pronounced for larger values of roughness parameter

The polarisation mixing can be explained by the approach used in this study. The emissions from the facet in horizontal (

The lowering of the intensity has two possible explanations. First is that our model does not take into account shadowing effects. When local incidence angle is greater than 90

The second explanation of this effect is associated with shape of the Fresnel emissivity curves.
The polarisation difference for large incidence angles is larger than for the near-nadir ones. Therefore, the mean of the two polarisations (

The above results are obtained with a Monte Carlo simulation. This method is a time-consuming approach. Therefore, we propose a parameterisation of the simulation results. The two effects, the polarisation mixing and the lowering of brightness temperature, can be expressed in a fashion similar to the HQ model proposed by

The emissions from the specular surface are an essential input for the geometrical roughness model used in this study. The exact shape of the simulated brightness temperature curves depends on the probability distribution of slopes as well as on the emission characteristics of the specular surface. In this paragraph, we will investigate how the shape of the

The sea ice permittivities from the MILLAS model range between

In this section, we investigate how sensitive the model is to its main variables: surface temperature, ice thickness, snow thickness, surface roughness, and the implicit assumption of 100 % sea ice concentration. This is a mandatory step toward the evaluation of the model (Sect.

The two most important factors influencing the L-band brightness temperature over sea ice are the ice concentration and the ice thickness. We calculate the sensitivity of our model with regard to sea ice concentration by assuming a linear mixing of water and thick ice fractions within the radiometer footprint. The brightness temperature of seawater

The sensitivity of the

Change in the brightness temperature as predicted by the MILLAS emission model as a function of surface temperature. The different line styles correspond to the different snow thickness assumptions. The calculation was carried out for the sea ice thickness of 1 m and surface roughness set to zero.

Table with sensitivities of the brightness temperature at nadir, 45, and 60

Table

The assumption about snow thickness has a considerable effect on the sea ice

In the MILLAS model, ice permittivity is parameterised with ice temperature. The non-monotonic shape of the curves is caused by change in ice permittivity. Therefore, the sensitivities are calculated for two temperature ranges: lower (250–265 K) and higher (265–270 K). Table

As far as the large-scale surface roughness is concerned, the sensitivity increases almost linearly for the values of

In order to interpret the results of the comparison between the simulation and measurements, it is necessary to evaluate the uncertainties associated with the input parameters: surface temperature, ice thickness, and snow thickness.
In the following paragraphs, we use ”mean model sensitivity for the cold conditions” for the averaged absolute sensitivity of

The uncertainty associated with surface temperature is estimated as the product of the sensitivity of the model times the measurement uncertainty. The surface temperature measurements carried out with the KT19.85 have an accuracy of 0.5 K. The mean surface temperature in the region covered by ice was 251.7

The uncertainty associated with sea ice thickness is estimated as the product of the sensitivity of the model times the measurement uncertainty.
The sea ice thickness measurements in this study are derived from the resampled ALS elevation data. The mean standard deviation of the resampled elevation measurements is 0.08 m. The assumption about the densities of snow, ice, and water combined with the assumption on the snow thickness of

The uncertainty associated with snow thickness is estimated as the product of the sensitivity of the model times the measurement uncertainty.
Unfortunately, the snow thickness measurements are not available. The snow layer, although transparent for the L-band radiation, is not invisible. The refraction on the snow–ice and snow–air interfaces alters the local incidence angles. Snow cover also has an effect on the temperature profile within the ice. This indirectly affects the permittivity of sea ice. All these factors make an estimation of the uncertainty caused by snow thickness especially hard to quantify. We assume that snow thickness uncertainty is equal to the mean standard deviation of the resampled elevation measurements, that is 0.08 m. The mean model sensitivity to snow thickness for the cold conditions is 8.6 K m

An important factor which is not directly included in the model is the sea ice concentration. In the model we assume sea ice concentration to be 100% in order to single out the much smaller contribution of surface roughness. However, if a linear mixing model is applied, the sensitivity to sea ice concentration is

To put the partial sensitivities into perspective, the expected changes in the

To conclude, the sensitivity analysis of the geometrical roughness model leads to the conclusion that the surface roughness effects will be hard to observe in the SMOSice 2014 flight data with the current emission model setup.

Scatter plots illustrating the comparisons between the EMIRAD-2 data and the

Scatter plots illustrating the comparisons between the EMIRAD-2 data and the

In this section, we compare the brightness temperature measured with the EMIRAD-2 radiometer with the brightness temperature simulations. The comparison is done on a 4.3 km section as to justify the assumption of the isotropic azimuth distribution. We want to determine the simulation setup that best reproduces the radiometer measurements and whether the inclusion of the surface roughness in the simulation brings significant improvement. The limitation of this approach is that we assume that the ice observed by the side-looking antenna and the ice below the flight path have the same properties. We consider the surface temperature, the sea ice thickness, and the surface roughness along the flight, and we use them to run the statistical roughness model, described in Sect.

For each radiometer channel we made four simulation setups: two without roughness (Flat no snow, Flat snow), and two with roughness included (Rough (GO) no snow, Rough (GO) snow). As for the performance metrics of the model setups, we use the coefficient of determination (

The values of

The results of the comparison are also presented in the form of histograms of the difference between the measured and simulated

The high values of RMSE and bias show a general misfit of the model to the data. The sensitivity study of the model presented in Sect.

Histograms of the differences between the EMIARAD2 measurements and simulation setups for four antenna feeds.

Performance metrics for the different

In this paper we address the knowledge gap concerning the influence of the decimetre-scale surface roughness on the L-band brightness temperature of sea ice. We used the airborne laser scanner (ALS) data to characterise the sea ice surface and to produce the digital elevation model (DEM) of the sea ice surface. From the DEM we derived the probability distribution of surface slopes (

The results have implications for the current and future L-band missions. The operational SMOS sea ice thickness product relies on near-nadir

Code and data are available from the authors on request.

LK was the project PI responsible for funding acquisition, project administration, and supervision. Conceptualisation of the work presented in this paper was done by MM and LK. The problem investigation and methodology was done by MM, and the software implementation was carried out by MM and NM. The data curation was done by SH and SSS. As far as the writing and manuscript preparation are concerned, MM prepared the draft and the data visualisation with LK and NM doing the first reviews and editing.

The authors declare that they have no conflict of interest.

The authors acknowledge the institutions providing the data and people involved in carrying out the measurements. The TerraSAR-X and TanDEM-X teams provided the SAR data for this study.

Special thanks are due to Yann Karr, PI of the SMOS mission, for his suggestions and comments. We are also grateful for the financial support that covered the publication costs.

This research was funded by the HGF Alliance, Remote Sensing and Earth System Dynamics. The European Space Agency co-financed the AWI research aircraft Polar 5 and helicopter flights (ESA contract 4000110477/14/NL/FF/lf; PI Stefan Hendricks) and the development and validation of SMOS sea ice thickness retrieval methods (ESA contracts 4000101476/10/NL/CT and 4000112022/14/I-AM; PI Lars Kaleschke). Technical University of Denmark (DTU) co-financed and conducted the measurements with the EMIRAD2 L-band radiometer on Polar 5.

This paper was edited by John Yackel and reviewed by Jack Landy and Georg Heygster.