Snow stands out from materials at the Earth’s surface owing to its unique optical properties. Snow optical properties are sensitive to the snow microstructure, triggering potent climate feedbacks. The impacts of snow microstructure on its optical properties such as reflectance are, to date, only partially understood.
However, precise modelling of snow reflectance, particularly bidirectional reflectance, are required in many problems, e.g. to correctly process satellite data over snow-covered areas.
This study presents a dataset that combines bidirectional reflectance measurements over 500–2500 nm and the X-ray tomography of the snow microstructure for three snow samples of two different morphological types. The dataset is used to evaluate the stereological approach from
Snow optical properties are crucial to quantify the effect of snow cover on the Earth energy balance. They are also unique since snow is the most reflective material on the Earth surface. The subtle interplays between snow microstructure and snow optical properties are responsible for several climate feedbacks
The effect of snow microstructure on the optical properties of snow is currently not fully understood. Up to now, many studies have focused
on retrieving the single-scattering properties of individual ice crystals with “idealized” shapes
Understanding and modelling the variations in snow directional reflectance with snow microstructure are essential to correctly interpret satellite data
The formalism developed by
More recently,
In addition,
To sum up, it has been shown that BRF, especially in high absorptive wavelengths, is more sensitive to snow morphology than snow albedo (bi-hemispherical reflectance). Yet no clear relationship has been either established theoretically or evaluated experimentally using optical measurements combined with an objective quantification of the snow microstructure. The objectives of the paper are thus to (i) describe one of the very few datasets that combined measurements of the bidirectional reflectance over the 500–2500 nm range and X-tomography characterization of the snow microstructure, (ii) evaluate the accuracy of the model of
The first section provides a description of the snow samples, the measurement strategy, the optical model, the processing of the X-ray tomography images, and the optical data. The second section presents the results in terms of temporal variability of the snow microstructure, accuracy of the optical measurements, snow microstructure characterization, and model evaluation. Discussions and conclusions are detailed in the last section.
The general idea of the experiment was to characterize both the snow microstructure and the BRF for the same macroscopic snow sample. The dataset consisted of three macroscopic snow samples: S1 analysed in March 2012 and S2 and S3 analysed in March 2013. S1 consisted of decomposing and fragmented particles/rounded grains (DF/RG) according to the classification of snow sample preparation, snow microstructure characterization (manual measurements, casting for X-ray analysis) and preparation of a sample for BRF measurements, BRF measurements, snow microstructure characterization (manual measurements, casting for X-ray analysis).
Steps 2 and 4 were performed to characterize the microstructure just before and after the BRF measurements and to control the possible evolution of the microstructure during the BRF measurements.
Figure
For the BRF measurements, the snow was sampled in a cylindrical sampler with no disturbance of the snow surface as in
Before this sampling, the snow SSA and density were measured, the SSA with DUFISSS (DUal Frequency Integrating Sphere for Snow SSA measurement;
For all the samples, the X-ray tomography was performed at 7
Summary of all the X-ray tomography images acquired. “B” and “A” refer to “before” and “after” the optical measurement respectively.
Microstructure of the samples S1, S2, and S3 as revealed by X-ray tomography. These visualizations correspond to subsets from the 3D images S1_B_1_7m
The bidirectional reflectance was measured with a sensor field of view of 2.05
Tables
All grey level images were segmented using the following three-step semi-automatic method:
(i) pre-processing of the image, including basic beam hardening and ring artefact corrections; (ii) detection of air bubbles and replacement of their levels by the mean grey value of 1-chloronaphthalene (see
Once segmented, the obtained binary images can be described in terms of
The
In the case of snow, which is known to be an anisotropic material with an orthotropic axis corresponding to the vertical (
All chords that cross the file borders are inherently dismissed by this estimation method; hence, no hypothesis on the exact nature of the phase (air or ice) outside of the processed image is required.
In what follows, the CLDs of the ice phase only are considered.
The mean chord length
The specific surface area was estimated using two different means: a
The stereological approach is directly based on the computation of the mean chord length
The voxel projection estimation, denoted SSA
As detailed in
Let
In what follows, we use the anisotropy factor
Note that this parameter does not necessarily capture the position of the maximum and minimum reflectances, especially in the visible wavelengths as discussed in
The model of snow reflectance used in this investigation is described in detail in
Sample microphysical properties calculated from the X-ray tomography images and retrieved from the spectral albedo. “B” and “A” refer to “before” and “after” the optical measurement respectively.
Further analysis showed that the albedo calculated with Eq. (
The model described in Assume that the CLD is exponential with the mean values calculated directly from the 3D images (Table Directly use the CLD calculated from the 3D images. The simulations are labelled
For the simulations, we used the database of ice optical properties provided by
The optical model described in the previous section can be used to retrieve SSA from a measured albedo spectrum. First, the volume fraction of ice
Here we first provide a comparison of the characterization of the snow microstructure obtained with the different methodologies (manual measurements, optical measurements, and X-ray tomography). In a second step, we evaluate the accuracy of the BRF measurements. The last two sections compare the BRF obtained from the model and from the measurements and evaluate the impact of the microstructure on the BRF.
The SSA was obtained by various methods using both optical measurements and X-ray tomography. The optical methods include DUFISSS, ASSSAP, and retrieval from the albedo spectrum (Sect.
Measured and retrieved albedo spectra of samples S1
Figure
SSA
Figure
Estimated density (first column) and SSA (second column) at various sampling depth in S1, S2, and S3. Values estimated from 3D images are represented by diamonds. Values estimated from measurements (manual weighting for density, DUFISSS, and ASSSAP for SSA) are represented by solid and dotted lines. The SSA retrieved from the spectral albedo is shown with vertical green lines. Values obtained before the optical scan are in blue and after in red. Note that the SSA obtained from 3D images represented in the figure is SSA
All three samples exhibit some variability both horizontally and vertically. The average density estimated from the 3D images is slightly higher than the manually measured one for S1 and S3 and slightly lower for S2. The average SSA calculated from the X-ray tomography is systematically lower than that estimated from DUFISSS and ASSSAP measurements and is in perfect agreement with the SSA retrieved from the albedo spectra. These discrepancies might be inherent to the methodology but could also be linked to the variation in the properties inside the sample. Note that an X-ray tomography image has a very small size (of the order of several millimetres), the optical measurements with DUFISSS and ASSSAP use surfaces with the size of about 5 cm, and the spectral albedo characterizes a sample as a whole.
Figure
Figure
The CLD determines optical properties of a mixture not explicitly but via its Laplace transform
If the argument
Figure
The characteristic functions calculated directly from the X-ray images at large values of argument
The characteristic function in Eq. (
The exponential CLD has the Laplace transform from Eq. (
Comparing the second-order term in Eq. (
The deviations from the exponential law
Values of
The deviation of the CLD from the exponential law matters, i.e. affects the optical properties, if the difference between Eqs. (
Thus, the absorption at which the deviation matters can be estimated as
Measured reflectances of the three samples (each panel) obtained for optically equivalent geometries.
Measured (circles) and modelled (curves) BRF for the three samples (S1:
Figure
This shows that the relative accuracy of the measurements estimated at 1 % in
Figure
To examine this effect, we simulate the snow reflectance in the most pronounced difference range 1400–1900 nm using the values of the complex refractive index of ice taken from different databases. Figure
Measured (circles) and simulated (EXP, lines) reflectances in the principal plane for S1
Measured (circles) and simulated (EXP) (curves) BRF of the three samples at vertical incidence at 800 nm.
Measured (circles) and simulated (EXP, curves) BRF for S1
BRF measured (circles) and simulated with the exponential (curves) and
Figures
Figures
Figure
Measured (first line) and simulated (second line) reflectances for the three samples (three columns) at 1320 nm. The incident zenith angle is 30
Measured (crosses) and simulated (dotted curves for
Figure
Measured (markers) and simulated (lines) reflectance in the principal plane (forward direction) for an incident zenith angle of 60
Figure
This study presents a dataset that combines the snow bidirectional reflectance over the 500–2500 nm range with different illumination geometries and 3D images of snow using X-ray tomography, which allows analysis of the snow microstructure, e.g. its SSA and density. The SSA is calculated using two different methods: the voxel projection method (VP) and the method based on the ice chord length distribution (CLD). The comparison between the two SSA values is in excellent agreement (
The analysis of the characteristic functions of random chords in the snow phase calculated directly from the 3D images has shown that the random chords obey the gamma distribution with the shape parameter
The comparison between the simulated and measured reflectance under a specific geometry (
To sum up, the results exhibit two different trends for small and medium/long optical paths in the snow.
For long/medium optical paths, the model predicts no impact of the CLD shape on the reflectance and is in good agreement with the measurement. The anisotropy is slightly overestimated in the simulations. A possible explanation can be related to the surface roughness, which is not accounted for in the simulations and generally leads to less anisotropic patterns The picture is different for the small optical paths, which refer to the high absorptive wavelengths and to oblique illumination and/or viewing. The model predicts an impact of the CLD. The use of the
The effect of crystal shape and SSA on snow BRF is intricate
To conclude, this unique dataset combining X-ray tomography imaging of snow microstructure and high-accuracy measurements of snow BRF was used to demonstrate the following.
Faceted crystals exhibit a more anisotropic reflectance than fragmented particles. The Other characteristics of snow microstructure besides SSA, e.g. the CLD shape, impact the angular reflectance of snow for high ice absorption and oblique viewing and illumination.
Geometry and spectral range of S1 optical measurements.
Geometry and spectral range of S2 optical measurements.
Geometry and spectral range of S3 optical measurements.
Measured (first line) and simulated (second line) reflectances for the three samples (three columns) at 800 nm. The incident zenith angle is 30
Measured (first line) and simulated (second line) reflectances for the three samples (three columns) at 1500 nm. The incident zenith angle is 30
BRF measured (circles) and simulated with the exponential (curves) and
BRF measured (circles) and simulated with the exponential (curves) and
SSA estimated from different methods for spheres and their relative error compared to the theoretical value SSA
Manual measurements of density. The heights of the upper and lower boundaries of the sample used for density measurements are indicated in the table.
Manual measurements of SSA. The heights of the upper and lower boundaries of the sample used for SSA measurements are indicated in the table.
The BRF dataset is available in the PANGAEA database along with the CLDs and the simulation results at
MD led and wrote the study. FF conducted the X-ray tomography measurements and the 3D image analysis. AM performed the analysis of the CLDs and their links to the snow reflectance and made the appropriate simulations. OB conducted the BRF measurements together with MD. PH and PL performed the 3D image processing. BL, AD, and NC prepared the snow samples with the two first authors and contributed to the X-ray tomography measurements. SRdR and EA contributed to the X-ray tomography measurements.
The authors declare that they have no conflict of interest.
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CNRM/CEN is part of Labex OSUG@2020 (ANR-10-LABX-0056). The 3SR lab is part of the LabEx Tec 21 (Investissements d’Avenir, grant agreement ANR-11-LABX-0030). The authors are thankful to Quentin Libois, Ghislain Picard, Henning Löwe, and Quirine Krol for fruitful discussions on the paper. Pascal Charrier, Jacques Roulle, Philippe Puglièse, and Laurent Pézard are also thanked for their help in the experimental part of the study. The authors further thank the two anonymous reviewers for the helpful comments on the manuscript.
This work was funded by ANR grants DigitalSnow (ANR-11-BS02-009), EBONI (ANR-16-CE01-0006), and MiMESis-3D (ANR-19-CE01-0009); the State Research Program “Photonics, Opto- and Microelectronics'; and the National Academy of Sciences of Belarus. Marie Dumont has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 949516, IVORI).
This paper was edited by Kaitlin Keegan and reviewed by two anonymous referees.