study of the reflectance of snow based on measurements and modeling · 2015-07-17 · study of the...
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Study of the reflectance of snow based on measurements and modeling
8/7/2015, Frédéric Flin
Alexander Regenscheit M2R 2014Supervised by
Marie Dumont and Frédéric Flin
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Definitions
� Albedo:� Ratio between reflected radiation into
the whole hemisphere over theincident irradiance
� Bidirectional reflection density function(BRDF):
� Ratio of reflected radiance in an infinitesimal solid angle direction overthe incident irradiance of a collimatedbeam
� Specific Surface Area (SSA):� Ratio between surface (interface
ice/air) and volume of ice� Measure for grain size
V
S
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Optical properties of snowBRDFAlbedo
� dominant multiscattering λ < 1 µm
� strong forward scattering for λ > 1 µm (absorption)
Snow
0°30°
60°
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Motivation
� Application of optical properties of snow :� Modeling of the snowpack (energy balance) (Brun et
al., 1989) � Remote sensing of reflectance (Dumont, 2010)� In situ measurements of SSA (DUFISSS, POSSSUM)
(Arnaud, 2011)
� Albedo and BRDF depending on the microstructureof snow (Haussener et al. 2012; Picard et al., 2009; Kaempfer et al., 2007)
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MotivationFor a better understanding of the relation betweenmicrostructure and optical properties:
� BRDF measurements of two different snow types weredone 2012/13 (IPAG) together with taking tomographyimages of this snow (3SR)
Goal of the internship� Comparison of these measurements with the results of
different models� Comparison of different models with each other� Evaluating the range of correctness of the models� Impact of grain shape on BRDF
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Content
�Measurements�Models�Results�Conclusion
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MeasurementsSampling for BRDF measurements at IPAG
Sampling for tomography at 3SR Lab
+Grain photographs
+Density measurements
+SSA measurements
Before and after BRDFmeasurements
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MeasurementsSampling for BRDF measurements at IPAG
Sampling for tomography at 3SR Lab
+Grain photographs
+Density measurements
+SSA measurements
Before and after BRDFmeasurements
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Measurements
�March 2012 – recent snow� Naturally deposited snow� Three tomography images (3SRLab)� 5 reflectance measurement configurations
(IPAG)
�March 2013 – faceted snow� 17 days under temperature gradient� Sieved snow� Two tomography images� 9 reflectance measurement configurations
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Models:Microstructural properties � optical properties
� DISORT: (Stamnes, 1988)� Exact solution of the radiative transfer equation� Mie-scattering (spheres)
� Photon tracking model PBRT: (Malgat, 2012)� Optical law based probability model� Calculates reflectance from digital images
� Analytical model: (Kokhanovsky, 2012)� Approximation of the radiative transfer equation, � Based on reflection function for snow grains, � Valid for weakly absorbing media� Two free parameters:
�M as a measure for the impurites�L = b²d (b = shape factor; d = mean diameter
of grains)
� To compare measurements with the models the SSA has to beequivalent
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Results
�Albedo:� DISORT vs PBRT for image of spheres� DISORT vs PBRT for tomography images of snow� DISORT and PBRT vs measurements
�BRDF:� Measurements vs analytical model� Measurements of different snow grains
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Albedo – DISORT vs PBRT - spheresNumerical samples:
-600 non-overlaping spheres of r = 50 voxels-Scaling on r
� density = 288 kg/m3
� SSA = 32.72 m2/kg-spheres do not intersect the image borders
PBRT multi-margins
1000 voxels
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Albedo – DISORT vs PBRT - spheres
Strong size dependence
No difference for spheres exceeding theborders of the image
SSA in m2/kg
PBRT multi-margins
1000 vox
?
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Albedo – DISORT vs PBRT - spheres
Strong size dependence
No difference for spheres exceeding theborders of the image
SSA in m2/kg
PBRT multi-margins
PBRT top-margin
1000 vox
1000 vox
� No impact of margins
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Albedo – DISORT vs PBRT - spheres
�� HeightHeight inincreasecrease � increasing albedo
�� HorHoriziz. . SurfSurf.. increaseincrease � decreasing albedo
�� extr4extr4: no elementary representative volume
� Depth, BC, REV problems ?
SSA in m2/kg
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Albedo – DISORT vs PBRT - snow
Recent Snow (I17m) Faceted Snow (TG1)
~1 mm
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Albedo – DISORT vs PBRT - snow
� Results of PBRT and DISORT are very closeuntil 1000 nm
� Reduction of image size has a lower influencein comparison to spheres
� Measurements agree with the results of DISORT for low absorbing range
Faceted Snow
Recent Snow
DISORT
PBRT
Physical Measurements
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�Results depending strongly on image size�Tomography images deliver PBRT results closer
to DISORT than spheres�Size effect is stronger for the spheres than for the
tomography images�Measurements confirm DISORT in weak
absorbing range
Albedo – DISORT vs PBRT
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� Influence of impurities (M) was neglected (λ ≥ 800 nm)� L = b²d :
� d = 6 / (SSA*ρ) � b = 3.6 shape factor for spheres
BRDF – Analytical Model vsMeasurements
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BRDF – Analytical Model vsMeasurements
Impurities = 0
Snow
20°
80°
-60°
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BRDF – Analytical Model vsMeasurements
Snow
20°
80°
-60°
Adjusted using SSA
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� Influence of impurities (M) was neglected (λ ≥ 800 nm)� L = b²d :
� d = 6 / (SSA*ρ) � b = 3.6 shape factor for spheres� b = 5.6 shape factor for non-spherical grains
BRDF – Analytical Model vsMeasurements
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BRDF – Analytical Model vsMeasurements
� Strong deviation between model and measurements forspherical shape
� Adaption of the model by varying the shape factor reduces thedeviation between model and measurements
� Shape factor for non-spherical grains is in agreement with the real grain shape for recent snow
� Model is more isotropic for 800 nm and 1000 nm, however lessisotropic for 1300 nm than the measurements
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BRDF – Impact of grain shape
� To investigate the impact of the grain shape themeasurements of two different types of snow are compared:
� Recent snow 2012 → rounded shape
� Faceted snow 2013
→ rounded shape on the top(ech1)
→ faceted shape on the top(ech2)
ech1
ech2
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BRDF – Impact of grain shape
� Same SSA for ech1 and ech2 (2013)
� Different BRDF for ech1 and ech2
� Similar BRDF for 2012 and 2013 ech1
Snow
20°
80°
60°
Upward-oriented facetsDownward-oriented facetsRecent snow - No faceting
0°
-60°
-60°
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BRDF – Impact of grain shape
� For the same SSA but different grain shape different BRDF values were measured
� In the case of similar grain shape but different SSA valuessimilar BRDF values were measured
� Very strong diffusion in forward direction was observed forthe sample with facetted grains on the top compared to the results for rounded grains
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Conclusion and outlook
DISORT:� Confirmation of DISORT albedo modeling for low absorbing
range (900 – 1100 nm) with measurementsPBRT:� PBRT could not be validated → strong size dependence� Outlook:→ Investigation of surface size and depth impact→ Find a representative elementary volume→ Influence of the amount of photons→ Testing the influence of impurities
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Conclusion and outlook
Analytical model:
� Could not describe the measurements� Adjusting the shape factor led to a better result� Very high anisotropy of the model for the wavelength 1300 nm
compared to the measurements (out of validity range)
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Conclusion and outlook
Impact of grain shape on BRDF:
� The impact of the shape on the BRDF was found to be strong� For the faceted snow on top a very strong forward diffusion,
compared to recent snow and faceted grains oriented to thebottom, was observed.→ could be a key to characterize the degree of metamorphism
for faceted snow
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Bibliography� Brun, E., Martin, E., Simon, V., Gendre, C., and Coléou, C. : An
energy and mass model of snow cover suitable for operational avalancheforecasting, J. Glaciol., 35, 333 – 342, 1989.
� Kaempfer, T., Hopkins, M., and Perovich, D. : A three-dimensionalmicrostructure-based photon-tracking model of radiative transfer in snow, Journal of Geophysical Research : Atmospheres (1984–2012), 112, 2007.
� Picard, G., Brucker, L., Fily, M., Gallée, H., and Krinner, G. : Modelingtime series of microwave brightness temperature in Antarctica, J.
Glaciol., 55, 537 – 551, 2009.� Haussener, S., Gergely, M., Schneebeli, M., and Steinfeld, A.
:Determination of the macroscopic optical properties of snow based on exact morphology and direct pore-level heat transfer modeling, Journal of Geophysical Research : Earth Surface (2003–2012), 117, 2012.
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Spectrometer
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Obtention of 3D images by X-ray tomography
Principle of X-ray tomography
Several radiographies of the sample at different angular
positions
3D binary image of the sample
Thresholding and image processing
Tomography
� Resolutionbetween 7 and 9 µm
3 mm
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DISORT� Exact solution of radiative transfer equation, continuous
medium
� Inputs are single scattering properties� Log normal distribution:
� Logarithm of radius of spheres is normallydistributed
� Mie scattering:� elastic scattering of el. magnetic waves by
spheres� size of particles in range of wavelength
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Photon tracking model PBRT� Adapted to tomography images by R.
Malgat and D. Coeurjolly(LIRIS,DigitalSnow Project)
� Interaction between ray and snow grainsare governed by Snell's and Fresnel'slaw as well as the absorption law of Bouguer – Lambert
� Probability of reflected or transmittedphoton deduced from ratio of Fresnel'slaw of reflected and incident radianceand a Monte-Carlo based calculation of a random number between 0 and 1
� Number > I_r/I_i → reflection� Number < I_r/I_i → transmission
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Analytical Model� Based on single scattering phase function� Takes into account directional signatures� Valid for weakly absorbing range (ice <1,24 µm)