SNOW AND ICE


BACKGROUND

	Spectral data:  Until recently, frost and snow spectra were calculated using 
the optical constants of ice in a Mie theory and radiative transfer model (Dozier 
and Warren, 1982).  Field measurements (Warren et al., 1986) show that the 
Dozier and Warren model is accurate in the VNIR and SWIR.  We have recently 
measured the directional hemispherical reflectance spectra of such materials for 
the first time in the MWIR and TIR (Salisbury et al., 1994), and find that the 
calculated spectra for frost are correct, but calculated snow spectra are in error 
by up to 6%, depending on grain size and degree of cementation.  We have also 
developed an improved scattering model to explain the differences (Wald, 1994).  
As might be expected, our measurement of the spectrum of smooth ice agrees 
with that calculated from the Fresnel equations.

	BRDF data:  Directional reflectance and emittance for frost and snow have 
been calculated with the same models used to calculate spectra.  Again, the 
Dozier and Warren (1982) model appears accurate in the VNIR and SWIR, and 
we find little difference between the results of their model and that of Wald (1994) 
for loose snow grains, which have Lambertian-type behavior at all wavelengths.  
Crusted snow, however, has a very strong specular component in the thermal 
infrared, as discussed more fully below.  Smooth, clear ice, of course, is specular 
at all wavelengths.


FROST, SNOW AND ICE

	Spectral data:  Our thermal infrared directional hemispherical reflectance 
measurements of frost and snow (Salisbury et al., 1994) were matched at 2.0 µm 
with VNIR/SWIR spectra calculated using the Dozier and Warren (1982) delta 
Eddington model.  The grain size of our frost is not given, and our snow spectra 
are labeled simply "fine", "medium granular", and "coarse granular".  Precise 
grain sizes are not given because, as explained more fully in Salisbury et al. 
(1994), and Wald (1994), grain shape, size range, and cementation effects make 
a single grain size description misleading.  However, the VNIR/SWIR delta 
Eddington calculation uses a single grain size.  The single "effective" grain size 
that matched the reflectance of our measured samples at 2.0 µm wavelength was 
10 µm for the frost, 24 µm for the fine snow, 82 µm for the medium granular 
snow, and 178 µm for the coarse granular snow.  The physical grain size of the 
granular snow was much larger under the microscope, averaging about 400 µm 
and 1500 µm for the medium and coarse granular, respectively.  The optical grain 
size was much smaller, because this is a function of the abundance and size 
range of scattering centers within grains (at least in the VNIR/SWIR, where the 
grains are relatively transparent), such as air bubbles or internal grain 
boundaries.

The spectrum for ice was calculated using the Fresnel equations.  Although our 
measured spectrum was very close to that calculated in the thermal infrared 
(Salisbury et al., 1994), the slight surface imperfections of our ice would become 
more and more significant scattering centers with decreasing wavelength.  
Hence, the Fresnel calculation was used for the generic ice spectrum.  

	Caveat:  As is typical for aged snow, our medium and coarse granular 
snow grains are cemented into a crust, which introduces a strong specular 
reflectance component in the thermal infrared, as discussed briefly above.   In 
fact, we find that as snow ages and grains become larger and more completely 
cemented together into a continuous crust, snow approaches the spectral and 
directional behavior of ice in the thermal infrared.  It should be noted here that, 
just as crusted snow resembles ice in its spectral and BRDF behavior in the 
thermal infrared, ice tends to resemble coarse, crusted snow in the VNIR/SWIR.  
That is, smooth, clear ice has an extremely low reflectance in the VNIR/SWIR,  
forming what is called "black ice", which is rare.  Natural ice typically has some 
snow on its surface, and/or the surface is rough, and its interior contains grain 
boundaries and air bubbles.  The presence of these scattering centers results in 
strong diffuse scattering, especially in the VNIR.  As the wavelength increases 
beyond the scale of these scattering enters, and predominantly volume scattering 
is replaced by surface scattering, the BRDF changes from largely diffuse in the 
VNIR/SWIR to largely specular in the thermal infrared.  Thus, an analyst should 
not use the spectral and scattering characteristics of smooth ice for an ice-
covered surface in the VNIR/SWIR, except under unusual (black ice) 
circumstances.  Most ice has the spectral and BRDF properties of our coarse, 
granular, crusted snow in both reflectance and emittance.

Both frost and fresh, fine snow should be Lambertian at all wavelengths, just as 
smooth, clear ice should be specular at all wavelengths.  Aged, crusted snow 
should be predominantly Lambertian in the VNIR/SWIR and predominantly 
specular in the thermal infrared.



REFERENCES


Dozier, J., and Warren, S. G., 1982, Effect of viewing angle on the infrared 
brightness temperature of snow: Water resources Research,, v. 18, p. 1424-
1434.

Salisbury, J. W. and D'Aria, D. M., 1992, Emissivity of terrestrial materials in the 
8-14 µm atmospheric window:  Remote Sensing of Environment, v. 42, p. 83-106.

Salisbury, J. W., D'Aria, D. M., and Wald, A. E., 1994, Measurements of thermal 
infrared spectral reflectance of frost, snow, and ice: Jour. of Geophysical 
Research, v. 99, p. 24,235-24,240.

Wald, A. E., 1994, Modeling thermal infrared (2-14 µm) reflectance of frost and 
snow: Jour. of Geophysical Research, v. 99, p. 24,241-24,250. 

Warren, S. G., T. C. Grenfell, and P. C. Mullen, 1986, Optical properties of 
Antarctic snow, Antarctic Journal of the United States, v.21, p. 247-248