Supplementary Figure 1
MODIS true-color images over western Himalayas (left column); Aerosol Optical Depth (middle
column); and MODIS surface reflectance for western Himalayas (right column) on 27 May 2003
(top panel), 9-10 June 2003 (middle panel) and 15 June 2003 (bottom panel).
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Supplementary Figure 2
MODIS spectral surface reflectance (left) and Top-Of-Atmosphere (TOA) reflectance (right)
over the western Himalayan snow cover is shown for three 5-day averaged periods: 1-5 June, 610 June and 11-15 June. The gradient between wavelengths 0.47μm and 0.86μm (VIS-NIR) is
observed for both surface and TOA reflectance. Note, in addition to aerosol extinction, the TOA
reflectance is affected by other atmospheric effects such as Rayleigh scattering (particularly at
the shorter wavelength, i.e. 0.47μm) and gaseous absorption.
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Supplementary Figure 3
Mass Absorption Coefficient (top panel) and Single Scattering Albedo (bottom panel) of the
input dust model averaged for four size bins (0.1 – 1.0μm; 1.0 – 2.5μm; 2.5 – 5.0μm; 5.010.0μm). Symbols denote the MODIS wavelengths at 0.47μm, 0.55μm, 0.65μm and 0.86μm.
(Dust optical properties database provided by Mark Flanner and Charles Zender).
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Snow Reflectance Model
The snow reflectance model, various inputs and sensitivity study shown in the paper (section 3.2,
Fig. 3) are summarized here, while the relevant details can be found in [Kokhanovsky and Zege,
2004; Kokhanovsky et al., 2011; Kokhanovsky and Breon, 2012]. For snow reflectance
simulations, (and mixed with impurity), we use the analytical bidirectional reflectance
distribution function (BRDF) model of snow reflectance [Kokhanovsky et al., 2011;
Kokhanovsky and Breon, 2012], which is a two-parameter model that accounts for sensitivity to
snow grain size and impurity in snow. Specifically, this model is suited for applications to
multispectral remote sensing such that it computes directional reflectance of snow as a function
of snow grain size, impurity and sun-satellite geometry. This model has been effectively applied
for various snow types over the Himalayan basin to retrieve snow grain size and albedo using
multi-spectral band methods [Negi and Kokhanovsky, 2011]. In general, snow cover is close to a
lambertian surface, however, it does exhibit directional characteristic of reflectance and therefore
this snow BRDF model allows us to compute the reflectance observed by satellite (in a
directional sense, which is important for remote sensing applications).
The model is described in the following notation [Kokhanovsky and Breon, 2012]:
where,
- γ= 4π(χ + M)/λ, χ is the imaginary part of ice refractive index, λ is the wavelength.
- the value of L is approximately equal to 13d, where d is the average optical diameter of snow
grains and M is directly proportional to the mass concentration of pollutants in snow.
- “θ” is the scattering angle given in degrees.
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- R is the Reflection function (R = πL/μsFo), widely used in the remote sensing community. ‘L’ is
the radiance, μs=cos(θs), and Fo is the incident solar flux.
- Imaginary part of refractive index (spectral) of ice is obtained from Warren and Brandt (2008),
for the wavelengths 0.47μm, 0.55μm, 0.65μm, 0.86μm, 1.2μm, 1.6μm, 2.1μm.
- Imaginary part of refractive index for contaminated snow (ice mixed with impurity) is
indirectly obtained by the “total absorption coefficient (kall)”, based on the formulation described
in Yasunari et al., 2011. Once we have kall, we obtain the “net” imaginary part of refractive index
(mi) from the general approximation of ice volume absorption coefficient [Wiscombe and
Warren, 1980]:
k = 4πmi/λ
- The input mass concentrations of dust deposition for the Himalayas are not available in the
literature, so we used similar range of measurement-based estimates of dust deposition
(100ppmw to 600ppmw) in snowpack in a Japanese urban location [Aoki et al., 2011; Yasunari et
al., 2011], to qualitatively perform sensitivity calculations.
- Sun-Satellite Geometry: For the particular sensitivity simulation shown in the main part of the
paper (section 3.2, Fig. 3), we use the following sun-satellite geometry inputs with Solar Zenith
Angle (SZA)=30°; View Zenith Angle=20°; Relative Azimuth Angle (RAA)=140°. Note, the
value of SZA is typical for the Himalayan region during May-June, while the RAA was selected
to be larger than 40° to avoid errors at angles near the backscattering geometry [Lyapustin et al.,
2009].
- For sensitivity simulations of dust impurity in snow, spectral Mass Absorption Coefficients of
dust (shown in supplementary figure 2), averaged for four size bins (0.1 – 1.0μm; 1.0 – 2.5μm;
2.5 – 5.0μm; 5.0-10.0μm), is used in the formulation described in Yasunari et al. 2011, which are
then used to obtain the total absorption coefficient of dust-contaminated snow. The dust optical
properties database is provided by Mark Flanner and Charles Zender.
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