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Keywords:

  • MODIS;
  • aerosol;
  • black carbon;
  • dust;
  • radiative forcing;
  • snow

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Background
  5. 3. Data and Methods
  6. 4. Validation
  7. 5. Results
  8. 6. Summary and Discussion
  9. Acknowledgments
  10. References
  11. Supporting Information

[1] The episodic deposition of dust and carbonaceous particles to snow decreases snow surface albedo and enhances absorption of solar radiation, leading to accelerated snowmelt, negative glacier mass balance, and the snow-albedo feedback. Until now, no remote sensing retrieval has captured the spatial and temporal variability of this forcing. Here we present the MODIS Dust Radiative Forcing in Snow (MODDRFS) model that retrieves surface radiative forcing by light absorbing impurities in snow cover from Moderate Resolution Imaging Spectroradiometer (MODIS) surface reflectance data. Validation of MODDRFS with a 7-year record of in situ measurements indicates the radiative forcing retrieval has positive bias at lower values and slight negative bias above 200 W m−2, subject to mixed pixel uncertainties. With bias-correction, MODDRFS has a root mean squared error of 32 W m−2 and mean absolute error of 25 W m−2. We demonstrate MODDRFS in the Upper Colorado River Basin and Hindu Kush-Himalaya.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Background
  5. 3. Data and Methods
  6. 4. Validation
  7. 5. Results
  8. 6. Summary and Discussion
  9. Acknowledgments
  10. References
  11. Supporting Information

[2] Mountain snowmelt dominates the fresh water supply to more than 1/6 of Earth's human population [Barnett et al., 2005]. While much effort has been spent on understanding the impacts of anthropogenic climate change on snowmelt [Howat and Tulaczyk, 2005; Mote et al., 2005], recent in situ observations and modeling show that surface radiative forcing of snow and glacier melt by light absorbing impurities (LAI) such as dust and carbonaceous particles also markedly accelerates snowmelt and modifies regional water cycles [Hansen and Nazarenko, 2004; Painter et al., 2007; Flanner et al., 2009; Qian et al., 2009; Painter et al., 2010].

[3] In the Upper Colorado River Basin, USA, detailed energy balance and radiation measurements show that surface radiative forcing by desert dust from the Colorado Plateau shortens snow cover duration by 25–50 days [Painter et al., 2007; Skiles et al., 2012]. Dust loading there has increased five to seven-fold since the Anglo-settlement of the western US in the mid-1800s [Neff et al., 2008]. Extrapolating these point measurements to the entire upper basin suggests that this increase in dust loading and reduction in snow albedo from the earlier background load has brought peak runoff three weeks earlier and caused a loss of 5% in total annual runoff [Painter et al., 2010].

[4] Growing point observations and modeling simulations also suggest that increasing LAI deposition to snow in the Hindu Kush-Himalaya may be leading to accelerated snowmelt and glacier retreat [Ramanathan et al., 2007; Kaspari et al., 2009]. In the eastern Himalaya, dust loading to mountain snow increased four-fold since the mid 19th century [Thompson et al., 2000] and black carbon loading to snow increased three-fold since the 1970s [Kaspari et al., 2011]. These results, along with studies of the damaging health impacts of black carbon and other industrial pollutants, have led to recent calls for reductions in emissions from the United Nations Environmental Programme [2011]and the US Department of State's initiation of the Climate and Clean Air Coalition to Reduce Short-Lived Climate Pollutants. However, all of these studies of radiative impacts of LAI in snow or ice have derived from or been constrained by starkly limited in situ measurements because we have lacked remote sensing measurements of radiative forcing by LAI in snow and installation and maintenance of in situ infrastructure is extremely difficult in these harsh and dangerous environments. To address this void in our knowledge, we have developed the MODIS Dust Radiative Forcing in Snow (MODDRFS) model to retrieve radiative forcing by LAI in snow cover.

2. Background

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Background
  5. 3. Data and Methods
  6. 4. Validation
  7. 5. Results
  8. 6. Summary and Discussion
  9. Acknowledgments
  10. References
  11. Supporting Information

[5] Snow without absorbing impurities has the highest albedo of any naturally occurring Earth surface. The spectral albedo of pure snow (αpure) is sensitive to changes in snow optical grain radius (OGR) and the solar zenith angle for direct beam solar radiation (Figure 1). As grain size increases, spectral albedo drops primarily in the near infrared and shortwave infrared where the imaginary part of the complex index of refraction for ice is orders of magnitude greater than in the visible portion [Wiscombe and Warren, 1980]. As solar zenith angle increases, forward single scattering becomes more dominant thus increasing spectral albedo.

image

Figure 1. (a) Snow albedo variation with grain size. (b) NDGSI for MODIS data with sensitivity to solar zenith angle. (c) Snow albedo variation with dust concentration. (d) Same as Figure 1c, but with MODIS bandpasses indicated in transparent wavelengths and parts of spectrum not sampled by black-obscured wavelengths.

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[6] When impurities such as dust or carbonaceous particles are present however, snow albedo decreases primarily in the visible wavelengths (VIS) with the reduction occurring at longer wavelengths as concentration and/or absorption increases (Figure 1c) [Singh et al., 2010; Brandt et al., 2011]. This albedo drop results from the contrast of the imaginary part of the complex refractive index for the light absorbing particles with that of the highly transparent ice [Warren and Wiscombe, 1980]. Our experience suggests that the aeolian deposition of LAI to snow does not accumulate to the degree that the spectral reflectance of the surface shifts from snow to soil (see Skiles et al. [2012] for LAI concentrations in the UCRB). We hypothesize (but do not test here) that such a shift occurs only from rock fall or in glacier moraines from glacial transport.

[7] Radiative forcing by LAI in snow is considered in terms of its direct effect and two feedbacks [Hansen and Nazarenko, 2004], with further definition of at-surface or at-tropopause.In this work, we retrieve at-surface radiative forcing. The direct effect comes from the enhanced absorption of solar irradiance by the LAI themselves, primarily in the VIS and NIR. The first feedback comes from the enhanced absorption by larger grain size due to accelerated snow grain growth driven by the direct effect. This affects the entire spectrum by reinforcing the direct absorption in the VIS and increasing the absorption in the NIR through shortwave infrared by the larger absorbing path length. Finally, the second feedback comes from the enhanced absorption of solar irradiance by the usually darker substrate (i.e. soil, rock, and/or vegetation), exposed earlier due to the direct and first feedback.

[8] Radiative forcing by LAI in snow and the ability to quantify it with optical remote sensing come from two physical properties: (i) larger particles (greater than ∼5.0 μm) tend to accumulate near the snow surface as ablation advances [Conway et al., 1996], and (ii) transported LAI arrive and concentrate during late winter and spring when solar irradiance is increasing and most of the seasonal snow accumulation has occurred [Wake and Mayewski, 1994; Kaspari et al., 2009]. The LAI therefore often lie near the surface where they can absorb solar radiation and immediately conduct that energy to surrounding snow grains [Painter et al., 2012].

3. Data and Methods

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Background
  5. 3. Data and Methods
  6. 4. Validation
  7. 5. Results
  8. 6. Summary and Discussion
  9. Acknowledgments
  10. References
  11. Supporting Information

[9] MODIS data have enabled the analysis of snow properties beyond snow covered area (SCA) because its radiometric range in the VIS does not saturate at the large radiances from snow. Other multi-spectral sensors such as the pre-Landsat-8 Thematic Mappers and the NASA Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) saturate at reflectances usually less than 50% in the VIS, leaving the impact of LAI unknowable. Fortunately, the dynamic range in the VIS bands of the Operational Line Imager (OLI) on Landsat-8 should not saturate over snow, thereby enabling frequent rigorous validation of the MODDRFS product. The location and dynamic range of MODIS band passes enables the detection of changes in absorption in the VIS and changes in grain size expressed in the NIR/SWIR (Figure 1d).

3.1. MODDRFS

[10] The MODDRFS algorithm infers per-pixel radiative forcing by LAI in snow using MODIS surface reflectance data (Terra MODIS MOD09GA, Aqua MODIS MYD09GA; we speak to MOD09GA only for brevity) and a coupled radiative transfer model for snow. MODDRFS determines the spectral reflectance differences between the measured MODIS spectrum and the modeled clean snow spectrum of the same OGR. Integration of the band-wise multiplication of this spectral difference with local spectral irradiance that accounts for terrain variations gives the instantaneous at-surface radiative forcing (W m−2).

[11] MODDRFS first determines those pixels that can provide more robust retrievals (relatively free of mixing) from the MODIS Snow Covered Area and Grainsize (MODSCAG) fractional snow and vegetation products [Painter et al., 2009]. MODSCAG finds maximal snow cover in winter/spring from a time series approach, from which we determine the per-pixel potential for complete cover. Among those pixels, we then use each acquisition's retrievals of fractional vegetation to remove those pixels that have a mixed cover of vegetation that has been exposed since maximum cover. We do not take this step for the mixed cover of rock because it would be confused with and remove pixels impacted by LAI (which introduces error -section 5.2 below).

[12] As with the spectral albedo of snow, the spectral hemispherical-directional reflectance factor (HDRF [Schaepman-Strub et al., 2006] – the MOD09GA retrieval) of snow also varies with grain size (Figure 1). We estimate the OGR and identify the clean snow HDRF through the normalized difference grain size index (NDGSI):

  • display math

where MODIS2 is the MOD09GA surface reflectance in MODIS band 2 (band center ∼0.858 μm) and MODIS5 is the MOD09GA surface reflectance in MODIS band 5 (band center ∼1.240 μm) (Figure 1d). NDGSI has a logarithmic relationship with OGR due to the decreasing changes in HDRF with increases in OGR, and is sensitive to solar zenith angle (SZA) (Figure 1b). From the OGR, we determine the clean snow spectrum for the same OGR and SZA with the discrete ordinates solution to the radiative transfer equation. The description of these clean snow spectra is given in the auxiliary material.

[13] We use the Santa Barbara DISORT Atmospheric Radiative Transfer (SBDART) model in conjunction with the 3 arc second Shuttle Radar Topography Mission (SRTM) digital elevation model (DEM) to estimate per-pixel clear sky incident spectral irradiance. The University of Wisconsin's MODIS Terra overpass predictor (http://eosweb.ssec.wisc.edu/) was used to determine the time of acquisition and solar ephemeris. Direct and diffuse spectral irradiance are first modeled in SBDART for a range of SZA and elevation bands. Incident spectral irradiances are then determined at 1/5th MODIS pixel spatial resolution and up-scaled to obtain the mean per-MODIS pixel irradiance spectrum. Per-pixel terrain slope and aspect give the plane to which we correct the direct component of level-surface solar irradiance according to the following relationship:

  • display math

where β is the local solar zenith angle, θs is the solar zenith angle for a level surface, ϕs is the solar azimuth angle, θn is the surface slope, and ϕnis the surface aspect. We then determine corrected per-pixel solar spectral irradiances,Ecorrected,λ, according to:

  • display math

where Edirect and Ediffuseare the direct and diffuse spectral irradiances. This calculation assumes that the diffuse and terrain-scattered irradiances are identical. It is valid to first order and ameliorates the need for a complex, intensive topographic treatment for this global product.

[14] Because MODIS does not measure the entire hemisphere-reflected flux, we must use the modeled understanding of the relationship between the MODIS-derived spectral HDRF and hemispherical spectral albedos [Schaepman-Strub et al., 2006]. Here we use scalars, c, between the directional reflectance spectrum at the observation geometry, R, and the spectral albedo for the same irradiance geometry:

  • display math

where λ denotes the wavelength, θ0 and θr the solar and viewing zenith angles, ϕr the relative azimuth and ζatm the atmospheric properties.

[15] Because of the lack of spectral continuity in the MODIS spectrum we do not know the wavelength at which the measured and modeled clean spectra diverge (Figure 1c). To account for this, the measured spectrum is fit to the clean spectrum at MODIS2 (band center wavelength ∼0.858 μm and upper end ∼0.876 μm) and we determine the radiative forcing for the wavelength range down to 0.35 μm. Moreover, because of the discrete bands, we model the irradiances and spline albedos to a continuous spectrum of 0.01 μm bands across the range 0.350–0.876 μm. We then retrieve the radiative forcing estimate, F, from the following:

  • display math

where Ecorrected, λ is the corrected irradiance, αclean, λ is the clean snow spectral albedo of the MODIS OGR, αMODIS, λ is the spectral albedo of the MODIS pixel, and Δλ is 0.01 μm. The retrieved radiative forcings are then instantaneous values and not daily averages convolved with the diurnal cycle of irradiances.

4. Validation

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Background
  5. 3. Data and Methods
  6. 4. Validation
  7. 5. Results
  8. 6. Summary and Discussion
  9. Acknowledgments
  10. References
  11. Supporting Information

[16] Validation of MODDRFS, and any other future remote sensing retrievals of surface radiative forcing by LAI, is limited by a relative paucity of in situ data. The only in situ temporally extensive measurements of radiative forcing by LAI of which we are aware come from the Western Energy Balance of Snow (WEBS) network of energy balance and radiation towers operated by collaborators and the lead author in the Colorado River Basin. This network consists of heavily instrumented towers in snow-covered regions to facilitate modeling of the energy balance and melt of snow cover, and LAI radiative forcing in the snow cover. These unique measurements have provided important insights into the controls on snowmelt by LAI radiative forcing [Painter et al., 2007] and their impact on runoff timing and loss of volume [Painter et al., 2010, 2012; Skiles et al., 2012].

[17] We validate the instantaneous MODDRFS against the coincident in situ surface radiative forcing data from two WEBS stations (alpine and subalpine) in the Senator Beck Basin Study Area (SBBSA), San Juan Mountains in the Upper Colorado River Basin (37° 54′ 30″ N, 107° 43′ 30″ W). In addition to standard measurements of meteorology (air temperature, wind speed, relative humidity, all at two heights), the towers measure incident and reflected broadband solar radiation and incident and reflected NIR/SWIR solar radiation [Painter et al., 2012]. From the radiation measurements, we determine hourly LAI radiative forcing from the relationships described in Painter et al. [2007]. We choose the coincident in situ hourly data in which the MODIS acquisition falls.

[18] We assess only MODDRFS/MODIS data with sensor zenith angles <30° over the alpine and sub-alpine energy balance towers in SBBSA. At larger sensor zenith angles, the ground instantaneous field of view expands well beyond that at nadir and spatial mixing becomes severe [Dozier et al., 2008], rendering the MODDRFS retrieval unreliable. The spectral range that MODDRFS infers surface radiative forcing (0.350–0.876 μm) does not perfectly align with that of the energy balance towers (0.305–0.780 μm). Part of the MODDRFS error described below comes from this difference.

5. Results

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Background
  5. 3. Data and Methods
  6. 4. Validation
  7. 5. Results
  8. 6. Summary and Discussion
  9. Acknowledgments
  10. References
  11. Supporting Information

[19] We show MODDRFS for the Hindu Kush-Himalaya (HKH) in Asia on 21 June 2010 (Figures 2a and S1a) and the Upper Colorado River Basin, USA on 18 May 2009 (Figures 2b and S1b). These example retrievals indicate that gradients occur in radiative forcing across regional and finer scales.

image

Figure 2. (a) Dust radiative forcing in snow for Hindu Kush-Himalaya on 21 June 2010 at time of MODIS overpass, ∼05:40 UTC. (b) Dust radiative forcing in snow for eastern half of the Upper Colorado River Basin on 18 May 2009 at time of MODIS overpass, ∼17:55 UTC.

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[20] In the HKH, south and western ranges have higher forcings reaching >200 W m−2, most likely due to their exposure to transport of LAI from the deserts of the Middle East, Asia and North Africa, and industrial regions in Pakistan and India (Figure 2a). Within individual ranges, the most distinctive gradient is the decrease in forcing with increasing elevation. However, it is important to note that MODIS only provides the capacity to retrieve a daily snapshot of forcing. As snowmelt advances, dust layers may emerge at higher elevations and affect similar radiative forcings to those observed earlier at lower elevations.

[21] In the Upper Colorado River Basin, regional gradients are also revealed with variations that are likewise sensitive to the mountain proximity to sources of LAI. In the southern box in Figure 2 (San Juan Mountains, CO), closest to the dust source regions of the Colorado Plateau, radiative forcing by LAI is relatively constant across the domain with a mean forcing of ∼250 W m−2. In the central box (Elk Range to Front Range, CO), greater spatial variability is expressed with a range of forcings from 250 W m−2 in the southwest to ∼100 W m−2 in the northeast, most remote from the dust source regions. The northwest part of the Upper Colorado shows the most pronounced spatial variation. From the 30–70 W m−2 in the Wind River range in the southeast part of this subregion to 200 W m−2 in the plateaus west of Yellowstone Lake in the northwest part. This latter region is downwind of dust producing regions of the Snake River Plain, Idaho.

[22] Figure 3 shows the validation of MODDRFS based on data from 2005–2011. At the subalpine site, the root mean squared error (RMSE) for MODDRFS against Ftower was 39 W m−2, with mean absolute error (MAE) of 22 W m−2, and mean error of +8 W m−2. The errors show a positive MODDRFS bias at lower Ftower easing to a smaller magnitude negative bias at higher Ftower. The linear least squares fit of MODDRFS and F data is MODDRFS = β1 Ftower + β0, where β1 = 0.72 ± 0.15 (95% confidence interval) and β0 = 31.9 ± 19.3 with an R2 of 0.83. To 95% confidence, β1 and β0 are different from 1.0 and 0.0, respectively.

image

Figure 3. Validation of MODDRFS retrieved F with in situ estimated F from Swamp Angel Study Plot and Senator Beck Study Plot, Colorado across 2005 through 2011.

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[23] At the alpine site, the RMSE for MODDRFS against Ftower was 36 W m−2, with a MAE of 26 W m−2, and mean error of +7 W m−2. As with the subalpine site, MODDRFS overestimates radiative forcing at lower Ftower and slightly underestimates at the higher Ftower. The least squares fit to the MODDRFS and Ftower data has β1 = 0.67 ± 0.17 and β0 = 36.9 ± 21.1 with an R2 of 0.86. Again, to 95% confidence, β1 and β0 are different from 1.0 and 0.0, respectively.

[24] For these data combined, the linear least squares regression has RMSE of 33 W m−2, with a MAE of 28 W m−2, and mean error of 10 W m−2. The regression yields coefficients of β1 = 0.75 ± 0.11 and β0 = 31.2 ± 14.4 with an R2 of 0.86 (Figure 3). In all cases, MODDRFS has a positive bias at lower Ftower and slightly negative bias at higher Ftower.

5.1. Bias Correction

[25] The assessments of MODDRFS at the sub-alpine and alpine towers are consistent in magnitude of errors and in their biased relationships within the uncertainties of 95% confidence intervals (Figure 3). Given the relatively high R2, we can assess a correction of the bias to provide more robust results calibrated from the towers. We force the fit to a slope of 1.0 and intercept of 0.0 based on the energy balance data. We fully recognize that this relationship is specific to the WEBS towers in the San Juan Mountains, USA, and is thus regionally specific. Nevertheless, these are the only viable measurements globally for such purpose and thus we proceed cautiously. The final bias-corrected MODDRFS retrieval is:

  • display math

The RMSE for the bias-corrected MODDRFS retrievals is 32 W m−2, MAE is 25 W m−2, but by definition the mean error is 0.0 W m−2. Taken piecewise, errors in raw and bias-corrected MODDRFS retrievals are both sensitive to magnitude of forcing (Figure 3). For the radiative forcing range 0–100 W m−2 at the towers, the RMSE for uncorrected MODDRFS is 37 W m−2and for bias-corrected is 29 W m−2. In the range 100–200 W m−2, the RMSE for uncorrected and bias-corrected are 23 and 24 W m−2, respectively. The errors rise again in the range 200–300 W m−2 to 38 and 34 W m−2, respectively. Note that the MODDRFS algorithm determines radiative forcing whereas it is not designed to invert for LAI concentration. However, subsequent work can use assumptions of the spectral complex refractive index of the LAI to invert the MODDRFS retrievals for an effective concentration. These retrievals will be highly uncertain however.

5.2. Uncertainties

[26] Uncertainties in the MODDRFS retrieval are driven by the sensor properties, atmospheric correction, snow geographic and geomorphological properties, and subpixel terrain heterogeneity. The discrete and variably spaced bands of MODIS prevent continuous measurement of a continuously variable forcing like that which LAI impart to snow albedo. Therefore, this retrieval is semi-quantitative whereas a spectrometer with contiguous bands across the spectrum allows the more quantitative retrieval. The uncertainty of the retrieval of MOD09GA over snow and its ability to discriminate aerosols from those in snow during deposition events have not been assessed. Implicit in MODDRFS is that MOD09GA robustly corrects for aerosols but this should be evaluated in further work to determine this impact.

[27] The nominal footprint of MODIS at nadir is ∼463 m but as sensor zenith angle increases so does the area of observation. By the edge of the MODIS scan, the GIFOV reaches 10 times that of nadir [Dozier et al., 2008]. The point spread function further results in overlap at nadir between adjacent observations such that 25% of the signal is from adjacent areas, while only 75% comes from the nominal area [Tan et al., 2006].

[28] Even at the nominal ∼463 m footprint, spatial heterogeneity of mountain snow cover makes it rare to find complete snow cover without exposure of some rock, soil, and/or vegetation. Furthermore, geolocation uncertainty of the MODIS grid (∼half a pixel for the tiled products - [Wolfe et al., 2002]) can lead to ambiguous comparisons between varying mixtures in MODIS pixels and the corresponding point measurement. In future implementations, we will use the MODDRFS retrievals to feed back on the MODSCAG fractional retrievals for LAI-affected end-members to reduce this uncertainty. Finally, surface roughness of the snow surface (e.g. sastrugi) can modify the HDRF of the snow surface to appear darker in the visible wavelengths than a level or even known surface gradient to the degree that a DEM characterizes this gradient. As such, application of MODDRFS to polar regions where sastrugi occupy vast areas, SZA are large, and LAI concentrations are low should be treated cautiously or not at all.

6. Summary and Discussion

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Background
  5. 3. Data and Methods
  6. 4. Validation
  7. 5. Results
  8. 6. Summary and Discussion
  9. Acknowledgments
  10. References
  11. Supporting Information

[29] Scientists, policy makers, and resource managers are increasingly aware of the potential impacts of radiative forcing by LAI in snow and ice relative to glacier mass balance, regional hydrology, and climate. MODDRFS reduces a critical void in our knowledge of the spatial and temporal variations of radiative forcing by LAI around the globe. MODIS' spectral and spatial samplings, coupled with its greater radiometric dynamic range, facilitate this semi-quantitative retrieval not available from its predecessor (AVHRR, Landsat Thematic Mappers) or contemporary (ASTER) spaceborne imagers. MODDRFS is the first regularly produced retrieval of radiative forcing by LAI in snow and is currently being distributed for the western United States and Hindu Kush through Himalaya via the JPL Snow Data Server (http://snow.jpl.nasa.gov/). We are now working on the details of leveraging the instantaneous MODIS retrieval with geostationary retrievals of diurnal at-surface irradiances to generate daily mean radiative forcings by LAI.

[30] Looking forward, more robust quantitative retrieval will come from spaceborne imaging spectrometers such as the NASA Decadal Survey Hyperspectral Infrared Imager (HyspIRI). Its spectral sampling will allow continuous measurement across the spectrum and its 60 m spatial sampling will allow unambiguous retrievals in homogeneous snow.

Acknowledgments

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Background
  5. 3. Data and Methods
  6. 4. Validation
  7. 5. Results
  8. 6. Summary and Discussion
  9. Acknowledgments
  10. References
  11. Supporting Information

[31] This work was funded by NSF grant ATM04323237 and NASA projects NNX10A097G and NNX09A038HS01. Part of this work was performed at the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA.

[32] The Editor thanks Stephen Warren and an anonymous reviewer for their assistance in evaluating this paper.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Background
  5. 3. Data and Methods
  6. 4. Validation
  7. 5. Results
  8. 6. Summary and Discussion
  9. Acknowledgments
  10. References
  11. Supporting Information

Supporting Information

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Background
  5. 3. Data and Methods
  6. 4. Validation
  7. 5. Results
  8. 6. Summary and Discussion
  9. Acknowledgments
  10. References
  11. Supporting Information

Auxiliary material for this article contains a description of DISORT modeling of clean snow hemispherical-directional reflectance factors and albedos and figures showing MODIS color composites.

Auxiliary material files may require downloading to a local drive depending on platform, browser, configuration, and size. To open auxiliary materials in a browser, click on the label. To download, Right-click and select “Save Target As…” (PC) or CTRL-click and select “Download Link to Disk” (Mac).

Additional file information is provided in the readme.txt.

FilenameFormatSizeDescription
grl29420-sup-0001-readme.txtplain text document1Kreadme.txt
grl29420-sup-0002-txts01.pdfPDF document84KText S1. DISORT modeling of clean snow hemispherical-directional reflectance factors and albedos.
grl29420-sup-0003-fs01.jpgJPEG image1975KFigure S1. MODIS color composite of the Hindu-Kush through Himalaya area of interest.
grl29420-sup-0004-fs02.jpgJPEG image875KFigure S2. MODIS color composite of the Upper Colorado River Basin area of interest.

Please note: Wiley Blackwell is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.