• Adam, J., , and Lettenmaier D. , 2003: Adjustment of global gridded precipitation for systematic bias. J. Geophys. Res., 108, 4257, doi:10.1029/2002JD002499.

    • Search Google Scholar
    • Export Citation
  • Adler, R., , Kidd C. , , Petty G. , , Morissey M. , , and Goodman H. , 2001: Intercomparison of global precipitation products: The Third Precipitation Intercomparison Project (PIP–3). Bull. Amer. Meteor. Soc., 82, 13771396.

    • Search Google Scholar
    • Export Citation
  • Anderson, E., 1976: A point energy and mass balance model of a snow cover. NOAA Tech. Rep. NWS HYDRO-17 NWS 19, 150 pp.

  • Andreadis, K. M., , Liang D. , , Tsang L. , , Lettenmaier D. P. , , and Josberger E. G. , 2008a: Characterization of errors in a coupled snow hydrology–microwave emission model. J. Hydrometeor., 9, 149164.

    • Search Google Scholar
    • Export Citation
  • Andreadis, K. M., , Storck P. , , and Lettenmaier D. P. , 2008b: Modeling snow accumulation and ablation processes in forested environments. Water Resour. Res., 45, W05429, doi:10.1029/2008WR007042.

    • Search Google Scholar
    • Export Citation
  • Armstrong, R., , and Brodzik M. , 2002: Hemispheric-scale comparison and evaluation of passive-microwave snow algorithms. Ann. Glaciol., 34, 3844.

    • Search Google Scholar
    • Export Citation
  • Armstrong, R., , Knowles K. , , Brodzik M. , , and Hardman M. , 2003: DMSP SSM/I Pathfinder daily EASE-grid brightness temperatures. National Snow and Ice Data Center, Boulder, CO, digital media. [Available online at http://nsidc.org/data/docs/daac/nsidc0032_ssmi_ease_tbs.gd.html.]

  • Bartelt, P., , and Lehning M. , 2002: A physical SNOWPACK model for the Swiss avalanche warning: Part I: Numerical model. Cold Reg. Sci. Technol., 35, 123145.

    • Search Google Scholar
    • Export Citation
  • Boone, A., , and Etchevers P. , 2001: An intercomparison of three snow schemes of varying complexity coupled to the same land surface model: Local-scale evaluation at an alpine site. J. Hydrometeor., 2, 374394.

    • Search Google Scholar
    • Export Citation
  • Bowling, L. C., , Pomeroy J. W. , , and Lettenmaier D. P. , 2004: Parameterization of blowing-snow sublimation in a macroscale hydrology model. J. Hydrometeor., 5, 745762.

    • Search Google Scholar
    • Export Citation
  • Brun, E., 1989: Investigation on wet-snow metamorphism in respect of liquid-water content. Ann. Glaciol., 13, 2226.

  • Brun, E., , Martin E. , , Simon V. , , Gendre C. , , and Coléou C. , 1989: An energy and mass model of snow cover suitable for operational avalanche forecasting. J. Glaciol., 35, 333342.

    • Search Google Scholar
    • Export Citation
  • Chang, A., , Foster J. , , and Hall D. , 1987: Nimbus-7 SMMR derived global snow cover parameters. Ann. Glaciol., 9, 3944.

  • Cherkauer, K. A., , and Lettenmaier D. P. , 2003: Simulation of spatial variability in snow and frozen soil. J. Geophys. Res., 108, 8858, doi:10.1029/2003JD003575.

    • Search Google Scholar
    • Export Citation
  • Cohen, J., , and Entekhabi D. , 1999: Eurasian snow cover variability and northern hemisphere climate predictability. Geophys. Res. Lett., 26, 345348.

    • Search Google Scholar
    • Export Citation
  • Colbeck, S., 1991: The layered character of snow covers. Rev. Geophys., 29, 8196.

  • Colbeck, S., 1993: The vapor diffusion coefficient for snow. Water Resour. Res., 29, 109109.

  • Dennis, J. E., Jr., , and Schnable R. B. , 1983: Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice-Hall, 394 pp.

  • Derksen, C., , Walker A. , , and Goodison B. , 2003: A comparison of 18 winter seasons of in situ and passive microwave-derived snow water equivalent estimates in Western Canada. Remote Sens. Environ., 88, 271282.

    • Search Google Scholar
    • Export Citation
  • Derksen, C., , Walker A. , , and Goodison B. , 2005: Evaluation of passive microwave snow water equivalent retrievals across the boreal forest/tundra transition of western Canada. Remote Sens. Environ., 96 (3–4), 315327.

    • Search Google Scholar
    • Export Citation
  • Derksen, C., , Silis A. , , Sturm M. , , Holmgren J. , , Liston G. , , Huntington H. , , and Solie D. , 2009: Northwest Territories and Nunavut snow characteristics from a subarctic traverse: Implications for passive microwave remote sensing. J. Hydrometeor., 10, 448463.

    • Search Google Scholar
    • Export Citation
  • Dong, J., , Walker J. , , and Houser P. , 2005: Factors affecting remotely sensed snow water equivalent uncertainty. Remote Sens. Environ., 97, 6882.

    • Search Google Scholar
    • Export Citation
  • Duguay, C., , Green J. , , Derksen C. , , English M. , , Rees A. , , Sturm M. , , and Walker A. , 2005: Preliminary assessment of the impact of lakes on passive microwave snow retrieval algorithms in the Arctic. Proc. 62nd Eastern Snow Conf., Waterloo, Ontario, Canada, Eastern Snow Conference, 223–228.

  • Durand, M., , and Margulis S. , 2006: Feasibility test of multifrequency radiometric data assimilation to estimate snow water equivalent. J. Hydrometeor., 7, 443457.

    • Search Google Scholar
    • Export Citation
  • Durand, M., , Kim E. , , and Margulis S. , 2008: Quantifying uncertainty in modeling snow microwave radiance for a mountain snowpack at the point-scale, including stratigraphic effects. IEEE Trans. Geosci. Remote Sens., 46, 17531767.

    • Search Google Scholar
    • Export Citation
  • Elder, K., , Cline D. , , Liston G. , , and Armstrong R. , 2009: NASA cold land processes experiment (CLPX 2002/03): Field measurements of snowpack properties and soil moisture. J. Hydrometeor., 10, 320329.

    • Search Google Scholar
    • Export Citation
  • Etchevers, P., and Coauthors, 2004: Validation of the energy budget of an alpine snowpack simulated by several snow models (SnowMIP project). Ann. Glaciol., 38, 150158.

    • Search Google Scholar
    • Export Citation
  • Foster, J., , Sun C. , , Walker J. , , Kelly R. , , Chang A. , , Dong J. , , and Powell H. , 2005: Quantifying the uncertainty in passive microwave snow water equivalent observations. Remote Sens. Environ., 94, 187203.

    • Search Google Scholar
    • Export Citation
  • Goodison, B., , Walker A. , , Choudhury B. , , Kerr Y. , , Njoku E. , , and Pampaloni P. , 1995: Canadian development and use of snow cover information from passive microwave satellite data. Passive Microwave Remote Sensing of Land-Atmosphere Interactions, B. J. Choudhury et al., Eds., VSP, 245–262.

  • Graf, T., , Koike T. , , Fujii H. , , Brodzik M. , , and Armstrong R. , 2003: CLPX-Ground: Ground based passive microwave radiometer (GBMR-7) data. National Snow and Ice Data Center, Boulder, CO, digital media. [Available online at http://nsidc.org/data/nsidc-0165.html.]

  • Hall, D., , Chang A. , , and Foster J. , 1986: Detection of the depth-hoar layer in the snow-pack of the Arctic Coastal Plain of Alaska, USA, using satellite data. J. Glaciol., 32, 8794.

    • Search Google Scholar
    • Export Citation
  • Hallikainen, M., , and Jolma P. , 1992: Comparison of algorithms for retrieval of snow water equivalent from Nimbus-7 SMMR data in Finland. IEEE Trans. Geosci. Remote Sens., 30, 124131.

    • Search Google Scholar
    • Export Citation
  • Heim, R., , and Dewey K. F. , 1984: Circulation patterns and temperature fields associated with extensive snow cover on the North American continent. Phys. Geogr., 4, 6685.

    • Search Google Scholar
    • Export Citation
  • Jin, J., , Gao X. , , Sorooshian S. , , Yang Z. , , Bales R. , , Dickinson R. , , Sun S. , , and Wu G. , 1999: One-dimensional snow water and energy balance model for vegetated surfaces. Hydrol. Processes, 13, 24672482.

    • Search Google Scholar
    • Export Citation
  • Jordan, R., 1991: A one-dimensional temperature model for a snow cover: Technical documentation for SNTHERM 89. U.S. Army Cold Regions Research and Engineering Laboratory Tech. Rep. CRREL-SR-91-16, 61 pp.

  • Josberger, E., , and Mognard N. , 2002: A passive microwave snow depth algorithm with a proxy for snow metamorphism. Hydrol. Processes, 16, 15571568.

    • Search Google Scholar
    • Export Citation
  • Kelly, R., , Chang A. , , Tsang L. , , and Foster J. , 2003: A prototype AMSR-E global snow area and snow depth algorithm. IEEE Trans. Geosci. Remote Sens., 41, 230242.

    • Search Google Scholar
    • Export Citation
  • Koren, V., , Schaake J. , , Mitchell K. , , Duan Q. , , Chen F. , , and Baker J. , 1999: A parameterization of snowpack and frozen ground intended for NCEP weather and climate models. J. Geophys. Res., 104 (D16), 19 56919 585.

    • Search Google Scholar
    • Export Citation
  • Künzi, K., , Patil S. , , and Rott H. , 1982: Snow-cover parameters retrieved from Nimbus-7 scanning multichannel microwave radiometer (SMMR) data. IEEE Trans. Geosci. Remote Sens., 20, 452467.

    • Search Google Scholar
    • Export Citation
  • Lehning, M., , Fierz C. , , and Lundy C. , 2001: An objective snow profile comparison method and its application to SNOWPACK. Cold Reg. Sci. Technol., 33 (2–3), 253261.

    • Search Google Scholar
    • Export Citation
  • Lehning, M., , Bartelt P. , , Brown B. , , Fierz C. , , and Satyawali P. , 2002: A physical SNOWPACK model for the Swiss avalanche warning: Part II. Snow microstructure. Cold Reg. Sci. Technol., 35, 147167.

    • Search Google Scholar
    • Export Citation
  • Liang, D., , Xu X. , , Tsang L. , , Andreadis K. , , and Josberger E. , 2008: The effects of layers in dry snow on its passive microwave emissions using dense media radiative transfer theory based on the quasicrystalline approximation (QCA/DMRT). IEEE Trans. Geosci. Remote Sens., 46, 36633671.

    • Search Google Scholar
    • Export Citation
  • Liang, X., , Lettenmaier D. P. , , Wood E. F. , , and Burges S. J. , 1994: A simple hydrologically based model of land surface water and energy fluxes for general circulation models. J. Geophys. Res., 99 (D7), 14 41514 428.

    • Search Google Scholar
    • Export Citation
  • Loth, B., , Graf H. , , and Oberhuber J. , 1993: Snow cover model for global climate simulations. J. Geophys. Res., 98 (D6), 10 45110 464.

  • Mätzler, C., , and Hüppi R. , 1989: Review of signature studies for microwave remote sensing of snowpacks. Adv. Space Res., 9, 253265.

    • Search Google Scholar
    • Export Citation
  • Maurer, E., , Wood A. , , Adam J. , , Lettenmaier D. , , and Nijssen B. , 2002: A long-term hydrologically based dataset of land surface fluxes and states for the conterminous United States. J. Climate, 15, 32373251.

    • Search Google Scholar
    • Export Citation
  • Pulliainen, J., 2006: Mapping of snow water equivalent and snow depth in boreal and sub-arctic zones by assimilating space-borne microwave radiometer data and ground-based observations. Remote Sens. Environ., 101, 257269.

    • Search Google Scholar
    • Export Citation
  • Rees, A., , Lemmetyinen J. , , Derksen C. , , Pulliainen J. , , and English M. , 2010: Observed and modelled effects of ice lens formation on passive microwave brightness temperatures over snow covered tundra. Remote Sens. Environ., 114, 116126.

    • Search Google Scholar
    • Export Citation
  • Reichle, R., , Walker J. , , Koster R. , , and Houser P. , 2002: Extended versus ensemble Kalman filtering for land data assimilation. J. Hydrometeor., 3, 728740.

    • Search Google Scholar
    • Export Citation
  • Rosenfeld, S., , and Grody N. , 2000: Anomalous microwave spectra of snow cover observed from Special Sensor Microwave/Imager measurements. J. Geophys. Res., 105 (D11), 14 91314 926.

    • Search Google Scholar
    • Export Citation
  • Schmugge, T. J., , Kustas W. P. , , Ritchie J. C. , , Jackson T. J. , , and Rango A. , 2002: Remote sensing in hydrology. Adv. Water Resour., 25 (8–12), 13671385.

    • Search Google Scholar
    • Export Citation
  • Schweizer, J., , and Kronholm K. , 2007: Snow cover spatial variability at multiple scales: Characteristics of a layer of buried surface hoar. Cold Reg. Sci. Technol., 47, 207223.

    • Search Google Scholar
    • Export Citation
  • Shepard, D., 1984: Computer mapping: The SYMAP interpolation algorithm. Spatial Statistics and Models, G. L. Gaile and C. J. Wilmott, Eds., Springer, 133–145.

  • Shi, X., , Sturm M. , , Liston G. , , Jordan R. , , and Lettenmaier D. , 2009: SnowSTAR2002 transect reconstruction using a multilayered energy and mass balance snow model. J. Hydrometeor., 10, 11511167.

    • Search Google Scholar
    • Export Citation
  • Sturm, M., 1992: Snow distribution and heat flow in the taiga. Arct. Alp. Res., 24, 145152.

  • Sturm, M., , and Benson C. , 1997: Vapor transport, grain growth and depth-hoar development in the subarctic snow. J. Glaciol., 43, 4259.

    • Search Google Scholar
    • Export Citation
  • Sturm, M., , and Liston G. , 2003: The snow cover on lakes of the Arctic Coastal Plain of Alaska, USA. J. Glaciol., 49, 370380.

  • Sturm, M., , and Benson C. , 2004: Scales of spatial heterogeneity for perennial and seasonal snow layers. Ann. Glaciol., 38, 253260.

  • Sturm, M., , Holmgren J. , , Koenig M. , , and Morris K. , 1997: The thermal conductivity of seasonal snow. J. Glaciol., 43, 2641.

  • Sun, S., , Jin J. , , and Xue Y. , 1999: A simple snow-atmosphere-soil transfer model. J. Geophys. Res., 104 (D16), 19 58719 597.

  • Thornton, P., , and Running S. , 1999: An improved algorithm for estimating incident daily solar radiation from measurements of temperature, humidity, and precipitation. Agric. For. Meteor., 93, 211228.

    • Search Google Scholar
    • Export Citation
  • Tsang, L., , Kong J. , , and Shin R. , 1985: Theory of Microwave Remote Sensing. Wiley, 632 pp.

  • Tsang, L., , Chen C. , , Chang A. , , Guo J. , , and Ding K. , 2000: Dense media radiative transfer theory based on quasi-crystalline approximation with applications to passive microwave remote sensing of snow. Radio Sci., 35, 731749.

    • Search Google Scholar
    • Export Citation
  • Tsang, L., , Pan J. , , Liang D. , , Li Z. X. , , Cline D. , , and Tan Y. H. , 2007: Modeling active microwave remote sensing of snow using dense media radiative transfer (DMRT) theory with multiple scattering effects. IEEE Trans. Geosci. Remote Sens., 45, 9901004.

    • Search Google Scholar
    • Export Citation
  • Uppala, S., and Coauthors, 2005: The ERA-40 Re-Analysis. Quart. J. Roy. Meteor. Soc., 131, 29613012.

  • Verseghy, D. L., 1991: CLASS—A Canadian land surface scheme for GCMS. I. Soil model. Int. J. Climatol., 11, 111133.

  • Wiesmann, A., , and Mätzler C. , 1999: Microwave emission model of layered snowpacks. Remote Sens. Environ., 70, 307316.

  • Wigmosta, M., , Vail L. , , and Lettenmaier D. , 1994: A distributed hydrology-vegetation model for complex terrain. Water Resour. Res., 30, 16651680.

    • Search Google Scholar
    • Export Citation
  • Yang, Z., , Dickinson R. , , Robock A. , , and Vinnikov K. , 1997: Validation of the snow submodel of the Biosphere–Atmosphere Transfer Scheme with Russian snow cover and meteorological observational data. J. Climate, 10, 353373.

    • Search Google Scholar
    • Export Citation
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    Simulated snow water equivalent for the multiple and single-layer VIC models compared with snowpit measurements from the CLPX LSOS.

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    Snowpack profile agreement scores for temperature, density, and grain size between VIC model predictions and CLPX LSOS snow pits during 2002/03.

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    Simulated snowpack thickness, density, and grain size for each layer at the LSOS site that were used as input to the DMRT model.

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    Observed (vertical bars) and one-layer (circles) and five-layer (triangles) simulated brightness temperatures at horizontal (black) and vertical (gray) polarizations at (top) 18.7 and (bottom) 36.5 GHz from the CLPX LSOS site, Colorado.

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    (a) Simulated vs observed brightness temperature polarization differences for the five-layer (triangles) and one-layer (circles) models, 18.7 (black) and 36.5 (gray) GHz. (b) Simulated vs observed brightness temperature frequency differences for the five-layer (triangles) and one-layer (circles) models, horizontal (black) and vertical (gray) polarizations.

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    Satellite SSM/I brightness temperature at 37 GHz (vertical polarization) vs corresponding SWE measurements from the SnowSTAR2002 transect.

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    Simulated (gray circles) and observed (black squares) snow water equivalent along the SnowSTAR2002 transect.

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    Observed TB from SSM/I and simulated TB from the one- and five-layer VIC/DMRT along the SnowSTAR2002 transect for both horizontal and vertical polarizations at (a) 18.7 and (b) 36.5 GHz.

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    Simulated snowpack thickness, density, and grain size for each layer at each SnowSTAR site that were used as input to the DMRT model.

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    Simulated TB from the one- and five-layer linked VIC/DMRT forced with rescaled precipitation against observed TB from SSM/I for both 18.7 and 36.5 GHz.

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    Snow depth along the SnowSTAR2002 transect measured at snow pits (circles) and simulated by the one- and five-layer models, without (prior), and with (posterior) assimilation of SSM/I brightness temperature observations.

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Implications of Representing Snowpack Stratigraphy for the Assimilation of Passive Microwave Satellite Observations

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  • 1 Byrd Polar Research Center, Ohio State University, Columbus, Ohio
  • | 2 Civil and Environmental Engineering, University of Washington, Seattle, Washington
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Abstract

Under certain conditions, passive microwave satellite observations can be used to estimate snow water equivalent (SWE) across large areas, either through direct retrieval or data assimilation. However, the layered character of snowpacks increases the complexities of estimation algorithms. A multilayer model of snowpack stratigraphy that can serve as the forward model of a snow data assimilation system is described and evaluated. The model’s ability to replicate large-scale snowpack layer features is evaluated using observations from the Cold Land Processes Experiment (Colorado, 2002 and 2003) and a 2002 Nome–Barrow snowpit transect [Snow Science Traverse—Alaska Region (SnowSTAR2002)]. The multilayer model linked with a radiative transfer scheme improved the estimation of brightness temperatures both in terms of absolute values and frequency/polarization differences (error reductions ranging from 47% to 72%) relative to a one-layer model with similar, but depth-averaged, physics at the Colorado sites. The two models were also employed along the SnowSTAR2002 transect of snowpit measurements. The general unavailability of meteorological forcings along the transect made the use of coarse-scale reanalysis data necessary to simulate snow properties and microwave radiances. Errors in the precipitation forcings led to overestimation of SWE, and the simulated brightness temperatures from the two models showed large differences, due mostly to the inability of the single-layer model to simulate the observed larger grain sizes. These differences had implications for the estimation of snow depth; assimilation of Special Sensor Microwave Imager (SSM/I) observations into the multilayer model resulted in improved snow depth estimates (RMSEs of 18.1 cm versus 34.1 cm without assimilation), while the single-layer assimilation slightly decreased the estimation skill (RMSEs of 34.1 versus 33.6 cm).

Current affiliation: Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California.

Corresponding author address: K. M. Andreadis, Jet Propulsion Laboratory, 4800 Oak Grove Dr., Pasadena, CA 91109. E-mail: konstantinos.m.andreadis@jpl.nasa.gov

Abstract

Under certain conditions, passive microwave satellite observations can be used to estimate snow water equivalent (SWE) across large areas, either through direct retrieval or data assimilation. However, the layered character of snowpacks increases the complexities of estimation algorithms. A multilayer model of snowpack stratigraphy that can serve as the forward model of a snow data assimilation system is described and evaluated. The model’s ability to replicate large-scale snowpack layer features is evaluated using observations from the Cold Land Processes Experiment (Colorado, 2002 and 2003) and a 2002 Nome–Barrow snowpit transect [Snow Science Traverse—Alaska Region (SnowSTAR2002)]. The multilayer model linked with a radiative transfer scheme improved the estimation of brightness temperatures both in terms of absolute values and frequency/polarization differences (error reductions ranging from 47% to 72%) relative to a one-layer model with similar, but depth-averaged, physics at the Colorado sites. The two models were also employed along the SnowSTAR2002 transect of snowpit measurements. The general unavailability of meteorological forcings along the transect made the use of coarse-scale reanalysis data necessary to simulate snow properties and microwave radiances. Errors in the precipitation forcings led to overestimation of SWE, and the simulated brightness temperatures from the two models showed large differences, due mostly to the inability of the single-layer model to simulate the observed larger grain sizes. These differences had implications for the estimation of snow depth; assimilation of Special Sensor Microwave Imager (SSM/I) observations into the multilayer model resulted in improved snow depth estimates (RMSEs of 18.1 cm versus 34.1 cm without assimilation), while the single-layer assimilation slightly decreased the estimation skill (RMSEs of 34.1 versus 33.6 cm).

Current affiliation: Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California.

Corresponding author address: K. M. Andreadis, Jet Propulsion Laboratory, 4800 Oak Grove Dr., Pasadena, CA 91109. E-mail: konstantinos.m.andreadis@jpl.nasa.gov

1. Introduction

Snow is a key component of the land surface hydrologic cycle, especially in mid- to high latitudes. From a hydrological standpoint, snowpacks act as storage reservoirs that modulate the seasonal cycle of runoff. The space–time distribution of snow can also affect atmospheric processes as a result of the strong contrast in albedo and surface temperature between snow-covered and snow-free surfaces. These contrasts can alter atmospheric circulation patterns (Heim and Dewey 1984; Cohen and Entekhabi 1999). The spatial and temporal sparseness of in situ observation networks globally have led to reliance on remotely sensed observations of snow properties, especially snow cover extent, at large scales (Schmugge et al. 2002). However, a number of uncertainties exist in satellite-based estimates of snow water equivalent (SWE)—the key hydrological variable associated with snow (Foster et al. 2005).

Satellite observations of snow properties have been available for more than 40 years from both visible and passive microwave sensors. Although visible wavelength sensors provide a basis for estimating snow cover extent, they do not provide information about snow water storage, which is hydrologically more important. Passive microwave remote sensing has been used to operationally map snow cover and depth since the 1970s (Chang et al. 1987; Kelly et al. 2003); however, its use for estimating snow depth and water equivalent is generally limited to relatively thin, cold snowpacks. Previous studies have shown correlations between passive microwave brightness temperatures and snow depth (e.g., Künzi et al. 1982; Hallikainen and Jolma 1992; Josberger and Mognard 2002; Derksen et al. 2003), but many limitations nevertheless make direct retrieval of snow properties from passive microwave sensors problematic (Foster et al. 2005; Derksen et al. 2005). These problems include 1) the coarse spatial resolution of current sensors, 2) signal “saturation” (the microwave signal is almost fully attenuated at a certain snow depth, related to the penetration depth for different frequencies, resulting in very little sensitivity of the microwave signal for increasing snow mass) (Dong et al. 2005), 3) presence of liquid water in the snowpack when absorption controls brightness temperature and hence limits retrieval algorithms, 4) dense forest cover (which can cause complications due to partial masking of the snow microwave signal), and 5) snow metamorphism, which can strongly alter microwave emissivity and thus complicate retrieval algorithms.

An alternative approach to using satellite observations alone is to merge them with physically based model predictions to constrain retrieval algorithms and potentially account for the uncertainties (e.g., through data assimilation; see, e.g., Durand and Margulis 2006; Pulliainen 2006). Such an approach usually requires coupling a large-scale snow hydrology model and a microwave emission model. Results from previous studies, which have evaluated microwave brightness temperatures predicted by such linked models (e.g., Durand et al. 2008), highlighted the discrepancy between the assumption of homogeneous snowpacks inherent in most land surface models and the fact that snow is a naturally layered medium (Andreadis et al. 2008a). The layered character of snowpacks can exert strong controls on their microwave emission signature (Rosenfeld and Grody 2000), and in cases when the wavelength is comparable to either layer thicknesses or particle sizes, and when there are sufficient differences in the dielectric properties between layers, microwave signals can be very different for otherwise comparable snowpacks (Colbeck 1991). For example, the presence of an ice layer within a snowpack can change its horizontally polarized brightness temperature by about 40 K at 19 GHz (Rees et al. 2010), while depth hoar also can decrease brightness temperature by increasing scattering due to its prevailing larger snow crystals at 37 GHz (Hall et al. 1986). For these reasons, representing snowpack layering in the linked snow hydrology and microwave emission model (i.e., forward model) would potentially improve the estimation of snow water equivalent from data assimilation systems that incorporate snowpack information based on passive microwave retrievals.

Current passive microwave satellite products have a spatial resolution of order 25 km; therefore, the forward model needs to be applicable over spatial scales of that order. The question then arises as to which snowpack features are resolvable at such spatial scales, and should be represented in a linked hydrology/microwave emission model. Snowpack layering is affected by meteorological (wind, air temperature, precipitation, and solar radiation) as well as topographic (slope and aspect) and physiographic (presence or absence of vegetation) controls. Sturm and Benson (2004) examined the spatial heterogeneity of snowpack stratigraphy over spatial scales ranging from 10 m to more than 200 km using snowpit measurements collected on the Arctic coastal plain of Alaska. They found that at scales greater than 100 m, topographic variations can result in substantial variations in precipitation, wind, and solar radiation, which in turn are reflected in heterogeneity in snowpack stratigraphy, while such variations can also be caused by snow–vegetation interactions (Sturm 1992). However, notwithstanding these small-scale variations, at scales larger than about 10 km, there was a general coherence in the snowpack layers, which had relatively strong spatial correlations across the 8140 km2 Kuparuk River basin (Sturm and Benson 2004). Weather appeared to be the primary driver for this synoptic-scale variability that led to snow layers remaining recognizable over distances on the order of 160 km, notwithstanding that the landscape and its interactions with weather introduced relatively smaller-scale heterogeneity that modulated the larger-scale trends. The combined effects of controls at these two scales was noted by Schweizer and Kronholm (2007), who observed a layer of surface hoar over an approximately 250-km2 area, the spatial coherence of which was eventually reduced by local effects of wind and aspect variability.

The objective of this study is to describe and evaluate a macroscale multilayer snow model that is intended to reflect spatial variability in the controlling processes, and be able to replicate large-scale snowpack layer features and their effect on passive microwave emissivity, while being easy to implement at the scale of large continental river basins (order 105–106 km2). Such a model, which must account for subgrid variability in topography and land cover and their interactions with precipitation, air temperature, and wind would potentially be able to capture the large-scale layering features that affect satellite retrievals, such as surface and depth hoar, by simulating snowpack physics within these relatively homogeneous areas. The model we have developed with this objective in mind is described in the following section. Section 3 evaluates the model both in terms of snow stratigraphy and microwave emission predictions, but also in the context of a simple data assimilation experiment where its ability to improve SWE estimation over larger scales is demonstrated.

2. Model description

Like all energy balance snow models, our multilayer model is based on the solution of the mass and energy balance over a snow column. We describe the foundations for the model below along with a brief description of its implementation in a macroscale setting.

a. General model structure

Many snowpack models have been developed for different applications including hydrological prediction, global and regional weather and climate prediction, and avalanche forecasting (Etchevers et al. 2004). These models vary in complexity, ranging from simple force–restore schemes (Yang et al. 1997), to approaches that assume snowpacks to be homogeneous media (Verseghy 1991; Wigmosta et al. 1994; Koren et al. 1999), to multilayered representations with detailed snowpack physics (Brun et al. 1989; Jordan 1991; Bartelt and Lehning 2002). Given our objectives, a physically based representation of snowpack internal processes is required that is of intermediate complexity (e.g., Loth et al. 1993; Sun et al. 1999). Our approach is similar to previous studies in the sense that it adapts an existing snow model (as did Jin et al. 1999) and couples it to a land surface scheme (as did Boone and Etchevers 2001).

The land surface scheme used in this study is the Variable Infiltration Capacity (VIC) model (Liang et al. 1994), which solves the water and energy balance of a soil column over a gridded domain accounting for subgrid variability in land cover by partitioning each model grid cell into tiles based on topography and land cover. Spatial heterogeneity in runoff generating processes is represented by a parameterization of the combined effects of topographic and small-scale spatial variability in soil properties. Water and energy states and fluxes are simulated for each “homogeneous” tile and averaged over each model grid cell. The multilayer snowpack model we develop here is intended to be linked to VIC in such a way as to retain the interactivity between the current “one and a half-layer” (thin surface layer for energy computations, and a deeper pack layer where required) snowpack model and other components including canopy snow interception and energetics (Andreadis et al. 2008b), frozen soils (Cherkauer and Lettenmaier 2003), and blowing snow (Bowling et al. 2004) submodels.

b. Energy balance

We represent the snowpack as a layered medium, with energy exchange between snow and the atmosphere limited to the surface layer taking the form
e1
where Q* is the energy available for melting or refreezing, Qs ↓ is the downward shortwave radiation, α is the snow albedo, is the downward longwave radiation, is the emitted longwave radiation where ε is the emissivity, σ is the Stefan–Boltzmann constant and Ts is the snow surface temperature, Qh is the sensible heat flux (including advected sensible heat flux), Qe is the latent heat flux (including heat flux from sublimation), Qa is the advected heat from rainfall, Qc is the heat conducted to/from the deeper snowpack, Qlw is the heat associated with liquid water percolation, ΔH is the change in heat content [=cihm(TtTt−1)/Δt] where ci is the heat capacity of ice, hm is the snow water equivalent, and Tt, Tt−1 are the temperatures at the current and previous time steps, respectively. Albedo is calculated as a function of snow age using an empirical relationship (Andreadis et al. 2008b), while incoming shortwave and longwave radiations are provided either from measurements or can be estimated (Thornton and Running 1999). Turbulent heat fluxes and advected energy from rainfall are calculated using the formulations in Wigmosta et al. (1994) depending on atmospheric pressure, air temperature, rainfall amount, wind speed, and saturation vapor pressure and temperature at the snow surface.
Heat conduction through the snowpack is modeled as
e2
where kj is the heat conductivity, and ∂T/∂z is the temperature gradient across layer j (if this layer is the bottom layer, Qc becomes the ground heat flux). Heat conductivity can be estimated in a number of ways; here, it is calculated from a quadratic relationship between conductivity and density derived from a measurement dataset that encompassed most types of seasonal snow cover (Sturm et al. 1997). The energy balance for the internal layers can be formulated as
e3
where Qs,j is the shortwave radiation penetrating to this layer, Qlw,j is the energy associated with water movement from layer j to j + 1 [=cw(Ul,jTj)/Δt] and cw is the heat capacity of water and Ul,j the liquid water flux from layer j, Qc,j is heat conducted from layer j to j + 1, and Qh,j is the latent heat released from vapor diffusion from layer j to j + 1 [=Ls(Uυ,jρw)/Δt] with Ls being the latent heat of sublimation, Uυ,j the vapor flux from layer j, and ρw the water density. The energy balance is solved as a system of equations using the iterative discrete Newton algorithm (Dennis and Schnable 1983) or as an Euler backward tridiagonal system (Loth et al. 1993) if the first method does not converge.

c. Mass balance

After solving for the snowpack temperature profile, the amounts of water that have melted or refrozen are calculated and liquid water is allowed to percolate from one layer to another using a 3.5% retention capacity. Along with the liquid water flux, vapor fluxes are calculated from the Clausius–Clapeyron equation:
e4
where ps is the vapor saturation pressure, R is the water vapor gas constant, and Ds is the vapor diffusion coefficient for snow estimated from Colbeck (1993).

Two important processes related to snow metamorphism are densification and grain growth. The former is caused by compaction of snow layers, destructive (equi-temperature), constructive (temperature gradient), and melt metamorphism. Anderson (1976) developed a model for snow densification taking these processes into account, which has been adapted to the VIC model with the essentially single-layer formulation (Andreadis et al. 2008b). We extended to the multilayer version by calculating snow density changes for each layer. The snow grain growth model is adapted from Lehning et al. (2002), and uses empirical relationships for equilibrium growth metamorphism (small temperature gradients, less than 5 K m−1), and wet snow metamorphism (presence of liquid water in the snowpack) (Brun 1989). When temperature gradients are larger than 5 K m−1, higher growth rates are assumed (kinetic growth metamorphism) and both layer-to-layer and intralayer vapor transport contribute to the water vapor supply (Sturm and Benson 1997).

To reduce computational requirements, some constraints were placed on the combination of layers to keep the number of layers below a user-defined prescribed maximum (five in this study). A new layer is created after every snowfall event as long as it has a snow water equivalent greater than 5 mm, while the surface layer snow mass (in terms of SWE) is not allowed to exceed 20 mm. At the end of each time step, two neighboring layers are combined if both are cold (average temperature < 0°) and their temperature gradient is less than 5 K m−1. When the maximum number of layers is exceeded by invoking these criteria, the two adjacent layers with the minimum temperature gradient and density difference are combined. Although ice layers are not explicitly created, the model keeps track of the refrozen water content of each layer thus representing ice layers implicitly.

3. Results

a. Cold Land Processes Experiment, Colorado

The Cold Land Processes Experiment (CLPX) was a multisensor and multiscale field campaign conducted during the winters of 2002 and 2003 over a set of nested study areas in Colorado and Wyoming. A set of snowpit measurements were taken in a 100 × 100 m clearing, designated as the local-scale observation site (LSOS), in addition to radiometric measurements from a ground-based microwave radiometer (GBMR-7). Snowpit measurements included snow depth, water equivalent, density, temperature, and grain size profiles that were collected between November 2002 and March 2003, while the GBMR-7 measurements included brightness temperatures at 18.7, 23.8, 36.5, and 89 GHz during selected days in January and December 2002 and February and March 2003 (Graf et al. 2003). During those times, snow depths ranged between 55 and 100 cm, grain sizes between 0.67 and 2.36 mm, while air temperatures ranged between −11° and 0°C (Elder et al. 2009).

This set of measurements offered an opportunity to test simultaneously the ability of VIC to reproduce stratigraphic profiles and to simulate the corresponding passive microwave response after coupling with a radiative transfer model. The model was allowed to have a maximum number of five layers, and was forced with daily precipitation, maximum and minimum air temperature, and wind speed from the LSOS in situ (point) measurements aggregated from hourly to daily. This was done to emulate the general data availability and computational feasibility when applying such macroscale hydrological models in offline settings (Maurer et al. 2002). The simulation period was from 1 October 2002 (no snow) to 25 March 2003, with the melting period not included because of the problems that liquid water causes in passive microwave remote sensing of snow. The model used internal algorithms to disaggregate the daily meteorological data (by partitioning precipitation into equal-magnitude increments with diurnal variability introduced to air temperature) and/or to calculate required inputs at the model time step (in the case of relative humidity and incoming shortwave and longwave radiation) as outlined in Maurer et al. (2002).

1) Snowpack stratigraphy

Before examining how well snowpack stratigraphy is simulated by the multilayer model, it is important to evaluate the accuracy of the model’s simulations of snow water equivalent. Figure 1 shows the simulated SWE for both the five-layer and standard (surface and pack layer) VIC snow models compared with snowpit measurements. Both model simulations are quite close to the observed SWE, although they slightly underestimate snow accumulation in March 2003. The good agreement of the models is somewhat expected, because they are forced by observed daily precipitation at a nonforested site. The differences in simulated SWE between the two model versions are minimal; the single- and multilayer models have mean squared errors of 9.4 mm (6.1%) and 11.7 mm (7.3%), respectively. In terms of SWE estimation, potential error sources mostly include snowfall, radiative fluxes (especially during ablation), and the presence of canopy. However, the differences between the two models are mostly attributable to small differences in sublimation rates.

Fig. 1.
Fig. 1.

Simulated snow water equivalent for the multiple and single-layer VIC models compared with snowpit measurements from the CLPX LSOS.

Citation: Journal of Hydrometeorology 13, 5; 10.1175/JHM-D-11-056.1

The VIC multilayer snow model simulates a single snowpack profile over each subgrid land cover/elevation tile of a model pixel, the latter covering an area between about 40 and 150 km2. Comparing those effective (over the spatial domain) profiles with snowpit measurements taken at a single point would be difficult for reasons including variability in topography, deviations of snow depth, shifting of layers, etc. We used an objective snow profile comparison method to evaluate the model predictions in comparison with snowpit measurements. This method (Lehning et al. 2001) first maps the model profile layers to the snowpit profile layers and then calculates a comparison score ranging from 0 (no agreement) to 1 (identical profiles) for each parameter (temperature, density, and grain size). Figure 2 shows the agreement scores between the model-predicted profiles and the CLPX LSOS snow pits for temperature, density, and grain size. The agreement is relatively high (mean of 0.83) throughout the measurement period with the exception of the beginning of January 2003. Apart from mid-November 2002, the agreement scores for density are also relatively high (mean of 0.82), while grain size scores are consistently greater than 0.75 with an average of 0.86. Although this objective comparison method is meant to be complementary to the direct visual comparison of modeled and observed profiles, it provides a quantitative means for comparing the model profiles with the single-location snowpit measurements, and shows that the model is able to capture the snowpack stratigraphic features to a relatively high degree.

Fig. 2.
Fig. 2.

Snowpack profile agreement scores for temperature, density, and grain size between VIC model predictions and CLPX LSOS snow pits during 2002/03.

Citation: Journal of Hydrometeorology 13, 5; 10.1175/JHM-D-11-056.1

2) Ground-based microwave brightness temperatures

Potential improvements in microwave emission model predictions when using a multiple-layer linked (hydrologic and radiative transfer) model relative to the single-layer model were assessed using the GBMR-7 measurements. The latter were taken on selected dates in February 2003 within the LSOS site and included measurements of brightness temperature at 18.7, 23.0, 36.5, and 89.0 GHz (both horizontal and vertical polarizations at incidence angles between 30° and 70°). There was snowfall during all the selected dates, with the exception of 18 and 19 February, while air temperature ranged between −18° and 0.7°C. The microwave emission model used is based on the dense media radiative transfer (DMRT) theory and quasi-crystalline approximation (Tsang et al. 1985, 2000). The model does not make the assumption of independent scattering, and takes into account interparticle forces that lead to adhesion and collective scattering, calculating microwave emissivity as a function of snow depth, density, grain size, and temperature (Tsang et al. 2007). The degree of particle clustering is modeled through a stickiness parameter, which also affects the frequency dependence of the extinction coefficient. Recently, the DMRT model was extended to a multilayer formulation, and was shown to agree very well with the GBMR-7 ground measurements when forced with observed snow stratigraphy (Liang et al. 2008). Brightness temperature simulations are performed by coupling VIC and DMRT offline—that is, directly using the VIC multilayer snow model stratigraphy to drive the DMRT model with both models having the same number of layers (five). In cases when VIC predicted an ice layer, it was added explicitly to DMRT with the predicted thickness and a density of 917 kg/m3. The stickiness parameter was set to the default value of 0.1 for all snowpack layers, although it can be different for each layer and could be tuned (no calibration was performed for these simulations). The snow properties (thickness, density, and grain size) simulated by VIC that are used as input to the DMRT model are shown in Fig. 3 for each of the five (prescribed maximum) snowpack layers.

Fig. 3.
Fig. 3.

Simulated snowpack thickness, density, and grain size for each layer at the LSOS site that were used as input to the DMRT model.

Citation: Journal of Hydrometeorology 13, 5; 10.1175/JHM-D-11-056.1

Figure 4 compares the single- and multiple-layer simulations of brightness temperatures (TB)with the GBMR-7 measurements at 18.7 GHz (Fig. 4a) and 36.5 GHz (Fig. 4b) at both horizontal and vertical polarizations. The improvement in predicting 18.7-GHz TB using five layers is evident for all measurement dates except 19 February for the vertical and 20 February for both polarizations. Similarly, for 36.5 GHz the five-layer model better predicted TB with the exception of 21 February for the horizontal and 22 February for the vertical polarization. The corresponding prediction root-mean-square errors (RMSEs) for the four frequency channels (18.7 GHz horizontal and vertical, and 36.5 GHz horizontal and vertical) were 14.0, 5.5, 13.3, and 9.4 K for the single-layer linked model and 5.5, 2.9, 5.2, and 3.4 K for the five-layer VIC/DMRT model. Correlation between the predicted and mean observed TB, as estimated by the Pearson coefficient, for the same frequency channels were −0.35, 0.29, −0.10, and 0.53 for the single-layer linked model and 0.48, 0.75, 0.70, and 0.62 for the five-layer linked model. These results appear to confirm the hypothesis in previous work using the single-layer VIC/DMRT (Andreadis et al. 2008a) that predictions of TB for horizontal polarizations were problematic because of the reflection at layer boundaries, which was not captured by the single-layer model and mostly affects horizontal polarization (Wiesmann and Mätzler 1999). Errors in the five-layer VIC/DMRT model predictions in TB arguably are attributable to forcing of the linked model with only daily accumulated precipitation and average air temperature, with hourly meteorological forcings potentially leading to more accurate snowpack profile and hence TB simulations. Moreover, approximations in the snow physics of the VIC multilayer model could have contributed to the errors in TB predictions. Liang et al. (2008) showed close agreement between the GBMR-7-observed and model-predicted TB when the multilayer DMRT was forced with the observed snowpack properties.

Fig. 4.
Fig. 4.

Observed (vertical bars) and one-layer (circles) and five-layer (triangles) simulated brightness temperatures at horizontal (black) and vertical (gray) polarizations at (top) 18.7 and (bottom) 36.5 GHz from the CLPX LSOS site, Colorado.

Citation: Journal of Hydrometeorology 13, 5; 10.1175/JHM-D-11-056.1

Various SWE retrieval algorithms from passive microwave observations are based on the frequency differences (Goodison et al. 1995), while polarization differences can provide information about the snowpack vertical variability (Mätzler and Hüppi 1989). Examining how well the models capture these differences, using the GBMR measurements from the CLPX shows that the five-layer linked model is able to reproduce the observed frequency and polarization differences in the LSOS site better than the single-layer model (Fig. 5). The errors in predicting polarization differences, in terms of RMSE and correlation, for the one-layer model were 8.7 and 7.3 K (correlations of −0.51 and 0.39) for 18.7 and 36.5 GHz, which were reduced (increased) by the five-layer model to 2.3 and 1.0 K (correlations of 0.78 and 0.90), respectively. The error reduction is also evident in the scatterplot in Fig. 5a, which shows simulated versus observed polarization differences. In the case of the five-layer-model-predicted polarization difference at 19 GHz, there appears to be an outlier at ~12 K; however, even excluding this measurement, the correlations of the five-layer model are still improved relative to the one-layer model (0.54 versus −0.32). Figure 5b shows simulated versus observed frequency differences for both one- and five-layer models and both polarizations. The one-layer model has similar frequency difference prediction errors for both polarizations, 7.4 and 6.1 K (correlations of 0.22 and 0.17) for the horizontal and vertical, while the five-layer model slightly decreases those errors to 7.3 and 4.0 K (increases correlations to 0.35 and 0.59), respectively. The multilayer DMRT has a similar formulation to the single-layer version in terms of the frequency dependence, and mostly affects the polarization difference (Liang et al. 2008).

Fig. 5.
Fig. 5.

(a) Simulated vs observed brightness temperature polarization differences for the five-layer (triangles) and one-layer (circles) models, 18.7 (black) and 36.5 (gray) GHz. (b) Simulated vs observed brightness temperature frequency differences for the five-layer (triangles) and one-layer (circles) models, horizontal (black) and vertical (gray) polarizations.

Citation: Journal of Hydrometeorology 13, 5; 10.1175/JHM-D-11-056.1

b. SnowSTAR2002 Transect, Alaska

A series of snowpack stratigraphy measurements (designated SnowSTAR2002) were taken in arctic Alaska along a transect extending 1200 km from Nome to Barrow during March and April 2002 (Sturm and Liston 2003; Sturm and Benson 2004). These measurements span distances that range from 10 m to 200 km between snow pits, and include snow depth, density, grain size, temperature, water equivalent, hardness, type, and fractions of wet, recent snow, slabs, and hoar. The prevalent land cover along the traverse is tundra; most of the transect is fairly flat with relatively low relief and most elevations were below 500 m (MSL). These data provide the opportunity to evaluate the relationship between large-scale (5–25 km) variability in stratigraphy and satellite-observed passive microwave emissions, given the relative homogeneity and absence of dense forest cover.

Satellite observations of microwave brightness temperature [Level 3 Equal-Area Scalable Earth-Grid (EASE-Grid) product], taken from the Special Sensor Microwave Imager (SSM/I) (Armstrong et al. 2003), were used to examine the change in microwave TB with snow depth. Figure 6 shows SWE measurements taken from the SnowSTAR2002 transect on the x axis, and the corresponding 25 km × 25 km SSM/I brightness temperature observation at 37 GHz (vertical polarization and nighttime pass, local times ranging between approximately 2200 and 0000). Although the representation of the 25-km TB observations with in situ measurements of properties is not ideal because of their difference in spatial scales, it is clear that using a linear relationship between SWE and TB (or channel differences between 19- and 37-GHz TB) similar to the ones used in operational SWE estimation algorithms (Armstrong and Brodzik 2002) would be problematic. Similar conclusions can be drawn by examining the variation of the 19-GHz TB with SWE (not shown). Snow metamorphism (e.g., depth hoar), the presence of lakes within each SSM/I pixels that can increase the area’s TB (Duguay et al. 2005; Derksen et al. 2009), as well as the loss of sensitivity of TB for increasing SWE depending on the frequency are among the reasons why explicit modeling of the microwave brightness temperature is required for the estimation of SWE over a heterogeneous land surface area.

Fig. 6.
Fig. 6.

Satellite SSM/I brightness temperature at 37 GHz (vertical polarization) vs corresponding SWE measurements from the SnowSTAR2002 transect.

Citation: Journal of Hydrometeorology 13, 5; 10.1175/JHM-D-11-056.1

1) Hydrologic simulations

The accuracy of model predictions of snow mass and properties depends to a large degree on the availability and quality of the meteorological forcings (e.g., precipitation and air temperature). In situ measurement networks of meteorological variables are quite sparse, both spatially and temporally, while satellite-observed or model-derived meteorological datasets can have large uncertainties (Adam and Lettenmaier 2003) and even large differences between datasets (Adler et al. 2001). Satellite passive microwave observations could potentially be of value in constraining the uncertainties in meteorological forcings that propagate to the model predictions of SWE, in areas where such limitations exist. However, ingesting satellite observations of TB into a hydrologic model requires accurate forward modeling; therefore, the impact of simulating snowpack stratigraphy in the estimation of SWE needs to be assessed. Consequently, we performed snow hydrologic simulations along the SnowSTAR2002 transect with both the one- and five-layer snow models. The required daily meteorological forcings (precipitation, air temperature, and wind speed) were provided by the 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40) of meteorological observations globally, including conventional and satellite measurements and atmospheric model predictions (Uppala et al. 2005). The Synographic Mapping System (SYMAP) algorithm (Shepard 1984) was used to interpolate the data from the ERA-40 spatial resolution of ~1.125° to the measurement locations.

Simulated SWE was overestimated across the transect, shown in Fig. 7 with an average estimation error of 89.3 mm. This discrepancy is attributable mostly to overestimation of precipitation by ERA-40; comparisons with in situ observations from the snow telemetry (SNOTEL) network showed large differences in cumulative precipitation (Shi et al. 2009). On the other hand, daily maximum and minimum air temperatures from ERA-40 showed relatively good agreement with SNOTEL measurements. Nonetheless, other factors might have also contributed to SWE errors such as underestimation of sublimation. SWE simulations between the one- and five-layer models were almost identical, but the snow depth estimates were different (due to differences in predicted snow density), although both were higher than the observed depths (RMSE of 43.7 cm for the five-layer model).

Fig. 7.
Fig. 7.

Simulated (gray circles) and observed (black squares) snow water equivalent along the SnowSTAR2002 transect.

Citation: Journal of Hydrometeorology 13, 5; 10.1175/JHM-D-11-056.1

The corresponding simulated TB from both the single- and multilayer models along with the SSM/I observations at the SnowSTAR2002 transect measurement locations are shown in Fig. 8. These simulations were performed after setting the stickiness parameter for DMRT to 0.2 to better represent the larger grain sizes for arctic environments (Sturm and Benson 1997). The stickiness parameter is implicitly related to the grain size, and the value choice was rather qualitative, although it could have been tuned through calibration. Both the one- and five-layer linked VIC/DMRT models were forced with ERA-40 precipitation and air temperature, which leads to large uncertainties in the simulated SWE and, consequently, in the simulated TB when compared with the SSM/I observations. Since both models use the same precipitation inputs, the simulated SWE between the one- and five-layer VIC models were similar; however, the TB simulated by the two linked models exhibited large differences for all four frequency channels. The one-layer simulated TB exhibits relatively small variability due to VIC not being able to capture the effects of snowpack layering across the transect, leading to a “bulk” grain size with little spatial variation. Simulated SWE between the one- and five-layer models were similar, therefore the differences in the simulated TB can be attributed to differences in snow density, grain size, and temperature, as well as the assumption of a homogeneous snowpack by the one-layer model. The VIC-simulated snow properties (thickness, density, and grain size) for each snowpack layer that were used to drive DMRT at each SnowSTAR site are shown in Fig. 9. The objective of these comparisons was not to show agreement with the SSM/I observations or the measured snowpack profiles; that would be impossible because of the uncertainty in the precipitation and air temperature forcing the VIC models. On the contrary, the objective was to demonstrate the need for ingesting the available satellite observations for estimating SWE and to explore the implications of using the two linked models in the context of forward modeling for a snow assimilation system.

Fig. 8.
Fig. 8.

Observed TB from SSM/I and simulated TB from the one- and five-layer VIC/DMRT along the SnowSTAR2002 transect for both horizontal and vertical polarizations at (a) 18.7 and (b) 36.5 GHz.

Citation: Journal of Hydrometeorology 13, 5; 10.1175/JHM-D-11-056.1

Fig. 9.
Fig. 9.

Simulated snowpack thickness, density, and grain size for each layer at each SnowSTAR site that were used as input to the DMRT model.

Citation: Journal of Hydrometeorology 13, 5; 10.1175/JHM-D-11-056.1

The impact of precipitation errors on the simulated TB can be examined if the precipitation forcing the linked VIC/DMRT model is rescaled so that the simulated SWE matched the observed SWE from the SnowSTAR2002 snow pits, similarly to the approach from Shi et al. (2009). After rescaling precipitation, simulated snow depth (apart from SWE) is relatively close to the observed (from SnowSTAR2002) values despite the remaining uncertainties in air temperature. Spatially averaged RMSEs before and after precipitation rescaling were 89.5 and 4.8 mm for SWE and 43.7 and 7.8 cm for snow depth. The simulated TB values using the rescaled precipitation are shown in Fig. 10 for the 18.7- and 36.5-GHz frequencies (only vertical polarization) from both the one- and five-layer models, with similar results obtained for the horizontal polarization frequency channels. The one-layer VIC/DMRT model is still unable to capture the variability in TB observed from SSM/I, despite being conditioned with the measured SWE, with linear correlation coefficients of 0.33 and 0.52 for 18.7 and 36.5 GHz, respectively. On the other hand, the five-layer simulated TB had smaller errors than the one-layer model, especially for the lower-frequency channel leading to correlations of 0.83 and 0.80 for the 18.7- and 36.5-GHz frequencies, respectively. Differences between the SSM/I and simulated TB still exist and can be attributed to a number of reasons including the difference in spatial scale of the SSM/I pixel SWE and the SnowSTAR2002-measured SWE that is used to condition the model, as well as uncertainties that remain in simulated snow properties. The latter’s impact can also explain why the higher-frequency simulated TB exhibits some uncertainty, since 36.5-GHz TB is more sensitive to snow grain size relative to the 18.7-GHz frequency. Nonetheless, the five-layer model better reproduced the SSM/I-observed TB when informed with the “correct” precipitation and SWE, which suggests the potential of improving SWE estimates through inversion of the SSM/I observations.

Fig. 10.
Fig. 10.

Simulated TB from the one- and five-layer linked VIC/DMRT forced with rescaled precipitation against observed TB from SSM/I for both 18.7 and 36.5 GHz.

Citation: Journal of Hydrometeorology 13, 5; 10.1175/JHM-D-11-056.1

2) Data assimilation

The differences between the one- and five-layer models, as well as the ones from the SSM/I observations, give rise to questions about the information content of the SSM/I observations and their ability to compensate for the errors in the ERA-40 precipitation, and the impact of employing the one- versus five-layer models in the SWE estimation algorithm. A simple data assimilation experiment was performed to evaluate the differences in estimating SWE by ingesting SSM/I observations into a single- or multilayer snow hydrology model. The assimilation technique employed was the extended Kalman filter (EKF), which approximates optimal state estimation for nonlinear problems (Reichle et al. 2002). The state for this experiment was snow depth at each of the Snow Science Traverse—Alaska Region (SnowSTAR2002) sites, with prior values simulated by VIC forced with the ERA-40 meteorological data. The updated snow depth, which incorporates the SSM/I observations, is given by
e5
where z, z+ are the prior and posterior snow depth state vectors, is the model error covariance matrix assumed to be diagonal (i.e., spatially uncorrelated model errors) with and σi ~ N(0.05, 0.02) × zi, the observation error covariance matrix (zero-mean Gaussian with a 2.0 K standard deviation), the linearized observation operator (the Jacobian ∂TB/∂z approximated by a finite difference scheme), and y is the observation vector populated by the 18.7-GHz vertically polarized TB at each SnowSTAR2002 site i.

Figure 11 shows snow depth along the SnowSTAR2002 transect measured from snow pits and simulated by the one- and five-layer models with and without assimilating the SSM/I TB observations. The results clearly show that the ingestion of the SSM/I observations into the one-layer VIC/DMRT model had almost no impact on the estimated snow depth. In contrast, when the SSM/I observations were assimilated into the five-layer linked model, the estimated snow depth decreased, resulting in smaller errors when compared with snowpit measurements. In particular, the prior RMS errors were 33.6 and 28.2 cm for the one- and five-layer models, respectively, while the posterior RMSEs were 34.1 and 18.1 cm for the respective models. The lack of effect on estimated snow depth when the one-layer model was used resulted partly because of the relatively small differences between the simulated and observed TB (Fig. 8a). On the other hand, assimilating the SSM/I observations into the five-layer linked model led to a general improvement in the snow depth estimates along the transect. Although snow depth errors were reduced in terms of RMSE, linear correlations for the assimilated five-layer estimates were smaller than the prior correlations (0.47 versus 0.61, not statistically significant). One hypothesis about the lower correlation coefficients is the discrepancy in spatial scale between the snowpit measurements and the simulated snow depth (10–25 km), which suggests that although passive microwave satellite observations contain information on the snow mass they cannot resolve smaller-scale spatial variability. A potential approach to overcome such limitations would be to assimilate also finer-resolution satellite observations, such as MODIS snow cover extent.

Fig. 11.
Fig. 11.

Snow depth along the SnowSTAR2002 transect measured at snow pits (circles) and simulated by the one- and five-layer models, without (prior), and with (posterior) assimilation of SSM/I brightness temperature observations.

Citation: Journal of Hydrometeorology 13, 5; 10.1175/JHM-D-11-056.1

4. Summary and discussion

A snowpack stratigraphy model was incorporated into a macroscale hydrology model that accounts for the effects of topography and vegetation on snow accumulation and ablation. The model was used to simulate snow temperature, grain size, and density profiles using meteorological data that would generally be available for large-scale basins globally (daily precipitation and air temperature). Comparisons with CLPX snowpit measurements showed average agreement scores ranging from 0.82 to 0.86 for the simulated snow properties, which were then used to drive the DMRT model to simulate TB’s. These simulations were performed with both a one- and five-layer linked model, and were evaluated through comparisons with ground-based measurements at 18.7 and 36.5 GHz, which showed that explicitly simulating snowpack stratigraphy resulted in closer agreement both in terms of absolute values and polarization/frequency differences. The two VIC/DMRT linked models were also used to simulate snow properties and TB’s along an Alaska transect of snowpit measurements (SnowSTAR2002). The general unavailability of meteorological forcings along the transect made the use of coarse-scale ERA-40 reanalysis dataset necessary to simulate snow properties and microwave radiances. Other forcing datasets could have been used (e.g., interpolated from SNOTEL measurements), but ERA-40 was chosen because it is readily available globally, allowing for the evaluation of passive microwave snow observations in that context. Errors in ERA-40 precipitation led to overestimation of SWE, but the simulated TB from the two models showed large differences, which were caused by the inability of the one-layer model to simulate the observed larger grain sizes. These differences had implications for the estimation of SWE; assimilation of SSM/I observations into the five-layer model resulted in improved snow depth estimates (RMSEs of 18.1 cm versus 34.1 cm without assimilation), while the one-layer assimilation slightly decreased the estimation skill (RMSEs of 34.1 cm versus 33.6 without SSM/I information).

The lower relief at the satellite scales and the sparse forest cover in Alaska are ideal for evaluating the passive microwave observations. However, in other areas where snow is of key significance to water resources (such as the western United States), complex topography, dense forest cover, and higher spatial variability in snow properties will impede estimation. Results from our data assimilation experiment suggest that SSM/I observations contain information to compensate for errors in precipitation and snow mass, but are limited in reproducing smaller-scale (less than 10–15 km) spatial variability. Future work should perform more detailed assimilation experiments over areas with complex topography and forest cover, using observations at multiple frequency channels, with model errors directly tied to precipitation and temperature uncertainties, and evaluate the information content of passive microwave satellite observations. Although improvements in snow mass estimates may be incremental and dependent on a number of factors, it is important to explore and develop approaches to incorporate and digest the long-term satellite dataset, especially for regions where no only in situ measurements of snow properties are essentially nonexistent, but meteorological forcings for hydrological models are uncertain.

Acknowledgments

The authors thank Leung Tsang, Ding Liang, and Xiaolan Xu for providing the DMRT code, as well as Matthew Sturm and Glen Liston for making the SnowSTAR2002 data available. This work was suppored in part by NASA Grant NNG06GD79G to the University of Washington.

REFERENCES

  • Adam, J., , and Lettenmaier D. , 2003: Adjustment of global gridded precipitation for systematic bias. J. Geophys. Res., 108, 4257, doi:10.1029/2002JD002499.

    • Search Google Scholar
    • Export Citation
  • Adler, R., , Kidd C. , , Petty G. , , Morissey M. , , and Goodman H. , 2001: Intercomparison of global precipitation products: The Third Precipitation Intercomparison Project (PIP–3). Bull. Amer. Meteor. Soc., 82, 13771396.

    • Search Google Scholar
    • Export Citation
  • Anderson, E., 1976: A point energy and mass balance model of a snow cover. NOAA Tech. Rep. NWS HYDRO-17 NWS 19, 150 pp.

  • Andreadis, K. M., , Liang D. , , Tsang L. , , Lettenmaier D. P. , , and Josberger E. G. , 2008a: Characterization of errors in a coupled snow hydrology–microwave emission model. J. Hydrometeor., 9, 149164.

    • Search Google Scholar
    • Export Citation
  • Andreadis, K. M., , Storck P. , , and Lettenmaier D. P. , 2008b: Modeling snow accumulation and ablation processes in forested environments. Water Resour. Res., 45, W05429, doi:10.1029/2008WR007042.

    • Search Google Scholar
    • Export Citation
  • Armstrong, R., , and Brodzik M. , 2002: Hemispheric-scale comparison and evaluation of passive-microwave snow algorithms. Ann. Glaciol., 34, 3844.

    • Search Google Scholar
    • Export Citation
  • Armstrong, R., , Knowles K. , , Brodzik M. , , and Hardman M. , 2003: DMSP SSM/I Pathfinder daily EASE-grid brightness temperatures. National Snow and Ice Data Center, Boulder, CO, digital media. [Available online at http://nsidc.org/data/docs/daac/nsidc0032_ssmi_ease_tbs.gd.html.]

  • Bartelt, P., , and Lehning M. , 2002: A physical SNOWPACK model for the Swiss avalanche warning: Part I: Numerical model. Cold Reg. Sci. Technol., 35, 123145.

    • Search Google Scholar
    • Export Citation
  • Boone, A., , and Etchevers P. , 2001: An intercomparison of three snow schemes of varying complexity coupled to the same land surface model: Local-scale evaluation at an alpine site. J. Hydrometeor., 2, 374394.

    • Search Google Scholar
    • Export Citation
  • Bowling, L. C., , Pomeroy J. W. , , and Lettenmaier D. P. , 2004: Parameterization of blowing-snow sublimation in a macroscale hydrology model. J. Hydrometeor., 5, 745762.

    • Search Google Scholar
    • Export Citation
  • Brun, E., 1989: Investigation on wet-snow metamorphism in respect of liquid-water content. Ann. Glaciol., 13, 2226.

  • Brun, E., , Martin E. , , Simon V. , , Gendre C. , , and Coléou C. , 1989: An energy and mass model of snow cover suitable for operational avalanche forecasting. J. Glaciol., 35, 333342.

    • Search Google Scholar
    • Export Citation
  • Chang, A., , Foster J. , , and Hall D. , 1987: Nimbus-7 SMMR derived global snow cover parameters. Ann. Glaciol., 9, 3944.

  • Cherkauer, K. A., , and Lettenmaier D. P. , 2003: Simulation of spatial variability in snow and frozen soil. J. Geophys. Res., 108, 8858, doi:10.1029/2003JD003575.

    • Search Google Scholar
    • Export Citation
  • Cohen, J., , and Entekhabi D. , 1999: Eurasian snow cover variability and northern hemisphere climate predictability. Geophys. Res. Lett., 26, 345348.

    • Search Google Scholar
    • Export Citation
  • Colbeck, S., 1991: The layered character of snow covers. Rev. Geophys., 29, 8196.

  • Colbeck, S., 1993: The vapor diffusion coefficient for snow. Water Resour. Res., 29, 109109.

  • Dennis, J. E., Jr., , and Schnable R. B. , 1983: Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice-Hall, 394 pp.

  • Derksen, C., , Walker A. , , and Goodison B. , 2003: A comparison of 18 winter seasons of in situ and passive microwave-derived snow water equivalent estimates in Western Canada. Remote Sens. Environ., 88, 271282.

    • Search Google Scholar
    • Export Citation
  • Derksen, C., , Walker A. , , and Goodison B. , 2005: Evaluation of passive microwave snow water equivalent retrievals across the boreal forest/tundra transition of western Canada. Remote Sens. Environ., 96 (3–4), 315327.

    • Search Google Scholar
    • Export Citation
  • Derksen, C., , Silis A. , , Sturm M. , , Holmgren J. , , Liston G. , , Huntington H. , , and Solie D. , 2009: Northwest Territories and Nunavut snow characteristics from a subarctic traverse: Implications for passive microwave remote sensing. J. Hydrometeor., 10, 448463.

    • Search Google Scholar
    • Export Citation
  • Dong, J., , Walker J. , , and Houser P. , 2005: Factors affecting remotely sensed snow water equivalent uncertainty. Remote Sens. Environ., 97, 6882.

    • Search Google Scholar
    • Export Citation
  • Duguay, C., , Green J. , , Derksen C. , , English M. , , Rees A. , , Sturm M. , , and Walker A. , 2005: Preliminary assessment of the impact of lakes on passive microwave snow retrieval algorithms in the Arctic. Proc. 62nd Eastern Snow Conf., Waterloo, Ontario, Canada, Eastern Snow Conference, 223–228.

  • Durand, M., , and Margulis S. , 2006: Feasibility test of multifrequency radiometric data assimilation to estimate snow water equivalent. J. Hydrometeor., 7, 443457.

    • Search Google Scholar
    • Export Citation
  • Durand, M., , Kim E. , , and Margulis S. , 2008: Quantifying uncertainty in modeling snow microwave radiance for a mountain snowpack at the point-scale, including stratigraphic effects. IEEE Trans. Geosci. Remote Sens., 46, 17531767.

    • Search Google Scholar
    • Export Citation
  • Elder, K., , Cline D. , , Liston G. , , and Armstrong R. , 2009: NASA cold land processes experiment (CLPX 2002/03): Field measurements of snowpack properties and soil moisture. J. Hydrometeor., 10, 320329.

    • Search Google Scholar
    • Export Citation
  • Etchevers, P., and Coauthors, 2004: Validation of the energy budget of an alpine snowpack simulated by several snow models (SnowMIP project). Ann. Glaciol., 38, 150158.

    • Search Google Scholar
    • Export Citation
  • Foster, J., , Sun C. , , Walker J. , , Kelly R. , , Chang A. , , Dong J. , , and Powell H. , 2005: Quantifying the uncertainty in passive microwave snow water equivalent observations. Remote Sens. Environ., 94, 187203.

    • Search Google Scholar
    • Export Citation
  • Goodison, B., , Walker A. , , Choudhury B. , , Kerr Y. , , Njoku E. , , and Pampaloni P. , 1995: Canadian development and use of snow cover information from passive microwave satellite data. Passive Microwave Remote Sensing of Land-Atmosphere Interactions, B. J. Choudhury et al., Eds., VSP, 245–262.

  • Graf, T., , Koike T. , , Fujii H. , , Brodzik M. , , and Armstrong R. , 2003: CLPX-Ground: Ground based passive microwave radiometer (GBMR-7) data. National Snow and Ice Data Center, Boulder, CO, digital media. [Available online at http://nsidc.org/data/nsidc-0165.html.]

  • Hall, D., , Chang A. , , and Foster J. , 1986: Detection of the depth-hoar layer in the snow-pack of the Arctic Coastal Plain of Alaska, USA, using satellite data. J. Glaciol., 32, 8794.

    • Search Google Scholar
    • Export Citation
  • Hallikainen, M., , and Jolma P. , 1992: Comparison of algorithms for retrieval of snow water equivalent from Nimbus-7 SMMR data in Finland. IEEE Trans. Geosci. Remote Sens., 30, 124131.

    • Search Google Scholar
    • Export Citation
  • Heim, R., , and Dewey K. F. , 1984: Circulation patterns and temperature fields associated with extensive snow cover on the North American continent. Phys. Geogr., 4, 6685.

    • Search Google Scholar
    • Export Citation
  • Jin, J., , Gao X. , , Sorooshian S. , , Yang Z. , , Bales R. , , Dickinson R. , , Sun S. , , and Wu G. , 1999: One-dimensional snow water and energy balance model for vegetated surfaces. Hydrol. Processes, 13, 24672482.

    • Search Google Scholar
    • Export Citation
  • Jordan, R., 1991: A one-dimensional temperature model for a snow cover: Technical documentation for SNTHERM 89. U.S. Army Cold Regions Research and Engineering Laboratory Tech. Rep. CRREL-SR-91-16, 61 pp.

  • Josberger, E., , and Mognard N. , 2002: A passive microwave snow depth algorithm with a proxy for snow metamorphism. Hydrol. Processes, 16, 15571568.

    • Search Google Scholar
    • Export Citation
  • Kelly, R., , Chang A. , , Tsang L. , , and Foster J. , 2003: A prototype AMSR-E global snow area and snow depth algorithm. IEEE Trans. Geosci. Remote Sens., 41, 230242.

    • Search Google Scholar
    • Export Citation
  • Koren, V., , Schaake J. , , Mitchell K. , , Duan Q. , , Chen F. , , and Baker J. , 1999: A parameterization of snowpack and frozen ground intended for NCEP weather and climate models. J. Geophys. Res., 104 (D16), 19 56919 585.

    • Search Google Scholar
    • Export Citation
  • Künzi, K., , Patil S. , , and Rott H. , 1982: Snow-cover parameters retrieved from Nimbus-7 scanning multichannel microwave radiometer (SMMR) data. IEEE Trans. Geosci. Remote Sens., 20, 452467.

    • Search Google Scholar
    • Export Citation
  • Lehning, M., , Fierz C. , , and Lundy C. , 2001: An objective snow profile comparison method and its application to SNOWPACK. Cold Reg. Sci. Technol., 33 (2–3), 253261.

    • Search Google Scholar
    • Export Citation
  • Lehning, M., , Bartelt P. , , Brown B. , , Fierz C. , , and Satyawali P. , 2002: A physical SNOWPACK model for the Swiss avalanche warning: Part II. Snow microstructure. Cold Reg. Sci. Technol., 35, 147167.

    • Search Google Scholar
    • Export Citation
  • Liang, D., , Xu X. , , Tsang L. , , Andreadis K. , , and Josberger E. , 2008: The effects of layers in dry snow on its passive microwave emissions using dense media radiative transfer theory based on the quasicrystalline approximation (QCA/DMRT). IEEE Trans. Geosci. Remote Sens., 46, 36633671.

    • Search Google Scholar
    • Export Citation
  • Liang, X., , Lettenmaier D. P. , , Wood E. F. , , and Burges S. J. , 1994: A simple hydrologically based model of land surface water and energy fluxes for general circulation models. J. Geophys. Res., 99 (D7), 14 41514 428.

    • Search Google Scholar
    • Export Citation
  • Loth, B., , Graf H. , , and Oberhuber J. , 1993: Snow cover model for global climate simulations. J. Geophys. Res., 98 (D6), 10 45110 464.

  • Mätzler, C., , and Hüppi R. , 1989: Review of signature studies for microwave remote sensing of snowpacks. Adv. Space Res., 9, 253265.

    • Search Google Scholar
    • Export Citation
  • Maurer, E., , Wood A. , , Adam J. , , Lettenmaier D. , , and Nijssen B. , 2002: A long-term hydrologically based dataset of land surface fluxes and states for the conterminous United States. J. Climate, 15, 32373251.

    • Search Google Scholar
    • Export Citation
  • Pulliainen, J., 2006: Mapping of snow water equivalent and snow depth in boreal and sub-arctic zones by assimilating space-borne microwave radiometer data and ground-based observations. Remote Sens. Environ., 101, 257269.

    • Search Google Scholar
    • Export Citation
  • Rees, A., , Lemmetyinen J. , , Derksen C. , , Pulliainen J. , , and English M. , 2010: Observed and modelled effects of ice lens formation on passive microwave brightness temperatures over snow covered tundra. Remote Sens. Environ., 114, 116126.

    • Search Google Scholar
    • Export Citation
  • Reichle, R., , Walker J. , , Koster R. , , and Houser P. , 2002: Extended versus ensemble Kalman filtering for land data assimilation. J. Hydrometeor., 3, 728740.

    • Search Google Scholar
    • Export Citation
  • Rosenfeld, S., , and Grody N. , 2000: Anomalous microwave spectra of snow cover observed from Special Sensor Microwave/Imager measurements. J. Geophys. Res., 105 (D11), 14 91314 926.

    • Search Google Scholar
    • Export Citation
  • Schmugge, T. J., , Kustas W. P. , , Ritchie J. C. , , Jackson T. J. , , and Rango A. , 2002: Remote sensing in hydrology. Adv. Water Resour., 25 (8–12), 13671385.

    • Search Google Scholar
    • Export Citation
  • Schweizer, J., , and Kronholm K. , 2007: Snow cover spatial variability at multiple scales: Characteristics of a layer of buried surface hoar. Cold Reg. Sci. Technol., 47, 207223.

    • Search Google Scholar
    • Export Citation
  • Shepard, D., 1984: Computer mapping: The SYMAP interpolation algorithm. Spatial Statistics and Models, G. L. Gaile and C. J. Wilmott, Eds., Springer, 133–145.

  • Shi, X., , Sturm M. , , Liston G. , , Jordan R. , , and Lettenmaier D. , 2009: SnowSTAR2002 transect reconstruction using a multilayered energy and mass balance snow model. J. Hydrometeor., 10, 11511167.

    • Search Google Scholar
    • Export Citation
  • Sturm, M., 1992: Snow distribution and heat flow in the taiga. Arct. Alp. Res., 24, 145152.

  • Sturm, M., , and Benson C. , 1997: Vapor transport, grain growth and depth-hoar development in the subarctic snow. J. Glaciol., 43, 4259.

    • Search Google Scholar
    • Export Citation
  • Sturm, M., , and Liston G. , 2003: The snow cover on lakes of the Arctic Coastal Plain of Alaska, USA. J. Glaciol., 49, 370380.

  • Sturm, M., , and Benson C. , 2004: Scales of spatial heterogeneity for perennial and seasonal snow layers. Ann. Glaciol., 38, 253260.

  • Sturm, M., , Holmgren J. , , Koenig M. , , and Morris K. , 1997: The thermal conductivity of seasonal snow. J. Glaciol., 43, 2641.

  • Sun, S., , Jin J. , , and Xue Y. , 1999: A simple snow-atmosphere-soil transfer model. J. Geophys. Res., 104 (D16), 19 58719 597.

  • Thornton, P., , and Running S. , 1999: An improved algorithm for estimating incident daily solar radiation from measurements of temperature, humidity, and precipitation. Agric. For. Meteor., 93, 211228.

    • Search Google Scholar
    • Export Citation
  • Tsang, L., , Kong J. , , and Shin R. , 1985: Theory of Microwave Remote Sensing. Wiley, 632 pp.

  • Tsang, L., , Chen C. , , Chang A. , , Guo J. , , and Ding K. , 2000: Dense media radiative transfer theory based on quasi-crystalline approximation with applications to passive microwave remote sensing of snow. Radio Sci., 35, 731749.

    • Search Google Scholar
    • Export Citation
  • Tsang, L., , Pan J. , , Liang D. , , Li Z. X. , , Cline D. , , and Tan Y. H. , 2007: Modeling active microwave remote sensing of snow using dense media radiative transfer (DMRT) theory with multiple scattering effects. IEEE Trans. Geosci. Remote Sens., 45, 9901004.

    • Search Google Scholar
    • Export Citation
  • Uppala, S., and Coauthors, 2005: The ERA-40 Re-Analysis. Quart. J. Roy. Meteor. Soc., 131, 29613012.

  • Verseghy, D. L., 1991: CLASS—A Canadian land surface scheme for GCMS. I. Soil model. Int. J. Climatol., 11, 111133.

  • Wiesmann, A., , and Mätzler C. , 1999: Microwave emission model of layered snowpacks. Remote Sens. Environ., 70, 307316.

  • Wigmosta, M., , Vail L. , , and Lettenmaier D. , 1994: A distributed hydrology-vegetation model for complex terrain. Water Resour. Res., 30, 16651680.

    • Search Google Scholar
    • Export Citation
  • Yang, Z., , Dickinson R. , , Robock A. , , and Vinnikov K. , 1997: Validation of the snow submodel of the Biosphere–Atmosphere Transfer Scheme with Russian snow cover and meteorological observational data. J. Climate, 10, 353373.

    • Search Google Scholar
    • Export Citation
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