• Andreadis, K. M., , and Lettenmaier D. P. , 2006: Assimilating remotely sensed snow observations into a macroscale hydrology model. Adv. Water Resour., 29, 872886, doi:10.1016/j.advwatres.2005.08.004.

    • Search Google Scholar
    • Export Citation
  • Arsenault, K. R., , Houser P. R. , , De Lannoy G. J. M. , , and Dirmeyer P. A. , 2013: Impacts of snow cover fraction data assimilation on modeled energy and moisture budgets. J. Geophys. Res. Atmos., 118, 74897504, doi:10.1002/jgrd.50542.

    • Search Google Scholar
    • Export Citation
  • Barlage, M., and Coauthors, 2010: Noah land surface model modifications to improve snowpack prediction in the Colorado Rocky Mountains. J. Geophys. Res., 115, D22101, doi:10.1029/2009JD013470.

    • Search Google Scholar
    • Export Citation
  • Bonan, G. B., 1996: A land surface model (LSM version 1.0) for ecological, hydrological, and atmospheric studies: Technical description and user’s guide. NCAR Tech. Note NCAR/TN-417+STR, 150 pp., doi:10.5065/D6DF6P5X.

  • Boniface, K., , Braun J. J. , , McCreight J. L. , , and Nievinski F. G. , 2015: Comparison of snow data assimilation system with GPS reflectometry snow depth in the western United States. Hydrol. Processes, 29, 24252437, doi:10.1002/hyp.10346.

    • Search Google Scholar
    • Export Citation
  • Bowler, N. E., , Flowerdew J. , , and Pring S. R. , 2013: Tests of different flavours of EnKF on a simple model. Quart. J. Roy. Meteor. Soc., 139, 15051519, doi:10.1002/qj.2055.

    • Search Google Scholar
    • Export Citation
  • Buehner, M., , Houtekamer P. L. , , Charette C. , , Mitchell H. L. , , and He B. , 2010a: Intercomparison of variational data assimilation and the ensemble Kalman filter for global deterministic NWP. Part I: Description and single-observation experiments. Mon. Wea. Rev., 138, 15501566, doi:10.1175/2009MWR3157.1.

    • Search Google Scholar
    • Export Citation
  • Buehner, M., , Houtekamer P. L. , , Charette C. , , Mitchell H. L. , , and He B. , 2010b: Intercomparison of variational data assimilation and the ensemble Kalman filter for global deterministic NWP. Part II: One-month experiments with real observations. Mon. Wea. Rev., 138, 15671586, doi:10.1175/2009MWR3158.1.

    • Search Google Scholar
    • Export Citation
  • Buehner, M., , Morneau J. , , and Charette C. , 2013: Four-dimensional ensemble-variational data assimilation for global deterministic weather prediction. Nonlinear Processes Geophys., 20, 669682, doi:10.5194/npg-20-669-2013.

    • Search Google Scholar
    • Export Citation
  • Che, T., , Li X. , , Jin R. , , and Huang C. , 2014: Assimilating passive microwave remote sensing data into a land surface model to improve the estimation of snow depth. Remote Sens. Environ., 143, 5463, doi:10.1016/j.rse.2013.12.009.

    • Search Google Scholar
    • Export Citation
  • Chen, F., , Crow W. T. , , Starks P. J. , , and Moriasi D. N. , 2011a: Improving hydrologic predictions of a catchment model via assimilation of surface soil moisture. Adv. Water Resour., 34, 526536, doi:10.1016/j.advwatres.2011.01.011.

    • Search Google Scholar
    • Export Citation
  • Chen, Y., , Yang K. , , He J. , , Qin J. , , Shi J. , , Du J. , , and He Q. , 2011b: Improving land surface temperature modeling for dry land of China. J. Geophys. Res., 116, D20104, doi:10.1029/2011JD015921.

    • Search Google Scholar
    • Export Citation
  • Clark, M. P., , Slater A. G. , , Barrett A. P. , , Hay L. E. , , McCabe G. J. , , Rajagopalan B. , , and Leavesley G. H. , 2006: Assimilation of snow covered area information into hydrologic and land-surface models. Adv. Water Resour., 29, 12091221, doi:10.1016/j.advwatres.2005.10.001.

    • Search Google Scholar
    • Export Citation
  • Dai, Y., , and Zeng Q. , 1997: A land surface model (IAP94) for climate studies part I: Formulation and validation in off-line experiments. Adv. Atmos. Sci., 14, 433460, doi:10.1007/s00376-997-0063-4.

    • Search Google Scholar
    • Export Citation
  • Dai, Y., and Coauthors, 2001: Common Land Model (CLM): Technical documentation and user’s guide. Georgia Institute of Technology, 69 pp.

  • Dai, Y., and Coauthors, 2003: The Common Land Model. Bull. Amer. Meteor. Soc., 84, 10131023, doi:10.1175/BAMS-84-8-1013.

  • De Lannoy, G. J. M., , Reichle R. H. , , Arsenault K. R. , , Houser P. R. , , Kumar S. , , Verhoest N. E. C. , , and Pauwels V. R. N. , 2012: Multiscale assimilation of Advanced Microwave Scanning Radiometer–EOS snow water equivalent and Moderate Resolution Imaging Spectroradiometer snow cover fraction observations in northern Colorado. Water Resour. Res., 48, W01522, doi:10.1029/2011WR010588.

    • Search Google Scholar
    • Export Citation
  • Desroziers, G., , Camino J.-T. , , and Berre L. , 2014: 4DEnVar: Link with 4D state formulation of variational assimilation and different possible implementations. Quart. J. Roy. Meteor. Soc., 140, 20972110, doi:10.1002/qj.2325.

    • Search Google Scholar
    • Export Citation
  • Dickinson, R. E., , Henderson-Sellers A. , , and Kennedy P. J. , 1993: Biosphere–Atmosphere Transfer Scheme (BATS) version 1e as coupled to the NCAR Community Climate Model. NCAR Tech. Note NCAR/TN-387+STR, 88 pp., doi:10.5065/D67W6959.

  • Evensen, G., 2003: The ensemble Kalman filter: Theoretical formulation and practical implementation. Ocean Dyn., 53, 343367, doi:10.1007/s10236-003-0036-9.

    • Search Google Scholar
    • Export Citation
  • Evensen, G., , and Van Leeuwen P. J. , 2000: An ensemble Kalman smoother for nonlinear dynamics. Mon. Wea. Rev., 128, 18521867, doi:10.1175/1520-0493(2000)128<1852:AEKSFN>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Fairbairn, D., , Pring S. R. , , Lorenc A. C. , , and Roulstone I. , 2014: A comparison of 4DVar with ensemble data assimilation methods. Quart. J. Roy. Meteor. Soc., 140, 281294, doi:10.1002/qj.2135.

    • Search Google Scholar
    • Export Citation
  • Fertig, E. J., , Harlim J. , , and Hunt B. R. , 2007: A comparative study of 4D‐VAR and a 4D ensemble Kalman filter: Perfect model simulations with Lorenz‐96. Tellus, 59A, 96100, doi:10.1111/j.1600-0870.2006.00205.x.

    • Search Google Scholar
    • Export Citation
  • Fletcher, S. J., , Liston G. E. , , Hiemstra C. A. , , and Miller S. D. , 2012: Assimilating MODIS and AMSR-E snow observations in a snow evolution model. J. Hydrometeor., 13, 14751492, doi:10.1175/JHM-D-11-082.1.

    • Search Google Scholar
    • Export Citation
  • Frei, A., , Tedesco M. , , Lee S. , , Foster J. , , Hall D. K. , , Kelly R. , , and Robinson D. A. , 2012: A review of global satellite-derived snow products. Adv. Space Res., 50, 10071029, doi:10.1016/j.asr.2011.12.021.

    • Search Google Scholar
    • Export Citation
  • Hall, D. K., , Riggs G. A. , , and Salomonson V. V. , 2006: MODIS/Terra snow cover daily L3 global 500 m grid V005 (updated daily). National Snow and Ice Data Center, Boulder, CO, digital media. [Available online at http://nsidc.org/data/docs/daac/modis_v5/mod10a1_modis_terra_snow_daily_global_500m_grid.gd.html.]

  • Huang, X., , Liang T. , , Zhang X. , , and Guo Z. , 2011: Validation of MODIS snow cover products using Landsat and ground measurements during the 2001–2005 snow seasons over northern Xinjiang, China. Int. J. Remote Sens., 32, 133152, doi:10.1080/01431160903439924.

    • Search Google Scholar
    • Export Citation
  • Hunt, B. R., and Coauthors, 2004: Four-dimensional ensemble Kalman filtering. Tellus, 56A, 273277, doi:10.1111/j.1600-0870.2004.00066.x.

    • Search Google Scholar
    • Export Citation
  • Kolberg, S., , Rue H. , , and Gottschalk L. , 2006: A Bayesian spatial assimilation scheme for snow coverage observations in a gridded snow model. Hydrol. Earth Syst. Sci., 10, 369381, doi:10.5194/hess-10-369-2006.

    • Search Google Scholar
    • Export Citation
  • Kumar, S. V., , Peters-Lidard C. D. , , Arsenault K. R. , , Getirana A. , , Mocko D. , , and Liu Y. , 2015: Quantifying the added value of snow cover area observations in passive microwave snow depth data assimilation. J. Hydrometeor., 16, 17361741, doi:10.1175/JHM-D-15-0021.1.

    • Search Google Scholar
    • Export Citation
  • Liang, T. G., , Liu X. Y. , , Wu C. X. , , Guo Z. G. , , and Huang X. D. , 2007: An evaluation approach for snow disasters in the pastoral areas of northern Xinjiang, PR China. N. Z. J. Agric. Res., 50, 369380, doi:10.1080/00288230709510305.

    • Search Google Scholar
    • Export Citation
  • Liu, C., , Xiao Q. , , and Wang B. , 2008: An ensemble-based four-dimensional variational data assimilation scheme. Part I: Technical formulation and preliminary test. Mon. Wea. Rev., 136, 33633373, doi:10.1175/2008MWR2312.1.

    • Search Google Scholar
    • Export Citation
  • Liu, C., , Xiao Q. , , and Wang B. , 2009: An ensemble-based four-dimensional variational data assimilation scheme. Part II: Observing system simulation experiments with Advanced Research WRF (ARW). Mon. Wea. Rev., 137, 16871704, doi:10.1175/2008MWR2699.1.

    • Search Google Scholar
    • Export Citation
  • Liu, Y., , Peters-Lidard C. D. , , Kumar S. , , Foster J. L. , , Shaw M. , , Tian Y. , , and Fall G. M. , 2013: Assimilating satellite-based snow depth and snow cover products for improving snow predictions in Alaska. Adv. Water Resour., 54, 208227, doi:10.1016/j.advwatres.2013.02.005.

    • Search Google Scholar
    • Export Citation
  • Lorenc, A. C., 1986: Analysis methods for numerical weather prediction. Quart. J. Roy. Meteor. Soc., 112, 11771194, doi:10.1002/qj.49711247414.

    • Search Google Scholar
    • Export Citation
  • Lorenc, A. C., 2003: The potential of the ensemble Kalman filter for NWP—A comparison with 4D-Var. Quart. J. Roy. Meteor. Soc., 129, 31833203, doi:10.1256/qj.02.132.

    • Search Google Scholar
    • Export Citation
  • Malik, M. J., , van der Velde R. , , Vekerdy Z. , , and Su Z. , 2012: Assimilation of satellite-observed snow albedo in a land surface model. J. Hydrometeor., 13, 11191130, doi:10.1175/JHM-D-11-0125.1.

    • Search Google Scholar
    • Export Citation
  • Niu, G. Y., , and Yang Z. L. , 2007: An observation‐based formulation of snow cover fraction and its evaluation over large North American river basins. J. Geophys. Res., 112, D21101, doi:10.1029/2007JD008674.

    • Search Google Scholar
    • Export Citation
  • Qiu, X., 2011: Usage of flow-dependent background error covariance in data assimilation and radar wind retrieval (in Chinese). Ph.D. thesis, College of Atmospheric Sciences, Lanzhou University, 129 pp.

  • Regonda, S. K., , Rajagopalan B. , , Clark M. , , and Pitlick J. , 2005: Seasonal cycle shifts in hydroclimatology over the western United States. J. Climate, 18, 372384, doi:10.1175/JCLI-3272.1.

    • Search Google Scholar
    • Export Citation
  • Reichle, R. H., , Koster R. D. , , Liu P. , , Mahanama S. P. P. , , Njoku E. G. , , and Owe M. , 2007: Comparison and assimilation of global soil moisture retrievals from the Advanced Microwave Scanning Radiometer for the Earth Observing System (AMSR-E) and the Scanning Multichannel Microwave Radiometer (SMMR). J. Geophys. Res., 112, D09108, doi:10.1029/2006JD008033.

    • Search Google Scholar
    • Export Citation
  • Rodell, M., , and Houser P. R. , 2004: Updating a land surface model with MODIS-derived snow cover. J. Hydrometeor., 5, 10641075, doi:10.1175/JHM-395.1.

    • Search Google Scholar
    • Export Citation
  • Sakov, P., , and Oke P. R. , 2008: A deterministic formulation of the ensemble Kalman filter: An alternative to ensemble square root filters. Tellus, 60A, 361371, doi:10.1111/j.1600-0870.2007.00299.x.

    • Search Google Scholar
    • Export Citation
  • Sakov, P., , Evensen G. , , and Bertino L. , 2010: Asynchronous data assimilation with the EnKF. Tellus, 62A, 2429, doi:10.1111/j.1600-0870.2009.00417.x.

    • Search Google Scholar
    • Export Citation
  • Salomonson, V. V., , and Appel I. , 2004: Estimating fractional snow cover from MODIS using the normalized difference snow index. Remote Sens. Environ., 89, 351360, doi:10.1016/j.rse.2003.10.016.

    • Search Google Scholar
    • Export Citation
  • Simic, A., , Fernandes R. , , Brown R. , , Romanov P. , , and Park W. , 2004: Validation of VEGETATION, MODIS, and GOES + SSM/I snow‐cover products over Canada based on surface snow depth observations. Hydrol. Processes, 18, 10891104, doi:10.1002/hyp.5509.

    • Search Google Scholar
    • Export Citation
  • Slater, A. G., , and Clark M. P. , 2006: Snow data assimilation via an ensemble Kalman filter. J. Hydrometeor., 7, 478493, doi:10.1175/JHM505.1.

    • Search Google Scholar
    • Export Citation
  • Su, H., , Yang Z.-L. , , Niu G.-Y. , , and Dickinson R. E. , 2008: Enhancing the estimation of continental-scale snow water equivalent by assimilating MODIS snow cover with the ensemble Kalman filter. J. Geophys. Res., 113, D08120, doi:10.1029/2007JD009232.

    • Search Google Scholar
    • Export Citation
  • Sun, A. Y., , Morris A. , , and Mohanty S. , 2009: Comparison of deterministic ensemble Kalman filters for assimilating hydrogeological data. Adv. Water Resour., 32, 280292, doi:10.1016/j.advwatres.2008.11.006.

    • Search Google Scholar
    • Export Citation
  • Talagrand, O., 1981: A study of the dynamics of four‐dimensional data assimilation. Tellus, 33A, 4360, doi:10.1111/j.2153-3490.1981.tb01729.x.

    • Search Google Scholar
    • Export Citation
  • Taylor, K. E., 2001: Summarizing multiple aspects of model performance in a single diagram. J. Geophys. Res., 106, 71837192, doi:10.1029/2000JD900719.

    • Search Google Scholar
    • Export Citation
  • Thirel, G., , Salamon P. , , Burek P. , , and Kalas M. , 2011: Assimilation of MODIS snow cover area data in a distributed hydrological model. Hydrol. Earth Syst. Sci. Discuss., 8, 13291364, doi:10.5194/hessd-8-1329-2011.

    • Search Google Scholar
    • Export Citation
  • Thirel, G., , Salamon P. , , Burek P. , , and Kalas M. , 2013: Assimilation of MODIS snow cover area data in a distributed hydrological model using the particle filter. Remote Sens., 5, 58255850, doi:10.3390/rs5115825.

    • Search Google Scholar
    • Export Citation
  • Tian, X., , Xie Z. , , and Dai A. , 2008: An ensemble-based explicit four-dimensional variational assimilation method. J. Geophys. Res., 113, D21124, doi:10.1029/2008JD010358.

    • Search Google Scholar
    • Export Citation
  • Wang, S., , Xue M. , , and Min J. , 2013: A four‐dimensional asynchronous ensemble square-root filter (4DEnSRF) algorithm and tests with simulated radar data. Quart. J. Roy. Meteor. Soc., 139, 805819, doi:10.1002/qj.1987.

    • Search Google Scholar
    • Export Citation
  • Wang, T., and Coauthors, 2013: Evaluation of an improved intermediate complexity snow scheme in the ORCHIDEE land surface model. J. Geophys. Res. Atmos., 118, 60646079, doi:10.1002/jgrd.50395.

    • Search Google Scholar
    • Export Citation
  • Wang, X., , and Lei T. , 2014: GSI-based four-dimensional ensemble–variational (4DEnsVar) data assimilation: Formulation and single-resolution experiments with real data for NCEP Global Forecast System. Mon. Wea. Rev., 142, 33033325, doi:10.1175/MWR-D-13-00303.1.

    • Search Google Scholar
    • Export Citation
  • Whitaker, J. S., , and Hamill T. M. , 2002: Ensemble data assimilation without perturbed observations. Mon. Wea. Rev., 130, 19131924, doi:10.1175/1520-0493(2002)130<1913:EDAWPO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Xu, J., , and Shu H. , 2014: Assimilating MODIS-based albedo and snow cover fraction into the Common Land Model to improve snow depth simulation with direct insertion and deterministic ensemble Kalman filter methods. J. Geophys. Res. Atmos., 119, 10 68410 701, doi:10.1002/2014JD022012.

    • Search Google Scholar
    • Export Citation
  • Xu, J., , Shu H. , , and Dong L. , 2014: DEnKF—Variational hybrid snow cover fraction data assimilation for improving snow simulations with the Common Land Model. Remote Sens., 6, 10 61210 635, doi:10.3390/rs61110612.

    • Search Google Scholar
    • Export Citation
  • Xue, Y. K., , Sun S. F. , , Kahan D. S. , , and Jiao Y. J. , 2003: Impact of parameterizations in snow physics and interface processes on the simulation of snow cover and runoff at several cold region sites. J. Geophys. Res., 108, 8859, doi:10.1029/2002JD003174.

    • Search Google Scholar
    • Export Citation
  • Yang, K., , He J. , , Tang W. , , Qin J. , , and Cheng C. C. , 2010: On downward shortwave and longwave radiations over high altitude regions: Observation and modeling in the Tibetan Plateau. Agric. For. Meteor., 150, 3846, doi:10.1016/j.agrformet.2009.08.004.

    • Search Google Scholar
    • Export Citation
  • Zaitchik, B. F., , and Rodell M. , 2009: Forward-looking assimilation of MODIS-derived snow-covered area into a land surface model. J. Hydrometeor., 10, 130148, doi:10.1175/2008JHM1042.1.

    • Search Google Scholar
    • Export Citation
  • Zhang, M., , and Zhang F. , 2012: E4DVar: Coupling an ensemble Kalman filter with four-dimensional variational data assimilation in a limited-area weather prediction model. Mon. Wea. Rev., 140, 587600, doi:10.1175/MWR-D-11-00023.1.

    • Search Google Scholar
    • Export Citation
  • Zhang, Y. F., , Hoar T. J. , , Yang Z. L. , , Anderson J. L. , , Toure A. M. , , and Rodell M. , 2014: Assimilation of MODIS snow cover through the Data Assimilation Research Testbed and the Community Land Model version 4. J. Geophys. Res. Atmos., 119, 70917103, doi:10.1002/2013JD021329.

    • Search Google Scholar
    • Export Citation
  • Zhou, Q., , and Sun B. , 2013: Reliability of long-term snow depth data sets from remote sensing over the western arid zone of China. Remote Sens. Lett., 4, 10391048, doi:10.1080/2150704X.2013.832841.

    • Search Google Scholar
    • Export Citation
  • Zhuang, X., , Guo C. , , Zhao Z. , , and Zhang L. , 2010: Snow cover variation analysis in Altay area of Xinjiang (in Chinese). J. Arid Meteor., 28, 190197.

    • Search Google Scholar
    • Export Citation
  • View in gallery

    The geographic locations of the five sites in the Altay region of northern Xinjiang, China, on the (a) land-cover map from Xu and Shu (2014) and (b) DEM with ~1 km spatial resolution.

  • View in gallery

    The new (blue) and old (green) accumulation SDCs, generated by fitting in situ SD observations to MODIS SCFs (red) during the accumulation period from January 2004 to October 2008 at the (a) Aletai, (b) Buerjin, (c) Fuyun, (d) Jimunai, and (e) Qinghe sites. Inset in each panel is the sample in situ SD (horizontal) and MODIS SCF (vertical) error bars. The abscissa scales in the panels differ.

  • View in gallery

    As in Fig. 2, but for ablation SDCs during the ablation period from January 2004 to October 2008.

  • View in gallery

    Comparisons of MODIS SCF (red), old SCF (green), and new SCF (blue) estimated with an SDC and in situ SD observations from November 2008 to March 2009 at the (a) Aletai, (b) Buerjin, (c) Fuyun, (d) Jimunai, and (e) Qinghe sites. (f) The sample MODIS SCF error bars of the five sites are plotted.

  • View in gallery

    Comparisons of MODIS SCF (red), old SCF (green), and new SCF (blue) at the (a) Aletai, (b) Buerjin, (c) Fuyun, (d) Jimunai, and (e) Qinghe sites. (f) The sample MODIS SCF error bars of the five sites are plotted.

  • View in gallery

    Comparisons of the SD time series from in situ (red), the old SDC simulation (green), and the new SDC simulation (blue) at the (a) Aletai, (b) Buerjin, (c) Fuyun, (d) Jimunai, and (e) Qinghe sites. (f) The sample in situ SD error bars of the five sites are plotted. The ordinate scales in (a)–(e) are different.

  • View in gallery

    The NEPR of the CoLM simulated SD with the new SDC.

  • View in gallery

    Comparisons of the SD time series for in situ SD observations (purple) and the analyzed SD from the old SDC simulation (green), the new SDC simulation (blue), DEnKF (cyan), and 2DEnVar (red) at the (a) Aletai, (b) Buerjin, (c) Fuyun, (d) Jimunai, and (e) Qinghe sites. The assimilation window length is set to 4 days in the 2DEnVar experiment. (f) The sample in situ SD error bars of the five sites are plotted. The ordinate scales in (a)–(e) are different.

  • View in gallery

    Taylor diagram of the analyzed SD in different snow DA experiments at the (a) Aletai, (b) Buerjin, (c) Fuyun, (d) Jimunai, and (e) Qinghe sites. The black half-solid circle, termed the “reference” field, represents the standard deviation of in situ SD observations, while other fields are referred to as model-simulated fields. The color bar represents the bias between the analyzed SDs and in situ SD observations. The ordinate and abscissa scales in (a)–(e) are different.

  • View in gallery

    The NEPR of the analyzed SD in the DEnKF (blue) and 2DEnVar (red) experiments.

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Improvement of the Snow Depth in the Common Land Model by Coupling a Two-Dimensional Deterministic Ensemble Model with a Variational Hybrid Snow Cover Fraction Data Assimilation Scheme and a New Observation Operator

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  • 1 Guangzhou Institute of Geography, and Key Lab of Guangdong for Utilization of Remote Sensing and Geographical Information System, and Guangdong Open Laboratory of Geospatial Information Technology and Application, Guangzhou, China
  • 2 Department of Computer Science, Guangdong University of Education, Guangzhou, China
  • 3 State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan University, and Collaborative Innovation Center of Geospatial Technology, Wuhan, China
  • 4 Guangzhou Institute of Geography, and Key Lab of Guangdong for Utilization of Remote Sensing and Geographical Information System, and Guangdong Open Laboratory of Geospatial Information Technology and Application, Guangzhou, China
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Abstract

During snow cover fraction (SCF) data assimilation (DA), the simplified observation operator and presence of cloud cover cause large errors in the assimilation results. To reduce these errors, a new snow cover depletion curve (SDC), known as an observation operator in the DA system, is statistically fitted to in situ snow depth (SD) observations and Moderate Resolution Imaging Spectroradiometer (MODIS) SCF data from January 2004 to October 2008. Using this new SDC, a two-dimensional deterministic ensemble–variational hybrid DA (2DEnVar) method of integrating the deterministic ensemble Kalman filter (DEnKF) and a two-dimensional variational DA (2DVar) is proposed. The proposed 2DEnVar is then used to assimilate the MODIS SCF into the Common Land Model (CoLM) at five sites in the Altay region of China for data from November 2008 to March 2009. The analysis performance of the 2DEnVar is compared with that of the DEnKF. The results show that the 2DEnVar outperforms the DEnKF as it effectively reduces the bias and root-mean-square error during the snow accumulation and ablation periods at all sites except for the Qinghe site. In addition, the 2DEnVar, with more assimilated MODIS SCF observations, produces more innovations (observation minus forecast) than the DEnKF, with only one assimilated MODIS SCF observation. The problems of cloud cover and overestimation are addressed by the 2DEnVar.

Corresponding author e-mail: Jianhui Xu, xujianhui306@163.com

Abstract

During snow cover fraction (SCF) data assimilation (DA), the simplified observation operator and presence of cloud cover cause large errors in the assimilation results. To reduce these errors, a new snow cover depletion curve (SDC), known as an observation operator in the DA system, is statistically fitted to in situ snow depth (SD) observations and Moderate Resolution Imaging Spectroradiometer (MODIS) SCF data from January 2004 to October 2008. Using this new SDC, a two-dimensional deterministic ensemble–variational hybrid DA (2DEnVar) method of integrating the deterministic ensemble Kalman filter (DEnKF) and a two-dimensional variational DA (2DVar) is proposed. The proposed 2DEnVar is then used to assimilate the MODIS SCF into the Common Land Model (CoLM) at five sites in the Altay region of China for data from November 2008 to March 2009. The analysis performance of the 2DEnVar is compared with that of the DEnKF. The results show that the 2DEnVar outperforms the DEnKF as it effectively reduces the bias and root-mean-square error during the snow accumulation and ablation periods at all sites except for the Qinghe site. In addition, the 2DEnVar, with more assimilated MODIS SCF observations, produces more innovations (observation minus forecast) than the DEnKF, with only one assimilated MODIS SCF observation. The problems of cloud cover and overestimation are addressed by the 2DEnVar.

Corresponding author e-mail: Jianhui Xu, xujianhui306@163.com

1. Introduction

As a component of the Earth system, snow plays a key role in Earth’s hydrological processes, land surface energy balance, and climate change (Frei et al. 2012; Simic et al. 2004; T. Wang et al. 2013). Located in the hinterland of the Eurasian continent, the Altay region of northern Xinjiang is an important seasonal snow area of China and the base for animal husbandry in Xinjiang. The accurate tracking of seasonal snow accumulation and ablation is of great concern for monitoring the water cycle of the Altay region. The seasonal snowmelt recharges the rivers. However, prolonged, heavy snowfall may cause snow disasters and even lead to snowmelt flooding. Serious snow disasters exert negative influences on transportation, electric power, communications, agriculture, and animal husbandry. They threaten lives and property and destroy the regional socioeconomic structure (Liang et al. 2007). Fortunately, accurate estimates of snow depth (SD) help water managers predict the timing and volume of peak spring snowmelt (Boniface et al. 2015; Regonda et al. 2005) and snow disasters, increasing preparedness.

To obtain accurate snow estimates, many researchers have focused on the snow data assimilation (DA) by assimilating snow-related observations into hydrological and land surface models, for example, the Noah land surface model, Variable Infiltration Capacity model, Community Land Model, and Common Land Model (CoLM). Most researchers have used the rule-based direct insertion (Fletcher et al. 2012; Liu et al. 2013; Rodell and Houser 2004; Zaitchik and Rodell 2009), the ensemble Kalman filter (EnKF; Andreadis and Lettenmaier 2006; Arsenault et al. 2013; De Lannoy et al. 2012; Su et al. 2008), the ensemble square-root filter (EnSRF; Clark et al. 2006; Slater and Clark 2006), the Bayesian scheme (Kolberg et al. 2006), and the particle filter (Thirel et al. 2011, 2013) DA methods to assimilate the snow cover fraction (SCF; Arsenault et al. 2013; Zhang et al. 2014), SD (Liu et al. 2013), GPS reflectometry SD (Boniface et al. 2015), and snow albedo (Malik et al. 2012; Xu and Shu 2014) into the hydrological and land surface models to improve snow estimates. Because the SCF DA is susceptible to the presence of cloud cover, alternative data types, such as passive microwave brightness temperature observations, are assimilated into land surface models to improve SD estimates (Che et al. 2014; Kumar et al. 2015). In these snow DA methods, the EnKF method (Evensen 2003) has been successfully applied to improve snow estimates in different hydrological and land surface models. However, the traditional EnKF with perturbed observations may introduce sampling errors, which lead to suboptimal results (Whitaker and Hamill 2002). De Lannoy et al. (2012) have also pointed out that perturbing the full SCF would decrease the SCF observations, which leads to an underestimation of the snow water equivalent (SWE) estimates in the SCF DA. Accordingly, to improve the SD simulations, a deterministic ensemble Kalman filter (DEnKF; Sakov and Oke 2008) without perturbing observations has been proposed and implemented in assimilating SCF observations into the CoLM (Xu and Shu 2014; Xu et al. 2014).

Although snow simulations are improved by assimilating satellite data into the CoLM with the DEnKF–albedo method of Xu and Shu (2014) and the DEnKF–variational (DEnVar) method of Xu et al. (2014), overestimation of the analyzed SDs may occur at some sites during the accumulation and ablation periods. This may be attributed to large positive innovations (observation minus forecast). They are caused by the fact that a simplified observation operator may underestimate the predicted SCF observation H(xb), where H is the observation operator, xb are the forecast state variables, and b represents the model forecast. In this study, to reduce errors introduced by the simplified observation operator, a new snow cover depletion curve (SDC), also known as an observation operator in the DA system, is developed by statistically fitting the data to the historical in situ SD observations and Moderate Resolution Imaging Spectroradiometer (MODIS) SCF products during the accumulation and ablation periods. The new SDC can then be used as the snow process model in the CoLM to improve snow simulations.

Previous studies have documented that the MODIS SCF data assimilation may be influenced by the presence of cloud cover, because the presence of cloud cover makes SCF observations unavailable for data assimilation. The current popular DA methods such as the four-dimensional variational DA (4DVar; Lorenc 1986; Talagrand 1981), the four-dimensional ensemble Kalman filter (4DEnKF; Fertig et al. 2007; Hunt et al. 2004), the asynchronous ensemble Kalman filter (AEnKF; Sakov et al. 2010), the four-dimensional ensemble square-root filter algorithm (4DEnSRF; Qiu 2011; S. Wang et al. 2013), the ensemble Kalman smoother (Evensen and Van Leeuwen 2000), and the combinations of 4DVar and EnKF (Buehner et al. 2010a,b; Desroziers et al. 2014; Fairbairn et al. 2014; Liu et al. 2008, 2009; Tian et al. 2008; Zhang and Zhang 2012) may be helpful in alleviating the influence of cloud cover to some extent by assimilating more observations distributed over time into the land surface model. However, 4DVar is required to develop the tangent linear and adjoint models of the forecast model and observation operator, and the 4DEnKF may introduce sampling errors by perturbing observations. Therefore, based on the Gridpoint Statistical Interpolation analysis system (GSI) operated at the National Centers for Environmental Prediction (NCEP), Wang and Lei (2014) developed a four-dimensional ensemble–variational DA (4DEnsVar). The 4DEnsVar integrates 4DVar and EnSRF. An alternative to EnSRF without observation perturbations is the DEnKF (Sakov and Oke 2008), which is easier to implement than the EnSRF (Sun et al. 2009) and has greater potential for improving analysis updates, compared to the stochastic EnKF (Bowler et al. 2013; Sakov and Oke 2008). Furthermore, the DEnKF has been successfully applied to assimilate MODIS SCF into the CoLM for improving SD simulations (Xu and Shu 2014; Xu et al. 2014). Therefore, to reduce the influence of the presence of cloud cover, based on the proposed SDC above, this study proposes a new two-dimensional deterministic ensemble–variational hybrid DA (2DEnVar) method, based partly on the works of Liu et al. (2008) and Buehner et al. (2010a). The 2DEnVar integrates DEnKF and two-dimensional variational DA (2DVar). The 2DEnVar is used to assimilate SCF observations into the CoLM for snow simulation improvements. The 2DEnVar without observation perturbations takes advantage of the background error covariance of the DEnKF and the 2DVar in preventing filter divergence. In addition, the 2DEnVar does not require the tangent linear models of the CoLM and the observation operator or their adjoint models.

The model and data are introduced in section 2. Section 3 gives a detailed description of the snow DA schemes, including the DA methods, SDC, and experimental design. The experimental results are discussed in section 4, and concluding remarks are presented in section 5.

2. Model and data

a. Common Land Model

In this study, the state-of-the-art, single-column CoLM (Dai et al. 2003) is employed as a platform for investigating all DA methods. The CoLM combines the advanced features of three well-known land surface models, including the Land Surface Model (LSM; Bonan 1996), the Biosphere–Atmosphere Transfer Scheme (BATS; Dickinson et al. 1993), and the 1994 version of the Chinese Academy of Science Institute of Atmospheric Physics LSM (IAP94; Dai and Zeng 1997). The CoLM has 10 unevenly spaced vertical soil layers and up to five snow layers. Each snow layer scheme accounts for the layer-based liquid water retention, the thawing/freezing, the snow melting, and the heat energy. At every time step, the snow layers can be combined or divided in terms of the snow layer thicknesses. The snow compaction processes, which include the destructive metamorphism, the densification process due to snow overburden, and snow melting, determine the SD of each snow layer in the CoLM. The total SD is obtained by adding together the snow layers in the CoLM:
e1
where denotes the snow depth (m) in layer j and snl denotes the number of snow layers.
As one of the key snow processes, the SCF can affect much of the CoLM physics. The SCF affects not only averaged surface albedo, but the subsequent CoLM energy flux and temperature calculations, which in turn affects the snow simulations (Arsenault et al. 2013; Barlage et al. 2010). In the CoLM, SCF is parameterized as a diagnostic variable, which is derived from a snow state variable, such as the total SD or SWE:
e2
where is the roughness length for the bare soil with a default value of 0.01 m and is the total snow depth, which can be rewritten as a function of the SWE and snow density. The SCF value is then used to calculate the direct and diffuse beam averaged surface albedos for both the visible bands and near-infrared bands, and subsequently, to calculate the energy fluxes. More details about the snow processes in the CoLM can be found in Dai et al. (2001, 2003).

b. Experimental sites

This study area (46°–49°N, 85°–91°E) is in the Altay region of the northern Xinjiang region of China, where five meteorological sites are located in a homogeneous land-cover area (Fig. 1). Influenced by the Siberian high, the study region experiences a long, cold, and snowy winter (Zhuang et al. 2010), which lasts about 120 days from November to March of the following year (Huang et al. 2011). Daily in situ SD observations of the five sites were provided by the Institute of Desert Meteorology, China Meteorological Administration. In this study, daily in situ SD observations from January 2004 to March 2009 were used to implement the following experiments. Previous studies have used these observations for comparison and validation of MODIS snow products and SD datasets retrieved from passive microwave remote sensing (Huang et al. 2011; Zhou and Sun 2013). In this study, the SD observations from November 2008 to March 2009 are considered as a validation dataset to evaluate the analysis performance of the snow DA methods. The mean SDs from November 2008 to March 2009 are 32.71, 15.41, 15.99, 22.8, and 14.35 cm for the Aletai, Buerjin, Fuyun, Jimunai, and Qinghe sites, respectively.

Fig. 1.
Fig. 1.

The geographic locations of the five sites in the Altay region of northern Xinjiang, China, on the (a) land-cover map from Xu and Shu (2014) and (b) DEM with ~1 km spatial resolution.

Citation: Journal of Hydrometeorology 18, 1; 10.1175/JHM-D-16-0149.1

c. MODIS snow cover fraction

In the snow DA experiments, the Collection 5 MODIS/Terra Snow Cover Daily L3 Global 500 m Grid (MOD10A1) SCF product (Hall et al. 2006) is assimilated into the CoLM for improvement of the SD simulations. The MOD10A1 SCF product at about 0230 UTC is generated by calculating a normalized difference snow index with MODIS band 4 and band 6 (Salomonson and Appel 2004). The SCF product with a spatial resolution of 500 m during the period from January 2004 to March 2009 was downloaded from the National Snow and Ice Data Center (http://nsidc.org/data/mod10a1). To be consistent with the spatial resolution of the CoLM, the 500-m SCF product is resampled to a 0.01° SCF product using a nearest-neighbor resampling method, using NASA’s MODIS Reprojection Tool. The MODIS SCF product from November 2008 to March 2009 is considered as the “observation” to be assimilated into the CoLM, while the MODIS SCF product from January 2004 to October 2008 is used to estimate a new SDC, known as an observation operator, with in situ SD observations.

3. Methods

a. Deterministic ensemble Kalman filter

The updated equations of the DEnKF (Sakov and Oke 2008) are formulated as
e3
e4
e5
e6
where and are the forecast and analysis ensemble means of the state variables (e.g., SD in this study) at analysis time , respectively; represents the forecast state variables; i is the ensemble member index; and N is the ensemble size. Matrix is known as the Kalman gain matrix, and is the background error covariance estimated by Eq. (6). Variable is the observation error variance, and is the observation set (e.g., MODIS SCF in this study). In the DEnKF, the observation set is not perturbed. Variable is the observation operator, and is the tangent linear version of .
The analysis perturbation is updated by halving the Kalman gain in the DEnKF:
e7
where is the forecast ensemble perturbation and is the analysis ensemble perturbation.
Finally, the analysis ensemble is generated by adding the analysis ensemble perturbations to the analysis ensemble mean:
e8

b. Hybrid 2DEnVar method

In the three-dimensional variational DA (3DVar), Lorenc (2003) first introduced ensemble perturbations in an ensemble forecast to precondition the control variable w. The method has been widely applied to the 4DVar system (Buehner et al. 2010a, 2013; Liu et al. 2008), where the flow-dependent background error covariance from EnKF is easily introduced into the cost function of 4DVar, and the tangent linear model of the forecast model and its adjoint model do not have to be calculated. Here, we propose a new hybrid 4DEnVar method that combines the necessary components from DEnKF and 4DVar. In the 4DEnVar without observation perturbations, there are four steps: 1) the ensemble mean from the DEnKF ensemble is used as the first estimate for each 4DVar cycle, and the background error covariance derived from DEnKF is introduced into the 4DVar cost function; 2) the DEnKF analysis ensemble mean is replaced by the 4DVar analysis; 3) the analysis perturbations for the next cycle of ensemble forecasts are updated with DEnKF; and 4) the analysis ensemble is updated by adding the analysis perturbations to the analysis ensemble mean.

Similar to the works of Liu et al. (2008), we use the background perturbations from DEnKF to precondition the 4DVar control variables w in 4DEnVar. The cost function in the control variable space becomes:
e9
where M is the assimilation window length, T represents the matrix transposition, b represents the model forecast, dtm is the innovation at time tm, and is the forecast ensemble perturbation at time tm, calculated using Eq. (10):
e10
where is the tangent linear model of the CoLM, is the background state vector at time tm and is the ensemble mean of the background state vector. The background error estimated from the ensemble perturbations can be transformed to observation space using
e11
The gradient and Hessian matrix of the cost function [Eq. (9)] are rewritten as
e12
e13
where is the identity matrix. The adjoint models are easily avoided in Eqs. (12) and (13) by transforming the background error to observation space with Eq. (11). Moreover, Eq. (11) demonstrates that the 4DEnVar does not need a linear approximation of the CoLM forecast model and observation operator. In this work, we employ a conjugate-gradient method for the minimization of the quadratic cost function in Eq. (9). If the optimal control variables are determined, the 4DEnVar analysis at time is obtained with Eq. (14):
e14
The 4DEnVar analysis ensemble is then obtained by summing the DEnKF analysis ensemble perturbations in Eq. (7) and the 4DEnVar analysis in Eq. (14):
e15
For both the DEnKF and 4DEnVar methods, the updated snow state in Eqs. (8) and (15) is further used to update the other CoLM snow states for each of the snow layers according to Eq. (1). For example, the SD in each snow layer is directly updated by the updated total SD in :
e16
where j denotes the index of the snow layers; and are the forecast and updated SD at snow layer j, respectively; and is the forecast total SD at time . Finally, the snow layer state variables are further updated to account for the combining and dividing of snow layers by following the existing parameterization of the snow layering schemes in the CoLM (Dai et al. 2001).

Because the 4DEnVar is implemented at a single grid point with a 0.01° (~1 km) spatial resolution, it is more appropriate to designate 4DEnVar as 2DEnVar. In this study, the DEnKF and 2DEnVar methods are implemented to assimilate the MODIS SCF observations into the CoLM.

c. New SDC

1) Establishment of new SDC

Xu and Shu (2014) have documented that a simplified SDC in the CoLM, known as an observation operator, may underestimate the predicted SCF observation H(xb), leading to a large positive innovation [yoH(xb)] in snow DA experiments. This leads to the overestimation of the SD estimates over the accumulation and ablation periods. To decrease errors introduced by the simplified SDC, new accumulation and ablation SDCs were statistically fitted to the available in situ SD observations and MODIS SCFs during the accumulation and ablation periods from January 2004 to October 2008, respectively. The fixed transition date between accumulation and ablation periods was defined jointly by combining the snowmelt occurrence time and in situ snow depth from January 2004 to October 2008. The new accumulation and ablation SDCs and their expressions are shown in Figs. 2 and 3, respectively. Then, the new accumulation and ablation SDCs, known as observation operators, were used to convert in situ SD observation into in situ SCF validation “ground truth.” The root-mean-square errors (RMSEs) between in situ SCFs and MODIS SCFs from January 2004 to October 2008 were calculated and considered as the MODIS SCF observation error, which is characterized by the observation error standard deviation for the DA experiments. The final MODIS SCF observation errors (RMSEs) for the five sites during the accumulation and ablation periods are shown in Table 1.

Fig. 2.
Fig. 2.

The new (blue) and old (green) accumulation SDCs, generated by fitting in situ SD observations to MODIS SCFs (red) during the accumulation period from January 2004 to October 2008 at the (a) Aletai, (b) Buerjin, (c) Fuyun, (d) Jimunai, and (e) Qinghe sites. Inset in each panel is the sample in situ SD (horizontal) and MODIS SCF (vertical) error bars. The abscissa scales in the panels differ.

Citation: Journal of Hydrometeorology 18, 1; 10.1175/JHM-D-16-0149.1

Fig. 3.
Fig. 3.

As in Fig. 2, but for ablation SDCs during the ablation period from January 2004 to October 2008.

Citation: Journal of Hydrometeorology 18, 1; 10.1175/JHM-D-16-0149.1

Table 1.

Expressions and statistics of the new SDCs during the accumulation and ablation periods, fitted with in situ SD observations and MODIS SCFs from January 2004 to October 2008.

Table 1.

In Fig. 2, the estimated SCF with the new accumulation SDC over the accumulation period approaches the MODIS SCF more closely than does the old SDC. Overall, the old SCFs are well below the MODIS SCFs, which leads to the underestimation of the predicted SCF and large errors in the snow simulations in the CoLM. Furthermore, large MODIS SCF observation errors are introduced in the snow DA since the old SDC is used as the observation operator; for example, the MODIS SCF observation errors at the Buerjin and Aletai sites are up to 16.74% and 35.02%, respectively (Xu and Shu 2014). Compared with the old SDC, the new accumulation SDC significantly decreases errors of the estimated SCF, as shown in Table 1 of this manuscript and Table 3 of Xu and Shu (2014). The new SCF at the Buerjin site shows the largest RMSE of 0.114 and the smallest coefficient of determination R2 of 0.854. This RMSE approximately approaches the mean absolute error of 0.1 for the MODIS SCF product. However, the error for the new SCF at the Buerjin site is less than that of the old SCF. The new accumulation SDC at the Aletai site has the best fit, as the R2 of the new SCF reaches 0.969, and the RMSE is reduced from 0.35 (Xu and Shu 2014) to 0.041 (Table 1).

In Fig. 3, the new SDC shows better performance than the old SDC during the ablation period at all sites, except for the Buerjin site, which can effectively avoid the underestimation of the predicted SCF. The estimated SCF with the new SDC more closely approaches the MODIS SCF than does that with the old SDC during the ablation period. Table 1 also shows that the R2 values and RMSEs of the new SCF are greater than 0.925 and less than 0.06, respectively, during the ablation period at all sites. For the Buerjin site, the new SDC shows patterns similar to the old SDC. However, the new SCF approaches the MODIS SCF more closely than does the old SCF (Fig. 3b), which has an RMSE of only 0.025 and an R2 value of 0.925 (Table 1).

Generally, compared with the old SDC, the new accumulation and ablation SDCs, which are statistically fit to the historical in situ SD observations and MODIS SCF products, can better represent the actual relationship between SD and SCF. The new SDCs do not significantly underestimate the predicted SCF observation H(xb), and they effectively reduce large errors introduced by the old SDC and MODIS SCF observation errors in the snow DA. Furthermore, the data in Table 1 and Figs. 2 and 3 indicate that the new accumulation SDC with larger errors in the estimated SCF has a slightly worse fit than the ablation SDC. Xu and Shu (2014) have pointed out that the MODIS SCF product during the accumulation period may have smaller observation errors than those during the ablation period in the snow DA.

2) Validation of new SDC

To validate the performance of the new SDC in predicting the SCF, the MODIS SCF product from November 2008 to March 2009 was used as the “reference” value for evaluating the accuracy of the estimated SCF with in situ SD. First, combining the accumulation and ablation SDCs, the new SCFs were estimated by in situ SD observations from November 2008 to March 2009. Then, the error statistics of the new SCF, including bias, RMSE, and R2, were calculated for validation of the new SDC.

As shown in Fig. 4, the old SDC would lead to the overall underestimation of the estimated SCF at all sites, except for the Buerjin site. For the Buerjin site, the old SCF is slightly less than the MODIS SCF, but worse than the new SCF (Fig. 4b). In contrast to the old SCF, the new SCF does not underestimate or overestimate SCF and illustrates a time series consistent with the MODIS SCF at all sites, except for the Qinghe site. For the Qinghe site, the new SCF is overall larger than the MODIS SCF. Figure 4e shows that the new SCF is overestimated during the accumulation period from November 2008 to March 2009, while it shows good consistency with the MODIS SCF during the ablation period.

Fig. 4.
Fig. 4.

Comparisons of MODIS SCF (red), old SCF (green), and new SCF (blue) estimated with an SDC and in situ SD observations from November 2008 to March 2009 at the (a) Aletai, (b) Buerjin, (c) Fuyun, (d) Jimunai, and (e) Qinghe sites. (f) The sample MODIS SCF error bars of the five sites are plotted.

Citation: Journal of Hydrometeorology 18, 1; 10.1175/JHM-D-16-0149.1

During the accumulation period at the Fuyun site, the old SCF is underestimated with a bias of −0.349 and has the largest RMSE of 0.402 (Table 2). For the Buerjin site with the minimum error, the old SCF has a bias of −0.097, an RMSE of 0.151, and an R2 value of 0.830. In Table 2, the bias, RMSE, and R2 show that the new accumulation SDC does significantly improve the SCF estimates when compared with the old SDC during the accumulation period at the five sites. The RMSE of the new accumulation SCF is reduced by 92.23%, 27.41%, 80.72%, 59.13%, and 68.51% at the Aletai, Buerjin, Fuyun, Jimunai, and Qinghe sites, respectively. However, the new accumulation SDC would slightly overestimate the SCF estimates at the Buerjin, Fuyun, and Qinghe sites, where the bias is only 0.030, 0.040, and 0.067, respectively (Table 2).

Table 2.

Validation of the estimated SCF with in situ SD observations and the SDC during the accumulation period from November 2008 to March 2009.

Table 2.

During the ablation period, although the old SCF is still underestimated at all sites except for the Buerjin site, the bias and RMSE are smaller than those during the accumulation period (Table 3). In Tables 2 and 3, the old SCF during the ablation period obtains a better agreement with the MODIS SCF compared with that during the accumulation period. However, the old SCF still has a large bias and RMSE at the Fuyun site, where the maximum bias and RMSE are reduced to −0.216 and 0.271, respectively. Table 3 shows that the new ablation SDC significantly improves the accuracy of the estimated SCF during the ablation period at all sites except for the Qinghe site. For the Fuyun site, the new ablation SCF has a bias of −0.006, an RMSE of 0.037, and the largest R2 value of 0.993. For the Qinghe site, the new ablation SCF with an R2 value of 0.871 shows a slightly poorer agreement with the MODIS SCF, compared to the old SCF with an R2 value of 0.971 (Fig. 3). However, the bias and RMSE of the new ablation SCF are smaller than those of the old SCF. Therefore, it is inferred that the new ablation SDC can also effectively improve the SCF estimates.

Table 3.

Validation of the estimated SCF with in situ SD observations and the SDC during the ablation period from November 2008 to March 2009.

Table 3.

In conclusion, the fitted accumulation and ablation SDCs with the historical MODIS SCF products and in situ SD observations are reasonable and represent the inherent relationship between SD and SCF, which leads to improvement of the SCF estimates. Overall, the new SCF during the accumulation period has larger errors than that during the ablation period at most sites. The validation results coincide essentially with the above conclusions for the establishment of the accumulation and ablation SDCs.

d. Experimental design

In this study, all simulations and assimilations in the CoLM are performed at a single grid point with a 0.01° (~1 km) spatial resolution at five sites in the Altay region. The CoLM was driven by the China Meteorological Forcing Dataset (CMFD) with a 0.1° spatial resolution and 3-h temporal resolution. The datasets (Chen et al. 2011b; Yang et al. 2010) were downloaded from the Environmental and Ecological Science Data Center for West China (WestDC; http://westdc.westgis.ac.cn/). CMFD contains precipitation rate (mm s−1), air temperature (K), wind speed (m s−1), specific humidity (kg kg−1), surface pressure (Pa), and downward shortwave solar and longwave radiation (W m−2).

A simulation with an inherent SDC (Dai et al. 2001; Dickinson et al. 1993) in the CoLM is conducted from January 2004 to March 2009. The SD simulation from November 2008 to March 2009 is considered as the old SDC simulation (without assimilation) and as a benchmark for the validation of the analysis results from different experiments.

Four experiments are performed with the CoLM: 1) a simulation with an inherent SDC of the CoLM, termed old SD; 2) a simulation with a new SDC, termed new SD; 3) an assimilation of the MODIS SCF with the new SDC and DEnKF, termed DEnKF; and 4) an assimilation of the MODIS SCF with the new SDC and 2DEnVar, termed 2DEnVar.

For the new SDC experiment, the above accumulation and ablation SDCs are incorporated into the CoLM to simulate the SD from November 2008 to March 2009.

Based on the new SDC experiment, the DEnKF and 2DEnVar are implemented to assimilate the available MODIS SCF into the CoLM. In the DEnKF and 2DEnVar experiments, the new SDCs are also used as an observation operator, and the corresponding RMSEs that were calculated with the new SDCs in section 3c(1) are used as the MODIS SCF observation error variance. If the MODIS SCF and the simulated SD are greater than zero, then the MODIS SCF is assimilated into the CoLM. An ensemble size of 25 is selected as in previous studies (De Lannoy et al. 2012; Su et al. 2008; Xu et al. 2014). During the DA, the perturbations are introduced into the atmospheric forcing fields and the SD state of the CoLM to represent the distribution of these model input errors empirically [following the approach of De Lannoy et al. (2012), Reichle et al. (2007), and Xu and Shu (2014)]. The CoLM prognostic variable for the SD is subject to multiplicative perturbation with a mean of 1 and a standard deviation of 0.01. The perturbation settings of the selected atmospheric forcing variables are listed in Table 4. Furthermore, the cross correlations between the atmospheric forcing variables are imposed on the perturbations and given in Table 4. However, the perturbations do not consider the spatial correlation because the DEnKF and 2DEnVar are implemented at a single grid point with a 0.01° (~1 km) spatial resolution.

Table 4.

Perturbation settings of the selected forcing variables [precipitation P, air temperature T, downward shortwave radiation (SW), and downward longwave radiation (LW)] and their cross correlations.

Table 4.

Differing from the DEnKF, the 2DEnVar integrates the advantages of the DEnKF and 2DVar and requires ensembles within a specific time window. In the 2DEnVar experiment, the assimilation window length is set to 4 days for assimilation of the daily MODIS SCF product. The DEnKF provides the forecast ensemble mean and background error covariance over a 4-day assimilation time window for the 2DVar cost function. The analysis ensemble mean in DEnKF is replaced by the 2DVar analysis. The analysis perturbations of ensemble forecasts are updated with DEnKF, and the analysis ensemble for the next cycle of the ensemble forecasts is updated by adding the analysis perturbations to the analysis ensemble mean.

4. Results and discussion

a. Effect of the new SDC on the snow simulations

In Fig. 5, the old SDC simulated SCF in the CoLM exhibits a time series inconsistent with the MODIS SCF and is substantially underestimated for all sites. The worst results occur at the Jimunai site, where the bias between the old SDC simulated SCF and the MODIS SCF reaches −0.551, while the RMSE is as high as 0.627 and the R2 value is only 0.167 (Table 5). For the Buerjin site, the R2 of the old SDC simulated SCF is only 0.44. This suggests a similar time variation with the MODIS SCF, especially for the ablation period (Fig. 5). However, there is still a large negative bias of 0.21 (Table 5), which indicates underestimation of SCF simulations in the CoLM. It can be deduced from the above results that the old SDC of the CoLM may overall underestimate simulated SCFs.

Fig. 5.
Fig. 5.

Comparisons of MODIS SCF (red), old SCF (green), and new SCF (blue) at the (a) Aletai, (b) Buerjin, (c) Fuyun, (d) Jimunai, and (e) Qinghe sites. (f) The sample MODIS SCF error bars of the five sites are plotted.

Citation: Journal of Hydrometeorology 18, 1; 10.1175/JHM-D-16-0149.1

Table 5.

Analysis of the old SCF against the new SCF from November 2008 to March 2009.

Table 5.

As shown in Fig. 5, the new SDC can improve the SCF simulations in the CoLM as compared with the old SDC. The new SCFs illustrate a time series consistent with the MODIS SCF, which has an R2 value of 0.652, 0.508, 0.728, and 0.619 at the Aletai, Buerjin, Fuyun, and Qinghe sites, respectively. The best results occur at the Aletai site, where the bias of the new SCF is reduced to −0.065 and the RMSE is reduced to 0.236 (Table 5). This indicates an improvement of 55.97% in the magnitude of the SCF simulations. For the Jimunai site, although the new SDC can improve SCF simulations in the CoLM to some extent, the new SCF is still overall underestimated, as shown in Fig. 5d. The new SCF does not show a similar time series with the MODIS SCF and has a small R2 value of 0.265, a large bias of −0.325, and an RMSE of 0.456 (Table 5).

Figure 6 shows the new SDC and old SDC simulated SDs in the CoLM. In Fig. 6, the old SDC simulated SD exhibits a similar time variation with in situ SD, but the old SDC simulated SD during an earlier snow ablation period (not shown) is substantially underestimated for all sites except for the Fuyun site. Although there is a good SD simulation at the Fuyun site, the old SDC simulated SD is still underestimated during the ablation period. The worst results with the largest negative bias occur at the Jimunai site. To reduce the simulated errors of SD introduced by the old SDC, the new accumulation and ablation SDCs are integrated into the CoLM to update the SD simulations. As shown in Fig. 6, the new SDCs have a direct impact on SD simulations, which does improve the snow accumulation and ablation processes to some extent. However, there are still large biases in the new SD, especially for the Jimunai site. The underestimation of the new SD may be partly attributed to errors in the atmospheric forcing data, the vegetation cover fraction, and the albedo (Xu and Shu 2014; Xue et al. 2003). Although the new SDC can improve SD simulations at the Jimunai site, the new SCF still has large errors (Fig. 5d) that may also lead to underestimation in the SD simulations.

Fig. 6.
Fig. 6.

Comparisons of the SD time series from in situ (red), the old SDC simulation (green), and the new SDC simulation (blue) at the (a) Aletai, (b) Buerjin, (c) Fuyun, (d) Jimunai, and (e) Qinghe sites. (f) The sample in situ SD error bars of the five sites are plotted. The ordinate scales in (a)–(e) are different.

Citation: Journal of Hydrometeorology 18, 1; 10.1175/JHM-D-16-0149.1

The normalized error percent reduction (NEPR; Chen et al. 2011a) shown in Fig. 7 indicates that the new SDC does improve the SD simulations as compared to the old SDC at all sites. For the Fuyun site, the new SD with the smallest bias is the closest to in situ SD, and its RMSE is reduced by 38.10% (Fig. 7). However, Fig. 6c shows that large errors are still identified during the ablation period. For the Buerjin site, the NEPR of the new SD is only 2.06% (Fig. 7), which indicates little improvement over the SD simulations. This is attributed to the slight difference between the new and old SCFs (Fig. 6b).

Fig. 7.
Fig. 7.

The NEPR of the CoLM simulated SD with the new SDC.

Citation: Journal of Hydrometeorology 18, 1; 10.1175/JHM-D-16-0149.1

Our experimental results show that the new SD in the CoLM is still overall underestimated, but that the new SDC can improve the SD simulations to some extent, as compared with the old SDC. This indicates that optimizing the SDC can improve the simulation of the snow accumulation and ablation processes. However, the proposed statistical SDC with only one SD parameter does not vary with seasons and does not consider other parameters, especially those that vary with time like the snow density. Therefore, the new SDC cannot substantially improve the snow process simulations in the CoLM. Additional parameters, such as time-varying snow density, may be integrated into the SDC, or a more sophisticated SDC could be exploited in the CoLM in the future, such as the SDC combined with snow density from Niu and Yang (2007).

b. Comparison of different data assimilation methods

Figure 8 shows the analyzed SD time series from the DEnKF and 2DEnVar experiments, where the new SDC is used as the observation operator. In Fig. 8, the analyzed SDs of the DEnKF and 2DEnVar have a similar time series. The 2DEnVar shows a better analysis performance than the DEnKF at all sites except for the Qinghe site. In the 2DEnVar experiments, the analyzed SDs during the accumulation and ablation periods are elevated to a value that is very close to in situ SD observations at all sites except for the Qinghe site. For the Jimunai site, the 2DEnVar obtains better analysis performance than the DEnKF. During the accumulation period, the analyzed SD of the 2DEnVar exhibits a time series consistent with in situ SD. In contrast, the analyzed SD of the 2DEnVar is still underestimated and has a large bias during the ablation period. As compared with the analyzed SD of the DEnKF, the analyzed SD of the 2DEnVar is substantially improved. Because of the presence of cloud cover, the MODIS SCF observations are unavailable for data assimilation, which leads to the underestimation of the analyzed SD in the DA experiments (Xu and Shu 2014). Therefore, the analyzed SD of the DEnKF is well below in situ SD at the Jimunai site during the ablation period, as shown in Fig. 8d. However, in the 2DEnVar experiment, more MODIS SCF observations are available over the assimilation window and are assimilated into the CoLM, which effectively decreases the adverse effect of cloud cover. Figure 8d shows that the 2DEnVar can effectively improve the SD simulations in the CoLM, especially for the period from 8 to 20 February 2009, with a 13-day absence of the MODIS SCF (Xu and Shu 2014). For the Qinghe site, the analyzed SDs of DEnKF and 2DEnVar are inferior to the new SD, which means that the assimilation of the MODIS SCF observations does deteriorate, instead of improving, the SD simulations (Fig. 8e). This is because the new SDC as an observation operator overestimates the predicted SCF observations H(xb), which leads to a negative innovation yoH(xb). Figure 4e also shows that the new SCFs are overall larger than the MODIS SCF observations. For the Qinghe site, the 2DEnVar shows worse analysis performance than the DEnKF because of more negative innovations. These negative innovations are caused by assimilation of more SCF observations over the assimilation window in the 2DEnVar experiment.

Fig. 8.
Fig. 8.

Comparisons of the SD time series for in situ SD observations (purple) and the analyzed SD from the old SDC simulation (green), the new SDC simulation (blue), DEnKF (cyan), and 2DEnVar (red) at the (a) Aletai, (b) Buerjin, (c) Fuyun, (d) Jimunai, and (e) Qinghe sites. The assimilation window length is set to 4 days in the 2DEnVar experiment. (f) The sample in situ SD error bars of the five sites are plotted. The ordinate scales in (a)–(e) are different.

Citation: Journal of Hydrometeorology 18, 1; 10.1175/JHM-D-16-0149.1

However, the analyzed SDs of the DEnKF and 2DEnVar with a new observation operator are not overestimated during the accumulation and ablation periods. This indicates that the new SDC can better and more accurately represent the actual relationship between the SCF and the SD. The new observation operator may well reduce these instances of overestimation for the assimilation results.

In Fig. 8, the analyzed SD produces late snow accumulations and early snowpack melt-offs at most sites except at the Buerjin and Fuyun sites as compared with in situ SD. This is partly due to the underestimation of albedo in the CoLM. However, in this study, we only concentrate on improving the SDC and reducing the negative impact of cloud cover on the assimilation results without considering joint assimilation with snow albedo.

To compare the overall difference of the DEnKF and 2DEnVar experiments, these assimilation results were evaluated with a Taylor diagram (Taylor 2001) and NEPR. The Taylor diagram in Fig. 9 is constructed with the standard deviations of the analyzed and in situ SDs and their correlation coefficients. The bias between the analyzed and in situ SDs is also identified in the Taylor diagram. In Fig. 9, the red half-solid circle, termed the “reference” field, represents the standard deviation of in situ SD observations, while other fields are referred to as “model simulated” fields. The distance between the model-simulated and reference fields quantifies how closely the analyzed SD pattern of the CoLM matches in situ SD.

Fig. 9.
Fig. 9.

Taylor diagram of the analyzed SD in different snow DA experiments at the (a) Aletai, (b) Buerjin, (c) Fuyun, (d) Jimunai, and (e) Qinghe sites. The black half-solid circle, termed the “reference” field, represents the standard deviation of in situ SD observations, while other fields are referred to as model-simulated fields. The color bar represents the bias between the analyzed SDs and in situ SD observations. The ordinate and abscissa scales in (a)–(e) are different.

Citation: Journal of Hydrometeorology 18, 1; 10.1175/JHM-D-16-0149.1

Figure 9 shows that the analyzed SDs of the DEnKF and 2DEnVar with negative bias are underestimated at all sites, and the minimum negative bias of −0.005 m occurs at the Buerjin site in the 2DEnVar experiment. For the Aletai site, the standard deviation of the analyzed SD in the 2DEnVar experiment is close to that in the DEnKF experiment, but the former analyzed SD has a larger correlation coefficient of 0.95 and a smaller RMSE than the latter. Furthermore, the analyzed SD in the 2DEnVar experiment shows less bias than that in the DEnKF experiment. The above results indicate that the 2DEnVar shows better analysis performance than the DEnKF. Similar results occur at the Jimunai site as shown in Fig. 9d. In Fig. 9b, the analyzed SD in the 2DEnVar experiment has almost the same standard deviation as that in the DEnKF experiment at the Buerjin site, but the 2DEnVar has a larger correlation coefficient and a smaller bias than the DEnKF. Therefore, the 2DEnVar obtains better analysis performance than does the DEnKF. In contrast, the 2DEnVar shows worse analysis performance than the DEnKF at the Qinghe site, as a large RMSE and bias occur in the 2DEnVar experiment (see Fig. 9d). Figure 9d also shows that the new SDC without data assimilation shows the best result, and it can improve the SD simulations as compared to the other experiments.

As shown in Fig. 10, both the DEnKF and 2DEnVar can efficiently improve SD simulations at all sites, except for the Qinghe site, as compared with the new SDC experiment. However, the 2DEnVar shows the best analysis performance because it can significantly reduce the errors of the SD simulations shown in Fig. 10. The largest improvement of the analyzed SD in the 2DEnVar experiment is up to 88.55% at the Buerjin site, followed by the Jimunai site with an NEPR of 71.17%. However, the positive NEPR in the DEnKF experiment is larger than the negative NEPR in the 2DEnVar experiment at the Qinghe site. This indicates that the DEnKF obtains better analysis performance than the 2DEnVar, and the 2DEnVar does deteriorate the SD simulations because of more negative innovations.

Fig. 10.
Fig. 10.

The NEPR of the analyzed SD in the DEnKF (blue) and 2DEnVar (red) experiments.

Citation: Journal of Hydrometeorology 18, 1; 10.1175/JHM-D-16-0149.1

Overall, both the DEnKF and 2DEnVar can improve the SD simulations; however, the latter shows better analysis performance. More MODIS SCF observations assimilated with the 2DEnVar can produce more snow accumulations than the DEnKF with only one MODIS SCF observation. However, more negative innovations may result in the deterioration of the SD simulations. In summary, the 2DEnVar shows the best performance.

5. Conclusions

To reduce the errors introduced by the simplified SDC of the CoLM, also known as the observation operator in the snow DA, a new SDC was statistically fitted to the historical MODIS SCF observations and in situ SD observations from January 2004 to October 2008. The new SDC, as the snow process model, was applied in snow simulations of the CoLM. The results show that the new SDC can directly improve the SCF simulations, which leads to an improvement of the SD simulations. However, the new SDC is only related to the snow depth state variable of the CoLM and is independent of the time-varying parameters, such as snow density. Therefore, the new SCF does not exhibit the seasonal variation characteristics well. This may lead to an overestimation of the predicted SCF observations that are overall larger than the MODIS SCF observations, as shown in Fig. 4e. Based on the SCF parameterization scheme integrated with snow density from Niu and Yang (2007), a more reasonable SDC could be exploited for snow data assimilation by combining it with the historical snow-related observations in the CoLM in the future.

Based on the new SDC, to reduce the unavailability of the MODIS SCF observations caused by the presence of cloud cover, a 2DEnVar integrating DEnKF and 2DVar was proposed to assimilate more available SCF observations within the assimilation window into the CoLM for improving snow simulations. The 2DEnVar benefits from the state-dependent background error covariance estimated from the DEnKF ensemble, while taking advantage of the 2DVar. Furthermore, the 2DEnVar does not require the development of the tangent linear models of the CoLM and observation operators and their adjoint models.

The DEnKF and 2DEnVar experiments were performed at five sites in the Altay region of China from November 2008 to March 2009. Our results indicate that both DA methods can reduce the bias and RMSE of the analyzed SD during the accumulation and ablation periods. The analyzed SDs of the two DA methods are superior to the new and old SDC simulated SDs at most sites. Overall, the 2DEnVar performs the best, as it can effectively reduce the bias and RMSE of the analyzed SD at all sites except for the Qinghe site. This indicates that the 2DEnVar assimilating more MODIS SCF observations shows better analysis performance than the DEnKF with the assimilation of only one MODIS SCF observation. This is because the 2DEnVar may produce more innovations than the DEnKF. Furthermore, the influence of the presence of cloud cover is alleviated more effectively as more available MODIS SCF observations within the assimilation window are adopted in the 2DEnVar experiment. Therefore, the 2DEnVar does improve snow simulations in the CoLM, especially for the period from 8 to 20 February 2009, including a 13-day absence of the MODIS SCF at the Jimunai site (see Fig. 8d). However, the 2DEnVar shows the worst result for increasing the bias and RMSE of snow simulations at the Qinghe site. This is because most of the predicted SCF observations within the assimilation window (Fig. 4e) are overestimated by the new SDC, which produces more negative innovations.

Acknowledgments

We sincerely thank the reviewers for their helpful comments and suggestions about our manuscript. We thank Editage (www.editage.cn) for English language editing. We thank the Institute of Desert Meteorology, China Meteorological Administration, for providing in situ snow depth data of five sites in the Altay region. We thank the Data Assimilation and Modeling Center for Tibetan Multi-spheres, Institute of Tibetan Plateau Research, for providing the forcing dataset (http://westdc.westgis.ac.cn/). We also thank the National Snow and Ice Data Center (NSIDC) for the MODIS snow cover fraction data (MOD10A1) (http://nsidc.org/data/mod10a1). This research is jointly supported by the Creative Talents Fund of Guangzhou Institute of Geography (043), the Science and Technology Planning Project of Guangdong Province (2016A020210059), the Natural Science Foundation of Guangdong Province (2014A030313747), the Water Conservancy Science and Technology Innovation Project of Guangdong Province (2015-13), the Scientific Platform and Innovation Capability Construction Program of Guangdong Academy of Sciences (2016GDASPT-0103), and the Fundamental Research Funds for the Central Universities (2042016kf0176).

REFERENCES

  • Andreadis, K. M., , and Lettenmaier D. P. , 2006: Assimilating remotely sensed snow observations into a macroscale hydrology model. Adv. Water Resour., 29, 872886, doi:10.1016/j.advwatres.2005.08.004.

    • Search Google Scholar
    • Export Citation
  • Arsenault, K. R., , Houser P. R. , , De Lannoy G. J. M. , , and Dirmeyer P. A. , 2013: Impacts of snow cover fraction data assimilation on modeled energy and moisture budgets. J. Geophys. Res. Atmos., 118, 74897504, doi:10.1002/jgrd.50542.

    • Search Google Scholar
    • Export Citation
  • Barlage, M., and Coauthors, 2010: Noah land surface model modifications to improve snowpack prediction in the Colorado Rocky Mountains. J. Geophys. Res., 115, D22101, doi:10.1029/2009JD013470.

    • Search Google Scholar
    • Export Citation
  • Bonan, G. B., 1996: A land surface model (LSM version 1.0) for ecological, hydrological, and atmospheric studies: Technical description and user’s guide. NCAR Tech. Note NCAR/TN-417+STR, 150 pp., doi:10.5065/D6DF6P5X.

  • Boniface, K., , Braun J. J. , , McCreight J. L. , , and Nievinski F. G. , 2015: Comparison of snow data assimilation system with GPS reflectometry snow depth in the western United States. Hydrol. Processes, 29, 24252437, doi:10.1002/hyp.10346.

    • Search Google Scholar
    • Export Citation
  • Bowler, N. E., , Flowerdew J. , , and Pring S. R. , 2013: Tests of different flavours of EnKF on a simple model. Quart. J. Roy. Meteor. Soc., 139, 15051519, doi:10.1002/qj.2055.

    • Search Google Scholar
    • Export Citation
  • Buehner, M., , Houtekamer P. L. , , Charette C. , , Mitchell H. L. , , and He B. , 2010a: Intercomparison of variational data assimilation and the ensemble Kalman filter for global deterministic NWP. Part I: Description and single-observation experiments. Mon. Wea. Rev., 138, 15501566, doi:10.1175/2009MWR3157.1.

    • Search Google Scholar
    • Export Citation
  • Buehner, M., , Houtekamer P. L. , , Charette C. , , Mitchell H. L. , , and He B. , 2010b: Intercomparison of variational data assimilation and the ensemble Kalman filter for global deterministic NWP. Part II: One-month experiments with real observations. Mon. Wea. Rev., 138, 15671586, doi:10.1175/2009MWR3158.1.

    • Search Google Scholar
    • Export Citation
  • Buehner, M., , Morneau J. , , and Charette C. , 2013: Four-dimensional ensemble-variational data assimilation for global deterministic weather prediction. Nonlinear Processes Geophys., 20, 669682, doi:10.5194/npg-20-669-2013.

    • Search Google Scholar
    • Export Citation
  • Che, T., , Li X. , , Jin R. , , and Huang C. , 2014: Assimilating passive microwave remote sensing data into a land surface model to improve the estimation of snow depth. Remote Sens. Environ., 143, 5463, doi:10.1016/j.rse.2013.12.009.

    • Search Google Scholar
    • Export Citation
  • Chen, F., , Crow W. T. , , Starks P. J. , , and Moriasi D. N. , 2011a: Improving hydrologic predictions of a catchment model via assimilation of surface soil moisture. Adv. Water Resour., 34, 526536, doi:10.1016/j.advwatres.2011.01.011.

    • Search Google Scholar
    • Export Citation
  • Chen, Y., , Yang K. , , He J. , , Qin J. , , Shi J. , , Du J. , , and He Q. , 2011b: Improving land surface temperature modeling for dry land of China. J. Geophys. Res., 116, D20104, doi:10.1029/2011JD015921.

    • Search Google Scholar
    • Export Citation
  • Clark, M. P., , Slater A. G. , , Barrett A. P. , , Hay L. E. , , McCabe G. J. , , Rajagopalan B. , , and Leavesley G. H. , 2006: Assimilation of snow covered area information into hydrologic and land-surface models. Adv. Water Resour., 29, 12091221, doi:10.1016/j.advwatres.2005.10.001.

    • Search Google Scholar
    • Export Citation
  • Dai, Y., , and Zeng Q. , 1997: A land surface model (IAP94) for climate studies part I: Formulation and validation in off-line experiments. Adv. Atmos. Sci., 14, 433460, doi:10.1007/s00376-997-0063-4.

    • Search Google Scholar
    • Export Citation
  • Dai, Y., and Coauthors, 2001: Common Land Model (CLM): Technical documentation and user’s guide. Georgia Institute of Technology, 69 pp.

  • Dai, Y., and Coauthors, 2003: The Common Land Model. Bull. Amer. Meteor. Soc., 84, 10131023, doi:10.1175/BAMS-84-8-1013.

  • De Lannoy, G. J. M., , Reichle R. H. , , Arsenault K. R. , , Houser P. R. , , Kumar S. , , Verhoest N. E. C. , , and Pauwels V. R. N. , 2012: Multiscale assimilation of Advanced Microwave Scanning Radiometer–EOS snow water equivalent and Moderate Resolution Imaging Spectroradiometer snow cover fraction observations in northern Colorado. Water Resour. Res., 48, W01522, doi:10.1029/2011WR010588.

    • Search Google Scholar
    • Export Citation
  • Desroziers, G., , Camino J.-T. , , and Berre L. , 2014: 4DEnVar: Link with 4D state formulation of variational assimilation and different possible implementations. Quart. J. Roy. Meteor. Soc., 140, 20972110, doi:10.1002/qj.2325.

    • Search Google Scholar
    • Export Citation
  • Dickinson, R. E., , Henderson-Sellers A. , , and Kennedy P. J. , 1993: Biosphere–Atmosphere Transfer Scheme (BATS) version 1e as coupled to the NCAR Community Climate Model. NCAR Tech. Note NCAR/TN-387+STR, 88 pp., doi:10.5065/D67W6959.

  • Evensen, G., 2003: The ensemble Kalman filter: Theoretical formulation and practical implementation. Ocean Dyn., 53, 343367, doi:10.1007/s10236-003-0036-9.

    • Search Google Scholar
    • Export Citation
  • Evensen, G., , and Van Leeuwen P. J. , 2000: An ensemble Kalman smoother for nonlinear dynamics. Mon. Wea. Rev., 128, 18521867, doi:10.1175/1520-0493(2000)128<1852:AEKSFN>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Fairbairn, D., , Pring S. R. , , Lorenc A. C. , , and Roulstone I. , 2014: A comparison of 4DVar with ensemble data assimilation methods. Quart. J. Roy. Meteor. Soc., 140, 281294, doi:10.1002/qj.2135.

    • Search Google Scholar
    • Export Citation
  • Fertig, E. J., , Harlim J. , , and Hunt B. R. , 2007: A comparative study of 4D‐VAR and a 4D ensemble Kalman filter: Perfect model simulations with Lorenz‐96. Tellus, 59A, 96100, doi:10.1111/j.1600-0870.2006.00205.x.

    • Search Google Scholar
    • Export Citation
  • Fletcher, S. J., , Liston G. E. , , Hiemstra C. A. , , and Miller S. D. , 2012: Assimilating MODIS and AMSR-E snow observations in a snow evolution model. J. Hydrometeor., 13, 14751492, doi:10.1175/JHM-D-11-082.1.

    • Search Google Scholar
    • Export Citation
  • Frei, A., , Tedesco M. , , Lee S. , , Foster J. , , Hall D. K. , , Kelly R. , , and Robinson D. A. , 2012: A review of global satellite-derived snow products. Adv. Space Res., 50, 10071029, doi:10.1016/j.asr.2011.12.021.

    • Search Google Scholar
    • Export Citation
  • Hall, D. K., , Riggs G. A. , , and Salomonson V. V. , 2006: MODIS/Terra snow cover daily L3 global 500 m grid V005 (updated daily). National Snow and Ice Data Center, Boulder, CO, digital media. [Available online at http://nsidc.org/data/docs/daac/modis_v5/mod10a1_modis_terra_snow_daily_global_500m_grid.gd.html.]

  • Huang, X., , Liang T. , , Zhang X. , , and Guo Z. , 2011: Validation of MODIS snow cover products using Landsat and ground measurements during the 2001–2005 snow seasons over northern Xinjiang, China. Int. J. Remote Sens., 32, 133152, doi:10.1080/01431160903439924.

    • Search Google Scholar
    • Export Citation
  • Hunt, B. R., and Coauthors, 2004: Four-dimensional ensemble Kalman filtering. Tellus, 56A, 273277, doi:10.1111/j.1600-0870.2004.00066.x.

    • Search Google Scholar
    • Export Citation
  • Kolberg, S., , Rue H. , , and Gottschalk L. , 2006: A Bayesian spatial assimilation scheme for snow coverage observations in a gridded snow model. Hydrol. Earth Syst. Sci., 10, 369381, doi:10.5194/hess-10-369-2006.

    • Search Google Scholar
    • Export Citation
  • Kumar, S. V., , Peters-Lidard C. D. , , Arsenault K. R. , , Getirana A. , , Mocko D. , , and Liu Y. , 2015: Quantifying the added value of snow cover area observations in passive microwave snow depth data assimilation. J. Hydrometeor., 16, 17361741, doi:10.1175/JHM-D-15-0021.1.

    • Search Google Scholar
    • Export Citation
  • Liang, T. G., , Liu X. Y. , , Wu C. X. , , Guo Z. G. , , and Huang X. D. , 2007: An evaluation approach for snow disasters in the pastoral areas of northern Xinjiang, PR China. N. Z. J. Agric. Res., 50, 369380, doi:10.1080/00288230709510305.

    • Search Google Scholar
    • Export Citation
  • Liu, C., , Xiao Q. , , and Wang B. , 2008: An ensemble-based four-dimensional variational data assimilation scheme. Part I: Technical formulation and preliminary test. Mon. Wea. Rev., 136, 33633373, doi:10.1175/2008MWR2312.1.

    • Search Google Scholar
    • Export Citation
  • Liu, C., , Xiao Q. , , and Wang B. , 2009: An ensemble-based four-dimensional variational data assimilation scheme. Part II: Observing system simulation experiments with Advanced Research WRF (ARW). Mon. Wea. Rev., 137, 16871704, doi:10.1175/2008MWR2699.1.

    • Search Google Scholar
    • Export Citation
  • Liu, Y., , Peters-Lidard C. D. , , Kumar S. , , Foster J. L. , , Shaw M. , , Tian Y. , , and Fall G. M. , 2013: Assimilating satellite-based snow depth and snow cover products for improving snow predictions in Alaska. Adv. Water Resour., 54, 208227, doi:10.1016/j.advwatres.2013.02.005.

    • Search Google Scholar
    • Export Citation
  • Lorenc, A. C., 1986: Analysis methods for numerical weather prediction. Quart. J. Roy. Meteor. Soc., 112, 11771194, doi:10.1002/qj.49711247414.

    • Search Google Scholar
    • Export Citation
  • Lorenc, A. C., 2003: The potential of the ensemble Kalman filter for NWP—A comparison with 4D-Var. Quart. J. Roy. Meteor. Soc., 129, 31833203, doi:10.1256/qj.02.132.

    • Search Google Scholar
    • Export Citation
  • Malik, M. J., , van der Velde R. , , Vekerdy Z. , , and Su Z. , 2012: Assimilation of satellite-observed snow albedo in a land surface model. J. Hydrometeor., 13, 11191130, doi:10.1175/JHM-D-11-0125.1.

    • Search Google Scholar
    • Export Citation
  • Niu, G. Y., , and Yang Z. L. , 2007: An observation‐based formulation of snow cover fraction and its evaluation over large North American river basins. J. Geophys. Res., 112, D21101, doi:10.1029/2007JD008674.

    • Search Google Scholar
    • Export Citation
  • Qiu, X., 2011: Usage of flow-dependent background error covariance in data assimilation and radar wind retrieval (in Chinese). Ph.D. thesis, College of Atmospheric Sciences, Lanzhou University, 129 pp.

  • Regonda, S. K., , Rajagopalan B. , , Clark M. , , and Pitlick J. , 2005: Seasonal cycle shifts in hydroclimatology over the western United States. J. Climate, 18, 372384, doi:10.1175/JCLI-3272.1.

    • Search Google Scholar
    • Export Citation
  • Reichle, R. H., , Koster R. D. , , Liu P. , , Mahanama S. P. P. , , Njoku E. G. , , and Owe M. , 2007: Comparison and assimilation of global soil moisture retrievals from the Advanced Microwave Scanning Radiometer for the Earth Observing System (AMSR-E) and the Scanning Multichannel Microwave Radiometer (SMMR). J. Geophys. Res., 112, D09108, doi:10.1029/2006JD008033.

    • Search Google Scholar
    • Export Citation
  • Rodell, M., , and Houser P. R. , 2004: Updating a land surface model with MODIS-derived snow cover. J. Hydrometeor., 5, 10641075, doi:10.1175/JHM-395.1.

    • Search Google Scholar
    • Export Citation
  • Sakov, P., , and Oke P. R. , 2008: A deterministic formulation of the ensemble Kalman filter: An alternative to ensemble square root filters. Tellus, 60A, 361371, doi:10.1111/j.1600-0870.2007.00299.x.

    • Search Google Scholar
    • Export Citation
  • Sakov, P., , Evensen G. , , and Bertino L. , 2010: Asynchronous data assimilation with the EnKF. Tellus, 62A, 2429, doi:10.1111/j.1600-0870.2009.00417.x.

    • Search Google Scholar
    • Export Citation
  • Salomonson, V. V., , and Appel I. , 2004: Estimating fractional snow cover from MODIS using the normalized difference snow index. Remote Sens. Environ., 89, 351360, doi:10.1016/j.rse.2003.10.016.

    • Search Google Scholar
    • Export Citation
  • Simic, A., , Fernandes R. , , Brown R. , , Romanov P. , , and Park W. , 2004: Validation of VEGETATION, MODIS, and GOES + SSM/I snow‐cover products over Canada based on surface snow depth observations. Hydrol. Processes, 18, 10891104, doi:10.1002/hyp.5509.

    • Search Google Scholar
    • Export Citation
  • Slater, A. G., , and Clark M. P. , 2006: Snow data assimilation via an ensemble Kalman filter. J. Hydrometeor., 7, 478493, doi:10.1175/JHM505.1.

    • Search Google Scholar
    • Export Citation
  • Su, H., , Yang Z.-L. , , Niu G.-Y. , , and Dickinson R. E. , 2008: Enhancing the estimation of continental-scale snow water equivalent by assimilating MODIS snow cover with the ensemble Kalman filter. J. Geophys. Res., 113, D08120, doi:10.1029/2007JD009232.

    • Search Google Scholar
    • Export Citation
  • Sun, A. Y., , Morris A. , , and Mohanty S. , 2009: Comparison of deterministic ensemble Kalman filters for assimilating hydrogeological data. Adv. Water Resour., 32, 280292, doi:10.1016/j.advwatres.2008.11.006.

    • Search Google Scholar
    • Export Citation
  • Talagrand, O., 1981: A study of the dynamics of four‐dimensional data assimilation. Tellus, 33A, 4360, doi:10.1111/j.2153-3490.1981.tb01729.x.

    • Search Google Scholar
    • Export Citation
  • Taylor, K. E., 2001: Summarizing multiple aspects of model performance in a single diagram. J. Geophys. Res., 106, 71837192, doi:10.1029/2000JD900719.

    • Search Google Scholar
    • Export Citation
  • Thirel, G., , Salamon P. , , Burek P. , , and Kalas M. , 2011: Assimilation of MODIS snow cover area data in a distributed hydrological model. Hydrol. Earth Syst. Sci. Discuss., 8, 13291364, doi:10.5194/hessd-8-1329-2011.

    • Search Google Scholar
    • Export Citation
  • Thirel, G., , Salamon P. , , Burek P. , , and Kalas M. , 2013: Assimilation of MODIS snow cover area data in a distributed hydrological model using the particle filter. Remote Sens., 5, 58255850, doi:10.3390/rs5115825.

    • Search Google Scholar
    • Export Citation
  • Tian, X., , Xie Z. , , and Dai A. , 2008: An ensemble-based explicit four-dimensional variational assimilation method. J. Geophys. Res., 113, D21124, doi:10.1029/2008JD010358.

    • Search Google Scholar
    • Export Citation
  • Wang, S., , Xue M. , , and Min J. , 2013: A four‐dimensional asynchronous ensemble square-root filter (4DEnSRF) algorithm and tests with simulated radar data. Quart. J. Roy. Meteor. Soc., 139, 805819, doi:10.1002/qj.1987.

    • Search Google Scholar
    • Export Citation
  • Wang, T., and Coauthors, 2013: Evaluation of an improved intermediate complexity snow scheme in the ORCHIDEE land surface model. J. Geophys. Res. Atmos., 118, 60646079, doi:10.1002/jgrd.50395.

    • Search Google Scholar
    • Export Citation
  • Wang, X., , and Lei T. , 2014: GSI-based four-dimensional ensemble–variational (4DEnsVar) data assimilation: Formulation and single-resolution experiments with real data for NCEP Global Forecast System. Mon. Wea. Rev., 142, 33033325, doi:10.1175/MWR-D-13-00303.1.

    • Search Google Scholar
    • Export Citation
  • Whitaker, J. S., , and Hamill T. M. , 2002: Ensemble data assimilation without perturbed observations. Mon. Wea. Rev., 130, 19131924, doi:10.1175/1520-0493(2002)130<1913:EDAWPO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Xu, J., , and Shu H. , 2014: Assimilating MODIS-based albedo and snow cover fraction into the Common Land Model to improve snow depth simulation with direct insertion and deterministic ensemble Kalman filter methods. J. Geophys. Res. Atmos., 119, 10 68410 701, doi:10.1002/2014JD022012.

    • Search Google Scholar
    • Export Citation
  • Xu, J., , Shu H. , , and Dong L. , 2014: DEnKF—Variational hybrid snow cover fraction data assimilation for improving snow simulations with the Common Land Model. Remote Sens., 6, 10 61210 635, doi:10.3390/rs61110612.

    • Search Google Scholar
    • Export Citation
  • Xue, Y. K., , Sun S. F. , , Kahan D. S. , , and Jiao Y. J. , 2003: Impact of parameterizations in snow physics and interface processes on the simulation of snow cover and runoff at several cold region sites. J. Geophys. Res., 108, 8859, doi:10.1029/2002JD003174.

    • Search Google Scholar
    • Export Citation
  • Yang, K., , He J. , , Tang W. , , Qin J. , , and Cheng C. C. , 2010: On downward shortwave and longwave radiations over high altitude regions: Observation and modeling in the Tibetan Plateau. Agric. For. Meteor., 150, 3846, doi:10.1016/j.agrformet.2009.08.004.

    • Search Google Scholar
    • Export Citation
  • Zaitchik, B. F., , and Rodell M. , 2009: Forward-looking assimilation of MODIS-derived snow-covered area into a land surface model. J. Hydrometeor., 10, 130148, doi:10.1175/2008JHM1042.1.

    • Search Google Scholar
    • Export Citation
  • Zhang, M., , and Zhang F. , 2012: E4DVar: Coupling an ensemble Kalman filter with four-dimensional variational data assimilation in a limited-area weather prediction model. Mon. Wea. Rev., 140, 587600, doi:10.1175/MWR-D-11-00023.1.

    • Search Google Scholar
    • Export Citation
  • Zhang, Y. F., , Hoar T. J. , , Yang Z. L. , , Anderson J. L. , , Toure A. M. , , and Rodell M. , 2014: Assimilation of MODIS snow cover through the Data Assimilation Research Testbed and the Community Land Model version 4. J. Geophys. Res. Atmos., 119, 70917103, doi:10.1002/2013JD021329.

    • Search Google Scholar
    • Export Citation
  • Zhou, Q., , and Sun B. , 2013: Reliability of long-term snow depth data sets from remote sensing over the western arid zone of China. Remote Sens. Lett., 4, 10391048, doi:10.1080/2150704X.2013.832841.

    • Search Google Scholar
    • Export Citation
  • Zhuang, X., , Guo C. , , Zhao Z. , , and Zhang L. , 2010: Snow cover variation analysis in Altay area of Xinjiang (in Chinese). J. Arid Meteor., 28, 190197.

    • Search Google Scholar
    • Export Citation
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