*Article* **Generating Observation-Based Snow Depletion Curves for Use in Snow Cover Data Assimilation**

#### **Kristi R. Arsenault 1,\* and Paul R. Houser 2**


Received: 1 November 2018; Accepted: 10 December 2018; Published: 14 December 2018

**Abstract:** Snow depletion curves (SDC) are functions that are used to show the relationship between snow covered area and snow depth or water equivalent. Previous snow cover data assimilation (DA) studies have used theoretical SDC models as observation operators to map snow depth to snow cover fraction (SCF). In this study, a new approach is introduced that uses snow water equivalent (SWE) observations and satellite-based SCF retrievals to derive SDC relationships for use in an Ensemble Kalman filter (EnKF) to assimilate snow cover estimates. A histogram analysis is used to bin the SWE observations, which the corresponding SCF observations are then averaged within, helping to constrain the amount of data dispersion across different temporal and regional conditions. Logarithmic functions are linearly regressed with the binned average values, for two U.S. mountainous states: Colorado and Washington. The SDC-based logarithmic functions are used as EnKF observation operators, and the satellite-based SCF estimates are assimilated into a land surface model. Assimilating satellite-based SCF estimates with the observation-based SDC shows a reduction in SWE-related RMSE values compared to the model-based SDC functions. In addition, observation-based SDC functions were derived for different intra-annual and physiographic conditions, and landcover and elevation bands. Lower SWE-based RMSE values are also found with many of these categorical observation-based SDC EnKF experiments. All assimilation experiments perform better than the open-loop runs, except for the Washington region's 2004–2005 snow season, which was a major drought year that was difficult to capture with the ensembles and observations.

**Keywords:** snow cover; snow depletion curve; MODIS; data assimilation; land surface model
