**7. Conclusions**

In this study, we presented a new approach to estimating snow depletion curves and their application for assimilating snow cover fraction observations, using an EnKF approach and a land surface model with a multi-layer snow physics scheme. We use observed SWE and snow cover fraction estimates to derive new SDCs, using a larger array of observations than previous studies, spanning two different mountainous regions in the U.S., in Washington and Colorado. We refer to these new SDC observation operators as "observation-based" and benchmarked their skill against the default, model-based SDC function. The SDC observation-based observation operators showed improvement over the default model-based SCF forecasts and snow state analysis. A secondary goal of this study was to apply this SDC-type approach to see how accounting for varying vegetation, elevation, and temporal conditions may better capture heterogeneous features related to the snowpack and snow cover patterns when assimilating snow cover observations. Vegetation-based curves showed improvement over the lumped annual observation-based SDC, especially for Colorado. Finally, the new SDC-based observation operators are used to derive the observational errors, which were used in the EnKF method's snow cover observation perturbations. Accounting for different errors related to the varying conditions provides different weighting of the snow cover observations against that of the model in the EnKF innovation and update steps.

These results along with other previous SCA DA studies do show promise in that there are positive impacts without much tuning, but additional testing with the observation operators, model, and observations is still needed [10,18]. In future work, more a priori information about the MODIS SCF predictions could be included to deriving and tuning functions, like the ones developed here for this DA application. For example, determining error information with regard to MODIS SCF 100% estimates in connection with the meteorological forcing fields, e.g., ability to estimate snowfall for same observed 100% SCF events or the role that temperature can play in MODIS SCA errors [55]. Also, more adaptive type SDC schemes, which could be more representative at a point, could be developed that adjust relative to changing conditions. Different approaches could be applied to optimize these observational based SDCs and improve the overall performance of the EnKF system.

**Supplementary Materials:** The following are available online at http://www.mdpi.com/2076-3263/8/12/484/s1, Figure S1: Presenting the binned scatterplots for the two mountain regions. Figure S2: Showing the robustness of the scatterbin histogram approach for deriving the SDCs. Figure S3: Monthly SDC relationships derived from binned scatterplot approach for the Washington state domain. Figure S4: Similar to Figure S3, but for Colorado state domain. Figure S5: SDC relationships derived for two different elevation bands for Washington domain. Figure S6: Similar to Figure S5, but for the Colorado domain. Figure S7: SDC relationships derived for different vegetation types from binned scatterplot approach for Washington. Figure S8: Similar to Figure S7, but for Colorado. Figure S9: Independent check on the snow water equivalent bins for different dominant vegetation types and in relation to elevation, for Washington domain. Figure S10: Similar to Figure S9, but for Colorado. Figure S11: Timeseries comparison of the experiments' spatially averaged predicted SCF (in %) for the different observation operators and SCF observations, presented for the melt season. Figure S12: Individual SNOTEL site comparisons between different SDC-type observation operators.

**Author Contributions:** Much of the work, including methodology, code development, validation and analysis, was performed by K.R.A., and overall supervision and funding acquisition was provided by P.R.H. The original draft preparation and writing was done by K.R.A., and review and editing was done by P.R.H.

**Funding:** This research was originally funded by grants given by the U.S. National Oceanic and Atmospheric Administration and the National Aeronautics and Space Administration.

**Acknowledgments:** We want to acknowledge the original support and computing resources provided by The Center for Ocean-Land-Atmosphere Studies (COLA) at George Mason University in Fairfax, Virginia, U.S.A.

**Conflicts of Interest:** The authors declare no conflict of interest.
