**6. Discussion**

In this study, we have explored how different observation-based snow depletion curve (SDC) characteristics can be derived and used as observation-based observation operators in EnKF assimilation updates when assimilating MODIS, or other satellite-based, snow cover fraction estimates. Different SDC logarithmic functions, representing different physiographic and temporal conditions, were also explored as observation-based observation operators in a full suite of EnKF experiments. Using logarithmic functions with a y-axis intercept value, not set to 0, means that MODIS SCF values may not be assimilated below that value (e.g., 40% SCF). In a way, this acts as a cutoff for lower MODIS SCF values (e.g., less than 30%), which could contain contaminated SCF values, due to unresolved patchiness in a pixel and NDSI algorithm pixel discrimination issues [53]. Also, the fact that many of the logarithmic curves never fully reach 100% SCF could allow MODIS SCF pixels that are near 100% to have an impact on the snow analysis, when the model SCF forecasts are much lower than 100%. This situation can work well when the LSM consistently underestimates SWE, relative to the in situ SWE observations. Therefore, for LSMs with a low SWE bias or precipitation input bias (e.g., an undercatch issue), this SDC approach can partly compensate for the low bias, especially when assimilating snow cover in higher mountain catchments locations. However, if an LSM or snow model has a high SWE bias compared to the observations, then this observed type SDC could contribute to overestimating and adding too much snow to the model.

In other snow cover data assimilation studies, most curves are designed to reach 100% SCF, even for coarser grid scale experiments [13]. If model SWE forecast conditions remain high enough that the predicted SCF ensemble forecasts remain at 100%, with little ensemble spread in SCF, then there can be very little to no impact on the SWE analysis if the observed SCF is much less than 100%, e.g., partial coverage for the gridcell [14]. Another minor downside to having an SDC-type observation operator reach 100% snow cover, like the case for many LSM curves, the EnKF-based model SCF forecast ensemble can become underestimated, if perturbations force the members to fall below 100%, even if both the MODIS and model predicted SCF were originally at 100%. This can also occur when perturbing the MODIS SCF observations. When the observed SCF is at 100%, this can also reduce that value when perturbed, leading to underestimated SWE analysis [14]. Rules can be applied in the EnKF method as to how the ensemble members, e.g., within the observation-perturbed ensemble, ge<sup>t</sup> distributed or updated near the 100% SCF point. This could include a set of rules for reducing the SWE analysis by a certain fraction when there is a partial amount of observed SCF or by modifying the observation error covariance, σ**total**, that controls the ensemble or uncertainty spread [based on 14]. One slight advantage to the SNOTEL-MODIS observation-based observation operators, *obs*-**h**, is that they reflect an average SCF percentage of what the satellite detects for a given range of conditions. Thus, if the predicted SCF is 80% and is the upper threshold in the SDC function, then 20% of the area could be considered exposed vegetation cover or average SCF conditions, for say, lower elevation regions.

Based on the filter statistics shown in Tables 2 and 3, there still remains some large differences between the magnitudes of the model predicted SCF and the MODIS SCF observations. One approach to address these innovation biases would be to scale the MODIS SCF values to reflect higher ones, bringing them into closer agreemen<sup>t</sup> with the predicted SCF values [54]. Another option would be to place additional constraints on the observation operators or SCF observations themselves, or to further tune the observations or the curves towards the other, so that the filter statistics reflect less bias between observations and the model. In this study, by deriving the observation-based observation operators with the MODIS SCF observations, it helps to bring the predicted SCF values closer in agreemen<sup>t</sup> to the observations. With almost all data assimilation approaches, tuning may be the unavoidable course to be taken, so the final analysis may reflect the best that both the model and observations have to offer.
