**5. Results**

#### *5.1. Applying the SDC Observation Operators to the Data Assimilation Experiments*

Using observations outside of the assimilation experiment period to derive the SDC formulas should test the new observation operators' ability to improve the snow state analysis. Here, the two *obs*-**h** based logarithmic functions, derived for WA and CO, are applied with the EnKF algorithm and compared with the *model*-**h** based EnKF experiments. As an initial comparison between these two EnKF experiments, Figures 5 and 6 provide timeseries of spatially averaged SWE and RMSE of SWE values (both in mm), respectively, across the SNOTEL validation points for the two regions and two Water Years (2004, 2005). For all four cases, the *obs*-**h** EnKF experiment produces higher averaged SWE conditions over the *model*-**h** EnKF run, especially for CO, bringing it in closer agreemen<sup>t</sup> with the SNOTEL spatially averaged SWE (Figure 5). The patterns of averaged accumulation and melt are similar to that of averaged SNOTEL SWE, just the magnitudes are lower for both the *model*-**h** and *obs*-**h** experiments, relative to the open-loop (OL) run. In addition, greater reduction in spatially averaged RMSE values corresponds to the *obs*-**h** based experiment (Figure 6), with most of the reduction in RMSE shown for CO.

**Figure 5.** Spatially averaged SWE comparison is made between SNOTEL observations (open circles), the OL run (grey line), *model*-**h** EnKF experiment (red line), and *obs*-**h** EnKF (green line) experiments for both (**a**) WA and (**b**) CO regions. Values given within the parentheses indicate the <sup>σ</sup>total values for the experiment.

**Figure 6.** Spatially averaged RMSE SWE values (in mm) for both (**a**) WA and (**b**) CO for the OL run (grey line), *model*-**h** EnKF (red line) and *obs*-**h** EnKF (green line) experiments.

#### *5.2. Annual- vs. Varying Conditions based Observation Operators*

Previous snowcover DA studies have accounted for physiographic and seasonal-varying snow differences in their observation operators, however, they did not explore their overall impact on their EnKF experiments (e.g., [13]). In this section, the previously derived SDC logarithmic functions, representing different physiographic and temporal conditions, are explored as observation-based observation operators in a suite of EnKF experiments. Each group of physiographic- and temporal-varying conditions represents only a few categories (e.g., five UMD vegetation classes of thirteen total). The SDC function parameters, slope and intercept, and observational errors are mapped to other classes or bands similar in nature. For example, each vegetation class, like evergreen needleleaf forest, has its own set of function parameters and errors to better represent each set of separate conditions (e.g., snow conditions differ between leafless deciduous and needled conifer-based trees). Similarly, for elevation bands, elevations lower than the lower band limit used (e.g., an 800 m elevation pixel below the 1000 m lower limit for WA) use the function parameters and errors for that lower elevation band. Again, this might not truly reflect low elevation locations in mountainous areas, especially where MODIS SCA pixels are not known to detect snow cover presence as well (e.g., [50]).

By investigating the different conditions, e.g., vegetation types separate from elevation bands, we can see what individual impacts they may have versus all lumped together. For each region, three additional EnKF experiments were generated that incorporate the monthly, vegetation class, and elevation band type SDC functions, separately. Thus, for the EnKF experiment employing the vegetation class function parameters, the EnKF analysis updates will reflect the effects of those varying vegetation SDCs only. The same applies for the different months and elevation bands. To distinguish the different EnKF experiment types, they are simply named by their characteristic and that they are *obs*-**h** function types: Monthly, vegetation type (veg), and elevation (elev) *obs*-**h**, as highlighted in Table 1. The three different experiments are run for WYs 2004–2005, and compared with the *model*-**h** based EnKF experiments.

The first set of results are summarized in Table 2, which include overall means, standard deviation, RMSE, and correlation coefficient values between the simulation SWE results and SNOTEL SWE observations. These results are based on the reduced number of SNOTEL locations, 40 stations for WA and 78 for CO, since CLM2 was found to produce "glacier-like" points (i.e., lack of snowmelt in summer months) at the other 16 WA and 20 CO station gridcell locations. Table 2 shows lower RMSE values for many of the *obs*-**h** EnKF experiments, especially for CO in both years and less of an impact for WA, like WY2004. The lower RMSE values for CO's WY2005, noted as an anomalously positive snow year (from our eleven observation years), may be related to the curve parameters, especially for the vegetation type *obs*-**h** EnKF experiment, which would be dominated by lower SCF average values for CO. With it being a higher snow year than the 11-year average (2000–2010), higher MODIS SCF values would then "add" more snow to the model SWE analysis, thus resulting in higher SWE values and closer agreemen<sup>t</sup> to the observations.

To show how the RMSE values of each DA experiment relate to the open-loop run, Figure 7 shows each experiment's SWE-based RMSE values normalized with respect to those of the open-loop based on [51]. A normalized RMSE value less than one indicates the experiment may perform better than its control run, which is the open-loop in this case [51]. All experiments perform better than the open-loop runs, except for WA's WY2005, which was a major drought year and difficult to capture with the ensembles and observations. Also, the ±1 standard deviation values (inner yellow error bars) in Figure 7 show smaller ranges for many of the *obs*-**h** experiments, especially the vegetation *obs*-**h** case for CO.

To see how this performance translates into EnKF metrics, the normalized innovation means and standard deviations for each experiment and water year are provided in Table 3. The means tend slightly closer to 0 for the *obs*-**h** than the *model*-h based experiments, indicating differences between the individual MODIS SCF values and model predicted SCF values were overall smaller. This may sugges<sup>t</sup> that the *obs*-**h** curves predicted SCF values that were in slightly better agreemen<sup>t</sup> with the MODIS observations. The exception again was WY2005 for WA where there were greater differences, indicated by much higher negative mean values. This may relate to the shape of the curves and thus predicting higher SCF forecast values than the MODIS estimates. For the normalized innovation standard deviations, the values increase to near 1 with almost all the *obs*-**h** experiments, which may indicate that the model errors and observational errors may be more consistent in the filter (e.g., [52]) than those associated with the *model*-**h** EnKF experiments. This could possibly indicate better agreemen<sup>t</sup> in MODIS SCF values with the model predicted SCF produced by the *obs*-**h** curves.


**Table 2.** Comparison of summary SWE statistics for the period, October-June, between observation operator experiments. Bold numbers indicate experiments with reduced RMSE values relative to the open-loop and *model*-**h** EnKF experiments. SD refers to standard deviation.

**Figure 7.** Comparison of each experiment's SWE RMSE values normalized by the open-loop (OL) RMSE values for the five experiments: *Model*-**h** EnKF run, and the annual, monthly, vegetation, and elevation varying *obs*-**h** EnKF experiments for WA (**<sup>a</sup>**,**b**) and CO (**<sup>c</sup>**,**d**) for WY2004 (left) and WY2005 (right). Black open squares indicate the statistical mean, yellow error bar lines indicate ±1 stdev unit from mean, and green error bar lines indicate the maximum and minimum extents of the normalized statistic. Values below 1 sugges<sup>t</sup> improvement over the OL run.


**Table 3.** Table of normalized innovation values, including the mean and standard deviation (SD) for the different observation operator, *h*, experiments.
