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This study assimilated Sentinel-1 C-band backscatter observations over snow-covered terrain into the Noah-Multiparameterization land surface model using support vector machine (SVM) regression and an ensemble Kalman filter to improve the modeled terrestrial snow mass estimates. The data assimilation (DA) experiment was conducted across Western Colorado from September 2016 to August 2017. As part of the DA experiments, the impact of a rule-based update was evaluated by comparing snow water equivalent (SWE) estimates via DA (with [${\rm {DA}}_{\rm {v1}}$] and without [${\rm {DA}}_{\rm {v2}}$] the rule-based update) against SNOTEL SWE measurements. Results confirmed that rule-based update helped minimize SVM controllability issues, and in turn, improved the accuracy of SWE estimates relative to both open loop (OL) and ${\rm {DA}}_{\rm {v2}}$. Comparison of SWE estimates from Sentinel-1 ${\rm {DA}}_{\rm {v1}}$ against SNOTEL SWE revealed that 75% of stations showed improvements in bias and correlation coefficient relative to the OL. Assimilated SWE estimates also showed statistical improvements during both the snow accumulation and snow ablation periods. However, unbiased root mean square error showed a slight increase during the snow ablation period due to the large variability in the electromagnetic response of C-band backscatter over deep and/or wet snow. Improvement of the SWE estimates also resulted in improving river discharge estimates compared to in situ measurements. River discharge using Sentinel-1 ${\rm {DA}}_{\rm {v1}}$ improved the Nash–Sutcliffe efficiency at all available stations. These results suggest that physically constrained SVM can serve as an efficient observation operator for snow mass DA through explicit consideration of the first-order C-band scattering mechanisms over different terrestrial snow conditions.

The main objective of this article is to develop a physically constrained support vector machine (SVM) to predict C-band backscatter over snow-covered terrain as a function of geophysical inputs that reasonably represent the relevant characteristics of the snowpack. Sentinel-1 observations, in conjunction with geophysical variables from the Noah-MP land surface model, were used as training targets and input datasets, respectively. Robustness of the SVM prediction was analyzed in terms of training targets, training windows, and physical constraints related to snow liquid water content. The results showed that a combination of ascending and descending overpasses yielded the highest coverage of prediction (15.2%) while root mean square error (RMSE) ranged from 2.06 to 2.54 dB and unbiased RMSE ranged from 1.54 to 2.08 dB, but that the combined overpasses were degraded compared with ascending-only and descending-only training target sets due to the mixture of distinctive microwave signals during different times of the day (i.e., 6 a.m. versus 6 p.m. local time). Elongation of the training window length also increased the spatial coverage of prediction (given the sparsity of the training sets), but resulted in introducing more random errors. Finally, delineation of dry versus wet snow pixels for SVM training resulted in improving the accuracy of predicted backscatter relative to training on a mixture of dry and wet snow conditions. The overall results suggest that the prediction accuracy of the SVM was strongly linked with the first-order physics of the electromagnetic response of different snow conditions.

The main objective of this article is to develop a physically constrained support vector machine (SVM) to predict C-band backscatter over snow-covered terrain as a function of geophysical inputs that reasonably represent the relevant characteristics of the snowpack. Sentinel-1 observations, in conjunction with geophysical variables from the Noah-MP land surface model, were used as training targets and input datasets, respectively. Robustness of the SVM prediction was analyzed in terms of training targets, training windows, and physical constraints related to snow liquid water content. The results showed that a combination of ascending and descending overpasses yielded the highest coverage of prediction (15.2%) while root mean square error (RMSE) ranged from 2.06 to 2.54 dB and unbiased RMSE ranged from 1.54 to 2.08 dB, but that the combined overpasses were degraded compared with ascending-only and descending-only training target sets due to the mixture of distinctive microwave signals during different times of the day (i.e., 6 A.M. versus 6 P.M. local time). Elongation of the training window length also increased the spatial coverage of prediction (given the sparsity of the training sets), but resulted in introducing more random errors. Finally, delineation of dry versus wet snow pixels for SVM training resulted in improving the accuracy of predicted backscatter relative to training on a mixture of dry and wet snow conditions. The overall results suggest that the prediction accuracy of the SVM was strongly linked with the first-order physics of the electromagnetic response of different snow conditions.