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.

中文翻译：

---

使用地表模型和支持向量机回归预测科罗拉多州西部积雪地形上的主动微波后向散射

本文的主要目的是开发一种物理约束支持向量机 (SVM) 来预测雪覆盖地形上的 C 波段反向散射，作为地球物理输入的函数，该函数合理地表示积雪的相关特征。Sentinel-1 观测与来自 Noah-MP 地表模型的地球物理变量相结合，分别用作训练目标和输入数据集。从训练目标、训练窗口和与雪液态水含量相关的物理约束方面分析了 SVM 预测的鲁棒性。结果表明，上升和下降立交桥的组合产生了最高的预测覆盖率（15.2%），而均方根误差（RMSE）范围为 2.06 至 2.54 dB，无偏 RMSE 范围为 1.54 至 2.08 dB，是与 6 相比下午当地时间）。训练窗口长度的延长也增加了预测的空间覆盖率（考虑到训练集的稀疏性），但导致引入了更多的随机误差。最后，用于 SVM 训练的干雪和湿雪像素的描绘导致相对于干湿雪混合条件下的训练，提高了预测反向散射的准确性。总体结果表明，SVM 的预测精度与不同雪况下电磁响应的一阶物理密切相关。