Abstract In this paper, a novel approach to estimate fractional snow cover (FSC) from MODIS data in a complex and heterogeneous Alpine terrain is represented by using a state-of-the-art nonparametric spline regression method, namely, multivariate adaptive regression splines (MARS). For this purpose, twenty MODIS - Landsat 8 image pairs acquired between April 2013 and December 2016 over European Alps are used. Fifteen of the image pairs are employed during model training and five images are reserved as an independent test dataset. MARS models are trained by using MODIS top-of-atmosphere reflectance values of bands 1–7, normalized difference snow index, normalized difference vegetation index and land cover class as predictor variables. Reference FSC maps are generated from higher spatial resolution Landsat 8 binary snow cover maps. Multilayer feedforward artificial neural network (ANN) models are also trained by using the same input data. During the training and the testing, the effects of the training data size and the sampling type on the predictive performance of ANN and MARS models are investigated. An additional search is also conducted to reveal whether the choice of the transfer function used in the output layer of ANN has a significant contribution to the network's FSC mapping performance. The final ANN and MARS FSC products are at 500 m spatial resolution. The results on the independent test scenes indicate that the developed ANN models with linear and hyperbolic tangent transfer functions in the output layer and the MARS models are in good agreement with reference FSC data with the same average values of R = 0.93. In contrast, the standard MODIS snow fraction product, namely, MOD10 FSC, exhibits slightly poorer performance with average R = 0.88. The proposed MARS approach is statistically proven to have the same performance with ANN, yet it is computationally more efficient in model building.

中文翻译：

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利用多元自适应回归样条从 MODIS 数据中检索部分积雪面积

摘要 在本文中，通过使用最先进的非参数样条回归方法，即多元自适应回归样条（多元自适应回归样条），提出了一种在复杂且异质的高山地形中从 MODIS 数据估计雪覆盖率 (FSC) 的新方法。火星）。为此，使用了 2013 年 4 月至 2016 年 12 月在欧洲阿尔卑斯山上采集的 20 个 MODIS - Landsat 8 图像对。在模型训练期间使用了 15 个图像对，5 个图像被保留作为独立的测试数据集。MARS 模型使用 MODIS 1-7 波段的大气顶反射值、归一化差异雪指数、归一化差异植被指数和土地覆盖等级作为预测变量进行训练。参考 FSC 地图是从更高空间分辨率的 Landsat 8 二元积雪地图生成的。多层前馈人工神经网络 (ANN) 模型也使用相同的输入数据进行训练。在训练和测试过程中，研究了训练数据大小和采样类型对 ANN 和 MARS 模型预测性能的影响。还进行了额外的搜索，以揭示 ANN 输出层中使用的传递函数的选择是否对网络的 FSC 映射性能有重大贡献。最终的 ANN 和 MARS FSC 产品的空间分辨率为 500 m。独立测试场景的结果表明，在输出层中具有线性和双曲正切传递函数的开发 ANN 模型和 MARS 模型与参考 FSC 数据非常吻合，其平均值为 R = 0.93。相比之下，标准 MODIS 雪分数产品，即 MOD10 FSC，表现出稍差的性能，平均 R = 0.88。所提出的 MARS 方法经统计证明与 ANN 具有相同的性能，但它在模型构建中的计算效率更高。