The Upper Indus Basin, Himalayas provides water for 270 million people and countless ecosystems. However, precipitation, a key component to hydrological modelling, is poorly understood in this area. A key challenge surrounding this uncertainty comes from the complex spatial-temporal distribution of precipitation across the basin. In this work we propose Gaussian processes with structured non-stationary kernels to model precipitation patterns in the UIB. Previous attempts to quantify or model precipitation in the Hindu Kush Karakoram Himalayan region have often been qualitative or include crude assumptions and simplifications which cannot be resolved at lower resolutions. This body of research also provides little to no error propagation. We account for the spatial variation in precipitation with a non-stationary Gibbs kernel parameterised with an input dependent lengthscale. This allows the posterior function samples to adapt to the varying precipitation patterns inherent in the distinct underlying topography of the Indus region. The input dependent lengthscale is governed by a latent Gaussian process with a stationary squared-exponential kernel to allow the function level hyperparameters to vary smoothly. In ablation experiments we motivate each component of the proposed kernel by demonstrating its ability to model the spatial covariance, temporal structure and joint spatio-temporal reconstruction. We benchmark our model with a stationary Gaussian process and a Deep Gaussian processes.

翻译：上印度河流域,喜马拉雅山脉为2.7亿人和无数生态系统提供水。然而,降水是水文建模的关键组成部分,但该地区对降水了解甚少。围绕这一不确定性的一个关键挑战来自整个流域降雨量的复杂空间时空分布。在这项工作中,我们提出高斯进程结构化的非静止内核结构化,以模拟UIB地区的降水模式。以前在兴都库什卡拉科拉姆喜马拉雅山地区,量化或模拟降水的尝试往往是定性的,或包括无法在低分辨率下解决的粗度假设和简化。这一研究机构也很少提供无误传播。我们用非静止的Gib内核参数参数参数参数参数参数参数参数来说明降水量的空间变化。这让海边功能样本能够适应印度河沿岸地区独特的地表地形所固有的不同降水模式。投入依赖的长度由潜伏的Gausian进程和定位平方平方阵列式阵列调节,使功能超常度模型变化。在深度实验中,我们通过深度实验将每个组成部分的地平位模型显示我们提议的空间空间空间台阶结构。