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：印度河上游流域（喜马拉雅地区）为2.7亿人口及无数生态系统提供水源。然而，作为水文模型关键要素的降水，在该区域尚未得到充分认知。这种不确定性的核心挑战源于流域内降水的复杂时空分布特征。本研究提出采用具有结构化非平稳核的高斯过程，对印度河上游流域的降水模式进行建模。此前针对兴都库什-喀喇昆仑-喜马拉雅地区降水量化或建模的尝试多局限于定性分析，或存在无法在低分辨率下解决的粗略假设与简化，同时该领域研究几乎未涉及误差传播机制。我们采用参数化输入依赖长度尺度的非平稳Gibbs核，有效刻画降水空间变异性，使后验函数样本能够适应印度河区域独特底层地形固有的降水模式变化。输入依赖长度尺度由具有平稳平方指数核的潜高斯过程调控，确保函数层超参数平滑变化。通过消融实验，我们验证了所提核各组分在空间协方差建模、时间结构建模及联合时空重构中的有效性。将本模型与平稳高斯过程及深度高斯过程进行基准对比测试。