Spatio temporal statistical models to improve short term rain forecasts

该项目的目标是利用统计和物理动力学建模方法与可能性和贝叶斯推理，以改善动态预测的空间和时间降水模式。预计这可以通过依靠以前的工作来实现，其中数据来源包括雷达反射率，卫星数据或三维雷达分析。提高雷达临近预报的精度和可靠性是本研究的重点，本文将探索一种新的雷达临近预报方法，将随机平流扩散方程转化为具有稀疏演化算子的向量自回归（VAR）过程。高空间和时间分辨率的预测涉及物理模拟的细节、统计模型中的参数数量和计算资源之间的权衡。该项目的科学贡献将是使用高维时空统计模型进行预测的新贝叶斯方法。该项目将对基于简单持久性或平流方法的现有临近预报方法进行比较（Prudden等人，2020），更复杂的随机偏微分方程（Sigrist等人，2014）和先进的机器学习方法，如神经网络（Ayzel et al.，2019).集成嵌套拉普拉斯近似（INLA，芸香等人，2009）方法利用稀疏矩阵方法和数值近似来有效地计算用于快速贝叶斯推断的高维积分。稀疏矩阵方法将用于模拟随机平流扩散方程，INLA可用于推断统计模型参数的贝叶斯后验分布。雷达临近预报中误差模式的空间和时间相关结构的真实表示是一个关键组成部分。为此，博士项目将探索基于随机偏微分方程的参数方法（Sigrist et al.，2015），以及基于经验copula的经验方法（Clark et al.，2004）和模拟技术。

The objective of this project is to leverage statistical and physical-dynamical modelling approach with likelihood and Bayesian Inference to improve dynamical predictions of spatial and temporal precipitation patterns. It is expected that this may be achieved by leaning on previous works where sources of data have included radar reflectivity, satellite data or 3-D radar analysis. Improvement of forecast skill and forecast reliability are of key interest in this study.A new approach to radar nowcasting that will be explored in the project is the formulation of numerical solutions of the stochastic advection diffusion equation as a vector autoregressive (VAR) process with a sparse evolution operator. Predictions at high spatial and temporal resolutions involve a trade-off between detailedness of the physical simulation, the number of parameters in statistical models, and computational resources. The scientific contributions of the project will be novel Bayesian methods for forecasting with high-dimensional spatio-temporal statistical models.The project will conduct a comparison of existing nowcasting methods based on simple persistence or advection methods (Prudden et al., 2020), more complicated stochastic partial differential equations (Sigrist et al., 2014), and advanced machine learning methodology such as neural networks (Ayzel et al., 2019).The Integrated Nested Laplace Approximation (INLA, Rue et al., 2009) approach exploits sparse matrix methods and numerical approximations to efficiently calculate high dimensional integrals for fast Bayesian inference. Sparse matrix methods will be used to simulate stochastic advection diffusion equations and INLA can be used to infer Bayesian posterior distributions of statistical model parameters.A truthful representation of the spatial and temporal correlation structure of error patterns in radar nowcasting is a crucial component.To this end, the PhD project will explore parametric approaches based on stochastic partial differential equations (Sigrist et al., 2015), as well as empirical approaches based on empirical copulas (Clark et al.,2004) and analogue techniques.