Spatio temporal statistical models to improve short term rain forecasts

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.