Model-Based and Data-Driven methods for Statistical Downscaling of meteorological data

This work arises from an intership at the HPC department of CINECA. Meteorological fields such as the air temperature near the Earth's surface are of the utmost importance in the study of the weather and climate, which impact most aspects of the modern society. The ERA5 global climate reanalysis is a widely used tool in this field; despite its high resolution of 31 km, however, it cannot adequately capture local features. In spatially limited areas, they can be simulated either with dynamic or statistical Downscaling techniques. Our goal is to assess the viability of multiple different approaches to statistically Downscale ERA5 using a 2 km resolution reanalysis as a ground truth. The 3 classes of approaches we consider are Model-based Variational models, Hybrid Plug and Play and data-driven Deep learning models. We first frame the task as an inverse problem. Maximizing the posterior distribution given the observed data results in a minimization problem involving a data fidelity term and a regularization term expressing our prior knowledge. The objective function to be minimized may not have a direct solution, in this case the ADMM algorithm allows us to divide the minimization process into easier to solve subproblems. A further benefit of the ADMM algorithm is its modular structure. Separating the data fidelity and regularization part, allows for the regularization term to be incorporated into a denoising problem, which may be solved by an external denoiser. Using a Neural Network as a denoiser, we are able to implicitly learn a prior, instead of relying on general regularizers. After recent advances in end-to-end Deep Learning, it has been used as a promising alternative approach. The main architecture we test is known as a U-Net, a CNN successfully been used in fields ranging from object detection and classification to denoising and medical imaging. We compare the performance of the selected methods using a range of scalar metrics, as well as spatial Bias.