Kilometer-scale weather data is crucial for real-world applications but remains computationally intensive to produce using traditional weather simulations. An emerging solution is to use deep learning models, which offer a faster alternative for climate downscaling. However, their reliability is still in question, as they are often evaluated using standard machine learning metrics rather than insights from atmospheric and weather physics. This paper benchmarks recent state-of-the-art deep learning models and introduces physics-inspired diagnostics to evaluate their performance and reliability, with a particular focus on geographic generalization and physical consistency. Our experiments show that, despite the seemingly strong performance of models such as CorrDiff, when trained on a limited set of European geographies (e.g., central Europe), they struggle to generalize to other regions such as Iberia, Morocco in the south, or Scandinavia in the north. They also fail to accurately capture second-order variables such as divergence and vorticity derived from predicted velocity fields. These deficiencies appear even in in-distribution geographies, indicating challenges in producing physically consistent predictions. We propose a simple initial solution: introducing a power spectral density loss function that empirically improves geographic generalization by encouraging the reconstruction of small-scale physical structures. The code for reproducing the experimental results can be found at https://github.com/CarloSaccardi/PSD-Downscaling

Reanalysis datasets constitute the main source of spatially homogeneous information for climate analysis since they provide long records (spanning several decades) of physically consistent hourly/daily gridded data for many variables produced globally with a particular atmospheric general circulation model (AGCM) assimilating the available observations (see https://reanalyses.org for an overview of the current reanalyses). Besides the historical records, in some cases reanalyses provide near real-time information that allows monitoring the state of the climate. For instance, ERA5 [Hersbach et al., 2020] is the latest ECMWF climate reanalysis, providing hourly data on many atmospheric and land-surface parameters at 0.25º resolution, from 1940 to near real-time. However, much of this data is generated at coarse spatial resolutions, typically on the order of tens of kilometres, hampering their application for local and regional climate analysis, including extreme weather events, which often occur on smaller spatial scales. Enhancing the spatial resolution of reanalyses datasets is therefore critical for improving its utility for local-scale climate analysis and decision-making. A number of downscaling methods have been developed over the last decades for improving the spatial resolution of AGCM outputs based on two main approaches [Maraun and Widmann, 2017]: dynamical and statistical downscaling. Dynamical downscaling employs regional atmospheric models (Limited Area Models, LAMs) over limited areas of interest, driven at the boundaries by the AGCM outputs, to increase their coarse-resolution. This approach allows to solve regional/local processes and provides physically consistent results, but is limited by its high computational demands. It has been recently applied to generate regional reanalysis over continental-wide areas, such as the CERRA renalysis over Europe using the HARMONIE-ALADIN regional model (driven by ERA5) at a 5.5km resolution.

The Copernicus Regional Reanalysis for Europe, CERRA, is a high-resolution regional reanalysis dataset for the European domain. In recent years it has shown significant utility across various climate-related tasks, ranging from forecasting and climate change research to renewable energy prediction, resource management, air quality risk assessment, and the forecasting of rare events, among others. Unfortunately, the availability of CERRA is lagging two years behind the current date, due to constraints in acquiring the requisite external data and the intensive computational demands inherent in its generation. As a solution, this paper introduces a novel method using diffusion models to approximate CERRA downscaling in a data-driven manner, without additional informations. By leveraging the lower resolution ERA5 dataset, which provides boundary conditions for CERRA, we approach this as a super-resolution task. Focusing on wind speed around Italy, our model, trained on existing CERRA data, shows promising results, closely mirroring original CERRA data. Validation with in-situ observations further confirms the model's accuracy in approximating ground measurements.