# Weakly-Constrained 4D Var for Downscaling with Uncertainty using Data-Driven Surrogate Models

arXiv: https://arxiv.org/abs/2503.02665 · HTML: https://mlsanity.com/paper/2503.02665/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 68 references that are in the map.
- First posted on arXiv 4 Mar 2025.

## Builds on (most cited first, 16 of 16)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [GraphCast: Learning skillful medium-range global weather forecasting](https://mlsanity.com/paper/2212.12794/) (2022)
- [Adaptive Fourier Neural Operators: Efficient Token Mixers for Transformers](https://mlsanity.com/paper/2111.13587/) (2021)
- [GenCast: Diffusion-based ensemble forecasting for medium-range weather](https://mlsanity.com/paper/2312.15796/) (2023)
- [FengWu: Pushing the Skillful Global Medium-range Weather Forecast beyond 10 Days Lead](https://mlsanity.com/paper/2304.02948/) (2023)
- [Forecasting Global Weather with Graph Neural Networks](https://mlsanity.com/paper/2202.07575/) (2022)
- [Pangu-Weather: A 3D High-Resolution Model for Fast and Accurate Global Weather Forecast](https://mlsanity.com/paper/2211.02556/) (2022)
- [Fourier Neural Operators for Arbitrary Resolution Climate Data Downscaling](https://mlsanity.com/paper/2305.14452/) (2023)
- [Can AI weather models predict out-of-distribution gray swan tropical cyclones?](https://mlsanity.com/paper/2410.14932/) (2024)
- [ClimAlign: Unsupervised statistical downscaling of climate variables via normalizing flows](https://mlsanity.com/paper/2008.04679/) (2020)
- [Generative Diffusion-based Downscaling for Climate](https://mlsanity.com/paper/2404.17752/) (2024)
- [TRU-NET: A Deep Learning Approach to High Resolution Prediction of Rainfall](https://mlsanity.com/paper/2008.09090/) (2020)
- [End-to-End Image Super-Resolution via Deep and Shallow Convolutional Networks](https://mlsanity.com/paper/1607.07680/) (2016)
- [Climate Variable Downscaling with Conditional Normalizing Flows](https://mlsanity.com/paper/2405.20719/) (2024)
- [An Optimization Framework to Improve 4D-Var Data Assimilation System Performance](https://mlsanity.com/paper/1308.1860/) (2013)

## Abstract (arXiv)

Dynamic downscaling typically involves using numerical weather prediction (NWP) solvers to refine coarse data to higher spatial resolutions. Data-driven models such as FourCastNet have emerged as a promising alternative to the traditional NWP models for forecasting. Once these models are trained, they are capable of delivering forecasts in a few seconds, thousands of times faster compared to classical NWP models. However, as the lead times, and, therefore, their forecast window, increase, these models show instability in that they tend to diverge from reality. In this paper, we propose to use data assimilation approaches to stabilize them when used for downscaling tasks. Data assimilation uses information from three different sources, namely an imperfect computational model based on partial differential equations (PDE), from noisy observations, and from an uncertainty-reflecting prior. In this work, when carrying out dynamic downscaling, we replace the computationally expensive PDE-based NWP models with FourCastNet in a ``weak-constrained 4DVar framework" that accounts for the implied model errors. We demonstrate the efficacy of this approach for a hurricane-tracking problem; moreover, the 4DVar framework naturally allows the expression and quantification of uncertainty. We demonstrate, using ERA5 data, that our approach performs better than the ensemble Kalman filter (EnKF) and the unstabilized FourCastNet model, both in terms of forecast accuracy and forecast uncertainty.