# Distributional Regression U-Nets for the Postprocessing of Precipitation Ensemble Forecasts

arXiv: https://arxiv.org/abs/2407.02125 · HTML: https://mlsanity.com/paper/2407.02125/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 76 references that are in the map.
- First posted on arXiv 2 Jul 2024.

## Builds on (most cited first, 21 of 21)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [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)
- [FengWu: Pushing the Skillful Global Medium-range Weather Forecast beyond 10 Days Lead](https://mlsanity.com/paper/2304.02948/) (2023)
- [ranger: A Fast Implementation of Random Forests for High Dimensional Data in C++ and R](https://mlsanity.com/paper/1508.04409/) (2015)
- [Forecasting Global Weather with Graph Neural Networks](https://mlsanity.com/paper/2202.07575/) (2022)
- [Neural networks for post-processing ensemble weather forecasts](https://mlsanity.com/paper/1805.09091/) (2018)
- [Deep Learning for Post-Processing Ensemble Weather Forecasts](https://mlsanity.com/paper/2005.08748/) (2020)
- [Machine learning methods for postprocessing ensemble forecasts of wind gusts: A systematic comparison](https://mlsanity.com/paper/2106.09512/) (2021)
- [Uncertainty Quantification in Complex Simulation Models Using Ensemble Copula Coupling](https://mlsanity.com/paper/1302.7149/) (2013)
- [Forecaster's Dilemma: Extreme Events and Forecast Evaluation](https://mlsanity.com/paper/1512.09244/) (2015)
- [Distributional Regression Forests for Probabilistic Precipitation Forecasting in Complex Terrain](https://mlsanity.com/paper/1804.02921/) (2018)
- [Neural Networks for Extreme Quantile Regression with an Application to Forecasting of Flood Risk](https://mlsanity.com/paper/2208.07590/) (2022)
- [Deep graphical regression for jointly moderate and extreme Australian wildfires](https://mlsanity.com/paper/2308.14547/) (2023)
- [Censored and shifted gamma distribution based EMOS model for probabilistic quantitative precipitation forecasting](https://mlsanity.com/paper/1512.04068/) (2015)
- [Forest-based methods and ensemble model output statistics for rainfall ensemble forecasting](https://mlsanity.com/paper/1711.10937/) (2017)
- [Aggregating distribution forecasts from deep ensembles](https://mlsanity.com/paper/2204.02291/) (2022)
- [Convolutional autoencoders for spatially-informed ensemble post-processing](https://mlsanity.com/paper/2204.05102/) (2022)

## Built on by (most cited first, 2 of 2)

- [A Composite-Loss Graph Neural Network for the Multivariate Post-Processing of Ensemble Weather Forecasts](https://mlsanity.com/paper/2509.02784/) (2025)
- [Forecasting threshold exceedance of atmospheric variables at a specific location](https://mlsanity.com/paper/2605.31079/) (2026)

## Abstract (arXiv)

Accurate precipitation forecasts have a high socio-economic value due to their role in decision-making in various fields such as transport networks and farming. We propose a global statistical postprocessing method for grid-based precipitation ensemble forecasts. This U-Net-based distributional regression method predicts marginal distributions in the form of parametric distributions inferred by scoring rule minimization. Distributional regression U-Nets are compared to state-of-the-art postprocessing methods for daily 21-h forecasts of 3-h accumulated precipitation over the South of France. Training data comes from the M'et'eo-France weather model AROME-EPS and spans 3 years. A practical challenge appears when consistent data or reforecasts are not available. Distributional regression U-Nets compete favorably with the raw ensemble. In terms of continuous ranked probability score, they reach a performance comparable to quantile regression forests (QRF). However, they are unable to provide calibrated forecasts in areas associated with high climatological precipitation. In terms of predictive power for heavy precipitation events, they outperform both QRF and semi-parametric QRF with tail extensions.