# Statistical versus machine learning-based spatial interpolation of post-processed ensemble weather forecasts

arXiv: https://arxiv.org/abs/2609.07512 · HTML: https://mlsanity.com/paper/2609.07512/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 37 references that are in the map.
- First posted on arXiv 7 Sep 2026.

## Builds on (most cited first, 14 of 14)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Neural networks for post-processing ensemble weather forecasts](https://mlsanity.com/paper/1805.09091/) (2018)
- [Combining predictive distributions for statistical post-processing of ensemble forecasts](https://mlsanity.com/paper/1607.08096/) (2016)
- [Bayesian Nonparametric Calibration and Combination of Predictive Distributions](https://mlsanity.com/paper/1502.07246/) (2015)
- [Machine learning for total cloud cover prediction](https://mlsanity.com/paper/2001.05948/) (2020)
- [Truncated generalized extreme value distribution based EMOS model for calibration of wind speed ensemble forecasts](https://mlsanity.com/paper/2008.11539/) (2020)
- [Graph Neural Networks and Spatial Information Learning for Post-Processing Ensemble Weather Forecasts](https://mlsanity.com/paper/2407.11050/) (2024)
- [Clustering-based spatial interpolation of parametric post-processing models](https://mlsanity.com/paper/2401.14393/) (2024)
- [Probabilistic measures afford fair comparisons of AIWP and NWP model output](https://mlsanity.com/paper/2506.03744/) (2025)
- [A Composite-Loss Graph Neural Network for the Multivariate Post-Processing of Ensemble Weather Forecasts](https://mlsanity.com/paper/2509.02784/) (2025)
- [Enhancing multivariate post-processed visibility predictions utilizing CAMS forecasts](https://mlsanity.com/paper/2406.14159/) (2024)
- [Self-attentive Transformer for Fast and Accurate Postprocessing of Temperature and Wind Speed Forecasts](https://mlsanity.com/paper/2412.13957/) (2024)

## Abstract (arXiv)

Statistical post-processing improves ensemble weather forecasts, but generating calibrated predictions at locations without observations remains challenging. This study compares statistical and machine-learning-based methods for post-processing ECMWF 2-m temperature and 10-m wind speed forecasts at observed and unobserved stations in Germany. We consider EMOS-based approaches, distributional regression networks, Transformers, and graph neural networks under both limited and extended predictor settings. For temperature, we also investigate linear forecast combinations and propose an altitude-aware linear pool (ALP). The results show that post-processing improves upon the raw ensemble in most settings, but no single method performs best across all variables, station groups, and evaluation metrics. The proposed ALP provides a small but significant improvement over the standard linear pool at unobserved locations.