# High-resolution Calibrated Probabilistic Hourly Precipitation from a Deterministic Forecast

arXiv: https://arxiv.org/abs/2608.12685 · HTML: https://mlsanity.com/paper/2608.12685/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 55 references that are in the map.
- First posted on arXiv 13 Aug 2026.

## Builds on (most cited first, 6 of 6)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Attention U-Net: Learning Where to Look for the Pancreas](https://mlsanity.com/paper/1804.03999/) (2018)

## Built on by (most cited first, 1 of 1)

- [Methodological Changes to the Attention ResUNet Hourly Precipitation Postprocessor](https://mlsanity.com/paper/2609.38609/) (2026)

## Abstract (arXiv)

An ``Attention Residual U-Net'' method is described for probabilistic quantitative precipitation forecasting (PQPF) that predicts the hourly probability of no precipitation plus the distribution of positive precipitation from a weighted mixture of two Gamma distributions. The neural network is trained on patches of numerical weather prediction (NWP) hourly precipitation from The Weather Company's convection-permitting GRAF (Global high-Resolution Atmospheric Forecasting) model along with terrain information and column-average relative humidity from the National Oceanic and Atmospheric Administration's (NOAA's) Global Forecast System (GFS). The target data are NOAA's Multi-Radar, Multi-Sensor (MRMS) gauge-corrected, quality controlled radar data sampled to the same grid as the GRAF data. The network outputs distributional parameters for each model grid point. Training uses negative log-likelihood as a proper scoring rule, with climatological initialization for stable convergence. Inference is performed as a single forward pass over the contiguous United States (CONUS) domain, with edge-replication padding to satisfy the network's spatial-divisibility requirement. The subsequent forecasts are spatially detailed, highly reliable, and skillful with respect to climatology and a simpler reference forecast method. The method is particularly useful for estimating probabilities in regions with large terrain variation.