# Uncertainty Estimation with Deep Learning for Rainfall-Runoff Modelling

arXiv: https://arxiv.org/abs/2012.14295 · HTML: https://mlsanity.com/paper/2012.14295/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Dec 2020.

## Built on by (most cited first, 9 of 9)

- [Conformal Prediction for Time Series with Modern Hopfield Networks](https://mlsanity.com/paper/2303.12783/) (2023)
- [Flood forecasting with machine learning models in an operational framework](https://mlsanity.com/paper/2111.02780/) (2021)
- [Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrology](https://mlsanity.com/paper/2310.05227/) (2023)
- [Enhancing predictive skills in physically-consistent way: Physics Informed Machine Learning for Hydrological Processes](https://mlsanity.com/paper/2104.11009/) (2021)
- [Continental-scale streamflow modeling of basins with reservoirs: towards a coherent deep-learning-based strategy](https://mlsanity.com/paper/2101.04423/) (2021)
- [AI Increases Global Access to Reliable Flood Forecasts](https://mlsanity.com/paper/2307.16104/) (2023)
- [Accurate and Reliable Forecasting using Stochastic Differential Equations](https://mlsanity.com/paper/2103.15041/) (2021)
- [Joint distribution of upstream runoff governs downstream river-discharge prediction uncertainty in distributed ML models](https://mlsanity.com/paper/2607.03217/) (2026)
- [Knowledge distillation as a pathway toward next-generation intelligent ecohydrological modeling systems](https://mlsanity.com/paper/2509.01972/) (2025)

## Abstract (arXiv)

Deep Learning is becoming an increasingly important way to produce accurate hydrological predictions across a wide range of spatial and temporal scales. Uncertainty estimations are critical for actionable hydrological forecasting, and while standardized community benchmarks are becoming an increasingly important part of hydrological model development and research, similar tools for benchmarking uncertainty estimation are lacking. We establish an uncertainty estimation benchmarking procedure and present four Deep Learning baselines, out of which three are based on Mixture Density Networks and one is based on Monte Carlo dropout. Additionally, we provide a post-hoc model analysis to put forward some qualitative understanding of the resulting models. Most importantly however, we show that accurate, precise, and reliable uncertainty estimation can be achieved with Deep Learning.