Uncertainty estimation with deep learning for rainfall–runoff modeling

Abstract

Abstract. 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 prediction, 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. This contribution demonstrates that accurate uncertainty predictions can be obtained with deep learning. We establish an uncertainty estimation benchmarking procedure and present four deep learning baselines. Three baselines are based on mixture density networks, and one is based on Monte Carlo dropout. The results indicate that these approaches constitute strong baselines, especially the former ones. Additionally, we provide a post hoc model analysis to put forward some qualitative understanding of the resulting models. The analysis extends the notion of performance and shows that the model learns nuanced behaviors to account for different situations.

Flood forecasting with machine learning models in an operational framework

“…The system estimates the uncertainty of the water stage following the approach detailed in Klotz et al (2022). The time-dependent distribution over the predicted stage is modeled using a (countable) mixture of asymmetric Laplacians (CMAL, Klotz et al, 2022).…”

“…The system estimates the uncertainty of the water stage following the approach detailed in Klotz et al (2022). The time-dependent distribution over the predicted stage is modeled using a (countable) mixture of asymmetric Laplacians (CMAL, Klotz et al, 2022). The parameters of this distribution are generated by feeding the hidden state of the forecast LSTM into a dedicated head layer for each forecasted time step.…”

Uncertainty Analysis in Multi‐Sector Systems: Considerations for Risk Analysis, Projection, and Planning for Complex Systems

“…An interesting approach is the application of machine learning methods for uncertainty quantification. Klotz et al (2021) demonstrate how deep neural networks, typically thought of as black-box models, can be used to estimate uncertainties for a hydrological system, while also showing an example of how to obtain some measure of interpretability with a post hoc interrogation of fitted machine learning models. The power of careful implementations of machine learning methods which embed mechanistic insights into the model structure as an alternative for learning and uncertainty quantification for complex systems, rather than explicitly process-based modeling, is starting to be explored in the hydrological literature (Kratzert, Klotz, Herrnegger, et al, 2019;Kratzert, Klotz, Shalev, et al, 2019).…”

A Case Study of Tidal Analysis Using Theory-Based Artificial Intelligence Techniques for Disaster Management in Taehwa River, South Korea

“…Another reason might be the introduction of noise into the dataset during modelling. Although, deep learning models performed better with increasing data size [40][41][42][43][44], but the harmonic analysis procedure introduces noise and more bias to larger datasets. Further subsample analysis shows an improvement in NSE of almost all models that incorporated wind input from 0.67 to 0.90.…”