Articles | Volume 29, issue 21
https://doi.org/10.5194/hess-29-6221-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-29-6221-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
13 Nov 2025
Research article |
| 13 Nov 2025
| 13 Nov 2025
How to deal w___ missing input data
Google Research, Zurich, Switzerland
Invited contribution by Martin Gauch, recipient of the EGU Hydrological Sciences Virtual Outstanding Student and PhD candidate Presentation Award 2021.
Frederik Kratzert
Google Research, Vienna, Austria
Daniel Klotz
Google Research, Vienna, Austria
IT:U Interdisciplinary Transformation University, Linz, Austria
Grey Nearing
Google Research, Zurich, Switzerland
Deborah Cohen
Google Research, Tel Aviv, Israel
Oren Gilon
Google Research, Tel Aviv, Israel
Related authors
Deborah Cohen, Rony Amira, Rom Aschner, Yuval Carny, Ben Feinstein, Hadas Fester, Shmulik Fronman, Martin Gauch, Oren Gilon, Rotem Green, Avinatan Hassidim, Daniel Klotz, Frederik Kratzert, Dan Korenfeld, Gila Loike, Amit Markel, Yossi Matias, Rotem Mayo, Asher Metzger, Benny Mosheyev, Aviel Niego, Stephanie Rees, Emily Reinstein, Amitay Sicherman, Guy Shalev, Omri Shefi, Yuval Shildan, Ido Zemach, Oleg Zlydenko, and Grey Nearing
EGUsphere, https://doi.org/10.5194/egusphere-2026-2283, https://doi.org/10.5194/egusphere-2026-2283, 2026
This preprint is open for discussion and under review for Geoscientific Model Development (GMD).
Short summary
Short summary
We improved our global river model to provide earlier, more reliable streamflow predictions. Testing over approximately 1,000 watersheds, we found it predicts river flows up to six days further into the future for monitored rivers, and one day further for unmonitored ones. Releasing our code publicly empowers the science community to improve global water forecasting.
Eduardo Acuña Espinoza, Frederik Kratzert, Daniel Klotz, Martin Gauch, Manuel Álvarez Chaves, Ralf Loritz, and Uwe Ehret
Hydrol. Earth Syst. Sci., 29, 1749–1758, https://doi.org/10.5194/hess-29-1749-2025, https://doi.org/10.5194/hess-29-1749-2025, 2025
Short summary
Short summary
Long short-term memory (LSTM) networks have demonstrated state-of-the-art performance for rainfall-runoff hydrological modelling. However, most studies focus on predictions at a daily scale, limiting the benefits of sub-daily (e.g. hourly) predictions in applications like flood forecasting. In this study, we introduce a new architecture, multi-frequency LSTM (MF-LSTM), designed to use inputs of various temporal frequencies to produce sub-daily (e.g. hourly) predictions at a moderate computational cost.
Eduardo Acuña Espinoza, Ralf Loritz, Frederik Kratzert, Daniel Klotz, Martin Gauch, Manuel Álvarez Chaves, and Uwe Ehret
Hydrol. Earth Syst. Sci., 29, 1277–1294, https://doi.org/10.5194/hess-29-1277-2025, https://doi.org/10.5194/hess-29-1277-2025, 2025
Short summary
Short summary
Data-driven techniques have shown the potential to outperform process-based models in rainfall–runoff simulations. Hybrid models, combining both approaches, aim to enhance accuracy and maintain interpretability. Expanding the set of test cases to evaluate hybrid models under different conditions, we test their generalization capabilities for extreme hydrological events.
Daniel Klotz, Peter Miersch, Thiago V. M. do Nascimento, Fabrizio Fenicia, Martin Gauch, and Jakob Zscheischler
Earth Syst. Sci. Data Discuss., https://doi.org/10.5194/essd-2024-450, https://doi.org/10.5194/essd-2024-450, 2025
Revised manuscript accepted for ESSD
Short summary
Short summary
Data availability is central to hydrological science. It is the basis for advancing our understanding of hydrological processes, building prediction models, and anticipatory water management. We present a data-driven daily runoff reconstruction product for natural streamflow. We name it EARLS: European aggregated reconstruction for large-sample studies. The reconstructions represent daily simulations of natural streamflow across Europe and cover the period from 1953 to 2020.
Frederik Kratzert, Martin Gauch, Daniel Klotz, and Grey Nearing
Hydrol. Earth Syst. Sci., 28, 4187–4201, https://doi.org/10.5194/hess-28-4187-2024, https://doi.org/10.5194/hess-28-4187-2024, 2024
Short summary
Short summary
Recently, a special type of neural-network architecture became increasingly popular in hydrology literature. However, in most applications, this model was applied as a one-to-one replacement for hydrology models without adapting or rethinking the experimental setup. In this opinion paper, we show how this is almost always a bad decision and how using these kinds of models requires the use of large-sample hydrology data sets.
Andreas Auer, Martin Gauch, Frederik Kratzert, Grey Nearing, Sepp Hochreiter, and Daniel Klotz
Hydrol. Earth Syst. Sci., 28, 4099–4126, https://doi.org/10.5194/hess-28-4099-2024, https://doi.org/10.5194/hess-28-4099-2024, 2024
Short summary
Short summary
This work examines the impact of temporal and spatial information on the uncertainty estimation of streamflow forecasts. The study emphasizes the importance of data updates and global information for precise uncertainty estimates. We use conformal prediction to show that recent data enhance the estimates, even if only available infrequently. Local data yield reasonable average estimations but fall short for peak-flow events. The use of global data significantly improves these predictions.
Daniel Klotz, Martin Gauch, Frederik Kratzert, Grey Nearing, and Jakob Zscheischler
Hydrol. Earth Syst. Sci., 28, 3665–3673, https://doi.org/10.5194/hess-28-3665-2024, https://doi.org/10.5194/hess-28-3665-2024, 2024
Short summary
Short summary
The evaluation of model performance is essential for hydrological modeling. Using performance criteria requires a deep understanding of their properties. We focus on a counterintuitive aspect of the Nash–Sutcliffe efficiency (NSE) and show that if we divide the data into multiple parts, the overall performance can be higher than all the evaluations of the subsets. Although this follows from the definition of the NSE, the resulting behavior can have unintended consequences in practice.
Grey S. Nearing, Daniel Klotz, Jonathan M. Frame, Martin Gauch, Oren Gilon, Frederik Kratzert, Alden Keefe Sampson, Guy Shalev, and Sella Nevo
Hydrol. Earth Syst. Sci., 26, 5493–5513, https://doi.org/10.5194/hess-26-5493-2022, https://doi.org/10.5194/hess-26-5493-2022, 2022
Short summary
Short summary
When designing flood forecasting models, it is necessary to use all available data to achieve the most accurate predictions possible. This manuscript explores two basic ways of ingesting near-real-time streamflow data into machine learning streamflow models. The point we want to make is that when working in the context of machine learning (instead of traditional hydrology models that are based on
bio-geophysics), it is not necessary to use complex statistical methods for injecting sparse data.
Juliane Mai, Hongren Shen, Bryan A. Tolson, Étienne Gaborit, Richard Arsenault, James R. Craig, Vincent Fortin, Lauren M. Fry, Martin Gauch, Daniel Klotz, Frederik Kratzert, Nicole O'Brien, Daniel G. Princz, Sinan Rasiya Koya, Tirthankar Roy, Frank Seglenieks, Narayan K. Shrestha, André G. T. Temgoua, Vincent Vionnet, and Jonathan W. Waddell
Hydrol. Earth Syst. Sci., 26, 3537–3572, https://doi.org/10.5194/hess-26-3537-2022, https://doi.org/10.5194/hess-26-3537-2022, 2022
Short summary
Short summary
Model intercomparison studies are carried out to test various models and compare the quality of their outputs over the same domain. In this study, 13 diverse model setups using the same input data are evaluated over the Great Lakes region. Various model outputs – such as streamflow, evaporation, soil moisture, and amount of snow on the ground – are compared using standardized methods and metrics. The basin-wise model outputs and observations are made available through an interactive website.
Jonathan M. Frame, Frederik Kratzert, Daniel Klotz, Martin Gauch, Guy Shalev, Oren Gilon, Logan M. Qualls, Hoshin V. Gupta, and Grey S. Nearing
Hydrol. Earth Syst. Sci., 26, 3377–3392, https://doi.org/10.5194/hess-26-3377-2022, https://doi.org/10.5194/hess-26-3377-2022, 2022
Short summary
Short summary
The most accurate rainfall–runoff predictions are currently based on deep learning. There is a concern among hydrologists that deep learning models may not be reliable in extrapolation or for predicting extreme events. This study tests that hypothesis. The deep learning models remained relatively accurate in predicting extreme events compared with traditional models, even when extreme events were not included in the training set.
Thomas Lees, Steven Reece, Frederik Kratzert, Daniel Klotz, Martin Gauch, Jens De Bruijn, Reetik Kumar Sahu, Peter Greve, Louise Slater, and Simon J. Dadson
Hydrol. Earth Syst. Sci., 26, 3079–3101, https://doi.org/10.5194/hess-26-3079-2022, https://doi.org/10.5194/hess-26-3079-2022, 2022
Short summary
Short summary
Despite the accuracy of deep learning rainfall-runoff models, we are currently uncertain of what these models have learned. In this study we explore the internals of one deep learning architecture and demonstrate that the model learns about intermediate hydrological stores of soil moisture and snow water, despite never having seen data about these processes during training. Therefore, we find evidence that the deep learning approach learns a physically realistic mapping from inputs to outputs.
Daniel Klotz, Frederik Kratzert, Martin Gauch, Alden Keefe Sampson, Johannes Brandstetter, Günter Klambauer, Sepp Hochreiter, and Grey Nearing
Hydrol. Earth Syst. Sci., 26, 1673–1693, https://doi.org/10.5194/hess-26-1673-2022, https://doi.org/10.5194/hess-26-1673-2022, 2022
Short summary
Short summary
This contribution evaluates distributional runoff predictions from deep-learning-based approaches. We propose a benchmarking setup and establish four strong baselines. The results show that accurate, precise, and reliable uncertainty estimation can be achieved with deep learning.
Deborah Cohen, Rony Amira, Rom Aschner, Yuval Carny, Ben Feinstein, Hadas Fester, Shmulik Fronman, Martin Gauch, Oren Gilon, Rotem Green, Avinatan Hassidim, Daniel Klotz, Frederik Kratzert, Dan Korenfeld, Gila Loike, Amit Markel, Yossi Matias, Rotem Mayo, Asher Metzger, Benny Mosheyev, Aviel Niego, Stephanie Rees, Emily Reinstein, Amitay Sicherman, Guy Shalev, Omri Shefi, Yuval Shildan, Ido Zemach, Oleg Zlydenko, and Grey Nearing
EGUsphere, https://doi.org/10.5194/egusphere-2026-2283, https://doi.org/10.5194/egusphere-2026-2283, 2026
This preprint is open for discussion and under review for Geoscientific Model Development (GMD).
Short summary
Short summary
We improved our global river model to provide earlier, more reliable streamflow predictions. Testing over approximately 1,000 watersheds, we found it predicts river flows up to six days further into the future for monitored rivers, and one day further for unmonitored ones. Releasing our code publicly empowers the science community to improve global water forecasting.
Ulrike Proske, John Hillier, Stefan Gaillard, Theresa Blume, Eduardo Queiroz Alves, Susanne Buiter, Ken S. Carslaw, Kirsten von Elverfeldt, Tim H. M. van Emmerik, Barbara Ervens, Rolf Hut, Sam Illingworth, Daniel Klotz, and Jonas Pyschik
EGUsphere, https://doi.org/10.5194/egusphere-2026-987, https://doi.org/10.5194/egusphere-2026-987, 2026
This preprint is open for discussion and under review for Geoscience Communication (GC).
Short summary
Short summary
We explain a new article type that is being introduced in participating EGU publications. "LESSONS" articles describe the Limitations, Errors, Surprises, Shortcomings and Opportunities for New Science emerging from the scientific process. The publication of non-positive results and associated learnings aims to complete an unbiased record of the research effort, contributes to open and transparent science, allows the authors and others to learn, and may open opportunities for new science.
Sanika Baste, Sebastian Lerch, Daniel Klotz, and Ralf Loritz
EGUsphere, https://doi.org/10.5194/egusphere-2026-469, https://doi.org/10.5194/egusphere-2026-469, 2026
Short summary
Short summary
Probabilistic runoff predictions are capable of providing information about the possibility of occurrence of rare and high-stake events, which are largely underestimated by deterministic predictions, as they predict an expectation of the conditional runoff predictions. This additional information can be leveraged to aid flood warning communication by learning reward-based rules for selecting quantiles from the predictive distributions based on hydrological and societal contexts.
Sanika Baste, Daniel Klotz, Eduardo Acuña Espinoza, Andras Bardossy, and Ralf Loritz
Hydrol. Earth Syst. Sci., 29, 5871–5891, https://doi.org/10.5194/hess-29-5871-2025, https://doi.org/10.5194/hess-29-5871-2025, 2025
Short summary
Short summary
This study evaluates the extrapolation performance of long short-term memory (LSTM) networks in rainfall–runoff modeling, specifically under extreme precipitation conditions. The findings reveal that the LSTM cannot predict discharge values beyond a theoretical limit and that this limit is well below the extremity of its training data. This behavior results from the LSTM's gating structures rather than saturation of the cell states alone.
Claudia Färber, Henning Plessow, Simon A. Mischel, Frederik Kratzert, Nans Addor, Guy Shalev, and Ulrich Looser
Earth Syst. Sci. Data, 17, 4613–4625, https://doi.org/10.5194/essd-17-4613-2025, https://doi.org/10.5194/essd-17-4613-2025, 2025
Short summary
Short summary
Large-sample datasets are essential in hydrological science to support modelling studies and advance process understanding. Caravan is a community initiative to create a large-sample hydrology dataset of meteorological forcing data, catchment attributes and discharge data for catchments around the world. This dataset is a subset of hydrological discharge data and station-based watersheds from the Global Runoff Data Centre (GRDC), which are covered by an open data policy.
Eduardo Acuña Espinoza, Frederik Kratzert, Daniel Klotz, Martin Gauch, Manuel Álvarez Chaves, Ralf Loritz, and Uwe Ehret
Hydrol. Earth Syst. Sci., 29, 1749–1758, https://doi.org/10.5194/hess-29-1749-2025, https://doi.org/10.5194/hess-29-1749-2025, 2025
Short summary
Short summary
Long short-term memory (LSTM) networks have demonstrated state-of-the-art performance for rainfall-runoff hydrological modelling. However, most studies focus on predictions at a daily scale, limiting the benefits of sub-daily (e.g. hourly) predictions in applications like flood forecasting. In this study, we introduce a new architecture, multi-frequency LSTM (MF-LSTM), designed to use inputs of various temporal frequencies to produce sub-daily (e.g. hourly) predictions at a moderate computational cost.
Eduardo Acuña Espinoza, Ralf Loritz, Frederik Kratzert, Daniel Klotz, Martin Gauch, Manuel Álvarez Chaves, and Uwe Ehret
Hydrol. Earth Syst. Sci., 29, 1277–1294, https://doi.org/10.5194/hess-29-1277-2025, https://doi.org/10.5194/hess-29-1277-2025, 2025
Short summary
Short summary
Data-driven techniques have shown the potential to outperform process-based models in rainfall–runoff simulations. Hybrid models, combining both approaches, aim to enhance accuracy and maintain interpretability. Expanding the set of test cases to evaluate hybrid models under different conditions, we test their generalization capabilities for extreme hydrological events.
Daniel Klotz, Peter Miersch, Thiago V. M. do Nascimento, Fabrizio Fenicia, Martin Gauch, and Jakob Zscheischler
Earth Syst. Sci. Data Discuss., https://doi.org/10.5194/essd-2024-450, https://doi.org/10.5194/essd-2024-450, 2025
Revised manuscript accepted for ESSD
Short summary
Short summary
Data availability is central to hydrological science. It is the basis for advancing our understanding of hydrological processes, building prediction models, and anticipatory water management. We present a data-driven daily runoff reconstruction product for natural streamflow. We name it EARLS: European aggregated reconstruction for large-sample studies. The reconstructions represent daily simulations of natural streamflow across Europe and cover the period from 1953 to 2020.
Gab Abramowitz, Anna Ukkola, Sanaa Hobeichi, Jon Cranko Page, Mathew Lipson, Martin G. De Kauwe, Samuel Green, Claire Brenner, Jonathan Frame, Grey Nearing, Martyn Clark, Martin Best, Peter Anthoni, Gabriele Arduini, Souhail Boussetta, Silvia Caldararu, Kyeungwoo Cho, Matthias Cuntz, David Fairbairn, Craig R. Ferguson, Hyungjun Kim, Yeonjoo Kim, Jürgen Knauer, David Lawrence, Xiangzhong Luo, Sergey Malyshev, Tomoko Nitta, Jerome Ogee, Keith Oleson, Catherine Ottlé, Phillipe Peylin, Patricia de Rosnay, Heather Rumbold, Bob Su, Nicolas Vuichard, Anthony P. Walker, Xiaoni Wang-Faivre, Yunfei Wang, and Yijian Zeng
Biogeosciences, 21, 5517–5538, https://doi.org/10.5194/bg-21-5517-2024, https://doi.org/10.5194/bg-21-5517-2024, 2024
Short summary
Short summary
This paper evaluates land models – computer-based models that simulate ecosystem dynamics; land carbon, water, and energy cycles; and the role of land in the climate system. It uses machine learning and AI approaches to show that, despite the complexity of land models, they do not perform nearly as well as they could given the amount of information they are provided with about the prediction problem.
Frederik Kratzert, Martin Gauch, Daniel Klotz, and Grey Nearing
Hydrol. Earth Syst. Sci., 28, 4187–4201, https://doi.org/10.5194/hess-28-4187-2024, https://doi.org/10.5194/hess-28-4187-2024, 2024
Short summary
Short summary
Recently, a special type of neural-network architecture became increasingly popular in hydrology literature. However, in most applications, this model was applied as a one-to-one replacement for hydrology models without adapting or rethinking the experimental setup. In this opinion paper, we show how this is almost always a bad decision and how using these kinds of models requires the use of large-sample hydrology data sets.
Andreas Auer, Martin Gauch, Frederik Kratzert, Grey Nearing, Sepp Hochreiter, and Daniel Klotz
Hydrol. Earth Syst. Sci., 28, 4099–4126, https://doi.org/10.5194/hess-28-4099-2024, https://doi.org/10.5194/hess-28-4099-2024, 2024
Short summary
Short summary
This work examines the impact of temporal and spatial information on the uncertainty estimation of streamflow forecasts. The study emphasizes the importance of data updates and global information for precise uncertainty estimates. We use conformal prediction to show that recent data enhance the estimates, even if only available infrequently. Local data yield reasonable average estimations but fall short for peak-flow events. The use of global data significantly improves these predictions.
Daniel Klotz, Martin Gauch, Frederik Kratzert, Grey Nearing, and Jakob Zscheischler
Hydrol. Earth Syst. Sci., 28, 3665–3673, https://doi.org/10.5194/hess-28-3665-2024, https://doi.org/10.5194/hess-28-3665-2024, 2024
Short summary
Short summary
The evaluation of model performance is essential for hydrological modeling. Using performance criteria requires a deep understanding of their properties. We focus on a counterintuitive aspect of the Nash–Sutcliffe efficiency (NSE) and show that if we divide the data into multiple parts, the overall performance can be higher than all the evaluations of the subsets. Although this follows from the definition of the NSE, the resulting behavior can have unintended consequences in practice.
Louise J. Slater, Louise Arnal, Marie-Amélie Boucher, Annie Y.-Y. Chang, Simon Moulds, Conor Murphy, Grey Nearing, Guy Shalev, Chaopeng Shen, Linda Speight, Gabriele Villarini, Robert L. Wilby, Andrew Wood, and Massimiliano Zappa
Hydrol. Earth Syst. Sci., 27, 1865–1889, https://doi.org/10.5194/hess-27-1865-2023, https://doi.org/10.5194/hess-27-1865-2023, 2023
Short summary
Short summary
Hybrid forecasting systems combine data-driven methods with physics-based weather and climate models to improve the accuracy of predictions for meteorological and hydroclimatic events such as rainfall, temperature, streamflow, floods, droughts, tropical cyclones, or atmospheric rivers. We review recent developments in hybrid forecasting and outline key challenges and opportunities in the field.
Grey S. Nearing, Daniel Klotz, Jonathan M. Frame, Martin Gauch, Oren Gilon, Frederik Kratzert, Alden Keefe Sampson, Guy Shalev, and Sella Nevo
Hydrol. Earth Syst. Sci., 26, 5493–5513, https://doi.org/10.5194/hess-26-5493-2022, https://doi.org/10.5194/hess-26-5493-2022, 2022
Short summary
Short summary
When designing flood forecasting models, it is necessary to use all available data to achieve the most accurate predictions possible. This manuscript explores two basic ways of ingesting near-real-time streamflow data into machine learning streamflow models. The point we want to make is that when working in the context of machine learning (instead of traditional hydrology models that are based on
bio-geophysics), it is not necessary to use complex statistical methods for injecting sparse data.
Sella Nevo, Efrat Morin, Adi Gerzi Rosenthal, Asher Metzger, Chen Barshai, Dana Weitzner, Dafi Voloshin, Frederik Kratzert, Gal Elidan, Gideon Dror, Gregory Begelman, Grey Nearing, Guy Shalev, Hila Noga, Ira Shavitt, Liora Yuklea, Moriah Royz, Niv Giladi, Nofar Peled Levi, Ofir Reich, Oren Gilon, Ronnie Maor, Shahar Timnat, Tal Shechter, Vladimir Anisimov, Yotam Gigi, Yuval Levin, Zach Moshe, Zvika Ben-Haim, Avinatan Hassidim, and Yossi Matias
Hydrol. Earth Syst. Sci., 26, 4013–4032, https://doi.org/10.5194/hess-26-4013-2022, https://doi.org/10.5194/hess-26-4013-2022, 2022
Short summary
Short summary
Early flood warnings are one of the most effective tools to save lives and goods. Machine learning (ML) models can improve flood prediction accuracy but their use in operational frameworks is limited. The paper presents a flood warning system, operational in India and Bangladesh, that uses ML models for forecasting river stage and flood inundation maps and discusses the models' performances. In 2021, more than 100 million flood alerts were sent to people near rivers over an area of 470 000 km2.
Juliane Mai, Hongren Shen, Bryan A. Tolson, Étienne Gaborit, Richard Arsenault, James R. Craig, Vincent Fortin, Lauren M. Fry, Martin Gauch, Daniel Klotz, Frederik Kratzert, Nicole O'Brien, Daniel G. Princz, Sinan Rasiya Koya, Tirthankar Roy, Frank Seglenieks, Narayan K. Shrestha, André G. T. Temgoua, Vincent Vionnet, and Jonathan W. Waddell
Hydrol. Earth Syst. Sci., 26, 3537–3572, https://doi.org/10.5194/hess-26-3537-2022, https://doi.org/10.5194/hess-26-3537-2022, 2022
Short summary
Short summary
Model intercomparison studies are carried out to test various models and compare the quality of their outputs over the same domain. In this study, 13 diverse model setups using the same input data are evaluated over the Great Lakes region. Various model outputs – such as streamflow, evaporation, soil moisture, and amount of snow on the ground – are compared using standardized methods and metrics. The basin-wise model outputs and observations are made available through an interactive website.
Jonathan M. Frame, Frederik Kratzert, Daniel Klotz, Martin Gauch, Guy Shalev, Oren Gilon, Logan M. Qualls, Hoshin V. Gupta, and Grey S. Nearing
Hydrol. Earth Syst. Sci., 26, 3377–3392, https://doi.org/10.5194/hess-26-3377-2022, https://doi.org/10.5194/hess-26-3377-2022, 2022
Short summary
Short summary
The most accurate rainfall–runoff predictions are currently based on deep learning. There is a concern among hydrologists that deep learning models may not be reliable in extrapolation or for predicting extreme events. This study tests that hypothesis. The deep learning models remained relatively accurate in predicting extreme events compared with traditional models, even when extreme events were not included in the training set.
Thomas Lees, Steven Reece, Frederik Kratzert, Daniel Klotz, Martin Gauch, Jens De Bruijn, Reetik Kumar Sahu, Peter Greve, Louise Slater, and Simon J. Dadson
Hydrol. Earth Syst. Sci., 26, 3079–3101, https://doi.org/10.5194/hess-26-3079-2022, https://doi.org/10.5194/hess-26-3079-2022, 2022
Short summary
Short summary
Despite the accuracy of deep learning rainfall-runoff models, we are currently uncertain of what these models have learned. In this study we explore the internals of one deep learning architecture and demonstrate that the model learns about intermediate hydrological stores of soil moisture and snow water, despite never having seen data about these processes during training. Therefore, we find evidence that the deep learning approach learns a physically realistic mapping from inputs to outputs.
Daniel Klotz, Frederik Kratzert, Martin Gauch, Alden Keefe Sampson, Johannes Brandstetter, Günter Klambauer, Sepp Hochreiter, and Grey Nearing
Hydrol. Earth Syst. Sci., 26, 1673–1693, https://doi.org/10.5194/hess-26-1673-2022, https://doi.org/10.5194/hess-26-1673-2022, 2022
Short summary
Short summary
This contribution evaluates distributional runoff predictions from deep-learning-based approaches. We propose a benchmarking setup and establish four strong baselines. The results show that accurate, precise, and reliable uncertainty estimation can be achieved with deep learning.
Frederik Kratzert, Daniel Klotz, Sepp Hochreiter, and Grey S. Nearing
Hydrol. Earth Syst. Sci., 25, 2685–2703, https://doi.org/10.5194/hess-25-2685-2021, https://doi.org/10.5194/hess-25-2685-2021, 2021
Short summary
Short summary
We investigate how deep learning models use different meteorological data sets in the task of (regional) rainfall–runoff modeling. We show that performance can be significantly improved when using different data products as input and further show how the model learns to combine those meteorological input differently across time and space. The results are carefully benchmarked against classical approaches, showing the supremacy of the presented approach.
Cited articles
Addor, N., Newman, A. J., Mizukami, N., and Clark, M. P.: The CAMELS data set: catchment attributes and meteorology for large-sample studies, Hydrol. Earth Syst. Sci., 21, 5293–5313, https://doi.org/10.5194/hess-21-5293-2017, 2017. a, b
Afifi, A. A. and Elashoff, R. M.: Missing Observations in Multivariate Statistics I. Review of the Literature, Journal of the American Statistical Association, 61, 595–604, 1966. a
Alammar, J.: Visualizing A Neural Machine Translation Model (Mechanics of Seq2seq Models With Attention), Google Research Blog, https://jalammar.github.io/visualizing-neural-machine-translation-mechanics-of-seq2seq-models-with-attention/ (last access: 10 November 2025), 2018. a
Auer, A., Gauch, M., Kratzert, F., Nearing, G., Hochreiter, S., and Klotz, D.: A data-centric perspective on the information needed for hydrological uncertainty predictions, Hydrol. Earth Syst. Sci., 28, 4099–4126, https://doi.org/10.5194/hess-28-4099-2024, 2024. a
Bahdanau, D., Cho, K., and Bengio, Y.: Neural Machine Translation by Jointly Learning to Align and Translate, in: 3rd International Conference on Learning Representations (ICLR), arXiv, https://doi.org/10.48550/arXiv.1409.0473, 2015. a, b, c
Bishop, C. M. and Bishop, H.: Deep learning: Foundations and concepts, Springer Nature, https://doi.org/10.1007/978-3-031-45468-4, 2023. a
Brown, T., Mann, B., Ryder, N., Subbiah, M., Kaplan, J. D., Dhariwal, P., Neelakantan, A., Shyam, P., Sastry, G., Askell, A., Agarwal, S., Herbert-Voss, A., Krueger, G., Henighan, T., Child, R., Ramesh, A., Ziegler, D., Wu, J., Winter, C., Hesse, C., Chen, M., Sigler, E., Litwin, M., Gray, S., Chess, B., Clark, J., Berner, C., McCandlish, S., Radford, A., Sutskever, I., and Amodei, D.: Language Models are Few-Shot Learners, in: Advances in Neural Information Processing Systems, vol. 33, 1877–1901, Curran Associates, https://proceedings.neurips.cc/paper/2020/hash/1457c0d6bfcb4967418bfb8ac142f64a-Abstract.html (last access: 10 November 2025), 2020. a
Clerc-Schwarzenbach, F., Selleri, G., Neri, M., Toth, E., van Meerveld, I., and Seibert, J.: Large-sample hydrology – a few camels or a whole caravan?, Hydrol. Earth Syst. Sci., 28, 4219–4237, https://doi.org/10.5194/hess-28-4219-2024, 2024. a
Devlin, J., Chang, M., Lee, K., and Toutanova, K.: BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding, in: Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, 4171–4186, Association for Computational Linguistics, https://doi.org/10.18653/v1/N19-1423, 2019. a
Dosovitskiy, A., Beyer, L., Kolesnikov, A., Weissenborn, D., Zhai, X., Unterthiner, T., Dehghani, M., Minderer, M., Heigold, G., Gelly, S., Uszkoreit, J., and Houlsby, N.: An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale, in: 9th International Conference on Learning Representations (ICLR), openreview.net, https://openreview.net/forum?id=YicbFdNTTy (last access: 10 November 2025), 2021. a
Dumoulin, V., Perez, E., Schucher, N., Strub, F., Vries, H. d., Courville, A., and Bengio, Y.: Feature-wise transformations, Distill, https://doi.org/10.23915/distill.00011, 2018. a
Ebrahimi, S., Arik, S. O., Dong, Y., and Pfister, T.: LANISTR: Multimodal learning from structured and unstructured data, arXiv [preprint], https://doi.org/10.48550/arXiv.2305.16556, 2023. a
Frame, J. M., Araki, R., Bhuiyan, S. A., Bindas, T., Rapp, J., Bolotin, L., Deardorff, E., Liu, Q., Haces-Garcia, F., Liao, M., Frazier, N., and Ogden, F. L.: Machine Learning for a Heterogeneous Water Modeling Framework, JAWRA Journal of the American Water Resources Association, 61, e70000, https://doi.org/10.1111/1752-1688.70000, 2025. a
Franken, T., Gullentops, C., Wolfs, V., Defloor, W., Cabus, P., and De Jongh, I.: An operational framework for data driven low flow forecasts in Flanders, EGU General Assembly 2022, Vienna, Austria, 23–27 May 2022, EGU22-6191, https://doi.org/10.5194/egusphere-egu22-6191, 2022. a
Gao, Y., Merz, C., Lischeid, G., and Schneider, M.: A review on missing hydrological data processing, Environmental earth sciences, 77, 47, https://doi.org/10.1007/s12665-018-7228-6, 2018. a
Gauch, M.: Models and predictions for “How to deal w___ missing input data”, Zenodo [data set], https://doi.org/10.5281/zenodo.16983185, 2025a. a
Gauch, M.: How to deal w___ missing inputs: Code (v1.0), Zenodo [code, ICE], https://doi.org/10.5281/zenodo.17362593, 2025b. a
Gauch, M., Kratzert, F., Gilon, O., Gupta, H., Mai, J., Nearing, G., Tolson, B., Hochreiter, S., and Klotz, D.: In Defense of Metrics: Metrics Sufficiently Encode Typical Human Preferences Regarding Hydrological Model Performance, Water Resources Research, 59, e2022WR033918, https://doi.org/10.1029/2022WR033918, 2023. a, b, c, d
Graves, A.: Generating Sequences With Recurrent Neural Networks, arXiv [preprint], https://doi.org/10.48550/arXiv.1308.0850, 2013. a
Gupta, H. V., Kling, H., Yilmaz, K. K., and Martinez, G. F.: Decomposition of the mean squared error and NSE performance criteria: Implications for improving hydrological modelling, Journal of Hydrology, 377, 80–91, 2009. a
He, K., Chen, X., Xie, S., Li, Y., Dollár, P., and Girshick, R.: Masked Autoencoders Are Scalable Vision Learners, in: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 16000–16009, https://doi.org/10.1109/CVPR52688.2022.01553, 2022. a
Kratzert, F.: CAMELS Extended Maurer Forcing Data, HydroShare [data set], https://doi.org/10.4211/hs.17c896843cf940339c3c3496d0c1c077, 2019a. a
Kratzert, F.: CAMELS Extended NLDAS Forcing Data, HydroShare [data set], https://doi.org/10.4211/hs.0a68bfd7ddf642a8be9041d60f40868c, 2019b. a
Kratzert, F., Klotz, D., Shalev, G., Klambauer, G., Hochreiter, S., and Nearing, G.: Towards learning universal, regional, and local hydrological behaviors via machine learning applied to large-sample datasets, Hydrol. Earth Syst. Sci., 23, 5089–5110, https://doi.org/10.5194/hess-23-5089-2019, 2019. a, b
Kratzert, F., Klotz, D., Hochreiter, S., and Nearing, G. S.: A note on leveraging synergy in multiple meteorological data sets with deep learning for rainfall–runoff modeling, Hydrol. Earth Syst. Sci., 25, 2685–2703, https://doi.org/10.5194/hess-25-2685-2021, 2021. a, b, c, d, e, f, g, h, i, j, k, l, m
Kratzert, F., Gauch, M., Nearing, G., and Klotz, D.: NeuralHydrology – A Python library for Deep Learning research in hydrology, Journal of Open Source Software, 7, 4050, https://doi.org/10.21105/joss.04050, 2022. a
Kratzert, F., Nearing, G., Addor, N., Erickson, T., Gauch, M., Gilon, O., Gudmundsson, L., Hassidim, A., Klotz, D., Nevo, S., Shalev, G., and Matias, Y.: Caravan – A global community dataset for large-sample hydrology, Scientific Data, 10, 61, https://doi.org/10.1038/s41597-023-01975-w, 2023. a
Kratzert, F., Gauch, M., Klotz, D., and Nearing, G.: HESS Opinions: Never train a Long Short-Term Memory (LSTM) network on a single basin, Hydrol. Earth Syst. Sci., 28, 4187–4201, https://doi.org/10.5194/hess-28-4187-2024, 2024. a, b
Maurer, E. P., Wood, A. W., Adam, J. C., Lettenmaier, D. P., and Nijssen, B.: A Long-Term Hydrologically Based Dataset of Land Surface Fluxes and States for the Conterminous United States, Journal of Climate, 15, 3237–3251, 2002. a
Mitchell, M. and Jolley, J.: Research design explained, Holt, Rinehart & Winston Inc., ISBN: 0030040248, https://psycnet.apa.org/record/1987-98845-000 (last access: 10 November 2025), 1988. a
Nash, J. E. and Sutcliffe, J. V.: River flow forecasting through conceptual models part I – A discussion of principles, Journal of Hydrology, 10, 282–290, 1970. a
Nearing, G., Cohen, D., Dube, V., Gauch, M., Gilon, O., Harrigan, S., Hassidim, A., Klotz, D., Kratzert, F., Metzger, A., Nevo, S., Pappenberger, F., Prudhomme, C., Shalev, G., Shenzis, S., Tekalign, T. Y., Weitzner, D., and Matias, Y.: Global prediction of extreme floods in ungauged watersheds, Nature, volume 627, 559–563 pp., https://doi.org/10.1038/s41586-024-07145-1, 2024. a, b
Newman, A. J., Clark, M. P., Sampson, K., Wood, A., Hay, L. E., Bock, A., Viger, R. J., Blodgett, D., Brekke, L., Arnold, J. R., Hopson, T., and Duan, Q.: Development of a large-sample watershed-scale hydrometeorological data set for the contiguous USA: data set characteristics and assessment of regional variability in hydrologic model performance, Hydrol. Earth Syst. Sci., 19, 209–223, https://doi.org/10.5194/hess-19-209-2015, 2015. a, b
Perez, E., Strub, F., de Vries, H., Dumoulin, V., and Courville, A.: FiLM: Visual Reasoning with a General Conditioning Layer, Proceedings of the AAAI Conference on Artificial Intelligence, 32, 3942–3951 pp., https://doi.org/10.1609/aaai.v32i1.11671, 2018. a
Raffel, C., Shazeer, N., Roberts, A., Lee, K., Narang, S., Matena, M., Zhou, Y., Li, W., and Liu, P. J.: Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer, Journal of Machine Learning Research, 21, 1–67, 2020. a
Ramsauer, H., Schäfl, B., Lehner, J., Seidl, P., Widrich, M., Gruber, L., Holzleitner, M., Adler, T., Kreil, D., Kopp, M. K., Klambauer, G., Brandstetter, J., and Hochreiter, S.: Hopfield Networks is All You Need, in: 9th International Conference on Learning Representations (ICLR), openreview.net, https://openreview.net/forum?id=tL89RnzIiCd (last access: 10 November 2025), 2021. a
Rasiya Koya, S. and Roy, T.: Temporal Fusion Transformers for streamflow Prediction: Value of combining attention with recurrence, Journal of Hydrology, 637, 131301, https://doi.org/10.1016/j.jhydrol.2024.131301, 2024. a
Read, L., Sampson, A. K., Lambl, D., Butcher, P., Gulland, L., and Elkurdy, M.: Lessons learned applying a machine learning hydrologic forecast model in a live forecasting competition, in: AGU Fall Meeting Abstracts, Vol. 2021, H22A–07, 2021. a
Rohrer, B.: Transformers from Scratch, https://e2eml.school/transformers.html (last access: 10 November 2025), 2021. a
Schafer, J. L.: Analysis of incomplete multivariate data, CRC press, http://dx.doi.org/10.1201/9781439821862, 1997. a
Shalev, G. and Kratzert, F.: Caravan MultiMet: Extending Caravan with Multiple Weather Nowcasts and Forecasts, arXiv [preprint], https://doi.org/10.48550/arXiv.2411.09459, 2024. a
Srivastava, N., Hinton, G., Krizhevsky, A., Sutskever, I., and Salakhutdinov, R.: Dropout: a simple way to prevent neural networks from overfitting, J. Mach. Learn. Res., 15, 1929–1958, 2014. a
Thornton, P. E., Running, S. W., and White, M. A.: Generating surfaces of daily meteorological variables over large regions of complex terrain, Journal of Hydrology, 190, 214–251, 1997. a
Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., Kaiser, L. u., and Polosukhin, I.: Attention is All you Need, in: Advances in Neural Information Processing Systems, vol. 30, Curran Associates, https://proceedings.neurips.cc/paper/2017/hash/3f5ee243547dee91fbd053c1c4a845aa-Abstract.html (last access: 10 November 2025), 2017. a, b
Wells, J.: Compilation of records of surface waters of the United States through September 1950: Part 1-B. North Atlantic slope basins, New York to York River, Tech. rep., US Geological Survey, https://doi.org/10.3133/wsp1302, 1960. a
Wu, R., Zhang, A., Ilyas, I., and Rekatsinas, T.: Attention-based Learning for Missing Data Imputation in HoloClean, Proceedings of Machine Learning and Systems, 2, 307–325, 2020. a
Xia, Y., Mitchell, K., Ek, M., Sheffield, J., Cosgrove, B., Wood, E., Luo, L., Alonge, C., Wei, H., Meng, J., Livneh, B., Lettenmaier, D., Koren, V., Duan, Q., Mo, K., Fan, Y., and Mocko, D.: Continental-scale water and energy flux analysis and validation for the North American Land Data Assimilation System project phase 2 (NLDAS-2): 1. Intercomparison and application of model products, Journal of Geophysical Research: Atmospheres, 117, https://doi.org/10.1029/2011JD016048, 2012. a
Yozgatligil, C., Aslan, S., Iyigun, C., and Batmaz, I.: Comparison of missing value imputation methods in time series: the case of Turkish meteorological data, Theoretical and applied climatology, 112, 143–167, 2013. a
Short summary
Missing input data are one of the most common challenges when building deep learning hydrological models. We present and analyze different methods that can produce predictions when certain inputs are missing during training or inference. Our proposed strategies provide high accuracy while allowing for more flexible data handling and being robust to outages in operational scenarios.
Missing input data are one of the most common challenges when building deep learning...
