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
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Short summary
Short summary
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Revised manuscript under review for ESSD
Short summary
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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
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Frederik Kratzert, Martin Gauch, Daniel Klotz, and Grey Nearing
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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
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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
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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
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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.
Martin Gauch, Frederik Kratzert, Daniel Klotz, Grey Nearing, Jimmy Lin, and Sepp Hochreiter
Hydrol. Earth Syst. Sci., 25, 2045–2062, https://doi.org/10.5194/hess-25-2045-2021, https://doi.org/10.5194/hess-25-2045-2021, 2021
Short summary
Short summary
We present multi-timescale Short-Term Memory (MTS-LSTM), a machine learning approach that predicts discharge at multiple timescales within one model. MTS-LSTM is significantly more accurate than the US National Water Model and computationally more efficient than an individual LSTM model per timescale. Further, MTS-LSTM can process different input variables at different timescales, which is important as the lead time of meteorological forecasts often depends on their temporal resolution.
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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...
