Articles | Volume 28, issue 17
https://doi.org/10.5194/hess-28-4099-2024
© Author(s) 2024. 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-28-4099-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
12 Sep 2024
Research article |
| 12 Sep 2024
| 12 Sep 2024
A data-centric perspective on the information needed for hydrological uncertainty predictions
Andreas Auer
CORRESPONDING AUTHOR
ELLIS Unit Linz and LIT AI Lab, Institute for Machine Learning, Johannes Kepler University Linz, Linz, Austria
Martin Gauch
Google Research, Zurich, Switzerland
Frederik Kratzert
Google Research, Vienna, Austria
Grey Nearing
Google Research, Mountain View, California, USA
Sepp Hochreiter
ELLIS Unit Linz and LIT AI Lab, Institute for Machine Learning, Johannes Kepler University Linz, Linz, Austria
Daniel Klotz
Department of Compound Environmental Risks, Helmholtz Centre for Environmental Research – UFZ, Leipzig, Germany
Related authors
No articles found.
Martin Gauch, Frederik Kratzert, Daniel Klotz, Grey Nearing, Deborah Cohen, and Oren Gilon
EGUsphere, https://doi.org/10.5194/egusphere-2025-1224, https://doi.org/10.5194/egusphere-2025-1224, 2025
Short summary
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.
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.
Sanika Baste, Daniel Klotz, Eduardo Acuña Espinoza, Andras Bardossy, and Ralf Loritz
EGUsphere, https://doi.org/10.5194/egusphere-2025-425, https://doi.org/10.5194/egusphere-2025-425, 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 conditions. The findings reveal that the LSTM cannot predict discharge values beyond a theoretical limit, which is well below the extremity of its training data. This behavior results from the LSTM's gating structures rather than saturation of cell states alone.
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
Preprint under review 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.
Claudia Färber, Henning Plessow, Simon Mischel, Frederik Kratzert, Nans Addor, Guy Shalev, and Ulrich Looser
Earth Syst. Sci. Data Discuss., https://doi.org/10.5194/essd-2024-427, https://doi.org/10.5194/essd-2024-427, 2024
Revised manuscript accepted for ESSD
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.
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.
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.
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.
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, 2017a. a
Addor, N., Newman, A., Mizukami, M., and Clark, M. P.: Catchment attributes for large-sample studies data repository: Boulder, CO, UCAR/NCAR [data set], https://gdex.ucar.edu/dataset/camels/file.html 2017b. a
Angelopoulos, A. N. and Bates, S.: A gentle introduction to conformal prediction and distribution-free uncertainty quantification, arXiv [preprint], https://doi.org/10.48550/arXiv.2107.07511, 2021. a
Auer, A.: Code – A data-centric perspective on the information needed for hydrological uncertainty predictions, Zenodo [code], https://doi.org/10.5281/zenodo.10674231, 2024a. a
Auer, A.: Models and Model States – A data-centric perspective on the information needed for hydrological uncertainty predictions, Zenodo [data set], https://doi.org/10.5281/zenodo.10653863, 2024b. a
Auer, A.: CMAL – Non PUB – A data-centric perspective on the information needed for hydrological uncertainty predictions, Zenodo [data set], https://doi.org/10.5281/zenodo.10654345, 2024c. a
Auer, A.: CMAL – PUB – A data-centric perspective on the information needed for hydrological uncertainty predictions, Zenodo [data set], https://doi.org/10.5281/zenodo.10654399, 2024d. a
Auer, A., Gauch, M., Klotz, D., and Hochreiter, S.: Conformal Prediction for Time Series with Modern Hopfield Networks, in: Thirty-seventh Conference on Neural Information Processing Systems, New Orleans, Louisiana, USA, 10–16 December 2023, https://openreview.net/forum?id=KTRwpWCMsC (last access: 31 August 2024), 2023. a, b, c, d, e, f, g, h, i, j, k, l, m
Bertola, M., Blöschl, G., Bohac, M., Borga, M., Castellarin, A., Chirico, G. B., Claps, P., Dallan, E., Danilovich, I., Ganora, D., Gorbachova, L., Ledvinka, O., Mavrova-Guirguinova, M., Montanari, A., Ovcharuk, V., Viglione, A., Volpi, E., Arheimer, B., Aronica, G.T., Bonacci, O., Čanjevac, I., Csik, A., Frolova, N., Gnandt, B., Gribovszki, Z., Gül, A., Günther, K., Guse, B., Hannaford, J., Harrigan, S., Kireeva, M., Kohnová, S., Komma, J., Kriauciuniene, J., Kronvang, B., Lawrence, D., Lüdtke, S., Mediero, L., Merz, B., Molnar, P., Murphy, C., Oskoruš, D., Osuch, M., Parajka, J., Pfister, L., Radevski, I., Sauquet, E., Schröter, K., Šraj, M., Szolgay, J., Turner, S., Valent, P., Veijalainen, N., Ward, P. J., Willems, P., and Zivkovic, N.: Megafloods in Europe can be anticipated from observations in hydrologically similar catchments, Nat. Geosci., 16, 982–988, https://doi.org/10.1038/s41561-023-01300-5, 2023. a, b, c
Beven, K.: Facets of uncertainty: epistemic uncertainty, non-stationarity, likelihood, hypothesis testing, and communication, Hydrolog. Sci. J., 61, 1652–1665, https://doi.org/10.1080/02626667.2015.1031761, 2016a. a
Beven, K.: Facets of uncertainty: epistemic uncertainty, non-stationarity, likelihood, hypothesis testing, and communication, Hydrolog. Sci. J., 61, 1652–1665, 2016b. a
Beven, K. and Binley, A.: GLUE: 20 years on, Hydrol. Process., 28, 5897–5918, 2014. a
Bhatnagar, A., Wang, H., Xiong, C., and Bai, Y.: Improved Online Conformal Prediction via Strongly Adaptive Online Learning, in: International Conference on Machine Learning, Honolulu, Hawaii, USA, 2023, https://api.semanticscholar.org/CorpusID:256868761 (last access: 31 August 2024), 2023. a
Bishop, C. M.: Mixture density networks, Tech. rep., Neural Computing Research Group, https://publications.aston.ac.uk/id/eprint/373/1/NCRG_94_004.pdf (last access: 5 September 2024), 1994. a
Clark, M. P., Wilby, R. L., Gutmann, E. D., Vano, J. A., Gangopadhyay, S., Wood, A. W., Fowler, H. J., Prudhomme, C., Arnold, J. R., and Brekke, L. D.: Characterizing uncertainty of the hydrologic impacts of climate change, Current Climate Change Reports, 2, 55–64, 2016. a
Demargne, J., Wu, L., Regonda, S. K., Brown, J. D., Lee, H., He, M., Seo, D.-J., Hartman, R., Herr, H. D., Fresch, M., Schaake, J., and Zhu, Y.: The science of NOAA's operational hydrologic ensemble forecast service, B. Am. Meteorol. Soc., 95, 79–98, 2014. a
Foygel Barber, R., Candes, E. J., Ramdas, A., and Tibshirani, R. J.: Conformal prediction beyond exchangeability, arXiv [preprint], https://doi.org/10.48550/arXiv.2202.13415, 2022. a, b
Frame, J. M., Kratzert, F., Klotz, D., Gauch, M., Shalev, G., Gilon, O., Qualls, L. M., Gupta, H. V., and Nearing, G. S.: Deep learning rainfall–runoff predictions of extreme events, Hydrology and Earth System Sciences, 26, 3377–3392, 2022. a
Gauch, M., Mai, J., and Lin, J.: The proper care and feeding of CAMELS: How limited training data affects streamflow prediction, Environ. Modell. Softw., 135, 104926, https://doi.org/10.1016/j.envsoft.2020.104926, 2021. a
Geirhos, R., Jacobsen, J.-H., Michaelis, C., Zemel, R. S., Brendel, W., Bethge, M., and Wichmann, F.: Shortcut learning in deep neural networks, Nature Machine Intelligence, 2, 665–673, https://api.semanticscholar.org/CorpusID:215786368 (last access: 31 August 2024), 2020. a
Gibbs, I. and Candes, E. J.: Adaptive conformal inference under distribution shift, Adv. Neur. In., 34, 1660–1672, 2021. a
Gupta, A. and Govindaraju, R. S.: Uncertainty quantification in watershed hydrology: Which method to use?, J. Hydrol., 616, 128749, https://doi.org/10.1016/j.jhydrol.2022.128749, 2023. a
Haines, A., Finlayson, B., and McMahon, T.: A Global Classification of River Regimes, Appl. Geogr., 8, 255–272, https://doi.org/10.1016/0143-6228(88)90035-5, 1988. a
Harris, N. M., Gurnell, A. M., Hannah, D. M., and Petts, G. E.: Classification of river regimes: a context for hydroecology, Hydrol. Process., 14, 2831–2848, https://doi.org/10.1002/1099-1085(200011/12)14:16/17<2831::AID-HYP122>3.0.CO;2-O, 2000. a
Kavetski, D., Kuczera, G., and Franks, S. W.: Bayesian analysis of input uncertainty in hydrological modeling: 2. Application, Water Resour. Res., 42, W03407, https://doi.org/10.1029/2005WR004368, 2006. a
Klotz, D., Kratzert, F., Gauch, M., Keefe Sampson, A., Brandstetter, J., Klambauer, G., Hochreiter, S., and Nearing, G.: Uncertainty estimation with deep learning for rainfall–runoff modeling, Hydrol. Earth Syst. Sci., 26, 1673–1693, https://doi.org/10.5194/hess-26-1673-2022, 2022. a, b, c, d, e, f, g, h, i, j
Koutsoyiannis, D. and Montanari, A.: Bluecat: A Local Uncertainty Estimator for Deterministic Simulations and Predictions, Water Resour. Res., 58, e2021WR031215, https://doi.org/10.1029/2021WR031215, 2022. a, b, c
Kratzert, F.: CAMELS Extended Maurer Forcing Data, Hydroshare [data set], https://doi.org/10.4211/hs.17c896843cf940339c3c3496d0c1c077, 2019. a
Kratzert, F., Klotz, D., Herrnegger, M., Sampson, A. K., Hochreiter, S., and Nearing, G. S.: Toward Improved Predictions in Ungauged Basins: Exploiting the Power of Machine Learning, Water Resour. Res., 55, 11344–11354, https://doi.org/10.1029/2019WR026065, 2019a. a, b, c
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, 2019b. a
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
Kratzert, F., Gauch, M., Klotz, D., and Nearing, G.: HESS Opinions: Never train an LSTM on a single basin, Hydrol. Earth Syst. Sci. Discuss. [preprint], https://doi.org/10.5194/hess-2023-275, in review, 2024. a
Lapuschkin, S., Wäldchen, S., Binder, A., Montavon, G., Samek, W., and Müller, K.-R.: Unmasking Clever Hans predictors and assessing what machines really learn, Nat. Commun., 10, 1096, https://doi.org/10.1038/s41467-019-08987-4, 2019. a
Li, W., Duan, Q., Miao, C., Ye, A., Gong, W., and Di, Z.: A review on statistical postprocessing methods for hydrometeorological ensemble forecasting, Wiley Interdisciplinary Reviews: Water, 4, e1246, https://doi.org/10.1002/wat2.1246, 2017. a
Mai, J., Shen, H., Tolson, B. A., Gaborit, É., Arsenault, R., Craig, J. R., Fortin, V., Fry, L. M., Gauch, M., Klotz, D., Kratzert, F., O'Brien, N., Princz, D. G., Rasiya Koya, S., Roy, T., Seglenieks, F., Shrestha, N. K., Temgoua, A. G. T., Vionnet, V., and Waddell, J. W.: The Great Lakes Runoff Intercomparison Project Phase 4: the Great Lakes (GRIP-GL), Hydrol. Earth Syst. Sci., 26, 3537–3572, https://doi.org/10.5194/hess-26-3537-2022, 2022. a
Montanari, A. and Koutsoyiannis, D.: A blueprint for process-based modeling of uncertain hydrological systems, Water Resour. Res., 48, W09555, https://doi.org/10.1029/2011WR011412, 2012. a
Montero-Manso, P. and Hyndman, R. J.: Principles and algorithms for forecasting groups of time series: Locality and globality, Int. J. Forecast., 37, 1632–1653, 2021. 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, 627, 559–563, 2024. a
Nearing, G. S., Tian, Y., Gupta, H. V., Clark, M. P., Harrison, K. W., and Weijs, S. V.: A philosophical basis for hydrological uncertainty, Hydrolog. Sci. J., 61, 1666–1678, 2016. a
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
Newman, A. J., Mizukami, N., Clark, M. P., Wood, A. W., Nijssen, B., and Nearing, G.: Benchmarking of a Physically Based Hydrologic Model, J. Hydrometeorol., 18, 2215–2225, https://doi.org/10.1175/JHM-D-16-0284.1, 2017. a
Ramsauer, H., Schäfl, B., Lehner, J., Seidl, P., Widrich, M., Gruber, L., Holzleitner, M., Pavlović, M., Sandve, G. K., Greiff, V., Kreil, D., Kopp, M., Klambauer, G., Brandstetter, J., and Hochreiter, S.: Hopfield networks is all you need, in: 9th International Conference on Learning Representations (ICLR), Vienna, Austria, 2021, https://openreview.net/pdf/4dfbed3a6ececb7282dfef90fd6c03812ae0da7b.pdf (last access: 31 August 2024), 2021. a, b, c
Rozos, E., Koutsoyiannis, D., and Montanari, A.: KNN vs. Bluecat – Machine Learning vs. Classical Statistics, Hydrology, 9, 101, https://doi.org/10.3390/hydrology9060101, 2022. a
Samaniego, L., Kumar, R., Thober, S., Rakovec, O., Zink, M., Wanders, N., Eisner, S., Müller Schmied, H., Sutanudjaja, E. H., Warrach-Sagi, K., and Attinger, S.: Toward seamless hydrologic predictions across spatial scales, Hydrol. Earth Syst. Sci., 21, 4323–4346, https://doi.org/10.5194/hess-21-4323-2017, 2017. a
Schweppe, R., Thober, S., Müller, S., Kelbling, M., Kumar, R., Attinger, S., and Samaniego, L.: MPR 1.0: a stand-alone multiscale parameter regionalization tool for improved parameter estimation of land surface models, Geosci. Model Dev., 15, 859–882, https://doi.org/10.5194/gmd-15-859-2022, 2022. a
Shrestha, D. L. and Solomatine, D. P.: Data-driven approaches for estimating uncertainty in rainfall-runoff modelling, International Journal of River Basin Management, 6, 109–122, 2008. 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, edited by: Guyon, I., Luxburg, U. V., Bengio, S., Wallach, H., Fergus, R., Vishwanathan, S., and Garnett, R., vol. 30, Curran Associates, Inc., Long Beach, California, USA, 2017, https://proceedings.neurips.cc/paper_files/paper/2017/file/3f5ee243547dee91fbd053c1c4a845aa-Paper.pdf (last access: 31 August 2024), 2017. a, b
Wani, O., Beckers, J. V. L., Weerts, A. H., and Solomatine, D. P.: Residual uncertainty estimation using instance-based learning with applications to hydrologic forecasting, Hydrol. Earth Syst. Sci., 21, 4021–4036, https://doi.org/10.5194/hess-21-4021-2017, 2017. a, b
Xu, C. and Xie, Y.: Conformal prediction for time series, arXiv [preprint], https://doi.org/10.48550/arXiv.2010.09107, 2022a. a, b
Xu, C. and Xie, Y.: Sequential Predictive Conformal Inference for Time Series, arXiv [preprint], https://doi.org/10.48550/arXiv.2212.03463, 2022b. a
Zaffran, M., Dieuleveut, A., F'eron, O., Goude, Y., and Josse, J.: Adaptive Conformal Predictions for Time Series, in: International Conference on Machine Learning, Baltimore, Maryland, USA, 17–23 July 2022, https://api.semanticscholar.org/CorpusID:246863519 (last access: 31 August 2024), 2022. a
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.
This work examines the impact of temporal and spatial information on the uncertainty estimation...
