Articles | Volume 29, issue 12
https://doi.org/10.5194/hess-29-2521-2025
© 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-29-2521-2025
© Author(s) 2025. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Review article
| 
17 Jun 2025
Review article |
| 17 Jun 2025
| 17 Jun 2025
Machine learning in stream and river water temperature modeling: a review and metrics for evaluation
Claudia Rebecca Corona
CORRESPONDING AUTHOR
Department of Civil and Environmental Engineering, Colorado School of Mines, Golden, CO 80401, United States
Terri Sue Hogue
Department of Civil and Environmental Engineering, Colorado School of Mines, Golden, CO 80401, United States
Hydrologic Science and Engineering Program, Colorado School of Mines, Golden, CO 80401, United States
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Samuel Saxe, William Farmer, Jessica Driscoll, and Terri S. Hogue
Hydrol. Earth Syst. Sci., 25, 1529–1568, https://doi.org/10.5194/hess-25-1529-2021, https://doi.org/10.5194/hess-25-1529-2021, 2021
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We compare simulated values from 47 models estimating surface water over the USA. Results show that model uncertainty is substantial over much of the conterminous USA and especially high in the west. Applying the studied models to a simple water accounting equation shows that model selection can significantly affect research results. This paper concludes that multimodel ensembles help to best represent uncertainty in conclusions and suggest targeted research efforts in arid regions.
Samuel Saxe, Terri S. Hogue, and Lauren Hay
Hydrol. Earth Syst. Sci., 22, 1221–1237, https://doi.org/10.5194/hess-22-1221-2018, https://doi.org/10.5194/hess-22-1221-2018, 2018
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We investigate the impact of wildfire on watershed flow regimes, examining responses across the western United States. On a national scale, our results confirm the work of prior studies: that low, high, and peak flows typically increase following a wildfire. Regionally, results are more variable and sometimes contradictory. Our results may be significant in justifying the calibration of watershed models and in contributing to the overall observational analysis of post-fire streamflow response.
P. Vahmani and T. S. Hogue
Hydrol. Earth Syst. Sci., 18, 4791–4806, https://doi.org/10.5194/hess-18-4791-2014, https://doi.org/10.5194/hess-18-4791-2014, 2014
P. D. Micheletty, A. M. Kinoshita, and T. S. Hogue
Hydrol. Earth Syst. Sci., 18, 4601–4615, https://doi.org/10.5194/hess-18-4601-2014, https://doi.org/10.5194/hess-18-4601-2014, 2014
S. R. Lopez, T. S. Hogue, and E. D. Stein
Hydrol. Earth Syst. Sci., 17, 3077–3094, https://doi.org/10.5194/hess-17-3077-2013, https://doi.org/10.5194/hess-17-3077-2013, 2013
Related subject area
Subject: Rivers and Lakes | Techniques and Approaches: Modelling approaches
How seasonal hydroclimate variability drives the triple oxygen and hydrogen isotope composition of small lake systems in semiarid environments
Learning from a large-scale calibration effort of multiple lake temperature models
The influence of permafrost and other environmental factors on stream thermal sensitivity across Yukon, Canada
Assessing national exposure to and impact of glacial lake outburst floods considering uncertainty under data sparsity
Modeling Lake Titicaca's water balance: the dominant roles of precipitation and evaporation
An efficient hybrid downscaling framework to estimate high-resolution river hydrodynamics
Effect of floodplain trees on apparent friction coefficient in straight compound channels
The role of neotectonics and climate variability in the Pleistocene-to-Holocene hydrological evolution of the Fuente de Piedra playa lake (southern Iberian Peninsula)
On the cause of large daily river flow fluctuations in the Mekong River
A hybrid data-driven approach to analyze the drivers of lake level dynamics
Estimating velocity distribution and flood discharge at river bridges using entropy theory – insights from computational fluid dynamics flow fields
Isotopic evaluation of the National Water Model reveals missing agricultural irrigation contributions to streamflow across the western United States
Timing of spring events changes under modelled future climate scenarios in a mesotrophic lake
Effects of high-quality elevation data and explanatory variables on the accuracy of flood inundation mapping via Height Above Nearest Drainage
Understanding the compound flood risk along the coast of the contiguous United States
Benchmarking high-resolution hydrologic model performance of long-term retrospective streamflow simulations in the contiguous United States
Sources of skill in lake temperature, discharge and ice-off seasonal forecasting tools
Past and future climate change effects on the thermal regime and oxygen solubility of four peri-alpine lakes
Exploring tracer information in a small stream to improve parameter identifiability and enhance the process interpretation in transient storage models
How do inorganic nitrogen processing pathways change quantitatively at daily, seasonal, and multiannual scales in a large agricultural stream?
Seasonal forecasting of lake water quality and algal bloom risk using a continuous Gaussian Bayesian network
Spatially referenced Bayesian state-space model of total phosphorus in western Lake Erie
Future water temperature of rivers in Switzerland under climate change investigated with physics-based models
Physical controls and a priori estimation of raising land surface elevation across the southwestern Bangladesh delta using tidal river management
Evaluation and interpretation of convolutional long short-term memory networks for regional hydrological modelling
Synthesizing the impacts of baseflow contribution on concentration–discharge (C–Q) relationships across Australia using a Bayesian hierarchical model
Calibrating 1D hydrodynamic river models in the absence of cross-section geometry using satellite observations of water surface elevation and river width
A global algorithm for identifying changing streamflow regimes: application to Canadian natural streams (1966–2010)
Streamflow drought: implication of drought definitions and its application for drought forecasting
Quantifying floodwater impacts on a lake water budget via volume-dependent transient stable isotope mass balance
River runoff in Switzerland in a changing climate – changes in moderate extremes and their seasonality
River runoff in Switzerland in a changing climate – runoff regime changes and their time of emergence
Machine-learning methods for stream water temperature prediction
Bathymetry and latitude modify lake warming under ice
Lake thermal structure drives interannual variability in summer anoxia dynamics in a eutrophic lake over 37 years
Reservoir evaporation in a Mediterranean climate: comparing direct methods in Alqueva Reservoir, Portugal
Diverging hydrological drought traits over Europe with global warming
Anthropogenic influence on the Rhine water temperatures
A new form of the Saint-Venant equations for variable topography
Simulations of future changes in thermal structure of Lake Erken: proof of concept for ISIMIP2b lake sector local simulation strategy
Assessment of the geomorphic effectiveness of controlled floods in a braided river using a reduced-complexity numerical model
Worldwide lake level trends and responses to background climate variation
Modeling inorganic carbon dynamics in the Seine River continuum in France
A data-based predictive model for spatiotemporal variability in stream water quality
Flooding in the Mekong Delta: the impact of dyke systems on downstream hydrodynamics
Reconstruction of the 1941 GLOF process chain at Lake Palcacocha (Cordillera Blanca, Peru)
Historical modelling of changes in Lake Erken thermal conditions
Improving lake mixing process simulations in the Community Land Model by using K profile parameterization
Upgraded global mapping information for earth system modelling: an application to surface water depth at the ECMWF
Sediment transport modelling in riverine environments: on the importance of grain-size distribution, sediment density, and suspended sediment concentrations at the upstream boundary
Claudia Voigt, Fernando Gázquez, Lucía Martegani, Ana Isabel Sánchez Villanueva, Antonio Medina, Rosario Jiménez-Espinosa, Juan Jiménez-Millán, and Miguel Rodríguez-Rodríguez
Hydrol. Earth Syst. Sci., 29, 1783–1806, https://doi.org/10.5194/hess-29-1783-2025, https://doi.org/10.5194/hess-29-1783-2025, 2025
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This research explores the use of a new isotope tracer, 17O excess, to better understand how hydrological processes drive large seasonal water level changes in small lakes in semiarid regions. The study shows that triple oxygen isotopes offer a more detailed understanding of these changes compared to traditional methods. These findings are valuable for reconstructing past climates and predicting how climate change, influenced by human activity, will affect small lakes in these dry areas.
Johannes Feldbauer, Jorrit P. Mesman, Tobias K. Andersen, and Robert Ladwig
Hydrol. Earth Syst. Sci., 29, 1183–1199, https://doi.org/10.5194/hess-29-1183-2025, https://doi.org/10.5194/hess-29-1183-2025, 2025
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Models help to understand natural systems and are used to predict changes based on scenarios (e.g., climate change). To simulate water temperature and deduce impacts on water quality in lakes, 1D lake models are often used. There are several such models that differ regarding their assumptions and mathematical process description. This study examines the performance of four such models on a global dataset of 73 lakes and relates their performance to the model structure and lake characteristics.
Andras J. Szeitz and Sean K. Carey
Hydrol. Earth Syst. Sci., 29, 1083–1101, https://doi.org/10.5194/hess-29-1083-2025, https://doi.org/10.5194/hess-29-1083-2025, 2025
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Stream temperature sensitivity in northern regions responds to many of the same environmental controls as in temperate regions, but the presence of annually frozen ground (permafrost) influences catchment hydrology and stream temperature regimes. Permafrost can have positive and negative influences on thermal regimes. The net effect of northern environmental change on stream temperature is complex and uncertain, but permafrost will likely play a role through its control on cold region hydrology.
Huili Chen, Qiuhua Liang, Jiaheng Zhao, and Sudan Bikash Maharjan
Hydrol. Earth Syst. Sci., 29, 733–752, https://doi.org/10.5194/hess-29-733-2025, https://doi.org/10.5194/hess-29-733-2025, 2025
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Glacial lake outburst floods (GLOFs) can cause serious damage. To assess their risks, we developed an innovative framework using remote sensing, Bayesian models, flood modelling, and open-source data. This enables us to evaluate GLOFs on a national scale, despite limited data and challenges accessing high-altitude lakes. We evaluated dangerous lakes in Nepal, identifying those most at risk. This work is crucial for understanding GLOF risks, and the framework can be transferred to other areas.
Nilo Lima-Quispe, Denis Ruelland, Antoine Rabatel, Waldo Lavado-Casimiro, and Thomas Condom
Hydrol. Earth Syst. Sci., 29, 655–682, https://doi.org/10.5194/hess-29-655-2025, https://doi.org/10.5194/hess-29-655-2025, 2025
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This study estimated the water balance of Lake Titicaca using an integrated modeling framework that considers natural hydrological processes and net irrigation consumption. The proposed approach was implemented at a daily scale for a period of 35 years. This framework is able to simulate lake water levels with good accuracy over a wide range of hydroclimatic conditions. The findings demonstrate that a simple representation of hydrological processes is suitable for use in poorly gauged regions.
Zeli Tan, Donghui Xu, Sourav Taraphdar, Jiangqin Ma, Gautam Bisht, and L. Ruby Leung
EGUsphere, https://doi.org/10.5194/egusphere-2024-3816, https://doi.org/10.5194/egusphere-2024-3816, 2025
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Flow depth and velocity determine many river functions, but their high-resolution simulations are expensive. Here, we developed a downscaling approach that can provide fast and accurate estimation of high-resolution river hydrodynamics. The 84-fold acceleration achieved by the method makes reliable flood risk analysis that needs hundreds or thousands of model runs feasible. More importantly, it provides an opportunity to couple large-scale hydrodynamics with local processes in river models.
Adam P. Kozioł, Adam Kiczko, Marcin Krukowski, Elżbieta Kubrak, Janusz Kubrak, Grzegorz Majewski, and Andrzej Brandyk
Hydrol. Earth Syst. Sci., 29, 535–545, https://doi.org/10.5194/hess-29-535-2025, https://doi.org/10.5194/hess-29-535-2025, 2025
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Floodplain trees play a crucial role in increasing flow resistance. Their impact extends beyond floodplains to affect the main channel. The experiments reveal the influence of floodplain trees on the discharge capacity of channels with varying roughness. We determine resistance coefficients for different roughness levels of the main channel bottom. The research contributes to a deeper understanding of open-channel flow dynamics and has practical implications for river engineering.
Alejandro Jiménez-Bonilla, Lucía Martegani, Miguel Rodríguez-Rodríguez, Fernando Gázquez, Manuel Díaz-Azpíroz, Sergio Martos, Klaus Reicherter, and Inmaculada Expósito
Hydrol. Earth Syst. Sci., 28, 5311–5329, https://doi.org/10.5194/hess-28-5311-2024, https://doi.org/10.5194/hess-28-5311-2024, 2024
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We conducted an interdisciplinary study of the Fuente de Piedra playa lake's evolution in southern Spain. We made water balances for the Fuente de Piedra playa lake's lifespan. Our results indicate that the Fuente de Piedra playa lake's level moved and tilted south-west, which was caused by active faults.
Khosro Morovati, Keer Zhang, Lidi Shi, Yadu Pokhrel, Maozhou Wu, Paradis Someth, Sarann Ly, and Fuqiang Tian
Hydrol. Earth Syst. Sci., 28, 5133–5147, https://doi.org/10.5194/hess-28-5133-2024, https://doi.org/10.5194/hess-28-5133-2024, 2024
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This study examines large daily river flow fluctuations in the dammed Mekong River, developing integrated 3D hydrodynamic and response time models alongside a hydrological model with an embedded reservoir module. This approach allows estimation of travel times between hydrological stations and contributions of subbasins and upstream regions. Findings show a power correlation between upstream discharge and travel time, and significant fluctuations occurred even before dam construction.
Márk Somogyvári, Dieter Scherer, Frederik Bart, Ute Fehrenbach, Akpona Okujeni, and Tobias Krueger
Hydrol. Earth Syst. Sci., 28, 4331–4348, https://doi.org/10.5194/hess-28-4331-2024, https://doi.org/10.5194/hess-28-4331-2024, 2024
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We study the drivers behind the changes in lake levels, creating a series of models from least to most complex. In this study, we have shown that the decreasing levels of Groß Glienicker Lake in Germany are not simply the result of changes in climate but are affected by other processes. In our example, reduced inflow from a growing forest, regionally sinking groundwater levels and the modifications in the local rainwater infrastructure together resulted in an increasing lake level loss.
Farhad Bahmanpouri, Tommaso Lazzarin, Silvia Barbetta, Tommaso Moramarco, and Daniele P. Viero
Hydrol. Earth Syst. Sci., 28, 3717–3737, https://doi.org/10.5194/hess-28-3717-2024, https://doi.org/10.5194/hess-28-3717-2024, 2024
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The entropy model is a reliable tool to estimate flood discharge in rivers using observed level and surface velocity. Often, level and velocity sensors are placed on bridges, which may disturb the flow. Using accurate numerical models, we explored the entropy model reliability nearby a multi-arch bridge. We found that it is better to place sensors and to estimate the discharge upstream of bridges; downstream, the entropy model needs the river-wide distribution of surface velocity as input data.
Annie L. Putman, Patrick C. Longley, Morgan C. McDonnell, James Reddy, Michelle Katoski, Olivia L. Miller, and J. Renée Brooks
Hydrol. Earth Syst. Sci., 28, 2895–2918, https://doi.org/10.5194/hess-28-2895-2024, https://doi.org/10.5194/hess-28-2895-2024, 2024
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Accuracy of streamflow estimates where water management and use are prevalent, such as the western US, reflect hydrologic modeling decisions. To evaluate process inclusion decisions, we equipped a hydrologic model with tracers and compared estimates to observations. The tracer-equipped model performed well, and differences between the model and observations suggest that the inclusion of water from irrigation may improve model performance in this region.
Jorrit P. Mesman, Inmaculada C. Jiménez-Navarro, Ana I. Ayala, Javier Senent-Aparicio, Dennis Trolle, and Don C. Pierson
Hydrol. Earth Syst. Sci., 28, 1791–1802, https://doi.org/10.5194/hess-28-1791-2024, https://doi.org/10.5194/hess-28-1791-2024, 2024
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Spring events in lakes are key processes for ecosystem functioning. We used a coupled catchment–lake model to investigate future changes in the timing of spring discharge, ice-off, spring phytoplankton peak, and onset of stratification in a mesotrophic lake. We found a clear trend towards earlier occurrence under climate warming but also that relative shifts in the timing occurred, such as onset of stratification advancing more slowly than the other events.
Fernando Aristizabal, Taher Chegini, Gregory Petrochenkov, Fernando Salas, and Jasmeet Judge
Hydrol. Earth Syst. Sci., 28, 1287–1315, https://doi.org/10.5194/hess-28-1287-2024, https://doi.org/10.5194/hess-28-1287-2024, 2024
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Floods are significant natural disasters that affect people and property. This study uses a simplified terrain index and the latest lidar-derived digital elevation maps (DEMs) to investigate flood inundation extent quality. We examined inundation quality influenced by different spatial resolutions and other variables. Results showed that lidar DEMs enhance inundation quality, but their resolution is less impactful in our context. Further studies on reservoirs and urban flooding are recommended.
Dongyu Feng, Zeli Tan, Donghui Xu, and L. Ruby Leung
Hydrol. Earth Syst. Sci., 27, 3911–3934, https://doi.org/10.5194/hess-27-3911-2023, https://doi.org/10.5194/hess-27-3911-2023, 2023
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This study assesses the flood risks concurrently induced by river flooding and coastal storm surge along the coast of the contiguous United States using statistical and numerical models. We reveal a few hotspots of such risks, the critical spatial variabilities within a river basin and over the whole US coast, and the uncertainties of the risk assessment. We highlight the importance of weighing different risk measures to avoid underestimating or exaggerating the compound flood impacts.
Erin Towler, Sydney S. Foks, Aubrey L. Dugger, Jesse E. Dickinson, Hedeff I. Essaid, David Gochis, Roland J. Viger, and Yongxin Zhang
Hydrol. Earth Syst. Sci., 27, 1809–1825, https://doi.org/10.5194/hess-27-1809-2023, https://doi.org/10.5194/hess-27-1809-2023, 2023
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Hydrologic models developed to assess water availability need to be systematically evaluated. This study evaluates the long-term performance of two high-resolution hydrologic models that simulate streamflow across the contiguous United States. Both models show similar performance overall and regionally, with better performance in minimally disturbed basins than in those impacted by human activity. At about 80 % of the sites, both models outperform the seasonal climatological benchmark.
François Clayer, Leah Jackson-Blake, Daniel Mercado-Bettín, Muhammed Shikhani, Andrew French, Tadhg Moore, James Sample, Magnus Norling, Maria-Dolores Frias, Sixto Herrera, Elvira de Eyto, Eleanor Jennings, Karsten Rinke, Leon van der Linden, and Rafael Marcé
Hydrol. Earth Syst. Sci., 27, 1361–1381, https://doi.org/10.5194/hess-27-1361-2023, https://doi.org/10.5194/hess-27-1361-2023, 2023
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We assessed the predictive skill of forecasting tools over the next season for water discharge and lake temperature. Tools were forced with seasonal weather predictions; however, most of the prediction skill originates from legacy effects and not from seasonal weather predictions. Yet, when skills from seasonal weather predictions are present, additional skill comes from interaction effects. Skilful lake seasonal predictions require better weather predictions and realistic antecedent conditions.
Olivia Desgué-Itier, Laura Melo Vieira Soares, Orlane Anneville, Damien Bouffard, Vincent Chanudet, Pierre Alain Danis, Isabelle Domaizon, Jean Guillard, Théo Mazure, Najwa Sharaf, Frédéric Soulignac, Viet Tran-Khac, Brigitte Vinçon-Leite, and Jean-Philippe Jenny
Hydrol. Earth Syst. Sci., 27, 837–859, https://doi.org/10.5194/hess-27-837-2023, https://doi.org/10.5194/hess-27-837-2023, 2023
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The long-term effects of climate change will include an increase in lake surface and deep water temperatures. Incorporating up to 6 decades of limnological monitoring into an improved 1D lake model approach allows us to predict the thermal regime and oxygen solubility in four peri-alpine lakes over the period 1850–2100. Our modeling approach includes a revised selection of forcing variables and provides a way to investigate the impacts of climate variations on lakes for centennial timescales.
Enrico Bonanno, Günter Blöschl, and Julian Klaus
Hydrol. Earth Syst. Sci., 26, 6003–6028, https://doi.org/10.5194/hess-26-6003-2022, https://doi.org/10.5194/hess-26-6003-2022, 2022
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There is an unclear understanding of which processes regulate the transport of water, solutes, and pollutants in streams. This is crucial since these processes control water quality in river networks. Compared to other approaches, we obtained clearer insights into the processes controlling solute transport in the investigated reach. This work highlights the risks of using uncertain results for interpreting the processes controlling water movement in streams.
Jingshui Huang, Dietrich Borchardt, and Michael Rode
Hydrol. Earth Syst. Sci., 26, 5817–5833, https://doi.org/10.5194/hess-26-5817-2022, https://doi.org/10.5194/hess-26-5817-2022, 2022
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In this study, we set up a water quality model using a 5-year paired high-frequency water quality dataset from a large agricultural stream. The simulations were compared with the 15 min interval measurements and showed very good fits. Based on these, we quantified the N uptake pathway rates and efficiencies at daily, seasonal, and yearly scales. This study offers an overarching understanding of N processing in large agricultural streams across different temporal scales.
Leah A. Jackson-Blake, François Clayer, Sigrid Haande, James E. Sample, and S. Jannicke Moe
Hydrol. Earth Syst. Sci., 26, 3103–3124, https://doi.org/10.5194/hess-26-3103-2022, https://doi.org/10.5194/hess-26-3103-2022, 2022
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We develop a Gaussian Bayesian network (GBN) for seasonal forecasting of lake water quality and algal bloom risk in a nutrient-impacted lake in southern Norway. Bayesian networks are powerful tools for environmental modelling but are almost exclusively discrete. We demonstrate that a continuous GBN is a promising alternative approach. Predictive performance of the GBN was similar or improved compared to a discrete network, and it was substantially less time-consuming and subjective to develop.
Timothy J. Maguire, Craig A. Stow, and Casey M. Godwin
Hydrol. Earth Syst. Sci., 26, 1993–2017, https://doi.org/10.5194/hess-26-1993-2022, https://doi.org/10.5194/hess-26-1993-2022, 2022
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Water within large water bodies is constantly moving. Consequently, water movement masks causal relationships that exist between rivers and lakes. Incorporating water movement into models of nutrient concentration allows us to predict concentrations at unobserved locations and at observed locations on days not sampled. Our modeling approach does this while accommodating nutrient concentration data from multiple sources and provides a way to experimentally define the impact of rivers on lakes.
Adrien Michel, Bettina Schaefli, Nander Wever, Harry Zekollari, Michael Lehning, and Hendrik Huwald
Hydrol. Earth Syst. Sci., 26, 1063–1087, https://doi.org/10.5194/hess-26-1063-2022, https://doi.org/10.5194/hess-26-1063-2022, 2022
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This study presents an extensive study of climate change impacts on river temperature in Switzerland. Results show that, even for low-emission scenarios, water temperature increase will lead to adverse effects for both ecosystems and socio-economic sectors throughout the 21st century. For high-emission scenarios, the effect will worsen. This study also shows that water seasonal warming will be different between the Alpine regions and the lowlands. Finally, efficiency of models is assessed.
Md Feroz Islam, Paul P. Schot, Stefan C. Dekker, Jasper Griffioen, and Hans Middelkoop
Hydrol. Earth Syst. Sci., 26, 903–921, https://doi.org/10.5194/hess-26-903-2022, https://doi.org/10.5194/hess-26-903-2022, 2022
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The potential of sedimentation in the lowest parts of polders (beels) through controlled flooding with dike breach (tidal river management – TRM) to counterbalance relative sea level rise (RSLR) in 234 beels of SW Bangladesh is determined in this study, using 2D models and multiple regression. Lower beels located closer to the sea have the highest potential. Operating TRM only during the monsoon season is sufficient to raise the land surface of most beels by more than 3 times the yearly RSLR.
Sam Anderson and Valentina Radić
Hydrol. Earth Syst. Sci., 26, 795–825, https://doi.org/10.5194/hess-26-795-2022, https://doi.org/10.5194/hess-26-795-2022, 2022
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We develop and interpret a spatiotemporal deep learning model for regional streamflow prediction at more than 200 stream gauge stations in western Canada. We find the novel modelling style to work very well for daily streamflow prediction. Importantly, we interpret model learning to show that it has learned to focus on physically interpretable and physically relevant information, which is a highly desirable quality of machine-learning-based hydrological models.
Danlu Guo, Camille Minaudo, Anna Lintern, Ulrike Bende-Michl, Shuci Liu, Kefeng Zhang, and Clément Duvert
Hydrol. Earth Syst. Sci., 26, 1–16, https://doi.org/10.5194/hess-26-1-2022, https://doi.org/10.5194/hess-26-1-2022, 2022
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We investigate the impact of baseflow contribution on concentration–flow (C–Q) relationships across the Australian continent. We developed a novel Bayesian hierarchical model for six water quality variables across 157 catchments that span five climate zones. For sediments and nutrients, the C–Q slope is generally steeper for catchments with a higher median and a greater variability of baseflow contribution, highlighting the key role of variable flow pathways in particulate and solute export.
Liguang Jiang, Silja Westphal Christensen, and Peter Bauer-Gottwein
Hydrol. Earth Syst. Sci., 25, 6359–6379, https://doi.org/10.5194/hess-25-6359-2021, https://doi.org/10.5194/hess-25-6359-2021, 2021
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River roughness and geometry are essential to hydraulic river models. However, measurements of these quantities are not available in most rivers globally. Nevertheless, simultaneous calibration of channel geometric parameters and roughness is difficult as they compensate for each other. This study introduces an alternative approach of parameterization and calibration that reduces parameter correlations by combining cross-section geometry and roughness into a conveyance parameter.
Masoud Zaerpour, Shadi Hatami, Javad Sadri, and Ali Nazemi
Hydrol. Earth Syst. Sci., 25, 5193–5217, https://doi.org/10.5194/hess-25-5193-2021, https://doi.org/10.5194/hess-25-5193-2021, 2021
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Streamflow regimes are changing globally particularly in cold regions. We develop a novel algorithm for detecting shifting streamflow regimes using changes in first and second moments of ensemble streamflow features. This algorithm is generic and can be used globally. To showcase its application, we assess alterations in Canadian natural streams from 1966 to 2010 to provide the first temporally consistent, pan-Canadian assessment of change in natural streamflow regimes, coast to coast to coast.
Samuel J. Sutanto and Henny A. J. Van Lanen
Hydrol. Earth Syst. Sci., 25, 3991–4023, https://doi.org/10.5194/hess-25-3991-2021, https://doi.org/10.5194/hess-25-3991-2021, 2021
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This paper provides a comprehensive overview of the differences within streamflow droughts derived using different identification approaches, namely the variable threshold, fixed threshold, and the Standardized Streamflow Index, including an analysis of both historical drought and implications for forecasting. Our results clearly show that streamflow droughts derived from different approaches deviate from each other in terms of drought occurrence, timing, duration, and deficit volume.
Janie Masse-Dufresne, Florent Barbecot, Paul Baudron, and John Gibson
Hydrol. Earth Syst. Sci., 25, 3731–3757, https://doi.org/10.5194/hess-25-3731-2021, https://doi.org/10.5194/hess-25-3731-2021, 2021
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A volume-dependent transient isotopic mass balance model was developed for an artificial lake in Canada, in a context where direct measurements of surface water fluxes are difficult. It revealed that floodwater inputs affected the dynamics of the lake in spring but also significantly influenced the long-term water balance due to temporary subsurface storage of floodwater. Such models are paramount for understanding the vulnerability of lakes to changes in groundwater quantity and quality.
Regula Muelchi, Ole Rössler, Jan Schwanbeck, Rolf Weingartner, and Olivia Martius
Hydrol. Earth Syst. Sci., 25, 3577–3594, https://doi.org/10.5194/hess-25-3577-2021, https://doi.org/10.5194/hess-25-3577-2021, 2021
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This study analyses changes in magnitude, frequency, and seasonality of moderate low and high flows for 93 catchments in Switzerland. In lower-lying catchments (below 1500 m a.s.l.), moderate low-flow magnitude (frequency) will decrease (increase). In Alpine catchments (above 1500 m a.s.l.), moderate low-flow magnitude (frequency) will increase (decrease). Moderate high flows tend to occur more frequent, and their magnitude increases in most catchments except some Alpine catchments.
Regula Muelchi, Ole Rössler, Jan Schwanbeck, Rolf Weingartner, and Olivia Martius
Hydrol. Earth Syst. Sci., 25, 3071–3086, https://doi.org/10.5194/hess-25-3071-2021, https://doi.org/10.5194/hess-25-3071-2021, 2021
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Runoff regimes in Switzerland will change significantly under climate change. Projected changes are strongly elevation dependent with earlier time of emergence and stronger changes in high-elevation catchments where snowmelt and glacier melt play an important role. The magnitude of change and the climate model agreement on the sign increase with increasing global mean temperatures and stronger emission scenarios. This amplification highlights the importance of climate change mitigation.
Moritz Feigl, Katharina Lebiedzinski, Mathew Herrnegger, and Karsten Schulz
Hydrol. Earth Syst. Sci., 25, 2951–2977, https://doi.org/10.5194/hess-25-2951-2021, https://doi.org/10.5194/hess-25-2951-2021, 2021
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In this study we developed machine learning approaches for daily river water temperature prediction, using different data preprocessing methods, six model types, a range of different data inputs and 10 study catchments. By comparing to current state-of-the-art models, we could show a significant improvement of prediction performance of the tested approaches. Furthermore, we could gain insight into the relationships between model types, input data and predicted stream water temperature.
Cintia L. Ramón, Hugo N. Ulloa, Tomy Doda, Kraig B. Winters, and Damien Bouffard
Hydrol. Earth Syst. Sci., 25, 1813–1825, https://doi.org/10.5194/hess-25-1813-2021, https://doi.org/10.5194/hess-25-1813-2021, 2021
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When solar radiation penetrates the frozen surface of lakes, shallower zones underneath warm faster than deep interior waters. This numerical study shows that the transport of excess heat to the lake interior depends on the lake circulation, affected by Earth's rotation, and controls the lake warming rates and the spatial distribution of the heat flux across the ice–water interface. This work contributes to the understanding of the circulation and thermal structure patterns of ice-covered lakes.
Robert Ladwig, Paul C. Hanson, Hilary A. Dugan, Cayelan C. Carey, Yu Zhang, Lele Shu, Christopher J. Duffy, and Kelly M. Cobourn
Hydrol. Earth Syst. Sci., 25, 1009–1032, https://doi.org/10.5194/hess-25-1009-2021, https://doi.org/10.5194/hess-25-1009-2021, 2021
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Using a modeling framework applied to 37 years of dissolved oxygen time series data from Lake Mendota, we identified the timing and intensity of thermal energy stored in the lake water column, the lake's resilience to mixing, and surface primary production as the most important drivers of interannual dynamics of low oxygen concentrations at the lake bottom. Due to climate change, we expect an increase in the spatial and temporal extent of low oxygen concentrations in Lake Mendota.
Carlos Miranda Rodrigues, Madalena Moreira, Rita Cabral Guimarães, and Miguel Potes
Hydrol. Earth Syst. Sci., 24, 5973–5984, https://doi.org/10.5194/hess-24-5973-2020, https://doi.org/10.5194/hess-24-5973-2020, 2020
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In Mediterranean environments, evaporation is a key component of reservoir water budgets. Prediction of surface evaporation becomes crucial for adequate reservoir water management. This study provides an applicable method for calculating evaporation based on pan measurements applied at Alqueva Reservoir (southern Portugal), one of the largest artificial lakes in Europe. Moreover, the methodology presented here could be applied to other Mediterranean reservoirs.
Carmelo Cammalleri, Gustavo Naumann, Lorenzo Mentaschi, Bernard Bisselink, Emiliano Gelati, Ad De Roo, and Luc Feyen
Hydrol. Earth Syst. Sci., 24, 5919–5935, https://doi.org/10.5194/hess-24-5919-2020, https://doi.org/10.5194/hess-24-5919-2020, 2020
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Climate change is anticipated to alter the demand and supply of water at the earth's surface. This study shows how hydrological droughts will change across Europe with increasing global warming levels, showing that at 3 K global warming an additional 11 million people and 4.5 ×106 ha of agricultural land will be exposed to droughts every year, on average. These effects are mostly located in the Mediterranean and Atlantic regions of Europe.
Alex Zavarsky and Lars Duester
Hydrol. Earth Syst. Sci., 24, 5027–5041, https://doi.org/10.5194/hess-24-5027-2020, https://doi.org/10.5194/hess-24-5027-2020, 2020
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River water temperature is an important parameter for water quality and an important variable for physical, chemical and biological processes. River water is also used as a cooling agent by power plants and production facilities. We study long-term trends in river water temperature and correlate them to meteorological influences and power production or economic indices.
Cheng-Wei Yu, Ben R. Hodges, and Frank Liu
Hydrol. Earth Syst. Sci., 24, 4001–4024, https://doi.org/10.5194/hess-24-4001-2020, https://doi.org/10.5194/hess-24-4001-2020, 2020
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This study investigates the effects of bottom slope discontinuity on the stability of numerical solutions for the Saint-Venant equations. A new reference slope concept is proposed to ensure smooth source terms and eliminate potential numerical oscillations. It is shown that a simple algebraic transformation of channel geometry provides a smooth reference slope while preserving the correct cross-sectional flow area and the piezometric pressure gradient that drives the flow.
Ana I. Ayala, Simone Moras, and Donald C. Pierson
Hydrol. Earth Syst. Sci., 24, 3311–3330, https://doi.org/10.5194/hess-24-3311-2020, https://doi.org/10.5194/hess-24-3311-2020, 2020
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The impacts of different levels of global warming on the thermal structure of Lake Erken are assessed. We used the General Ocean Turbulence Model (GOTM) to simulate water temperature driven by meteorological scenarios supplied by the Inter-Sectoral Impact Model Intercomparison Project (ISIMIP) and tested its ability at different frequencies. Then, daily ISIMIP meteorological scenarios were disaggregated and assessed for the effects of climate change on lake thermal structure.
Luca Ziliani, Nicola Surian, Gianluca Botter, and Luca Mao
Hydrol. Earth Syst. Sci., 24, 3229–3250, https://doi.org/10.5194/hess-24-3229-2020, https://doi.org/10.5194/hess-24-3229-2020, 2020
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Although geomorphic recovery is a key issue in many rivers worldwide, controlled floods have been rarely designed using geomorphological criteria. An integrated approach is used to assess the effects of different controlled-flood scenarios in a strongly regulated river. None of the controlled-flood strategies provide significant morphological benefits. Nevertheless, this study represents a significant contribution for the management and restoration of highly disturbed rivers.
Benjamin M. Kraemer, Anton Seimon, Rita Adrian, and Peter B. McIntyre
Hydrol. Earth Syst. Sci., 24, 2593–2608, https://doi.org/10.5194/hess-24-2593-2020, https://doi.org/10.5194/hess-24-2593-2020, 2020
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Lake levels go up and down due to natural variability in the climate. But the effects of natural variability on lake levels can sometimes be confused for the influence of humans. Here we used long-term data from 200 globally distributed lakes and an advanced statistical approach to show that the effects of natural variability on lake levels can be disentangled from other effects leading to better estimates of long-term changes that may be partially caused by humans.
Audrey Marescaux, Vincent Thieu, Nathalie Gypens, Marie Silvestre, and Josette Garnier
Hydrol. Earth Syst. Sci., 24, 2379–2398, https://doi.org/10.5194/hess-24-2379-2020, https://doi.org/10.5194/hess-24-2379-2020, 2020
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Rivers have been recognized as an active part of the carbon cycle where transformations are associated with CO2 outgassing. To understand it, we propose a modeling approach with the biogeochemical model, pyNuts-Riverstrahler. We implemented it on the human-impacted Seine River. Sources of carbon to the river were characterized by field measurements in groundwater and in wastewater. Outgassing was the most important in streams, and peaks were simulated downstream of wastewater treatment effluent.
Danlu Guo, Anna Lintern, J. Angus Webb, Dongryeol Ryu, Ulrike Bende-Michl, Shuci Liu, and Andrew William Western
Hydrol. Earth Syst. Sci., 24, 827–847, https://doi.org/10.5194/hess-24-827-2020, https://doi.org/10.5194/hess-24-827-2020, 2020
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This study developed predictive models to represent the spatial and temporal variation of stream water quality across Victoria, Australia. The model structures were informed by a data-driven approach, which identified the key controls of water quality variations from long-term records. These models are helpful to identify likely future changes in water quality and, in turn, provide critical information for developing management strategies to improve stream water quality.
Vo Quoc Thanh, Dano Roelvink, Mick van der Wegen, Johan Reyns, Herman Kernkamp, Giap Van Vinh, and Vo Thi Phuong Linh
Hydrol. Earth Syst. Sci., 24, 189–212, https://doi.org/10.5194/hess-24-189-2020, https://doi.org/10.5194/hess-24-189-2020, 2020
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The Vietnamese Mekong Delta (VMD) is a rice bowl of not only Vietnam, but also the world; agriculture is the main source of livelihood in the delta. The VMD is facing threats related to water management and hydraulic structures. Dykes are built to protect agricultural crops in the floodplains and may influence water regimes downstream in the VMD. If the VMD floodplains are completely protected by dykes, yearly mean water levels could increase by 3 cm (at Can Tho) and 1.5 cm (at My Thuan).
Martin Mergili, Shiva P. Pudasaini, Adam Emmer, Jan-Thomas Fischer, Alejo Cochachin, and Holger Frey
Hydrol. Earth Syst. Sci., 24, 93–114, https://doi.org/10.5194/hess-24-93-2020, https://doi.org/10.5194/hess-24-93-2020, 2020
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In 1941, the glacial lagoon Lake Palcacocha in the Cordillera Blanca (Peru) drained suddenly. The resulting outburst flood/debris flow consumed another lake and had a disastrous impact on the town of Huaraz 23 km downstream. We reconstuct this event through a numerical model to learn about the possibility of prediction of similar processes in the future. Remaining challenges consist of the complex process interactions and the lack of experience due to the rare occurrence of such process chains.
Simone Moras, Ana I. Ayala, and Don C. Pierson
Hydrol. Earth Syst. Sci., 23, 5001–5016, https://doi.org/10.5194/hess-23-5001-2019, https://doi.org/10.5194/hess-23-5001-2019, 2019
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We used a hydrodynamic model to reconstruct daily historical water temperature of Lake Erken (Sweden) between 1961 and 2017 to demonstrate the ongoing effect of climate change on lake thermal conditions. The results show that the lake has warmed most rapidly in the last 30 years and that it is now subject to a longer and more stable stratification. The methods used here to reconstruct historical water temperature records can be easily extended to other lakes.
Qunhui Zhang, Jiming Jin, Xiaochun Wang, Phaedra Budy, Nick Barrett, and Sarah E. Null
Hydrol. Earth Syst. Sci., 23, 4969–4982, https://doi.org/10.5194/hess-23-4969-2019, https://doi.org/10.5194/hess-23-4969-2019, 2019
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We improved lake mixing process simulations by applying a vertical mixing scheme, K profile parameterization (KPP), in the Community Land Model (CLM) version 4.5, developed by the National Center for Atmospheric Research. The current vertical mixing scheme in CLM requires an arbitrarily enlarged eddy diffusivity to enhance water mixing. The coupled CLM-KPP considers a boundary layer for eddy development. The improved lake model provides an important tool for lake hydrology and ecosystem studies.
Margarita Choulga, Ekaterina Kourzeneva, Gianpaolo Balsamo, Souhail Boussetta, and Nils Wedi
Hydrol. Earth Syst. Sci., 23, 4051–4076, https://doi.org/10.5194/hess-23-4051-2019, https://doi.org/10.5194/hess-23-4051-2019, 2019
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Lakes influence weather and climate of regions, especially if several of them are located close by. Just by using upgraded lake depths, based on new or more recent measurements and geological methods of depth estimation, errors of lake surface water forecasts produced by the European Centre for Medium-Range Weather Forecasts became 12–20 % lower compared with observations for 27 lakes collected by the Finnish Environment Institute. For ice-off date forecasts errors changed insignificantly.
Jérémy Lepesqueur, Renaud Hostache, Núria Martínez-Carreras, Emmanuelle Montargès-Pelletier, and Christophe Hissler
Hydrol. Earth Syst. Sci., 23, 3901–3915, https://doi.org/10.5194/hess-23-3901-2019, https://doi.org/10.5194/hess-23-3901-2019, 2019
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This article evaluates the influence of sediment representation in a sediment transport model. A short-term simulation is used to assess how far changing the sediment characteristics in the modelling experiment changes riverbed evolution and sediment redistribution during a small flood event. The study shows in particular that representing sediment with extended grain-size and grain-density distributions allows for improving model accuracy and performances.
Cited articles
Abadi, M., Agarwal, A., Barham, P., Brevdo, E., Chen, Z., Citro, C., Corrado, G. S., Davis, A., Dean, J., Devin, M., Ghemawat, S., Goodfellow, I., Harp, A., Irving, G., Isard, M., Jia, Y., Jozefowicz, R., Kaiser, L., Kudlur, M., Levenberg, J., Mane, D., Monga, R., Moore, S., Murray, D., Olah, C., Schuster, M., Shlens, J., Steiner, B., Sutskever, I., Talwar, K., Tucker, P., Vanhoucke, V., Vasudevan, V., Viegas, F., Vinyals, O., Warden, P., Wattenberg, M., Wicke, M., Yu, Y., and Zheng, X.: TensorFlow: large-scale machine learning on heterogeneous distributed systems, https://tensorflow.org, last access: 1 November 2015.
Abdi, R., Rust, A., and Hogue, T. S.: Development of a multilayer deep neural network model for predicting hourly river water temperature from meteorological data, Front. Environ. Sci., 9, 738322, https://doi.org/10.3389/fenvs.2021.738322, 2021.
Acito, F.: Predictive analytics with KNIME: Analytics for citizen data scientists, Springer Nature Switzerland, Cham, https://doi.org/10.1007/978-3-031-45630-5, 2023.
Ahmadi-Nedushan, B., St-Hilaire, A., Ouarda, T. B. M. J., Bilodeau, L., Robichaud, É., Thiémonge, N., and Bobée, B.: Predicting river water temperatures using stochastic models: case study of the Moisie River (Québec, Canada), Hydrol. Process., 21, 21–34, https://doi.org/10.1002/hyp.6353, 2007.
Akaike, H., Petrov, B. N., and Csaki, F.: Information theory and an extension of the maximum likelihood principle, Second international symposium on information theory, Akademiai Kiado, Budapest, Hungary, 2–8 September 1971, 267–281, https://link.springer.com/chapter/10.1007/978-1-4612-1694-0_15, 1973.
Anderson, D. and Burnham, K.: Model selection and multi-model inference, Second, Springer-Verlag, NY, 63, 10, https://doi.org/10.1007/b97636, 2004.
Anmala, J. and Turuganti, V.: Comparison of the performance of decision tree (DT) algorithms and extreme learning machine (ELM) model in the prediction of water quality of the Upper Green River watershed, Water Environ. Res., 93, 2360–2373, https://doi.org/10.1002/wer.1642, 2021.
Apaydin, H., Taghi Sattari, M., Falsafian, K., and Prasad, R.: Artificial intelligence modelling integrated with Singular Spectral analysis and Seasonal-Trend decomposition using Loess approaches for streamflow predictions, J. Hydrol., 600, 126506, https://doi.org/10.1016/j.jhydrol.2021.126506, 2021.
Arismendi, I., Safeeq, M., Dunham, J. B., and Johnson, S. L.: Can air temperature be used to project influences of climate change on stream temperature?, Environ. Res. Lett., 9, 084015, https://doi.org/10.1088/1748-9326/9/8/084015, 2014.
Banks, H. T. and Joyner, M. L.: AIC under the framework of least squares estimation, Appl. Math. Lett., 74, 33–45, https://doi.org/10.1016/j.aml.2017.05.005, 2017.
Bansal, K. and Tripathi, A. K.: Dual level attention based lightweight vision transformer for streambed land use change classification using remote sensing, Comput. Geosci., 191, 105676, https://doi.org/10.1016/j.cageo.2024.105676, 2024.
Barbarossa, V., Bosmans, J., Wanders, N., King, H., Bierkens, M. F. P., Huijbregts, M. A. J., and Schipper, A. M.: Threats of global warming to the world's freshwater fishes, Nat. Commun., 12, 1701, https://doi.org/10.1038/s41467-021-21655-w, 2021.
Bartholow, J. M.: Stream temperature investigations: field and analytical methods, US Fish and Wildlife Service, Biological Report 89:17, Washington, D.C., 139 pp. 1989.
Baydaroğlu, Ö. and Demir, I.: Temporal and spatial satellite data augmentation for deep learning-based rainfall nowcasting, J. Hydroinform., 26, 589–607, https://doi.org/10.2166/hydro.2024.235, 2024.
Bengio, Y., Simard, P., and Frasconi, P.: Learning long-term dependencies with gradient descent is difficult, IEEE T. Neutral. Networ., 5, 157–166, https://doi.org/10.1109/72.279181, 1994.
Bengio, Y., Courville, A., and Vincent, P.: Representation learning: A review and new perspectives, IEEE T. Pattern Anal., 35, 1798–1828, https://doi.org/10.48550/arXiv.1206.5538, 2013.
Benyahya, L., Caissie, D., St-Hilaire, A., Ouarda, T. B. M. J., and Bobée, B.: A review of statistical water temperature models, Can. Water Resour. J., 32, 179–192, https://doi.org/10.4296/cwrj3203179, 2007.
Beven, K.: Deep learning, hydrological processes and the uniqueness of place, Hydrol. Process., 34, 3608–3613, https://doi.org/10.1002/hyp.13805, 2020.
Bisong, E.: Google Colaboratory, in: Building machine learning and deep learning models on Google cloud platform: A comprehensive guide for beginners, edited by: Bisong, E., Apress, Berkeley, CA, 59–64, https://doi.org/10.1007/978-1-4842-4470-8_7, 2019.
Breiman, L.: Random forests, Mach. Learn., 45, 5–32, 2001.
Brown, G. W.: Predicting temperatures of small streams, Water Resour. Res., 5, 68–75, https://doi.org/10.1029/WR005i001p00068, 1969.
Buhmann, M. D.: Radial basis functions, Acta Numer., 9, 1–38, https://doi.org/10.1017/S0962492900000015, 2000.
Cairns Jr., J., Heath, A. G., and Parker, B. C.: Temperature influence on chemical toxicity to aquatic organisms, Water Pollution Control Federation, 47, 267–280, 1975.
Caissie, D., El-Jabi, N., and St-Hilaire, A.: Stochastic modelling of water temperatures in a small stream using air to water relations, Can. J. Civil Eng., 25, 250–260, https://doi.org/10.1139/l97-091, 1998.
Chang, H. and Psaris, M.: Local landscape predictors of maximum stream temperature and thermal sensitivity in the Columbia River Basin, USA, Sci. Total Environ., 461–462, 587–600, https://doi.org/10.1016/j.scitotenv.2013.05.033, 2013.
Chen, Y. D., Carsel, R. F., McCutcheon, S. C., and Nutter, W. L.: Stream temperature simulation of forested riparian areas: I. Watershed-scale model development, J. Environ. Eng., 124, 304–315, https://doi.org/10.1061/(ASCE)0733-9372(1998)124:4(304), 1998a.
Chen, Y. D., McCutcheon, S. C., Norton, D. J., and Nutter, W. L.: Stream temperature simulation of forested riparian areas: II. Model application, J. Environ. Eng., 124, 316–328, https://doi.org/10.1061/(ASCE)0733-9372(1998)124:4(316), 1998b.
Chenard, J. and Caissie, D.: Stream temperature modelling using artificial neural networks: application on Catamaran Brook, New Brunswick, Canada, Hydrol. Process., 22, 3361–3372, https://doi.org/10.1002/hyp.6928, 2008.
Cho, K., van Merrienboer, B., Gulcehre, C., Bahdanau, D., Bougares, F., Schwenk, H., and Bengio, Y.: Learning phrase representations using RNN encoder-decoder for statistical machine translation, in: EMNLP 2014, Proceedings of the Conference on Empirical Methods in Natural Language Processing, 25–29 October 2014, Doha, Qatar, [cs, stat], 11, https://doi.org/10.48550/arXiv.1406.1078, 2014.
Cluis, D. A.: Relationship between stream water temperature and ambient air temperature, Hydrol. Res., 3, 65–71, https://doi.org/10.2166/nh.1972.0004, 1972.
Cole, J. C., Maloney, K. O., Schmid, M., and McKenna, J. E.: Developing and testing temperature models for regulated systems: A case study on the Upper Delaware River, J. Hydrol., 519, 588–598, https://doi.org/10.1016/j.jhydrol.2014.07.058, 2014.
Corona, C. R. and Hogue, T. S.: Stream Temperature Machine Learning Review Performance Metrics Data, https://www.hydroshare.org/resource/68edf1673096480bacc6bd104215e9dc/, last access: 27 January 2025.
Cortes, C. and Vapnik, V.: Support-vector networks, Mach. Learn., 20, 273–297, https://doi.org/10.1007/BF00994018, 1995.
Cover, T. and Hart, P.: Nearest neighbor pattern classification, IEEE Trans. Inform. Theory, 13, 21–27, https://doi.org/10.1109/TIT.1967.1053964, 1967.
CUAHSI Inc.: Consortium of Universities for the Advancement of Hydrologic Sciences Inc. (CUAHSI), HydroShare, https://www.hydroshare.org/, last access: 30 December 2024.
Dawdy, D. R. and Thompson, T. H.: Digital computer simulation in hydrology, Journal AWWA, 59, 685–688, https://doi.org/10.1002/j.1551-8833.1967.tb03398.x, 1967.
Detenbeck, N. E., Morrison, A. C., Abele, R. W., and Kopp, D. A.: Spatial statistical network models for stream and river temperature in New England, USA, Water Resour. Res., 52, 6018–6040, https://doi.org/10.1002/2015WR018349, 2016.
DeWeber, J. T. and Wagner, T.: A regional neural network ensemble for predicting mean daily river water temperature, J. Hydrol., 517, 187–200, https://doi.org/10.1016/j.jhydrol.2014.05.035, 2014.
Drainas, K., Kaule, L., Mohr, S., Uniyal, B., Wild, R., and Geist, J.: Predicting stream water temperature with artificial neural networks based on open-access data, Hydrol. Process., 37, e14991, https://doi.org/10.1002/hyp.14991, 2023.
Dugdale, S. J., Hannah, D. M., and Malcolm, I. A.: River temperature modelling: A review of process-based approaches and future directions, Earth-Sci. Rev., 175, 97–113, https://doi.org/10.1016/j.earscirev.2017.10.009, 2017.
Edinger, J. E., Duttweiler, D. W., and Geyer, J. C.: The response of water temperatures to meteorological conditions, Water Resour. Res., 4, 1137–1143, 1968.
Elman, J. L.: Finding structure in time, Cognitive Science, 14, 179–211, https://doi.org/10.1207/s15516709cog1402_1, 1990.
Fahlman, S. and Lebiere, C.: The cascade-correlation learning architecture, Adv. Neur. In., 2, 524–532, https://dl.acm.org/doi/10.5555/109230.107380, 1990.
Faraway, J. and Chatfield, C.: Time series forecasting with neural networks: A comparative study using the air line data, J. R. Stat. Sco. C-Appl., 47, 231–250, https://doi.org/10.1111/1467-9876.00109, 1998.
Feigl, M., Lebiedzinski, K., Herrnegger, M., and Schulz, K.: Machine-learning methods for stream water temperature prediction, Hydrol. Earth Syst. Sci., 25, 2951–2977, https://doi.org/10.5194/hess-25-2951-2021, 2021.
Fix, E. and Hodges, J. L.: Discriminatory analysis: Nonparametric discrimination: Small sample performance, https://www.jstor.org/stable/1403797 (last access: 27 January 2025), 1952.
Foreman, M. G. G., Lee, D. K., Morrison, J., Macdonald, S., Barnes, D., and Williams, I. V.: Simulations and retrospective analyses of fraser watershed flows and temperatures, Atmos.-Ocean, 39, 89–105, https://doi.org/10.1080/07055900.2001.9649668, 2001.
Friedberg, R. M.: A learning machine: Part I, IBM J. Res. & Dev., 2, 2–13, https://doi.org/10.1147/rd.21.0002, 1958.
Fuller, M. R., Detenbeck, N. E., Leinenbach, P., Labiosa, R., and Isaak, D.: Spatial and temporal variability in stream thermal regime drivers for three river networks during the summer growing season, J. American Water Resour. Assoc., 60, 57–78, https://doi.org/10.1111/1752-1688.13158, 2023.
Gallice, A., Schaefli, B., Lehning, M., Parlange, M. B., and Huwald, H.: Stream temperature prediction in ungauged basins: review of recent approaches and description of a new physics-derived statistical model, Hydrol. Earth Syst. Sci., 19, 3727–3753, https://doi.org/10.5194/hess-19-3727-2015, 2015.
Gers, F. A. and Schmidhuber, J.: Recurrent nets that time and count, in: IJCNN 2000, Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks, Neural Computing: New Challenges and Perspectives for the New Millennium, 7 July 2000, Como, Italy, 189–194, https://doi.org/10.1109/IJCNN.2000.861302, 2000.
Ghobadi, F. and Kang, D.: Improving long-term streamflow prediction in a poorly gauged basin using geo-spatiotemporal mesoscale data and attention-based deep learning: A comparative study, J. Hydrol., 615, 128608, https://doi.org/10.1016/j.jhydrol.2022.128608, 2022.
GitHub Inc.: GitHub, https://www.github.com/github/, last access: 31 December 2024.
Google, Inc.: Gemini, a large language model, Alphabet, Inc., https://gemini.google.com, last access: 27 January 2025.
Graf, R. and Aghelpour, P.: Daily river water temperature prediction: A comparison between neural network and stochastic techniques, Atmosphere, 12, 1154, https://doi.org/10.3390/atmos12091154, 2021.
Graf, R., Zhu, S., and Sivakumar, B.: Forecasting river water temperature time series using a wavelet–neural network hybrid modelling approach, J. Hydrol., 578, 124115, https://doi.org/10.1016/j.jhydrol.2019.124115, 2019.
Grbić, R., Kurtagić, D., and Slišković, D.: Stream water temperature prediction based on Gaussian process regression, Expert Syst. Appl., 40, 7407–7414, https://doi.org/10.1016/j.eswa.2013.06.077, 2013.
Greff, K., Srivastava, R. K., Koutník, J., Steunebrink, B. R., and Schmidhuber, J.: LSTM: A search space odyssey, IEEE T. Neur. Net. Lear., 28, 2222–2232, https://doi.org/10.48550/arXiv.1503.04069, 2016.
Gupta, H. V., Sorooshian, S., and Yapo, P. O.: Status of automatic calibration for hydrologic models: Comparison with multilevel expert calibration, J. Hydrol. Eng., 4, 135–143, https://doi.org/10.1061/(ASCE)1084-0699(1999)4:2(135), 1999.
Hadzima-Nyarko, M., Rabi, A., and Šperac, M.: Implementation of artificial neural networks in modeling the water-air temperature relationship of the River Drava, Water Resour. Manage., 28, 1379–1394, https://doi.org/10.1007/s11269-014-0557-7, 2014.
Hani, I., St-Hilaire, A., and Ouarda, T. B. M. J.: Machine-learning modeling of hourly potential thermal refuge area: A case study from the Sainte-Marguerite River (Quebec, Canada), River Res. Appl., rra.4191, https://doi.org/10.1002/rra.4191, 2023.
Hastie, T. and Tibshirani, R.: Generalized additive models: Some applications, J. Am. Stat. Assoc., 82, 371–386, https://doi.org/10.1080/01621459.1987.10478440, 1987.
Hastie, T., Friedman, J., and Tibshirani, R.: The elements of statistical learning, Springer New York, New York, NY, https://doi.org/10.1007/978-0-387-21606-5, 2001.
He, E., Xie, Y., Sun, A., Zwart, J., Yang, J., Jin, Z., Wang, Y., Karimi, H., and Jia, X.: Fair graph learning using constraint-aware priority adjustment and graph masking in river networks, AAAI, 38, 22087–22095, https://doi.org/10.1609/aaai.v38i20.30212, 2024.
Hebert, C., Caissie, D., Satish, M. G., and El-Jabi, N.: Modeling of hourly river water temperatures using artificial neural networks, Water Qual. Res. J., 49, 144–162, https://doi.org/10.2166/wqrjc.2014.007, 2014.
Heddam, S., Kim, S., Danandeh Mehr, A., Zounemat-Kermani, M., Ptak, M., Elbeltagi, A., Malik, A., and Tikhamarine, Y.: Bat algorithm optimised extreme learning machine (Bat-ELM): A novel approach for daily river water temperature modelling, Geogr. J., 189, 78–89, https://doi.org/10.1111/geoj.12478, 2022a.
Heddam, S., Ptak, M., Sojka, M., Kim, S., Malik, A., Kisi, O., and Zounemat-Kermani, M.: Least square support vector machine-based variational mode decomposition: a new hybrid model for daily river water temperature modeling, Environ. Sci. Pollut. Res., 29, 71555–71582, https://doi.org/10.1007/s11356-022-20953-0, 2022b.
Helsel, D. R. and Hirsch, R. M.: Chapter A3: Statistical Methods in Water Resources, in: Techniques of Water Resources Investigations, Book 4, U.S. Geological Survey, 522, https://doi.org/10.3133/twri04A3, 2002.
Hinton, G. E.: How neural networks learn from experience, Sci. Am., 267, 144–151, 1992.
Hochreiter, S. and Schmidhuber, J.: Long short-term memory, Neural Comput., 9, 1735–1780, https://doi.org/10.1162/neco.1997.9.8.1735, 1997.
Hong, Y.-S. T. and Bhamidimarri, R.: Dynamic neuro-fuzzy local modeling system with a nonlinear feature extraction for the online adaptive warning system of river temperature affected by waste cooling water discharge, Stoch. Environ. Res. Risk Assess., 26, 947–960, https://doi.org/10.1007/s00477-011-0543-z, 2012.
Hsu, K., Gupta, H. V., and Sorooshian, S.: Artificial neural network modeling of the rainfall-runoff process, Water Resour. Res., 31, 2517–2530, https://doi.org/10.1029/95WR01955, 1995.
Huang, G.-B., Zhu, Q.-Y., and Siew, C.-K.: Extreme learning machine: Theory and applications, Neurocomputing, 70, 489–501, https://doi.org/10.1016/j.neucom.2005.12.126, 2006.
Irani, J., Pise, N., and Phatak, M.: Clustering techniques and the similarity measures used in clustering: A survey, IJCA, 134, 9–14, https://doi.org/10.5120/ijca2016907841, 2016.
Isaak, D. J., Wenger, S. J., Peterson, E. E., Ver Hoef, J. M., Nagel, D. E., Luce, C. H., Hostetler, S. W., Dunham, J. B., Roper, B. B., Wollrab, S. P., Chandler, G. L., Horan, D. L., and Parkes-Payne, S.: The NorWeST summer stream temperature model and scenarios for the Western U.S.: A crowd-sourced database and new geospatial tools foster a user community and predict broad climate warming of rivers and streams, Water Resour. Res., 53, 9181–9205, https://doi.org/10.1002/2017WR020969, 2017.
Islam, M. N. and Sivakumar, B.: Characterization and prediction of runoff dynamics: a nonlinear dynamical view, Adv. Water Resour., 25, 179–190, https://doi.org/10.1016/S0309-1708(01)00053-7, 2002.
Ivakhnenko, A. G.: Heuristic self-organization in problems of engineering cybernetics, Automatica, 6, 207–219, https://doi.org/10.1016/0005-1098(70)90092-0, 1970.
Ivakhnenko, A. G. and Ivakhnenko, G. A.: The review of problems solvable by algorithms of the group method of data handling (GMDH), Pattern recognition and image analysis, 5, 527–535, 1995.
Jaber, F. and Shukla, S.: MIKE SHE: Model use, calibration, and validation, T. ASABE, 55, 1479–1489, https://doi.org/10.13031/2013.42255, 2012.
Jang, J.-S. R.: ANFIS: adaptive-network-based fuzzy inference system, IEEE Trans. Syst., Man, Cybern., 23, 665–685, https://doi.org/10.1109/21.256541, 1993.
Janson, D. J. and Frenzel, J. F.: Training product unit neural networks with genetic algorithms, IEEE Expert, 8, 26–33, https://doi.org/10.1109/64.236478, 1993.
Jeong, K., Lee, J., Lee, K. Y., and Kim, B.: Artificial neural network-based real time water temperature prediction in the Soyang River, The Transactions of The Korean Institute of Electrical Engineers, 65, 2084–2093, https://doi.org/10.5370/KIEE.2016.65.12.2084, 2016.
Jiang, D., Xu, Y., Lu, Y., Gao, J., and Wang, K.: Forecasting water temperature in cascade reservoir operation-influenced river with machine learning models, Water, 14, 2146, https://doi.org/10.3390/w14142146, 2022.
Johnson, S. L. and Jones, J. A.: Stream temperature responses to forest harvest and debris flows in western Cascades, Oregon, Can. J. Fish. Aquat. Sci., 57, 10, https://doi.org/10.1139/f00-109, 2000.
Kalogirou, S. A.: Solar energy engineering: processes and systems, 3rd edn., Elsevier, 902 pp., https://doi.org/10.1016/B978-0-12-374501-9.X0001-5, 2023.
Karunanithi, N., Grenney, W. J., Whitley, D., and Bovee, K.: Neural networks for river flow prediction, J. Comput. Civil Eng., 8, 201–220, https://doi.org/10.1061/(ASCE)0887-3801(1994)8:2(201), 1994.
Khosravi, M., Duti, B. M., Yazdan, M. M. S., Ghoochani, S., Nazemi, N., and Shabanian, H.: Multivariate multi-step long short-term memory neural network for simultaneous stream-water variable prediction, Eng, 4, 1933–1950, https://doi.org/10.3390/eng4030109, 2023.
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.
Knoben, W. J. M., Freer, J. E., and Woods, R. A.: Technical note: Inherent benchmark or not? Comparing Nash–Sutcliffe and Kling–Gupta efficiency scores, Hydrol. Earth Syst. Sci., 23, 4323–4331, https://doi.org/10.5194/hess-23-4323-2019, 2019.
Kratzert, F., Klotz, D., Brenner, C., Schulz, K., and Herrnegger, M.: Rainfall–runoff modelling using Long Short-Term Memory (LSTM) networks, Hydrol. Earth Syst. Sci., 22, 6005–6022, https://doi.org/10.5194/hess-22-6005-2018, 2018.
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.
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.
Krishnaraj, A. and Deka, P. C.: Spatial and temporal variations in river water quality of the Middle Ganga Basin using unsupervised machine learning techniques, Environ. Monit. Assess., 192, 744, https://doi.org/10.1007/s10661-020-08624-4, 2020.
Krizhevsky, A., Sutskever, I., and Hinton, G. E.: ImageNet classification with deep convolutional neural networks, Adv. Neur. In., 25, 1–9, https://doi.org/10.1145/3065386, 2012.
Kwak, J., St-Hilaire, A., and Chebana, F.: A comparative study for water temperature modelling in a small basin, the Fourchue River, Quebec, Canada, Hydrol. Sci. J., 62, 64–75, https://doi.org/10.1080/02626667.2016.1174334, 2016.
Laanaya, F., St-Hilaire, A., and Gloaguen, E.: Water temperature modelling: comparison between the generalized additive model, logistic, residuals regression and linear regression models, Hydrolog. Sci. J., 62, 1078–1093, https://doi.org/10.1080/02626667.2016.1246799, 2017.
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.
Lea, C., Vidal, R., Reiter, A., and Hager, G. D.: Temporal convolutional networks: A unified approach to action segmentation, Proceedings of the 14th European Conference Computer Vision – ECCV 2016 Workshops: Part III, 11–16 October 2016, Amsterdam, Netherlands, 47–54, https://doi.org/10.1007/978-3-319-49409-8_7, 2016.
LeCun, Y., Boser, B., Denker, J., Henderson, D., Howard, R., Hubbard, W., and Jackel, L.: Handwritten digit recognition with a back-propagation network, in: NIPS '89, Proceedings of the third International Conference on Neural Information Processing Systems, Denver, Colorado, USA, 1 January 1989, 396–404, https://dl.acm.org/doi/10.5555/2969830.2969879, 1989.
LeCun, Y., Huang, F. J., and Bottou, L.: Learning methods for generic object recognition with invariance to pose and lighting, in: CVPR 2004, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, CVPR 2004, 27 June–2 July 2004, Washington, D.C., U.S., II-97–104, https://doi.org/10.1109/CVPR.2004.1315150, 2004.
Lee, S.-Y., Fullerton, A. H., Sun, N., and Torgersen, C. E.: Projecting spatiotemporally explicit effects of climate change on stream temperature: A model comparison and implications for coldwater fishes, J. Hydrol., 588, 125066, https://doi.org/10.1016/j.jhydrol.2020.125066, 2020.
Legates, D. R. and McCabe, G. J.: Evaluating the use of “goodness-of-fit” measures in hydrologic and hydroclimatic model validation, Water Resour. Res., 35, 233–241, https://doi.org/10.1029/1998WR900018, 1999.
Liu, D., Xu, Y., Guo, S., Xiong, L., Liu, P., and Zhao, Q.: Stream temperature response to climate change and water diversion activities, Stoch. Environ. Res. Risk Assess., 32, 1397–1413, https://doi.org/10.1007/s00477-017-1487-8, 2018.
Loh, W.-Y.: Classification and Regression Tree Methods. In Encyclopedia of Statistics in Quality and Reliability, edited by: Ruggeri, F., Kenett, R. S., and Faltin, F. W., 315–323, https://doi.org/10.1002/9780470061572.eqr492, 2008.
Loinaz, M. C., Davidsen, H. K., Butts, M., and Bauer-Gottwein, P.: Integrated flow and temperature modeling at the catchment scale, J. Hydrol., 495, 238–251, https://doi.org/10.1016/j.jhydrol.2013.04.039, 2013.
Lu, H. and Ma, X.: Hybrid decision tree-based machine learning models for short-term water quality prediction, Chemosphere, 249, 126169, https://doi.org/10.1016/j.chemosphere.2020.126169, 2020.
Maheu, A., Poff, N. L., and St-Hilaire, A.: A classification of stream water temperature regimes in the conterminous USA, River Res. Appl., 32, 896–906, https://doi.org/10.1002/rra.2906, 2016.
Majerska, M., Osuch, M., and Wawrzyniak, T.: Long-term patterns and changes of unglaciated High Arctic stream thermal regime, Sci. Total Environ., 923, 171298, https://doi.org/10.1016/j.scitotenv.2024.171298, 2024.
Martínez-Estudillo, A., Martínez-Estudillo, F., Hervás-Martínez, C., and García-Pedrajas, N.: Evolutionary product unit based neural networks for regression, Neural Networks, 19, 477–486, https://doi.org/10.1016/j.neunet.2005.11.001, 2006.
McCulloch, W. S. and Pitts, W.: A logical calculus of the ideas immanent in nervous activity, The bulletin of mathematical biophysics, 5, 115–133, https://doi.org/10.1007/BF02478259, 1943.
Microsoft, Inc.: Microsoft Copilot, a large language model, https://copilot.microsoft.com, last access: 27 January 2025.
Møller, M. F.: A scaled conjugate gradient algorithm for fast supervised learning, Neural networks, 6, 525–533, https://doi.org/10.1016/S0893-6080(05)80056-5, 1993.
Moore, A. W., Schneider, J., and Deng, K.: Efficient locally weighted polynomial regression predictions, in: ICML '97, Proceedings of the Fourteenth International Machine Learning Conference, 8–12 July 1997, San Francisco, California, USA, 9, 236–244, ISBN 978-1-55860-486-5, 1997.
Moriasi, D. N., Arnold, J. G., Liew, M. W. V., Bingner, R. L., Harmel, R. D., and Veith, T. L.: Model evaluation guidelines for systematic quantification of accuracy in watershed simulations, T. ASABE, 50, 885–900, https://doi.org/10.13031/2013.23153, 2007.
Moriasi, D. N., Gitau, M. W., Pai, N., and Daggupati, P.: Hydrologic and water quality models: Performance measures and evaluation criteria, T. ASABE, 58, 1763–1785, https://doi.org/10.13031/trans.58.10715, 2015.
Morse, W. L.: Stream temperature prediction model, Water Resour. Res., 6, 290–302, https://doi.org/10.1029/WR006i001p00290, 1970.
Morshed, J. and Kaluarachchi, J. J.: Application of artificial neural network and genetic algorithm in flow and transport simulations, Adv. Water Resour., 22, 145–158, https://doi.org/10.1016/S0309-1708(98)00002-5, 1998.
Musavi, M. T., Ahmed, W., Chan, K. H., Faris, K. B., and Hummels, D. M.: On the training of radial basis function classifiers, Neural networks, 5, 595–603, https://doi.org/10.1016/S0893-6080(05)80038-3, 1992.
Nash, J. E. and Sutcliffe, J. V.: River flow forecasting through conceptual models, part I – A discussion of principles, J. Hydrol., 10, 282–290, https://doi.org/10.1016/0022-1694(70)90255-6, 1970.
Nearing, G. S., Kratzert, F., Sampson, A. K., Pelissier, C. S., Klotz, D., Frame, J. M., Prieto, C., and Gupta, H. V.: What role does hydrological science play in the age of machine learning?, Water Resour. Res., 57, e2020WR028091, https://doi.org/10.1029/2020WR028091, 2021.
OpenAI, Inc.: ChatGPT (27 Jan version), a large language model, https://chat.openai.com/chat, last access: 27 January 2025.
Ouellet, V., St-Hilaire, A., Dugdale, S. J., Hannah, D. M., Krause, S., and Proulx-Ouellet, S.: River temperature research and practice: Recent challenges and emerging opportunities for managing thermal habitat conditions in stream ecosystems, Sci. Total Environ., 736, 139679, https://doi.org/10.1016/j.scitotenv.2020.139679, 2020.
Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Köpf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., and Chintala, S.: PyTorch: An imperative style, high-performance deep learning library, arXiv [preprint], https://doi.org/10.48550/arXiv.1912.01703, 3 December 2019.
Patra, R. W., Chapman, J. C., Lim, R. P., Gehrke, P. C., and Sunderam, R. M.: Interactions between water temperature and contaminant toxicity to freshwater fish, Environ. Toxicol. Chem., 34, 1809–1817, https://doi.org/10.1002/etc.2990, 2015.
Philippus, D., Sytsma, A., Rust, A., and Hogue, T. S.: A machine learning model for estimating the temperature of small rivers using satellite-based spatial data, Remote Sens. Environ., 311, 114271, https://doi.org/10.1016/j.rse.2024.114271, 2024a.
Philippus, D., Corona, C. R., and Hogue, T. S.: Improved annual temperature cycle function for stream seasonal thermal regimes, J. American Water Resour. Assoc., 60, 1080–1094, https://doi.org/10.1111/1752-1688.13228, 2024b.
Piccolroaz, S., Calamita, E., Majone, B., Gallice, A., Siviglia, A., and Toffolon, M.: Prediction of river water temperature: a comparison between a new family of hybrid models and statistical approaches, Hydrol. Process., 30, 3901–3917, https://doi.org/10.1002/hyp.10913, 2016.
Piotrowski, A. P., Napiorkowski, M. J., Napiorkowski, J. J., and Osuch, M.: Comparing various artificial neural network types for water temperature prediction in rivers, J. Hydrol., 529, 302–315, https://doi.org/10.1016/j.jhydrol.2015.07.044, 2015.
Piotrowski, A. P., Napiorkowski, J. J., and Piotrowska, A. E.: Impact of deep learning-based dropout on shallow neural networks applied to stream temperature modelling, Earth-Sci. Rev., 201, 103076, https://doi.org/10.1016/j.earscirev.2019.103076, 2020.
Piotrowski, A. P., Marzena, O., and Napiorkowski, J. J.: Influence of the choice of stream temperature model on the projections of water temperature in rivers, J. Hydrol., 601, 1–21, https://doi.org/10.1016/j.jhydrol.2021.126629, 2021.
Poff, N. L., Tokar, S., and Johnson, P.: Stream hydrological and ecological responses to climate change assessed with an artificial neural network, Limnol. Oceanogr., 41, 857–863, https://doi.org/10.4319/lo.1996.41.5.0857, 1996.
Poole, G. C. and Berman, C. H.: An ecological perspective on in-stream temperature: Natural heat dynamics and mechanisms of human-caused thermal degradation, Environ. Manage, 27, 787–802, https://doi.org/10.1007/s002670010188, 2001.
Portet, S.: A primer on model selection using the Akaike Information Criterion, Infectious Disease Modelling, 5, 111–128, https://doi.org/10.1016/j.idm.2019.12.010, 2020.
Qiu, R., Wang, Y., Wang, D., Qiu, W., Wu, J., and Tao, Y.: Water temperature forecasting based on modified artificial neural network methods: Two cases of the Yangtze River, Sci. Total Environ., 737, 139729, https://doi.org/10.1016/j.scitotenv.2020.139729, 2020.
Rabi, A., Hadzima-Nyarko, M., and Šperac, M.: Modelling river temperature from air temperature: case of the River Drava (Croatia), Hydrolog. Sci. J., 60, 1490–1507, https://doi.org/10.1080/02626667.2014.914215, 2015.
Rahmani, F., Lawson, K., Ouyang, W., Appling, A., Oliver, S., and Shen, C.: Exploring the exceptional performance of a deep learning stream temperature model and the value of streamflow data, Environ. Res. Lett., 16, 1–11, https://doi.org/10.1088/1748-9326/abd501, 2020.
Rahmani, F., Shen, C., Oliver, S., Lawson, K., and Appling, A.: Deep learning approaches for improving prediction of daily stream temperature in data-scarce, unmonitored, and dammed basins, Hydrol. Process., 35, e14400, https://doi.org/10.1002/hyp.14400, 2021.
Rahmani, F., Appling, A., Feng, D., Lawson, K., and Shen, C.: Identifying structural priors in a hybrid differentiable model for stream water temperature modeling, Water Resour. Res., 59, e2023WR034420, https://doi.org/10.1029/2023WR034420, 2023.
Rajesh, M. and Rehana, S.: Prediction of river water temperature using machine learning algorithms: a tropical river system of India, J. Hydroinform., 23, 605–626, 2021.
Rehana, S.: River water temperature modelling under climate change using support vector regression, in: Hydrology in a Changing World, edited by: Singh, S. K. and Dhanya, C. T., Springer International Publishing, Cham, 171–183, https://doi.org/10.1007/978-3-030-02197-9_8, 2019.
Rehana, S. and Rajesh, M.: Assessment of impacts of climate change on indian riverine thermal regimes using hybrid deep learning methods, Water Resour. Res., 59, e2021WR031347, https://doi.org/10.1029/2021WR031347, 2023.
Risley, J. C., Roehl, E. A., and Conrads, P. A.: Estimating water temperatures in small streams in western Oregon using neural network models, U.S. Geological Survey, https://doi.org/10.3133/wri024218, 2003.
Risley, J. C., Constantz, J., Essaid, H., and Rounds, S.: Effects of upstream dams versus groundwater pumping on stream temperature under varying climate conditions: Upstream Dam and Groundwater Pumping Impacts, Water Resour. Res., 46, 1–32, https://doi.org/10.1029/2009WR008587, 2010.
Rogers, J. B., Stein, E. D., Beck, M. W., and Ambrose, R. F.: The impact of climate change induced alterations of streamflow and stream temperature on the distribution of riparian species, PLoS ONE, 15, e0242682, https://doi.org/10.1371/journal.pone.0242682, 2020.
Rozos, E.: Assessing hydrological simulations with machine learning and statistical models, Hydrology, 10, 49, https://doi.org/10.3390/hydrology10020049, 2023.
Sadler, J. M., Appling, A. P., Read, J. S., Oliver, S. K., Jia, X., Zwart, J. A., and Kumar, V.: Multi-task deep learning of daily streamflow and water temperature, Water Resour. Res., 58, e2021WR030138, https://doi.org/10.1029/2021WR030138, 2022.
Sahoo, G. B., Schladow, S. G., and Reuter, J. E.: Forecasting stream water temperature using regression analysis, artificial neural network, and chaotic non-linear dynamic models, J. Hydrol., 378, 325–342, https://doi.org/10.1016/j.jhydrol.2009.09.037, 2009.
Segura, C., Caldwell, P., Sun, G., McNulty, S., and Zhang, Y.: A model to predict stream water temperature across the conterminous USA, Hydrol. Process., 29, 2178–2195, https://doi.org/10.1002/hyp.10357, 2015.
Shamseldin, A. Y.: Application of a neural network technique to rainfall-runoff modelling, J. Hydrol., 199, 272–294, https://doi.org/10.1016/S0022-1694(96)03330-6, 1997.
Shen, C.: A transdisciplinary review of deep learning research and its relevance for water resources scientists, Water Resour. Res., 54, 8558–8593, https://doi.org/10.1029/2018WR022643, 2018.
Shi, X., Chen, Z., Wang, H., Yeung, D.-Y., Wong, W.-K., and Woo, W.: Convolutional LSTM network: A machine learning approach for precipitation nowcasting, in: NIPS '15, Proceedings of the 29th International Conference on Neural Information Processing Systems, 7–12 December 2015, Montreal, Canada, 802–810, https://dl.acm.org/doi/10.5555/2969239.2969329 (last access: 12 June 2025), 2015.
Siegel, J. E., Fullerton, A. H., FitzGerald, A. M., Holzer, D., and Jordan, C. E.: Daily stream temperature predictions for free-flowing streams in the Pacific Northwest, USA, PloS Water, 2, 1–27, https://doi.org/10.1371/journal.pwat.0000119, 2023.
Sinokrot, B. A. and Stefan, H. G.: Stream temperature dynamics: Measurements and modeling, Water Resour. Res., 29, 2299–2312, https://doi.org/10.1029/93WR00540, 1993.
Sivri, N., Kilic, N., and Ucan, O. N.: Estimation of stream temperature in Firtina Creek (Rize-Turkiye) using artificial neural network model, J. Environ. Biol., 28, 67–72, 2007.
Skoulikaris, C., Venetsanou, P., Lazoglou, G., Anagnostopoulou, C., and Voudouris, K.: Spatio-temporal interpolation and bias correction ordering analysis for hydrological simulations: An assessment on a mountainous river basin, Water, 14, 660, https://doi.org/10.3390/w14040660, 2022.
Smith, K. and Lavis, M. E.: Environmental influences on the temperature of a small upland stream, Oikos, 26, 228, https://doi.org/10.2307/3543713, 1975.
Solomatine, D. P., Maskey, M., and Shrestha, D. L.: Instance-based learning compared to other data-driven methods in hydrological forecasting, Hydrol. Process., 22, 275–287, https://doi.org/10.1002/hyp.6592, 2008.
Souaissi, Z., Ouarda, T. B. M. J., and St-Hilaire, A.: Non-parametric, semi-parametric, and machine learning models for river temperature frequency analysis at ungauged basins, Ecol. Inform., 75, 102107, https://doi.org/10.1016/j.ecoinf.2023.102107, 2023.
Specht, D. F.: A general regression neural network, IEEE T. Neutral. Networ., 2, 568–576, https://doi.org/10.1109/72.97934, 1991.
Srivastava, N., Hinton, G., Krizhevsky, A., Sutskever, I., and Salakhutdinov, R.: Dropout: A simple way to prevent neural net- works from overfitting, J. Mach. Learn. Res., 15, 1929–1958, https://dl.acm.org/doi/10.5555/2627435.2670313 (last access: 30 December 2024), 2014.
St-Hilaire, A., Morin, G., El-Jabi, N., and Caissie, D.: Water temperature modelling in a small forested stream: implication of forest canopy and soil temperature, Can. J. Civil Eng., 27, 1095–1108, https://doi.org/10.1139/l00-021, 2000.
St-Hilaire, A., Ouarda, T. B. M. J., Bargaoui, Z., Daigle, A., and Bilodeau, L.: Daily river water temperature forecast model with a k-nearest neighbour approach, Hydrol. Process., 26, 1302–1310, https://doi.org/10.1002/hyp.8216, 2011.
Suykens, J. A. and Vandewalle, J.: Least squares support vector machine classifiers, Neural. Process. Lett., 9, 293–300, https://doi.org/10.1023/A:1018628609742, 1999.
Tao, Y., Wang, Y., Rhoads, B., Wang, D., Ni, L., and Wu, J.: Quantifying the impacts of the Three Gorges Reservoir on water temperature in the middle reach of the Yangtze River, J. Hydrol., 582, 124476, https://doi.org/10.1016/j.jhydrol.2019.124476, 2020.
Temizyurek, M. and Dadaser-Celik, F.: Modelling the effects of meteorological parameters on water temperature using artificial neural networks, Water Sci. Technol., 77, 1724–1733, https://doi.org/10.2166/wst.2018.058, 2018.
Theurer, F. D., Voos, K. A., and Miller, W. J.: Instream water temperature model, Western Energy and Land Use Team, Division of Biological Services, Research and Development, USDI, Fish W., Instream Flow Information Paper, 16, 352 pp., 1984.
Thirumalaiah, K. and Deo, M. C.: Real-Time flood forecasting using neural networks, Comput.-Aided Civ. Inf., 13, 101–111, https://doi.org/10.1111/0885-9507.00090, 1998.
Tibshirani, R.: Regression shrinkage and selection via the lasso, J. R. Stat. Soc., 58, 267–288, https://doi.org/10.1111/j.2517-6161.1996.tb02080.x, 1996.
Tipping, M. E.: Sparse Bayesian learning and the relevance vector machine, J. Mach. Learn. Res., 1, 211–244, https://doi.org/10.1162/15324430152748236, 2001.
Toffolon, M. and Piccolroaz, S.: A hybrid model for river water temperature as a function of air temperature and discharge, Environ. Res. Lett., 10, 114011, https://doi.org/10.1088/1748-9326/10/11/114011, 2015.
Topp, S. N., Barclay, J., Diaz, J., Sun, A. Y., Jia, X., Lu, D., Sadler, J. M., and Appling, A. P.: Stream temperature prediction in a shifting environment: Explaining the influence of deep learning architecture, Water Resour. Res., 59, e2022WR033880, https://doi.org/10.1029/2022WR033880, 2023.
Ulaski, M. E., Warkentin, L., Naman, S. M., and Moore, J. W.: Spatially variable effects of streamflow on water temperature and thermal sensitivity within a salmon-bearing watershed in interior British Columbia, Canada, River Res. Appl., 39, 2036–2047, https://doi.org/10.1002/rra.4200, 2023.
Varadharajan, C., Appling, A. P., Arora, B., Christianson, D. S., Hendrix, V. C., Kumar, V., Lima, A. R., Müller, J., Oliver, S., Ombadi, M., Perciano, T., Sadler, J. M., Weierbach, H., Willard, J. D., Xu, Z., and Zwart, J.: Can machine learning accelerate process understanding and decision-relevant predictions of river water quality?, Hydrol. Process., 36, e14565, https://doi.org/10.1002/hyp.14565, 2022.
Venkateswarlu, T. and Anmala, J.: Importance of land use factors in the prediction of water quality of the Upper Green River watershed, Kentucky, USA, using random forest, Environ. Dev. Sustain., 26, 23961–23984, https://doi.org/10.1007/s10668-023-03630-1, 2023.
Voza, D. and Vuković, M.: The assessment and prediction of temporal variations in surface water quality – a case study, Environ. Monit. Assess., 190, 434, https://doi.org/10.1007/s10661-018-6814-0, 2018.
Wade, J., Kelleher, C., and Hannah, D. M.: Mach. Learn. unravels controls on river water temperature regime dynamics, J. Hydrol., 623, 129821, https://doi.org/10.1016/j.jhydrol.2023.129821, 2023.
Walker, J. and Lawson, J.: Natural stream temperature variations in a catchment, Water Res., 11, 373–377, https://doi.org/10.1016/0043-1354(77)90025-2, 1977.
Wallace, J. B. and Webster, J. R.: The role of macroinvertebrates in stream ecosystem function, Annu. Rev. Entomol., 41, 115–139, https://doi.org/10.1146/annurev.en.41.010196.000555, 1996.
Wanders, N., Thober, S., Kumar, R., Pan, M., Sheffield, J., Samaniego, L., and Wood, E. F.: Development and Evaluation of a Pan-European Multimodel Seasonal Hydrological Forecasting System, J. Hydrometeorol., 20, 99–115, https://doi.org/10.1175/JHM-D-18-0040.1, 2019.
Ward, J. C.: Annual variation of stream water temperature, J. Sanit. Eng. Div. ASCE, 89, 1–16, https://doi.org/10.1061/JSEDAI.0000463, 1963.
Ward, J. V.: Riverine landscapes: Biodiversity patterns, disturbance regimes, and aquatic conservation, Biol. Conserv., 83, 269–278, https://doi.org/10.1016/S0006-3207(97)00083-9, 1998.
Webb, R. W., Fassnacht, S. R., and Gooseff, M. N.: Wetting and Drying Variability of the Shallow Subsurface Beneath a Snowpack in California's Southern Sierra Nevada, Vadose Zone J., 14, vzj2014.12.0182, https://doi.org/10.2136/vzj2014.12.0182, 2015.
Wei, X.: Evaluation of transformer model and self-attention mechanism in the Yangtze River basin runoff prediction, J. Hydrol.: Regional Studies, 47, 13, https://doi.org/10.1016/j.ejrh.2023.101438, 2023.
Weierbach, H., Lima, A. R., Willard, J. D., Hendrix, V. C., Christianson, D. S., Lubich, M., and Varadharajan, C.: Stream temperature predictions for river basin management in the Pacific Northwest and mid-Atlantic regions using machine learning, Water, 14, 1032, https://doi.org/10.3390/w14071032, 2022.
Wild, R., Nagel, C., and Geist, J.: Climate change effects on hatching success and embryonic development of fish: Assessing multiple stressor responses in a large-scale mesocosm study, Sci. Total Environ., 893, 164834, https://doi.org/10.1016/j.scitotenv.2023.164834, 2023.
Wu, Z., Pan, S., Long, G., Jiang, J., and Zhang, C.: Graph WaveNet for deep spatial-temporal graph modeling, in: IJCAI '19, Proceedings of the 28th International Joint Conference on Artificial Intelligence, 10–16 August 2019, Macao, China, 1907–1913, https://dl.acm.org/doi/10.5555/3367243.3367303 (last access: 30 December 2024), 2019.
Xu, T. and Liang, F.: Mach. Learn. for hydrologic sciences: An introductory overview, WIREs Water, 8, e1533, https://doi.org/10.1002/wat2.1533, 2021.
Yang, M., Yang, Q., Shao, J., Wang, G., and Zhang, W.: A new few-shot learning model for runoff prediction: Demonstration in two data scarce regions, Environ. Modell. Softw., 162, 105659, https://doi.org/10.1016/j.envsoft.2023.105659, 2023.
Yao, K., Cohn, T., Vylomova, K., Duh, K., and Dyer, C.: Depth-Gated LSTM, 2015 Jelinek Summer Workshop on Speech and Language Technology, arXiv [preprint], 5, https://doi.org/10.48550/arXiv.1508.03790, 2015.
Zanoni, M. G., Majone, B., and Bellin, A.: A catchment-scale model of river water quality by Machine Learning, Sci. Total Environ., 838, 156377, https://doi.org/10.1016/j.scitotenv.2022.156377, 2022.
Zhu, S. and Heddam, S.: Modelling of maximum daily water temperature for streams: Optimally pruned extreme learning machine (OPELM) versus radial basis function neural networks (RBFNN), Environ. Process., 6, 789–804, https://doi.org/10.1007/s40710-019-00385-8, 2019.
Zhu, S. and Piotrowski, A. P.: River/stream water temperature forecasting using artificial intelligence models: a systematic review, Acta Geophys., 68, 1433–1442, https://doi.org/10.1007/s11600-020-00480-7, 2020.
Zhu, S., Nyarko, E. K., Hadzima-Nyarko, M., Heddam, S., and Wu, S.: Assessing the performance of a suite of machine learning models for daily river water temperature prediction, PeerJ, 7, e7065, https://doi.org/10.7717/peerj.7065, 2019a.
Zhu, S., Heddam, S., Wu, S., Dai, J., and Jia, B.: Extreme learning machine-based prediction of daily water temperature for rivers, Environ. Earth Sci., 78, 202, https://doi.org/10.1007/s12665-019-8202-7, 2019b.
Zhu, S., Heddam, S., Nyarko, E. K., Hadzima-Nyarko, M., Piccolroaz, S., and Wu, S.: Modeling daily water temperature for rivers: comparison between adaptive neuro-fuzzy inference systems and artificial neural networks models, Environ. Sci. Pollut. Res., 26, 402–420, https://doi.org/10.1007/s11356-018-3650-2, 2019c.
Zhu, S., Hadzima-Nyarko, M., Gao, A., Wang, F., Wu, J., and Wu, S.: Two hybrid data-driven models for modeling water-air temperature relationship in rivers, Environ. Sci. Pollut. Res., 26, 12622–12630, https://doi.org/10.1007/s11356-019-04716-y, 2019d.
Zwart, J. A., Diaz, J., Hamshaw, S., Oliver, S., Ross, J. C., Sleckman, M., Appling, A. P., Corson-Dosch, H., Jia, X., Read, J., Sadler, J., Thompson, T., Watkins, D., and White, E.: Evaluating deep learning architecture and data assimilation for improving water temperature forecasts at unmonitored locations, Front. Water, 5, 1184992, https://doi.org/10.3389/frwa.2023.1184992, 2023a.
Zwart, J. A., Oliver, S. K., Watkins, W. D., Sadler, J. M., Appling, A. P., Corson-Dosch, H. R., Jia, X., Kumar, V., and Read, J. S.: Near-term forecasts of stream temperature using deep learning and data assimilation in support of management decisions, JAWRA Journal of the American Water Resources Association, 59, 317–337, https://doi.org/10.1111/1752-1688.13093, 2023b.
Short summary
Stream water temperature (SWT) is a key indicator of water quality with implications for public use and health, ecosystem function, and aquatic life survival. Advances in modeling have helped improve our understanding of SWT dynamics, but challenges remain. Recently, machine learning (ML) has been used in SWT modeling, but questions remain about how the use of ML improves insight into SWT causes and effects. This work reviews ML-SWT modeling studies (and metrics) and considers future directions.
Stream water temperature (SWT) is a key indicator of water quality with implications for public...
