Articles | Volume 24, issue 9
https://doi.org/10.5194/hess-24-4641-2020
© Author(s) 2020. 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-24-4641-2020
© Author(s) 2020. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Coupled machine learning and the limits of acceptability approach applied in parameter identification for a distributed hydrological model
Department of Geosciences, University of Oslo, Oslo, Norway
Thomas V. Schuler
Department of Geosciences, University of Oslo, Oslo, Norway
John F. Burkhart
Department of Geosciences, University of Oslo, Oslo, Norway
Morten Hjorth-Jensen
Department of Geosciences, University of Oslo, Oslo, Norway
Department of Physics and Astronomy, Michigan State University, Michigan, USA
Related authors
No articles found.
Thomas James Barnes, Thomas Vikhamar Schuler, Karianne Staalesen Lilleøren, and Louise Steffensen Schmidt
EGUsphere, https://doi.org/10.5194/egusphere-2025-108, https://doi.org/10.5194/egusphere-2025-108, 2025
Preprint archived
Short summary
Short summary
Ribbed moraines are a common, but poorly understood landform within formerly glaciated regions. There are many competing theories for their formation. As such, this paper addresses some of these theories by taking modelled ice conditions and physical characteristics of the landscapes in which they form and, then comparing them to the location of ribbed moraines. Using this we can identify conditions where ribbed moraines are more often present, and therefore we identify the most likely theories.
Henning Åkesson, Kamilla Hauknes Sjursen, Thomas Vikhamar Schuler, Thorben Dunse, Liss Marie Andreassen, Mette Kusk Gillespie, Benjamin Aubrey Robson, Thomas Schellenberger, and Jacob Clement Yde
EGUsphere, https://doi.org/10.5194/egusphere-2025-467, https://doi.org/10.5194/egusphere-2025-467, 2025
Short summary
Short summary
We model the historical and future evolution of the Jostedalsbreen ice cap in Norway, projecting substantial and largely irreversible mass loss for the 21st century, and that the ice cap will split into three parts. Further mass loss is in the pipeline, with a disappearance during the 22nd century under high emissions. Our study demonstrates an approach to model complex ice masses, highlights uncertainties due to precipitation, and calls for further research on long-term future glacier change.
Coline Bouchayer, Ugo Nanni, Pierre-Marie Lefeuvre, John Hult, Louise Steffensen Schmidt, Jack Kohler, François Renard, and Thomas V. Schuler
The Cryosphere, 18, 2939–2968, https://doi.org/10.5194/tc-18-2939-2024, https://doi.org/10.5194/tc-18-2939-2024, 2024
Short summary
Short summary
We explore the interplay between surface runoff and subglacial conditions. We focus on Kongsvegen glacier in Svalbard. We drilled 350 m down to the glacier base to measure water pressure, till strength, seismic noise, and glacier surface velocity. In the low-melt season, the drainage system adapted gradually, while the high-melt season led to a transient response, exceeding drainage capacity and enhancing sliding. Our findings contribute to discussions on subglacial hydro-mechanical processes.
Thomas J. Barnes, Thomas V. Schuler, Simon Filhol, and Karianne S. Lilleøren
Earth Surf. Dynam., 12, 801–818, https://doi.org/10.5194/esurf-12-801-2024, https://doi.org/10.5194/esurf-12-801-2024, 2024
Short summary
Short summary
In this paper, we use machine learning to automatically outline landforms based on their characteristics. We test several methods to identify the most accurate and then proceed to develop the most accurate to improve its accuracy further. We manage to outline landforms with 65 %–75 % accuracy, at a resolution of 10 m, thanks to high-quality/high-resolution elevation data. We find that it is possible to run this method at a country scale to quickly produce landform inventories for future studies.
Andrea Spolaor, Federico Scoto, Catherine Larose, Elena Barbaro, Francois Burgay, Mats P. Bjorkman, David Cappelletti, Federico Dallo, Fabrizio de Blasi, Dmitry Divine, Giuliano Dreossi, Jacopo Gabrieli, Elisabeth Isaksson, Jack Kohler, Tonu Martma, Louise S. Schmidt, Thomas V. Schuler, Barbara Stenni, Clara Turetta, Bartłomiej Luks, Mathieu Casado, and Jean-Charles Gallet
The Cryosphere, 18, 307–320, https://doi.org/10.5194/tc-18-307-2024, https://doi.org/10.5194/tc-18-307-2024, 2024
Short summary
Short summary
We evaluate the impact of the increased snowmelt on the preservation of the oxygen isotope (δ18O) signal in firn records recovered from the top of the Holtedahlfonna ice field located in the Svalbard archipelago. Thanks to a multidisciplinary approach we demonstrate a progressive deterioration of the isotope signal in the firn core. We link the degradation of the δ18O signal to the increased occurrence and intensity of melt events associated with the rapid warming occurring in the archipelago.
Louise Steffensen Schmidt, Thomas Vikhamar Schuler, Erin Emily Thomas, and Sebastian Westermann
The Cryosphere, 17, 2941–2963, https://doi.org/10.5194/tc-17-2941-2023, https://doi.org/10.5194/tc-17-2941-2023, 2023
Short summary
Short summary
Here, we present high-resolution simulations of glacier mass balance (the gain and loss of ice over a year) and runoff on Svalbard from 1991–2022, one of the fastest warming regions in the Arctic. The simulations are created using the CryoGrid community model. We find a small overall loss of mass over the simulation period of −0.08 m yr−1 but with no statistically significant trend. The average runoff was found to be 41 Gt yr−1, with a significant increasing trend of 6.3 Gt per decade.
Sebastian Westermann, Thomas Ingeman-Nielsen, Johanna Scheer, Kristoffer Aalstad, Juditha Aga, Nitin Chaudhary, Bernd Etzelmüller, Simon Filhol, Andreas Kääb, Cas Renette, Louise Steffensen Schmidt, Thomas Vikhamar Schuler, Robin B. Zweigel, Léo Martin, Sarah Morard, Matan Ben-Asher, Michael Angelopoulos, Julia Boike, Brian Groenke, Frederieke Miesner, Jan Nitzbon, Paul Overduin, Simone M. Stuenzi, and Moritz Langer
Geosci. Model Dev., 16, 2607–2647, https://doi.org/10.5194/gmd-16-2607-2023, https://doi.org/10.5194/gmd-16-2607-2023, 2023
Short summary
Short summary
The CryoGrid community model is a new tool for simulating ground temperatures and the water and ice balance in cold regions. It is a modular design, which makes it possible to test different schemes to simulate, for example, permafrost ground in an efficient way. The model contains tools to simulate frozen and unfrozen ground, snow, glaciers, and other massive ice bodies, as well as water bodies.
Anirudha Mahagaonkar, Geir Moholdt, and Thomas V. Schuler
The Cryosphere Discuss., https://doi.org/10.5194/tc-2023-4, https://doi.org/10.5194/tc-2023-4, 2023
Revised manuscript not accepted
Short summary
Short summary
Surface meltwater lakes along the margins of the Antarctic Ice Sheet can be important for ice shelf dynamics and stability. We used optical satellite imagery to study seasonal evolution of meltwater lakes in Dronning Maud Land. We found large interannual variability in lake extents, but with consistent seasonal patterns. Although correlation with summer air temperature was strong locally, other climatic and environmental factors need to be considered to explain the large regional variability.
Chloé Scholzen, Thomas V. Schuler, and Adrien Gilbert
The Cryosphere, 15, 2719–2738, https://doi.org/10.5194/tc-15-2719-2021, https://doi.org/10.5194/tc-15-2719-2021, 2021
Short summary
Short summary
We use a two-dimensional model of water flow below the glaciers in Kongsfjord, Svalbard, to investigate how different processes of surface-to-bed meltwater transfer affect subglacial hydraulic conditions. The latter are important for the sliding motion of glaciers, which in some cases exhibit huge variations. Our findings indicate that the glaciers in our study area undergo substantial sliding because water is poorly evacuated from their base, with limited influence from the surface hydrology.
Juditha Undine Schmidt, Bernd Etzelmüller, Thomas Vikhamar Schuler, Florence Magnin, Julia Boike, Moritz Langer, and Sebastian Westermann
The Cryosphere, 15, 2491–2509, https://doi.org/10.5194/tc-15-2491-2021, https://doi.org/10.5194/tc-15-2491-2021, 2021
Short summary
Short summary
This study presents rock surface temperatures (RSTs) of steep high-Arctic rock walls on Svalbard from 2016 to 2020. The field data show that coastal cliffs are characterized by warmer RSTs than inland locations during winter seasons. By running model simulations, we analyze factors leading to that effect, calculate the surface energy balance and simulate different future scenarios. Both field data and model results can contribute to a further understanding of RST in high-Arctic rock walls.
Elena Barbaro, Krystyna Koziol, Mats P. Björkman, Carmen P. Vega, Christian Zdanowicz, Tonu Martma, Jean-Charles Gallet, Daniel Kępski, Catherine Larose, Bartłomiej Luks, Florian Tolle, Thomas V. Schuler, Aleksander Uszczyk, and Andrea Spolaor
Atmos. Chem. Phys., 21, 3163–3180, https://doi.org/10.5194/acp-21-3163-2021, https://doi.org/10.5194/acp-21-3163-2021, 2021
Short summary
Short summary
This paper shows the most comprehensive seasonal snow chemistry survey to date, carried out in April 2016 across 22 sites on 7 glaciers across Svalbard. The dataset consists of the concentration, mass loading, spatial and altitudinal distribution of major ion species (Ca2+, K+,
Na2+, Mg2+,
NH4+, SO42−,
Br−, Cl− and
NO3−), together with its stable oxygen and hydrogen isotope composition (δ18O and
δ2H) in the snowpack. This study was part of the larger Community Coordinated Snow Study in Svalbard.
Christian Zdanowicz, Jean-Charles Gallet, Mats P. Björkman, Catherine Larose, Thomas Schuler, Bartłomiej Luks, Krystyna Koziol, Andrea Spolaor, Elena Barbaro, Tõnu Martma, Ward van Pelt, Ulla Wideqvist, and Johan Ström
Atmos. Chem. Phys., 21, 3035–3057, https://doi.org/10.5194/acp-21-3035-2021, https://doi.org/10.5194/acp-21-3035-2021, 2021
Short summary
Short summary
Black carbon (BC) aerosols are soot-like particles which, when transported to the Arctic, darken snow surfaces, thus indirectly affecting climate. Information on BC in Arctic snow is needed to measure their impact and monitor the efficacy of pollution-reduction policies. This paper presents a large new set of BC measurements in snow in Svalbard collected between 2007 and 2018. It describes how BC in snow varies across the archipelago and explores some factors controlling these variations.
John F. Burkhart, Felix N. Matt, Sigbjørn Helset, Yisak Sultan Abdella, Ola Skavhaug, and Olga Silantyeva
Geosci. Model Dev., 14, 821–842, https://doi.org/10.5194/gmd-14-821-2021, https://doi.org/10.5194/gmd-14-821-2021, 2021
Short summary
Short summary
We present a new hydrologic modeling framework for interactive development of inflow forecasts for hydropower production planning and other operational environments (e.g., flood forecasting). The software provides a Python user interface with an application programming interface (API) for a computationally optimized C++ model engine, giving end users extensive control over the model configuration in real time during a simulation. This provides for extensive experimentation with configuration.
Andreas Alexander, Jaroslav Obu, Thomas V. Schuler, Andreas Kääb, and Hanne H. Christiansen
The Cryosphere, 14, 4217–4231, https://doi.org/10.5194/tc-14-4217-2020, https://doi.org/10.5194/tc-14-4217-2020, 2020
Short summary
Short summary
In this study we present subglacial air, ice and sediment temperatures from within the basal drainage systems of two cold-based glaciers on Svalbard during late spring and the summer melt season. We put the data into the context of air temperature and rainfall at the glacier surface and show the importance of surface events on the subglacial thermal regime and erosion around basal drainage channels. Observed vertical erosion rates thereby reachup to 0.9 m d−1.
Ankit Pramanik, Jack Kohler, Katrin Lindbäck, Penelope How, Ward Van Pelt, Glen Liston, and Thomas V. Schuler
The Cryosphere Discuss., https://doi.org/10.5194/tc-2020-197, https://doi.org/10.5194/tc-2020-197, 2020
Revised manuscript not accepted
Short summary
Short summary
Freshwater discharge from tidewater glaciers influences fjord circulation and fjord ecosystem. Glacier hydrology plays crucial role in transporting water underneath glacier ice. We investigated hydrology beneath the tidewater glaciers of Kongsfjord basin in Northwest Svalbard and found that subglacial water flow differs substantially from surface flow of glacier ice. Furthermore, we derived freshwater discharge time-series from all the glaciers to the fjord.
Cited articles
Abebe, A. and Price, R.: Managing uncertainty in hydrological models using
complementary models, Hydrolog. Sci. J., 48, 679–692, 2003.
Appelhans, T., Mwangomo, E., Hardy, D. R., Hemp, A., and Nauss, T.:
Evaluating machine learning approaches for the interpolation of monthly air
temperature at Mt. Kilimanjaro, Tanzania, Spat. Stat., 14, 91–113,
2015.
Bair, E. H., Abreu Calfa, A., Rittger, K., and Dozier, J.: Using machine learning for real-time estimates of snow water equivalent in the watersheds of Afghanistan, The Cryosphere, 12, 1579–1594, https://doi.org/10.5194/tc-12-1579-2018, 2018.
Bárdossy, A. and Singh, S. K.: Robust estimation of hydrological model parameters, Hydrol. Earth Syst. Sci., 12, 1273–1283, https://doi.org/10.5194/hess-12-1273-2008, 2008.
Beven, K.: Changing ideas in hydrology – the case of physically-based
models, J. Hydrol., 105, 157–172, 1989.
Beven, K.: A manifesto for the equifinality thesis, J. Hydrol.,
320, 18–36, 2006.
Beven, K. and Binley, A.: The future of distributed models: model
calibration and uncertainty prediction, Hydrol. Process., 6, 279–298,
1992.
Bhattacharya, B., Price, R. K., and Solomatine, D. P.: Machinelearning approach to modeling sediment transport, J. Hydraul. Eng., 133, 440–450, 2007.
Blasone, R.-S., Vrugt, J. A., Madsen, H., Rosbjerg, D., Robinson, B. A., and
Zyvoloski, G. A.: Generalized likelihood uncertainty estimation (GLUE) using
adaptive Markov Chain Monte Carlo sampling, Adv. Water Resour., 31,
630–648, 2008.
Blazkova, S. and Beven, K.: A limits of acceptability approach to model
evaluation and uncertainty estimation in flood frequency estimation by
continuous simulation: Skalka catchment, Czech Republic, Water Resour.
Res., 45, W00b16, https://doi.org/10.1029/2007wr006726, 2009.
Breiman, L.: Random forests, Mach. Learn., 45, 5–32, 2001.
Buckingham, D., Skalka, C., and Bongard, J.: Inductive machine learning for
improved estimation of catchment-scale snow water equivalent, J. Hydrol., 524, 311–325, 2015.
Burba, F., Ferraty, F., and Vieu, P.: k-Nearest Neighbour method in
functional nonparametric regression, J. Nonparametr. Stat.,
21, 453–469, 2009.
Burkhart, J., Helset, S., Abdella, Y., and Lappegard, G.: Operational
Research: Evaluating Multimodel Implementations for 24/7 Runtime
Environments, Abstract H51F-1541 presented at the Fall Meeting, AGU, 11–15 December 2016, San Francisco, California, USA, 2016.
Choi, H. T. and Beven, K.: Multi-period and multi-criteria model
conditioning to reduce prediction uncertainty in an application of TOPMODEL
within the GLUE framework, J. Hydrol., 332, 316–336, 2007.
Clark, M. P., Kavetski, D., and Fenicia, F.: Pursuing the method of multiple
working hypotheses for hydrological modeling, Water Resour. Res., 47, W09301, https://doi.org/10.1029/2010WR009827,
2011.
Copernicus land monitoring service: CORINE land cover, available at:
https://land.copernicus.eu/pan-european/corine-land-cover, last
access: 18 September 2020.
Dee, D. P., Uppala, S., Simmons, A., Berrisford, P., Poli, P., Kobayashi,
S., Andrae, U., Balmaseda, M., Balsamo, G., and Bauer, P.: The ERA-Interim
reanalysis: Configuration and performance of the data assimilation system,
Q. J. Roy. Meteor. Soc., 137, 553–597, 2011.
El Tabach, E., Lancelot, L., Shahrour, I., and Najjar, Y.: Use of artificial
neural network simulation metamodelling to assess groundwater contamination
in a road project, Mathematical Computer Modelling, 45, 766–776, 2007.
Emmerich, M. T., Giannakoglou, K. C., and Naujoks, B.: Single-and
multiobjective evolutionary optimization assisted by Gaussian random field
metamodels, IEEE T. Evolut. Comput., 10, 421–439,
2006.
Fenicia, F., Kavetski, D., and Savenije, H. H.: Elements of a flexible
approach for conceptual hydrological modeling: 1. Motivation and theoretical
development, Water Resour. Res., 47, W11510, https://doi.org/10.1029/2010WR010174, 2011.
Hemker, T., Fowler, K. R., Farthing, M. W., and von Stryk, O.: A
mixed-integer simulation-based optimization approach with surrogate
functions in water resources management, Optimization Engineering, 9,
341–360, 2008.
Hornberger, G. M. and Spear, R. C.: Approach to the preliminary analysis of
environmental systems, J. Environ. Manage., 12, 7–18, 1981.
Hsieh, C.-T.: Some potential applications of artificial neural systems in financial management,
J. Syst. Manage., 44, 12–16, 1993.
Hsieh, W. W.: Machine learning methods in the environmental sciences: Neural
networks and kernels, Cambridge university press, Cambridge, UK, 2009.
Hussain, M. F., Barton, R. R., and Joshi, S. B.: Metamodeling: radial basis
functions, versus polynomials, Eur. J. Oper. Res.,
138, 142–154, 2002.
Iman, R. L. and Conover, W.: Small sample sensitivity analysis techniques
for computer models. with an application to risk assessment, Commun. Stat. Theory, 9, 1749–1842, 1980.
Jones, D. R.: A taxonomy of global optimization methods based on response
surfaces, J. Global Optim., 21, 345–383, 2001.
Kavetski, D. and Fenicia, F.: Elements of a flexible approach for
conceptual hydrological modeling: 2. Application and experimental insights,
Water Resour. Res., 47, W11511, https://doi.org/10.1029/2011WR010748, 2011.
Kennedy, M. C. and O'Hagan, A.: Bayesian calibration of computer models,
J. Roy. Stat. Soc. B, 63, 425–464, 2001.
Kingston, G. B., Maier, H. R. and Dandy, G. C.: Review of Artificial
Intelligence Techniques and their Applications to Hydrological Modeling and
Water Resources Management. Part 1 – Simulation, available at:
https://www.researchgate.net/publication/277005048_Review_of_Artificial_Intelligence_Techniques_and_their_Applications_to_Hydrological_Modeling_and_Water_Resources_Management_Part_1_-_Simulation, last access: 15 December 2018.
Kirchner, J. W.: Catchments as simple dynamical systems: Catchment
characterization, rainfall-runoff modeling, and doing hydrology backward,
Water Resour. Res., 45, W02429, https://doi.org/10.1029/2008WR006912, 2009.
Kuczera, G. and Parent, E.: Monte Carlo assessment of parameter uncertainty
in conceptual catchment models: the Metropolis algorithm, J. Hydrol., 211, 69–85, 1998.
Kuhn, M.: Building predictive models in R using the caret package, J. Stat. Softw., 28, 1–26, 2008.
Lambert, A.: Catchment models based on ISO-functions, J. Instn. Water Engrs.,
26, 413–422, 1972.
Li, J., Heap, A. D., Potter, A., and Daniell, J. J.: Application of machine
learning methods to spatial interpolation of environmental variables,
Environ. Model. Softw., 26, 1647–1659, 2011.
Liu, Y., Freer, J., Beven, K., and Matgen, P.: Towards a limits of
acceptability approach to the calibration of hydrological models: Extending
observation error, J. Hydrol., 367, 93–103, 2009.
Marofi, S., Tabari, H., and Abyaneh, H. Z.: Predicting spatial distribution
of snow water equivalent using multivariate non-linear regression and
computational intelligence methods, Water Resour. Manage., 25,
1417–1435, 2011.
Matt, F. N., Burkhart, J. F., and Pietikäinen, J.-P.: Modelling hydrologic impacts of light absorbing aerosol deposition on snow at the catchment scale, Hydrol. Earth Syst. Sci., 22, 179–201, https://doi.org/10.5194/hess-22-179-2018, 2018.
McKay, M. D., Beckman, R. J., and Conover, W. J.: Comparison of three
methods for selecting values of input variables in the analysis of output
from a computer code, Technometrics, 21, 239–245, 1979.
Mekanik, F., Imteaz, M., Gato-Trinidad, S., and Elmahdi, A.: Multiple
regression and Artificial Neural Network for long-term rainfall forecasting
using large scale climate modes, J. Hydrol., 503, 11–21, 2013.
Mitchell, T. M.: Machine learning, McGraw Hill, Burr Ridge, IL, USA, 45, 870–877, 1997.
Modaresi, F., Araghinejad, S., and Ebrahimi, K.: Selected model fusion: an
approach for improving the accuracy of monthly streamflow forecasting,
J. Hydroinform., 20, 917–933, 2018.
Nielsen, M.: Neural Networks and Deep Learning, available at:
http://neuralnetworksanddeeplearning.com/, last access: 15 September 2018.
Norwegian mapping authority (Kartverket):
https://www.kartverket.no/, last access: 1 September 2016.
Nyhus, E.: Implementation of GARTO as an infiltration routine in a full
hydrological model, MS thesis, Norwegian University of Science and Technology (NTNU), Trondheim, Norway, 2017.
Oakley, J. E. and O'Hagan, A.: Probabilistic sensitivity analysis of
complex models: a Bayesian approach, J. Roy. Stat.
Soc. B, 66, 751–769, 2004.
Okun, O. and Priisalu, H.: Random forest for gene expression based cancer
classification: overlooked issues, Iberian Conference on Pattern Recognition
and Image Analysis, 6–8 June 2007, Girona, Spain, 483–490, 2007.
Olden, J. D. and Jackson, D. A.: Illuminating the “black box”: a
randomization approach for understanding variable contributions in
artificial neural networks, Ecol. Model., 154, 135–150, 2002.
Pianosi, F., Shrestha, D. L., and Solomatine, D. P.: ANN-based
representation of parametric and residual uncertainty of models, IEEE IJCNN, The 2010 International Joint Conference on Neural Networks (IJCNN), 18–23 July 2010, Barcelona, Spain,
1–6, https://doi.org/10.1109/IJCNN.2010.5596852, 2010.
Pianosi, F., Beven, K., Freer, J., Hall, J. W., Rougier, J., Stephenson, D.
B., and Wagener, T.: Sensitivity analysis of environmental models: A
systematic review with practical workflow, Environ. Model.
Softw., 79, 214–232, 2016.
Priestley, C. and Taylor, R.: On the assessment of surface heat flux and
evaporation using large-scale parameters, Mon. weather Rev., 100,
81–92, 1972.
Ransom, K. M., Nolan, B. T., Traum, J. A., Faunt, C. C., Bell, A. M.,
Gronberg, J. A. M., Wheeler, D. C., Rosecrans, C. Z., Jurgens, B., and
Schwarz, G. E.: A hybrid machine learning model to predict and visualize
nitrate concentration throughout the Central Valley aquifer, California,
USA, Sci. Total Environ., 601, 1160–1172, 2017.
Ratto, M., Castelletti, A., and Pagano, A.: Emulation techniques for the
reduction and sensitivity analysis of complex environmental models, Environ. Model. Softw., 34, 1–4, https://doi.org/10.1016/j.envsoft.2011.11.003, 2012.
Razavi, S., Tolson, B. A., and Burn, D. H.: Review of surrogate modeling in
water resources, Water Resour. Res., 48, W07401, https://doi.org/10.1029/2011WR011527, 2012.
Refsgaard, J. C.: Parameterisation, calibration and validation of
distributed hydrological models, J. Hydrol., 198, 69–97, 1997.
Regis, R. G. and Shoemaker, C. A.: Local function approximation in
evolutionary algorithms for the optimization of costly functions, IEEE
T. Evolut. Comput., 8, 490–505, 2004.
Reichert, P., White, G., Bayarri, M. J., and Pitman, E. B.: Mechanism-based
emulation of dynamic simulation models: Concept and application in
hydrology, Comput. Stat. Data An., 55, 1638–1655, 2011.
Renard, B., Kavetski, D., Kuczera, G., Thyer, M., and Franks, S. W.:
Understanding predictive uncertainty in hydrologic modeling: The challenge
of identifying input and structural errors, Water Resour. Res., 46, W05521, https://doi.org/10.1029/2009WR008328,
2010.
Sajikumar, N. and Thandaveswara, B.: A non-linear rainfall–runoff model
using an artificial neural network, J. Hydrol., 216, 32–55, 1999.
Senent-Aparicio, J., Jimeno-Sáez, P., Bueno-Crespo, A.,
Pérez-Sánchez, J., and Pulido-Velázquez, D.: Coupling
machine-learning techniques with SWAT model for instantaneous peak flow
prediction, Biosyst. Eng., 177, 67–77, 2018.
Shen, Z. Y., Chen, L., and Chen, T.: Analysis of parameter uncertainty in hydrological and sediment modeling using GLUE method: a case study of SWAT model applied to Three Gorges Reservoir Region, China, Hydrol. Earth Syst. Sci., 16, 121–132, https://doi.org/10.5194/hess-16-121-2012, 2012.
Shrestha, D. L., Kayastha, N., and Solomatine, D. P.: A novel approach to parameter uncertainty analysis of hydrological models using neural networks, Hydrol. Earth Syst. Sci., 13, 1235–1248, https://doi.org/10.5194/hess-13-1235-2009, 2009.
Shrestha, D. L., Kayastha, N., Solomatine, D., and Price, R.: Encapsulation
of parametric uncertainty statistics by various predictive machine learning
models: MLUE method, J. Hydroinform., 16, 95–113, 2014.
Snauffer, A. M., Hsieh, W. W., Cannon, A. J., and Schnorbus, M. A.: Improving gridded snow water equivalent products in British Columbia, Canada: multi-source data fusion by neural network models, The Cryosphere, 12, 891–905, https://doi.org/10.5194/tc-12-891-2018, 2018.
Solomatine, D. P. and Shrestha, D. L.: A novel method to estimate model
uncertainty using machine learning techniques, Water Resour. Res., 45, W00B11, https://doi.org/10.1029/2008WR006839,
2009.
Statkraft: Statkraft information page, available at:
https://www.statkraft.com/, last access: 20 June 2018.
Stedinger, J. R., Vogel, R. M., Lee, S. U., and Batchelder, R.: Appraisal of
the generalized likelihood uncertainty estimation (GLUE) method, Water
Resour. Res., 44, W00B06, https://doi.org/10.1029/2008WR006822, 2008.
Tabari, H., Marofi, S., Abyaneh, H. Z., and Sharifi, M.: Comparison of
artificial neural network and combined models in estimating spatial
distribution of snow depth and snow water equivalent in Samsami basin of
Iran, Neural Comput. Appl., 19, 625–635, 2010.
Teweldebrhan, A. T., Burkhart, J. F., and Schuler, T. V.: Parameter uncertainty analysis for an operational hydrological model using residual-based and limits of acceptability approaches, Hydrol. Earth Syst. Sci., 22, 5021–5039, https://doi.org/10.5194/hess-22-5021-2018, 2018.
Teweldebrhan, A., Burkhart, J., Schuler, T., and Xu, C.-Y.: Improving the
Informational Value of MODIS Fractional Snow Cover Area Using Fuzzy Logic
Based Ensemble Smoother Data Assimilation Frameworks, Remote Sens., 11,
28, https://doi.org/10.3390/rs11010028, 2019.
Torres, A. F., Walker, W. R., and McKee, M. J.: Forecasting daily potential
evapotranspiration using machine learning and limited climatic data,
Agr. Water Manage., 98, 553–562, 2011.
Uhlenbrook, S., Seibert, J., Leibundgut, C., and Rodhe, A.: Prediction
uncertainty of conceptual rainfall-runoff models caused by problems in
identifying model parameters and structure, Hydrolog. Sci. J.,
44, 779–797, 1999.
Vrugt, J. A., Gupta, H. V., Bouten, W., and Sorooshian, S.: A Shuffled
Complex Evolution Metropolis algorithm for optimization and uncertainty
assessment of hydrologic model parameters, Water Resour. Res., 39, 1201, https://doi.org/10.1029/2002WR001642,
2003.
Vrugt, J. A., Ter Braak, C. J., Gupta, H. V., and Robinson, B. A.:
Equifinality of formal (DREAM) and informal (GLUE) Bayesian approaches in
hydrologic modeling, Stoch. Env. Res. Risk A.,
23, 1011–1026, 2009.
Wagener, T., McIntyre, N., Lees, M., Wheater, H., and Gupta, H.: Towards
reduced uncertainty in conceptual rainfall-runoff modelling: Dynamic
identifiability analysis, Hydrol. Process., 17, 455–476, 2003.
Wang, S., Huang, G., Baetz, B., and Huang, W.: A polynomial chaos ensemble
hydrologic prediction system for efficient parameter inference and robust
uncertainty assessment, J. Hydrol., 530, 716–733, 2015.
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.
Wu, C. and Chau, K.-W.: Data-driven models for monthly streamflow time
series prediction, Eng. Appl. Artif. Intel., 23,
1350–1367, 2010.
Xiong, L. and O'Connor, K. M.: An empirical method to improve the
prediction limits of the GLUE methodology in rainfall-runoff modeling,
J. Hydrol., 349, 115–124, 2008.
Xiong, L., Wan, M., Wei, X., and O'Connor, K. M.: Indices for assessing the
prediction bounds of hydrological models and application by generalised
likelihood uncertainty estimation, Hydrolog. Sci. J., 54,
852–871, 2009.
Yang, J., Reichert, P., Abbaspour, K. C., and Yang, H.: Hydrological
modelling of the Chaohe Basin in China: Statistical model formulation and
Bayesian inference, J. Hydrol., 340, 167–182, 2007.
Yang, J., Jakeman, A., Fang, G., and Chen, X.: Uncertainty analysis of a
semi-distributed hydrologic model based on a Gaussian Process emulator,
Environ. Model. Softw., 101, 289–300, 2018.
Yu, J., Qin, X., and Larsen, O.: Applying ANN emulators in uncertainty
assessment of flood inundation modelling: a comparison of two surrogate
schemes, Hydrolog. Sci. J., 60, 2117–2131, 2015.
Zhao, Y., Taylor, J. S., and Chellam, S. J.: Predicting RO/NF water quality
by modified solution diffusion model and artificial neural networks, J. Membrane Sci., 263, 38–46, 2005.