Articles | Volume 25, issue 5
https://doi.org/10.5194/hess-25-2951-2021
© Author(s) 2021. 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-25-2951-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
31 May 2021
Research article |
| 31 May 2021
| 31 May 2021
Machine-learning methods for stream water temperature prediction
Institute for Hydrology and Water Management, University of Natural Resources and Life Sciences, Vienna, Austria
Katharina Lebiedzinski
Institute for Hydrology and Water Management, University of Natural Resources and Life Sciences, Vienna, Austria
Mathew Herrnegger
Institute for Hydrology and Water Management, University of Natural Resources and Life Sciences, Vienna, Austria
Karsten Schulz
Institute for Hydrology and Water Management, University of Natural Resources and Life Sciences, Vienna, Austria
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Cited articles
Abba, S. I., Hadi, S. J., and Abdullahi, J.: River water modelling prediction using multi-linear regression, artificial neural network, and adaptive neuro-fuzzy inference system techniques, in: Procedia Computer Science, Elsevier B.V., Budapest, Hungary, 75–82, https://doi.org/10.1016/j.procs.2017.11.212, 2017. a, b
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. a
Akaike, H.: Information theory as an extension of the likelihood principle., in: Second Akademiai International Symposium on Information Theory, edited by: Petrov, B. N. and Csaki, F., Kiado, Budapest, 267–281, 1973. a
Allaire, J. J. and Tang, Y.: tensorflow: R Interface to “TensorFlow”, available at: https://github.com/rstudio/tensorflow (last access: 13 Jauary 2021), 2020. a
Álvarez, D. and Nicieza, A. G.: Compensatory response “defends” energy levels but not growth trajectories in brown trout, Salmo trutta L.,
P. Roy. Soc. B-Biol. Sci., 272, 601–607,
https://doi.org/10.1098/rspb.2004.2991, 2005. a
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. a, b
Baldi, P. and Sadowski, P.: The dropout learning algorithm, Artif. Intell., 210, 78–122, https://doi.org/10.1016/j.artint.2014.02.004, 2014. a
Beaufort, A., Moatar, F., Curie, F., Ducharne, A., Bustillo, V., and
Thiéry, D.: River Temperature Modelling by Strahler Order at the
Regional Scale in the Loire River Basin, France,
River Res. Appl., 32, 597–609, https://doi.org/10.1002/rra.2888, 2016. a, b
Bélanger, M., El-Jabi, N., Caissie, D., Ashkar, F., and Ribi, J. M.:
Water temperature prediction using neural networks and multiple linear
regression, Revue des Sciences de l'Eau, 18, 403–421,
https://doi.org/10.7202/705565ar, 2005. a, b
Bengio, Y., Courville, A., and Vincent, P.: Representation learning: A review and new perspectives, IEEE T. Pattern Anal., 35, 1798–1828, https://doi.org/10.1109/TPAMI.2013.50, 2013. a
Bentéjac, C., Csörgő, A., and Martínez-Muñoz, G.: A
comparative analysis of gradient boosting algorithms, Artif. Intell. Rev., 54, 1937–1967, https://doi.org/10.1007/s10462-020-09896-5, 2021. a, b
Benyahya, L., Caissie, D., St-Hilaire, A., Ouarda, T. B., and Bobée, B.: A Review of Statistical Water Temperature Models,
Can. Water Resour. J., 32, 179–192, https://doi.org/10.4296/cwrj3203179, 2007. a, b
BMLFUW: Hydrological Atlas of Austria, 3rd Edn., Bundesmin-isterium für Land- und Forstwirtschaft, Umwelt und Wasser-wirtschaft, Vienna, Austria, ISBN 3-85437-250-7, 2007. a
Boisneau, C., Moatar, F., Bodin, M., and Boisneau, P.: Does global warming
impact on migration patterns and recruitment of Allis shad (Alosa alosa L.)
young of the year in the Loire River, France?, in: Fish and Diadromy in
Europe (ecology, management, conservation), Springer, Dordrecht, the Netherlands, 179–186, https://doi.org/10.1007/978-1-4020-8548-2_14, 2008. a
Breiman, L.: Bagging predictors, Mach. Learn., 24, 123–140,
https://doi.org/10.1007/bf00058655, 1996. a
Breiman, L.: Random forests, Mach. Learn., 45, 5–32,
https://doi.org/10.1023/A:1010933404324, 2001. a, b, c
Brinckmann, S., Krähenmann, S., and Bissolli, P.: High-resolution daily gridded data sets of air temperature and wind speed for Europe, Earth Syst. Sci. Data, 8, 491–516, https://doi.org/10.5194/essd-8-491-2016, 2016. a
Caissie, D.: The thermal regime of rivers: A review, Freshwater Biol., 51, 1389–1406, https://doi.org/10.1111/j.1365-2427.2006.01597.x, 2006. a
Caissie, D. and Luce, C. H.: Quantifying streambed advection and conduction
heat fluxes, Water Resour. Res., 53, 1595–1624,
https://doi.org/10.1002/2016WR019813, 2017. a
Caldwell, R. J., Gangopadhyay, S., Bountry, J., Lai, Y., and Elsner, M. M.:
Statistical modeling of daily and subdaily stream temperatures: Application
to the Methow River Basin, Washington, Water Resour. Res., 49,
4346–4361, https://doi.org/10.1002/wrcr.20353, 2013. a, b, c
Central Hydrographical Bureau: eHYD, available at: https://www.ehyd.gv.at/, last access: 26 May 2021. a
Chen, T. and Guestrin, C.: XGBoost: A scalable tree boosting system, in:
Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery
and Data Mining, San Francisco, California, USA, 13–17 August 2016, 785–794, https://doi.org/10.1145/2939672.2939785, 2016. a, b
Chen, T., He, T., Benesty, M., Khotilovich, V., Tang, Y., Cho, H., Chen, K.,
Mitchell, R., Cano, I., Zhou, T., Li, M., Xie, J., Lin, M., Geng, Y., and Li,
Y.: xgboost: Extreme Gradient Boosting, available at:
https://cran.r-project.org/package=xgboost (last access: 13 January 2021), 2020. a
Chenard, J.-F. 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. a
Cho, K., Van Merriënboer, B., Gulcehre, C., Bahdanau, D., Bougares, F., Schwenk, H., and Bengio, Y.: Learning phrase representations using RNN
encoder-decoder for statistical machine translation, in: Proceedings
of the EMNLP 2014 – 2014 Conference on Empirical Methods in Natural Language Processing, 25–29 October 2014, Doha, Qatar, 1724–1734, https://doi.org/10.3115/v1/d14-1179, 2014. a, b
Claesen, M. and De Moor, B.: Hyperparameter Search in Machine Learning,
arXiv [preprint], arXiv:1502.02127 (last access: 4 December 2020), 2015. a
Crank, J. and Nicolson, P.: A practical method for numerical evaluation of
solutions of partial differential equations of the heat-conduction type,
Math. Proc. Cambridge, 43, 50–67, https://doi.org/10.1017/S0305004100023197, 1947. a
Crisp, D. and Howson, G.: Effect of air temperature upon mean water
temperature in streams in the north Pennines and English Lake District,
Freshwater Biol., 12, 359–367, https://doi.org/10.1111/j.1365-2427.1982.tb00629.x,
1982. a, b
Dallas, H.: Water temperature and riverine ecosystems: An overview of
knowledge and approaches for assessing biotic responses, with special
reference to South Africa, Water Sa, 34, 393–404, https://doi.org/10.4314/wsa.v34i3.180634, 2008. a
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. a
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. a, b, c, d
Dunn, O. J.: Multiple Comparisons Using Rank Sums, Technometrics, 6,
241–252, https://doi.org/10.1080/00401706.1964.10490181, 1964. a
Feigl, M.: MoritzFeigl/wateRtemp: HESS submission (Version v0.2.0), Zenodo, https://doi.org/10.5281/zenodo.4438575, 2021a. a, b
Feigl, M.: MoritzFeigl/ML_methods_for_stream_water_temperature_
prediction: HESS paper (Version v1.0), Zenodo, https://doi.org/10.5281/zenodo.4438582, 2021b. a
Fernández-Delgado, M., Cernadas, E., Barro, S., and Amorim, D.: Do we need hundreds of classifiers to solve real world classification problems?, J. Mach. Learn. Res., 15, 3133–3181, 2014. a
Freund, Y. and Schapire, R. E.: A decision-theoretic generalization of on-line learning and an application to boosting, in: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Springer Verlag, 23–37, https://doi.org/10.1007/3-540-59119-2_166, 1995. a
Friberg, N., DybkjÆr, J. B., Olafsson, J. S., Gislason, G. M., Larsen,
S. E., and Lauridsen, T. L.: Relationships between structure and function in
streams contrasting in temperature, Freshwater Biol., 54, 2051–2068,
https://doi.org/10.1111/j.1365-2427.2009.02234.x, 2009. a
Friedman, J. H.: Greedy function approximation: A gradient boosting machine, Ann. Stat., 29, 1189–1232, https://doi.org/10.1214/aos/1013203451, 2001. a
Friedman, J. H.: Stochastic gradient boosting, Comput. Stat. Data An., 38, 367–378, https://doi.org/10.1016/S0167-9473(01)00065-2, 2002. a
Gauch, M., Tang, R., Mai, J., Tolson, B., Gharari, S., and Lin, J.: Machine
Learning for Streamflow Prediction: Current Status and Future Prospects, 9–13 December 2019, San Francisco, USA,
AGU Fall Meeting Abstracts, 2019, H33L–2127, 2019. a
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. a
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. Manag., 28, 1379–1394,
https://doi.org/10.1007/s11269-014-0557-7, 2014. a, b, c
Haiden, T., Kann, A., Wittmann, C., Pistotnik, G., Bica, B., and Gruber, C.:
The integrated nowcasting through comprehensive analysis (INCA) system and
its validation over the Eastern Alpine region, Weather Forecast., 26,
166–183, https://doi.org/10.1175/2010WAF2222451.1, 2011. a
Haiden, T., Kann, A., and Pistotnik, G.: Nowcasting with INCA During
SNOW-V10, Pure Appl. Geophys., 171, 231–242,
https://doi.org/10.1007/s00024-012-0547-8, 2014. a
Hannah, D. M. and Garner, G.: River water temperature in the United Kingdom, Prog. Phys. Geog., 39, 68–92,
https://doi.org/10.1177/0309133314550669, 2015. a
Hannah, D. M., Webb, B. W., and Nobilis, F.: River and stream temperature:
dynamics, processes, models and implications, Hydrol. Process., 22,
899–901, https://doi.org/10.1002/hyp.6997, 2008. a
Hansen, L. K. and Salamon, P.: Neural Network Ensembles, IEEE T. Pattern Anal., 12, 993–1001,
https://doi.org/10.1109/34.58871, 1990. a
Harvey, R., Lye, L., Khan, A., and Paterson, R.: The influence of air
temperature on water temperature and the concentration of dissolved oxygen in
Newfoundland Rivers, Can. Water Resour. J., 36, 171–192,
https://doi.org/10.4296/cwrj3602849, 2011. a
He, J., Yang, K., Tang, W., Lu, H., Qin, J., Chen, Y., and Li, X.: The first
high-resolution meteorological forcing dataset for land process studies over
China, Scientific Data, 7, 25, https://doi.org/10.1038/s41597-020-0369-y, 2020. a
Heddam, S., Ptak, M., and Zhu, S.: Modelling of daily lake surface water
temperature from air temperature: Extremely randomized trees (ERT) versus
Air2Water, MARS, M5Tree, RF and MLPNN, J. Hydrol., 588, 125130,
https://doi.org/10.1016/j.jhydrol.2020.125130, 2020. a
Hersbach, H., Bell, B., Berrisford, P., Hirahara, S., Horányi, A.,
Muñoz-Sabater, J., Nicolas, J., Peubey, C., Radu, R., Schepers, D.,
Simmons, A., Soci, C., Abdalla, S., Abellan, X., Balsamo, G., Bechtold, P.,
Biavati, G., Bidlot, J., Bonavita, M., De Chiara, G., Dahlgren, P., Dee,
D., Diamantakis, M., Dragani, R., Flemming, J., Forbes, R., Fuentes, M.,
Geer, A., Haimberger, L., Healy, S., Hogan, R. J., Hólm, E.,
Janisková, M., Keeley, S., Laloyaux, P., Lopez, P., Lupu, C., Radnoti,
G., de Rosnay, P., Rozum, I., Vamborg, F., Villaume, S., and Thépaut,
J. N.: The ERA5 global reanalysis, Q. J. Roy. Meteor. Soc., 146, 1999–2049, https://doi.org/10.1002/qj.3803, 2020. a
Hiebl, J. and Frei, C.: Daily temperature grids for Austria since
1961 – concept, creation and applicability,
Theor. Appl. Climatol., 124, 161–178, https://doi.org/10.1007/s00704-015-1411-4, 2016. a
Hiebl, J. and Frei, C.: Daily precipitation grids for Austria since
1961 – development and evaluation of a spatial dataset for hydroclimatic
monitoring and modelling, Theor. Appl. Climatol., 132,
327–345, https://doi.org/10.1007/s00704-017-2093-x, 2018. a
Hinton, G. E., Srivastava, N., Krizhevsky, A., Sutskever, I., and
Salakhutdinov, R. R.: Improving neural networks by preventing co-adaptation
of feature detectors, arXiv [preprint], arXiv:1207.0580 (last access:
7 August 2020), 2012. a, b
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. a, b, c
Hsu, C.-W., Chang, C.-C., and Lin, C.-J.: A Practical Guide to Support Vector Classification, Tech. Rep., Taipei, 2003. a
Ibrahem Ahmed Osman, A., Najah Ahmed, A., Chow, M. F., Feng Huang, Y., and El-Shafie, A.: (2021). Extreme gradient boosting (xgboost) model to predict the groundwater levels in Selangor Malaysia, Ain Shams Engineering Journal, https://doi.org/10.1016/j.asej.2020.11.011, in press, 2021. a
Imholt, C., Gibbins, C. N., Malcolm, I. A., Langan, S., and Soulsby, C.:
Influence of riparian cover on stream temperatures and the growth of the
mayfly Baetis rhodani in an upland stream, Aquat. Ecol., 44, 669–678,
https://doi.org/10.1007/s10452-009-9305-0, 2010. a
Jackson, F. L., Fryer, R. J., Hannah, D. M., Millar, C. P., and Malcolm, I. A.: A spatio-temporal statistical model of maximum daily river temperatures to
inform the management of Scotland's Atlantic salmon rivers under climate
change, Sci. Total Environ., 612, 1543–1558,
https://doi.org/10.1016/j.scitotenv.2017.09.010, 2018. a, b, c
Johnson, M. F., Wilby, R. L., and Toone, J. A.: Inferring air-water
temperature relationships from river and catchment properties, Hydrol. Process., 28, 2912–2928, https://doi.org/10.1002/hyp.9842, 2014. a
Jones, D. R., Schonlau, M., and Welch, W. J.: Efficient Global Optimization of Expensive Black-Box Functions, J. Global Optim., 13, 455–492, https://doi.org/10.1023/A:1008306431147, 1998. a
Joslyn, K.: Water quality factor prediction using supervised machine learning
REU Final Reports, 6, available at:
https://archives.pdx.edu/ds/psu/26231 (last access: 26 May 2021), 2018. a
Kȩdra, M.: Regional Response to Global Warming: Water Temperature Trends in Semi-Natural Mountain River Systems, Water, 12, 283,
https://doi.org/10.3390/w12010283, 2020. a
Kennedy, J. and Eberhart, R.: Particle swarm optimization, in: Proceedings of ICNN'95 – International Conference on Neural Networks, Perth, Australia, 27 November–1 December 1995,
1942–1948, https://doi.org/10.1109/ICNN.1995.488968, 1995. a
Klambauer, G., Unterthiner, T., Mayr, A., and Hochreiter, S.: Self-normalizing neural networks, arXiv [preprint], arXiv:1706.02515,
(last access: 3 August 2020), 2017. a
Kling, H., Stanzel, P., Fuchs, M., and Nachtnebel, H.-P.: Performance of the
COSERO precipitation–runoff model under non-stationary conditions in basins
with different climates, Hydrolog. Sci. J., 60, 1374–1393,
https://doi.org/10.1080/02626667.2014.959956, 2015. a
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. a, b
Kratzert, F., Klotz, D., Shalev, G., Klambauer, G., Hochreiter, S., and Nearing, G.: Towards learning universal, regional, and local hydrological behaviors via machine learning applied to large-sample datasets, Hydrol. Earth Syst. Sci., 23, 5089–5110, https://doi.org/10.5194/hess-23-5089-2019, 2019. a, b
Kruskal, W. H. and Wallis, W. A.: Use of Ranks in One-Criterion Variance
Analysis, J. Am. Stat. Assoc., 47, 583–621,
https://doi.org/10.1080/01621459.1952.10483441, 1952. a
Kuhn, M.: caret: Classification and Regression Training, R package version 6.0-86, available at: https://CRAN.R-project.org/package=caret (last access: 13 Jaunary 2021), 2020. a
Kushner, H. J.: A new method of locating the maximum point of an arbitrary
multipeak curve in the presence of noise, J. Fluid. Eng.-T. ASME, 86, 97–106, https://doi.org/10.1115/1.3653121, 1964. a, b
Laizé, C. L., Acreman, M. C., Schneider, C., Dunbar, M. J.,
Houghton-Carr, H. A., Flörke, M., and Hannah, D. M.: Projected flow
alteration and ecological risk for pan-European rivers, River Res. Appl., 30, 299–314, https://doi.org/10.1002/rra.2645, 2014. a
Li, H., Deng, X., Kim, D.-Y., and Smith, E. P.: Modeling maximum daily
temperature using a varying coefficient regression model, Water Resour. Res., 50, 3073–3087, https://doi.org/10.1002/2013WR014243, 2014. a, b, c
Li, W., Kiaghadi, A., and Dawson, C.: High temporal resolution
rainfall–runoff modeling using long-short-term-memory (LSTM) networks,
Neural Comput. Appl., 33, 1261–1278, https://doi.org/10.1007/s00521-020-05010-6, 2020. a, b
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. a
Mackey, A. P. and Berrie, A. D.: The prediction of water temperatures in chalk streams from air temperatures, Hydrobiologia, 210, 183–189,
https://doi.org/10.1007/BF00034676, 1991. a, b
McGlynn, B. L., McDonnell, J. J., Seibert, J., and Kendall, C.: Scale effects on headwater catchment runoff timing, flow sources, and
groundwater-streamflow relations, Water Resour. Res., 40, W07504,
https://doi.org/10.1029/2003WR002494, 2004. a
McKenna, J. E., Butryn, R. S., and McDonald, R. P.: Summer Stream Water
Temperature Models for Great Lakes Streams: New York, T. Am. Fish. Soc., 139, 1399–1414, https://doi.org/10.1577/t09-153.1, 2010. a
Močkus, J.: On Bayesian Methods for Seeking the Extremum, in:
Optimization Techniques IFIP Technical Conference, Novosibirsk, 1–7 July 1974, 400–404,
https://doi.org/10.1007/978-3-662-38527-2_55, 1975. a, b
Močkus, J.: Bayesian Approach to Global Optimization, Mathematics and Its Applications Series, Springer Netherlands, Dordrecht, The Netherlands, 270 pp., https://doi.org/10.1007/978-94-009-0909-0, 1989. a, b
Močkus, J., Tiesis, V., and Zilinskas, A.: The application of Bayesian methods for seeking the extremum, Towards global optimization, 2, 117–129, https://doi.org/10.1007/978-94-009-0909-0_8, 1978. a, b
Mohseni, O. and Stefan, H. G.: Stream temperature/air temperature
relationship: A physical interpretation, J. Hydrol., 218,
128–141, https://doi.org/10.1016/S0022-1694(99)00034-7, 1999. a, b
Nash, J. and Sutcliffe, J.: 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. a
Neumann, D. W., Rajagopalan, B., and Zagona, E. A.: Regression model for daily maximum stream temperature, J. Environ. Eng., 129,
667–674, https://doi.org/10.1061/(ASCE)0733-9372(2003)129:7(667), 2003. a
Ni, L., Wang, D., Wu, J., Wang, Y., Tao, Y., Zhang, J., and Liu, J.:
Streamflow forecasting using extreme gradient boosting model coupled with
Gaussian mixture model, J. Hydrol., 586, 124901,
https://doi.org/10.1016/j.jhydrol.2020.124901, 2020. a
Nielsen, D.: Tree Boosting With XGBoost: Why does XGBoost win every machine
learning competition?, Master's Thesis, Norwegian University of Science and
Technology, Norway, 98 pp., 2016. a
Pedersen, N. L. and Sand-Jensen, K.: Temperature in lowland Danish streams:
contemporary patterns, empirical models and future scenarios, Hydrol. Process., 21, 348–358, https://doi.org/10.1002/hyp.6237, 2007. a
Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R.
Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M., and Duchesnay, E.: Scikit-learn: Machine Learning in Python, Tech. Rep., available at: https://hal.inria.fr/hal-00650905v2 (last access: 4 December 2020), 2011. a
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. a, b, c
Pinkus, A.: Approximation theory of the MLP model in neural networks,
Acta Numer., 8, 143–195, https://doi.org/10.1017/S0962492900002919, 1999. a
Piotrowski, A. P. and Napiorkowski, J. J.: Performance of the air2stream model that relates air and stream water temperatures depends on the calibration method, J. Hydrol., 561, 395–412,
https://doi.org/10.1016/j.jhydrol.2018.04.016, 2018. a, b, c
Piotrowski, A. P. and Napiorkowski, J. J.: Simple modifications of the
nonlinear regression stream temperature model for daily data, J. Hydrol., 572, 308–328, https://doi.org/10.1016/j.jhydrol.2019.02.035, 2019. a, b, c, d
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. a
R Core Team: A Language and Environment for Statistical Computing, R
Foundation for Statistical Computing, Vienna, Austria, available at:
https://www.r-project.org/ (last access: 13 January 2021), 2020. a
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. a, b
Razafimaharo, C., Krähenmann, S., Höpp, S., Rauthe, M., and
Deutschländer, T.: New high-resolution gridded dataset of daily mean,
minimum, and maximum temperature and relative humidity for Central Europe
(HYRAS), Theor. Appl. Climatol., 142, 1531–1553,
https://doi.org/10.1007/s00704-020-03388-w, 2020. a
Reichstein, M., Camps-Valls, G., Stevens, B., Jung, M., Denzler, J.,
Carvalhais, N., and Prabhat: Deep learning and process understanding for
data-driven Earth system science, Nature, 566, 195–204,
https://doi.org/10.1038/s41586-019-0912-1, 2019. a
Risley, J. C., Roehl Jr., E. A., and Conrads, P. A.: Estimating Water
Temperatures in Small Streams in Estimating Water Temperatures in Small
Streams in Western Oregon Using Neural Network Models, Tech. Rep., USGS
Water- Resources Investigation Report 02-4218, https://doi.org/10.3133/wri024218,
2003. a
Rumelhart, D. E., Hinton, G. E., and Williams, R. J.: Learning representations by back-propagating errors, Nature, 323, 533–536, https://doi.org/10.1038/323533a0, 1986. a
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. a, b
Sand-Jensen, K. and Pedersen, N. L.: Differences in temperature, organic
carbon and oxygen consumption among lowland streams, Freshwater Biol., 50,
1927–1937, https://doi.org/10.1111/j.1365-2427.2005.01436.x, 2005. a
Schapire, R. E.: The Strength of Weak Learnability, Mach. Learn., 5,
197–227, https://doi.org/10.1023/A:1022648800760, 1990. a
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. a, b
Shank, D. B., Hoogenboom, G., and McClendon, R. W.: Dewpoint temperature
prediction using artificial neural networks,
J. Appl. Meteorol. Clim., 47, 1757–1769, https://doi.org/10.1175/2007JAMC1693.1, 2008. a
Smith, K.: The prediction of river water temperatures,
Hydrol. Sci. B., 26, 19–32, https://doi.org/10.1080/02626668109490859, 1981. a, b
Snoek, J., Larochelle, H., and Adams, R. P. (2012). Practical bayesian optimization of machine learning algorithms, arXiv [preprint], arXiv:1206.2944 (last access: 6 August 2020), 2012. a
Sohrabi, M. M., Benjankar, R., Tonina, D., Wenger, S. J., and Isaak, D. J.:
Estimation of daily stream water temperatures with a Bayesian regression
approach, Hydrol. Process., 31, 1719–1733, https://doi.org/10.1002/hyp.11139,
2017. a
Srinivas, N., Krause, A., Kakade, S. M., and Seeger, M.: Gaussian Process
Optimization in the Bandit Setting: No Regret and Experimental Design,
IEEE T. Inform. Theory, 58, 3250–3265,
https://doi.org/10.1109/TIT.2011.2182033, 2009. a
Srivastava, N., Hinton, G., Krizhevsky, A., and Salakhutdinov, R.: Dropout: A Simple Way to Prevent Neural Networks from Overfitting, Tech. Rep., 15, 1929-−1958, available at: http://jmlr.org/papers/v15/srivastava14a.html (last access: 7 August 2020), 2014. a
Stajkowski, S., Kumar, D., Samui, P., Bonakdari, H., and Gharabaghi, B.:
Genetic-algorithm-optimized sequential model for water temperature
prediction, Sustainability-Basel, 12, 5374, https://doi.org/10.3390/su12135374,
2020. a
Stefan, H. G. and Preud'homme, E. B.: Stream temperature estimation from air
temperature, J. Am. Water Resour. As., 29, 27–45, https://doi.org/10.1111/j.1752-1688.1993.tb01502.x, 1993. a, b
Stevens, H., Ficke, J., and Smoot, G.: Techniques of water-resources
investigations of the US Geological Survey, US Government Printing
Office, Washington, 65 pp., 1975. a
Tavares, M. H., Cunha, A. H. F., Motta-Marques, D., Ruhoff, A. L., Fragoso,
C. R., Munar, A. M., and Bonnet, M. P.: Derivation of consistent, continuous
daily river temperature data series by combining remote sensing and water
temperature models, Remote Sens. Environ., 241, 111721,
https://doi.org/10.1016/j.rse.2020.111721, 2020. a, b
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. a, b
Thornton, M. M., Shrestha, R., Wei, Y., Thornton, P. E., Kao, S., and Wilson, B. E.: Daymet: Daily Surface Weather Data on a 1-km Grid for North America, Version 4, ORNL DAAC, Oak Ridge, Tennessee, USA, https://doi.org/10.3334/ORNLDAAC/1840, 2020. a
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. a, b, c
Trinh, N. X., Trinh, T. Q., Phan, T. P., Thanh, T. N., and Thanh, B. N.: Water Temperature Prediction Models in Northern Coastal Area, Vietnam, Asian Review of Environmental and Earth Sciences, 6, 1–8,
https://doi.org/10.20448/journal.506.2019.61.1.8, 2019. a, b
Van Vliet, M. T., Franssen, W. H., Yearsley, J. R., Ludwig, F., Haddeland,
I., Lettenmaier, D. P., and Kabat, P.: Global river discharge and water
temperature under climate change, Global Environ. Chang., 23, 450–464,
https://doi.org/10.1016/j.gloenvcha.2012.11.002, 2013. a
Webb, B. W. and Zhang, Y.: Spatial and seasonal variability in the components of the river heat budget, Hydrol. Process., 11, 79–101,
https://doi.org/10.1002/(sici)1099-1085(199701)11:1<79::aid-hyp404>3.0.co;2-n, 1997. a
Webb, B. W., Clack, P. D., and Walling, D. E.: Water-air temperature
relationships in a Devon river system and the role of flow, Hydrol. Process., 17, 3069–3084, https://doi.org/10.1002/hyp.1280, 2003. a
Webb, B. W., Hannah, D. M., Moore, R. D., Brown, L. E., and Nobilis, F.:
Recent advances in stream and river temperature research, 22, 902–918
https://doi.org/10.1002/hyp.6994, 2008. a
Wenger, S. J., Isaak, D. J., Dunham, J. B., Fausch, K. D., Luce, C. H.,
Neville, H. M., Rieman, B. E., Young, M. K., Nagel, D. E., Horan, D. L., and
Chandler, G. L.: Role of climate and invasive species in structuring trout
distributions in the interior Columbia River Basin, USA,
Can. J. Fish. Aquat. Sci., 68, 988–1008, https://doi.org/10.1139/f2011-034, 2011. a
Werner, A. T., Schnorbus, M. A., Shrestha, R. R., Cannon, A. J., Zwiers, F. W., Dayon, G., and Anslow, F.: A long-term, temporally consistent, gridded daily meteorological dataset for northwestern North America, Scientific Data, 6, 180299, https://doi.org/10.1038/sdata.2018.299, 2019. a
White, B. W. and Rosenblatt, F.: Principles of Neurodynamics: Perceptrons and the Theory of Brain Mechanisms, Am. J. Psychol., 76, 705–707, https://doi.org/10.2307/1419730, 1963. a, b
Wickham, H.: ggplot2: Elegant Graphics for Data Analysis, Springer-Verlag, New York, USA, available at: https://ggplot2.tidyverse.org (last access: 7 August 2020), 2016. a
Willmott, C. J.: On the validation of models, Phys. Geogr., 2,
184–194, https://doi.org/10.1080/02723646.1981.10642213, 1981. a
Xiang, Z., Yan, J., and Demir, I.: A Rainfall‐Runoff Model With LSTM‐Based
Sequence‐to‐Sequence Learning, Water Resour. Res., 56, e2019WR02532,
https://doi.org/10.1029/2019WR025326, 2020. a, b
Yang, D. and Peterson, A.: River water temperature in relation to local air
temperature in the Mackenzie and Yukon basins, Arctic, 70, 47–58,
https://doi.org/10.14430/arctic4627, 2017. a, b
Yazidi, A., Goyal, R., Paes, A., Gruber, N., De, N. G., and Jockisch, A.: Are GRU Cells More Specific and LSTM Cells More Sensitive in Motive
Classification of Text?, Front. Artif. Intell., 3, 40, https://doi.org/10.3389/frai.2020.00040, 2020. a
Zentralanstalt für Meteorologie und Geodynamik: ZAMG homepage, available at: https://www.zamg.ac.at, last access: 26 May 2021. a
Zhilinskas, A. G.: Single-step Bayesian search method for an extremum of
functions of a single variable, Cybernetics, 11, 160–166,
https://doi.org/10.1007/BF01069961, 1975. a, b
Zhu, S. and Piotrowski, A. P.: River/stream water temperature forecasting
using artificial intelligence models: a systematic review, Acta Geophysica, 1–10, Springer,
https://doi.org/10.1007/s11600-020-00480-7, 2020. a
Zhu, S., Nyarko, E. K., and Hadzima-Nyarko, M.: Modelling daily water
temperature from air temperature for the Missouri River, PeerJ, 6, e4894,
https://doi.org/10.7717/peerj.4894, 2018. a, b, c, d
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. R., 26, 12622–12630,
https://doi.org/10.1007/s11356-019-04716-y, 2019a. a
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. R., 26, 402–420,
https://doi.org/10.1007/s11356-018-3650-2, 2019b.
a, b
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,
2019c. a
Short summary
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.
In this study we developed machine learning approaches for daily river water temperature...
