On the Calibration of Multigene Genetic Programming to Simulate Low Flows in the Moselle River

401 131


The aim of this paper is to calibrate a data-driven model to simulate Moselle River flows and compare the performance with three different hydrologic models from a previous study. For consistency a similar set up and error metric are used to evaluate the model results. Precipitation, potential evapotranspiration and streamflow from previous day have been used as inputs. Based on the calibration and validation results, the proposed multigene genetic programming model is the best performing model among four models. The timing and the magnitude of extreme low flow events could be captured even when we use root mean squared error as the objective function for model calibration. Although the model is developed and calibrated for Moselle River flows, the multigene genetic algorithm offers a great opportunity for hydrologic prediction and forecast problems in the river basins with scarce data issues.


Low flows, calibration, genetic programming, ANN, HBV and GR4J

Full Text:



Arsenault, R., Poulin, A., Côté, P., Brissette, F., 2014. Comparison of Stochastic Optimization Algorithms in Hydrological Model Calibration. J. Hydrol. Eng. 19, 1374–1384. doi:10.1061/(ASCE)HE.1943-5584.0000938

Danandeh Mehr, A., Kahya, E., Olyaie, E., 2013. Streamflow prediction using linear genetic programming in comparison with a neuro-wavelet technique. J. Hydrol. 505, 240–249. doi:10.1016/j.jhydrol.2013.10.003

Demirel, M.C., Booij, M.J., Hoekstra, A.Y., 2015. The skill of seasonal ensemble low-flow forecasts in the Moselle River for three different hydrological models. Hydrol. Earth Syst. Sci. 19, 275–291. doi:10.5194/hess-19-275-2015

Demirel, M.C., Booij, M.J., Hoekstra, A.Y., 2013a. Impacts of climate change on the seasonality of low flows in 134 catchments in the River Rhine basin using an ensemble of bias-corrected regional climate simulations. Hydrol. Earth Syst. Sci. 17, 4241–4257. doi:10.5194/hess-17-4241-2013

Demirel, M.C., Booij, M.J., Hoekstra, A.Y., 2013b. Effect of different uncertainty sources on the skill of 10 day ensemble low flow forecasts for two hydrological models. Water Resour. Res. 49, 4035–4053. doi:10.1002/wrcr.20294

Demirel, M.C., Venancio, A., Kahya, E., 2009. Flow forecast by SWAT model and ANN in Pracana basin, Portugal. Adv. Eng. Softw. 40, 467–473. doi:10.1016/j.advengsoft.2008.08.002

Duan, Q.Y., Gupta, V.K., Sorooshian, S., 1993. Shuffled complex evolution approach for effective and efficient global minimization. J. Optim. Theory Appl. 76, 501–521. doi:10.1007/BF00939380

Gandomi, A.H., Alavi, A.H., 2012. A new multi-gene genetic programming approach to nonlinear system modeling. Part I: materials and structural engineering problems. Neural Comput. Appl. 21, 171–187. doi:10.1007/s00521-011-0734-z

Ghorbani, M.A., Khatibi, R., Aytek, A., Makarynskyy, O., Shiri, J., 2010. Sea water level forecasting using genetic programming and comparing the performance with Artificial Neural Networks. Comput. Geosci. 36, 620–627. doi:10.1016/j.cageo.2009.09.014

Griffin, D., Anchukaitis, K.J., 2014. How unusual is the 2012-2014 California drought? Geophys. Res. Lett. 41, 9017–9023. doi:10.1002/2014GL062433

Gupta, H. V, Kling, H., Yilmaz, K.K., Martinez, G.F., 2009. Decomposition of the mean squared error and NSE performance criteria: Implications for improving hydrological modelling. J. Hydrol. 377, 80–91. doi:10.1016/j.jhydrol.2009.08.003

Guven, A., 2009. Linear genetic programming for time-series modelling of daily flow rate. J. Earth Syst. Sci. 118, 137–146. doi:10.1007/s12040-009-0022-9

Hansen, N., Ostermeier, A., 2001. Completely Derandomized Self-Adaptation in Evolution Strategies. Evol. Comput. 9, 159–195. doi:10.1162/106365601750190398

Hesami, A.M., Sorman, A., Yilmaz, M., 2016. Conditional Copula-Based Spatial–Temporal Drought Characteristics Analysis—A Case Study over Turkey. Water 8, 426. doi:10.3390/w8100426

Khan, M., Azamathulla, H.M., Tufail, M., 2012. Gene-expression programming to predict pier scour depth using laboratory data. J. Hydroinformatics 14, 628. doi:10.2166/hydro.2011.008

Koza, J.R., 1992. Genetic Programming: On the Programming of Computers by means of Natural Selection. MIT Press, Cambridge, MA.

Livneh, B., Kumar, R., Samaniego, L., 2015. Influence of soil textural properties on hydrologic fluxes in the Mississippi river basin. Hydrol. Process. 29, 4638–4655. doi:10.1002/hyp.10601

Madadgar, S., Afshar, A., 2009. An Improved Continuous Ant Algorithm for Optimization of Water Resources Problems. Water Resour. Manag. 23, 2119–2139. doi:10.1007/s11269-008-9373-2

Madsen, H., 2000. Automatic calibration of a conceptual rainfall-runoff model using multiple objectives. J. Hydrol. 235, 276–288. doi:10.1016/S0022-1694(00)00279-1

Nash, J.E., Sutcliffe, J.V., 1970. River flow forecasting through conceptual models part I — A discussion of principles. J. Hydrol. 10, 282–290. doi:10.1016/0022-1694(70)90255-6

Nicolle, P., Pushpalatha, R., Perrin, C., François, D., Thiéry, D., Mathevet, T., Le Lay, M., Besson, F., Soubeyroux, J.-M., Viel, C., Regimbeau, F., Andréassian, V., Maugis, P., Augeard, B., Morice, E., 2014. Benchmarking hydrological models for low-flow simulation and forecasting on French catchments. Hydrol. Earth Syst. Sci. 18, 2829–2857. doi:10.5194/hess-18-2829-2014

Nourani, V., Komasi, M., Mano, A., 2009. A Multivariate ANN-Wavelet Approach for Rainfall–Runoff Modeling. Water Resour. Manag. 23, 2877–2894. doi:10.1007/s11269-009-9414-5

Pal, I., Towler, E., Livneh, B., 2015. How Can We Better Understand Low River Flows as Climate Changes? Eos (Washington. DC). 96. doi:10.1029/2015EO033875

Poli, R., Langdon, W.B., McPhee, N.F., 2008. A Field guide to genetic programming. Published via http://lulu.com and freely available at http://www.gp-field-guide.org.uk, (With contributions by J. R. Koza).

Pushpalatha, R., Perrin, C., Le Moine, N., Mathevet, T., Andréassian, V., 2011. A downward structural sensitivity analysis of hydrological models to improve low-flow simulation. J. Hydrol. 411, 66–76. doi:10.1016/j.jhydrol.2011.09.034

Pushpalatha, R., Perrin, C., Moine, N. Le, Andréassian, V., 2012. A review of efficiency criteria suitable for evaluating low-flow simulations. J. Hydrol. 420–421, 171–182. doi:10.1016/j.jhydrol.2011.11.055

Roushangar, K., Mouaze, D., Shiri, J., 2014. Evaluation of genetic programming-based models for simulating friction factor in alluvial channels. J. Hydrol. 517, 1154–1161. doi:10.1016/j.jhydrol.2014.06.047

Samaniego, L., Kumar, R., Attinger, S., 2010. Multiscale parameter regionalization of a grid-based hydrologic model at the mesoscale. Water Resour. Res. 46, W05523. doi:10.1029/2008WR007327

Sattar, A.M.A., Gharabaghi, B., 2015. Gene expression models for prediction of longitudinal dispersion coefficient in streams. J. Hydrol. 524, 587–596. doi:10.1016/j.jhydrol.2015.03.016

Searson, D. P., Leahy, D. E., Willis, M.J., 2010. GPTIPS: an open source genetic programming toolbox for multigene symbolic regression, in: In Proceedings of the International Multi Conference of Engineers and Computer Scientists. p. Vol. 1, 77-80.

Searson, D., 2015. GPTIPS 2: an open-source software platform for symbolic data mining., in: Al., A.H.G. et (Ed.), Chapter 22 in Handbook of Genetic Programming Applications. Springer, New York, NY.

Searson, D., 2009. GPTIPS: Genetic Programming & Symbolic Regression for MATLAB [WWW Document]. URL http://gptips.sourceforge.net.

Smakhtin, V.U., 2001. Low flow hydrology: a review. J. Hydrol. 240, 147–186.

Tian, Y., Booij, M.J., Xu, Y.-P., 2014. Uncertainty in high and low flows due to model structure and parameter errors. Stoch. Environ. Res. Risk Assess. 28, 319–332. doi:10.1007/s00477-013-0751-9

Uyumaz, A., Danandeh Mehr, A., Kahya, E., Erdem, H., 2014. Rectangular side weirs discharge coefficient estimation in circular channels using linear genetic programming approach. J. Hydroinformatics 16, 1318. doi:10.2166/hydro.2014.112

Vormoor, K., Lawrence, D., Heistermann, M., Bronstert, A., 2015. Climate change impacts on the seasonality and generation processes of floods – projections and uncertainties for catchments with mixed snowmelt/rainfall regimes. Hydrol. Earth Syst. Sci. 19, 913–931. doi:10.5194/hess-19-913-2015

Zhang, X., Booij, M.J., Xu, Y.-P.Y.-P., 2015. Improved simulation of peak flows under climate change: Postprocessing or composite objective calibration? J. Hydrometeorol. 16, 2187–2208. doi:10.1175/JHM-D-14-0218.1

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.