A Structural Overview through GR(s) Models Characteristics for Better Yearly Runoff Simulation


In rainfall-runoff modelling, a monthly timescale and an annual one are sufficient for the management of deductions. However, to simulate the flow at a large time-step (annual), we generally precede the use of a model working for a finer time-step (daily) while aggregating the desired outputs. The finest time-steps are considered, apriori, as the most performant. By passing from one time-step to another, and in order to work in the desired time-step (annual) and calculate the potential gains or loss, this article proposed a comparative study between the aggregation method of outputs of a modal working at a finer time step, and a method in which we use a conceived model from the beginning. To ensure this comparative and empirical approach, the choice has been focused on (GRs) models to a daily time-step (GR4J), monthly time step (GR2M) and annual time step (GR1A). The modelling platform used is the same for all three models taking into account the specificities of each one: the same data sample, the same optimization method, and the same function criterion are used during the construction of these models. Due to the moving between these time steps, results show that the best way to simulate the annual flow is to use an appropriate and designed modal initially conceived to this time step. Indeed, this simulation seems to be less effective when using a model at a finer time-step (daily).

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S. Mouelhi, K. Madani and F. Lebdi, "A Structural Overview through GR(s) Models Characteristics for Better Yearly Runoff Simulation," Open Journal of Modern Hydrology, Vol. 3 No. 4, 2013, pp. 179-187. doi: 10.4236/ojmh.2013.34022.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] K. J. Beven and M. J. Kirkby, “A Physically Based, Variable Contributing Area Model of Basin Hydrology,” Hydrological Sciences Bulletin, Vol. 24, No. 1, 1979, pp. 43-69. http://dx.doi.org/10.1080/02626667909491834
[2] H. A. Thomas, “Improved Methods for Rational Water Assessment,” Water Resources Council, Washington DC, 1981.
[3] P. C. D. Milly, “Climate, Interseasonal Storage of Soil Water, and the Annual Water Balance,” Water Resources Research, Vol. 17, No. 1-2, 1994, pp. 19-24. http://dx.doi.org/10.1029/94WR00586
[4] C. Y. Xu and G. L. Vandewiele, “Parsimonious Monthly Rainfall-Runoff Models for Humid Basins with Different Input Requirements,” Advances in Water Resources, Vol. 18, No. 1, 1995, pp. 39-48.
[5] S. Bergstrom, “The HBV Model,” In: V. P. Singh, Ed., Computer Models in Watershed Modeling, Water Resources Publications, Highlands Ranch, Colorado, 1995, pp. 443-476.
[6] C. Perrin, C. Michel and V. Andréassian, “Improvement of a Parsimonious Model for Streamflow Simulation,” Journal of Hydrology, Vol. 279, No. 1, 2003, pp. 275-289. http://dx.doi.org/10.1016/S0022-1694(03)00225-7
[7] T. Mathevet, “Which Global Rainfall-Runoff Models in an Hourly Time Step? Development and Empirical Comparison of Models on a Large Sample of Watersheds,” Ph.D. Thesis, AgrosParisTech (Ex. ENGREF), 2005, 463 p.
[8] S. Mouelhi, C. Michel, C. Perrin and V. Andréassian, “Stepwise Development of a Two-Parameter Monthly Water Balance Model,” Journal of Hydrology, Vol. 318, No. 1-4, 2006, pp. 200-214. http://dx.doi.org/10.1016/j.jhydrol.2005.06.014
[9] S. Mouelhi, C. Michel, C. Perrin and V. Andréassian, “Linking Stream Flow to Rainfall at the Annual Time Step: The Manabe Bucket Model Revisited,” Journal of Hydrology, Vol. 328, No. 1-2, 2006, pp. 283-296. http://dx.doi.org/10.1016/j.jhydrol.2005.12.022
[10] D. A. Hughes, “Variable Time Intervals in Deterministic Hydrological Models,” Journal of Hydrology, Vol. 143, No. 3-4, 1993, pp. 217-232. http://dx.doi.org/10.1016/0022-1694(93)90193-D
[11] I. Nalbantis, “Use of Multiple-Time-Step Information in Rainfall-Runoff Modeling,” Journal of Hydrology, Vol. 165, No. 1, 1995, pp. 135-159. http://dx.doi.org/10.1016/0022-1694(94)02567-U
[12] D. Kavetski, G. Kuczera and S. W. Franks, “Semidistributed Hydrological Modeling: A ‘Saturation Path’ Perspective on TOPMODEL and VIC,” Water Resources Research, Vol. 39, No. 9, 2003, p. 1246. http://dx.doi.org/10.1029/2003WR002122
[13] I. Haddleland, D. P. Lettenmaier and T. Skaugen, “Reconciling Simulated Moisture Fluxes Resulting from Alternate Hydrologic Model Time Steps and Energy Budget Closure Assumptions,” American Meteorological Society, Vol. 7, No. 3, 2006, pp. 355-370.
[14] I. G. Littlewood and B. F. W. Croke, “Data Time-Step Dependency of Conceptual Rainfall—Stream Flow Model Parameters: An Empirical Study with Implications for Regionalization,” Hydrological Sciences Journal, Vol. 53, No. 4, 2008, pp. 685-695. http://dx.doi.org/10.1623/hysj.53.4.685
[15] H. Kling and H. P. Nachtnebel, “A Spatiotemporal Comparison of Water Balance Modeling in an Alpine Catchment,” Hydrological Processes, Vol. 23, No. 7, 2009, pp. 997-1009. http://dx.doi.org/10.1002/hyp.7207
[16] E. Widen-Nilsson, L. Gong, S. Halldin and C.-Y. Xu, “Model Performance and Parameter Behavior for Varying Time Aggregations and Evaluation Criteria in the WAS-MOD-M Global Water Balance Model,” Water Resources Research, Vol. 45, No. 5, 2009, 14 p. http://dx.doi.org/10.1029/2007WR006695
[17] M. P. Clark and D. Kavetski, “Ancient Numerical Daemons of Conceptual Hydrological Modeling: 1. Fidelity and Efficiency of Time Stepping Schemes,” Water Resources Research, Vol. 46, No. 10, 2010, 23 p. http://dx.doi.org/10.1029/2009WR008894
[18] C. Michel, “What Can We Do in Hydrology with a Conceptual Model with One Parameter?” La Houille Blanche, No. 1, 1983, pp. 39-44.
[19] Edijatno and C. Michel, “A Rainfall Runoff Model with Three Parameters,” La Houille Blanche, No. 2, 1989, pp. 113-121.
[20] Edijatno, “Development of a Basic Rainfall-Runoff Model to Daily Time,” Ph.D. Thesis, Louis Pasteur University/ENGEES, Strasbourg, 1991.
[21] Edijatno, N. O. Nascimento, X. Yang, Z. Makhlouf and C. Michel, “A Daily Watershes Model with Three Free Parameters,” Hydrological Sciences Journal, Vol. 44, No. 2, 1999, pp. 263-277. http://dx.doi.org/10.1080/02626669909492221
[22] Y. Rakem, “Critical Analysis and Mathematical Reformulation of Empirical Rainfall-Runoff (GR4J) Model,” Ph.D. Thesis, Ecole Nationale des Ponts et Chaussées, Paris, 1999.
[23] C. Perrin, “To an Improvement of a Lumped Rainfall-Runoff Model through a Comparative Approach,” Ph.D. Thesis, Institut National Polytechnique de Gronoble, Gronoble, 2000.
[24] C. Perrin, C. Michel and V. Andréassian, “Improvement of a Parsimonious Model for Streamflow Simulation,” Journal of Hydrology, Vol. 279, No. 1, 2003, pp. 275-289. http://dx.doi.org/10.1016/S0022-1694(03)00225-7
[25] Edijatno, “Improvement of a Simple Rainfall Runoff Model at a Daily Time Step on Small Watersheds,” Master Report, Cemagref Publication, 1987, 45 p.
[26] M. Kabouya, “Rainfall—Runoff Modeling at Monthly and Annual Time Step in Northern Algeria,” Ph.D. Thesis, Université Paris Sud, Laboratoire d’Hydrologie et de Géochimie Isotopique d’ORSAY, Paris, 1990, 374 p.
[27] M. Kabouya and C. Michel, “Estimation of Surface Water Resources at Monthly and Annual Time Step, Application to a Semi-Arid Country,” Revue des Sciences de l’Eau, Vol. 4, No. 4, 1991, pp. 569-587. http://dx.doi.org/10.7202/705116ar
[28] Z. Makhlouf, “Supplements on the GR4J Rainfall-Runoff Model and Estimation of Its Parameters,” Ph.D. Thesis, Paris XI Orsay, Cemagref, 1993.
[29] Z. Makhlouf and C. Michel, “A Two-Parameter Monthly Water Balance Model for Frensh Watersheds,” Journal of Hydrology, Vol. 162, No. 3-4, 1994, pp. 199-318. http://dx.doi.org/10.1016/0022-1694(94)90233-X
[30] N. O. Nascimento, “Assessment Using an Empirical Model of Human Actions Affect on the Rainfall-Runoff Relationship in Watershed Scale,” Ph.D. Thesis, ENPC, Paris, 1995.
[31] S. Mouelhi, “Towards a Coherent Chain of Global Conceptual Rainfall-Runoff Models at Multiyear, Yearly, Monthly and Daily Time Steps,” Ph.D. Thesis, Ecole Nationale du Génie Rural, des Eaux et Forêts, Paris, 2003.
[32] V. Andréassian, “Impacts of Forest Cover Change on the Hydrological Behavior of Watersheds,” Ph.D. Thesis, Université de Pierre et Marie Curie Paris VI, Paris, 2002.
[33] V. Andréassian, C. Perrin, C. Michel, I. Usart-Sanchez and J. Lavabre, “Impact of Imperfect Rainfall Knowledge on the Efficiency and the Parameters of Watershed Models,” Journal of Hydrology, Vol. 250, No. 1, 2001, pp. 206-223. http://dx.doi.org/10.1016/S0022-1694(01)00437-1
[34] C. Perrin, L. oudin, V. Andreassian, C. Rojas-Serna, C. Michel and T. Mathevet, “Impact of Limited Streamflow Data on the Efficiency and the Parameters of Rainfall—Runoff Models,” Hydrological Sciences Journal, Vol. 52, No. 1, 2007, pp. 131-151. http://dx.doi.org/10.1623/hysj.52.1.131
[35] B. Ambroise, J. L. Perrin and D. Reutenauer, “Multicriterian Validation of a Semi-Distributed Conceptual Model of the Water Cycle in the Fecht Catchment (Vosges Massif, France),” Water Resources Research, Vol. 31, No. 6, 1995, pp. 1467-1481. http://dx.doi.org/10.1029/94WR03293
[36] F. H. S. Chiew, M. J. Stewardson and T. A. McMahon, “Comparison of Six Rainfall-Runoff Modeling Approaches,” Journal of Hydrology, Vol. 147, No. 1-4, 1993, pp. 1-36. http://dx.doi.org/10.1016/0022-1694(93)90073-I
[37] J. E. Nash and J. V. Sutcliffe, “River Flow Forecasting Through Conceptual Models. Part I—A Discussion of Priciples,” Journal of Hydrology, Vol. 27, No. 3, 1970, pp. 282-290. http://dx.doi.org/10.1016/0022-1694(70)90255-6
[38] E. Servat, A. Dezetter and J. M. Lapetite, “Study and Selection of Calibration Criteria of Rainfall-Runoff Models,” IRD (ex. ORSTOM), Note 2, Programme ERREAU, IRD Publication, Montpellier, 1989.
[39] V. Klemes, “Operational Testing of Hydrological Simulation Models,” Journal of Hydrological Sciences, Vol. 31, No. 1, 1986, pp. 13-24. http://dx.doi.org/10.1080/02626668609491024

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