Relationship Between Calibration Time and Final Performance of Conceptual Rainfall-Runoff Models

Adam P Piotrowski,Jaroslaw J Napiorkowski,Marzena Osuch

doi:10.1007/s11269-018-2085-3

Adam P Piotrowski, Jaroslaw J Napiorkowski + Show 1 more

Open Access

https://doi.org/10.1007/s11269-018-2085-3

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Abstract

Various methods are used in the literature for calibration of conceptual rainfall-runoff models. However, very rarely the question on the relation between the number of model runs (or function calls) and the quality of solutions found is asked. In this study two lumped conceptual rainfall-runoff models (HBV and GR4J with added snow module) are calibrated for five catchments, located in temperate climate zones of USA and Poland, by means of three modern variants of Evolutionary Computation and Swarm Intelligence optimization algorithms with four different maximum numbers of function calls set to 1000, 3000, 10,000 and 30,000. At the calibration stage, when more than 10,000 function calls is used, only marginal improvement in model performance has been found, irrespective of the catchment or calibration algorithm. For validation data, the relation between the number of function calls and model performance is even weaker, in some cases the longer calibration, the poorer modelling performance. It is also shown that the opinion on the model performance based on different popular hydrological criteria, like the Nash-Sutcliffe coefficient or the Persistence Index, may be misleading. This is because very similar, largely positive values of Nash-Sutcliffe coefficient obtained on different catchments may be accompanied by contradictory values of the Persistence Index.

Highlights

Relations between elements of the hydrological cycle are well understood, their quantitative description is still a challenge
The relation between the number of function calls and the model performance is presented in Figs. 1, 2, 3, 4 and 5, where values of MSE, Persistence Index (PI), Fig. 1 Relation between the performance of HBV and GR4J models without and with error correction procedure for Fanno Creek, Oregon, USA, and the maximum number of function calls used during calibration
In case of the HBV model the results show a relatively simple pattern: when SPS-L-SHADE-EIG or GLPSO are used for calibration and error correction procedure is not applied, setting the number of function calls to 30,000 is the best choice, both for calibration and validation data

Summary

Introduction

Relations between elements of the hydrological cycle are well understood, their quantitative description is still a challenge. Many hydrologists are interested in processes that describe a relation between precipitation and runoff at the catchment scale. On many meteorological, land cover and soil-related factors that are variable at small spatial and temporal scales, the quantitative description of the processes that relates precipitation to runoff at the catchment is difficult. Even though it is well known that due to the concept of equifinality (Beven 2012) the solution found would strongly depend on the model representation, objective function or data, and would not have Bgeneral^ meaning (Vrugt et al 2008; Merz et al 2011; Osuch et al 2015), such approach to model calibration remains widespread, as discussed below

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