Evaluation Method of Multiobjective Functions’ Combination and Its Application in Hydrological Model Evaluation

Abstract

Parameter optimization of a hydrological model is intrinsically a high dimensional, nonlinear, multivariable, combinatorial optimization problem which involves a set of different objectives. Currently, the assessment of optimization results for the hydrological model is usually made through calculations and comparisons of objective function values of simulated and observed variables. Thus, the proper selection of objective functions’ combination for model parameter optimization has an important impact on the hydrological forecasting. There exist various objective functions, and how to analyze and evaluate the objective function combinations for selecting the optimal parameters has not been studied in depth. Therefore, to select the proper objective function combination which can balance the trade-off among various design objectives and achieve the overall best benefit, a simple and convenient framework for the comparison of the influence of different objective function combinations on the optimization results is urgently needed. In this paper, various objective functions related to parameters optimization of hydrological models were collected from the literature and constructed to nine combinations. Then, a selection and evaluation framework of objective functions is proposed for hydrological model parameter optimization, in which a multiobjective artificial bee colony algorithm named RMOABC is employed to optimize the hydrological model and obtain the Pareto optimal solutions. The parameter optimization problem of the Xinanjiang hydrological model was taken as the application case for long-term runoff prediction in the Heihe River basin. Finally, the technique for order preference by similarity to ideal solution (TOPSIS) based on the entropy theory is adapted to sort the Pareto optimal solutions to compare these combinations of objective functions and obtain the comprehensive optimal objective functions’ combination. The experiments results demonstrate that the combination 2 of objective functions can provide more comprehensive and reliable dominant options (i.e., parameter sets) for practical hydrological forecasting in the study area. The entropy-based method has been proved that it is effective to analyze and evaluate the performance of different combinations of objective functions and can provide more comprehensive and impersonal decision support for hydrological forecasting.

Impact of Catchment Discretization and Imputed Radiation on Model Response: A Case Study from Central Himalayan Catchment

“…Effect of the catchment discretization methods and radiation algorithms on model performance was further evaluated using NSE and LnNSE (Figure 7). The NSE and the LnNSE functions are a pair of conflicting objective functions, where the NSE function evaluates the ability to reproduce all stream flows, but it is known to be biased to predict peak flows [23], while the LnNSE function emphasizes low flows [62]. The model efficiency metrics were computed for each hydrologic year constituting the validation period.…”

Formulation of Wavelet Based Multi‐Scale Multi‐Objective Performance Evaluation (WMMPE) Metric for Improved Calibration of Hydrological Models

“…Yilmaz et al (2008) suggested careful selection of diagnostic evaluation metrics that emphasizes on various segments of hydrograph encompassing low flows, peak flows and a good water balance. The five assessment criterion chosen for this purpose are Fourth root Mean Quadruple Error (R4MS4E) (Baratti et al, 2003), log-NSE, Runoff Coefficient Percent Error (ROCE), Skill Score (SS) (Johnson & Sharma, 2009) and Mean Absolute Error (MAE) (Huo & Liu, 2020;Tian et al, 2019). R4MS4E and log-NSE are chosen to evaluate the performance of simulation in high and low flows respectively.…”

Transferability of a Conceptual Hydrological Model across Different Temporal Scales and Basin Sizes

“…The Xinanjiang (XAJ) model, a rainfall-runoff model developed by (Zhao 1992), has been widely used in China and many countries in the world for flood simulation in humid and semi-humid regions (Huo and Liu 2020;Liu et al 2016;Meng et al 2016;Yang et al 2020;Zhang et al 2019;Zhuo et al 2016). It is based on the concept of saturation excess runoff mechanism, which means that runoff is not produced until the soil moisture content of the aeration zone reaches field capacity.…”