Parameter identification and calibration of the Xin’anjiang model using the surrogate modeling approach

doi:10.1007/s11707-014-0424-0

Front. Earth Sci.

2014, Vol. 8

Issue (2) : 264-281 https://doi.org/10.1007/s11707-014-0424-0

RESEARCH ARTICLE

Parameter identification and calibration of the Xin’anjiang model using the surrogate modeling approach

Yan YE^1,⁵,Xiaomeng SONG^2,^3,^*(

),Jianyun ZHANG^2,³,Fanzhe KONG⁴,Guangwen MA⁵

1. College of Resources and Environment, Southwest University, Chongqing 400716, China
2. State Key Laboratory of Hydrology-Water Resources & Hydraulic Engineering, Nanjing Hydraulic Research Institute, Nanjing 210029, China
3. Research Center for Climate Change, the Ministry of Water Resources, Nanjing 210029, China
4. School of Resource and Earth Science, China University of Mining & Technology, Xuzhou 221008, China
5. College of Water Resource & Hydropower, Sichuan University, Chengdu 610065, China

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Abstract

Practical experience has demonstrated that single objective functions, no matter how carefully chosen, prove to be inadequate in providing proper measurements for all of the characteristics of the observed data. One strategy to circumvent this problem is to define multiple fitting criteria that measure different aspects of system behavior, and to use multi-criteria optimization to identify non-dominated optimal solutions. Unfortunately, these analyses require running original simulation models thousands of times. As such, they demand prohibitively large computational budgets. As a result, surrogate models have been used in combination with a variety of multi-objective optimization algorithms to approximate the true Pareto-front within limited evaluations for the original model. In this study, multi-objective optimization based on surrogate modeling (multivariate adaptive regression splines, MARS) for a conceptual rainfall-runoff model (Xin’anjiang model, XAJ) was proposed. Taking the Yanduhe basin of Three Gorges in the upper stream of the Yangtze River in China as a case study, three evaluation criteria were selected to quantify the goodness-of-fit of observations against calculated values from the simulation model. The three criteria chosen were the Nash-Sutcliffe efficiency coefficient, the relative error of peak flow, and runoff volume (REPF and RERV). The efficacy of this method is demonstrated on the calibration of the XAJ model. Compared to the single objective optimization results, it was indicated that the multi-objective optimization method can infer the most probable parameter set. The results also demonstrate that the use of surrogate-modeling enables optimization that is much more efficient; and the total computational cost is reduced by about 92.5%, compared to optimization without using surrogate modeling. The results obtained with the proposed method support the feasibility of applying parameter optimization to computationally intensive simulation models, via reducing the number of simulation runs required in the numerical model considerably.

Keywords Xin’anjiang model parameter calibration multi-objective optimization surrogate modeling

Corresponding Author(s): Xiaomeng SONG

Issue Date: 24 June 2014

Cite this article:

Yan YE,Xiaomeng SONG,Jianyun ZHANG, et al. Parameter identification and calibration of the Xin’anjiang model using the surrogate modeling approach[J]. Front. Earth Sci., 2014, 8(2): 264-281.

URL:

https://academic.hep.com.cn/fesci/EN/10.1007/s11707-014-0424-0
https://academic.hep.com.cn/fesci/EN/Y2014/V8/I2/264

Fig.1 Distribution of rain station, drainage network, and sub-catchments of Yanduhe catchment.

Tab.1 Characteristics of each sub-catchment

Fig.2 Flowchart for the XAJ model.

Tab.2 Ranges and physical meaning of parameters for the XAJ model

Fig.3 Flowchart of the meta-model-based optimization for the XAJ model.

Fig.4 Response surface plots for the three objective responses with parameters K and SM.

Fig.5 Cross-validation for the surrogate modeling.

Fig.6 Validation and test for the surrogate modeling.

Tab.3 Optimization results for ten parameters

Fig.7 Comparison of single-objective optimal value using surrogate modeling.

Tab.4 Criteria for the goodness-of-fit evaluation

Fig.8 Illustration of estimated Pareto front for the optimization of a three-objective function attained across surrogate modeling. The black arrows indicate direction of increasing preference. Marked optimal point corresponds to using a balanced aggregated objective function.

Fig.9 Normalized range of parameter values along the Pareto front shown in Fig. 8.

Fig.10 Hydrograph prediction uncertainty ranges associated with the Pareto solution set estimated from the surrogate modeling: (a)–(j) for the 10 flood events in the calibration, and (k)–(o) for the 5 flood events in the validation. Black solid lines indicate the observed hydrograph for 15 flood events. Short dash dot lines indicate the simulated hydrograph based on the optimization of balanced aggregated function. Black columns indicate the precipitation. Shaded area indicates the simulated hydrograph from Pareto front for three-objective function.

Fig.11 Scatter plots of observed and simulated discharge with optimization based on balanced aggregated function.

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