Searching for an Optimized Single-objective Function Matching Multiple Objectives with Automatic Calibration of Hydrological Models
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In the calibration of hydrological models, evaluation criteria are explicitly and quantitatively defined as single- or multi-objective functions when utilizing automatic calibration approaches. In most previous studies, there is a general opinion that no single-objective function can represent all important characteristics of even one specific hydrological variable (e.g., streamflow). Thus hydrologists must turn to multi-objective calibration. In this study, we demonstrated that an optimized single-objective function can compromise multi-response modes (i.e., multi-objective functions) of the hydrograph, which is defined as summation of a power function of the absolute error between observed and simulated streamflow with the exponent of power function optimized for specific watersheds. The new objective function was applied to 196 model parameter estimation experiment (MOPEX) watersheds across the eastern United States using the semi-distributed Xinanjiang hydrological model. The optimized exponent value for each watershed was obtained by targeting four popular objective functions focusing on peak flows, low flows, water balance, and flashiness, respectively. Results showed that the optimized single-objective function can achieve a better hydrograph simulation compared to the traditional single-objective function Nash-Sutcliffe efficiency coefficient for most watersheds, and balance high flow part and low flow part of the hydrograph without substantial differences compared to multi-objective calibration. The proposed optimal single-objective function can be practically adopted in the hydrological modeling if the optimal exponent value could be determined a priori according to hydrological/climatic/landscape characteristics in a specific watershed.
Keywordsautomatic calibration single-objective function multi-objective functions Xinanjiang model hydrological model
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- Hall J W, Tarantola S, Bates P D et al., 2005. Distributed sensitivity analysis of flood inundation model calibration. Journal of Hydraulic Engineering, 131(2): 117–126. doi: https://doi.org/10.1061/(ASCE)0733-9429(2005)131:2(117) CrossRefGoogle Scholar
- Jain S K, Sudheer K P, 2008. Fitting of hydrologic models: a close look at the Nash-Sutcliffe index. Journal of Hydrologic Engineering, 13(10): 981–986. doi: https://doi.org/10.1061/(ASCE)1084-0699(2008)13:10(981) CrossRefGoogle Scholar
- Khu S T, Madsen H, di Pierro F, 2008. Incorporating multiple observations for distributed hydrologic model calibration: an approach using a multi-objective evolutionary algorithm and clustering. Advances in Water Resources, 31(10): 1387–1398. doi: https://doi.org/10.1016/j.advwatres.2008.07.011 CrossRefGoogle Scholar
- McCuen R H, Knight Z, Cutter A G, 2006. Evaluation of the Nash-Sutcliffe efficiency index. Journal of Hydrologic Engineering, 11(6): 597–602. doi: https://doi.org/10.1061/(ASCE)1084-0699(2006)11:6(597) CrossRefGoogle Scholar
- Muleta M K, 2012. Model performance sensitivity to objective function during automated calibrations. Journal of Hydrologic Engineering, 17(6): 756–767. doi: https://doi.org/10.1061/(ASCE)HE.1943-5584.0000497 CrossRefGoogle Scholar
- Sun Y, Tian F Q, Yang L et al., 2014. Exploring the spatial variability of contributions from climate variation and change in catchment properties to streamflow decrease in a mesoscale basin by three different methods. Journal of Hydrology, 508: 170–180. doi: https://doi.org/10.1016/j.jhydrol.2013.11.004 CrossRefGoogle Scholar