Journal of Korean Society of Disaster and Security (한국방재안전학회논문집)

Korean Society of Disaster & Security (한국방재안전학회)
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Analysis of the Effect of Objective Functions on Hydrologic Model Calibration and Simulation

목적함수에 따른 매개변수 추정 및 수문모형 정확도 비교·분석

  • Lee, Gi Ha (Dept. of Advanced Science and Technology Convergence, Kyungpook National University) ;
  • Yeon, Min Ho (Dept. of Advanced Science and Technology Convergence, Kyungpook National University) ;
  • Kim, Young Hun (Dept. of Advanced Science and Technology Convergence, Kyungpook National University) ;
  • Jung, Sung Ho (Dept. of Advanced Science and Technology Convergence, Kyungpook National University)
  • 이기하 (경북대학교 미래과학기술융합학과) ;
  • 연민호 (경북대학교 미래과학기술융합학과) ;
  • 김영훈 (경북대학교 미래과학기술융합학과) ;
  • 정성호 (경북대학교 미래과학기술융합학과)
  • Received : 2022.03.14
  • Accepted : 2022.03.25
  • Published : 2022.03.31
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Abstract

An automatic optimization technique is used to estimate the optimal parameters of the hydrologic model, and different hydrologic response results can be provided depending on objective functions. In this study, the parameters of the event-based rainfall-runoff model were estimated using various objective functions, the reproducibility of the hydrograph according to the objective functions was evaluated, and appropriate objective functions were proposed. As the rainfall-runoff model, the storage function model(SFM), which is a lumped hydrologic model used for runoff simulation in the current Korean flood forecasting system, was selected. In order to evaluate the reproducibility of the hydrograph for each objective function, 9 rainfall events were selected for the Cheoncheon basin, which is the upstream basin of Yongdam Dam, and widely-used 7 objective functions were selected for parameter estimation of the SFM for each rainfall event. Then, the reproducibility of the simulated hydrograph using the optimal parameter sets based on the different objective functions was analyzed. As a result, RMSE, NSE, and RSR, which include the error square term in the objective function, showed the highest accuracy for all rainfall events except for Event 7. In addition, in the case of PBIAS and VE, which include an error term compared to the observed flow, it also showed relatively stable reproducibility of the hydrograph. However, in the case of MIA, which adjusts parameters sensitive to high flow and low flow simultaneously, the hydrograph reproducibility performance was found to be very low.

수문모형의 최적 매개변수를 추정하기 위해서 자동최적화기법이 자주 이용되며, 이러한 최적화기법은 관측값과 모의값의 오차를 최소로 하기 위해 목적함수를 필요로 한다. 다만, 다양한 목적함수 선택에 따라 각기 다른 수문응답 결과를 제공할 수 있다. 본 연구에서는 국내·외에서 사용되는 다양한 목적함수를 활용하여 단기 강우-유출 수문모형의 매개변수를 추정하고, 목적함수에 따른 수문곡선의 재현성을 평가하고, 적정 목적함수를 제시하고자 하였다. 강우-유출 모형으로는 현행 홍수예보에서 유역 유출모의에 활용되고 있는 집중형 수문모형인 저류함수모형을 선택하였으며, 모형의 5개 매개변수에 대해서 전역최적화기법인 SCE-UA를 적용하여 모형의 최적매개변수를 추정하였다. 목적함수별 수문곡선의 재현성 평가를 위해 용담댐 상류유역인 천천유역을 대상으로 9개의 강우사상을 추출하였으며, 7개의 목적함수를 선택하여 개별 강우사상별로 저류함수모형의 매개변수를 추정하고, 이를 활용한 모의 수문곡선의 재현성을 비교·분석하였다. 분석결과, 목적함수에 오차제곱을 포함하고 있는 RMSE, NSE, RSR이 Event 7을 제외한 모든 강우사상에 대해 가장 높은 정확도를 나타냈으며, 관측유량과 모의유량의 오차만을 반영한 ABIAS의 경우, 정확도가 가장 낮은 것으로 분석되었다. 또한, 관측유량 대비 오차 항을 포함하고 있는 PBIAS 및 VE의 경우 역시, 상기 3개(RMSE, NSE, RSR)의 결과와 유사하게 비교적 안정적인 수문곡선 재현성을 보여주었다. 다만, 고유량과 저유량을 동시에 고려하여 이에 민감한 매개변수를 조정하도록 개발된 MIA의 경우, 수문곡선 재현성 성능이 매우 낮은 것으로 나타났다.

Keywords

Acknowledgement

This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government (MSIT)(No. 2020R1A2C1102758).

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