Estimating time-varying parameters for monthly water balance model using particle filter: assimilation of stream flow data

입자 필터를 이용한 월 물 수지 모형의 시간변화 매개변수 추정: 하천유량 자료의 동화

  • Choi, Jeonghyeon (Division of Earth Environmental System Science (Major of Environmental Engineering), Pukyong National University) ;
  • Kim, Sangdan (Department of Environmental Engineering, Pukyong National University)
  • 최정현 (부경대학교 지구환경시스템과학부 (환경공학전공)) ;
  • 김상단 (부경대학교 환경공학과)
  • Received : 2021.02.16
  • Accepted : 2021.04.19
  • Published : 2021.06.30


Hydrological model parameters are essential for model simulation and can vary over time due to topography, climatic conditions, climate change and human activity. Consequently, the use of fixed parameters can lead to inaccurate stream flow simulations. The aim of this study is to investigate an appropriate method of estimating time-varying parameters using stream flow observations, and how the simulation efficiency changes when stream flow data are assimilated into the model. The data assimilation method can be used to automatically estimate the parameters of a hydrological model by adapting to a variety of changing environments. Stream flow observations were assimilated into a two parameter monthly water balance model using a particle filter. The simulation results using the time-varying parameters by the data assimilation method were compared with the simulation results using the fixed parameters by the SCEM method. First, we conducted synthesis experiments based on various scenarios to investigate if the particle filter method can adequately track parameters that change over time. After that, it was applied to actual watersheds and compared with the predictive performance of stream flow when using parameters that change with time and fixed parameters. The conclusions obtained through this study are as follows: (1) The predictive performance of the overall monthly stream flow time series was similar between the particle filter method and the SCEM method. (2) The monthly runoff prediction performance in the period except the rainy season was better in the simulation by the periodically changing parameters using the data assimilation method. (3) Uncertainty in the observational data of stream flow used for assimilation played an important role in the predictive performance of the particle filter.

수문 모형 매개변수는 모형 모의에 필수적이며, 지형, 기후조건, 기후변화와 인간 활동으로 인해 시간에 따라 달라질 수 있다. 결과적으로 고정된 매개변수의 사용은 부정확한 하천유량 모의로 이어질 수 있다. 본 연구의 목표는 하천유량 관측자료를 이용하여 시간에 따라 변하는 매개변수를 추정하는 방법을 살펴보고, 하천유량 자료가 모형에 동화될 때 모의 효율성이 어떻게 변하는지 분석하는 것이다. 자료 동화 방법은 변화하는 다양한 환경에 적응하여 수문 모형의 매개변수를 자동으로 추정하기 위하여 사용될 수 있다. 입자 필터를 이용하여 하천유량 관측치를 2개 매개변수 월 물 수지 모형에 동화했다. 자료 동화 방법으로 시간변화 매개변수를 사용한 모의 결과는 SCEM 방법으로 고정 매개변수를 사용한 모의 결과와 비교되었다. 먼저 다양한 시나리오에 기반한 합성 실험을 수행하여 입자 필터 방법이 시간에 따라 변화하는 매개변수를 적절하게 추적할 수 있는지를 살펴보았다. 이후 실제 유역에 적용하여 시간에 따라 변화하는 매개변수와 고정된 매개변수를 사용하였을 때의 하천유량 예측성능과 비교하였다. 본 연구를 통해 얻은 결론은 다음과 같다. (1) 전체적인 월 하천유량 시계열의 예측성능은 입자 필터 방법과 SCEM 방법이 서로 비슷하였다. (2) 우기를 제외한 시기의 월 유출고 예측성능은 자료 동화 방법을 이용한 주기적으로 변화하는 매개변수에 의한 모의가 더 우수하였다. (3) 동화에 사용되는 하천유량 관측자료의 불확실성은 입자 필터의 하천유량 예측성능에 중요한 역할을 하였다.


  1. Abbaszadeh, P., Moradkhani, H., and Yan, H. (2018). "Enhancing hydrologic data assimilation by evolutionary particle filter and Markov chain Monte Carlo." Advances in Water Resources, Vol. 111, pp. 192-204. doi: 10.1016/j.advwatres.2017.11.011
  2. Allen, R., Pereira, L., Raes, D., and Smith, M. (1998). Crop evapotranspiration - Guidelines for computing crop water requirements. FAO Irrigation and drainage paper 56, Food and Agriculture Organization of the United Nations, Rome, Italy.
  3. Brigode, P., Oudin, L., and Perrin, C. (2013). "Hydrological model parameter instability: A source of additional uncertainty in estimating the hydrological impacts of climate change?" Journal of Hydrology, Vol. 476, pp. 410-425. doi: 10.1016/j.jhydrol.2012.11.012
  4. Brown, A., Zhang, L., McMahon, T., Western, A., and Vertessy, R., (2005). "A review of paired catchment studies for determining changes in water yield resulting from alterations in vegetation." Journal of Hydrology, Vol. 310 No. 1-4, pp. 28-61. doi: 10.1016/j.jhydrol.2004.12.010
  5. Cao, Y., Ye, Y., Liang, L., Zhao, H., Jiang, Y., Wang, H., Yi, Z., Shang, Y., and Yan, D. (2019). "A modified particle filter-based data assimilation method for a high-precision 2D hydrodynamic model considering spatial-temporal variability of roughness: Simulation of dam-break flood inundation." Water Resources Research, Vol. 55, pp. 6049-6068. doi: 10.1029/2018WR023568
  6. Choi, D., Yang, J., Chung, G., and Kim, S. (2011). "A conceptual soil water model of catchment water balance: Which hydrologic components are needed to calibrated the model?" Journal of the Korean Society of Civil Engineers, Vol. 31, No. 3B, pp. 211-220. doi: 10.12652/Ksce.2011.31.3B.211 (in Korean)
  7. Choi, J., Lee, O., Won, J., and Kim. S. (2020). "Stochastic simple hydrologic partitioning model associated with Markov chain Monte Carlo and ensemble Kalman filter." Journal of Korean Society on Water Environment, Vol. 36, No. 5, pp. 353-363. doi: 10.15681/KSWE.2020.36.5.353 (in Korean)
  8. Clark, M., Rupp, D., Woods, R., Zheng, X., Ibbitt, R., Slater, A., Schmidt, J., and Uddstrom, M. (2008). "Hydrological data assimilation with the ensemble Kalman filter: Use of streamflow observations to update states in a distributed hydrological model." Advances in Water Resources, Vol. 31, No. 10, pp. 1309-1324. doi: 10.1016/j.advwatres.2008.06.005
  9. de Vos, N., Rientjes, T., and Gupta, H. (2010). "Diagnostic evaluation of conceptual rainfall-runoff models using temporal clustering. Hydrological Processes, Vol. 24, No. 20, pp. 2840-2850. doi: 10.1002/hyp.7698
  10. Dechantcm, M., and Moradkhani, H. (2012). "Examining the effectiveness and robustness of data assimilation methods for calibration and quantification of uncertainty in hydrologic forecasting." Water Resources Research, Vol. 48, W04518. doi: 10.1029/2011WR011011.
  11. Deng, C., Liu, P., Guo, S., Li, Z., and Wang, D. (2016). "Identification of hydrological model parameter variation using ensemble Kalman filter." Hydrology and Earth System Sciences, Vol. 20, No. 12, pp. 4949-4961. doi: 10.5194/hess-20-4949-2016
  12. Engel, B., Srinivasan, R., Arnold, J., Rewerts, C., and Brown, S. (1993). "Nonpoint-source (NPS) pollution modeling using models integrated with geographic information systems (GIS)." Water Science and Technology, Vol. 28, pp. 685-690. doi: 10.2166/wst.1993.0474
  13. Fan, Y., Huang, G., Baetz, B., Li, Y., Huang, K., Chen, X., and Gao, M. (2017). "Development of integrated approaches for hydrological data assimilation through combination of ensemble Kalman filter and particle filter methods." Journal of Hydrology, Vol. 550, pp. 412-426. doi: 10.1016/j.jhydrol.2017.05.010
  14. Feng, M., Liu, P., Guo, S., Shi, L., Deng, C., and Ming, B. (2017). "Deriving adaptive operating rules of hydropower reservoirs using time-varying parameters generated by the EnKF." Water Resources Research, Vol. 53, No. 8, pp. 6885-6907. doi: 10.1002/2016wr020180.
  15. Gharari, S., Hrachowitz, M., Fenicia, F., and Savenije, H. (2013). "An approach to identify time consistent model parameters: sub-period calibration." Hydrology and Earth System Science, Vol. 17, No. 1, pp. 149-161. doi: 10.5194/hess-17-149-2013
  16. Gordon, N., Salmond, D., and Smith, A. (1993). "Novel approach to nonlinear and non-Gaussian Bayesian state estimation." IEE Proceeding F (Radar and Signal Processing), Vol. 140, pp. 107-113. doi: 10.1049/ip-f-2.1993.0015
  17. Guo, S., Wang, J., Xiong, L., Ying, A., and Li, D. (2002). "A macroscale and semidistributed monthly water balance model to predict climate change impacts in China." Journal of Hydrology, Vol. 268, No. 1-4, pp, 1-15. doi: 10.1016/s0022-1694(02)00075-6
  18. Gupta, H., Kling, H., Yilmaz, K., and Martinez, G. (2009). "Decomposition of the mean squared error and NSE performance criteria: implications for improving hydrological modelling." Journal of Hydrology, Vol. 377, pp. 80-91. doi: 10.1016/j.jhydrol.2009.08.003
  19. Jeremiah, E., Marshall, L., Sisson, S.A., and Sharma, A. (2013). "Specifying a hierarchical mixture of experts for hydrologic modeling: Gating function variable selection." Water Resources Research, Vol. 49, No. 5, pp. 2926-2939. doi: 10.1002/wrcr.20150
  20. Lee, B., and Bae, D. (2011). "Streamflow forecast model on Nakdong river basin." Journal of Korea Water Resources Association, Vol. 50, No. 4, pp. 241-252. doi: 10.3741/JKWRA.2011.44.11.853 (in Korean)
  21. Lee, D., Kim, Y., Yu, W., and Lee, G. (2017). "Evaluation on applicability of on/off-line parameter calibration techniques in rainfall-runoff modeling." Journal of Korea Water Resources Association, Vol. 50, No. 4, pp. 241-252. doi: 10.3741/JKWRA.2017.50.4.241 (in Korean)
  22. Lee, J. (2006). Hydrology. Gumiseogwan.
  23. Legesse, D., Vallet-Coulomb, C., and Gasse, F. (2003). "Hydrological response of a catchment to climate and land use changes in Tropical Africa: Case study South Central Ethiopia." Journal of Hydrology, Vol. 275, No. 1-2, pp. 67-85. doi: 10.1016/s0022-1694(03)00019-2
  24. Leisenring, M., and Moradkhani, H. (2012). "Analysing the uncertainty of suspended sediment load prediction using sequential data assimilation." Journal of Hydrology, Vol. 468, pp. 268-282. doi: 10.1016/j.jhydrol.2012.08.049
  25. Marshall, L., Sharma, A., and Nott, D. (2006). "Modeling the catchment via mixtures: Issues of model specification and validation." Water Resources Research, Vol. 42, No. 11, W11409. doi: 10.1029/2005wr004613
  26. Merz, R., Parajka, J., and Bloeschl, G. (2011). "Time stability of catchment model parameters: Implications for climate impact analyses." Water Resources Research, Vol. 47, No. 2, W02531. doi: 10.1029/2010wr009505
  27. Moradkhani, H., DeChant, C., and Sorooshian, S. (2012). "Evolution of ensemble data assimilation for uncertainty quantification using the particle filter-Markov chain Monte Carlo method." Water Resources Research, Vol. 48. No. 12, doi: 10.1029/2012wr012144.
  28. Moradkhani, H., Hsu, K., Gupta, H., and Sorooshian, S. (2005a). "Uncertainty assessment of hydrologic model states and parameters: Sequential data assimilation using particle filter." Water Resources Research, Vol. 41, W05012. doi: 10.1029/2004WR003604
  29. Moradkhani, H., Sorooshian, S., Gupta, H., and Houser, P. (2005b). "Dual state-parameter estimation of hydrological models using ensemble Kalman filter." Advances in Water Resources, Vol. 28, No. 2, pp. 135-147. doi: 10.1016/j.advwatres.2004.09.002
  30. Nash, J., and Sutcliffe, J. (1970). "River flow forecasting through conceptual models part I - A discussion of principles." Journal of Hydrology, Vol. 10, pp. 282-290. doi: 10.1016/0022-1694(70)90255-6
  31. Noh, S., Tachikawa, Y., Shiiba, M., and Kim, S. (2011). "Dual state-parameter updating scheme on a conceptual hydrologic model using sequential Monte Carlo filters." Journal of Japan Society of Civil Engineers, Ser. B1 (Hydraulic Engineering), Vol. 67, pp. I_1-I_6.
  32. Pathiraja, S., Anghileri, D., Burlando, P., Sharma, A., Marshall, L., and Moradkhani, H. (2018). "Insights on the impact of systematic model errors on data assimilation performance in changing catchments." Advances in Water Resources, Vol. 113, pp. 202-222. doi: 10.1016/j.advwatres.2017.12.006
  33. Patil, S., and Stieglitz, M. (2015). "Comparing spatial and temporal transferability of hydrological model parameters." Journal of Hydrology, Vol. 525, pp. 409-417. doi: 10.1016/j.jhydrol.2015.04.003
  34. Ritter, A., and Munoz-Carpena, R. (2013). "Performance evaluation of hydrological models: Statistical significance for reducing subjectivity in goodness-of-fit assessments." Journal of Hydrology, Vol. 480, pp. 33-45. doi: 10.1016/j.jhydrol.2012.12.004
  35. Seibert, J., McDonnell, J., and Woodsmith, R. (2010). "Effects of wildfire on catchment runoff response: A modelling approach to detect changes in snow-dominated forested catchments." Hydrology Research, Vol. 41, No. 5, pp. 378-390. doi 10.2166/nh.2010.036
  36. Smith, P., Beven, K., and Tawn, J. (2008). "Detection of structural inadequacy in process-based hydrological models: A particlefiltering approach." Water Resources Research, Vol. 44, No. 1. doi: 10.1029/2006wr005205
  37. Thirel, G., Andreassian, V., Perrin, C., Audouy, J., Berthet, L., Edwards, P. Folton, N., Furusho, C., Kuentz, A., Lerat, J., Lindstrom, G., Martin, E., Mathevet, T., Merz, R., Parajka, J., Ruelland, D., and Vaze, J. (2015). "Hydrology under change: An evaluation protocol to investigate how hydrological models deal with changing catchments." Hydrological Sciences Journal, Vol. 60, No. 7-8, pp. 1184-1199. doi: 10.1080/02626667.2014.967248
  38. Vaze, J., Post, D., Chiew, F., Perraud, J., Viney, N., and Teng, J. (2010). "Climate non-stationarity-validity of calibrated rainfallrunoff models for use in climate change studies." Journal of Hydrology, Vol. 394, No. 3-4, pp. 447-457. doi: 10.1016/j.jhydrol.2010.09.018
  39. Vrugt, J., Gupta, H., Bouten, W., and Sorooshian, S. (2003). "A shuffled complex evolution metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters." Water Resources Research, Vol. 39, No. 8. doi: 10.1029/2002WR001642
  40. Vrugt, J., ter Braak, C., Diks, C., and Schoups, G. (2013). "Hydrologic data assimilation using particle Markov chain Monte Carlo simulation: Theory, concepts and applications." Advances in Water Resources, Vol. 51, pp. 457-478. doi: 10.1016/j.advwatres.2012.04.002
  41. Wagener, T., McIntyre, N., Lees, M., Wheater, H., and Gupta, H. (2003). "Towards reduced uncertainty in conceptual rainfallrunoff modelling: dynamic identifiability analysis." Hydrological Process, Vol. 17, No. 2, pp. 455-476. doi: 10.1002/hyp.1135
  42. Wang, D., Chen, Y., and Cai, X. (2009). "State and parameter estimation of hydrologic models using the constrained ensemble Kalman filter." Water Resources Research, Vol. 45, No. 11, W11416. doi: 10.1029/2008wr007401
  43. Westra, S., Thyer, M., Leonard, M., Kavetski, D., and Lambert, M. (2014). "A strategy for diagnosing and interpreting hydrological model nonstationarity." Water Resources Research, Vol. 50, No. 6, pp. 5090-5113. doi: 10.1002/2013wr014719
  44. Won, J., Choi, J., Lee, O., and Kim, S. (2020). "Copula-based joint drought index using SPI and EDDI and its application to climate change." Science of Total Environment, Vol. 744, 140701. doi: 10.1016/j.scitotenv.2020.140701
  45. Xiong, L., and Guo, S. (1999). "A two-parameter monthly water balance model and its application." Journal of Hydrology, Vol. 216, No. 1-2, pp. 111-123. doi: 10.1016/s0022-1694(98)00297-2
  46. Xiong, L., and Guo, S. (2012). "Appraisal of Budyko formula in calculating long-term water balance in humid watersheds of southern China." Hydrological Process, Vol. 26, No. 9, pp. 1370-1378. doi: 10.1002/hyp.8273
  47. Xiong, L., Liu, P., Cheng, L., Deng, C., Gui, Z., Zhang, X., and Liu, Y. (2019). "Identifying time-varying hydrological model parameters to improve simulation efficiency by the ensemble Kalman filter: A joint assimilation of streamflow and actual evapotranspiration." Journal of Hydrology, Vol. 568, pp. 758-768. doi: 10.1016/j.jhydrol.2018.11.038