Journal of Korean Society on Water Environment (한국물환경학회지)

Korean Society on Water Environment (한국물환경학회)
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Stochastic Simple Hydrologic Partitioning Model Associated with Markov Chain Monte Carlo and Ensemble Kalman Filter

마코프 체인 몬테카를로 및 앙상블 칼만필터와 연계된 추계학적 단순 수문분할모형

  • Choi, Jeonghyeon (Division of Earth Environmental System Science (Major of Environmental Engineering), Pukyong National University) ;
  • Lee, Okjeong (Department of Environmental Engineering, Pukyong National University) ;
  • Won, Jeongeun (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)) ;
  • 이옥정 (부경대학교 환경공학과) ;
  • 원정은 (부경대학교 지구환경시스템과학부 (환경공학전공)) ;
  • 김상단 (부경대학교 환경공학과)
  • Received : 2020.05.18
  • Accepted : 2020.08.04
  • Published : 2020.09.30
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Abstract

Hydrologic models can be classified into two types: those for understanding physical processes and those for predicting hydrologic quantities. This study deals with how to use the model to predict today's stream flow based on the system's knowledge of yesterday's state and the model parameters. In this regard, for the model to generate accurate predictions, the uncertainty of the parameters and appropriate estimates of the state variables are required. In this study, a relatively simple hydrologic partitioning model is proposed that can explicitly implement the hydrologic partitioning process, and the posterior distribution of the parameters of the proposed model is estimated using the Markov chain Monte Carlo approach. Further, the application method of the ensemble Kalman filter is proposed for updating the normalized soil moisture, which is the state variable of the model, by linking the information on the posterior distribution of the parameters and by assimilating the observed steam flow data. The stochastically and recursively estimated stream flows using the data assimilation technique revealed better representation of the observed data than the stream flows predicted using the deterministic model. Therefore, the ensemble Kalman filter in conjunction with the Markov chain Monte Carlo approach could be a reliable and effective method for forecasting daily stream flow, and it could also be a suitable method for routinely updating and monitoring the watershed-averaged soil moisture.

Keywords

References

  1. Abbaspour, K., Yang, J. Maximov, I., Siber, R., Bogner, K, Mieleitner, J., and Srinivasan, R. (2007). Modelling hydrology and water quality in the pre-Alpine/Alpine thur watershed using SWAT, Journal of Hydrology, 333, 413-430. https://doi.org/10.1016/j.jhydrol.2006.09.014
  2. Allen, R. G., Pereira, L. S., 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. Bae, D. (1997). Development of stochastic real-time flood forecast system by storage function method, Journal of Korea Water Resources Association, 30(5), 449-457. [Korean Literature]
  4. Bae, D., Lee, B., and Georgakakos, K. (2009). Stochastic continuous storage function model with ensemble Kalman filtering (I): Model development, Journal of Korea Water Resources Association, 42(11), 953-961. [Korean Literature] https://doi.org/10.3741/JKWRA.2009.42.11.953
  5. Brocca, L., Melone, F., Moramarco, T., Wagner, W., Naeimi, V., Bartalis, Z., and Hasenauer, S. (2010). Improving runoff prediction through the assimilation of the ASCAT soil moisture product, Hydrology and Earth System Sciences, 14, 1881-1893. https://doi.org/10.5194/hess-14-1881-2010
  6. Chen, F., Crow, W., Starks, P., and Moriasi, D. (2011). Improving hydrologic predictions of a catchment model via assimilation of surface soil moisture, Advances in Water Resources, 34, 526-536. https://doi.org/10.1016/j.advwatres.2011.01.011
  7. Cloke, H. and Pappenberger, F. (2009). Ensemble flood forecasting: a review, Journal of Hydrology, 375, 613-626. https://doi.org/10.1016/j.jhydrol.2009.06.005
  8. De Lannoy, G., Houser, P., Pauwels, V., and Verhoest, N. (2007). State and bias estimation for soil moisture profiles by an ensemble Kalman filter: effect of assimilation depth and frequency, Water Resources Research, 43, W06401. http://dx.doi.org/10.1029/2006WR005100
  9. Demargne, J., Wu, L., Regonda, S., Brown, J., Lee, H., He, M., Seo, D., Hartman, R., Fresch, M., and Zhu, Y. (2014). The science of NOAA's operational hydrologic ensemble forecast service, Bulletin of the American Meteorological Society, 95(1), 79-98. https://doi.org/10.1175/BAMS-D-12-00081.1
  10. Evensen, G. (2003). The ensemble Kalman filter: theoretical formulation and practical implementation, Ocean Dynamics, 53, 343-367. https://doi.org/10.1007/s10236-003-0036-9
  11. 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, 377(1-2), 80-91. https://doi.org/10.1016/j.jhydrol.2009.08.003
  12. Han River Flood Control Office (HRFCO). (2020). Water Resources Management Information System (WAMIS), http://www.wamis.go.kr (accessed Sept. 2020).
  13. Jazwinski, A. (1970). Stochastic processes and filtering theory, Academic Press, 376.
  14. Joh, H., Park, J., Jang, C., and Kim, S. (2012). Comparing prediction uncertainty analysis techniques of SWAT simulated streamflow applied to Chungju dam watershed, Journal of Korea Water Resources Association, 45(9), 861-874. [Korean Literature] https://doi.org/10.3741/JKWRA.2012.45.9.861
  15. Kalman, R. (1960). A new approach to linear filtering and prediction problems, Journal of Basic Engineering, 82(1), 35-45. https://doi.org/10.1115/1.3662552
  16. Kim, R., Won, J., Choi, J., Lee, O., and Kim, S. (2020). Application of Bayesian approach to parameter estimation of TANK model: Comparison of MCMC and GLUE methods, Journal of Korean Society on Water Environment, 36(4), 300-313. [Korean Literature] https://doi.org/10.15681/KSWE.2020.36.4.300
  17. Leach, J., Kornelsen, K., and Coulibaly, P. (2018). Assimilation of near-real time data products into models of an urban basin, Journal of Hydrology, 563, 51-64. https://doi.org/10.1016/j.jhydrol.2018.05.064
  18. Lee, B. and Bae, D. (2011). Streamflow forecast model on Nakdong river basin, Journal of Korea Water Resources Association, 44(11), 853-861. [Korean Literature] https://doi.org/10.3741/JKWRA.2011.44.11.853
  19. 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, 50(4), 241-252. [Korean Literature] https://doi.org/10.3741/JKWRA.2017.50.4.241
  20. Lee, O., Choi, J., Sim, I., Won, J., and Kim, S. (2020). Stochastic parsimonious hydrologic partitioning model under East Asia Monsoon climate and its application to climate change, Water, 12(1), 25. dol:10.3390/w12010025
  21. Li, Z. and Navon, I. (2001). Optimality of variational data assimilation and its relationship with the Kalman filter and smoother, Quarterly Journal of the Royal Meteorological Society, 127(572), 661-683. https://doi.org/10.1002/qj.49712757220
  22. Liu, H., Tian, F., Hu, H. C., Hu, H. P., and Siavapalan, M. (2013). Soil moisture control on patterns of grass green-up in Inner Mongolia: an index based approach, Hydrology and Earth System Sciences, 17, 805-815. https://doi.org/10.5194/hess-17-805-2013
  23. Liu, Y. and Gupta, H. (2007). Uncertainty in hydrologic modeling: toward an integrated data assimilation framework, Water Resources Research, 43, W07401. http://dx.doi.org/10.1029/2006WR005756
  24. Maybeck, P. (1979). Stochastic models, estimation, and control; Volume 1, Academic Press, New York.
  25. Me, W., Abell, J. M., and Hamilton, D. P. (2015). Effects of hydrologic conditions on SWAT model performance and parameter sensitivity for a small, mixed land use catchment in New Zealand, Hydrology and Earth System Sciences, 19, 4127-4147. https://doi.org/10.5194/hess-19-4127-2015
  26. Meng, S., Xie, X., and Yu, X. (2016). Tracing temporal changes of model parameters in rainfall-runoff modeling via a real-time data assimilation, Water, 8(1), 19. doi:10.3390/w8010019
  27. Moradkhani, H., Sorooshian, S., Gupta, H., and Houser, P. (2005). Dual state-parameter estimation of hydrological models using ensemble Kalman filter, Advances in Water Resources, 28, 135-147. https://doi.org/10.1016/j.advwatres.2004.09.002
  28. Nash, J. and Sutcliffe, J. (1970). River flow forecasting through conceptual models part I-A discussion of principles, Journal of Hydrology, 10, 282-290. https://doi.org/10.1016/0022-1694(70)90255-6
  29. Patil, S. and Stieglitz, M. (2015). Comparing spatial and temporal transferability of hydrological model parameters, Journal of Hydrology, 525, 409-417. https://doi.org/10.1016/j.jhydrol.2015.04.003
  30. Rafieeinasab, A., Seo, D., Lee, H., and Kim, S. (2014). Comparative evaluation of maximum likelihood ensemble filter and ensemble Kalman filter for real-time assimilation of streamflow data into operational hydrologic models, Journal of Hydrology, 519, 2663-2675. https://doi.org/10.1016/j.jhydrol.2014.06.052
  31. Reichle, R., McLaughlin, D., and Entekhabi, D. (2002). Hydrologic data assimilation with the ensemble Kalman filter, Monthly Weather Review, 130(1), 103-114. https://doi.org/10.1175/1520-0493(2002)130<0103:HDAWTE>2.0.CO;2
  32. 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, 480, 33-45. https://doi.org/10.1016/j.jhydrol.2012.12.004
  33. Ryu, J., Kang, H., Choi, J., Kong, D., Gum, D., Jang, C., and Lim, K. (2012). Application of SWAT-CUP for streamflow auto-calibration at Soyang-gang dam watershed, Journal of Korean Society on Water Environment, 28(3), 347-358. [Korean Literature]
  34. Schaake, J., Hamill, T., Buizza, R., and Clark, M. (2007). HEPEX, the hydrological ensemble prediction experiment, Bulletin of the American Meteorological Society, 88, 1541-1547. https://doi.org/10.1175/BAMS-88-10-1541
  35. Schellekens, J., Weerts, A., Moore, R., Pierce, C., and Hildon, S. (2011). The use of MOGREPS ensemble rainfall forecasts in operational flood forecasting systems across England and Wales, Advances in Geosciences, 29, 77-84. https://doi.org/10.5194/adgeo-29-77-2011
  36. Thielen, J., Schaake, J., Hartman, R., and Buizza, R. (2008). Aims, challenges and progress of the Hydrological Ensemble Prediction Experiment (HEPEX). following the third HEPEX workshop held in Stresa 27 to 29 June 2007. Atmospheric Science Letters, 9(2), 29-35. https://doi.org/10.1002/asl.168
  37. Troch, P., Paniconi, C., and McLaughlin, D. (2003). Catchmentscale hydrological modeling and data assimilation, Advances in Water Resources, 26, 131-135. https://doi.org/10.1016/S0309-1708(02)00087-8
  38. U.S. Department of Agriculture-Soil Conservation Service (USDA-SCS). (1985). National engineering handbook, Section 4, Hydrology, U.S. Department of Agriculture Soil Conservation Service, Washington, DC, USA.
  39. Weerts, A. and Serafy, G. (2006). Particle filtering and ensemble Kalman filtering for state updating with hydrological conceptual rainfall-runoff models, Water Resources Research, 42(9), W09403. http://dx.doi.org/10.1029/2005WR004093
  40. Werner, K., Brandon, D., Clark, M., and Gangopadhyay, S. (2005). Incorporating medium range numerical weather model output into the ensemble streamflow prediction system of the national weather service, Journal of Hydrometeorology, 6, 101-114. https://doi.org/10.1175/JHM411.1
  41. Werner, M., Cranston, M., Harrison, T., Whitfield, D., and Schellekens, J. (2009). Recent developments in operational flood forecasting in England, Wales and Scotland. Meteorological Applications, 16(1), 13-22. https://doi.org/10.1002/met.124
  42. Xie, X. and Zheng, D. (2010). Data assimilation for distributed hydrological catchment modeling via ensemble Kalman filter, Advances in Water Resources, 33(6), 678-690. https://doi.org/10.1016/j.advwatres.2010.03.012