Natural Flow Reconstruction Using Kalman Filter and Water Balance–Based Methods I: Theory
Publication: Journal of Hydrologic Engineering
Volume 19, Issue 12
Abstract
Because natural flow (NF) values are either not directly measured or have the potential to contain considerable error, when deemed necessary, the reconstruction of a reliable NF series is ostensibly important. Selecting the appropriate method depends on available data. For a time period before reservoir construction (pre-reservoir construction period), the only available data for ungauged basins came from the neighboring basins and simulated flow used in a rainfall-runoff model. A new Kalman-based method developed in this paper looks to reconstruct the NF series using the state fusion technique, which is then compared with the area ratio method, the maintenance of variance (Move) type III method, and the multivariable regression method using different quality indexes (QIs). In the perspective of the post-reservoir construction period, when hydrometric data (i.e., turbine flow, water level in the reservoir, and discharged flow) is collected in an ungauged basin (with no flow measurements), a new water balance equation (WBE)-based method is recommended for reconstructing and filtering the NF data using an optimization technique that would then be compared with the classic WBE that implements different QIs.
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Acknowledgments
The authors thank the Natural Sciences and Engineering Research Council of Canada (NSERC) by the Collaborative Research and Development Grants along with Hydro-Québec for financing the present project and providing some of the data presented in the study.
References
Bisson, J.-L. (1995). “Probable maximum flood of the Gatineau River.”, Forecast Service, Hydro-Quebec (in French).
Cheng, L., Hou, Z. G., Homma, N., Tan, M., and Gupta, M. M. (2009). “Solving convex optimization problems using recurrent neural networks in finite time.” 2009 Int. Joint Conf. on Neural Networks, IJCNN, 538–543.
Chu, P. P. (1992). “A neural network for solving optimization problems with linear equality constraints.” Proc., Int. Joint Conf., IJCNN, Vol. 2, 272–277.
Cunderlik, J. M., and Burn, D. H. (2003). “Non-stationary pooled flood frequency analysis.” J. Hydrol., 276(1–4), 210–223.
Dastorani, M. T., Moghadamnia, A., Piri, J., and Rico-Ramirez, M. (2010). “Application of ANN and ANFIS models for reconstructing missing flow data.” Environ. Monit. Assess., 166(1–4), 421–434.
Deb, K. (2000). “An efficient constraint handling method for genetic algorithms.” Comput. Meth. Appl. Mech. Eng., 186(2–4), 311–338.
Deb, K. (2002). “A fast and elitist multiobjective genetic algorithm: NSGA-II.” IEEE Trans. Evol. Comput., 6(2), 182–197.
Gunter, A., Krol, M., Carlos de Araujo, J., and Bronstert, A. (2004). “Simple water balance modelling of surface reservoir systems in a large data-scarce semiarid region.” Hydrol. Sci. J., 49(5), 901–918.
Hamon, W. R. (1960). “Estimating potential evapotranspiration.” B.S. thesis, Massachusetts Institute of Technology, Dept. of Civil and Sanitary Engineering, Cambridge, MA, 150.
Hernandez-Henriquez, A., Mlynowski, T. J., and Déry, S. J. (2010). “Reconstructing the natural stream-flow of a regulated river: A case study of La Grande Riviere, Quebec, Canada.” Can. Water Resour. J., 35(3), 301–316.
Hirsch, R. M. (1982). “A comparison of four streamflow record extension techniques.” Water Resour. Res., 18(4), 1081–1088.
Hughes, D. A., and Smakhtin, V. (1996). “Daily flow time series patching or extension: A spatial interpolation approach based on flow duration curves.” Hydrol. Sci. J., 41(6), 851–871.
Jones, P. D., Lister, D. H., and Kostopoulou, E. (2004). “Reconstructed river flow series from 1860’s to present (2002).”, Environment Agency, Bristol, U.K.
Joshi, V. U., and Tambe, D. (2010). “Estimation of infiltration rate, run-off and sediment yield under simulated rainfall experiments in upper Pravara basin, India: Effect of slope angle and grass-cover.” J. Earth Syst. Sci., 119(6), 763–773.
Kalakrishnan, M., Chitta, S., Theodorou, E., Pastor, P., and Schaal, S. (2011). “STOMP: Stochastic trajectory optimization for motion planning.” Int. Conf. on Robotics and Automation, IEEE.
Karamouz, M., Hosseinpour, A., and Nazif, S. (2011a). “Improvement of urban drainage system performance under climate change impact.” J. Hydrol. Eng., 395–412.
Karamouz, M., Noori, N., Moridi, A., and Ahmadi, A. (2011b). “Evaluation of floodplain variability considering climate change impacts.” Hydrol. Process., 25(1), 90–103.
Koutsoyiannis, D., and Efstratiadis, A. (2007). “Uncertainty assessment of future hydroclimatic predictions: A comparison of probabilistic and scenario-based approaches.” J. Hydrometeorol., 8(3), 261–281.
Kwiatkowski, D., Phillips, P. C. B., Schmidt, P., and Shin, Y. (1992). “Testing the null hypothesis of stationarity against the alternative of a unit root.” J. Econometrics, 54(1–3), 159–178.
Lee, D., and Schmidt, P. (1996). “On the power of the KPSS test of stationarity against fractionally-integrated alternatives.” J. Econometrics, 73(1), 285–302.
Matalas, N. C., and Jacobs, B. (1964). “A correlation procedure for augmenting hydrologic data.” Statistical Studies in Hydrology, Geological Survey Professional Paper 434-E, United States Government Printing Office, Washington, DC.
Moog, D. B., and Whiting, P. J. (1999). “Streamflow record extension using power transformations and application to sediment transport.” Water Resour. Res., 35(1), 243–254.
Nagpaul, P. S. (2005). Time series analysis in WinIDAMS, UNESCO, New Delhi, India.
Nash, J. E., and Sutcliffe, J. V. (1970). “River flow forecasting through conceptual models, Part I—A discussion of principles.” J. Hydrol., 10(3), 282–290.
Nicol, P. (2010). “Flood study for safety of Carillon dam, HSAMI model calibration, and assembling the routing model.” Internal Technical Rep., Hydro-Quebec (in French).
Noriega, G. (1992). “Application of Kalman filtering to real-time processing of geophysical data.” IEEE Trans. Geosci. Rem. Sens., 30(5), 897–910.
Oh, C. (2005). “The contribution of tourism development to economic growth in Korean economy.” Tourism Manage., 26(1), 39–44.
Parsuraman, K., Elshorbagy, A., and Carey, S. (2007). “Modelling the dynamics of the evapotranspiration process using genetic programming.” Hydrol. Sci. J., 52(3), 563–578.
Perreault, L. (2011). “Verification of probabilistic hydrological forecasts, version 1.0.”, Diffusion Hydro-Québec (in French).
Perreault, L., Hache, M., and Bobee, B. (1996). “Final report of project C2-statistical analysis of energy intake series.”, Chair in Statistical Hydrology Hydro-Québec (CRSNG) (in French).
Schreider, P., and Demuth, S. (1997). “Regionalization of low flows in southwest Germany.” Hydrol. Sci. J., 42(6), 845–858.
Shalev-Shwartz, S., and Tewari, A. (2011). “Stochastic methods for ℓ1-regularized loss minimization.” J. Mach. Learn. Res., 12(2011), 1865–1892.
Shiau, J. T., and Lee, H. C. (2005). “Derivation of optimal hedging rules for a water-supply reservoir through compromise programming.” Water Resour. Manage., 19(2), 111–132.
Sivapragasam, C., Vasudevan, G., Maran, J., Bose, C., Kaza, S., and Ganesh, N. (2009). “Modeling evaporation-seepage losses for reservoir water balance in semi-arid regions.” Water Resour. Manage., 23(5), 853–867.
Telis, P. A. (2001). “Estimation of infiltration rates of saturated soils at selected sites in the Caloosahatchee River basin, southwestern Florida.”, U.S. Dept. of the Interior, U.S. Geological Survey, Reston, VA.
Turner, G. H., and Twieg, D. B. (2005). “Study of temporal stationarity and spatial consistency of fMRI noise using independent component analysis.” IEEE Trans. Med. Imaging, 24(6), 712–718.
Vogel, R. M., and Stedinger, J. R. (1985). “Minimum variance streamflow record augmentation procedures.” Water Resour. Res., 21(5), 715–723.
Wen, L. (2009). “Reconstruction natural flow in a regulated system, the Murrumbidgee River, Australia, using time series analysis.” J. Hydrol., 364(3–4), 216–226.
Whitley, D. (1994). “A genetic algorithm tutorial.” Stat. Comput., 4(2), 65–85.
Yeung, C. W. (2004). “Rainfall-runoff and water-balance models for management of the Fena Valley Reservoir, Guam.” U.S. Geological Survey Scientific Investigations Rep. 2004-5287, U.S. Geological Survey, Reston, VA.
Zhou, Y., Xu, J., and Jing, Y. (2010). “Comparison of centralized multi-sensor measurement and state fusion methods with ensemble Kalman filter for process fault diagnosis.” Proc., Control and Decision Conf. (CCDC), IEEE, 3302–3307.
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© 2014 American Society of Civil Engineers.
History
Received: Jun 23, 2013
Accepted: Feb 6, 2014
Published online: Apr 12, 2014
Published in print: Dec 1, 2014
Discussion open until: Dec 15, 2014
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