Estimating Selected Parameters for the XAJ Model under Multicollinearity among Watershed Characteristics
Publication: Journal of Hydrologic Engineering
Volume 17, Issue 1
Abstract
Because the problem of prediction in ungauged basins (PUB) has become a central theme of hydrological research, there is a clear need to have an effective and efficient method that can help to transfer information from gauged basins to ungauged ones. Previous research relating the parameters of a hydrologic model to physical drainage basin characteristics has had limited success. Conventional regression procedures do not take into account multicollinearity among the basin characteristics, which have a great effect on the stability of regression equations. This study presents an unbiased ridge regression estimate (URR) that can provide robust regression equations in the presence of multicollinearity. The proposed method is applied to estimate parameters of the Xinanjiang model in 20 watersheds located in southeastern China. Compared with conventional estimations, such as ordinary least squares estimate and ordinary ridge regression estimate, the URR was reduced by 78% for root mean square error, 47% for variance, and 13.1% for Akaike’s Information Criterion. The coefficient of determination was increased by 49%.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This study is supported by the Common Will Vocation Science Research Funding of the Ministry of Water Resources of the People’s Republic of China Grant No. UNSPECIFIED200701031, Program for Changjiang Scholars and Innovative Research Team in University Grant No. UNSPECIFIEDIRT0717, National Natural Science Foundation of China Grant No. NNSFC50679024/E0903, Key Science and Technology Research Program of Ministry of Education of the People’s Republic of China Grant No. UNSPECIFIED308012, and the 111 Project under Grant No. UNSPECIFIEDB08048 and Natural Science Funding of Hohai University Grant No. UNSPECIFIED2007418911.
References
Abdullah, F. A., and Lettenmaier, D. P. (1997). “Development of regional parameter estimation equations for a macroscale hydrologic model.” J. Hydrol. (Amsterdam), 197(1), 230–257.
Adamowski, J. (2010). “Comparison of multivariate regression and artificial neural networks for peak urban water-demand forecasting: Evaluation of different ANN learning algorithms.” J. Hydrol. Eng., 15(10), 729–743.
Akdeniz, F., and Alan, T. K. (2004). “The moment of the operational almost unbiased ridge regression estimator.” Int. J. Appl. Math. Comput. Sci., 153(3), 673–684.
Asselman, N. E. M. (2000). “Fitting and interpretation of sediment rating curves.” J. Hydrol. (Amsterdam), 234(3-4), 228–248.
Bao, W. M. (1991). “The parameter estimation in the presence of colored noise.” J. Hydrosci. Hydraul. Eng., 12, 47–52.
Bao, W. M. (2006). Hydrological forecasting, China Water Power, Beijing, 92–137.
Bloschl, G., and Sivapalan, M. (1995). “Scale issues in hydrological modeling.” Scale issues in hydrological modeling, J. D. Kalma and M. Sivapalan, eds., Wiley, London, 9–48.
Boughton, W. (2009). “Selecting parameter values for the AWBM daily rainfall-runoff model for use on ungauged catchments.” J. Hydrol. Eng., 14(12), 1343–1350.
Bozdogan, H. (2000). “Akaike’s information criterion and recent developments in information complexity.” J. Math. Psych., 44(1), 62–91.
Burn, D. H., and Boorman, D. B. (1993). “Estimation of hydrological parameters at ungauged catchments.” J. Hydrol. (Amsterdam), 143(3-4), 429–454.
Cheng, C., Zhao, M., Chau, K. W., and Wu, X. (2006). “Using genetic algorithm and TOPSIS for Xinanjiang model calibration with a single procedure.” J. Hydrol. (Amsterdam), 316(1–4), 129–140.
Cong, S. Z. (1980) Hydrological statistics, Hydraulic Press, Beijing.
Fernandez, W., Vogel, R. M., and Sankarasubramanian, A. (2000). “Regional calibration of a watershed model.” Hydrol. Sci. J., 45(5), 689–707.
Guo, S., Wang, J., and Yang, J. (2001). “A semi-distributed hydrological model and its application in a macroscale basin in China.” Soil-vegetation—Atmosphere transfer schemes and large-scale hydrological models, A. J. Dolman, A. J. Hall, M. L. Kavvas, T. Oki and J. W. Pomeroy, eds., IAHS Press, Wallingford, Oxfordshire, UK, 270, 167–174.
Haltas, I., and Kavvas, M. L. (2009). “Modeling the kinematic wave parameters with regression methods.” J. Hydrol. Eng., 14(10), 1049–1058.
Hoerl, A. E. (1962). “Application of ridge analysis to regression problems.” Chem. Eng. Prog., 58(3), 54–59.
Hoerl, A. E., and Kennard, R. W. (1970a). “Ridge regression: Biased estimation for nonorthogonal problem.” Technometrics, 12(1), 55–67.
Hoerl, A. E., and Kennard, R. W. (1970b). “Ridge regression: Applications to nonorthogonal problems.” Technometrics, 12(1), 69–82.
Horowitz, A. J. (2003). “An evaluation of sediment rating curves for estimating suspended sediment concentrations for subsequent flux calculations.” Hydrol. Processes, 17(17), 3387–3409.
Huang, M., Liang, X., and Liang, Y. (2003). “A transferability study of model parameters for the variable infiltration capacity land surface scheme.” J. Geophys. Res., 108(D22), 8864, 16 PP.
Kitanidis, P. K., and Bras, R. L. (1979). “Collinearity and stability in the estimation of rainfall—runoff model parameters.” J. Hydrol. (Amsterdam), 42(1-2), 91–108.
Klemes, V. (1986). “Operational testing of hydrological simulation models.” Hydrol. Sci. J., 31(1), 13–24.
LI, X. Y., Weller, D. E., and Jordan, T. E. (2010). “Watershed model calibration using multi-objective optimization and multi-site averaging.” J. Hydrol. (Amsterdam), 380(3-4), 277–288.
Mosley, M. P. (1981). “Delimitation of New Zealand hydrologic regions.” J. Hydrol. (Amsterdam), 49(1-2), 173–192.
Muller-Wohlfeil, D.-I., Xu, C.-Y., and Iversen, H. L. (2003). “Estimation of monthly river discharge from Danish catchments.” Nord. Hydrol., 34(4), 295–320.
Qu, S. M., Bao, W. M., Shi, P., Yu, Z. B., and Jiang, P. (2009). “Water-stage forecasting in a multitributary tidal river using a bidirectional Muskingum method.” J. Hydrol. Eng., 14(12), 1299–1307.
Riggs, H. C. (1972). “Low-flow investigations.” Techniques of Water Resources Investigation of the U.S. Geological Survey, Book 4, U.S. Geological Survey, Washington, DC.
Sadeghi, S. H. R. et al. (2008). “Development, evaluation and interpretation of sediment rating curves for a Japanese small mountainous reforested watershed.” Geoderma, 144(1-2), 198–211.
Seibert, P. (1999). “Regionalisation of parameters for a conceptual rainfall-runoff model.” Agric. For. Meteorol., 98–99, 279–293.
Sichingabula, H. M. (1998). “Factors controlling variations in suspended sediment concentration for single-valued sediment rating curves, Fraser River, British Columbia, Canada.” Hydrol. Processes, 12(12), 1869–1894.
Tung, Y. K., Yeh, K. C., and Yang, J. C. (1997). “Regionalization of unit hydrograph parameters. 1. Comparison of regression analysis techniques.” Stochastic Hydrol. Hydraul., 11(2), 145–171.
Vandewiele, G. L., and Elias, A. (1995). “Monthly water balance of ungauged catchments obtained by geographical regionalization.” J. Hydrol. (Amsterdam), 170(1-4), 277–291.
Wang, Y., and Liu, Q. (2006). “Comparison of Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) in selection of stock–recruitment relationships.” Fish. Res., 77(2), 220–225.
Xu, C.-Y. (1999a). “Operational testing of a water balance model for predicting climate change impacts.” Agric. For. Meteorol., 98–99, 295–304.
Xu, C.-Y. (1999b). “Estimation of parameters of a conceptual water balance model for ungauged catchments.” Water Resour. Manage., 13(5), 353–368.
Xu, C. (2003). “Testing the transferability of regression equations derived from small sub-catchments to a large area in central Sweden.” Hydrol. Earth Syst. Sci., 7(3), 317–324.
Yapo, P. O., Gupat, H. V., and Sorooshian, S. (1996). “Automatic calibration of conceptual rainfall-runoff model: Sensitivity to calibration data.” J. Hydrol. (Amsterdam), 181(1-4), 23–48.
Zhao, R. J. (1992). “The Xinanjiang model applied in China.” J. Hydrol. (Amsterdam), 135(1–4), 371–381.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 17 • Issue 1 • January 2012
Pages: 118 - 128
Copyright
© 2012 American Society of Civil Engineers.
History
Received: Aug 2, 2010
Accepted: Apr 12, 2011
Published online: Apr 14, 2011
Published in print: Jan 1, 2012
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.