Abstract
In this paper, a rainfall-runoff modeling system is developed based on a nonlinear Volterra functional series and a hydrological conceptual modeling approach. Two models, i.e. the time-variant gain model (TVGM) and the distributed time-variant gain model (DTVGM) that are built on the platform of Digital Elevation Model (DEM), Remote Sensing (RS) and Unit Hydrological Process were proposed. The developed DTVGM model was applied to two cases in the Heihe River Basin that is located in the arid and semiarid region of northwestern China and the Chaobai River basin located in the semihumid region of northern China. The results indicate that, in addition to the classic dynamic differential approach to describe nonlinear processes in hydrological systems, it is possible to study such complex processes through the proposed systematic approach to identify prominent hydrological relations. The DTVGM, coupling the advantages of both nonlinear and distributed hydrological models, can simulate variant hydrological processes under different environment conditions. Satisfactory results were obtained in forecasting the time-space variations of hydrological processes and the relationships between land use/cover change and surface runoff variation.
Similar content being viewed by others
References
Dooge J. C. I., Linear theory of hydrological system, Agr. Res. Ser., Thch. Bulletin, No.1468, 1973, U.S.D.A.
Singh, V. P., Hydrological Systems, Vol.1. Rainfall-runoff Modeling. Englewood Cliffs, New Jersey, USA: Prentice-Hall. 1988.
Singh, V. P., Hydrological Systems: Watershed Modeling (Tran. by Zhao Weimin et al.), Zhenzhou: Yellow River Water Conservancy Press, 2000.
Ge, S. X., Modern Flood Forecasting Technologies (in Chinese), Beijing: China Water Resources and Hydropower Press, 1999.
Amorocho, J., Measures of the linearity of the hydrological system, J. Geophy. Res., 1963, 68(8): 2237–49.
Amorocho, J., Brandstetter, A., Determination of nonlinear functional response functions, in rainfall-runoff processes, Water Resour. Res., 1971, 7(5): 1087–1101.
Boneh, A., Diskin, M. H., Demonstration of nonlinear effects of a second order runoff model by field data, in Floods and Droughts ((eds. E. F. Schultz et al.), For Collins, Colo: Water Resour. Publications, 1973, 157–68.
Liu, C. C. K. Brutsaert, W., A nonlinear analysis of the relation-ship between rainfall and runoff for extreme floods, Water Resour. Res., 1978, 14(1): 75–83.
Diskin, M. H., Identification of a Volterra series conceptual model based on a cascade of nonlinear reservoir, J. Hydrol., 1984, 68: 231–245.
Nash, J. E., Brasi, B. I., A hybrid model for flow forecasting on large catchment, J. Hydrol., 1983, 65: 125–137.
Xia, J., Identification of a constrained nonlinear hydrological system described by Volterra Functional Series, Water Resour. Res., 1991, 27(9): 2415–2420.
Ahsan, M., O’Connor, K. M., A simple nonlinear rainfall-runoff model based on the concept of a variable gain factor, J. Hydrol., 1994, 155: 151–183.
Xia, J., K. M. O’Connor, Kachroo, R. K. et al., A nonlinear perturbation model considering catchment wetness and its application in river flow forecasting, Hydrological Journal, 1997, 200: 164–178.
Xia, J., A system approach to real time hydrological forecasts in watersheds, Water International, 2002, 27(1): 87–97.
Xia, J., Hydrological Nonlinear Theories and Approaches (in Chinese), Wuhan: Wuhan University Press, 2002, 16–25.
Minshall N. E., Predicting storm runoff on small experimental watersheds, Journal of the Hydraulics Division, Proceedings of the American Society of Civil Engineers 86(HY8), 1960, 17–38.
Institute of Geography Research (IGR), Hydrological Analysis & Experiments, Special Issue of Geography, Beijing: Science Press No.12, 1980.
Xia, J., Parameter identifiability of hydrological models with implicit structure, Hydrological Science Journal, 1989, 34(1–2): 1–19.
Singh, V. P., Computer models of watershed hydrology, Water Resources Publications, USA, 1995
Beven, K. J., Rainfall-Runoff Modelling, New York: John Wiley & Sons Ltd, 2001.
Abbott, M. B., Bathurst, J. C., Cunge, J. A. et al., An introduction to European Hydrological System-Systeme Hydrologique Europeen, “SHE”, 1. History and philosophy of a physically-based distributed modeling system, J. Hydrol., 1986, 87: 45–69.
Beven, K.J., Feyan, J., The Future of Distributed Hydrological Modelling, Special Issue of Hydrol. Processess, 2002, 16(2): 169–574.
Lu M., Koike, T., Hayakawa, N., Distributed XinAnjiang model using radar measured rainfall data, in: Water Resources & Environmental Research: Towards the 21st Century (Proc. Int. Conf.), 1996, 29–36.
Arnold, J. G., Williams, J. R., Srinivasan, R. et al., Model theory of SWAT. USDA, Agricultural Research Service Grassland, Soil and Water Research Laboratory, USA, 1997.
Su, F. G., Hao, Z. C., Research on the Macroscale Distributed Hydrological Model, in: Theoretical Studies and Technical Applications of Water Conservancy and Hydroelectric Power Engineering (in Chinese), Wuhan: Wuhan University of Technology Press, 2000, 237–243.
IUGG2003, Abstracts of Volume A and B, the XXIII General Assembly of International Union of Geodesy and Geophysics, 30 June -11 July, Sapporo, Japan July, 2003.
Napiorkowski, J. J., Strupczewski, W. G., The properties of the kernels of the Volterra Series descrebing slow deviation from a steady state in an open channel, J. Hydrol., 1981, 52: 185–198.
Amorocho J., Nonlinear hydrological analysis, In: Advance in Hydroscience ((ed. V. T. C. How), 1973, 9: 203–251.
Chow V. T., Kulandaiswamy V. C., General hydrological system model, Journal of the Hydraulics Division, Proceedings of the American Society of Civil Engineers 97(HY6), 1971, 791–804.
Bidwell, V. C., Regression analysis of nonlinear catchment system, Water Resour. Res., 1971, 7: 1118–26.
Diskin, M. H., and A. Boneh, Determination of optimal kernels for seconded order surface runoff system, Water Resour. Res., 1973, 9(2): 311–325.
Patry, G. G., Marino, M. A., Nonlinear runoff model: parameter identification, ASCE J. Hdraul. Eng. 1983, 109(6): 865–80.
Wang, G. S., Xia, J., Tan, G. et al., A Research on distributed time variant gain model: a case study on Chaohe River Basin, Progress in Geography (in Chinese), 2002, 21(6): 573–582.
Pereira, L. S., Pereira, A., Allen, R. G. et al., Evapotranspiration: concepts and future trend, Journal of Irrigation and Drainage Engineering ASCE, 1999, 4: 45–51.
Thompson, S. A., Hydrology for Water Management, Rotterdam: A. A. Balkema, 1999: 115–120, 205–240.
Garrick, M., Cunnane, C., Nash, J. E., A criterion of efficiency for rainfall-runoff models, J. Hydrol., 1978, 36(3/4): 375–381.
Kang, E. S., Cheng, G. D., Lan, Y. C. et al., The response model of runoff from inland river mountainous watershed of the arid area of northwest China to climatic changes, Science in China, Series D, (in Chinese), 1999, 29(Supp. 1): 47–54.
Li, X. B., A review of the international researches on land use/land cover change, Acta Geographica Sinica (in Chinese), 1996, 51(6): 553–557.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Xia, J., Wang, G., Tan, G. et al. Development of distributed time-variant gain model for nonlinear hydrological systems. Sci. China Ser. D-Earth Sci. 48, 713–723 (2005). https://doi.org/10.1360/03yd0183
Received:
Issue Date:
DOI: https://doi.org/10.1360/03yd0183