Skip to main content
SpringerLink
Log in

Development of distributed time-variant gain model for nonlinear hydrological systems

  • Published:
Science in China Series D: Earth Sciences Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Dooge J. C. I., Linear theory of hydrological system, Agr. Res. Ser., Thch. Bulletin, No.1468, 1973, U.S.D.A.

  2. Singh, V. P., Hydrological Systems, Vol.1. Rainfall-runoff Modeling. Englewood Cliffs, New Jersey, USA: Prentice-Hall. 1988.

    Google Scholar 

  3. Singh, V. P., Hydrological Systems: Watershed Modeling (Tran. by Zhao Weimin et al.), Zhenzhou: Yellow River Water Conservancy Press, 2000.

    Google Scholar 

  4. Ge, S. X., Modern Flood Forecasting Technologies (in Chinese), Beijing: China Water Resources and Hydropower Press, 1999.

    Google Scholar 

  5. Amorocho, J., Measures of the linearity of the hydrological system, J. Geophy. Res., 1963, 68(8): 2237–49.

    Article  Google Scholar 

  6. Amorocho, J., Brandstetter, A., Determination of nonlinear functional response functions, in rainfall-runoff processes, Water Resour. Res., 1971, 7(5): 1087–1101.

    Article  Google Scholar 

  7. 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.

    Google Scholar 

  8. 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.

    Article  Google Scholar 

  9. Diskin, M. H., Identification of a Volterra series conceptual model based on a cascade of nonlinear reservoir, J. Hydrol., 1984, 68: 231–245.

    Article  Google Scholar 

  10. Nash, J. E., Brasi, B. I., A hybrid model for flow forecasting on large catchment, J. Hydrol., 1983, 65: 125–137.

    Article  Google Scholar 

  11. Xia, J., Identification of a constrained nonlinear hydrological system described by Volterra Functional Series, Water Resour. Res., 1991, 27(9): 2415–2420.

    Article  Google Scholar 

  12. 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.

    Article  Google Scholar 

  13. 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.

    Article  Google Scholar 

  14. Xia, J., A system approach to real time hydrological forecasts in watersheds, Water International, 2002, 27(1): 87–97.

    Article  Google Scholar 

  15. Xia, J., Hydrological Nonlinear Theories and Approaches (in Chinese), Wuhan: Wuhan University Press, 2002, 16–25.

    Google Scholar 

  16. 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.

    Google Scholar 

  17. Institute of Geography Research (IGR), Hydrological Analysis & Experiments, Special Issue of Geography, Beijing: Science Press No.12, 1980.

    Google Scholar 

  18. Xia, J., Parameter identifiability of hydrological models with implicit structure, Hydrological Science Journal, 1989, 34(1–2): 1–19.

    Google Scholar 

  19. Singh, V. P., Computer models of watershed hydrology, Water Resources Publications, USA, 1995

    Google Scholar 

  20. Beven, K. J., Rainfall-Runoff Modelling, New York: John Wiley & Sons Ltd, 2001.

    Google Scholar 

  21. 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.

    Article  Google Scholar 

  22. Beven, K.J., Feyan, J., The Future of Distributed Hydrological Modelling, Special Issue of Hydrol. Processess, 2002, 16(2): 169–574.

    Google Scholar 

  23. 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.

  24. 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.

    Google Scholar 

  25. 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.

    Google Scholar 

  26. 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.

  27. 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.

    Article  Google Scholar 

  28. Amorocho J., Nonlinear hydrological analysis, In: Advance in Hydroscience ((ed. V. T. C. How), 1973, 9: 203–251.

  29. 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.

    Google Scholar 

  30. Bidwell, V. C., Regression analysis of nonlinear catchment system, Water Resour. Res., 1971, 7: 1118–26.

    Article  Google Scholar 

  31. Diskin, M. H., and A. Boneh, Determination of optimal kernels for seconded order surface runoff system, Water Resour. Res., 1973, 9(2): 311–325.

    Article  Google Scholar 

  32. Patry, G. G., Marino, M. A., Nonlinear runoff model: parameter identification, ASCE J. Hdraul. Eng. 1983, 109(6): 865–80.

    Google Scholar 

  33. 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.

    Google Scholar 

  34. 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.

    Article  Google Scholar 

  35. Thompson, S. A., Hydrology for Water Management, Rotterdam: A. A. Balkema, 1999: 115–120, 205–240.

    Google Scholar 

  36. Garrick, M., Cunnane, C., Nash, J. E., A criterion of efficiency for rainfall-runoff models, J. Hydrol., 1978, 36(3/4): 375–381.

    Article  Google Scholar 

  37. 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.

    Google Scholar 

  38. 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.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Key Laboratory of Water Cycle & Related Land Surface Processes, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, 100101, Beijing, China

    Xia Jun, Gangsheng Wang & Ge Tan

  2. State Key Laboratory of Water Resources & Hydropower Engineering Sciences, Wuhan University, 430072, Wuhan, China

    Xia Jun & Aizhong Ye

  3. Faculty of Engineering, University of Regina, 3737 Wascana Parkway, S4S 0A2, Sask, Regina, Canada

    G. H. Huang

Authors
  1. Xia Jun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gangsheng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ge Tan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Aizhong Ye
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. G. H. Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xia Jun.

Rights and permissions

Reprints 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

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1360/03yd0183

Keywords

Search

Navigation