Water Resources Management

, Volume 3, Issue 3, pp 205–230 | Cite as

A physically-based flood volume distribution model

  • Mohamed Nasr Allam
  • Abdullah Saad Al-Wagdany
Review Paper

Abstract

An analytically derived distribution model for flood volume is presented. The model is based on water balance computations during a rainstorm at the soil surface. It is applicable for mountainous watersheds with alluvial channels. Three hydrologic processes are considered: precipitation, infiltration, and runoff generation. Rainfall intensity and duration are presented with exponential distributions. They are assumed to be statistically independent. A linear rainfall-runoff relationship is proposed for the mountainous areas. The mountain runoff is regarded as a uniformly distributed water depth on the alluvial channels. The rainfall excess in the alluvial channels is computed to be equal to this depth plus the rainfall depth minus the infiltration losses. Infiltration in the channels is presented with Philip's expression, coupled with an empirical model for the computation of a long-term average value for the soil moisture content. The distribution model is verified through applications for three gauged watersheds in Saudi Arabia: Wadi Liyyah (174 km2), Wadi Turrabah (3720 km2), and Wadi Khulays (5220 km2). The results are found to be in a good agreement with observations.

Key words

Flood volume cumulative probability distribution mountainous watersheds precipitation infiltration Saudi Arabia 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Allam, M. N., 1989, Case study evaluation of geomorphologic rainfall-runoff model: incorporating Philip's infiltration expression,J. Water Resour., Planning and Management, ASCE, to appear.Google Scholar
  2. Alley, W. M., Dawdy, D. R., and Schaake, J. C. Jr., 1980, Parametric deterministic urban watershed model,Hydraulic Division, ASCE 105 [HY5].Google Scholar
  3. Alley, W. M. and Smith, P. e., 1982, Computer program user's manual, distributed routing rainfall runoff model — version II, USGS Open File Report 82–344.Google Scholar
  4. Ashkar, F. and Roussel, J., 1981, A multivariate statistical analysis of flood magnitude, in V. P. Singh (ed.),Statistical Analysis of Runoff, Water Resources Publications, pp. 665–668.Google Scholar
  5. Bain, L. J. and Engelhardt, M., 1981, Simple approximate distributional results for confidence and tolerance limits for the Weibull distribution based on maximum likelihood estimators,Technometrics 23, 15–20.Google Scholar
  6. Carman, P. C., 1937, Fluid flow throw granular beds,Trans. Inst. Chem. Eng. 15, 150–166.Google Scholar
  7. Crank, J., 1956,The Mathematics of Diffusion, Oxford University Press, New York.Google Scholar
  8. Cunnane, C., 1973, A particular comparison of annual maxima and partial duration series methods of flood frequency prediction,J. Hydrol. 18, 257–271.Google Scholar
  9. Dawdy, D. R., Schaake, J. C. Jr., and Alley, W. M., 1978, User's guide for distributed routing rainfall-runoff model, USGS Water Resources Inv. 78–90.Google Scholar
  10. Diaz-Granados, M. A., Valdes, J. B., and Bras, R. L., 1983, A derived flood frequency distribution based on the geomorphoclimatic IUH and the density function of rainfall excess, TR # 292, Ralph M. Parsons, Lab., MIT, Cambridge, Mass.Google Scholar
  11. Dien, M. A., 1985, Estimation of flood and recharge volumes in wadis Fattimah, Namman and Turrabah, MSc thesis, Faculty of Earth Sciences, King Abdulaziz Univ., Jeddah, Saudi Arabia.Google Scholar
  12. Eagleson, P. S., 1978a, Climate, soil and vegetation, 2. The distribution of annual precipitation derived from observed storm sequences,WRR 14, 713–721.Google Scholar
  13. Eagleson, P. S., 1978b, Climate, soil and vegetation, 3. A simplified model of soil moisture movement in the liquid phase,WRR 14, 722–730.Google Scholar
  14. Eagleson, P. S., 1978c, Climate, soil and vegetation, 5. A derived distribution of storm surface runoff,WRR 14, 741–748.Google Scholar
  15. Gradshteyn, I. S. and Ryzhik, I. M., 1965,Table of Integrals, Series and Products, Academic Press, New York.Google Scholar
  16. Lecterc, G. and Schaake, J. C. Jr., 1973, Methodology for assessing the potential impact of urban development on urban runoff and the relative efficiency of runoff control alternatives, Ralph M. Parsons Lab., Report. No. 167, M.I.T., Cambridge, U.S.A.Google Scholar
  17. Ministry of Agriculture and Water, 1980a, Rainfall intensity for 1963–1980, Report 98, Vol. 4, Riyadh, Saudi Arabia.Google Scholar
  18. Ministry of Agriculture and Water, 1980b, Monthly hydrologic data, runoff for 1966–1980, Report 98, Vol. 2, Riyadh, Saudi Arabia.Google Scholar
  19. Ministry of Agriculture and Water, 1984, Monthly climate data for 1966–1984, Volumes 99, 102, 107 and 110, Riyadh, Saudi Arabia.Google Scholar
  20. Nguyen, V., Phien, H. and In-na, N., 1987, An analytically derived distribution function for flood volume,Proc. Engineering Hydrology Symposium, ASCE, Williamsburg, Virginia.Google Scholar
  21. Philip, J. R., 1969, The theory of infiltration, in V. T. Chow (ed.),Advances in Hydroscience, Vol. 5, Academic Press, New York, pp. 215–296.Google Scholar
  22. Richards, L. A., 1931, Capillary conduction through porous mediums,Physics 1, 313–318.Google Scholar
  23. Sadhan, A. S., 1980, Water plan for Wadi Fattimah Basin, MSc thesis, Department of Agricultural Engineering, University of Wyoming.Google Scholar
  24. Singh, K. P. and Nakashima, M., 1981, A new methodology for flood frequency analysis with objective detection and modification of outliers, State Water Survey CR 272, Champaign, Illinois.Google Scholar
  25. Singh, K. P., 1987, A versatile methodology for flood frequency analysis,Proc. Engineering Hydrology Symposium, ASCE, Williamsburg, Virginia.Google Scholar
  26. Thomas, H. A., 1948, Frequency of minor floods,J. Boston Soc. Civil Eng. 35, 425–442.Google Scholar
  27. Tordorovic, P. and Zelenhasic, E., 1970, A stochastic model for flood analysis,WRR 6 1641–1642.Google Scholar
  28. Todorovic, P., 1978, Stochastic models of floods,WRR. 14, 345–365.Google Scholar

Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • Mohamed Nasr Allam
    • 1
  • Abdullah Saad Al-Wagdany
    • 1
  1. 1.Faculty of Meteorology, Environment, and Arid Land AgricultureKing Abdullaziz UniversityJeddahSaudi Arabia

Personalised recommendations