International Journal of Agricultural Engineering

Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

A Muskingum Model Based on Unit-Step and Transfer Function Approach for Prediction of Direct Runoff Hydrographs from a Small Watershed


Affiliations
1 Department of Soil and Water Conservation Engineering, Dr. Panjabrao Deshmukh Krishi Vidyapeeth, Akola (M.S.), India
2 Agricultural Engineering, Zonal Agricultural Research Station (M.P.K.V.), Karveer (M.S.), India
3 Jain Irrigation Systems Ltd. Ramthal Lift Irrigation Scheme, Bagalkot (Karnataka), India
     

   Subscribe/Renew Journal


The hydrological investigation was carried out to develop a mathematical expression for Muskingum model on the basis of application of unit-step function for prediction of direct runoff hydrographs from Shenda Park watershed, Kolhapur of Maharashtra state considering it to be a lumped, linear and timeinvariant system. Generally the ordinates of direct runoff are obtained directly as the inverse Laplace transform of the product of Laplace transform of the input and the transfer function of the system. The value of model parameter, storage constant (K) was estimated, which was found to be 0.37 (hr). Direct runoff hydrographs were developed against three values of weighing factor, X = 0.00 (reservoir routing), X = 0.05 (channel routing), and X = 0.10 (channel routing). Performance evaluation of developed model in determining direct runoff hydrograph ordinates was evaluated using various statistical indices. For weighing factor, X = 0.00, the overall average values of co-efficient of efficiency (CE), co-efficient of correlation (R), special correlation co-efficient (Rs), ischolar_main mean square error (RSME) and percentage absolute deviation in peak flow (PADp) and runoff volume (PADv) were found to be 0.902, 0.962, 0.926, 0.0013 and 17.66 and 2.65, respectively. Based on all the evaluation criteria, model can be easily applied for the prediction of direct runoff hydrograph ordinates for the study watershed.

Keywords

Direct Runoff Hydrograph, Muskingum Model, Laplace Transform.
Subscription Login to verify subscription
User
Notifications
Font Size


  • Chiew, F.H.S., Stewardson, M.J. and McMohan, T.A. (1993). Comparison of six rainfall runoff modeling approaches. J. Hydrol., 147 : 1-36.

  • Clark, C.O. (1945). Storage and the unit hydrograph. Transactions of American Society of Civil Engineers, 110 : 1419-1488.

  • Diskin, M.H. (1964). A basic study of the linearity of the rainfall-runoff process in watersheds. Thesis, Ph.D. University of Illinois, Urbana, ILLINOIS (U.S.).

  • Eagleson, P.S. and March, F. (1965). Approaches to linear synthesis of urban runoff systems. Report 85, Hydrodynamics Lab, Massachusetts Institute of Technology, Cambridge, M.A.

  • Jawed, K. (1973). Comparison of methods of deriving unit hydrographs, M.Sc. Thesis, Colorado State University, COLORADO.

  • Kulandaiswamy, V.C. and Basu, R.T. (1975). A mathematical model for basin runoff. In : Water for human needs, Proc. 2nd World Congress on Water Resources, New Delhi Vol. V. Technology and Ecology.

  • Kumar, P., Singh, J.K. and Singh, S.B. (2008). Runoff prediction by linear discrete input-output model. J. Agric. Engg., 45(4):36-43.

  • Nash, J.E. (1957). The form of the instantaneous unit hydrograph. International. Association of Sci. & Hydrology Publication, 45(3) : 114-121.

  • Nash, J.E. and Sutcliffe, J.V. (1970). River flow forecasting through conceptual models I-A discussion on principles. J. Hydrol., 10 (3) : 282-290.

  • Ogata, K. (1970). Modern control engineering. Prentice-Hall Englewood Cliffs, N.J.

  • Sarma, P.B.S., Dellur, J.W. and Rao, A.R. (1973). Comparison of rainfall-runoff models for urban areas. J. Hydrol., 18 : 329-347.

  • Singh, V.P. (1988). Hydrologic Systems : Vol. I : Rainfall-Runoff Modelling. Prentice-Hall, Englewood Cliffs, N.J.

  • Wang, G.T., Singh, V.P. and Yu, F.X. (1992). A rainfall-runoff model for small watersheds. J. Hydrol., 138 : 97-117.

  • Wang, G.T. and Wu, K. (1983). The unit-step function response for several hydrological conceptual models. J. Hydrol., 62 : 119-128.

  • Young, P.C. (2005). Rainfall-runoff modelling: Transfer function models. Enc. Hydrol. Sci., 11(1): 1-16.

  • Yu, P. S., Liu, C. L. and Lee, T. Y. (1994). Application of transfer function model to a storage runoff process. In: Hipel K.W., McLeod A.I. and Panu U.S. (Ed.). Stochastic & Stat. Methods Hydrol. & Environ. Engg., 3 : 87-97.


Abstract Views: 515

PDF Views: 0




  • A Muskingum Model Based on Unit-Step and Transfer Function Approach for Prediction of Direct Runoff Hydrographs from a Small Watershed

Abstract Views: 515  |  PDF Views: 0

Authors

S. N. Bansude
Department of Soil and Water Conservation Engineering, Dr. Panjabrao Deshmukh Krishi Vidyapeeth, Akola (M.S.), India
G. L. Chunale
Agricultural Engineering, Zonal Agricultural Research Station (M.P.K.V.), Karveer (M.S.), India
A. A. Shinde
Jain Irrigation Systems Ltd. Ramthal Lift Irrigation Scheme, Bagalkot (Karnataka), India

Abstract


The hydrological investigation was carried out to develop a mathematical expression for Muskingum model on the basis of application of unit-step function for prediction of direct runoff hydrographs from Shenda Park watershed, Kolhapur of Maharashtra state considering it to be a lumped, linear and timeinvariant system. Generally the ordinates of direct runoff are obtained directly as the inverse Laplace transform of the product of Laplace transform of the input and the transfer function of the system. The value of model parameter, storage constant (K) was estimated, which was found to be 0.37 (hr). Direct runoff hydrographs were developed against three values of weighing factor, X = 0.00 (reservoir routing), X = 0.05 (channel routing), and X = 0.10 (channel routing). Performance evaluation of developed model in determining direct runoff hydrograph ordinates was evaluated using various statistical indices. For weighing factor, X = 0.00, the overall average values of co-efficient of efficiency (CE), co-efficient of correlation (R), special correlation co-efficient (Rs), ischolar_main mean square error (RSME) and percentage absolute deviation in peak flow (PADp) and runoff volume (PADv) were found to be 0.902, 0.962, 0.926, 0.0013 and 17.66 and 2.65, respectively. Based on all the evaluation criteria, model can be easily applied for the prediction of direct runoff hydrograph ordinates for the study watershed.

Keywords


Direct Runoff Hydrograph, Muskingum Model, Laplace Transform.

References