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A runoff model is a mathematical model describing the rainfall–runoff relations of a rainfall ''catchment area'', drainage basin or ''watershed''. More precisely, it produces a surface runoff hydrograph in response to a rainfall event, represented by and input as a hyetograph. In other words, the model calculates the conversion of rainfall into runoff. A well known runoff model is the ''linear reservoir'', but in practice it has limited applicability. The runoff model with a ''non-linear reservoir'' is more universally applicable, but still it holds only for catchments whose surface area is limited by the condition that the rainfall can be considered more or less uniformly distributed over the area. The maximum size of the watershed then depends on the rainfall characteristics of the region. When the study area is too large, it can be divided into sub-catchments and the various runoff hydrographs may be combined using flood routing techniques. Rainfall-runoff models need to be calibrated before they can be used. ==Linear reservoir== The hydrology of a linear reservoir (figure 1) is governed by two equations.〔J.W. de Zeeuw, 1973. ''Hydrograph analysis for areas with mainly groundwater runoff''. In: Drainage Principle and Applications, Vol. II, Chapter 16, Theories of field drainage and watershed runoff. p 321-358. Publication 16, International Institute for Land Reclamation and Improvement (ILRI), Wageningen, The Netherlands.〕 #flow equation: Q = A.S, with units (), where L is length (e.g. mm) and T is time (e.g. h, day) #continuity or water balance equation: R = Q + dS/dT, with units () where: Q is the ''runoff'' or'' discharge'' R is the ''effective rainfall'' or ''rainfall excess'' or ''recharge'' A is the constant ''reaction factor'' or ''response factor'' with unit () S is the water storage with unit () dS is a differential or small increment of S dT is a differential or small increment of T Runoff equation A combination of the two previous equations results in a differential equation, whose solution is: * Q2 = Q1 exp + R (1 − exp ) This is the ''runoff equation'' or ''discharge equation'', where Q1 and Q2 are the values of Q at time T1 and T2 respectively while T2−T1 is a small time step during which the recharge can be assumed constant. Computing the total hydrograph Provided the value of A is known, the ''total hydrograph'' can be obtained using a successive number of time steps and computing, with the ''runoff equation'', the runoff at the end of each time step from the runoff at the end of the previous time step. Unit hydrograph The discharge may also be expressed as: Q = − dS/dT . Substituting herein the expression of Q in equation (1) gives the differential equation dS/dT = A.S, of which the solution is: S = exp(− A.t) . Replacing herein S by Q/A according to equation (1), it is obtained that: Q = A exp(− A.t) . This is called the instantaneous unit hydrograph (IUH) because the Q herein equals Q2 of the foregoing runoff equation using ''R'' = 0, and taking S as ''unity'' which makes Q1 equal to A according to equation (1). The availability of the foregoing ''runoff equation'' eliminates the necessity of calculating the ''total hydrograph'' by the summation of partial hydrographs using the ''IUH'' as is done with the more complicated convolution method.〔D.A. Kraijenhoff van de Leur, 1973. ''Rainfall-runoff relations and computational models''. In: Drainage Principle and Applications, Vol. II, Chapter 16, Theories of field drainage and watershed runoff. p 245-320. Publication 16, International Institute for Land Reclamation and Improvement (ILRI), Wageningen, The Netherlands.〕 Determining the response factor A When the ''response factor'' A can be determined from the characteristics of the watershed (catchment area), the reservoir can be used as a ''deterministic model'' or ''analytical model'', see hydrological modelling. Otherwise, the factor A can be determined from a data record of rainfall and runoff using the method explained below under ''non-linear reservoir''. With this method the reservoir can be used as a black box model. Conversions 1 mm/day corresponds to 10 m3/day per ha of the watershed 1 l/s per ha corresponds to 8.64 mm/day or 86.4 m3/day per ha 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Runoff model (reservoir)」の詳細全文を読む スポンサード リンク
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