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LERAT ET AL.: VALUE OF UPSTREAM FLOW MEASUREMENTS X - 132152. IGF , the parameter that controls the intercatchment groundwater flow (in millimeters),3. R, the capacity of the non-linear routing store (in millimeters),4. T B, the time base of the unit hydrograph (in days).3.3. Routing modelThe propagation model used to route the upstream flows toward the catchmentoutlet is based on a resolution of the diffusive wave equation first introduced by220Hayami [1951].With the hypothesis that the wave celerity and the diffusion remainconstant, Hayami [1951] proposed an analytical solution of this equation in the form oftel-00392240, version 1 - 5 Jun 2009the following convolution product:O(t) = ∫ t0I(t − τ)K(τ)dτ (4)with: I(t) = Q(0, t) − Q(0, 0)O(t) = Q(L, t) − Q(L, 0)K(t) =L2 √ πDexp [ (CL4D 2 −L− )]CtCt Lt 3/2where L is the length of the river reach, Q(0, t) and Q(L, t) the flows at the upstream anddownstream points of the river reach at time t, C the wave celerity, and D the diffusion225coefficient. This model was applied by several authors [Baptista and Michel, 1989; Corra-dini, 1991; Moramarco et al., 2005; Moussa, 2008] to propagate streamflow in natural riverchannels. Sensitivity tests (not presented here) revealed that the diffusion paremeter DD R A F T July 24, 2008, 3:43pm D R A F T