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X - 12LERAT ET AL.: VALUE OF UPSTREAM FLOW MEASUREMENTSThe third model, UP-Sim, constitutes an intermediate solution between the two previousmodels by calculating downstream discharges as:ˆQ T OT AL= RR (θ ′ , P INT , P E INT ) + ROUT(ρ ′ , ˆQ)UP(3)ˆQ UP = RR (θ ′′ , P UP , P E UP )The UP-Sim model uses two RR modules to calculate runoff from the UP and INT area.The parameters of the RR model on the intermediate area INT, θ ′ , and the parameters of200the ROUT model, ρ ′ , are identical to those of the UP-Meas model (these parameters aretel-00392240, version 1 - 5 Jun 2009205210not re-calibrated in UP-Sim). Parameters for the RR model on the UP subcatchment, θ ′′ ,are calibrated independently against measured streamflows from the UP gaging station.Hence, the UP-Sim model exploits upstream discharges indirectly via calibration of theRR model on UP.The characteristics of the three previous models are summarized in Table 2. Table 2In the two following sections, we briefly describe the RR and ROUT components of oursemidistributed model.3.2. Rainfall-runoff modelWe used GR4J, a continuous lumped rainfall-runoff model, to calculate runoff on thesubcatchment UP and the intermediate area INT. This model was applied over a widerange of hydroclimatic conditions [Perrin et al, 2003, Le Moine et al., 2007]. Figure 3presents the overall model scheme (see Perrin et al. [2003] for more mathematical details).This model has four free parameters:1. S, the capacity of the soil moisture accounting store (in millimeters),D R A F T July 24, 2008, 3:43pm D R A F T