Quels apports hydrologiques pour les modèles hydrauliques? Vers ...

LERAT ET AL.: VALUE OF UPSTREAM FLOW MEASUREMENTS X - 15mean squared error of flow ˆQ Mod calculated by a model Mod with the observed variance:( ˆQMod∑) 2t − Q ttCEff(Mod) = 1 − ∑( ) 2(5)Q − Qt250tA second formulation is used to better compare the performance of the benchmark modeltel-00392240, version 1 - 5 Jun 2009255260265Bench with the performance of an alternative model Mod, as advocated by Seibert [2001]:∑( ) 2ˆQMod t − Q t tREff(Mod/Bench) = 1 −√∑( ) 2(6)ˆQBench t − Q ttThis second formulation, called relative efficiency (REff), measures the reduction of theroot mean squared error when shifting from one model to another. It gives a more meaningfulestimation of the performance improvement than the comparison of CEff values:identical differences between two values of the CEff criteria can reflect very different situationsdepending on the value of CEff for the benchmark. An improvement of CEff from0.5 for the benchmark to 0.55 for the alternative model is not equivalent to an improvementfrom 0.9 to 0.95. In the first case, the relative improvement is small (REff=0.05),whereas it is large in the second (REff=0.3).Both criteria vary between −∞ and 1. A value of 1 corresponds to a perfect simulation.As indicated in section 3 and Figure 2, calibrated parameters are not identical for the section 3Figure 2three tested models used:1. In the benchmark model, five parameters are calibrated: four parameters for therainfall-runoff model (RR) on the subcatchment UP and the intermediate area INT (parametersets are kept identical on both subcatchments) and one for the routing model(ROUT ). The benchmark model is calibrated against streamflow measured at the downstreamgaging station TOTAL.D R A F T July 24, 2008, 3:43pm D R A F T