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X - 20LERAT ET AL.: VALUE OF UPSTREAM FLOW MEASUREMENTS355did not lead to improved correlations. Since the catchment surface constitutes a poorestimator of runoff, it is natural that the surface ratio provides the lowest correlationcoefficient. The 99 th percentile discharge ratio was found to be more informative thanthe mean annual discharge ratio, which can be explained by the heteroscedastic nature ofrainfall-runoff model residuals: the largest errors occur during high-flow events; therefore,360a significant upstream contribution during these very periods reduces these errors and hasan important effect on the overall mean squared error.tel-00392240, version 1 - 5 Jun 20093653705.2. What happens when upstream flow measurements decrease in quality ?In this section, we analyze the changes in performance using the UP-Meas model whenit is calibrated with corrupted upstream flow data. The error model used to corrupt themassumes that the error associated with streamflow measurements comes from rating curveuncertainties [Shrestha et al., 2007]. If we represent this curve by a power transformationof the form Q = a × H b , where Q is the streamflow, H the water level, and a and bthe rating curve parameters, a corrupted streamflow would be calculated by ˜Q = ã × H˜bwhere ã and ˜b are the corrupted parameter. Hence, ˜Q =ãa˜b/b× Q˜b/b = α × Q β which isagain a power transformation with two parameters α and β. Therefore we have appliedthis two-parameter power transform on initial upstream flow data.Corruption was focused on high flows because they are the best variable to explainthe influence of upstream flow measurements on downstream simulations according tothe results obtained in the previsous section. The final corruption transformation is thefollowing:˜Q UP (j) ={Q UP (j) if Q UP (j) < median(Q UP ),α × Q UP (j) β if Q UP (j) ≥ median(Q UP ).D R A F T July 24, 2008, 3:43pm D R A F T