A real-time flow Muskingum forecasting model for three main station of the Medjerda River

River flow forecasting has always been one of the most important issues in hydrology. Models of flood prediction are varied; there are a big number of algorithms from simple statistical receipt to the partial differential equations of Saint-Venant. In Tunisia, the flood problem arise the only perennial river, Medjerda, in particularly the plain of Ghardimaou-Jendouba-Bou Salem. The Muskingum model is the simple flood propagation model and is numerically equivalent to the Saint-Venant equations via the diffusion equation of a wave. In this research, Muskingum model is used to forecast 21 flood’s hydrographs for three stations in Medjerda River. This model requires two data from the upstream station one on the present time and the second on the forecasting time and a data from the downstream station on the present time. The delays of forecasting were 2, 4, 6 and 8 hours. The forecasting operation consisted in choosing reconstitution coefficients by Muskingum model for a previous flood that belong to the same season and had a near humidity index. To evaluate the quality of 252 forecasting operations, four numeric and three graphic performance measures were selected. The standard deviation error ’S’ was chosen to assess the mean quality error. A big difference for the peak flow prediction offer more damage than the little flow in the beginning and the end of flood, for that the peak relative error ’S1’ was calculated. The difference time between observed and forecasted peak have to be the minimum, so the peak time difference ’S2’ was defined. Hydrograph flow, Error flow and correlation between observed and calculated flow were the graphic criteria selected in this application. In the section Ghardimaou- Jendouba, the standard deviation error ’S’ varied from 2 to 190 m3/s, the peak relative error ’S1’ had low value -35 and 23% and the peak time difference ’S2’ 2 and 9 hours. While, for the section Jendouba-Bou Salem the value of the three criteria varied respectively from 2 to 236 m3/s, -24 to 30 % and -2 to 11hours. For the last section Ghardimaou-Bou Salem, the three criteria ranges between; 2 and 225 m3/s (for ’S’), -18 and 12% (for ’S1’) and 2 and 10 hours (for ’S2’). These results are satisfactory for the three sections and all delay. That were confirmed by the mean flow error ’E’ which where for the three section -2 m3/s for the forecasting delay 2 hours, -3 to -4 m3/s for 4 hours, -6 to -8 m3/s for 6 hours and -8 to -13 m3/s for 8 hours. The propagation model Muskingum gave adequate results for the flow forecasting