Forecasting discharges at the downstream end of a river reach through two simple Muskingum based procedures

The Muskingum–Cunge model (MC, ) can be used for real-time forecasting of discharges at the downstream end of a river reach for a predetermined lead time Δt∗, which is closely connected to the two routing parameters k and x (). Similarly, the Rating Curve Method (RCM, ) can be used for real-time forecasting of discharges at the downstream end of a river reach for an assigned lead time TL, equal to the mean travel time of the flood events in the river reach. In this article two procedures are presented, the first based on use of the MC model alone and the second on a cascade combination of the MC and RCM models. These two procedures enable real-time forecasting of the discharges at one end of a river reach – with or without taking account of lateral inflows – for variable lead times ranging between 1 h and the mean travel time of flood events in that reach, assuming that only the length and the mean slope and width of that reach are known. Each procedure is moreover associated with a suitable method for estimating the confidence band for the forecast which takes into account the heteroscedastic nature of forecasting errors. These two procedures were applied to two consecutive reaches of the Tiber river (Italy), characterised, respectively, by a strong and limited presence of lateral inflows, and to the reach obtained as a sum of the two. The results show the reliability of the two procedures: the first one produces good results for all forecast lead times considered, the second only when the lead times are close to the mean travel time and in such a case, especially when the mean travel time is long (long reach), it provides a forecast of better quality than the other procedure.