Confidence interval of real-time forecast stages provided by the STAFOM-RCM model: the case study of the Tiber River (Italy)

This study proposes a statistically based procedure to quantify the confidence interval (CI) to be associated to the stages forecast by a simple model called STAge FOrecasting Model-Rating Curve Model (STAFOM-RCM). This model can be used for single river reaches characterized by different intermediate drainage areas and mean wave travel times when real-time stage records, cross section surveys and rating curves are available at both ends. The model requires, at each time of forecast, an estimate of the lateral contribution qfor between the two sections delimiting the reach. The CI of the stage is provided by analyzing the statistical properties of model output in terms of lateral flow, and it is derived from the CI of the lateral contribution qfor which, in turn, is set up by associating to each qfor the qopt which allows STAFOM-RCM to reproduce the exact observed stage. From an operative point of view, the qfor values are ranked in order of magnitude and subdivided in classes where the qopt values can be represented through normal distributions of proper mean and variance from which an interval of selected confidence level for qfor is computed and transferred to the stage. Three river reaches of the Tiber river, in central Italy, are used as case study. A sensitivity analysis is also performed in order to identify the minimum calibration set of flood events. The CIs obtained are consistent with the level of confidence selected and have practical utility. An interesting aspect is that different CI widths can be produced for the same forecast stage since they depend on the estimate of qfor made at the time of forecast. Overall, the proposed procedure for CI estimate is simple and can be conveniently adapted for other forecasting models provided that they have physically based parameters which need to be updated during the forecast.