Evaluation of standard error of forecast of runoff volume using linear regression models

Optimizing reservoir operations requires forecasts of seasonal inflow and a good understanding of the associated uncertainties. When forecasting seasonal runoff volume to a reservoir using a linear regression model, hydrologic forecasters typically use the standard error of residuals as the standard error of forecast to give water managers a sense of uncertainties in the forecast. However, this practice accounts for only the random error and ignores the modeling error in the volume forecast, resulting in underestimation of the standard error of the forecast. The underestimation can become significant in extreme runoff years for which reservoir operations tend to be most critical. This paper presents the algorithm for calculating the standard error of forecast, which takes into consideration both random and modeling errors. A simple way of calculating the standard error of forecast using built-in functions in Microsoft Excel is described. An example is used to demonstrate the potentially significant underestimation of the true error of a forecast if modeling error is ignored.