Multi-model streamflow prediction using conditional bias-penalized multiple linear regression

Objective merging of multiple forecasts to improve forecast accuracy is of large interest in many disciplines. Multiple linear regression (MLR) is an extremely attractive technique for this purpose because of its simplicity and interpretability. For modeling and prediction of extremes such as floods using MLR, however, attenuation bias is a very serious issue as it results in systematic under- and over-prediction in the upper and lower tails of the predictand, respectively. In this work, we introduce conditional bias-penalized multiple linear regression (CBP-MLR) which reduces attenuation bias by jointly minimizing mean squared error (MSE) and Type-II error squared. Whereas CBP-MLR improves prediction over tails, it degrades the performance near median. To retain MLR-like performance near median while exploiting the ability of CBP-MLR to improve prediction over tails, we employ composite MLR (CompMLR) which linearly weight-averages the MLR and CBP-MLR estimates. For comparative evaluation, we apply the proposed technique to multi-model streamflow prediction using several operationally produced streamflow forecasts as predictors. The results for multiple forecast groups in the US National Weather Service Middle Atlantic River Forecast Center's service area show that the relative performance among different input forecasts varies most significantly with the range of the verifying observed streamflow, and that CompMLR is generally superior to the best performing forecasts in the mean squared error sense under widely varying conditions of predictability and predictive skill.