Estimating lag to peak between rainfall and peak streamflow with a mixed-effects model

We test the use of a mixed-effects model for estimating lag to peak for small basins in Maine (drainage areas from 0.8 to 78 km2). Lag to peak is defined as the time between the center of volume of the excess rainfall during a storm event and the resulting peak streamflow. A mixed-effects model allows for multiple observations at sites without violating model assumptions inherent in traditional ordinary least squares models, which assume each observation is independent. The mixed model includes basin drainage area and maximum 15-min rainfall depth for individual storms as explanatory features. Based on a remove-one-site cross-validation analysis, the prediction errors of this model ranged from 42% to +73%. The mixed model substantially outperformed three published models for lag to peak and one published model for centroid lag for estimating lag to peak for small basins in Maine. Lag to peak estimates are a key input to rainfallrunoff models used to design hydraulic infrastructure. The improved accuracy and consistency with model assumptions indicates that mixed models may provide increased data utilization that could enhance models and estimates of lag to peak in other regions.