Examination of Multiple Predictive Approaches for Estimating Dam Breach Peak Discharges

A database joining individual earthen dam breach failure studies is assembled and reanalyzed across all aggregate observations. Conventional regression methods are employed along with newer predictive approaches to estimating peak discharges resulting from an earthen dam failure. Goodness of fit is quantified through relative standard error and relative bias. These measures are computed and presented for previous predictive equations. Numerical optimization techniques are used to calibrate power law functions of one, two, and three predictors to estimate peak discharge from the aggregate database. Findings show that equations calibrated from the aggregate database have better goodness-of-fit metrics than those determined from their earlier, individual data sets. Improvement in relative standard error varies from essentially zero to as much as 50%. Two similar innovative techniques are applied to the aggregate database: region of influence (ROI) and k-nearest neighbor (kNN). Both of these approaches identify a subset of most similar observations from the database, given a specific test location. The ROI approach performs poorly in prediction mode, uniformly producing relative standard errors that are greater than the originally calibrated equations and that often exceed 100% of the standard deviation of the observations. Smaller relative standard errors are obtained as ROI size increases, contrary to the spirit of this approach. In contrast, the kNN approach performs well, with best results obtained for a simple numerical average of the $k$ nearest observations. The size of the optimum $k$ neighborhood varied from 3 to 29, with 12 being the median value among the cases examined. Regression equation calibration via logarithmic transformation is briefly explored, and the need to limit predictions to the test space within the convex hull of the observations is discussed.