Articles | Volume 20, issue 6
Research article
20 Jun 2016
Research article |  | 20 Jun 2016

Estimation of flood warning runoff thresholds in ungauged basins with asymmetric error functions

Elena Toth

Abstract. In many real-world flood forecasting systems, the runoff thresholds for activating warnings or mitigation measures correspond to the flow peaks with a given return period (often 2 years, which may be associated with the bankfull discharge). At locations where the historical streamflow records are absent or very limited, the threshold can be estimated with regionally derived empirical relationships between catchment descriptors and the desired flood quantile. Whatever the function form, such models are generally parameterised by minimising the mean square error, which assigns equal importance to overprediction or underprediction errors.

Considering that the consequences of an overestimated warning threshold (leading to the risk of missing alarms) generally have a much lower level of acceptance than those of an underestimated threshold (leading to the issuance of false alarms), the present work proposes to parameterise the regression model through an asymmetric error function, which penalises the overpredictions more.

The estimates by models (feedforward neural networks) with increasing degree of asymmetry are compared with those of a traditional, symmetrically trained network, in a rigorous cross-validation experiment referred to a database of catchments covering the country of Italy. The analysis shows that the use of the asymmetric error function can substantially reduce the number and extent of overestimation errors, if compared to the use of the traditional square errors. Of course such reduction is at the expense of increasing underestimation errors, but the overall accurateness is still acceptable and the results illustrate the potential value of choosing an asymmetric error function when the consequences of missed alarms are more severe than those of false alarms.

Short summary
Runoff thresholds for activating flood warnings might be estimated with regionally derived relationships between catchment descriptors and assigned flood quantiles. Since the consequences of overestimated thresholds (leading to missing alarms) are generally more severe than those of an underestimation (leading to false alarms), the work proposes to parameterise the regression model with an asymmetric error function, instead of using a traditional, symmetric square errors sum.