Characterization of peak flow events with local singularity method

Abstract. Three methods, return period, power-law frequency plot (concentration-area) and local singularity index, are introduced in the paper for characterizing peak flow events from river flow data for the past 100 years from 1900 to 2000 recorded at 25 selected gauging stations on rivers in the Oak Ridges Moraine (ORM) area, Canada. First a traditional method, return period, was applied to the maximum annual river flow data. Whereas the Pearson III distribution generally fits the values, a power-law frequency plot (C-A) on the basis of self-similarity principle provides an effective mean for distinguishing "extremely" large flow events from the regular flow events. While the latter show a power-law distribution, about 10 large flow events manifest departure from the power-law distribution and these flow events can be classified into a separate group most of which are related to flood events. It is shown that the relation between the average water releases over a time period after flow peak and the time duration may follow a power-law distribution. The exponent of the power-law or singularity index estimated from this power-law relation may be used to characterize non-linearity of peak flow recessions. Viewing large peak flow events or floods as singular processes can anticipate the application of power-law models not only for characterizing the frequency distribution of peak flow events, for example, power-law relation between the number and size of floods, but also for describing local singularity of processes such as power-law relation between the amount of water released versus releasing time. With the introduction and validation of singularity of peak flow events, alternative power-law models can be used to depict the recession property as well as other types of non-linear properties.