A unified statistical model for hydrological variables including the selection of threshold for the peak over threshold method

Abstract

[1] This paper explores the use of a mixture model for determining the marginal distribution of hydrological variables, consisting of a truncated central distribution that is representative of the central or main-mass regime, which for the cases studied is a lognormal distribution, and of two generalized Pareto distributions for the maximum and minimum regimes, representing the upper and lower tails, respectively. The thresholds defining the limits between these regimes and the central regime are parameters of the model and are calculated together with the remaining parameters by maximum likelihood. After testing the model with a simulation study we concluded that the upper threshold of the model can be used when applying the peak over threshold method. This will yield an automatic and objective identification of the threshold presenting an alternative to existing methods. The model was also applied to four hydrological data series: two mean daily flow series, the Thames at Kingston (United Kingdom), and the Guadalfeo River at Orgiva (Spain); and two daily precipitation series, Fort Collins (CO, USA), and Orgiva (Spain). It was observed that the model improved the fit of the data series with respect to the fit obtained with the lognormal (LN) and, in particular, provided a good fit for the upper tail. Moreover, we concluded that the proposed model is able to accommodate the entire range of values of some significant hydrological variables.Citation: Solari, S., and M. A. Losada (2012), A unified statistical model for hydrological variables including the selection of threshold for the peak over threshold method, Water Resour. Res., 48, W10541,

Developing signals to trigger adaptation to sea-level rise

“…Previous studies have tended to focus separately on either 'extreme' [4,10] sea levels or 'nuisance' [1] flooding. We have used a mixed-distribution model [36,37], which allows us to estimate the changing frequency of smaller, more frequent storm-tides which are used to design signals and triggers, while simultaneously modelling the changing frequency of more extreme storm-tides as adaptation-thresholds to be avoided. The mixed distributions for six NZ coastalgauge sites are shown in figure 2, and compared with Auckland (NZ) at six international sites in figure 3.…”

A framework for multivariate data-based at-site flood frequency analysis: Essentiality of the conjugal application of parametric and nonparametric approaches

“…However, selection of the threshold is a major concern in this approach. In previous studies, researchers considered two techniques for choosing a threshold: one method selects a fixed quantile corresponding to a relatively high nonexceedance probability (usually 95%, 99%, or 99.5%) and the other selects a threshold using graphical methods (Smith, 1987;Luceño et al, 2006;Solari and Losada, 2012). In the current study, the quantile method was implemented with a threshold of 95% (Coles, 2001;Khan et al, 2007) to extract the flood variables, i.e., P, V, and D. A graphical representation of the delineation of the flood variables is shown in Fig.…”

PeaksOverThreshold (POT): A methodology for automatic threshold estimation using goodness of fitp‐value

“…Threshold selection for the application of the Peaks Over Threshold (POT) method to a single sample is a long‐standing topic that is still unresolved [ Davison and Huser , ; Cavanaugh et al ., ]. Although there have been various proposals to automate threshold selection [e.g., Dupuis , ; Thompson et al ., ; Solari and Losada , , among others], the most common practice is to use graphical methods (see e.g., Coles [] for a detailed description of these methods and Solari and Losada [] for an application to some of the series used in this work), supplemented with some consideration of goodness of fit (GOF), such as the use of qq‐plots or GOF tests [ Davison and Huser , ]. As an alternative to selecting a single threshold, other authors have proposed averaging the results obtained from a series of thresholds [see e.g., Beguería , ].…”