Nonlinear response of precipitation to climate indices using a non‐stationary Poisson‐generalized Pareto model: case study of southeastern Canada

Abstract

Quantile estimates are generally interpreted in association with the return period concept in practical engineering. To do so with the peaks‐over‐threshold (POT) approach, combined Poisson‐generalized Pareto distributions (referred to as PD‐GPD model) must be considered. In this article, we evaluate the incorporation of non‐stationarity in the generalized Pareto distribution (GPD) and the Poisson distribution (PD) using, respectively, the smoothing‐based B‐spline functions and the logarithmic link function. Two models are proposed, a stationary PD combined to a non‐stationary GPD (referred to as PD0‐GPD1) and a combined non‐stationary PD and GPD (referred to as PD1‐GPD1). The teleconnections between hydro‐climatological variables and a number of large‐scale climate patterns allow using these climate indices as covariates in the development of non‐stationary extreme value models. The case study is made with daily precipitation amount time series from southeastern Canada and two climatic covariates, the Arctic Oscillation (AO) and the Pacific North American (PNA) indices. A comparison of PD0‐GPD1 and PD1‐GPD1 models showed that the incorporation of non‐stationarity in both POT models instead of solely in the GPD has an effect on the estimated quantiles. The use of the B‐spline function as link function between the GPD parameters and the considered climatic covariates provided flexible non‐stationary PD‐GPD models. Indeed, linear and nonlinear conditional quantiles are observed at various stations in the case study, opening an interesting perspective for further research on the physical mechanism behind these simple and complex interactions.

Spatial distribution of the level of return of extreme precipitation events in Northeast Brazil

“…Therefore, it is necessary to develop research that helps to understand how these events behave over time, in addition to predicting the probability of occurrence of a specific event at regular intervals of time. In this respect, extreme value theory (EVT) has often been used to model extreme weather events for both global studies (Serinaldi and Kilsby, 2014) and regional studies, such as in Canada (Thiombiano et al, 2018), Finland (Pedretti and Irannezhad, 2018), China (Tu et al, 2017;Mo et al, 2018), Portugal (Santos et al, 2017a), Jakarta (Siswanto et al, 2016), Vietnam (Gobin et al, 2016), Korea (Chen et al, 2016), and United States (Heaton et al, 2011). In Brazil, EVT has been used to characterize the distribution of rainfall extremes in the city of São Paulo (Sugahara et al, 2008), the Amazon Basin (Santos et al, 2015(Santos et al, , 2016 and the city of Curitiba (Pedron et al, 2016).…”

Peaks-over-threshold model in flood frequency analysis: a scoping review

“…They found that rainfall extremes could exhibit notable departures from independence, which could have important implications on POT based FFA under both stationary and non-stationary regimes. Thiombiano et al (2017) and Thiombiano et al (2018) presented how climate change indices can be used as covariates in a non-stationary framework in the POT modelling.…”

Improvement of Extreme Value Modeling for Extreme Rainfall Using Large-Scale Climate Modes and Considering Model Uncertainty

“…In addition, it reduces the analytical and computational burden of uncertainty assessment by narrowing down the number of model candidates. Even if several exogenous variables are used as covariates for nonstationary extreme value modeling, a number of candidate models can be considered due to probability distribution types [19], combinations of covariates [8,9], and their link function types [26,31,33]. Therefore, our suggested model selection procedure can be an efficient and reasonable way to select the most appropriate model.…”

“…The use of a more complex model (i.e., nonstationary distribution model) generally allows a good fit for the given samples, but this could provide quantile estimates with a large amount of uncertainty [3]. In general, however, the best model is selected using only the information criteria that assess the model performance based on the maximized log-likelihood (i.e., model fit) [26,[28][29][30][31][32][33], so that the selected nonstationary model usually yields unreliable design quantiles [16]. Cooley [34] demonstrated that relying solely on the information criteria is not enough to select an appropriate model because they cannot take into account uncertainty.…”