Trends and climate evolution: Statistical approach for very high temperatures in France

Abstract

The existence of an increasing trend in average temperatures during the last 50 years is widely acknowledged. Furthermore, there is compelling evidence of the variability of extremes, and rapid strides are made in studies of these events. Indeed, by extending the results of the "extreme value theory" (EVT) to the non-stationary case, analyses can examine the presence of trends in extreme values of stochastic processes. Definition of extreme events, their statistical significance as well as their interpretations have to be handled with great care when used for environmental concerns and public safety. Thus, we will discuss the validity of the hypothesis allowing the use of mathematical theories for these problems. To answer safety requirements, respect installation norms and reduce public risk, return levels are a major operational goal, obtained with the EVT. In this paper, we give quantitative results for observations of high temperatures over the 1950-2003 period in 47 stations in France. We examined the validity of the non-stationary EVT and introduced the notion of return levels (RL) in a time-varying context. Our analysis puts particular accent on the difference between methods used to describe extremes, to perform advanced fits and tests (climatic science), and those estimating the probability of rare future events (security problems in an evolving climate).After enouncing the method used for trend identification of extremes in term of easily interpretable parameters of distribution laws, we apply the procedure to long series of temperature measurements and check the influence of data length on trend estimation. We also address the problem of choosing the part of observations allowing appropriate extrapolation. In our analysis, we determined the influence of the 2003 heat wave on trend and return-level estimation comparing it to the RL in a stationary context. The application of the procedure to 47 stations spread over France is a first step for a refined spatial analysis. Working on the behavior of distribution parameters while assessing trend identification is a primary tool Springer 332 Climatic Change (2007) 81: in order to classify climatic change with respect to the location of the station and open a systematic work using the same methodology for other variables and multivariate studies.

Return Level Estimation of Extreme Rainfall over the Iberian Peninsula: Comparison of Methods

“…The estimation of RLs in a non-stationary context has been the subject of a growing number of papers in recent years. While some authors consider that taking non-stationarity into account implies too large uncertainties to be justified [17,18], others suggest methods for doing so together with new definitions for an RL in such a context [19][20][21][22][23][24].…”

Bayesian trend analysis for daily rainfall series of Barcelona

“…There are difficulties in identifying a model for F X , but the Generalized Pareto Distribution (GPD) provides a suitable model for excesses of X over a high enough threshold x 0 , Y = X − x 0 given X > x 0 , (Pickands, 1975). This GPD distribution is parametrized by a shape parameter, ξ , and a scale parameter β:…”

“…For strictly positive data, not only for precipitation, taking log's might be not unimportant. When using a natural scale, some modelling requirements, such as goodness-of-fit or compatibility with physical assumptions, appear to be fulfilled in an easier way than when using the usual raw scale in real space (Egozcue et al, 2006;Pawlowsky-Glahn et al, 2005). On the other hand, excesses over a threshold are modelled by a GPD with a limited maximum value (y sup = −β/ξ finite) in order to be consistent with physical limitations.…”

“…Within the same study, the possibility of an abrupt change due to an improvement in measurement technology is discussed (Raftery, 1989). Other climatic variables such as temperatures (Parey et al, 2007) or rainfall have been also assessed for trends, through nonparametric tests (Pujol et al, 2007) or linear regression type tests (Bodini and Cossu, 2010). However, some authors (Katz et al, 2002) consider that the evidence of trends based on least squares regression does not necessarily reflect properties of extremes like heavy tails.…”

Estimation of a diffusion model with trends taking into account the extremes. Application to temperature in France

“…It results from some works (see for instance Nogaj et al [24], Parey et al [26]) that the trends are not the same in extremes and in the central part, these trends are difficult to capture in the complete model. What is clear from the box plot data (see figure 6.1) is that the variability depends of course of time (seasonality) but also of state (temperature).…”