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

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 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.