We built a model of the daily temperature based on a diffusion process and address to extreme values not taken into account in the literature on this kind of models. We first study, using non parametric tools, the trends on mean and variance. In a second step we estimate a stationary model first non parametrically and then using likelihood methods. Extreme values are taken into account in the estimation of model and to obtain a definitive estimation we use in a specific framework extreme theory for diffusions. A test of suitable model by simulation is done.
The statistical theory of extremes is extended to observations that are non-stationary and not independent. The non-stationarity over time and space is controlled via the scedasis (tail scale) in the marginal distributions. Spatial dependence stems from multivariate extreme value theory. We establish asymptotic theory for both the weighted sequential tail empirical process and the weighted tail quantile process based on all observations, taken over time and space. The results yield two statistical tests for homoscedasticity in the tail, one in space and one in time. Further, we show that the c…
We propose a method to generate a warning system for the early detection of time clusters applied to public health surveillance data. This new method relies on the evaluation of a return period associated to any new count of a particular infection reported to a surveillance system. The method is applied to Salmonella surveillance in France and compared to the model developed by Farrington et al.
Each year, seasonal influenza epidemics cause hundreds of thousands of deaths worldwide and put high loads on health care systems. A main concern for resource planning is the risk of exceptionally severe epidemics. Taking advantage of recent results on multivariate Generalized Pareto models in Extreme Value Statistics we develop methods for real-time prediction of the risk that an ongoing influenza epidemic will be exceptionally severe and for real-time detection of anomalous epidemics and use them for prediction and detection of anomalies for influenza epidemics in France. Quality of predicti…
Drought is one of the most devastating environmental disasters. Analyzing historical changes in climate extremes is critical for mitigating its adverse impacts in the future. In the present study, the spatial and temporal characteristics of the global severe droughts using Palmer Drought Intensity Index (PDSI) from 1900 to 2014 are explored. K-means clustering is implemented to partition the extreme negative PDSI values. The global extreme droughts magnitude around the world from 1950 to 1980 were less intense compared to the other decades. In 2012, the largest areas around the world, especial…
Severe thunderstorms can have devastating impacts. Concurrently high values of convective available potential energy (CAPE) and storm relative helicity (SRH) are known to be conducive to severe weather, so high values of PROD=$\sqrt{\mathrm{CAPE}} \times$SRH have been used to indicate high risk of severe thunderstorms. We consider the extreme values of these three variables for a large area of the contiguous US over the period 1979-2015, and use extreme-value theory and a multiple testing procedure to show that there is a significant time trend in the extremes for PROD maxima in April, May and…
In recent environmental studies extreme events have a great impact. The yearly and monthly maxima of environment related indices can be analysed by the tools of extreme value theory. For instance, the monthly maxima of the fire weather index in British Columbian forests might be modelled by GEV distribution, but the stationarity of the time series is questionable. This property can lead us to different approaches to test if there is a significant trend in past few years data or not. An approach is a likelihood ratio based procedure which has favourable asymptotic properties, but for realistic …
There is substantial empirical and climatological evidence that precipitation extremes have become more extreme during the twentieth century, and that this trend is likely to continue as global warming becomes more intense. However, understanding these issues is limited by a fundamental issue of spatial scaling: most evidence of past trends comes from rain gauge data, whereas trends into the future are produced by climate models, which rely on gridded aggregates. To study this further, we fit the Generalized Extreme Value (GEV) distribution to the right tail of the distribution of both rain ga…
Extreme sea level estimates are fundamental for mitigating against coastal flooding as they provide insight for defence engineering. As the global climate changes, rising sea levels combined with increases in storm intensity and frequency pose an increasing risk to coastline communities. We present a new method for estimating extreme sea levels that accounts for the effects of climate change on extreme events that are not accounted for by mean sea level trends. We follow a joint probabilities methodology, considering skew surge and peak tides as the only components of sea levels. We model extr…
The estimation of extreme flood quantiles is challenging due to the relative scarcity of extreme data compared to typical target return periods. Several approaches have been developed over the years to face this challenge, including regional estimation and the use of historical flood data. This paper investigates the combination of both approaches using a multivariate peaks-over-threshold model, that allows estimating altogether the intersite dependence structure and the marginal distributions at each site. The joint distribution of extremes at several sites is constructed using a semi-paramet…
Extreme precipitation events with large spatial extents may have more severe impacts than localized events as they can lead to widespread flooding. It is debated how climate change may affect the spatial extent of precipitation extremes, whose investigation often directly relies on simulations from climate models. Here, we use a different strategy to investigate how future changes in spatial extents of precipitation extremes differ across climate zones and seasons in two river basins (Danube and Mississippi). We rely on observed precipitation extremes while exploiting a physics-based mean temp…
