Extreme Value Statistics of the Total Energy in an Intermediate-Complexity Model of the Midlatitude Atmospheric Jet. Part II: Trend Detection and Assessment

Abstract

A baroclinic model for the atmospheric jet at middle latitudes is used as a stochastic generator of nonstationary time series of the total energy of the system. A linear time trend is imposed on the parameter T E , descriptive of the forced equator-to-pole temperature gradient and responsible for setting the average baroclinicity in the model. The focus lies on establishing a theoretically sound framework for the detection and assessment of trend at extreme values of the generated time series. This problem is dealt with by fitting time-dependent generalized extreme value (GEV) models to sequences of yearly maxima of the total energy. A family of GEV models is used in which the location and scale parameters depend quadratically and linearly on time, respectively, while the shape parameter is kept constant. From this family, a GEV model is selected with Akaike's information criterion, complemented by the likelihood ratio test and by assessment through standard graphical diagnostics. The inferred location and scale parameters are found to depend in a rather smooth way on time and, therefore, on T E . In particular, power-law dependences of and on T E are obtained, in analogy with the results of a previous work where the same baroclinic model was run with fixed values of T E spanning the same range as in this case. It is emphasized under which conditions the adopted approach is valid.

Extremes and Recurrence in Dynamical Systems

“…Taking the so-called adiabatic approximation, one assumes that the change in the properties of the extremes is so slow in time that analyzing an individual trajectory is sufficient for capturing such t−dependence, with time being introduced as a covariate in the statistical inference procedure [72,56]. One needs to underline that giving a scientific meaning to such a -common -assumption is possible only in an intuitive, heuristic fashion.…”

Return levels of temperature extremes in southern Pakistan

“…Furthermore, a standard bias correction is applied to the ERA-Interim data to assess whether removing the bias in the bulk of the statistics substantially improves representation of the return levels of extremes. Given the shortness of the datasets, as we will show later, it is appropriate to analyze the extremes without taking into consideration possible long-term trends (Frei and Schär, 2001); see also the discussion in Felici et al (2007). The provision of POT-based information on stationary extremes is already quite relevant in terms of impacts for the public and private sectors as it fills a big data gap in Sindh.…”

Data and models for exploring sustainability of human well-being in global environmental change

“…Extreme events such as droughts, floods, or hurricanes, are expected to increase in intensity and frequency as an aspect of GEC [3], although statistical definition, physical understanding and forecast of climate extremes and their evolution still remain intrinsically challenging [100,101]. At the same time population in flood-prone areas is increasing.…”