The stochastic properties of high daily maximum temperatures applying crossing theory to modeling high-temperature event variables

Abstract

The statistical properties of the excursions of maximum daily temperatures above various critical thresholds of interest are analyzed with a view to developing models of heat wave events using more than 100 years of record from meteorological stations in Lake City, DeFuniak Springs, Avon Park, and Fort Myers, Florida. These stochastic variables include; event density (number of such events per unit time), duration, timing, and peak values over the threshold. The theoretical basis for the modeling is found in Crossing Theory. The methodology has the flexibility to extrapolate to such levels while also having the advantage of being able to be applied to spatially differentiated data to determine risks associated with hightemperature events during any time period or at any location of interest.

Modeling Properties of Influenza-Like Illness Peak Events with Crossing Theory

“…Results have also been extended to non-Gaussian processes [18] and can be applied to estimate the characteristics of ILI events. The magnitudes of events over the threshold and their durations can be approximated by an exponential-like distribution, such as the generalized Pareto distribution (GPD) [19,20], which can represent such data exhibiting both greater and lesser skew than the exponential itself. In combination with the Poisson assumption, it implies that the annual maximum or -peak week‖ [8] follows a generalized extreme value (GEV) distribution [19], the properties of which can be estimated from this approach, if desired.…”

“…In general, the criteria for adopting a specific distribution are; the goodness-of-fit, a strong theoretical basis and the relative ease of computation and interpretation. Although few influenza-related studies have focused on the statistical properties of peak events, the proposed approach has been extensively used in studies modeling extremes in various fields, including floods, stock market returns and daily maximum temperatures [19][20][21].…”

“…Occasions when weekly cases dropped marginally below the threshold level only to exceed it again in the next week are probably the result of the same event. Parallel considerations in the definition of flood and heat wave events can be found in Rosbjerg et al [19] and Keellings and Waylen [20]. -Events‖ failing to meet this independence criterion are combined and included in subsequent analysis as if they constitute a single event.…”

Combined Influence of the Arctic Oscillation and the Scandinavia Pattern on Spring Surface Air Temperature Variations Over Eurasia

“…Surface air temperature (SAT) is a crucial variable in climate variability (IPCC, ). Variations in SAT exert a large influence on crop growth, natural systems, food security assessment, and human activities (Beniston, ; Feudale & Shukla, ; Guan et al, ; IPCC, ; Keellings & Waylen, ; Kunkel et al, ; Labat et al, ; Yao, ; L. Ye et al, ; Zhai et al, ). The extreme high SAT in summer of 2003 over Europe led to substantial economic loss and human death (Feudale & Shukla, ; Stott et al, ).…”

“…Surface air temperature (SAT) is a crucial variable in climate variability (IPCC, 2013). Variations in SAT exert a large influence on crop growth, natural systems, food security assessment, and human activities (Beniston, 2004;Feudale & Shukla, 2010;Guan et al, 2015;IPCC, 2013;Keellings & Waylen, 2012;Kunkel et al, 1999;Labat et al, 2004;Yao, 1995;L. Ye et al, 2013;Zhai et al, 2005).…”