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

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 high-temperature events during any time period or at any location of interest.