The Statistical Properties of Freeze Date Variables and the Length of the Growing Season

Abstract

Knowledge of the probability distributions of first and last freeze, the length of the growing season and the probabilities of freezes on any day is of considerable practical importance. Generally, empirical approximations to these distributions are made, often by the Gaussian distribution. In this paper they are calculated using the theory of crossings of a threshold by a nonstationary Gaussian process. Fourier series are used to represent the seasonal variation of the mean and variance of daily minimum temperatures. First-order autocorrelation of temperatures are modeled on a monthly basis. The procedure is tested at two widely differing sites, Regina Airport, Saskatchewan, Canada and Lake City, Florida. Observed descriptive statistics of an freeze variables are reproduced well, particularly those of rarer events. The analysis may be repeated for any threshold temperature of interest as illustrated by an investigation of periods of temperatures below ?2.2°C at Lake City, and may be used to determine crossings above any level equally easily.