K. Glynis, Stochastic investigation of the behavior of land surface air temperature on global scale, Diploma thesis, 159 pages, Athens, October 2019.
Land surface air temperature is one of the most important hydroclimatic variables, and its extremes are of paramount importance. For this reason, it is imperative not only to know the exact shape of the temperature tails, but also their temporal evolution. The aim of this work is to investigate the stochastic behavior of land surface air temperature using Knowable (K-)moments. K-moments were chosen for this study, as they enable reliable estimation from samples and effective description of high order statistics, useful for marginal and joint distributions of stochastic processes. Multiple timeseries of the average, maximum and minimum air temperature are standardized with respect to the monthly variability of each record. We generate segments of the whole timeseries using consecutive rolling 30-year periods, from which we extract extreme values corresponding to four specific return period levels. Furthermore, timeseries of each air temperature variable (average, maximum and minimum) are used as input to an aggregated Climacogram, for deriving the Hurst parameter, through optimization of the parameters of a hybrid Hurst-Kolmogorov and Markov model. The Hurst parameter is later employed in a Monte Carlo simulation to produce synthetic records of similar stochastic properties through the Symmetric Moving Average (SMA) scheme. The synthetic records produced are processed in a similar manner as the observed, in order to compare them. Furthermore, the longest single records for each air temperature variable are selected and compared to the ensemble of observations, as well as the synthetic records.