Two Approaches for Statistical Prediction of Non-Gaussian Climate Extremes: A Case Study of Macao Hot Extremes during 1912-2012

The Gaussian assumption has been widely used without testing in many previous studies on climate variability and change that have used traditional statistical methods to estimate linear trends, diagnose physical mechanisms, or construct statistical prediction/downscaling models. In this study, the authors carefully test the normality of two hot extreme indices in Macao, China, during the last 100 years based on consecutive daily temperature observational data and find that the occurrences of both hot day and hot night indices are non-Gaussian. Simple least squares fitting is shown to overestimate the linear trend when the Gaussian assumption is violated. Two approaches are further proposed to statistically predict non-Gaussian temperature extremes: one uses a multiple linear regression model after transforming the non-Gaussian predictant to a quasi-Gaussian variable and uses Pearson's correlation test to identify potential predictors, and the other uses a generalized linear model when the transformation is difficult and uses a nonparametric Spearman's correlation test to identify potential predictors. The annual occurrences of hot days and hot nights in Macao are used as examples of these two approaches, respectively. The physical mechanisms for these two hot extremes in Macao are also investigated, and the results show that both are related to the interannual and interdecadal variability of a coupled El Nino-Southern Oscillation (ENSO)-East Asian summer monsoon system. Finally, the authors caution other researchers to test the assumed distribution of climate extremes and to apply appropriate statistical approaches.