Estimating the Statistical Significance of Cross–Correlations between Hydroclimatic Processes in the Presence of Long–Range Dependence

Hydroclimatic processes such as precipitation, temperature, wind speed and dew point are usually considered to be independent of each other. In this study, the cross−correlations between key hydrological−cycle processes are examined, initially by conducting statistical tests, then adding the impact of long−range dependence, which is shown to govern all these processes. Subsequently, an innovative stochastic test that can validate the significance of the cross−correlation among these processes is introduced based on Monte−Carlo simulations. The test works as follows: observations obtained from numerous global−scale timeseries were used for application to, and a comparison of, the traditional methods of validation of statistical significance, such as the t−test, after filtering the data based on length and quality, and then by estimating the cross−correlations on an annual−scale. The proposed method has two main benefits: it negates the need of the pre−whitening data series which could disrupt the stochastic properties of hydroclimatic processes, and indicates tighter limits for upper and lower boundaries of statistical significance when analyzing cross−correlations of processes that exhibit long−range dependence, compared to classical statistical tests. The results of this analysis highlight the need to acquire cross−correlations between processes, which may be significant in the case of long−range dependence behavior.