Non-gaussianity and asymmetry of the winter monthly precipitation estimation from the NAO

The present work assesses non-Gaussianity and asymmetry within the statistical response of the monthly winter (December–February) precipitation to the North Atlantic Oscillation (NAO) over the North Atlantic–European region (NAE). To evaluate asymmetry, data are split through the median of the NAO index and side correlations are computed for each regime [negative and positive phases of the NAO (NAO− and NAO+, respectively)]. The following statistically significant differences between these correlations are found: (a) near the central North Atlantic, around 40°N, 20°W, and southeast of Iceland, with much stronger correlations in the wet-favorable regime: NAO− in the first location and NAO+ in the second location; (b) around 42°N, 48°W in the west North Atlantic; and (c) south of Greenland and in the west Mediterranean near 36°N, where, in both cases, the correlation is only relevant for the dry-favorable NAO+ regime. Based on the above decomposition, a map of a statistical test of asymmetry, applicable for every bivariate distribution, is shown. To evaluate redundancy and non-Gaussianity, the mutual information (MI) is computed from information theory. Its positive contributions resulting from the linear correlation, a purely Gaussian term, and non-Gaussianity, which vanishes in pure Gaussian cases, are studied. The MI is estimated through two methods: 1) the truncated Edgeworth expansion of the bivariate probability density function in terms of Hermite polynomials and cumulants, and 2) the maximum entropy method. This method is quite general, while the first one is only applicable for small deviations from Gaussianity. The map of non-Gaussian MI over the NAE domain reveals some coherent regions, where the nonlinear component of the response of monthly winter precipitation to the NAO is more important. The MI is evaluated both for the original pair of variables and for that pair after being subjected to Gaussian anamorphosis in order to prevent the influence of marginal outliers and keep the applicability of the Edgeworth method.