In order to evaluate asymmetry, data is split through the median of the NAO index and side correlations are computed for each regime (NAO- and NAO+). Statistically significant differences between these correlations are found: a) near Central North-Atlantic, around (20ºW, 40ºN), and Southeast of Iceland, with much stronger correlations in the wet-favorable regime, respectively NAO- and NAO+; b) around (48ºW, 42ºN) in West North-Atlantic; c) in South of Greenland and West Mediterranean near 36ºN, where, in both cases, the correlation is only relevant for the dry-favorable NAO+ regime. Based on the above decomposition, we compute the map of a statistical test of asymmetry, applicable for every bivariate distribution.
In order to evaluate redundancy and Non-Gaussianity, the Mutual Information (MI) is computed from Information Theory. Its positive contributions due to the linear correlation, a purely Gaussian term, and due to Non-Gaussianity, which vanishes in pure Gaussian cases, are studied. MI is estimated through two methods: (1) The truncated Edgeworth expansion of the bivariate probability density function (PDF) in terms of Hermite polynomials and cumulants; (2) The Maximum Entropy Method. This method is quite general, while the first one is only applicable for small deviations from Gaussianity. Diagnostics of the Non-Gaussian counterpart of Mutual Information is useful since it gives an upper limit of the nonlinear potential discrimination of a downscaling non-gaussian probabilistic relationship. Computation of MI allows for the definition of an information correlation metrics that generalizes the linear Pearson correlation which vanishes iff all nonlinear correlations vanish.
We show the map of the Gaussian MI (fig. 1) and the correspondent for the Non-Gaussian MI (fig. 2) over the NAE domain revealing some coherent regions, where the nonlinear component of the response of monthly winter precipitation to NAO is more important.
MI is evaluated both for the original variable 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.