Observational analysis of decadal and long-term hydroclimate drivers in the Mediterranean region: role of the ocean–atmosphere system and anthropogenic forcing

Abstract

Using observations and reanalysis, we develop a robust statistical approach based on canonical correlation analysis (CCA) to explore the leading drivers of decadal and longer-term Mediterranean hydroclimate variability during the historical, half-year wet season. Accordingly, a series of CCA analyses are conducted with combined, multi-component large-scale drivers of Mediterranean precipitation and surface air temperatures. The results highlight the decadal-scale North Atlantic Oscillation (NAO) as the leading driver of hydroclimate variations across the Mediterranean basin. Markedly, the decadal variability of Atlantic-Mediterranean sea surface temperatures (SST), whose influence on the Mediterranean climate has so far been proposed as limited to the summer months, is found to enhance the NAO-induced hydroclimate response during the winter half-year season. As for the long-term, century scale trends, anthropogenic forcing, expressed in terms of the global SST warming (GW) signal, is robustly associated with basin-wide increase in surface air temperatures. Our analyses provide more detailed information than has heretofore been presented on the sub-seasonal evolution and spatial dependence of the large-scale climate variability in the Mediterranean region, separating the effects of natural variability and anthropogenic forcing, with the latter linked to a long-term drying of the region due to GW-induced local poleward shift of the subtropical dry zone. The physical understanding of these mechanisms is essential in order to improve model simulations and prediction of the decadal and longer hydroclimatic evolution in the Mediterranean area, which can help in developing adaptation strategies to mitigate the effect of climate variability and change on the vulnerable regional population.

Data availability

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Appendix

1.1 Key concepts in CCA

According to the literature (see e.g., Hair et al. 2010), the key concepts to analyze and interpret individual contributions derived from CCA results are defined as follows:

• Canonical coefficients. Parameters that give the contribution of the individual variables within the EV and RV sets to their corresponding canonical variate. These coefficients are equivalent to regression coefficients in multiple linear regression.

• Canonical variates. Time series that represent the linear combination (weighted sum) of two or more variables. These time series are defined for EV and RV.

• Canonical modes. Pairs of canonical variates, one for the set of EV and one for the set of RV. The strength of the link is given by canonical correlation.

• Canonical correlation. Measure of the strength of the relationship between the canonical variates for a given canonical mode. In effect, it represents the bivariate correlation between the two canonical variates.

• Shaded variance. Measure of the variance explained between canonical variates. It is calculated as the squared canonical correlation.

• Canonical loadings. Measure of the simple linear correlation between the individual variables within EV and RV sets and their respective canonical variates.

• Canonical cross-loadings. Correlation of each individual EV or RV with the opposite canonical variate. In other words, the individual EVs are correlated with the RV canonical variate and vice versa.

1.2 Individual contributions to canonical modes

The interpretation of canonical variates in a significant canonical mode is based on individual variables (PCs) within the EV and RV sets that contribute markedly to shared variances (i.e., R²). We restrict our attention to canonical modes by a series of criteria, which are (1) the level of statistical significance of the canonical correlation associated with a given canonical mode and its associated shared variance (i.e., squared canonical correlation), (2) canonical RV loadings, and (3) canonical EV cross-loadings. It is worth noting that canonical coefficients are traditionally used to examine the contribution of individual variables. Nevertheless, its utilization to interpret the relative importance of a variable is subject to criticism in the same way as beta coefficients in conventional regression techniques (Lambert and Durand 1975).

The level of significance for canonical correlations is set in this work at 0.05 (95%), which is the generally accepted level for considering a correlation coefficient statistically significant. We use the Wilks' Lambda as a measure for assessing the significance of discriminant functions (Wilks 1935; Bartlett 1947). The Wilks' Lambda likelihood ratio is a consistent test statistic under the classical assumptions that all groups arise from multivariate normal distributions (e.g., Nath and Pavur 1985; Friederichs and Hense 2003). It tests how well each level of EV contributes to the model. The scale ranges from 0 to 1, where 0 means total discrimination, and 1 means no discrimination. The null hypothesis should be rejected when Wilks' lambda is close to zero in combination with a small p-value (0.05 or lower). The p-values are calculated from an F-statistic, based on Rao’s approximation (Bartlett 1941) to evaluate the significance of Wilks' Lambda.

Once a given canonical mode is found to be robust in terms of its significant canonical correlation, the relative relevance of the original variables in the canonical mode involves the calculation of canonical loadings and cross-loadings. The canonical loading is interpreted as the relative contribution of each variable to the canonical mode. It takes into account each independent canonical mode and calculates the within-set variable-to-variate correlation. As for canonical cross-loadings, their calculation has been proposed as a complement to canonical loadings (Dillon and Goldstein 1984). This method implies the calculation of each original EV with the canonical RV variate, and vice versa. Therefore, cross-loadings provide the cross-set variable-to-variate correlation. We evaluate significant individual contributions in terms of canonical RV loadings and canonical EV cross-loadings. The significance level for canonical loadings and cross-loadings is tested by means of the Ebisuzaki’s method (Ebisuzaki 1997), which applies to time series that exhibit non-white spectra, or what is the same, time series that violate the assumption of independence that is fundamental to the classical t-test. The Ebisuzaki method consists of a non-parametric test based on generating a large number of random series (permutations) with the same power spectra as the original series but with random phases in the Fourier modes. The number of permutations in this study has been set to 1000.

When all the criteria of statistical significance described above are met, the acceptance of a canonical mode is restricted to the variance explained in the time series of the original anomalous field at each point in space by the canonical EV variate. It may be the case that all the criteria of statistical significance are met but the canonical EV variate is not representative of variability over the original field. In this case, the canonical mode is interpreted as a statistical artifact. This could be related to a negligible contribution of the leading PCs to the canonical RV variates (i.e., non-significant canonical RV loadings). We discard certain PCP and TEMP canonical modes because the characterization of the canonical variates (i.e., the evolution of the time series according to consecutive 3-month periods) is not coherent with the previous or subsequent canonical modes. This does not necessarily imply that the discarded modes do not involve physical causality. Canonical modes discarded according to one or more criteria can be seen in the supplementary material (Figs. S1, S2 and S3).

1.3 Variance inflation factor

The variance inflation factor (VIF) is a common collinearity diagnostic (e.g., Rawlings et al. 1998; James et al. 2017). In general, the VIF for the ith regression coefficient can be computed as:

$${VIF}_{i}=\frac{1}{1-{R}_{i}^{2}}$$

(A1)

where ${R}_{i}^{2}$ is the coefficient of multiple determination obtained by regressing each individual within-set variable onto the remaining variables. When the variation of the i^th single variable is largely explained by a linear combination of the remaining variables, ${R}_{i}^{2}$ is close to 1, and the VIF for that variable is correspondingly large. The inflation is measured relative to an ${R}_{i}^{2}$ of 0 (VIF of 1; no collinearity). VIFs are also the diagonal elements of the inverse of the correlation matrix (Belsley et al. 1980), a convenient result that eliminates the need to set up the various regressions. There are no statistical tests to rate for multicollinearity using the tolerance of VIF measures. Some authors use a VIF of 10 (inflates the standard error by 3.16) as a suggested upper limit to indicate a definite multicollinearity problem for an individual variable (e.g., Kutner et al. 2004; Zuur et al. 2010). More robustly, a VIF of 4 doubles the standard error. Without an established guidance to adopt a definite value, the tolerance of VIF is subject to the scope of the research problem being addressed.