SLA–chlorophyll-a variability and covariability in the Algero-Provençal Basin (1997–2007) through combined use of EOF and wavelet analysis of satellite data

Abstract

Data reduction and signal decomposition techniques have been applied to a large bio-physical remotely sensed dataset covering the decade 1997–2007. The aim was the estimation of the spatial (basin and sub-basin scales) and temporal (seasonal and interannual) variability of sea level anomalies and chlorophyll-a concentration in the Algero-Provençal Basin, as well as the study of their covariability. Empirical orthogonal functions, wavelet analysis, singular value decomposition and correlation maps have been successfully used to individuate the patterns of (co)variability of the investigated fields. The seasonal variability of the phytoplanktonic biomass is divided in two distinct modes, timewise and spacewise separated. Positive interannual events are related to anomalies in 1999 and 2005, while the main (negative) anomaly is that of summer 2003, associated to the European 2003 heatwave. The analysis of the sea level anomalies shows a minimum in the formation of anticyclonic Algerian eddies during that period. The largest anticorrelation between sea level anomalies and phytoplanktonic biomass is found in the central zone of the basin, suggesting a clear biological response to the shoaling/deepening of the isopycnae and so to the nutrient injection into the euphotic layer. The analysis suggests that the driver of the variability of the nutricline depth in this central area is the displacement (seasonal) of the North Balearic Front and the formation/action of the frontal eddies.

Appendix

1.1 A. Analysis methods

1.1.1 A.1 EOFs method

In order to detect the main patterns of spatial and temporal variability of the Chl and SLA series, we performed the EOFs analysis, also known as principal component analysis. The EOF method was introduced in meteorology by Lorenz (1956). From that moment, the EOFs have been widely used in climatology, meteorology, and oceanography (Preisendorfer 1988; Bretherton et al. 1992; Peng and Fyfe 1996; Bartolacci and Luther 1999; Baldacci et al. 2001; Bouzinac et al. 2003; Lopez-Calderon et al. 2006). This method allows to find the spatial and temporal variability patterns of the dataset and to estimate the amount of variance associated to each mode of variability in percentage terms (Preisendorfer 1988). We would like to underline that the modes of variability, also known as EOFs (EOF-1, EOF-2,...EOF-n), contain information about the variability of the dataset that is not necessarily related to physical features. The interpretation of the EOF modes just aims to relate the data modes with physics. The temporal amplitudes associated with the spatial patterns, referred to as EOF expansion coefficients or simply PCs, are also object of physical interpretation. In some cases, further statistical analysis was needed to correctly interpret PCs, especially when the signal contains non-stationary components.

The dataset (the same was done for SLA and Chl) has been organized as follows, in order to perform the EOF analysis: At first, we vectorized the matrices (of dimension x by y) containing the monthly fields of the variable in row vectors of dimension p = xy. Then we formed a matrix F of dimension n columns by p rows, where n is the number of observations (113 in our case) and p is the number of grid-meshes for each observation. We can consider each of the n columns of matrix F as a time series for a given location xy and each of the p rows as an observation (single monthly field) at a given time. The mean of each time series is then removed to obtain series with zero mean. Then R, the covariance matrix of F, is calculated by:

$$ R = F^t F \label{eqR} $$

(1)

where F ^t is the transposed matrix of F.

The eigenvalue problem is solved so that:

$$ R=C \Lambda C^t \label{eqeig} $$

(2)

where Λ is a diagonal matrix containing the eigenvalues λ _i of R and where each column c _i of C is the eigenvector corresponding to the λ _i eigenvalue. Each of the eigenvectors c _i is an EOF. The EOF-1 will be the c _i with the highest λ _i , i.e., the highest value of explained variance. The EOF-2 will be the c _i with the second λ _i value and so on. Each EOF, in vectorial form, is then re-converted in matrix before drawing the respective EOF map.

In order to see how an EOF evolves in time, we calculated the expansion coefficient a _j by:

$$ a_j=F c_j \label{eqPC} $$

(3)

a _j is composed by n components which are the projections of the maps contained in F on c _i (EOF _j ). a _j is the PC, i.e., the time evolution of each EOF _j .

1.2 A.2 Time series analysis and wavelet transform

The anomaly time series of each dataset have been calculated because in many cases, they may give useful information about interannual or anomalous events which cannot be correctly identified by EOF decomposition, for example, due to their phase coincidence with the main seasonal signal.

The anomaly time series of each dataset has been obtained by:

$$ x_n= \frac{x-x_m}{\sigma_m}, \label{eqanom} $$

(4)

where x is the monthly value, x _m is the monthly climatology for the corresponding month, and σ _m is the related monthly standard deviation. The anomaly time series so obtained have been analyzed through continuous wavelet transform and Fourier transform. For a comprehensive and useful view on wavelet analysis applied to geosciences, please see Torrence and Compo (1998) and Liu et al. (2007) which corrected a bias in Torrence and Compo (1998) method.

1.3 A.3 Correlation and SVD analysis

The r Pearson correlation coefficient between the variables has been computed in a time-integrated way (pixel by pixel) in order to describe the spatial patterns of SLA–Chl covariability. We performed the SVD analysis of the coupled datasets in order to give a more accurate picture of the coupling between physical and biological variables. The SVD analysis (Bjornsson and Venegas 1997; Bartolacci and Luther 1999) has many common points with the EOF decomposition because it separates datasets in modes of (co-)variability. On the contrary of EOF method, the SVD analysis aims to study coupled variables and to find the main patterns of covariability between two series. The explained covariability is expressed in terms of SCF, and each SCF value is associated with a pair of coupled maps drawing the coupled spatial patterns. The SVD analysis is applied on the so-called covariance matrix C. Given the two matrices S and P, containing respectively the dataset of SLA and Chl organized as matrix F for EOF method, the covariance matrix C is:

$$ C=S^t P \label{eqcovm} $$

(5)

where S ^t is the transposed matrix of S.

Then the SVD problem is solved. We found matrices U and V and the diagonal matrix L so that:

$$ C = U L V^t \label{eqsvd} $$

(6)

Matrices U and V are formed by vectors u _i and v _i which are pairs of coupled modes of covariability of SLA and Chl, explaining a l _i (singular values) part of the total covariance. The expansion coefficients of the two datasets may be found, as for EOFs, by the projections of the data (S and P) on the modes of covariability (U and V). Singular values l _i contained in L can therefore be considered an estimate of how much the covariance is explained by the respective pair of coupled modes u _i and v _i . In literature, u _i and v _i are often called left and right mode.

The fraction of explained covariance is expressed in terms of SCF, given by:

$$ SCF_i = \frac{{l_i}^2} {\Sigma {l_i}^2} \label{eqscf} $$

(7)

1.4 A.4 Front detection

In order to detect the North Balearic Front position and its temporal behavior, a simple gradient method has been applied iteratively to the 488 weekly ADT gridded maps covering the decade. Altimetric data have been used instead of SST data, which are more often used to detect the fronts in the oceans, because in some periods of the year there is not a clear thermic separation between the new reservoir of Atlantic waters occupying the Algerian Basin and resident waters. We observed that such a separation seems to have a clear signature, along the year, in the altimetric data.

For a reduced domain, between 39° N and 42.5° N, the algorithm, applied along meridional transects, finds the largest gradient. Therefore, the mean zonal position of the front is computed at each time step (1 week).