**2.1 Altimetry satellite data**

The satellite-borne altimetry is initially designed to estimate the sea surface height (SSH) by measuring the satellite-to-surface round-trip time of a radar pulse. These measurements however include the Earth's geoid which varies by tens of meters across the ocean and is not accurately estimated (Fu et al., 1994). This unknown geoid is removed from satellite observations by subtracting a long term mean of the altimeter measurements from the observations. However, this procedure removes also the mean dynamic SSH and satellite measurements refer only to SLA, which contains information on the geostrophic current fields, mesoscale eddy variability and changes in the thermocline depth (Le Traon et al., 1998; Stammer, 1997). Uncertainties on the location of the satellite on its orbit and disturbances of the radar pulse by the atmosphere introduce additional errors in the SLA

Using SVD Analysis of Combined Altimetry and Ocean Color

km and and e-folding time scale of 10 days.

Satellite Data for Assessing Basin Scale Physical-Biological Coupling in the Mediterranean Sea 127

the overall response of the sensor, an atmospheric correction algorithm and the application of bio-optical algorithms (Gordon, 1997, 1998). The ocean color data used in this work consists of level 3 standard processed 8-day maps of CHL from SeaWiFS and MODIS-A on a 9 x 9 km regular grid in the Mediterranean Sea obtained from NASA's Ocean Color web site (http://oceancolor.gsfc.nasa.gov, see also McClain (2009)). Merging data from SeaWiFS and MODIS-A increases the coverage and reduces the uncertainties in the retrieved variables (Maritorena et al., 2010). The CHL produced by those ocean color missions are consistent over a wide range of conditions (Morel et al., 2007). We interpolate cloud-free CHL data onto the SLA grid of 0.25º x 0.25º resolution using objective analysis with a length scale of 50

Satellite derived CHL through standard algorithms in the Mediterranean Sea is affected by a calibration problem displaying a bias when compared to in situ observations (Bosc et al., 2004; Volpe et al., 2007). This difficulty is related to the specific environmental bio-optical characteristics of the Mediterranean with respect to other oceanic regions having similar ranges of CHL. However, in the present work, we use the standard calibration algorithms because we are interested in the phytoplankton variability rather than in the absolute biomass values. The satellite derived CHL is used as a proxy for the phytoplankton biomass in the mixed layer. Although satellite derived CHL is limited to an optical depth, a reasonable correlation exists

The SLA and CHL variability in the Mediterranean are dominated by the seasonal cycle (Larnicol et al., 2002; Bosc et al., 2004). As a first step, it is necessary to remove these seasonal variations because otherwise they would dominate the resultant correlations. In our case, we calculate the seasonal cycles of SLA and CHL by averaging the value for each grid point and each 8-day window. We then subtract the seasonal cycles (8-day mean values) to the original time series for each grid point to create anomalies. Finally, we apply a low- and high-pass Lanczos filter with a cut-off period of 1 year at each grid point to compute the inter- and intra-

The analysis of the relationships between any two satellite data sets involving large number of grid points and time series can be performed in different ways. Correlation is a simple method available when the spatial and time domains of data sets are equal. The Pearson's correlation coefficient between two time series *p*(*t*) and *q*(*t*) with means *p* and *q* and

1

*T pq k k p q k <sup>r</sup> p pq q <sup>T</sup>* 

where *T* is the total number of observations. We compute the Pearson's correlation

A more sophisticated method to analyze the relationship between any two satellite data sets is the SVD analysis of the cross-covariance matrix between the two data sets with the same

1 ( 1)

**2.5 Singular value decomposition (SVD) analysis of the cross-covariance** 

(1)

between the depth integrated and the satellite CHL (Morel and Berthon, 1989).

**2.3 Seasonal cycles and inter- and intra-annual anomalies** 

annual anomalies, respectively, of SLA and CHL.

standard deviations *σ*p and *σq* is defined as

**2.4 Correlation coefficient** 

coefficient for each grid point.

measurement. Because of these errors, the first altimetry satellites such as Seasat or Geosat did not provide very usable and useful data. In 1993, the French Centre National d'Etudes Spatiales (CNES) and the US National Aeronautics and Space Administration (NASA) launched TOPEX/Poseidon satellite, which included a very precise positioning technique. Since then, new accurate altimetry missions were launched: ERS1/2 (in 1993), Geosat Follow-On (in 2000), Jason-1 (in 2002), TOPEX/Poseidon interleaved (in 2002), ENVISAT (in 2003) and Jason-2 (in 2008). The combination of these satellites enables high-precision altimetry and improves their spatial and temporal resolution.

It is now generally accepted that at least three altimeter missions are required to resolve the ocean mesoscale variability (Le Traon & Dibarboure, 1999; Pascual et al., 2007). However, merging multi-satellite data requires consistent SLA data sets. Homogeneous and intercalibrated SLA fields in the Mediterranean Sea created by merging TOPEX/Poseidon, ERS1/2, Geosat Follow-On, Jason-1/2, TOPEX/Poseidon interleaved, and ENVISAT altimeter measurements, are obtained from AVISO (http://www.aviso.oceanobs.com/) for the period October 1997 to December 2009. The data set includes 7-day maps of SLA on a 0.125º x 0.125º regular grid interpolated in time and space using a global objective analysis (Le Traon et al., 1998). The length scale of the interpolation and the e-folding time scale were set to 100 km and 10 days (Pujol & Larnicol, 2005). The SLA data is re-binned in space onto a 0.25º x 0.25º to reduce small-scale variability and in time to the satellite CHL 8-day window (see below) in order to be consistent with the temporal resolution of CHL data.

### **2.2 Ocean color satellite data**

The first instrument that demonstrated the viability of satellite ocean color measurements was the US National Oceanic and Atmospheric Administration (NOAA) and the NASA CZCS Experiment aboard the Nimbus-7 satellite (Gordon et al., 1983). Although other instruments had sensed ocean color from space, their spectral bands, spatial resolution and dynamic range were optimized for land or meteorological use, whereas every parameter in CZCS was optimized for use over water to the exclusion of any other type of sensing. The CZCS ocean color data, available from 1978 to 1986, allowed a considerable progress in the knowledge of spatial and temporal variations in surface CHL in various regions of the world ocean (Antoine et al., 1996; Behrenfeld & Falkowski, 1997; Platt & Sathyendranath, 1988).

The CZCS provided justification for future ocean color missions such as the Japanese National Space Development Agency (NASDA) Ocean Color and Temperature Scanner (OCTS) aboard the Advanced Earth Observing Satellite (ADEOS) from 1996 to 1997 (Kishino et al., 1997) or the NASA Sea Viewing Wide Field of View Sensor (SeaWiFS) aboard the Orbital Science Corporation (OSC) Orbview-II satellite from 1997 to 2010 (Hooker & McClain, 2000). Presently, the NASA Moderate Resolution Imaging Spectrometer (MODIS-A) aboard the NASA Aqua satellite (Esaias et al., 1998), and the European Space Agency (ESA) Medium Resolution Imaging Spectrometer (MERIS) aboard the ENVISAT satellite (Rast et al., 1999), both launched in 2002, provide a global monitoring of the ocean biomass. Other missions exist, with more limited coverage however, such as the Indian OCM (Chauhan et al., 2002) or the Korean OSMI (Yong et al., 1999).

To maintain the level of uncertainty of the derived products within predefined requirements, SeaWiFS and MODIS-A ocean color observations are calibrated using longterm in-situ field data (Bailey and Werdell, 2006). The calibration includes an adjustment of the overall response of the sensor, an atmospheric correction algorithm and the application of bio-optical algorithms (Gordon, 1997, 1998). The ocean color data used in this work consists of level 3 standard processed 8-day maps of CHL from SeaWiFS and MODIS-A on a 9 x 9 km regular grid in the Mediterranean Sea obtained from NASA's Ocean Color web site (http://oceancolor.gsfc.nasa.gov, see also McClain (2009)). Merging data from SeaWiFS and MODIS-A increases the coverage and reduces the uncertainties in the retrieved variables (Maritorena et al., 2010). The CHL produced by those ocean color missions are consistent over a wide range of conditions (Morel et al., 2007). We interpolate cloud-free CHL data onto the SLA grid of 0.25º x 0.25º resolution using objective analysis with a length scale of 50 km and and e-folding time scale of 10 days.

Satellite derived CHL through standard algorithms in the Mediterranean Sea is affected by a calibration problem displaying a bias when compared to in situ observations (Bosc et al., 2004; Volpe et al., 2007). This difficulty is related to the specific environmental bio-optical characteristics of the Mediterranean with respect to other oceanic regions having similar ranges of CHL. However, in the present work, we use the standard calibration algorithms because we are interested in the phytoplankton variability rather than in the absolute biomass values. The satellite derived CHL is used as a proxy for the phytoplankton biomass in the mixed layer. Although satellite derived CHL is limited to an optical depth, a reasonable correlation exists between the depth integrated and the satellite CHL (Morel and Berthon, 1989).
