*4.3. Validation of Reconstruction*

To assess the quality of the extrapolation resulting from our data fusion method, we validate it by analyzing 5 different regions (as shown in Figure 4); each region has at least an area of 8 × 8 degrees (200 × 200 pixels). For each of these areas a mask representing a cloud structure (of the typical size and shape found in chlorophyll images) is defined (the clouds are generated using a real MODIS SST 9-km daily image of 1 January 2006, and are kept fixed in time). Those masks have a surface of about 30% of the region on which they will be applied. To assess the quality of the fusion algorithm, we proceed in three steps. In the first step, points lying in the masked area of a daily Chl-*a* map are removed (notice that there will be additional missing points in the Chl-*a* map because of the gaps in the original remote sensing product; for instance, in the EP area (Figure 4) the average percentage of missing points is 85%). In the second step, the fusion algorithm is applied to the masked Chl-*a* map using the corresponding daily SST map as a template, extrapolating to the missing values. Finally, the extrapolated values are compared to the available original ones on the masked area for each image during the entire year 2006 (365 daily images). We require a minimum of 5% of original Chl-*a* values existed inside the masked area to perform the cross validation. This strategy allows comparing the original Chl-*a* and the retrieved one at the available masked points, and therefore the extrapolation ability of the fusion method.

The performance of the algorithm is studied in different Chl-*a* regimes: oligotrophic regions (Central Atlantic, CA and Pacific in front of California, CL) and eutrophic regions in higher latitudes (North Atlantic, NA), coastal upwelling areas (Benguela upwelling, BG) and the Equator (Equatorial Pacific, EP). NA region is defined by [19.61◦W–9.19◦W; 51.65◦N–57.91◦N] and 22% of the area is masked, EP region is defined by [142.54◦W–130.04◦W; 5.02◦S–0.40◦N] (29% of the area is masked), CL region is defined by [125.87◦W–117.53◦W; 22.48◦N–30.82◦N] (31% of the area is masked), BG region is defined by [9.56◦E–17.90◦E; 27.53◦S–19.19◦S] (35% of the area is masked) and CA is defined by [40.44◦W–30.03◦W; 22.48◦N–30.82◦N] with a 34% of the area being masked.

Examples of one daily image validation are shown in Figure 4 for each region. A quantitative measure of the quality of the reconstruction of the chlorophyll is given in terms of four parameters: the root mean square (rms), bias (mean) and standard deviation (std) of the reconstructed error and the correlation coefficient (r) between the masked and reconstructed values. In the case of the central

Atlantic and California regions, the concentration of chlorophyll is smaller, followed by the values found in the North Atlantic, the Equatorial Pacific and the Benguela upwelling where highest values of Chl-*a* concentration are found. Correlations coefficients between L4 and original Chl-*a* decrease for the regions where lower pigment concentrations are found. Better statistics are associated to areas of high primary production.

The validation for the entire year 2006 is summarized in Table 1; the mean seasonal values for each one of the statistical parameters and clouds are included. Our data fusion method succeeds in filling gaps with mean annual correlation coefficients ranging from 0.58 to 0.81 for the studied period and artificial clouds. Oligotrophic regions (North Atlantic and California) have mean regression coefficients which are significantly lower than the mean correlation coefficients values for the equatorial Pacific, the North Atlantic and the Benguela upwelling regions respectively. The smaller performance in oligotrophic regions is probably due to the small horizontal gradients of Chl-*a* there together with a larger signal-to-noise ratio. However, the absolute error of the reconstruction is always moderate. A slightly mean positive bias is systematically found, meaning that the L4 estimates are smaller than the original Chl-*a* values, probably due to the smoothing generated by the weighting function used in the fusion algorithm [16].

The seasonal segregation of validation results highlights a worse performance during the January-February-March period, with mean correlation coefficients ranging from 0.15 to 0.47 (Central Atlantic and Benguela upwelling, respectively). During the rest of seasons, the validation results greatly improve with correlation coefficients ranging from 0.67 to 0.94 in spring (AMJ), from 0.77 to 0.94 in summer (JAS) and from 0.74 to 0.94 in fall season (OND). In the winter season, the strengthening of winds and deepening of the mixed layer in mid and high latitudes create a large supply of nutrients from the deep ocean to the surface, which will be available for phytoplankton to proliferate in the following seasons. In equatorial and coastal upwelling regions (Equatorial Pacific and Benguela, respectively), the upwelling intensity also varies seasonally depending on wind strength and direction and the vertical structure of the water column. Under these circumstances, nutrient availability, vertical mixing and the depth of the mixed layer play crucial roles in the distribution of Chl-*a*, which could not be only explained by horizontal advection and the distribution of surface temperature.

The power density spectra (PDS) is computed as in [23] inside the boxes shown in in Figure 5 (top) for each daily file and then the median for the entire period 2006 is calculated. The spatial spectral analysis of MODIS Chl-*a*, MODIS L3 SST and Level 4 Chl-*a* products under the SPURS and STP regions (red and green boxes in Figure 5 (top)) shows that the actual spatial resolution of MODIS Chl-*a* and MODIS L3 SST is about 10 km and, and 15 km for the L4 Chl-*a* product (Figure 5 (bottom)). The intermittent character of MODIS Chl-*a* and the lower resolution of L4 Chl-*a* explain the vertical shift between their PDS.


**Table 1.** Mean seasonal results of daily reconstruction validation under artificial clouds for year 2006.

**Figure 4.** Artificial clouds generated for validation purposes in the Central Atlantic (CA), Benguela upwelling (BG), California Pacific (CL), Equatorial Pacific (EP) and North Atlantic (NA) (**top left panel**). Validation of reconstruction under artificial clouds for MODIS Chl-*a* concentration. For CA region day 95, BG region day 159, CL day 90, EP day 193, and NA day 193 of year 2006.

**Figure 5.** (**top**) Areas for power density spectra (PDS) computation: Red box represent SPURS region (22◦–28◦N and 28◦–60◦W) and green box represent STP region (27◦–33◦S and 106◦–170◦W). (**bottom**) Median of PDS for the year 2006 of MODIS L3 SST, MODIS Chl-*a*, and Level 4 Chl-*a* for the SPURS region (**left**) and the STP region (**right**).
