4.1. Scalar Synergy
Figure 1 shows examples of daily maps of MODIS Chl-
a concentration (top panel) and SST (middle panel) in 1 January 2006. The values of Chl-
a are derived from measurements in the visible part of the spectrum, which may be affected by artifacts like aerosols, sun glint and high turbidity of the water. Several flags are introduced to characterize Chl-
a data quality and a result, maps of Chl-
a usually suffer from a larger incompleteness than those of SST, which are derived from infrared measurements in the 4
m range. An example of the application of the fusion algorithm in the global ocean for 1 January 2006 is shown in the bottom panel of
Figure 1. As stated before, the algorithm allows estimating the local Chl-
a-SST regression by taking into account all possible couples of data (SST,Chl-
a) weighted using function
in Equation (
5). Fused Chl-
a maps integrate the relation between structures present in the SST and Chl-
a specific structures. In fused daily products we recognize some expected Chl-
a global patterns, near the ocean surface, where availability of sunlight is not limiting, phytoplankton growth depends on temperature and nutrient levels. High chlorophyll concentrations are found in nutrient-rich, cold polar waters and where ocean currents cause upwelling, which brings nutrient-rich deep-cold water to the surface.
We will focus in the region of the Gulf of California, a narrow sea between mainland Mexico and the Baja California peninsula, where high primary productivity levels are found as a result of an efficient nutrient transport of waters from under a shallow pycnocline into the euphotic zone [
21].
Figure 2 shows the input variables of our algorithm (top panel: Chl-
a, middle panel: SST) and the output fused Chl-
a (bottom panel). The corresponding singularity exponents are shown in the right column. Rich singularity structures can be recognized in the original chlorophyll concentration maps associated with the fronts mainly caused by the horizontal transport from high primary production areas onto less productive ones. The SST field exhibits also the richness of patterns associated with the circulation in that area. Where both images are not affected by data gaps, the singularity structure (although not the magnitude) is similar between them. Places where the correspondence of both singularity images fails may identify places at which intrinsic dynamics of the variable competes with flow advection.
Once the data fusion is applied, the L4 Chl-a is extrapolated to all the pixels where SST was available. The structure of Chl-a is well represented (compared to the original image), although a smoothing of the original variable degrades the dynamic range of the variable. The singularity exponents of the fused Chl-a data reveal that most of the structures present in the SST map are re-integrated in the chlorophyll map at the same time that Chl-a specific magnitude and structures are maintained; for instance, the strong gradient associated with the biological activity present in the Gulf of California, appear delineated in the fused Chl-a. This implies that the fusion algorithm can partially integrate SST structures without destroying Chl-a ones.
4.2. Interpretation of Auxiliary Parameters
As shown in Equation (
4), the functions
and
provide information about the local functional dependence between SST and Chl-
a. The local slope,
, will be negative at those places where SST decreases as Chl-
a increases in the neighborhood, and the converse. Considering that cold waters tend to have more nutrients than warm waters, phytoplankton is more abundant where surface waters are cold. So, as we move from one given point to another with colder water, Chl-
a would usually increase and thus the slope
will be negative. However, the relationship changes from point to point and it should be expected to change from one image to the next one.
Figure 3 shows the seasonal average of the slope and intercept (considering winter as January-February-March, spring as April-May-June, summer as July-August-Septemebr and fall as October-November-December).
The coherent patterns of the auxiliary parameters of the method delineate areas with different relation between Chl-
a and SST. In the same spirit, Longhurst [
22] introduced the concept of ocean biogeochemical provinces, characterized by their particular physical and biological behavior. Longhurst definition is based on the mixed layer depth lying close to the ocean-atmosphere interface. Specific provinces have common characteristics and can generally be classified as four general biomes: the coastal, polar, westerly and trade winds biomes. A visual comparison between local functions of the fusion method and the Longhurst definition is shown in
Figure 3.
As expected, negative slopes are present in the upwelling areas associated with the easternmost currents of the great anticyclonic gyres, corresponding to the Benguela and Canary currents in the Atlantic Ocean and the Peru and California currents in the Pacific Ocean. Notice that this negative slope is present all year long. These oceanic areas, as well as the upwelling zones and continental margins, are rich in Chl-a as a result of the proximity to areas where the resurgence of nutrients take place and the local circulation is favorable to nutrient accumulation. A band of cool, chlorophyll-rich water is also apparent all along the equator; the strongest signal at the Atlantic Ocean and the open waters of the Pacific Ocean also leads to negative values of the local intercept .
Negative values of are also found in areas where Chl-a concentration decreases as SST increases; this situation, which is typically found in the (oligotrophic) subtropical gyres, intensifies in the Atlantic Ocean during the northern hemisphere winter and spring. The Pacific Ocean exhibits an intensified negative pattern in the Northern subtropical gyre during boreal spring and a negative pattern in the southern hemisphere during austral spring. In both cases, such intensification in the oligotrophic subtropical gyres is driven by the seasonal cycle of sea surface temperature.
Subpolar gyres are also characterized by high Chl-a concentrations linked to nutrient accumulation during winter, when the mixing layer reaches the deep ocean followed by the stratification of the water column during spring. During the dark winter months, the local slope between SST and Chl-a is positive. However, when sunlight returns and nutrients are trapped near the surface during spring and summer, the phytoplankton flourishes in high concentration, seen as negative values of .
The local regression coefficient (not shown) has small values along the Equatorial Pacific, and in the Southern and Indian Ocean indicating that horizontal advection of Chl-a cannot be locally explained by SST variability in these regions only. Therefore, either additional variables should be taken into account, or a more sophisticated relation between Chl-a and SST should be used. For example, in ocean regions of High Nutrient Low Chlorophyll (HNLC) as the equatorial Pacific and the Southern Ocean, low Chl-a concentrations are due to a stoichiometric imbalance of iron which have no link to SST. Another possible cause for the low values of the local regression coefficient in some regions is the lack of enough points to provide a quality reconstruction. For instance, 85% of the data points are missing in the Equatorial Pacific due to the large cloudiness.
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 [19.61W–9.19W; 51.65N–57.91N] and 22% of the area is masked, EP region is defined by [142.54W–130.04W; 5.02S–0.40N] (29% of the area is masked), CL region is defined by [125.87W–117.53W; 22.48N–30.82N] (31% of the area is masked), BG region is defined by [9.56E–17.90E; 27.53S–19.19S] (35% of the area is masked) and CA is defined by [40.44W–30.03W; 22.48N–30.82N] 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.