**1. Introduction**

Global maps of Chl-*a* concentration at sea surfaces, similar to what happens with many other remote sensing products, suffer from data gaps. This is especially true for high-spatial resolution (few kilometers) daily maps, where orbital voids add to the data loss due to clouds, aerosols or sunglint. For this kind of products, gap-filling and noise-reduction techniques are required to provide uniform products suitable for environmental monitoring or the initialization of ecosystem models. To achieve this goal, data interpolation and noise reduction are commonly performed using univariate methods as, for example, [1]. Multivariate methods have also been applied to generate uniform products that combine information from different sensors; examples of multivariate approaches include optimal interpolation [2], empirical orthogonal functions [3,4], classification methods [5] and more recently using data-diven methods as analog data assimilation [6,7]. The method discussed in this paper is based on the empirical perception that fronts, eddies, and filaments are identifiable in the satellite imagery of different ocean variables (sea level, ocean color, sea surface temperature, sea surface salinity) and, sometimes, even in the raw radiance recorded by the satellites [8,9]. Remote sensing and drifter data have shown that the statistical distribution of surface ocean fields has characteristics of a flow in fully developed quasi-2D turbulence. Owing to the underlying turbulence of the ocean, the application of a technique known as singularity analysis [10] allows to retrieving information about ocean currents from images of any advected scalar.

The analysis of the spatial variability of pigment images found no difference between the wavenumber spectra of SST and ocean color maps, leading to the conclusion that phytoplankton cells in dynamic areas effectively behave as passive scalars [11,12]. In [13] it was shown that sea surface temperature and chlorophyll maps have the same multifractal structure. This fact can be interpreted as a consequence of the turbulent advection at the scales of observation and due to the existence of a common cascade process [14]. The multifractal structure of any scalar can be characterized through singularity analysis [15]. Singularity analysis is any technique capable of calculating a map of the singularity exponents associated with a given scalar. A singularity exponent is a non-dimensional number that characterizes the sharpness, or regularity, of the scalar around a given point [10]. Nieves et al. [13] showed that the singularity exponents extracted from SST, Chl-*a* or brightness temperature maps are very similar, a fact that was interpreted as an effect of the advection term. Notice that the equivalence among singularity exponents does not require advection to be the largest term in the equation of evolution. Advection is a non-linear term in the equation of evolution, and thus it is at the origin of singularities.

That the common singular structure of variables advected by the turbulent ocean has been exploited to reduce the noise in SMOS sea surface salinity maps using data from auxiliary, high-quality SST maps [16,17]. The same algorithm can be used not only to reduce noise but also to extrapolate provided that the template is defined at the missing points. Although the theoretical foundation of the data fusion method is relatively complex, its practical application is rather simple: a non-parametric, weighted local linear regression between Chl-*a* and SST maps are calculated at each point, then the regression parameters obtained at each point are applied to the value of SST at that point to infer a new variable of Chl-*a*.

The goal of this work is to assess the ability of a local linear regression approach to fill remote sensing chlorophyll concentration data gaps. This local relation between SST and Chl-*a* can be built from a single snapshot of both variables, so the implementation of the method is simple, computationally fast, and no training set is required; moreover, the method is well fit to deal with strong, rapid changes in the dynamics of the flow as far as it is always turbulent. Additionally, the analysis of the auxiliary parameters of the fusion algorithm allows characterizing the modulation of the seasonal correlation modulation between Chl-*a* and SST variables.

## **2. Satellite Data**

Two Aqua-MODIS ocean products from the NASA Aqua spacecraft are used in this study: Chl-*a* concentration Level-3 daily product, and standard MODIS Aqua Level 3 SST Thermal IR Daily 4 km Nighttime, both at 4 km × 4 km grid [18]. Our dataset period goes from January to December 2006. The data were downloaded from the Ocean Color web portal, http://oceancolor.gsfc.nasa.gov/. According to many studies, it is assumed that Chl-*a* follows a lognormal distribution [19] and so we work with the logarithm of chlorophyll concentrations for ease of use (theoretically the singularity exponents should not change if a monotonic function is applied to the data [10], but it is numerically more stable to work with a dynamic range comprising fewer orders of magnitude).
