**5. Discussion and Conclusions**

Satellite missions that measure chlorophyll concentration offer limited coverage due to orbital gaps, the presence of clouds and aerosols, sun glint, poor retrieval of the geophysical variables, etc. Combining data from several satellites can considerably increase the spatial coverage of daily maps. In this paper, we have used a method to merge the information coming from two different ocean scalars that share common multifractal characteristics. One of the two scalars, denoted as template, is assumed to have higher spatial coverage and signal-to-noise ratios than the other one, denoted as signal. The application presented here uses MODIS SST as template and MODIS Chl-*a* as signal. The template is used to extrapolate the signal by estimating local linear regression coefficients between Chl-*a* and SST, then applying them to the template to restore the signal.

The regression coefficients of the data fusion method exhibit geographical patterns that contain information about the relation between Chl-*a* and SST. The linear approximation, based on the hypothesis that the gradients of the regression coefficients are negligible as compared with the gradients of the variables Chl-*a* and SST, is less accurate on equatorial Pacific, Indian oceans, and during the winter season. In all these cases the present scheme needs to be extended. Besides, auxiliary environmental information, such as surface winds, mixed layer depth or nutrient concentration must be taken into account to fully understand the Chl-*a* behavior.

By exploiting the synergy between Chl-*a* and SST, it has been possible to increase the daily spatial coverage of MODIS Chl-*a*. The extrapolated fields have proved to be consistent with the observed ocean structures. A cross validation of the methodology, which consisted on create artificial gaps, apply the methodology and compare to the original Chl-*a* data, indicates correlation coefficients ranging from 0.67 to 0.94, except in winter season, when the correlation coefficients range from 0.15 to 0.47.

In conclusion, we have demonstrated the efficiency of blending SST and Chl-*a* to improve spatial coverage of chlorophyll products and to study the relation between ocean scalars. The resulting information can help to further characterize the spatio-temporal correlation between SST and Chl-*a*, and the temporal variation and long-term evolution of the biogeochemical provinces.

**Author Contributions:** Conceptualization, A.T. and M.U.; methodology, A.T. and M.U.; software, M.U., S.G. and J.B.P.; validation, M.U., S.G. and J.B.P.; writing—original draft preparation, M.U.; writing—review and editing, M.U., S.G., J.B.P. and A.T.; visualization, M.U., S.G. and J.B.P.; supervision, A.T. and J.B.P.; funding acquisition, A.T. and M.U. All authors have read and agreed to the published version of the manuscript.

**Funding:** M. Umbert is funded by the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Individual Fellowship Career Restart Panel (MSCA-IF-EF-CAR Number 840374).

**Acknowledgments:** The authors acknowledge Ocean Color service website for making publicly available their MODIS-Aqua data at http://oceancolor.gsfc.nasa.gov/. We acknowledge the insightful reviews, comments and suggestions by anonymous reviewers that helped improve the content and readability of the manuscript.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


c 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
