Empirical Function Method: A Precise Approach for Filling Data Gaps in Satellite Sea Surface Temperature Imagery

The acquisition of wide geophysical data of vast oceans by satellites can be impeded by clouds, which may result in gaps in the data acquired in the infrared and visual bands, such as sea surface temperature (SST) data, leading to limited data usage. To address this issue, we proposed a general and robust method, named the empirical function (EF) method, which involves expanding an ocean field with space-time-separation functions and determining the functions by minimizing the expansion’s residual on the observation data while considering the prior-knowledge constraint that an ocean field varies smoothly in space and time. To test the effectiveness of the EF method, we applied it to reconstruct the 14-year cloud-free SST data in the Gulf Stream region spanning from 24.5°N to 44°N and from 82.5°W to 54.5°W. The original data consist of the 0.025<inline-formula> <tex-math notation="LaTeX">$^{\circ }\,\,\times0.025^{\circ }$ </tex-math></inline-formula> gridded daily composite daytime SST products of the Moderate-Resolution Imaging Spectroradiometer on the Aqua Sun-synchronous satellite, with an annual data-missing rate fluctuating around 78% in the region. In addition, we validated the reconstructed data against in situ buoy measurements. The reconstructed SST data’s accuracies are <inline-formula> <tex-math notation="LaTeX">$-0.11\,\,^{\circ }\text{C}\,\,\pm $ </tex-math></inline-formula> 0.91 °C (bias ± standard deviation of error) and <inline-formula> <tex-math notation="LaTeX">$-0.12\,\,^{\circ }\text{C}\,\,\pm $ </tex-math></inline-formula> 0.67 °C in the areas without and with satellite observations, respectively, which are slightly lower and higher than the gappy satellite SST products’ accuracy of <inline-formula> <tex-math notation="LaTeX">$-0.14\,\,^{\circ }\text{C}\,\,\pm $ </tex-math></inline-formula> 0.77 °C.