A Robust Fixed Rank Kriging Method for Improving the Spatial Completeness and Accuracy of Satellite SST Products

Sea surface temperature (SST) plays a vital role in the Earth's atmosphere and climate systems. Complete and accurate SST observations are in great demand for forecasting tropical cyclones and projecting climate change. Satellite remote sensing has been used to retrieve SST globally, but missing values and biased observations impose difficulties on practical applications of these satellite-derived SST data. Conventional spatial statistics methods such as kriging have been widely used to fill the gaps. However, when such conventional methods are used to analyze a massive satellite data set of size
$n$
, the inversion of the
$n\times n$
covariance matrix may require
$O(n^3) $
computations, which make the computation very intensive or even infeasible. The fixed rank kriging (FRK) performs dimension reduction through multiresolution wavelet analysis so that it can dramatically reduce the computation cost of various kriging methods. However, the FRK cannot directly be used for incomplete data over spatially irregular regions such as SSTs, and the potential bias in the satellite data is not addressed. In this paper, we construct a data-driven bias-correction model for the correction of the bias in satellite SSTs and develop a robust FRK (R-FRK) method so that the dimension reduction can be used to the satellite data in irregular regions with missing data. We implement the bias-correction model and the R-FRK to the level-3 mapped night Moderate Resolution Imaging Spectroradiometer SSTs. The accuracy of the resulting predictions is assessed using the colocated drifting buoy SST observations, in terms of mean bias (bias), root-mean-squared error, and R squared (R
²
) . The spatial completeness is assessed by the availability of ocean pixels. The assessment results show that the spatially complete SSTs with high accuracy can be obtained through the bias-correction model and the R-FRK method developed in this paper.