Remote sensing data are often sparse relative to the space-time domains of geo-physical processes, so data from different instruments are used in conjunction with one another to take advantage of their complementary coverage. Yet, there is no comprehensive data fusion methodology for combining them in a principled, rigorous way. Remote sensing data are often massive, with incompatible support, and subject to biases. We approach this problem from a statistical point of view, and aim to estimate the conditional means of true but not directly observed processes from noisy and possibly biased data realizations, and also to estimate the uncertainties of these estimates. This dissertation proposes an optimal fusion methodology that scales linearly with data size, and resolves change of support and biases through a spatial statistical framework.

This methodology is based on Fixed-ranked Kriging (FRK), a variant of kriging that uses a special class of covariance functions for spatial interpolation of a single, massive input dataset. This simplifies the computations needed to calculate the kriging means and prediction errors. We extend the FRK framework to the case of two or more massive input datasets. The methodology does not require assumptions of stationary or isotropy, making it appropriate for a wide range of geophysical processes. The method also accounts for change of support, allowing estimation of the point-level covariance functions from aggregated data, and prediction to point-level locations. This new methodology is applied to aerosol optical depth data from two remote sensing instruments, where the total data size is on the order of tens of thousands.