Merging of multiple satellite datasets is a simple yet effective way to reduce prediction error. However, most merging methods for satellite data today are based on weighted averaging first proposed in 1969 for economic forecasting, which does not provide optimal outcomes when applied to satellite data. If our aim is to produce a merged data product that minimizes the prediction errors against a prediction target, there is no reason to insist that the merged product be an average of the parent datasets. A more disciplined approach based on mathematical optimization would be to minimize prediction errors. However, formulating merging as an optimization problem is insufficient by itself as the statistics needed for optimization, e.g. signal-to-noise ratio (SNR) of parent products, are often unavailable in practice and must be estimated jointly. In this paper, we address both of these problems for data merging. We first formulate optimal merging of satellite data as a SNR optimization (SNR-opt), and propose an estimation method to jointly estimate the required SNRs. This SNR-based approach has a natural interpretation as a multi-input single-output Wiener filter. Through extensive experimental validation on three global- scale satellite-derived soil moisture and land surface temperature products, we demonstrate that our SNR optimization significantly improves merging results over weighted averaging schemes.

Satellite-derived data provide useful information about the rationale of Earth’s functioning. While satellite remote sensing has been regarded as the almost only means for observing the entire Earth in near-real-time, errors in satellite observations have limited their direct usage in applications. Merging two or more data sources has been regarded as a simple but effective way to decrease such errors (e. g. minimizing mean square errors between the observation and truth). The principle of data merging is to combine independent information of each data source, improving over each individual product by canceling out random errors, with effectiveness by the degree of independence over the data sources. In the case of linearly combining data, qualitative assessments of the error (i.e. error variance/covariance and data-truth correlation) are essential to calculate the optimal weight for each candidate product. However, such reference “truth” is rarely available in practical. To overcome this limitation, a triple collocation (TC) technique is often used to estimate data error by using a data triplet without the truth. Despite the usefulness and simplicity of the TC-based error estimation, the inherent assumptions (e.g. error independence) in the approach tend to induce sub-optimal results in the error estimation and/or data combination. There have been also further efforts to address the limitation such as quadruple collocation (QC) using a data quadruple to partially estimate error cross-correlation and single/double instrumental variable methods to lessen the difficulty in obtaining multiple datasets. In this presentation, we review the status of error estimation and data merging approaches based on the collocation methods and then present challenges to be addressed through future research.