Estimating error cross-correlations in soil moisture data sets using extended collocation analysis

Authors: GRUBER, ALEX - Vienna University Of Technology; SU, SHUN-HSU - Vienna University Of Technology; Crow, Wade; ZWIEBECK, A. - Vienna University Of Technology; DORIGO - Vienna University Of Technology; WAGNER - Vienna University Of Technology

Submitted to: Journal of Geophysical Research Atmospheres
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 1/15/2016
Publication Date: 2/9/2016
Citation: Gruber, A., Su, S., Crow, W.T., Zwiebeck, A., Dorigo, Wagner 2016. Estimating error cross-correlations in soil moisture data sets using extended collocation analysis. Journal of Geophysical Research Atmospheres. 121:1208-1219. doi: 10.1002/2015JD024027.

Interpretive Summary: Satellite-based estimates of surface soil moisture are of potentially great value for a wide variety of important agricultural applications including: drought monitoring, yield forecasting, and irrigation scheduling. However, before these applications can be addressed, remote sensing retrievals must be fully-evaluated and assessed to determine their overall reliability. Over many regions of the world such assessment is extremely difficult owing to a severe lack of ground-based soil moisture instrumentation (to serve as a validation reference). Recently, new statistical techniques have been developed which provide accurate estimates of error in remotely-sensed soil moisture products in the absence of high-quality ground-based observations. These techniques allow - for the first time - a truly global characterization of errors in remotely-sensed soil moisture products. This paper explores a specific mathematical extension of these techniques which allows them to: 1) remain accurate over a wider variety of cases and 2) provide accurate assessments using shorter time series of soil moisture data. As such, it contributes significantly to our ability to assess, and therefore improve, satellite-derived soil moisture products. Improvements in these products will, in turn, speed their application into critical water resource and agricultural drought monitoring systems.

Technical Abstract: Consistent global soil moisture records are essential for studying the role of hydrologic processes within the larger earth system. Various studies have shown the benefit of assimilating satellite-based soil moisture data into water balance models or merging multi-source soil moisture retrievals into a unified data set in order to generate a continuous long-term soil moisture product. However, such merging and assimilation frameworks require an appropriate parameterization of the error structures of the underlying data sets. While triple collocation (TC) analysis has been widely recognized as powerful tool for estimating random error variances of coarse-resolution soil moisture data sets, the estimation of error cross-covariances remains an unresolved challenge. Here we propose a method for estimating error cross-correlations - referred to as extended collocation (EC) analysis - by generalizing the TC method to an arbitrary number of data sets and relaxing the therein made assumption of zero error cross-correlation for some data sets combinations. A synthetic experiment shows that EC analysis is able to recover true error cross-correlation levels with an RMSE of 0.03 [-] with negligible bias. Applied on real soil moisture retrievals from AMSR-E C-band and X-band channels together with ASCAT retrievals and modeled data from GLDAS-Noah, EC appears to reliably estimate strong non-zero error cross-correlations between the two AMSR-E products (median=0.72 [-]). We conclude that the proposed EC method represents an important step towards a fully parameterized error covariance matrix for coarse-resolution soil moisture data sets, which is vital for any rigorous data assimilation framework or data merging scheme.