Location: Hydrology and Remote Sensing LaboratoryTitle: Triple collocation: beyond three estimates and separation of structural/non-structural errors
|PAN, MING - PRINCETON UNIVERSITY|
|FISHER, COLBY - PRINCETON UNIVERSITY|
|CHANEY, N. - PRINCETON UNIVERSITY|
|ZHAN, W. - PRINCETON UNIVERSITY|
|AIRES, F. - COLLABORATOR|
|ENTEKHABI, DARA - COLLABORATOR|
|WOOD, E. - PRINCETON UNIVERSITY|
Submitted to: Remote Sensing of Environment
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 10/25/2015
Publication Date: 11/5/2015
Citation: Pan, M., Fisher, C., Chaney, N., Zhan, W., Aires, F., Crow, W.T., Entekhabi, D., Wood, E. 2015. Triple collocation: beyond three estimates and separation of structural/non-structural errors. Remote Sensing of Environment. 171:299-310.
Interpretive Summary: Remote-sensed surface soil moisture products must be fully validated before they can be used with confidence in agricultural applications like drought monitoring, yield forecasting and irrigation scheduling. However, such validation is complicated by a general lack of groundbased soil moisture observations and the severe resolution contrast between point-scale ground observations and footprint-scale (> 10 km)soil moisture retrievals obtained from space. Recently, a number of new validation techniques have been developed for satellite-derived soil moisture products that do not require the direct use of ground-based observations. These techniques allow satellite products to be evaluated over much wider spatial extents. This paper develops some critical methodological improvements to one of these techniques (i.e., triple collocation) and presents an improved approach for evaluating the accuracy of remotely-sensed surface soil moisture retrievals. It will be used to improve our ability to validate remotely-sensed surface soil moisture retrievals and speed their full application within agricultural decision support systems.
Technical Abstract: This study extends the popular triple collocation method for error assessment from three source estimates to an arbitrary number of source estimates, i.e., to solve the “multiple” collocation problem. The error assessment problem is solved through Pythagorean constraints in Hilbert space, which is slightly different from the original inner product solution but easier to extend to multiple collocation cases. The Pythagorean solution is fully equivalent to the original inner product solution for the triple collocation case. The multiple collocation turns out to be an over-constrained problem and a least squares solution is presented. As the most critical assumption of uncorrelated errors will surely fail in most multiple collocation problems, we propose to divide the source estimates into structural groups based on their production process and treat the structural and non-structural errors separately. Such error separation allows the source estimates to have their structural errors fully correlated within the same structural group, which is much more realistic than the original assumption. A new error assessment procedure is developed which performs the collocation twice, each for one type of errors (structural and non-structural), and then sums up the two types of errors. The new procedure is also fully backward compatible with the original triple collocation technique.Error assessment experiments are carried out for surface soil moisture data from multiple remote sensing models, land surface models, and in situ measurements.