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Title: Nonparametric triple collocation

item NEARING, G.S. - Goddard Space Flight Center
item YATHEENDRADES, S. - Goddard Space Flight Center
item Crow, Wade
item Bosch, David - Dave
item Cosh, Michael
item Goodrich, David - Dave
item Seyfried, Mark
item Starks, Patrick - Pat

Submitted to: Water Research
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 5/15/2017
Publication Date: 7/7/2017
Citation: Nearing, G., Yatheendrades, S., Crow, W.T., Bosch, D.D., Cosh, M.H., Goodrich, D.C., Seyfried, M.S., Starks, P.J. 2017. Nonparametric triple collocation. Water Research. 53(7):5516-5530.

Interpretive Summary: Remotely-sensed estimates of soil moisture and precipitation improve our ability to monitor the extent, duration, and severity of agricultural drought around the world. However, it is frequently difficult to evaluate these retrievals in regions of the world lacking adequate ground-based instrumentation. Recently, a new statistical technique called "Triple Collocation" has been developed which can provide error assessments for remotely-sensed products in the absence of high-quality, ground-based reference measurements. However, these assessments are only accurate if a specific set of statistical assumptions are honored. This manuscript describes an extension of the existing Triple Collocation theory which is valid under a wider variety of conditions. As a result, it enhances our ability to evaluate, and therefore improve, remote sensing data products critical for monitoring agricultural drought.

Technical Abstract: Triple collocation derives variance-covariance relationships between three or more independent measurement sources and an indirectly observed truth variable in the case where the measurement operators are linear-Gaussian. We generalize that theory to arbitrary observation operators by deriving nonparametric analogues to the total error and total correlation statistics as integrations of divergences from conditional to marginal probability ratios. The nonparametric solution to the full measurement problem is under-determined, and we therefore retrieve conservative bounds on the theoretical total nonparametric error and correlation statistics. We examine the application of both linear and nonlinear triple collocation to synthetic examples and to two real-data test cases related to (i) using sparse point-based measurements of precipitation to infer spatial averages, and to (ii) evaluating spaceborne soil moisture retrievals using in situ monitoring networks and dynamical process models. We report that nonlinear triple colocation generally results in better estimators of the target statistics than does linear triple collocation.