Abstract:
Triple collocation has found widespread application in the hydrological sciences because it provides
information about the errors in our measurements without requiring that we have any direct access
to the true value of the variable being measured. 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 additive. 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 underdetermined, 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 a real-data test case related to evaluating space-borne
soil moisture retrievals using sparse monitoring networks and dynamical process models.
