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Browsing by Author "Crow, Wade T."

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    An approach to quantifying the efficiency of a Bayesian filter
    (American Geophysical Union, 2013-04-26) Nearing, Grey S.; Gupta, Hoshin V.; Crow, Wade T.; Gong, Wei; University of Arizona; United States Department of Agriculture (USDA); Beijing Normal University; University of Alabama Tuscaloosa
    Data assimilation is the Bayesian conditioning of uncertain model simulations on observations to reduce uncertainty about model states. In practice, it is common to make simplifying assumptions about the prior and posterior state distributions, and to employ approximations of the likelihood function, which can reduce the efficiency of the filter. We propose metrics that quantify how much of the uncertainty in a Bayesian posterior state distribution is due to (i) the observation operator, (ii) observation error, and (iii) approximations of Bayes' Law. Our approach uses discrete Shannon entropy to quantify uncertainty, and we define the utility of an observation (for reducing uncertainty about a model state) as the ratio of the mutual information between the state and observation to the entropy of the state prior. These metrics make it possible to analyze the efficiency of a proposed observation system and data assimilation strategy, and provide a way to examine the propagation of information through the dynamic system model. We demonstrate the procedure on the problem of estimating profile soil moisture from observations at the surface (top 5 cm). The results show that when synthetic observations of 5 cm soil moisture are assimilated into a three-layer model of soil hydrology, the ensemble Kalman filter does not use all of the information available in observations.
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    The impact of vertical measurement depth on the information content of soil moisture times series data
    (2014-07-25) Qiu, Jianxiu; Crow, Wade T.; Nearing, Grey S.; Xingguo, Mo; Liu, Suxia; University of Alabama Tuscaloosa
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    Nonparametric triple collocation
    (American Geophysical Union, 2017-07-07) Nearing, Grey S.; Yatheendradas, Soni; Crow, Wade T.; Bosch, David D.; Cosh, Michael H.; Goodrich, David C.; Seyfried, Mark S.; Starks, Patrick J.; National Aeronautics & Space Administration (NASA); NASA Goddard Space Flight Center; National Center Atmospheric Research (NCAR) - USA; University System of Maryland; University of Maryland College Park; United States Department of Agriculture (USDA); University of Alabama Tuscaloosa
    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 non-linear 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.