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Browsing by Author "Gupta, Hoshin V."

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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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    Debates—The future of hydrological sciences: A (common) path forward? Using models and data to learn: A systems theoretic perspective on the future of hydrological science
    (2014-06-02) Gupta, Hoshin V.; Nearing, Grey S.; University of Alabama Tuscaloosa
    Key Points: Discovery can be advanced by taking a perspective based in Information Theory. Much can be gained by focusing on the a priori role of Process Modeling. System Parameterization can result in information loss.
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    Ensembles vs. information theory: supporting science under uncertainty
    (Springer, 2018) Nearing, Grey S.; Gupta, Hoshin V.; University of Alabama Tuscaloosa; University of Arizona
    Multi-model ensembles are one of the most common ways to deal with epistemic uncertainty in hydrology. This is a problem because there is no known way to sample models such that the resulting ensemble admits a measure that has any systematic (i.e., asymptotic, bounded, or consistent) relationship with uncertainty. Multi-model ensembles are effectively sensitivity analyses and cannot - even partially - quantify uncertainty. One consequence of this is that multi-model approaches cannot support a consistent scientific method - in particular, multi-model approaches yield unbounded errors in inference. In contrast, information theory supports a coherent hypothesis test that is robust to (i.e., bounded under) arbitrary epistemic uncertainty. This paper may be understood as advocating a procedure for hypothesis testing that does not require quantifying uncertainty, but is coherent and reliable (i.e., bounded) in the presence of arbitrary (unknown and unknowable) uncertainty. We conclude by offering some suggestions about how this proposed philosophy of science suggests new ways to conceptualize and construct simulation models of complex, dynamical systems.
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    Estimating information entropy for hydrological data: One-dimensional case
    (American Geophysical Union, 2014-06-19) Gong, Wei; Yang, Dawen; Gupta, Hoshin V.; Nearing, Grey; Beijing Normal University; Tsinghua University; University of Arizona; National Aeronautics & Space Administration (NASA); NASA Goddard Space Flight Center; Science Applications International Corporation (SAIC); University of Alabama Tuscaloosa
    There has been a recent resurgence of interest in the application of Information Theory to problems of system identification in the Earth and Environmental Sciences. While the concept of entropy has found increased application, little attention has yet been given to the practical problems of estimating entropy when dealing with the unique characteristics of two commonly used kinds of hydrologic data: rainfall and runoff. In this paper, we discuss four important issues of practical relevance that can bias the computation of entropy if not properly handled. The first (zero effect) arises when precipitation and ephemeral streamflow data must be viewed as arising from a discrete-continuous hybrid distribution due to the occurrence of many zero values (e. g., days with no rain/no runoff). Second, in the widely used bin-counting method for estimation of PDF's, significant error can be introduced if the bin width is not carefully selected. The third (measurement effect) arises due to the fact that continuously varying hydrologic variables can typically only be observed discretely to some degree of precision. The Fourth (skewness effect) arises when the distribution of a variable is significantly skewed. Here we present an approach that can deal with all four of these issues, and test them with artificially generated and real hydrological data. The results indicate that the method is accurate and robust.
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    The quantity and quality of information in hydrologic models
    (American Geophysical Union, 2015-01-26) Nearing, Grey S.; Gupta, Hoshin V.; National Aeronautics & Space Administration (NASA); NASA Goddard Space Flight Center; University of Arizona; University of Alabama Tuscaloosa
    The role of models in science is to facilitate predictions from hypotheses. Although the idea that models provide information is widely reported and has been used as the basis for model evaluation, benchmarking, and updating strategies, this intuition has not been formally developed and current benchmarking strategies remain ad hoc at a fundamental level. Here we interpret what it means to say that a model provides information in the context of the formal inductive philosophy of science. We show how information theory can be used to measure the amount of information supplied by a model, and derive standard model benchmarking and evaluation activities in this context. We further demonstrate that, via a process of induction, dynamical models store information from hypotheses and observations about the systems that they represent, and that this stored information can be directly measured.