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Improving Remote Sensed Data Products Using Bayesian Methodology for the Analysis of Computer Model Output
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| The NASA Science Directorate supports an array of Earth Observing satellites which provide global coverage, and whose observations are used to produce a wide array of data products, from measurements of sea surface temperature, to polar ice coverage, to plant type and growth rates. These data products are used in a wide variety of further scientific studies, and also as inputs to important policy decisions, especially those concerning the impact of human activity on the biosphere.
Many of the studies of human impact concern changes over time. To accurately characterize changes it is vitally important that the uncertainties in the estimates of the quantities being observed are known, so that the uncertainty in the estimated changes can be accurately determined -- making scientific or policy decisions based on estimates with large, or worse, unknown or poorly determined errors, is poor science and poor policy.
Many of the data products (e.g. Leaf Area Index, Net Primary Production, Photosynthetically Active Radiation from MODIS (Moderate Resolution Imaging Spectroradiometer)) are produced by inverting a Radiative Transfer Model (RTM), which simulates the upwelling radiation at the top of the atmosphere (and so observed by the satellite) as a function of the biospheric parameters (e.g. land cover type; available water; leaf chemistry; etc.). These RTMs are implemented as complex computer codes, and the analysis and inversion of these codes is a challenging task.
In the last several years the area of Bayesian Methods for the Analysis of Computer Model Output has made great progress, and is coming to a point where its wider application will show significant utility in the application domains. These methods are well developed in the statistics literature, but are almost unknown in the Geoscience/Remote Sensing domain (with the exception of Kriging). Applied to an RTM, these methods will allow the determination of: a) the uncertainty in the RTM output; b) the main effects, that is, which of the inputs is mainly responsible for the output uncertainty; c) validation using field data; d) rapid approximation of the RTM for use when computing the inverse; e) a direct model for the inverse incorporating uncertainty. Advances in these areas will improve the accuracy and utility of the data products.
The RTM in operational use for estimating LAI (leaf area index) and fPAR (fraction of photosynthetically active radiation) is the MOD15 algorithm. We propose initially to apply the methodology to the LCM (leaf-canopy model) RTM, a similar model to which we have more direct access. The methods and code developed will be readily applicable to MOD15 and other RTMs -- the RTM is treated as a "black box" by the methodology.
Initially, a Gaussian Process (GP) model will be built using runs of the LCM. Sensitivity analysis using the GP model approximation will be performed to determine where more information is required about the distributions of the input variables. The fast computations available with the GP model will enable practical inversion of the LCM, to determine the distribution over LAI given measured reflectances. Computing the distribution over LAI for each observation using the forward model as described above may not be sufficiently computationally cheap to implement over large areas. We will build a second GP model that directly models the inverse problem, using training data generated from the full inverse. This will model the relationship between satellite observations and the probability distribution over LAI, and will demonstrate a new generic approach to characterizing the uncertainty in inverse problems.
A successful conclusion of the work in this proposal would demonstrate the utility of the methodology in an important application domain, with significant scientific and policymaking consequences, and would significantly advance the state-of-the-practice in remote sensing science. |
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