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Improving Remote Sensed Data Products Using Bayesian Methodology for the Analysis of Computer Model Output (contd)
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| The NASA Science Directorate supports an array of Earth Observing satellites which provide global coverage, whose observations are
used to produce a wide array of data products, from sea surface temperature, to polar ice coverage, to plant type and growth rates.
These 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 (eg
Leaf Area Index (LAI), Photosynthetically Active Radiation (fPAR) from MODIS) 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 application domains. These methods are well developed in the statistics literature, but are almost
unknown in the Geoscience/Remote Sensing domain (apart from Kriging). Applied to an RTM, these methods will allow the
determination of: a) the uncertainty in the RTM output; b) the main effects, ie, 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 and fPAR is the MOD15 algorithm. We will initially 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 -- treated as a "black boxes" by the methodology. We will use a number of Bayesian
nonparametric methods to approximate the LCM, including Gaussian Processes, and Dirichlet Process Mixtures, to study the
robustness of the analysis to different models. The models will be built using runs of the LCM. First we will perform a sensitivity
analysis to determine which inputs have most effect on the variability of the output, and so determine where more information is
required about the distributions of the inputs. We will use the approximate model to enable practical inversion of the LCM, to
determine the distribution over LAI given measured reflectances. We will incorporate field data, and build a model of the bias between
the LCM and the field data. This will result in a fully calibrated inversion procedure. 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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