see NASA's 4 dimensional Data Assimilation Grand Challenge for more details of Makivic analysis of HPF for this application
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Forecast model and observational data are combined to produce a minimum error representation of the state of the atmosphere
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The goal of the analysis is to find a set of weights for each observation which will determine the contribution of that observation to the correction of model estimate at every grid point
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The formal solution can be expressed as a linear problem defined by the correlation matrix of observational error data
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Given that presently there are 150000 observations per assimilation cycle, one must resort to approximations
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Mini-Volume approximation technique scans for observations in a 1500 km radius arond a cluster of gridpoints. Effectively, a large linear problem is approximated by a large number of small linear problems for each mini-volume
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Before the covariance matrices are constructed observations are processed to eliminate and/or correct erroneous data (gross check and buddy check)
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Solution of mini-volume linear systems is a task parallel computation
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Everything else involves manipulations of large observational data, model data and mini-volume data arrays and can be efficiently expressed using HPF syntax
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