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A theoretical examination of the construction and characterization of super-observations obtained by optimality principles guided by information theory
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    This note characterizes the optimal construction of (possibly) multi-component super-observation (or 'super-obs') based upon the criterion of minimizing the information lost in the super-obbing process. It is asserted that, by an artificial intervention that adjusts the weights given to the super-ob, it is possible to 'structurally precondition' the assimilation problem to speed up the convergence of a Krylov-based iterative minimization (such as the conjugate gradient method, for example) without significantly changing the convergent limit of the process. By an examination of this optimal formulation in the context of a compact cluster of point data it is shown that, to the leading approximation in an asymptotic scaling parameter describing the cluster's size, the optimal multi-component super-ob is essentially identical to the multipole characterization of generalized super-obs suggested (on an intuitive basis) in an earlier note by Purser, Parrish and Masutani. [doi:10.7289/V5736NVN (http://dx.doi.org/10.7289/V5736NVN)]
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