| The effects of spherical distance approximations upon OI forecast error correlations - :11512 | National Weather Service (NWS)
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The effects of spherical distance approximations upon OI forecast error correlations
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  • Description:
    The accuracy of forecast error correlation functions prescribed in an optimal interpolation (OI) analysis system determines, to a large extent, the analysis accuracy. The height-height forecast error correlation function used in the OI system at NMC is a Gaussian function of approximate spherical distance. One approximation is used equatorward of 70° latitude and another is used poleward of 700. Since the wind-height and wind-wind correlation functions are derived from the height-height correlation via a geostrophic assumption, they depend on first and second derivatives of the approximate spherical distance. Derivatives of an approximation are generally less accurate than the approximation itself. We show that at 70° latitude the wind-wind cross-correlation function used operationally equatorward of 70° latitude has roughly twice the amplitude of the same correlation function based on the exact spherical distance. At lower latitudes, the correlations based on exact and approximate spherical distances are more comparable. We have not compared the approximate formulation used operationally poleward of 70° with the exact spherical distance formulation. The approximate distance formulations have been used operationally for the sake of computational efficiency. We introduce a different approximation to the spherical distance which results in more computational work than the operational formulation, but less work than an exact spherical distance formulation. We prove rigorously that all the correlations based on the new approximation differ from those based on the exact spherical distance by a negligible amount. The new approximate formulation is accurate at all latitudes, and therefore dispenses with the need for separate computations in low and high latitudes.

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