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J. J. Stephens

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J. J. Stephens

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J. J. Stephens

Abstract

Diagnostic relations are derived whose satisfaction yields a unique adjustment of observational data such that the balance equation is satisfied. In this formulation both the observed geopotential and velocity fields are incorporated, each according to its relative accuracy. Natural boundary conditions which arise in the variational formulation are discussed along with the conservation properties of the method.

Numerical experiments with analytic fields and additive noise are used to verify the formulation for three error models. Reductions in the error variance of the order of one-half are found for both random and persistent errors, including systematic departures from a balanced condition.

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J. J. STEPHENS

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Probability density distributions are derived and verified for the distance from an arbitrary point to stations randomly distributed in the plane. These distributions are essential to the analysis of the filtering properties of objective analysis schemes.

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J. J. STEPHENS

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A variational formulation minimizing the square of velocity differences is used to determine boundary conditions for determination of velocity potential and stream function for the horizontal wind. The boundary velocity is conserved locally, as are the areal total velocity, divergence, and vorticity fields.

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J. J. Stephens

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A two-dimensional extension of the Sampling Theorem with the inclusion of derivative samples is presented. It is shown that simultaneous sampling of geopotential and horizontal wind components on a mesh with elements Δx, Δy permits definition of waves of length Δx, and Δy along mesh lines under the geostrophic assumption. Additional independent estimates of either of the horizontal shear elements, ∂u/∂y or ∂v/∂y, permits the exact reconstruction of band-limited fields whose spectral decomposition includes waves of length Δx and Δy, or longer.

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J. J. STEPHENS

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The filtering response of the Cressman weight functions and a truncated low-pass filter are presented as functions of influence radius.

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J. J. Stephens

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Radar cross-sections for water and ice spheres, evaluated by using the complete Mie theory and the method of Aden, are presented for wavelengths ranging from 0.43 to 16.23 cm. The validity of the Rayleigh approximation is shown as a function of drop diameter, and the temperature dependence is shown for a wavelength of 3.2 cm. Oscillations of the normalized cross-section for water are explained in terms of multipole resonance effects.

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J. J. Stephens

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No Abstract Available.

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J. J. Stephens

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