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Richard Franke

Abstract

The sensitivity of multivariate optimum interpolation to variations in values of its parameters is investigated, including missing observation values. The influence of observation error misspecification and parameters in the spatial correlation function are also considered. The calculations are carried out on three different observation patterns: fairly uniform, partly uniform–partly sparse, and sparse. The decay rate of the correlation function is an important parameter to estimate properly, and estimates of height and wind errors should be consistent.

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Richard Franke

Abstract

An iterative (successive correction) method for objective analysis due to Bratseth is considered. The method converges to the statistical interpolation result in the limit. The properties of the scheme and a variant of it are discussed, and the results of some simulations on it which where performed earlier for other methods, are given and compared.

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Richard Franke

Abstract

The errors in objective analysis methods that are based on corrections to first-guess fields are considered. An expression that gives a decomposition of an error into three independent components is derived. To test the magnitudes of the contributions of each component, a series of computer simulations was conducted. The grid-to-observation-point interpolation schemes considered ranged from simple piecewise linear functions to highly accurate spline functions. The observation-to-grid interpolation methods considered included most of those in present meteorological use, such as optimum interpolation and successive corrections, as well as proposed schemes such as thin plate splines, and several variations of these schemes. The results include an analysis of cost versus skill; this information is summarized in plots for most combinations. The degradation in performance due to inexact parameter specification in statistical observation-to-grid interpolation schemes is addressed. The efficacy of the mean-squared error estimates in this situation is also explored.

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Richard Franke

Abstract

Height innovation data for a 2-month period from NOGAPS was analyzed to obtain height prediction and observation error covariances. Different methods of weighting the data in least squares approximations of the spatial covariance data were investigated using the second-order autoregressive (SOAR) correlation function, both with and without an additive constant (varying with pressure level). Based on the properties of the derived covariance matrices and the SOAR parameters, the SOAR without an additive constant was used for the horizontal approximations. The vertical correlations were fit using a combination of SOAR plus an additive constant and a transformation of the logP coordinate to another coordinate to achieve a best fit. The resulting three-dimensional approximation is partially separable, being the product of the horizontal covariance function (which depends on height) and the vertical correlation function. Figures demonstrating various aspects of the process and the results are given.

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Richard Franke and Edward Barker

Abstract

This article gives the details and results of an investigation into the properties of the temperature and relative humidity errors from the Navy Operational Global Atmospheric Prediction System for a 4-month period from March to June 1998. The spatial covariance data for temperature errors and for relative humidity errors were fit using eight different approximation functions/weighting methods. From these, two were chosen as giving good estimates of the parameters and variances of the prediction and observation errors and were used in further investigations. The vertical correlation between temperature errors at different levels and relative humidity errors at different levels was approximated using a combination of functional fitting and transformation of the pressure levels. The cross covariance between temperature and relative humidity errors at various pressure levels were approximated in two ways: 1) by directly computing and approximating the cross-covariance data, and 2) by approximating variance of the difference of normalized data. The latter led to more consistent results. Figures illustrating the results are included.

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