On Some Properties of Correlation Functions Used in Optimum Interpolation Schemes

Julian, Paul; Thiébaux, H. Jean

doi:10.1175/1520-0493(1975)103<0605:ospocf>2.0.co;2

Cited by 74 publications

(29 citation statements)

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“…A histogram of empirical data correlations is found, and curves are fitted using the method of least squares. A variety of correlation functions were examined in Julian and Thiebaux(1975) [17]. These climatological covariance matrices do not take into account any synoptic dependence.…”

Section: Introductionmentioning

confidence: 99%

The Impact of Background Error on Incomplete Observations for 4D-Var Data Assimilation with the FSU GSM

Navon

Daescu

Liu

2005

Lecture Notes in Computer Science

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In the study of 4D Var data assimilation of atmospheric models, an important issue to address is the case of incomplete observations in either space or time dimensions.To assess the impact of incomplete observations on the 4D Var data assimilation, we carried out assimilation experiments with dynamical core the new FSU GSM consisting of a T126L14 global spectral model in a parallel environment using MPI version of its adjoint model. This was done by reducing the number of observations in both the space and time dimensions respectively. The impact of the J b background error covariance term on the problem of incomplete observations in either time or space direction has been investigated Numerical experiments were carried out as follows: first, a twin experiment with observations available at every model grid point (thereafter referred to complete observations) was carried out to ensure that the assimilation system was well constructed, followed by a reduction in the available observations to every 2, 4 or 8 spatial grid points, respectively. Another set of experiments was carried out with data void areas where observations were missing at all ocean grid points locations.Similar experiments reducing the number of time instants where observations are available in the window of assimilation were also done. * Supported by N.S.F. Grant ATM-0201808 1The results obtained show that spatial incomplete observations lead to a slow down in the cost functional minimization. The impact of incomplete observations was even more pronounced for experiments where no observations were available over the southern oceans, in which case the lack of fit between a control run and the aforementioned could not be reduced.In contrast to above results, experiments involving reduction of the number of time instants where observations are available in the assimilation window allowed a successful retrieval of the initial data.To further investigate the issue of incomplete observations, we carried out another set of experiments by including the background term J b to the cost function. The background error covariance matrix was found to control the way in which information is spread from the observations and to provide statistically consistent increments at neighboring grid points.Impact of various scenarios of incomplete observations on ensuing forecasts, and root mean square error were investigated for 24-72h model forecasts for cases when the cost functional with included and/or excluded the background covariance term.

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Section: Introductionmentioning

confidence: 99%

The Impact of Background Error on Incomplete Observations for 4D-Var Data Assimilation with the FSU GSM

Navon

Daescu

Liu

2005

Lecture Notes in Computer Science

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“…The dependency of the correlation field on orientation as well as on distance is clearly shown. Following Julian and Thiebaux (1975) we defined the correlation functions along the zonal axis (*) and the meridional one (*y) to be the best fit to the correlation coefficients for all the stations within a longitudinal or latitudinal band of 150km centered on the reference station. For computational economy, the fitting was performed by using a simple cosine-damped linear expression where x and y are, respectively, the zonal and the meridional distances from the reference station, and a, a', b and b' the regression coefficients to be fitted by non-linear least square methods.…”

Section: Spatial Correlation Of U V Z and Tmentioning

confidence: 99%

“…This is probably one of the principal weak points of the objective analysis schemes in which the assumption of isotropy is made, at least for Z or T (Schlatter et al, 1976;Bergman, 1979;Julian, 1984). For our objective analysis, we still have to devise a more realistic anisotropic two-dimensional modelling of the correlation field (Julian and Thiebaux, 1975), eventually taking into account its seasonal dependency and the existence of the tilt of its axes, as shown by Seaman (1981), who obtained qualitatively similar results to ours, but for the Australian region.…”

Section: Structure Function and Observational Errormentioning

confidence: 99%

“…But the sparseness of the tropical observational network and the lack of reliable objective analysis schemes especially designed for the tropics constitute the main difficulties to study the tropical fields (Julian, 1984). Nowadays , although satellite data, such as the cloud wind vector and the outgoing longwave radiation (OLR), are being used more and more (Liebmann and Hartmann, 1982;Weickman et al, 1985), this sparseness in the observational network is only partially supplemented.…”

Section: Introductionmentioning

confidence: 99%

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An Observational Study of Tropical Large-Scale Fields: Part I: Statistical Analyses of the Wind Components, Geopotential Height and Temperature

Kazadi¹

1986

Journal of the Meteorological Society of Japan

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“…(6) as /iat-, the correlation between the true residual at the grid point/level (which is what we are trying to estimate as closely as possible) and that at the the ^'th observational location. This correlation is assumed to be a function of location only, and it is dependent on the characteristics of the guess field, F, as well as the true field, F. A considerable literature exists on the determination of this correlation (e.g., Thiebaux, 1975Thiebaux, , 1976Julian and Thiebaux, 1975;Hollett, 1975;Bergman, 1977). In currently operational optimum interpolation analysis schemes, simplifying assumptions are made about the nature of the /z correlation, and it is represented by an analytic function of the distance separating the two locations involved.…”

Section: =1mentioning

confidence: 99%

Role of Observational Errors in Optimum Interpolation Analysis

Bergman

1978

Bulletin of the American Meteorological Society

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The theory of optimum interpolation analysis is presented, with emphasis on the role that observational errors have in the analysis scheme. It is shown that an estimate of the rootmean-square observational error is required and also that the correlations between errors of observations, if nonzero, must be specified. Methods of determining these quantities from observational data statistics are discussed and examples shown. Finally, error-checking routines that either accept or reject data are described. It is pointed out that care should be exercised when checking for errors so that good and useful data are not inadvertently rejected.

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On Some Properties of Correlation Functions Used in Optimum Interpolation Schemes

Cited by 74 publications

References 0 publications

The Impact of Background Error on Incomplete Observations for 4D-Var Data Assimilation with the FSU GSM

The Impact of Background Error on Incomplete Observations for 4D-Var Data Assimilation with the FSU GSM

An Observational Study of Tropical Large-Scale Fields: Part I: Statistical Analyses of the Wind Components, Geopotential Height and Temperature

Role of Observational Errors in Optimum Interpolation Analysis

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