Search Results

You are looking at 1 - 10 of 12 items for

  • Author or Editor: H. Jean Thiebaux x
  • Refine by Access: All Content x
Clear All Modify Search
H. Jean Thiebaux

Abstract

The Gandin optimal analysis scheme leaves open the problem of determining the covariance matrix on which it depends. The choice of an autocorrelation function for geopotential, from which geostrophically consistent cross-correlations—and thus covariances—for heights and winds may be derived, influences the performance of the analysis. Four related functions are considered for representation of height field autocorrelations. They are compared on the basis of spectral behavior, capacity to conform with geostrophy, and accuracy of analyses employing them. A multivariate objective analysis test, with both regular and irregular configurations of predictor stations, compares performance of analyses based on modeled covariances with performance of an analysis using observed sample covariances.

Full access
H. Jean Thiébaux

Abstract

Space–time filtering has a long and often confusing history in the geosciences. It is called by different names in different areas of geoscience, where numerous applications have been developed. The variety of notations that have emerged adds to this confusion. A unified treatment of spatial–temporal estimation is presented, which highlights its duality and the associated trade-off in the construction of any optimal estimation algorithm.

The duality in optimal estimation comes from the requirement that the representation of the spatial–temporal statistical structure of the increments between the true field and the system-operator model used by the filter be matched with the true ensemble structure of the increment field. The associated trade-off arises from the following dichotomy: the closer the system-operator model corresponds to the true system operator, the less ensemble structure remains in the increment field. Conversely, the simpler the model of the system operator, the more residual statistical structure remains to be represented.

Several examples of estimation of spatial–temporal systems, in practice, are presented to illustrate the power of the duality. The rationale for determining the placement of effort in modeling the system operator vis-à-vis representing residual statistical structure is discussed.

Full access
H. Jean Thiebaux

Abstract

In estimating grid-point states with a multivariate, objective analysis procedure, knowledge of covariances of meteorological parameters observed at several locations is required. It is possible to improve accuracy in evaluation of the covariances if the true state of the observed atmosphere is assessed using the means of adjacent days' observations, at each state in the covariance computations.

Full access
H. Jean Thiebaux

Abstract

A matrix combination of vector-valued information on meteorological parameters is proposed for the incorporation of data from irregularly spaced observing systems, as well as data from forecasts and climatology. This is a generalization of a procedure which is well known in the treatment of scalar quantities. Its development here makes no assumptions of independence, either among the vector components or among data sources. The criterion which defines the matrices of the combination is minimization of the variances of the components of the estimate, and hence maximization of the estimate's stability.

For comparative purposes, in those data-use situations to which Gandin's optimal interpolation method applies, a multivariate extension of Gandin's procedure is made; and a means of comparing its field performance with that of the combination procedure introduced here is suggested.

Full access
H. Jean Thiébaux

Abstract

The possibility of improving point estimates through anisotropic interpolation is investigated. Experiments employing multivariate optimal interpolation compare rms errors for estimates based on an anisotropic geopotential correlation model with those based on three isotropic models and one using station‐specific sample correlations. Heights and winds are estimated conjointly for 87 consecutive days, using winter 500 mb data of a 48‐station North American network. By varying the array of stations in the observation set contributing to the estimates for a fixed location, measures of accuracy gains are established vis‐à‐vis observation network density and configuration.

Earlier work established the simple isotropic correlation model as a significant source of error in regions of low‐density data or irregular station configurations. With the representation of observed correlation behavior provided by a two‐dimensional correlation function modeling the well‐known anisotropy of the height field, it is shown that gains in accuracy may be substantial.

Implications for specification of the shape of optimal influence regions are discussed.

Full access
H. Jean Thiebaux

Abstract

No abstract available.

Full access
H. Jean Thiebaux

Abstract

Covariance models used in the data assimilation step of operational forecasting generally assume isotropy of height field correlations on constant pressure levels. Because of the evidence that this assumption is a significant source of forecast error, especially In regions of low density data, a two-dimensional anisotropic correlation model has been derived. Using a simple autoregressive scheme, cumbersome extension of the modeling problem has been avoided and much of the direction-dependent variability of observed statistics is resolved. Compared to deviations of observed correlation values around the best fitting isotropic model, the residual variance has been reduced by 56&%.

Full access
H. Jean Thiebaux and Ranjit M. Passi

Abstract

Properties of the optimal combination scheme for several vector estimates are developed for correlated estimates having common ensemble mean. Classic optimality properties of a linear combination of estimates from separate sources are established as corollaries of the more general optimization criterion. simultaneous minimization of variance components.

Full access
Paul R. Julian and H. Jean Thiebaux

Abstract

Objective analyses using the so-called method of optimum interpolation incorporates statistical information on the variable(s) by means of the covariance or correlation functions. The concern in this contribution is with some properties of the analytic forms of the correlation functions that are used to model the statistical structure. First, some attention is directed to the question of fitting the various analytic forms (containing adjustable constants) to samples of actual correlations. All but one of the candidate forms were indistinguishable on the basis of the residuals of the statistical fitting procedure. Second, the criterion of positive-definiteness of the correlation function is extended to stipulate that the transform (or spectrum) of the function should possess some features of the spectra of actual variables—the most important one being the spectral decay rate at high wavenumber. Again, all but one of the candidate forms (the same one as above) had transforms that were acceptable. Third, the degree of isotropy of the correlation fields is examined, both for scalar variables (geopotential, temperature) and for the wind field. Finally, the imposition of geostrophy requires some special considerations on the form of the correlation function. For all of these properties a variety of suggested analytic forms are compared and conclusions drawn.

Full access
H. Jean Thiébaux, Herschel L. Mitchell, and Donald W. Shantz

Abstract

A detailed study of hemispheric forecast-error (f.e.) statistics for the operational Canadian large-scale forecast model was made in preparation for reparameterization of the correlation function used in the data assimilation step of the forecast cycle. The choice of an appropriate function type for geopotential height and temperature f.e. lag-correlation representations was a major concern. A number of possible functional representations, both isotropic and anisotropic, were considered, and the goodness-of-fit of the various candidate functions to correlations computed from observed f.e. data were compared. The following special form of the second-order autoregressive function was adopted as the function of choice: (1 + c|s|)e c|s|, where |s| is geographic location separation.

An examination of f.e. correlation structure on a regional basis revealed large differences from region to region. Latitudinal, pressure-level, and seasonal dependencies of the statistical structure of constant pressure-surface height and temperature f.e. were also examined. Temperature f.e. correlations were found to have significantly narrower structure than the corresponding height f.e. correlations. In general, the width of the structure functions for both height and temperature f.e. was found to decrease with increasing latitude and with decreasing pressure. The extrapolated height correlations at zero separation were found to decrease significantly with pressure, indicating that the ratio of height prediction error to height observation error also decreases with pressure. An examination of the seasonal dependence of the f.e. correlation structure at 500 mb indicated that it was relatively small.

Implications for operational forecasting with periodic adjustment of the objective analysis scheme are discussed.

Full access