Search Results

You are looking at 1 - 10 of 45 items for

  • Author or Editor: J. J. Tribbia x
  • All content x
Clear All Modify Search
F. Baer and J. J. Tribbia

Abstract

The impact of gravity modes in atmospheric model predictions is assessed quantitatively by comparing integrations with a normal mode initialized primitive equation model and its corresponding pseudogeostrophic form to document some generally accepted presumptions. Analysis with a linear system yields horizontally scale-dependent differences in the Rossby frequencies derived from the two conditions (initialized and geostrophic) as well as differences in the initial divergence required. Nonlinear calculations indicate that initializing gravity modes in the primitive system does not affect the forecast of the Rossby modes. However, integration with the initialized primitive equation model shows differences in both the Rossby and gravity modes after five days when compared to the corresponding pseudogeostrophic model results, differences which depend both on horizontal scale and vertical mode. Comparison results become more similar if the geostrophic model is converted to balanced form. As the integration time is extended, the modal amplitudes predicted by the initialized primitive equation and geostrophic model rapidly become different. Yet the statistics of energy in the shorter scales for both these experiments during days 20–30 of the integrations are remarkably similar. Inclusion of forcing in the model showed changes in details of the response but not its fundamental character.

Full access
F. Baer and J. J. Tribbia

Abstract

A procedure is outlined which adjusts the initial conditions for any prediction model of a planetary fluid such that no motions of the fluid will evolve with high-frequency, gravity-type time scales despite the model's nonlinearity. Any model which can be characterized by a reasonably small Rossby number may be balanced by the method. The technique requires the determination of the normal modes of the linear part of the equations to be integrated—finite difference or spectral—and proceeds by an expansion technique to build up higher order, nonlinear adjustments to the initial state.

Full access
A. Navarra and J. Tribbia
Full access
Joseph J. Tribbia

Abstract

The variational problem of initial data specification from observations with the strong constraint of the elimination of transient gravity waves through nonlinear normal mode balancing is reconsidered. The exact formulation of this problem is contrasted to the approximate formulation previously given by Daley.

Through the judicious use of model normal modes, an alternative algorithm is developed which allows the use of confidence weights which reflect the fidelity of observations in a more realistic manner than previously possible. In particular, longitudinally varying confidence weights can be utilized. Examples of the use of this technique using the Machenhauer and the second-order Baer-Tribbia initialization are given. An attempt to ascertain the validity of Daley's method demonstrates the accuracy of this approximation and justifies its continued use.

Full access
Joseph J. Tribbia

Abstract

An algorithm for obtaining high-order mode initialization of the type first proposed by Baer and Tribbia is developed which is free from the major difficulty of previous methods—the necessity of calculating Frechet derivatives of the nonlinear terms. This new method is shown to be a logical extension of the technique proposed by Machenhauer; thus the asymptotic equivalence of the Machenhauer and Baer-Tribbia initialization methods is accomplished. A comparison between the new algorithm and the older method of calculating second-order initialization demonstrates the accuracy and ease of implementation of the new technique.

Full access
Joseph J. Tribbia

Abstract

The efficacy of the nonlinear initialization technique for use on global-scale numerical models is tested using a normal-mode, spectral model of the shallow-water equations on an equatorial beta-plane. Despite the nonexistence of strong, frequency separation for the ultralong, equatorially trapped modes, test integrations show that the nonlinear initialization scheme acts to smooth the most rapid oscillations in the system. Further integrations involving only spectral components associated with low-frequency, rotational modes show that the rotational mode trajectories are nearly unaffected by the presence of the balanced gravitational modes. The likely distortion of the divergence field obtained from a rotational-mode-only calculation makes this filtering-through-truncation technique appear unattractive, so an alternative scheme which uses both the truncation and nonlinear initialization schemes is proposed.

Full access
Joseph J. Tribbia

Abstract

Using a low-order, spectral, shallow-water model on an f-plane, the conditions under which height-constrained nonlinear normal mode initialization fails and the existence of realizable balancing wind fields are examined. The relationship of this nonrealizability condition and the ellipticity condition for the standard nonlinear balance equation is also examined. A conclusion from this analysis is that non-elliptic geopotential regions must be accompanied by transient gravity wave motion if there is no forcing mechanism.

The low-order results are extended through the use of a global shallow-water model. The relationship between the local f-plane results and the global results is analyzed and a strong correlation between the appearance of non-elliptic geopotential regions and the breakdown of the iteration scheme used in non-linear normal mode balancing is noted.

It is concluded that moderately weak anticyclonic disturbances in equatorial areas may act as regions of energy exchange between rotational and gravitational modes. Also, the climatological existence of these regions implies the necessity forcing to maintain them in the atmosphere and numerical forecast models.

Full access
A. Navarra and J. Tribbia

Abstract

A new method is presented to detect the portion of variability connected between two climatic fields. The method is a realization of the Procrustes problem, and it is a generalization of methods for analysis of variance such as the singular value decomposition (SVD) or canonical correlation analysis (CCA). The Procrustes formulation offers a general framework to link together variance analysis methods, and regression methods, including as special cases SVD and CCA.

Using this approach two fields can be divided into a subspace where variations of one field are connected to variations of the other field, the coupled manifold, and a subspace where variations are independent, the free manifold. The unified approach can be applied to prescribed SST experiments, in which case it recovers consistent results with other methods designed to identify the forced portion of variance, but it can now be extended also to the coupled case or to observations.

Some examples from prescribed SST simulation experiments and observations are discussed.

Full access
Martin Ehrendorfer and Joseph J. Tribbia

Abstract

Optimal perturbations, also referred to as singular vectors (SVs), currently constitute an important guideline for the generation of initial ensembles to be used for ensemble prediction. The optimality of these perturbations refers to their property of maximizing prespecified quadratic measures of error growth, given that tangent-linear error evolution is assumed. The goal of ensemble prediction is the accurate prediction of the uncertainty of forecasts made with dynamical numerical weather prediction models.

In the present paper the theoretical justification for the use of SVs in ensemble prediction systems is investigated. It is shown that, in a tangent-linear framework, SVs—constructed using covariance information valid at the initial time—evolve into the eigenvectors of the forecast error covariance matrix valid for the end of the optimization interval. As such, SVs represent the most efficient means for predicting the forecast error covariance matrix, given a prespecified number of allowable (tangent-linear) model integrations. Such optimal prediction is of particular importance in light of the fact that the forecast error covariance matrix is summarizing important information about the probability density function of the model state at a given future time.

Based on the above result, optimal covariance prediction through appropriately determined SVs is demonstrated here for a three-dimensional Lorenz model, as well as for a barotropic model of intermediate dimensionality, both within a perfect-model framework. In the case of the barotropic model it is found that less than 15% of the SVs suffice to account for more than 95% of the total final error variance. Viewed differently, at least 80% of the final error variance is accounted for by retaining those SVs that are amplifying in terms of an enstrophy norm. In addition, variances and covariances predicted through SVs agree closely with independently obtained Monte Carlo estimates, as long as the tangent-linear approximation is sufficiently accurate.

Further, the problem of approximating the forecast error covariance matrix in the presence of a state-independent model-error representation is briefly considered. The paper is concluded with a summary of the results and a discussion of their possible implications on data assimilation procedures and on the further development of ensemble prediction systems.

Full access
J. J. Tribbia and D. P. Baumhefner

Abstract

The reliability of reductions of forecasting error derived from changes in the quality of the initial data or model formulation is considered using a signal-to-noise analysis. Defining the initial data error as the data error source and the model error as the modelling source, we propose the use of the modeling error as a baseline against which potential reductions in data error may be calibrated. In the reverse sense, the data error can also be used to calibrate the reduction in the modeling error. A simple nonlinear model is used to illustrate examples of the above reliability test. Further applications of this test to actual numerical forecast experiments using analyses from both the augmented FWE database and the operational NMC data base are shown. Forecast comparisons using various suites of physical parameterizations are also presented.

Full access