Search Results

You are looking at 1 - 10 of 42 items for

  • Author or Editor: Joseph Tribbia x
  • All content x
Clear All Modify Search
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
Roger Temam and Joseph Tribbia

Abstract

It was shown by Oliger and Sundström, in 1978, that the initial boundary value problems for the hydrostatic primitive equations of meteorology and oceanography are ill posed if the boundaries are open and fixed in space. In this article it is shown, with theory and computation, that the same problems are well posed for a suitable set of local (pointwise applied) boundary conditions, if a mild vertical viscosity is added to the hydrostatic equation. Some indications on the behavior of the solutions, as the vertical viscosity parameter goes to zero, are also given. The Boussinesq equations are shown to be well posed in the same context of boundaries open and fixed in space. Finally, numerical simulations supporting the analysis are included.

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
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
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
Nedjeljka Žagar, Roberto Buizza, and Joseph Tribbia

Abstract

A new methodology for the analysis of ensemble prediction systems (ENSs) is presented and applied to 1 month (December 2014) of ECMWF operational ensemble forecasts. The method relies on the decomposition of the global three-dimensional wind and geopotential fields onto the normal-mode functions. The ensemble properties are quantified in terms of the 50-member ensemble spread associated with the balanced and inertio-gravity (IG) modes for forecast ranges every 12 h up to 7 days. Ensemble reliability is defined for the balanced and IG modes comparing the ensemble spread with the control analysis in each scale.

Modal analysis shows that initial uncertainties in the ECMWF ENS are largest in the tropical large-scale modes and their spatial distribution is similar to the distribution of the short-range forecast errors. Initially the ensemble spread grows most in the smallest scales and in the synoptic range of the IG modes but the overall growth is dominated by the increase of spread in balanced modes in synoptic and planetary scales in the midlatitudes. During the forecasts, the distribution of spread in the balanced and IG modes grows toward the climatological spread distribution characteristic of the analyses. In the 2-day forecast range, the global IG spread reaches 60% of its asymptotic value while the same percentage of the global balanced spread is reached after 5 days of forecasts. An underdispersiveness of the system is suggested to be associated with the lack of tropical variability, primarily the Kelvin waves.

Full access
Gregory S. Duane and Joseph J. Tribbia

Abstract

The relationship between blocking events in the Atlantic and Pacific sectors of the Northern Hemisphere midlatitudes is investigated in a Vautard–Legras two-layer quasigeostrophic channel model with two sectors, each sector forced by a separate baroclinic jet. It is found that the exchange of medium-scale eddies tends to cause anticorrelation between blocking events in the two sectors, while the large-scale flow components tend to cause positive correlation. The net correlation in blocking is more positive when the jets are skewed latitudinally, a result that is confirmed in the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis data and separately in a long run of a global circulation model (GCM).

The anticorrelating effect of the eddy exchange follows from the tendency of two distinct, coextensive, chaotically vacillating channel flows to synchronize when their corresponding medium-scale eddy components are coupled (a physically unrealizable configuration), regardless of differences in initial conditions. In the Vautard–Legras model, blocking in one sector weakly inhibits blocking in the opposite sector. Generalized synchronization between two channels with forcing in different sectors implies that the two inhibition effects combine coherently, giving anticorrelation in blocking activity. The anticorrelation effect is small because of the physical distance between the sectors and the resulting long advective time scales. That the smallest-scale eddies need not be coupled to affect synchronization would follow from the existence of an inertial manifold that slaves the smallest scales to the larger scales in each channel. The paradigm of low-order chaos synchronization may be relevant to climate dynamics in a variety of situations where such inertial manifolds exist.

Full access
Jun-Ichi Yano and Joseph J. Tribbia

Abstract

The Madden–Julian oscillation (MJO), a planetary-scale eastward-propagating coherent structure with periods of 30–60 days, is a prominent manifestation of intraseasonal variability in the tropical atmosphere. It is widely presumed that small-scale moist cumulus convection is a critical part of its dynamics. However, the recent results from high-resolution modeling as well as data analysis suggest that the MJO may be understood by dry dynamics to a leading-order approximation. Simple, further theoretical considerations presented herein suggest that if it is to be understood by dry dynamics, the MJO is most likely a strongly nonlinear solitary Rossby wave. Under a global quasigeostrophic equivalent-barotropic formulation, modon theory provides such analytic solutions. Stability and the longevity of the modon solutions are investigated with a global shallow-water model. The preferred modon solutions with the greatest longevities compare well overall with the observed MJO in scale and phase velocity within the factors.

Open access
Joseph J. Tribbia and David P. Baumhefner

Abstract

This paper presents the results of an ensemble of 20 predictability experiments derived from the NCAR Community Climate Model (CCM). Particular emphasis is placed on the question of the predictability of dynamically driven low-frequency components of the model atmosphere. The conclusion drawn, using time averaging alone as a means of isolating low-frequency variability, is that in the ensemble mean there is little skill in a 30-day mean forecast. Examination of the variability of skill among the ensemble members indicates that approximately 40 percent of the perturbed monthly mean forecasts would be useful. Examples of skillful and poor monthly mean predictions am shown and conclusions are drawn as to the implications of the results with regard to the likelihood of success of extended range deterministic forecasts.

Full access