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  • Author or Editor: Istvan Szunyogh x
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Nedjeljka Žagar
and
Istvan Szunyogh
Open access
Young-noh Yoon
,
Edward Ott
, and
Istvan Szunyogh

Abstract

Several localized versions of the ensemble Kalman filter have been proposed. Although tests applying such schemes have proven them to be extremely promising, a full basic understanding of the rationale and limitations of localization is currently lacking. It is one of the goals of this paper to contribute toward addressing this issue. The second goal is to elucidate the role played by chaotic wave dynamics in the propagation of information and the resulting impact on forecasts. To accomplish these goals, the principal tool used here will be analysis and interpretation of numerical experiments on a toy atmospheric model introduced by Lorenz in 2005. Propagation of the wave packets of this model is shown. It is found that, when an ensemble Kalman filter scheme is employed, the spatial correlation function obtained at each forecast cycle by averaging over the background ensemble members is short ranged, and this is in strong contrast to the much longer range correlation function obtained by averaging over states from free evolution of the model. Propagation of the effects of observations made in one region on forecasts in other regions is studied. The error covariance matrices from the analyses with localization and without localization are compared. From this study, major characteristics of the localization process and information propagation are extracted and summarized.

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Michael Oczkowski
,
Istvan Szunyogh
, and
D. J. Patil

Abstract

The complexity of atmospheric instabilities is investigated by a combination of numerical experiments and diagnostic tools that do not require the assumption of linear error dynamics. These tools include the well-established analysis of the local energetics of the atmospheric flow and the recently introduced ensemble dimension (E dimension). The E dimension is a local measure that varies in both space and time and quantifies the distribution of the variance between phase space directions for an ensemble of nonlinear model solutions over a geographically localized region. The E dimension is maximal, that is, equal to the number of ensemble members (k), when the variance is equally distributed between k phase space directions. The more unevenly distributed the variance, the lower the E dimension.

Numerical experiments with the state-of-the-art operational Global Forecast System (GFS) of the National Centers for Environmental Prediction (NCEP) at a reduced resolution are carried out to investigate the spatiotemporal evolution of the E dimension. This evolution is characterized by an initial transient phase in which coherent regions of low dimensionality develop through a rapid local decay of the E dimension. The typical duration of the transient is between 12 and 48 h depending on the flow; after the initial transient, the E dimension gradually increases with time.

The main goal of this study is to identify processes that contribute to transient local low-dimensional behavior. Case studies are presented to show that local baroclinic and barotropic instabilities, downstream development of upper-tropospheric wave packets, phase shifts of finite amplitude waves, anticyclonic wave breaking, and some combinations of these processes can all play crucial roles in lowering the E dimension.

The practical implication of the results is that a wide range of synoptic-scale weather events may exist whose prediction can be significantly improved in the short and early medium range by enhancing the prediction of only a few local phase space directions. This potential is demonstrated by a reexamination of the targeted weather observations missions from the 2000 Winter Storm Reconnaissance (WSR00) program.

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Michael J. Kavulich Jr.
,
Istvan Szunyogh
,
Gyorgyi Gyarmati
, and
R. John Wilson

Abstract

The paper investigates the processes that drive the spatiotemporal evolution of baroclinic transient waves in the Martian atmosphere by a simulation experiment with the Geophysical Fluid Dynamics Laboratory (GFDL) Mars general circulation model (GCM). The main diagnostic tool of the study is the (local) eddy kinetic energy equation. Results are shown for a prewinter season of the Northern Hemisphere, in which a deep baroclinic wave of zonal wavenumber 2 circles the planet at an eastward phase speed of about 70° Sol−1 (Sol is a Martian day). The regular structure of the wave gives the impression that the classical models of baroclinic instability, which describe the underlying process by a temporally unstable global wave (e.g., Eady model and Charney model), may have a direct relevance for the description of the Martian baroclinic waves. The results of the diagnostic calculations show, however, that while the Martian waves remain zonally global features at all times, there are large spatiotemporal changes in their amplitude. The most intense episodes of baroclinic energy conversion, which take place in the two great plain regions (Acidalia Planitia and Utopia Planitia), are strongly localized in both space and time. In addition, similar to the situation for terrestrial baroclinic waves, geopotential flux convergence plays an important role in the dynamics of the downstream-propagating unstable waves.

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David Kuhl
,
Istvan Szunyogh
,
Eric J. Kostelich
,
Gyorgyi Gyarmati
,
D. J. Patil
,
Michael Oczkowski
,
Brian R. Hunt
,
Eugenia Kalnay
,
Edward Ott
, and
James A. Yorke

Abstract

In this paper, the spatiotemporally changing nature of predictability is studied in a reduced-resolution version of the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS), a state-of-the-art numerical weather prediction model. Atmospheric predictability is assessed in the perfect model scenario for which forecast uncertainties are entirely due to uncertainties in the estimates of the initial states. Uncertain initial conditions (analyses) are obtained by assimilating simulated noisy vertical soundings of the “true” atmospheric states with the local ensemble Kalman filter (LEKF) data assimilation scheme. This data assimilation scheme provides an ensemble of initial conditions. The ensemble mean defines the initial condition of 5-day deterministic model forecasts, while the time-evolved members of the ensemble provide an estimate of the evolving forecast uncertainties. The observations are randomly distributed in space to ensure that the geographical distribution of the analysis and forecast errors reflect predictability limits due to the model dynamics and are not affected by inhomogeneities of the observational coverage.

Analysis and forecast error statistics are calculated for the deterministic forecasts. It is found that short-term forecast errors tend to grow exponentially in the extratropics and linearly in the Tropics. The behavior of the ensemble is explained by using the ensemble dimension (E dimension), a spatiotemporally evolving measure of the evenness of the distribution of the variance between the principal components of the ensemble-based forecast error covariance matrix.

It is shown that in the extratropics the largest forecast errors occur for the smallest E dimensions. Since a low value of the E dimension guarantees that the ensemble can capture a large portion of the forecast error, the larger the forecast error the more certain that the ensemble can fully capture the forecast error. In particular, in regions of low E dimension, ensemble averaging is an efficient error filter and the ensemble spread provides an accurate prediction of the upper bound of the error in the ensemble-mean forecast.

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