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NASA NTRS1995

Assimilation of Altimeter Data into a Quasigeostrophic Model of the Gulf Stream System: Dynamical Considerations - Part 1

The dynamical consequences of constraining a numerical model with sea surface height data have been investigated. The model used for this study is a quasigeostrophic model of the Gulf Stream region. The data that have been assimilated are maps of sea surface height obtained as the superposition of sea surface height variability deduced from the Geosat altimeter measurements and a mean field constructed from historical hydrographic data. The method used for assimilating the data is the nudging technique. Nudging has been implemented in such a way as to achieve a high degree of convergence of the surface model fields toward the observations. The assimilation of the surface data is thus equivalent to the prescription of a surface pressure boundary condition. The authors analyzed the mechanisms of the model adjustment and the characteristics of the resultant equilibrium state when the surface data are assimilated. Since the surface data are the superposition of a mean component and an eddy component, in order to understand the relative role of these two components in determining the characteristics of the final equilibrium state, two different experiments have been considered: in the first experiment only the climatological mean field is assimilated, while in the second experiment the total surface streamfunction field (mean plus eddies) has been used. It is shown that the model behavior in the presence of the surface data constraint can be conveniently described in terms of baroclinic Fofonoff modes. The prescribed mean component of the surface data acts as a 'surface topography' in this problem. Its presence determines a distortion of the geostrophic contours in the subsurface layers, thus constraining the mean circulation in those layers. The intensity of the mean flow is determined by the inflow/outflow conditions at the open boundaries, as well as by eddy forcing and dissipation.

Capotondi, Antonietta↗

NASA NTRS1987

An implementation of a barotropic quasigeostrophic model of ocean circulation on the MPP

The implementation on the Massively Parallel Processor (MPP) of a barotropic quasigeostrophic model of ocean circulation is discussed. The mathematical model, including scalings and boundary conditions is discussed. The numerical scheme, which uses compact differencing is also discussed. The implementation of this model on the MPP is then presented. Finally, some performance results are given and compared to results obtained using the VPS-32 and one processor of a CRAY-2.

Grosch, C. E.↗

NASA NTRS1995

Assimilation of Altimeter Data into a Quasigeostrophic Model of the Gulf Stream System: Assimilation Results - Part 2

The improvement in the climatological behavior of a numerical model as a consequence of the assimilation of surface data is investigated. The model used for this study is a quasigeostrophic (QG) model of the Gulf Stream region. The data that have been assimilated are maps of sea surface height that have been obtained as the superposition of sea surface height variability deduced from the Geosat altimeter measurements and a mean field constructed from historical hydrographic data. The method used for assimilating the data is the nudging technique. Nudging has been implemented in such a way as to achieve a high degree of convergence of the surface model fields toward the observations. Comparisons of the assimilation results with available in situ observations show a significant improvement in the degree of realism of the climatological model behavior, with respect to the model in which no data are assimilated. The remaining discrepancies in the model mean circulation seem to be mainly associated with deficiencies in the mean component of the surface data that are assimilated. On the other hand, the possibility of building into the model more realistic eddy characteristics through the assimilation of the surface eddy field proves very successful in driving components of the mean model circulation that are in relatively good agreement with the available observations. Comparisons with current meter time series during a time period partially overlapping the Geosat mission show that the model is able to 'correctly' extrapolate the instantaneous surface eddy signals to depths of approximately 1500 m. The correlation coefficient between current meter and model time series varies from values close to 0.7 in the top 1500 m to values as low as 0.1-0.2 in the deep ocean.

Capotondi, Antonietta↗

NASA NTRS1983

A baroclinic quasigeostrophic open ocean model

A baroclinic quasigeostrophic open ocean model is presented, calibrated by a series of test problems, and demonstrated to be feasible and efficient for application to realistic mid-oceanic mesoscale eddy flow regimes. Two methods of treating the depth dependence of the flow, a finite difference method and a collocation method, are tested and intercompared. Sample Rossby wave calculations with and without advection are performed with constant stratification and two levels of nonlinearity, one weaker than and one typical of real ocean flows. Using exact analytical solutions for comparison, the accuracy and efficiency of the model is tabulated as a function of the computational parameters and stability limits set; typically, errors were controlled between 1 percent and 10 percent RMS after two wave periods. Further Rossby wave tests with realistic stratification and wave parameters chosen to mimic real ocean conditions were performed to determine computational parameters for use with real and simulated data. Finally, a prototype calculation with quasiturbulent simulated data was performed successfully, which demonstrates the practicality of the model for scientific use.

Miller, R. N.↗

NASA NTRS1988

The dynamics of error growth in a quasigeostrophic channel model

The objective of the paper is to determine the extent to which baroclinic instability contributes to the growth of errors in simple, yet realistic models of atmospheric flow. The model used here is a two-level quasi-geostrophic channel model. Results of two predictability experiments are reported. In one experiment, the initial condition perturbation was confined to the highest wavenumbers and had an energy of 1 percent of the climatological energy of the model for these scales. In the other experiment, perturbations were put only in the planetary wave and had the same strength relative to climatology as in the first experiment, leading to much larger absolute errors.

Straus, David M.↗

NASA NTRS1995

Low-frequency variability and wavenumber selection in models with zonally symmetric forcing

The authors consider a two-layer quasigeostrophic model with linear surface drag and forcing that relaxes to a zonal baroclinically unstable equilibrium state consisting of a meridionally confined temperature gradient. It is observed that the most energetic wave in the time-mean climate has near zero frequency and is not driven by upscale nonlinear energy transfers. This wave has a zonal scale near the long-wave cutoff of the equilibrium state, and its energy balance is mainly between baroclinic generation and dissipation. This maintenance mechanism is different from that suggested by beta-plane, two-dimensional, and quasigeostrophic turbulence arguments and may be relevant to the dynamics of zonally asymmetric low-frequency variability in the atmosphere, particularly in the Southern Hemisphere.

Whitaker, Jeffrey S.↗

NASA NTRS1990

Large-scale dynamics and transport in the stratosphere

Stationary planetary waves in the southern stratosphere display a characteristic seasonal cycle. Previous research based on a one-dimensional model suggests that this behavior is mainly determined by seasonally varying transmission properties of the atmosphere with respect to wave propagation. The issue is investigated with the help of a hemispheric, linear, quasigeostrophic model. It reproduces well some of the observed qualitative features and is internally consistent in the sense that its seasonal wave cycle can be explained in terms of varying wave transmission properties of the mean circulation. On the other hand, the model does not yield the observed seasonal cycle. Despite considerable sensitivity to modifications in the basic state wind and dissipation parametrization, the model could not be reasonably fit to reproduce the observed seasonal cycle.

Plumb, R. A.↗

NASA NTRS1984

Simulation and assimilation of satellite altimeter data at the oceanic mesoscale

An improved "objective analysis' technique is used along with an altimeter signal statistical model, an altimeter noise statistical model, an orbital model, and synoptic surface current maps in the POLYMODE-SDE area, to evaluate the performance of various observational strategies in catching the mesoscale variability at mid-latitudes. In particular, simulated repetitive nominal orbits of ERS-1, TOPEX, and SPOT/POSEIDON are examined. Results show the critical importance of existence of a subcycle, scanning in either direction. Moreover, long repeat cycles ( 20 days) and short cross-track distances ( 300 km) seem preferable, since they match mesoscale statistics. Another goal of the study is to prepare and discuss sea-surface height (SSH) assimilation in quasigeostrophic models. Restored SSH maps are shown to meet that purpose, if an efficient extrapolation method or deep in-situ data (floats) are used on the vertical to start and update the model.

Demay, P.↗

NASA NTRS1980

Sudden stratospheric warmings forced by mountains

A global, quasigeostrophic model of planetary wave interaction with the mean zonal flow has been used to simulate sudden stratospheric warmings forced by mean tropospheric zonal winds interacting with orography. Planetary waves m = 1 and 2 are simultaneously computed and interact with each other only through the mean zonal flow. An increase in the jet stream maximum from 36 to 48 m/sec is sufficient to initiate repeated major warmings with an approximate 80 day cycle. These results are in agreement with the observed anticorrelation of the annual variation of the winter monthly averaged jet stream strength and polar night jet strength.

Schoeberl, M. R.↗

NASA NTRS1986

The structure, energetics and evolution of the dominant frequency-dependent three-dimensional atmospheric modes

The three-dimensional structure of the dominant modes of wintertime variability are examined, and the mode structures are determined by an EOF analysis of the coupled vertical mean and shear streamfunction fields for a wide range of time-scale classes. The time mean energy conversions are determined from a two-layer quasigeostrophic model. Lag-cross correlations between the dominant low-frequency modes tend to be small and/or symmetric about zero, the high frequency modes are found to show highly asymmetric sinusoidal cross correlation functions similar to traveling waves, and some intermediate and short-time scale modes exhibit correlations indicating an association with the decaying phases of blocking in the Pacific. It is suggested that the mean flow barotropic (baroclinic) instabilities are an important source of variance for some of the lowest (highest) fluctuations considered.

Schubert, S. D.↗

NASA NTRS1990

Satellite observations of instability in the middle atmosphere

Data from the Limb Infrared Monitor of the Stratosphere (LIMS) have been used to define zonally averaged basic-state temperature and zonal wind fields in the middle atmosphere for several periods during the winter of 1978-79. This basic state has been used to calculate the phase speeds, growth rates, and spatial structures of unstable modes using a linear, quasigeostrophic model. These results have been compared with temperature and ozone variance amplitudes from a spectral analysis of the same LIMS data. The comparison indicates that there is a close match between phase speeds for the most rapidly growing modes predicted by the model and phase speeds for statistically significant temperature and ozone variances. Both calculated and observed modes tend to be limited in latitudinal extent to a few tens of degrees and in vertical extent to about 10 km. These modes also tend to be nondispersive. Examples are given for the Southern Hemisphere near 0.25 mb (60 km) and for low latitudes of the Northern Hemisphere near 15 mb (30 km).

Elson, Lee S.↗

NASA NTRS2001

Hysteresis and Wavenumber Vacillation in Unstable Baroclinic Flows

Hysteresis and wavenumber vacillation are studied numerically in a weakly stratified quasigeostrophic model. In general, the amplitude of the most unstable wave increases, as the flow becomes more unstable. When the wave becomes saturated, the next longer wave will grow at the expanse of the most unstable wave and becomes the dominant wave. However, once the longwave state is established, it may remain in that regime even as the instability is decreased beyond the threshold where it first developed, thus constituting a hysteresis loop. In a highly unstable case, the flow may not show a preference for any single wave. Instead, the dominant wave aperiodically varies among several long waves. This phenomenon is known as wavenumber vacillation. Hysteresis is further examined in terms of eddy heat flux. It is shown that total eddy heat flux increases as the flow becomes more unstable, but displays a sharp drop when transition to a longer wave occurs. However, in a longwave state, the heat flux always decreases with decreasing instability even pass the threshold when wave transition first occurs.

Chou, Shih-Hung↗

NASA NTRS2006

Interaction of Moist Convection with Zonal Jets on Jupiter and Saturn

Observations suggest that moist convection plays an important role in the large-scale dynamics of Jupiter s and Saturn s atmospheres. Here we use a reduced-gravity quasigeostrophic model, with a parameterization of moist convection that is based on observations, to study the interaction between moist convection and zonal jets on Jupiter and Saturn. Stable jets with approximately the same width and strength as observations are generated in the model. The observed zonal jets violate the barotropic stability criterion but the modeled jets do so only if the flow in the deep underlying layer is westward. The model results suggest that a length scale and a velocity scale associated with moist convection control the width and strength of the jets. The length scale and velocity scale offer a possible explanation of why the jets of Saturn are stronger and wider than those of Jupiter.

Li, Liming↗

DOE OSTI2025

Nonlinear Ensemble Filtering with Diffusion Models: Application to the Surface Quasigeostrophic Dynamics

The intersection between classical data assimilation methods and novel machine learning techniques has attracted significant interest in recent years. Here, we explore another promising solution in which diffusion models are used to formulate a robust nonlinear ensemble filter for sequential data assimilation. Unlike standard machine learning methods, the proposed ensemble score filter (EnSF) is completely training free and can efficiently generate a set of analysis ensemble members. Here, in this study, we apply the EnSF to a surface quasigeostrophic model and compare its performance against the popular local ensemble transform Kalman filter (LETKF), which makes Gaussian assumptions in the analysis step. Numerical tests demonstrate that EnSF maintains stable performance in the absence of localization and for a variety of experimental settings. We find that while LETKF maintains optimal performance in the case of linear observations of the entire state and a perfect model, EnSF shows improvements over LETKF when nonlinear observations are assimilated and the system is subject to unexpected model errors. A spectral decomposition of the analysis results in this nonlinear observation regime shows that the largest improvements over LETKF occur at large scales (small wavenumbers), where LETKF lacks sufficient ensemble spread. Overall, this initial application of EnSF to a geophysical model of intermediate complexity motivates further development of the algorithm for more realistic problems.

Artificial intelligence↗

NASA NTRS1980

Maintenance of quasi-stationary waves in a two-level quasi-geostrophic spectral model with topography

A study of the maintenance of the quasistationary waves forced by topography using a truncated two-level quasigeostrophic spectral model in a zonal channel on a beta-plane is presented. The model's motion contains wavenumbers 0, n, and 2n in the zonal direction, where n is the lowest eddy wavenumber and also the wavenumber of the topography. The study covered the two cases defined by n=2 and n=3; the spectral mode was integrated by initially perturbing the stationary solution of the equations governing the spectral coefficients, and a detailed energetics study was made of the quasiequilibrium state to study the maintenance of the quasistationary waves. The energy conversions required for maintaining these waves when n=3 imply that they are generated mainly by baroclinic stability of the forced waves; this type of baroclinic wave tends to become stationary to draw efficiently on the available energy of the forced wave.

Yao, M.-S.↗

NASA NTRS1978

The zonally averaged circulation of the middle atmosphere

The steady-state, zonally averaged circulation of the middle atmosphere (15-125 km) is studied with a quasigeostrophic, numerical model that explicitly includes a self-consistent calculation of solar radiative heating due to O2 and O3 absorption, Newtonian cooling, Rayleigh friction, tropopause boundary conditions based on climatological averages, and the effects of vertically propagating planetary waves. It is found that the direct, radiatively driven pole-to-pole circulation at solstice is sufficient to account for the cold summer mesopause and warm isothermal winter mesosphere with associated zonal jets of realistic magnitude. The climatological heat and momentum fluxes associated with planetary wavenumber 2 have a negligible effect on the mean circulation. With planetary wavenumber 1, no steady-state solution could be obtained due to the formation of easterlies and hence critical layers in the winter mesosphere. The radiative heating associated with secondary peaks in the O3 density at the mesopause could render the polar mesopause region convectively unstable.

Schoeberl, M. R.↗

NASA NTRS1986

Chaotic motion in the Jovian atmosphere

Strong nonlinear interactions among unstable waves and the mean flow occur in a simplified quasigeostrophic spectral model of the upper troposphere of Jupiter. The upper boundary of the layer inhibits vertical motion while at the lower boundary perturbations of the potential temperature are not permitted. On an infinite beta plane the forced flow of alternating zones of prograde and retrograde zonal winds, decreasing with height, are linearly unstable and it is shown that the nonlinear terms stabilize the flow by bounding the growth of the eddies. Explicit viscosity terms are not needed. This does not imply that energy would not cascade to the small scale flow but suggests that the nature of the large scale flow is independent of the viscosity at small scales. Numerical time integration shows the flow to be chaotic but, in some cases, with transient propagating features and meandering zonal flow.

Pirraglia, Joseph↗

NASA NTRS1994

Baroclinic instability in the interiors of the giant planets: A cooling history of Uranus?

We propose a quasigeostrophic, baroclinic model for heat transport within the interior of a stably stratified Jovian planet, based on motion in thin cylindrical annuli. Density decreases from the center outward and is zero at the surface of the planet. In the homogeneous case (no core), we find instability for the poles hotter than the equator, but not for the reverse. If the motion is bounded by an impenetrable core, instability occurs for both cases. Much of the behavior can be explained by analogy to conventional baroclinic instability theory. Motivated by our results, we explore a possible connection between the highly inclined rotation axis of Uranus and its anomalously low surface heat flux. We assume that the planets formed hot. Our conjecture is that heat was efficiently convected outwards by baroclinic instability in Uranus (with the poles hotter than the equator), but not in the other three Jovian planets. The surface temperature was higher for the stably stratified case (Uranus), leading to a higher rate of infrared emission and faster cooling. Therefore, we propose that Uranus lost its internal heat sooner than Neptune because baroclinic motions, permitted by its inclination to the sun, were able to extract its internal heat while the surface was still warm.

Holme, Richard↗