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- Author or Editor: Andrew P. Ingersoll x

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## Abstract

We examine the evolution of baroclinic vortices in a time-dependent, nonlinear numerical model of a Jovian atmosphere. The model uses a normal-mode expansion in the vertical, using the barotropic and first two baroclinic modes. Results for the stability of baroclinic vortices on an *f* plane in the absence of a mean zonal flow are similar to results of Earth vortex models, although the presence of a fluid interior on the Jovian planets shifts the stability boundaries to smaller length scales. The presence of a barotropic mean zonal flow in the interior stabilizes vortices against instability and significantly modifies the finite amplitude form of baroclinic instabilities. The effect of a zonal flow on a form of barotropic instability produces periodic oscillations in the latitude and longitude of the vortex as observed at the level of the cloud tops. This instability may explain some, but not all, observations of longitudinal oscillations of vortices on the outer planets. Oscillations in aspect ratio and orientation of stable vortices in a zonal shear flow are observed in this baroclinic model, as in simpler twodimensional models. Such oscillations are also observed in the atmospheres of Jupiter and Neptune. The meridional propagation and decay of vortices on a *β* plane is inhibited by the presence of a mean zonal flow. The direction of propagation of a vortex relative to the mean zonal flow depends upon the sign of the meridional potential vorticity gradient; combined with observations of vortex drift rates, this may provide a constraint on model assumption for the flow in the deep interior of the Jovian planets.

## Abstract

We examine the evolution of baroclinic vortices in a time-dependent, nonlinear numerical model of a Jovian atmosphere. The model uses a normal-mode expansion in the vertical, using the barotropic and first two baroclinic modes. Results for the stability of baroclinic vortices on an *f* plane in the absence of a mean zonal flow are similar to results of Earth vortex models, although the presence of a fluid interior on the Jovian planets shifts the stability boundaries to smaller length scales. The presence of a barotropic mean zonal flow in the interior stabilizes vortices against instability and significantly modifies the finite amplitude form of baroclinic instabilities. The effect of a zonal flow on a form of barotropic instability produces periodic oscillations in the latitude and longitude of the vortex as observed at the level of the cloud tops. This instability may explain some, but not all, observations of longitudinal oscillations of vortices on the outer planets. Oscillations in aspect ratio and orientation of stable vortices in a zonal shear flow are observed in this baroclinic model, as in simpler twodimensional models. Such oscillations are also observed in the atmospheres of Jupiter and Neptune. The meridional propagation and decay of vortices on a *β* plane is inhibited by the presence of a mean zonal flow. The direction of propagation of a vortex relative to the mean zonal flow depends upon the sign of the meridional potential vorticity gradient; combined with observations of vortex drift rates, this may provide a constraint on model assumption for the flow in the deep interior of the Jovian planets.

## Abstract

Layer thickness variations in Jupiter's atmosphere are investigated by treating potential vorticity as a conserved tracer. Starting with the horizontal velocity field measured from *Voyager* images, fluid trajectories around the Great Red Spot (GRS) and White Oval BC are calculated. The flow is assumed to be frictionless, adiabatic, hydrostatic, and steady in the reference frame of the vortex. Absolute vorticity is followed along each trajectory; its magnitude is assumed to vary directly as the thickness, which is defined as the mass per unit area between potential temperature surfaces. To the accuracy of the observations. the inferred thickness is a separable function of trajectory and latitude. The latitude dependence has positive curvature near the GRS and BC. The relative variations of thickness with respect to latitude are generally larger than the relative variations of Coriolis parameter with respect to latitude—the beta effect. The data are a useful diagnostic which will help differentiate between models, of Jovian vortices. The present analysis employs a quasi-geostrophic model in which a thin upper weather layer, which contains the vortex, is supported hydrostatically by a much deeper lower layer. In this model, the upper free surface does not contribute to the observed variation of thickness along trajectories. Such variations are due exclusively to bottom topography—flow of the deep lower layer relative to the vortex. The observation are used to infer the form of the deep zonal velocity profile vs. latitude. The magnitude of the profile depends on the unknown static stability. The principal result is the existence of horizontal shear in the deep layer zonal velocity profile, i.e., the lower layer is not in solid body rotation and does not act like a flat solid surface. In this respect the data support the hypothesis of Ingersoll and Cuong concerning motions in the deep layer. However at some latitudes the data violate Ingersoll and Cuong's criterion governing the compactness of the vortices. At these latitudes the topography allows standing Rossby waves (wakes) extending far downstream to the west. Observed wavelike features, the filamentary regions, are possibly formed by this mechanism.

## Abstract

Layer thickness variations in Jupiter's atmosphere are investigated by treating potential vorticity as a conserved tracer. Starting with the horizontal velocity field measured from *Voyager* images, fluid trajectories around the Great Red Spot (GRS) and White Oval BC are calculated. The flow is assumed to be frictionless, adiabatic, hydrostatic, and steady in the reference frame of the vortex. Absolute vorticity is followed along each trajectory; its magnitude is assumed to vary directly as the thickness, which is defined as the mass per unit area between potential temperature surfaces. To the accuracy of the observations. the inferred thickness is a separable function of trajectory and latitude. The latitude dependence has positive curvature near the GRS and BC. The relative variations of thickness with respect to latitude are generally larger than the relative variations of Coriolis parameter with respect to latitude—the beta effect. The data are a useful diagnostic which will help differentiate between models, of Jovian vortices. The present analysis employs a quasi-geostrophic model in which a thin upper weather layer, which contains the vortex, is supported hydrostatically by a much deeper lower layer. In this model, the upper free surface does not contribute to the observed variation of thickness along trajectories. Such variations are due exclusively to bottom topography—flow of the deep lower layer relative to the vortex. The observation are used to infer the form of the deep zonal velocity profile vs. latitude. The magnitude of the profile depends on the unknown static stability. The principal result is the existence of horizontal shear in the deep layer zonal velocity profile, i.e., the lower layer is not in solid body rotation and does not act like a flat solid surface. In this respect the data support the hypothesis of Ingersoll and Cuong concerning motions in the deep layer. However at some latitudes the data violate Ingersoll and Cuong's criterion governing the compactness of the vortices. At these latitudes the topography allows standing Rossby waves (wakes) extending far downstream to the west. Observed wavelike features, the filamentary regions, are possibly formed by this mechanism.

## Abstract

A new formula is derived for calculating the moist adiabatic temperature profile of an atmosphere consisting of ideal gases with multiple condensing species. This expression unifies various formulas published in the literature and can be generalized to account for chemical reactions. Unlike previous methods, it converges to machine precision independent of mesh size. It accounts for any ratio of condensable vapors to dry gas, from zero to infinity, and for variable heat capacities as a function of temperature. Because the derivation is generic, the new formula is not only applicable to planetary atmospheres in the solar system but also to hot Jupiters and brown dwarfs in which a variety of alkali metals, silicates, and exotic materials condense. It is demonstrated that even though the vapors are ideal gases, they interact in their effects on the moist adiabatic lapse rate. Finally, the authors apply the new thermodynamic model to study the effects of downdrafts on the distribution of minor constituents and the thermal profile in the *Galileo* probe hot spot. The authors find that the *Galileo* probe measurements can be interpreted as a strong downdraft that displaces an air parcel from the 1-bar to the 4-bar level (1 bar = 100 000 Pa).

## Abstract

A new formula is derived for calculating the moist adiabatic temperature profile of an atmosphere consisting of ideal gases with multiple condensing species. This expression unifies various formulas published in the literature and can be generalized to account for chemical reactions. Unlike previous methods, it converges to machine precision independent of mesh size. It accounts for any ratio of condensable vapors to dry gas, from zero to infinity, and for variable heat capacities as a function of temperature. Because the derivation is generic, the new formula is not only applicable to planetary atmospheres in the solar system but also to hot Jupiters and brown dwarfs in which a variety of alkali metals, silicates, and exotic materials condense. It is demonstrated that even though the vapors are ideal gases, they interact in their effects on the moist adiabatic lapse rate. Finally, the authors apply the new thermodynamic model to study the effects of downdrafts on the distribution of minor constituents and the thermal profile in the *Galileo* probe hot spot. The authors find that the *Galileo* probe measurements can be interpreted as a strong downdraft that displaces an air parcel from the 1-bar to the 4-bar level (1 bar = 100 000 Pa).

## Abstract

A linearized primitive equation (LPE) model is developed to study thermal tides in the atmosphere of Venus. The LPE model describes diurnal and semidiurnal oscillations of a cyclostrophically balanced atmosphere in which zonal velocity varies with altitude and latitude. The numerical algorithm follows Staniforth and Daley. The solar thermal forcing is increased algebraically in time to separate the forced tidal response from free atmospheric oscillations. Parameters of the basic state and forcing agree with *Pioneer Venus* observations. Results of the model are compared with the solar-fixed component of brightness temperature variations measured by Taylor *et al*. and Elson using data from the *Pioneer Venus* orbiter infrared radiometer (OIR). The comparison is made by convolving the computed model radiances with the weighting functions of the OIR channels. Agreement between LPE model results and OIR observations is excellent. Two interesting features of the OIR data are accounted for, namely, the slow variation of phase with altitude and the dominance of the semidiurnal oscillation over the diurnal oscillation. Success of the LPE model opens the way for calculating tidal transports of heat and momentum and assessing the role of tides in maintaining the Venus super-rotation.

## Abstract

A linearized primitive equation (LPE) model is developed to study thermal tides in the atmosphere of Venus. The LPE model describes diurnal and semidiurnal oscillations of a cyclostrophically balanced atmosphere in which zonal velocity varies with altitude and latitude. The numerical algorithm follows Staniforth and Daley. The solar thermal forcing is increased algebraically in time to separate the forced tidal response from free atmospheric oscillations. Parameters of the basic state and forcing agree with *Pioneer Venus* observations. Results of the model are compared with the solar-fixed component of brightness temperature variations measured by Taylor *et al*. and Elson using data from the *Pioneer Venus* orbiter infrared radiometer (OIR). The comparison is made by convolving the computed model radiances with the weighting functions of the OIR channels. Agreement between LPE model results and OIR observations is excellent. Two interesting features of the OIR data are accounted for, namely, the slow variation of phase with altitude and the dominance of the semidiurnal oscillation over the diurnal oscillation. Success of the LPE model opens the way for calculating tidal transports of heat and momentum and assessing the role of tides in maintaining the Venus super-rotation.

## Abstract

The emission of internal gravity waves from a layer of dry convection embedded within a stable atmosphere with static stability and zonal winds varying in height is calculated. This theory is applied to Venus to investigate whether these waves can help support the westward maximum of angular momentum of Venus's middle atmosphere. The emission mechanism is similar to that suggested for driving the gravity modes of the Sun and relates the amplitude and spectrum of the waves to the amplitude and spectrum of the convection. Waves are damped by several mechanisms: wavebreaking in the stable atmosphere, critical layer absorption, reabsorption by the convection, and wave radiation to space. The authors use plane parallel geometry without rotation and assume sinusoidal wave fluctuations in the horizontal dimensions. The vertical dependence is determined using the WKBJ approximation.

It is found that convectively generated gravity waves do not exert an acceleration where the westward winds are greatest. Instead, they deposit westward momentum in a 1-km thick layer just above the convection. Other waves deposit eastward momentum far above the westward wind maximum where decelerations can exceed 20 m s^{−1} day^{−1}, comparable to deceleration amplitudes in Earth's mesosphere. Although the momentum fluxes by gravity waves are substantial, the vertical profile of acceleration does not match what is required for supporting Venus's atmospheric superrotation.

## Abstract

The emission of internal gravity waves from a layer of dry convection embedded within a stable atmosphere with static stability and zonal winds varying in height is calculated. This theory is applied to Venus to investigate whether these waves can help support the westward maximum of angular momentum of Venus's middle atmosphere. The emission mechanism is similar to that suggested for driving the gravity modes of the Sun and relates the amplitude and spectrum of the waves to the amplitude and spectrum of the convection. Waves are damped by several mechanisms: wavebreaking in the stable atmosphere, critical layer absorption, reabsorption by the convection, and wave radiation to space. The authors use plane parallel geometry without rotation and assume sinusoidal wave fluctuations in the horizontal dimensions. The vertical dependence is determined using the WKBJ approximation.

It is found that convectively generated gravity waves do not exert an acceleration where the westward winds are greatest. Instead, they deposit westward momentum in a 1-km thick layer just above the convection. Other waves deposit eastward momentum far above the westward wind maximum where decelerations can exceed 20 m s^{−1} day^{−1}, comparable to deceleration amplitudes in Earth's mesosphere. Although the momentum fluxes by gravity waves are substantial, the vertical profile of acceleration does not match what is required for supporting Venus's atmospheric superrotation.

## Abstract

Radio scintillations in Pioneer Venus radio Occultation data are simulated assuming that the index of refraction fluctuations in Venus's atmosphere responsible for the scintillations are directly caused by gravity wave fluctuations. The gravity waves are created by a global convection layer between 50- and 55-km attitude in Venus's atmosphere and propagate vertically. The authors compare the simulated scintillations with data from Pioneer Venus.

These gravity waves can explain the spectral shape and amplitude of the radio scintilations. The shape at high frequencies is controlled by wave breaking, which yields a saturated spectrum. The amplitude is subject to parameters such as the intensity of the convection, the angle between the zonal winds and the beam path, and the zonal wind profile at polar latitudes. To match the observed amplitude of the scintillations, the velocity variations of the energy-bearing eddies in the convection must be at least 2 m s^{−1}. This value is consistent with the Venus balloon results of Sagdeev et al. and is in the middle of the range considered by Leroy and Ingersoll in their study of convectively generated gravity waves. The later study, combined with the lower bound on velocity from the present study, then yields lower bounds on the vertical fluxes of momentum and energy in the Venus atmosphere.

## Abstract

Radio scintillations in Pioneer Venus radio Occultation data are simulated assuming that the index of refraction fluctuations in Venus's atmosphere responsible for the scintillations are directly caused by gravity wave fluctuations. The gravity waves are created by a global convection layer between 50- and 55-km attitude in Venus's atmosphere and propagate vertically. The authors compare the simulated scintillations with data from Pioneer Venus.

These gravity waves can explain the spectral shape and amplitude of the radio scintilations. The shape at high frequencies is controlled by wave breaking, which yields a saturated spectrum. The amplitude is subject to parameters such as the intensity of the convection, the angle between the zonal winds and the beam path, and the zonal wind profile at polar latitudes. To match the observed amplitude of the scintillations, the velocity variations of the energy-bearing eddies in the convection must be at least 2 m s^{−1}. This value is consistent with the Venus balloon results of Sagdeev et al. and is in the middle of the range considered by Leroy and Ingersoll in their study of convectively generated gravity waves. The later study, combined with the lower bound on velocity from the present study, then yields lower bounds on the vertical fluxes of momentum and energy in the Venus atmosphere.

## Abstract

Previous observations and simulations suggest that an approximate 3°–5°C warming occurred at intermediate depths in the North Atlantic over several millennia during Heinrich stadial 1 (HS1), which induces warm salty water (WSW) lying beneath surface cold freshwater. This arrangement eventually generates ocean convective available potential energy (OCAPE), the maximum potential energy releasable by adiabatic vertical parcel rearrangements in an ocean column. The authors find that basin-scale OCAPE starts to appear in the North Atlantic (~67.5°–73.5°N) and builds up over decades at the end of HS1 with a magnitude of about 0.05 J kg^{−1}. OCAPE provides a key kinetic energy source for thermobaric cabbeling convection (TCC). Using a high-resolution TCC-resolved regional model, it is found that this decadal-scale accumulation of OCAPE ultimately overshoots its intrinsic threshold and is released abruptly (~1 month) into kinetic energy of TCC, with further intensification from cabbeling. TCC has convective plumes with approximately 0.2–1-km horizontal scales and large vertical displacements (~1 km), which make TCC difficult to be resolved or parameterized by current general circulation models. The simulation herein indicates that these local TCC events are spread quickly throughout the OCAPE-contained basin by internal wave perturbations. Their convective plumes have large vertical velocities (~8–15 cm s^{−1}) and bring the WSW to the surface, causing an approximate 2°C sea surface warming for the whole basin (~700 km) within a month. This exposes a huge heat reservoir to the atmosphere, which helps to explain the abrupt Bølling–Allerød warming.

## Abstract

Previous observations and simulations suggest that an approximate 3°–5°C warming occurred at intermediate depths in the North Atlantic over several millennia during Heinrich stadial 1 (HS1), which induces warm salty water (WSW) lying beneath surface cold freshwater. This arrangement eventually generates ocean convective available potential energy (OCAPE), the maximum potential energy releasable by adiabatic vertical parcel rearrangements in an ocean column. The authors find that basin-scale OCAPE starts to appear in the North Atlantic (~67.5°–73.5°N) and builds up over decades at the end of HS1 with a magnitude of about 0.05 J kg^{−1}. OCAPE provides a key kinetic energy source for thermobaric cabbeling convection (TCC). Using a high-resolution TCC-resolved regional model, it is found that this decadal-scale accumulation of OCAPE ultimately overshoots its intrinsic threshold and is released abruptly (~1 month) into kinetic energy of TCC, with further intensification from cabbeling. TCC has convective plumes with approximately 0.2–1-km horizontal scales and large vertical displacements (~1 km), which make TCC difficult to be resolved or parameterized by current general circulation models. The simulation herein indicates that these local TCC events are spread quickly throughout the OCAPE-contained basin by internal wave perturbations. Their convective plumes have large vertical velocities (~8–15 cm s^{−1}) and bring the WSW to the surface, causing an approximate 2°C sea surface warming for the whole basin (~700 km) within a month. This exposes a huge heat reservoir to the atmosphere, which helps to explain the abrupt Bølling–Allerød warming.

## Abstract

On many planets there is a continuous heat supply to the surface and a continuous emission of infrared radiation to space by the atmosphere. Since the heat source is located at higher pressure than the heat sink, the system is capable of doing mechanical work. Atmospheric convection is a natural heat engine that might operate in this system. Based on the heat engine framework, a simple theory is presented for atmospheric convection that predicts the buoyancy, the vertical velocity, and the fractional area covered by either dry or moist convection in a state of statistical equilibrium. During one cycle of the convective heat engine, heat is taken from the surface layer (the hot source) and a portion of it is rejected to the free troposphere (the cold sink) from where it is radiated to space. The balance is transformed into mechanical work. The mechanical work is expended in the maintenance of the convective motions against mechanical dissipation. Ultimately, the energy dissipated by mechanical friction is transformed into heat. Then, a fraction of the dissipated energy is radiated to space while the remaining portion is recycled by the convecting air parcels. Increases in the fraction of energy dissipated at warmer temperature, at the expense of decreases in the fraction of energy dissipated at colder temperatures, lead to increases in the apparent efficiency of the convective heat engine. The volume integral of the work produced by the convective heat engine gives a measure of the statistical equilibrium amount of convective available potential energy (CAPE) that must be present in the planet's atmosphere so that the convective motions can be maintained against viscous dissipation. This integral is a fundamental global number qualifying the state of the planet in statistical equilibrium conditions. For the earth's present climate, the heat engine framework predicts a CAPE value of the order of 1000 J kg^{−1} for the tropical atmosphere. This value is in agreement with observations. It also follows from our results that the total amount of CAPE present in a convecting atmosphere should increase with increases in the global surface temperature (or the atmosphere's opacity to infrared radiation).

## Abstract

On many planets there is a continuous heat supply to the surface and a continuous emission of infrared radiation to space by the atmosphere. Since the heat source is located at higher pressure than the heat sink, the system is capable of doing mechanical work. Atmospheric convection is a natural heat engine that might operate in this system. Based on the heat engine framework, a simple theory is presented for atmospheric convection that predicts the buoyancy, the vertical velocity, and the fractional area covered by either dry or moist convection in a state of statistical equilibrium. During one cycle of the convective heat engine, heat is taken from the surface layer (the hot source) and a portion of it is rejected to the free troposphere (the cold sink) from where it is radiated to space. The balance is transformed into mechanical work. The mechanical work is expended in the maintenance of the convective motions against mechanical dissipation. Ultimately, the energy dissipated by mechanical friction is transformed into heat. Then, a fraction of the dissipated energy is radiated to space while the remaining portion is recycled by the convecting air parcels. Increases in the fraction of energy dissipated at warmer temperature, at the expense of decreases in the fraction of energy dissipated at colder temperatures, lead to increases in the apparent efficiency of the convective heat engine. The volume integral of the work produced by the convective heat engine gives a measure of the statistical equilibrium amount of convective available potential energy (CAPE) that must be present in the planet's atmosphere so that the convective motions can be maintained against viscous dissipation. This integral is a fundamental global number qualifying the state of the planet in statistical equilibrium conditions. For the earth's present climate, the heat engine framework predicts a CAPE value of the order of 1000 J kg^{−1} for the tropical atmosphere. This value is in agreement with observations. It also follows from our results that the total amount of CAPE present in a convecting atmosphere should increase with increases in the global surface temperature (or the atmosphere's opacity to infrared radiation).

## Abstract

Most current models of Jupiter's Great Red Spot (GRS) are cast in terms of a two-layer model, where a thin upper weather layer, which contains the vortex, overlies a much deeper layer, which is meant to represent the neutrally stratified deep atmosphere. Any motions in the deep layer are assumed to be zonal and steady. This two-layer model is dynamically equivalent to a one-layer model with meridionally varying solid bottom topography, called the reduced-gravity model. Specifying the motions, or lack thereof, in the lower layer of the two-layer model is equivalent to specifying the bottom topography, and hence the far-field potential vorticity, in the reduced-gravity model. Current models of the GRS start by guessing the deep motions and then proceed to study vortices using the implied bottom topography. Here, using the GRS cloud-top velocity data, we derive the bottom topography, up to a constant that depends on the unknown radius of deformation (or equivalently, the product of the reduced gravity and the mean thickness of the upper layer). The bottom topography is inferred from three quantities derived from the velocity data—Bernoulli streamfunction, kinetic energy per unit mass, and absolute vorticity—all of which are functions only of horizontal position in the reference frame of the vortex. Far from the vortex, potential vorticity versus latitude is calculated from the observed cloud-top zonal velocity and the derived bottom topography. The results show that the deep atmosphere is in differential motion and that the far-field potential vorticity gradient changes sign at several latitudes. Numerical shallow water experiments are performed, using both the derived bottom topography and the bottom topographies prescribed by current models. The results of three published studies are reproduced in our numerical experiments. Each of these models is successful in maintaining a long-lived, isolated vortex, but only the present model yields absolute vorticity profiles along streamlines that agree with those observed for the GRS by Dowling and Ingersoll. In all the models, large vortices form by merging with smaller vortices. In the present, observationally based model, and in one other published model, the smaller vortices arise spontaneously because the observed cloud-top zonal velocity profile is unstable. These two models require an additional momentum source to maintain the upper-layer zonal velocity profile. In the other two models, the bottom topography stabilizes the zonal velocity profile. If dissipation is present, the latter two models require an additional source of smaller vortices to maintain the larger one. A crucial unanswered question for the present model, and for Jupiter itself, is how the cloud-top zonal velocity profile is maintained in its present unstable state.

## Abstract

Most current models of Jupiter's Great Red Spot (GRS) are cast in terms of a two-layer model, where a thin upper weather layer, which contains the vortex, overlies a much deeper layer, which is meant to represent the neutrally stratified deep atmosphere. Any motions in the deep layer are assumed to be zonal and steady. This two-layer model is dynamically equivalent to a one-layer model with meridionally varying solid bottom topography, called the reduced-gravity model. Specifying the motions, or lack thereof, in the lower layer of the two-layer model is equivalent to specifying the bottom topography, and hence the far-field potential vorticity, in the reduced-gravity model. Current models of the GRS start by guessing the deep motions and then proceed to study vortices using the implied bottom topography. Here, using the GRS cloud-top velocity data, we derive the bottom topography, up to a constant that depends on the unknown radius of deformation (or equivalently, the product of the reduced gravity and the mean thickness of the upper layer). The bottom topography is inferred from three quantities derived from the velocity data—Bernoulli streamfunction, kinetic energy per unit mass, and absolute vorticity—all of which are functions only of horizontal position in the reference frame of the vortex. Far from the vortex, potential vorticity versus latitude is calculated from the observed cloud-top zonal velocity and the derived bottom topography. The results show that the deep atmosphere is in differential motion and that the far-field potential vorticity gradient changes sign at several latitudes. Numerical shallow water experiments are performed, using both the derived bottom topography and the bottom topographies prescribed by current models. The results of three published studies are reproduced in our numerical experiments. Each of these models is successful in maintaining a long-lived, isolated vortex, but only the present model yields absolute vorticity profiles along streamlines that agree with those observed for the GRS by Dowling and Ingersoll. In all the models, large vortices form by merging with smaller vortices. In the present, observationally based model, and in one other published model, the smaller vortices arise spontaneously because the observed cloud-top zonal velocity profile is unstable. These two models require an additional momentum source to maintain the upper-layer zonal velocity profile. In the other two models, the bottom topography stabilizes the zonal velocity profile. If dissipation is present, the latter two models require an additional source of smaller vortices to maintain the larger one. A crucial unanswered question for the present model, and for Jupiter itself, is how the cloud-top zonal velocity profile is maintained in its present unstable state.

## Abstract

A steady-state scheme for data assimilation in the context of a single, short period (relative to a day), sun-synchronous, polar-orbiting satellite is examined. If the satellite takes observations continuously, the gains, which are the weights for blending observations and predictions together, are steady in time. For a linear system forced by random noise, the optimal steady-state gains (Wiener gains) are equivalent to those of a Kalman filter. Computing the Kalman gains increases the computational cost of the model by a large factor, but computing the Wiener gains does not. The latter are computed by iteration using prior estimates of the gains to assimilate simulated observations of one run of the model, termed “truth,” into another run termed “prediction.” At each stage, the prediction errors form the basis for the next estimate of the gains. Steady state is achieved after three or four iterations. Further simplification is achieved by making the gains depend on longitudinal distance from the observation point, not on absolute longitude. For a single-layer primitive equation model, the scheme works well even if only the mass field is observed but not the velocity field. Although the scheme was developed for *Mars Observer*, it should be applicable to data retrieved from Earth atmosphere satellites, for example, *UARS*.

## Abstract

A steady-state scheme for data assimilation in the context of a single, short period (relative to a day), sun-synchronous, polar-orbiting satellite is examined. If the satellite takes observations continuously, the gains, which are the weights for blending observations and predictions together, are steady in time. For a linear system forced by random noise, the optimal steady-state gains (Wiener gains) are equivalent to those of a Kalman filter. Computing the Kalman gains increases the computational cost of the model by a large factor, but computing the Wiener gains does not. The latter are computed by iteration using prior estimates of the gains to assimilate simulated observations of one run of the model, termed “truth,” into another run termed “prediction.” At each stage, the prediction errors form the basis for the next estimate of the gains. Steady state is achieved after three or four iterations. Further simplification is achieved by making the gains depend on longitudinal distance from the observation point, not on absolute longitude. For a single-layer primitive equation model, the scheme works well even if only the mass field is observed but not the velocity field. Although the scheme was developed for *Mars Observer*, it should be applicable to data retrieved from Earth atmosphere satellites, for example, *UARS*.