Showing papers in "Journal of the Atmospheric Sciences in 1989"

Numerical Study of Convection Observed during the Winter Monsoon Experiment Using a Mesoscale Two-Dimensional Model

Abstract: A two-dimensional version of the Pennsylvania State University mesoscale model has been applied to Winter Monsoon Experiment data in order to simulate the diurnally occurring convection observed over the South China Sea. The domain includes a representation of part of Borneo as well as the sea so that the model can simulate the initiation of convection. Also included in the model are parameterizations of mesoscale ice phase and moisture processes and longwave and shortwave radiation with a diurnal cycle. This allows use of the model to test the relative importance of various heating mechanisms to the stratiform cloud deck, which typically occupies several hundred kilometers of the domain. Frank and Cohen's cumulus parameterization scheme is employed to represent vital unresolved vertical transports in the convective area. The major conclusions are: Ice phase processes are important in determining the level of maximum large-scale heating and vertical motion because there is a strong anvil componen...

Interannual variability in a tropical atmosphere−ocean model: influence of the basic state, ocean geometry and nonlinearity

Abstract: The behavior of a tropical coupled atmosphere/ocean model is analyzed for a range of different background states and ocean geometries. The model is essentially that of Cane and Zebiak for the tropical Pacific, except only temporally constant background states are considered here. For realistic background states and ocean geometry, the model solutions feature oscillations of period of 3–5 yr. By comparing the full model solution with a linearized version of the model, it is shown that the basic mechanism of the oscillation is contained within linear theory. A simple linear analog model is derived that describes the nature of the interannual variability in the coupled tropical atmosphere–ocean system. The analog model highlights the properties that produce coupled atmosphere–ocean instability in the eastern ocean basin, and the equatorial wave dynamics in the western ocean basin that are responsible for a delayed, negative feedback into this instability growth. The growth rate of the local instabil...

The Effect of Eurasian Snow Cover on Regional and Global Climate Variations

Abstract: The sensitivity of the global climate system to interannual variability of he Eurasian snow cover has been investigated with numerical models. It was found that heavier than normal Eurasian snow cover in spring leads to a “poor” monsoon over Southeast Asia thereby verifying an idea over 100 years old. The poor monsoon was characterized by reduced rainfall over India and Burma, reduced wind stress over the Indian Ocean, lower than normal temperatures on the Asian land mass and in the overlying atmospheric column, reduced tropical jet, increased soil moisture, and other features associated with poor monsoons. Lighter than normal snow cover led to a “good” monsoon with atmospheric anomalies like those described above but of opposite sign. Remote responses from the snow field perturbation include readjustment of the Northern Hemispheric mass field in midlatitude, an equatorially symmetric response of the tropical geopotential height and temperature field and weak, but significant, perturbations in the surface wind stress and heat flux in the tropical Pacific. The physics responsible for the regional response involves all elements of both the surface heat budget and heat budget of the full atmospheric column. In essence, the snow, soil and atmospheric moisture all act to keep the land and overlying atmospheric column colder than normal during a heavy snow simulation thus reducing the land–ocean temperature contrast needed to initiate the monsoon. The remote responses are driven by heating anomalies associated with both large scale air-sea interactions and precipitation events. The model winds from the heavy snow experiment were used to drive an ocean model. The SST field in that model developed a weak El Nino in the equatorial Pacific. A coupled ocean-atmosphere model simulation perturbed only by anomalous Eurasian snow cover was also run and it developed a much stranger El Nino in the Pacific. The coupled system clearly amplified the wind stress anomaly associated with the poor monsoon. These results show the important role of an evolving (not specified) sea surface temperature in numerical experiments and the real climate system. Our general results also demonstrate the importance of land processes in global climate dynamics and their possible role as one of the factors that could trigger ENSO events.

A GCM Parameterization for the Shortwave Radiative Properties of Water Clouds

Abstract: A new parameterization was developed for predicting the shortwave radiative properties of water clouds, suitable for inclusion in general circulation models (GCMs). The parameterization makes use of the simple relationships found by Slingo and Schrecker, giving the three input parameters required to calculate the cloud radiative properties (the optical depth, single scatter albedo and asymmetry parameter) in terms of the liquid water path and equivalent radius of the drop size distribution. The input parameters are then used to derive the cloud radiative properties, using standard two-stream equations for a single layer. The relationships were originally derived for fairly narrow spectral bands but it was found that it is possible to average the coefficients so as to use a much smaller number of bands, without sacrificing accuracy in calculating the cloud radiative properties. This makes the parameterization fast enough to be included in GCMs. The parameterization was programmed into the radiation scheme used in the U.K. Meteorological Office GCM. This scheme and the 24 band Slingo/Schrecker scheme were compared with each other and with observations, using a variety of published datasets. There is good agreement between the two schemes for both cloud albedo and absorption, even when only four spectral bands are employed in the GCM.

Solar radiative transfer in cirrus clouds. I - Single-scattering and optical properties of hexagonal ice crystals. II - Theory and computations of multiple scattering in an anisotropic medium

Abstract: The light scattering and absorption programs of Cai and Liou (1982) and Takano and Jaweera (1985) are extended to include hexagonal ice crystals randomly and horizontally oriented in space. The scattering and polarization results for the ice crystals are calculated. The results are compared with measurement data. The single-scattering properties for horizontally oriented columns and plates are presented and used to explain halos and arcs observed in the atmopshere. In the second section, the theory and computations for multiple scattering in cirrus clouds containing oriented ice crystals are presented. The radiative transfer in clouds composed of horizontally oriented ice crystals is formulated. Also, reflected and transmitted intensities, planetary albedo, and polarization in multiple scattering by ice crystals are discussed.

Low Froude Number Flow Past Three-Dimensional Obstacles. Part I: Baroclinically Generated Lee Vortices

Abstract: We study the flow of a density-stratified fluid past a three-dimensional obstacle, using a numerical model. Our special concern is the response of the fluid when the Froude number is near or less than unity. Linear theory is inapplicable in this range of Froude number, and the present numerical solutions show the rich variety of phenomena that emerge in this essentially nonlinear flow regime. Two such phenomena, which occupy Parts I and II of this study, are the formation of a pair of vertically oriented vortices on the lee side and a zone of flow reversal on the windward side of the obstacle. The Ice vortices have been explained as a consequence of the separation of the viscous boundary layer from the obstacle however, this boundary layer is absent (by design) in the present experiments and lee vortices still occur. We argue that a vertical component of vorticity develops on the lee side owing to the tilting of horizontally oriented vorticity produced baroclinically as the isentropes deform in r...

Large-Eddy Simulation of the Convective Atmospheric Boundary Layer

Abstract: Large-eddy simulations of a free convective atmospheric boundary layer with an overlying capping inversion are considered. Attention is given to the dependence of the results upon the various factors influencing the simulation: the subgrid model, the domain size, and the mesh resolution. By providing artificial constraints upon the convection the results also provide extra insight into the underlying dynamics. The gross features of the boundary layer, such as the overall energy budget, are not sensitive to the details of the simulations but a number of important factors are revealed. It has been found that near the surface the subgrid diffusivity must be larger than is usually supposed, in order for the vertical velocity skewness to have the correct sign. This region of the flow has a significant subgrid-scale heat flux and it seems that the subgrid model requires improvement in such cases. A revised model which under statically unstable conditions allows the mixing-length of the subgrid-scale tu...

Gravity Waves, Compensating Subsidence and Detrainment around Cumulus Clouds

Abstract: Gravity waves play an important role in the redistribution of heat and moisture in a deep convecting cloud field. We explore this role in a two-dimensional numerical experiment on a simple moist convecting system consisting of an isolated long-lasting nonprecipitating cloud in a calm atmosphere with no surface forcing. The cloud develops a horizontally averaged density variation with height which is neutrally buoyant with respect to a moist adiabatic. The buoyancy difference between the cloud and the undisturbed sounding produces circulations that can be understood as spreading gravity waves which adjust the environmental buoyancy to be equal to the cloud buoyancy by compensating subsidence. Unlike the circulations inside clouds, this adjustment takes place without turbulent mixing. Hence, the “buoyancy adjustment time” T1 during which the environment comes into rough buoyant equilibrium with the clouds is much shorter than the “mixing time” T2 which it takes a tracer, initially concentrated at s...

Improving the Anelastic Approximation

Abstract: A new diagnostic equation is presented which exhibits many advantages over the conventional forms of the anelastic continuity equation. Scale analysis suggests that use of this “pseudo-incompressible equation” is justified if the Lagrangian time scale of the disturbance is large compared with the time scale for sound wave propagation and the perturbation pressure is small compared to the vertically varying mean-state pressure. No assumption about the magnitude of the perturbation potential temperature or the strength of the mean-state stratification is required. In the various anelastic approximations, the influence of the perturbation density field on the mass balance is entirely neglected. In contrast, the mass-balance in the “pseudo-incompressible approximation” accounts for those density perturbations associated (through the equation of state) with perturbations in the temperature field. Density fluctuations associated with perturbations in the pressure field are neglected. The pseudo-incompr...

The Finite-Amplitude Nature of Tropical Cyclogenesis

Abstract: We have constructed a simple, balanced, axisymmetric model as a means of understanding the existence of the threshold amplitude for tropical cyclogenesis discovered by Rotunno and Emanuel. The model is similar to Ooyama's but is phrased in Schubert and Hack's potential radius coordinates. The essential difference between this and other balanced models lies in the representation of convective clouds. In the present model the cumulus updraft mass flux depends simply and directly on the buoyancy (on angular momentum surfaces) of lifted subcloud-layer air and is not explicitly constrained by moisture convergence. The downdraft mass flux is equal to the updraft flux multiplied by (1−ϵ), where ϵ is the precipitation efficiency. The complete spectrum of convective clouds in nature is here represented by two extremes: deep clouds with a precipitation efficiency of one, and shallow, nonprecipitating clouds. The former stabilize the atmosphere both by heating the free atmosphere and drying out the subcloud...

Evaluation of turbulent transport and dissipation closures in second-order modeling

Abstract: We show that the turbulence statistics from our (96)3 large-eddy-simulation (LES) studies of a convective boundary layer are in excellent agreement with those from the Deardorff–Willis laboratory convection tank. Using these LES data, we evaluate contemporary parameterizations for turbulent transport and dissipation in second-order closure models of the convective boundary layer. The gradient-diffusion parameterization for turbulent transport fares poorly, due in large part to the direct influence of buoyancy. This leads to poor predictions of the vertical profiles of some turbulence statistics. We also find that the characteristic length scales for the mechanical and thermal dissipation rates typically used in second-order closure models are a factor of 2–3 too small; this leads to underpredictions of turbulence kinetic energy levels. Finally, we find that the flux and variance budgets for conservative scalars are substantially different in top-down and bottom-up diffusion. In order to reproduce...

Some Aspects of Vortex Structure Related to Tropical Cyclone Motion

Abstract: Some effect of tropical cyclone structure on the vortex motion are examined in a nondivergent, barotropic numerical model with no basic current. As suggested earlier by DeMaria, the initial maximum wind speed has little effect on the track. Vortex translation associated with the beta effect depends sensitively on the strength of the flow between 300 and 1000 km from the center. If the flow in this annulus is made more cyclonic, the track will turn cyclonically and move more toward the west in the Northern Hemisphere. The dynamics of this beta-drift is studied via a decomposition into symmetric and asymmetric circulations. The symmetric flow experiences a slight weakening of the maximum wind speed and an anticyclonic circulation is induced beyond 600 km. The asymmetric circulation is dominated by an azimuthal wavenumber one circulation with an anticyclonic gyre east of the center, a cyclonic gyre to the west and a nearly uniform, broad-scale ventilation flow between the gyres. The vortex translati...

Optimal Excitation of Baroclinic Waves

Abstract: Development of perturbations in a baroclinic flow can arise both from exponential instability and from the transient growth of favorably configured disturbances that are not of normal mode form. The transient growth mechanism is able to account for development of neutral and damped waves as well as for an initial growth of perturbations asymptotically dominated by unstable modes at significantly greater than their asymptotic exponential rates. Unstable modes, which are the eigenfunctions of a structure equation, are discrete and typically few in number. In contrast, disturbances favorable for transient growth form a large subset of all perturbations. To assess the potential of transient growth to account for a particular phenomena it is useful to obtain from this subset the initial condition that gives the maximum development in a well-defined sense. These optimal perturbations have a role in the theory of transient development analogous to that of the normal modes in exponential instability theo...

Interactions among Radiation, Convection, and Large-Scale Dynamics in a General Circulation Model

Abstract: We have analyzed the effects of radiatively active clouds on the climate simulated by the UCLA/GLA GCM, with particular attention to the effects of the upper tropospheric stratiform clouds associated with deep cumulus convection, and the interactions of these clouds with convection and the large-scale circulation. Several numerical experiments have been performed to investigate the mechanisms through which the clouds influence the large-scale circulation. In the “NODETLQ” experiment, no liquid water or ice was detrained from cumulus clouds into the environment; all of the condensate was rained out. Upper level supersaturation cloudiness was drastically reduced, the atmosphere dried, and tropical outgoing longwave radiation increased. In the “NOANVIL” experiment, the radiative effects of the optically thich upper-level cloud sheets associated with deep cumulus convection were neglected. The land surface received more solar radiation in regions of convection, leading to enhanced surface fluxes and ...

Effects of implementing the simple biosphere model in a general circulation model

Abstract: The Simple Biosphere Model (SiB) of Sellers et al., was designed to simulate the interactions between the earth's land surface and the atmosphere by treating the vegetation explicitly and realistically, thereby incorporating the biophysical controls on the exchanges of radiation, momentum, sensible and latent heat between the two systems. This paper describes the steps taken to implement SiB in a modified version of the National Meteorological Center's global spectral general circulation model (GCM) and explores the impact of the implementation on the simulated land surface fluxes and near-surface meteorological conditions. The coupled model (SiB-GCM) was used to produce summer and winter simulations. The same GCM was used with a conventional hydrological model (Ctl-GCM) to produce comparable 'control' summer and winter simulations for comparison. It was found that SiB-GCM produced a more realistic partitioning of energy at the land surface than Ctl-GCM. Generally, SiB-GCM, produced more sensible heat flux and less latent heat flux over vegetated land than did Ctl-GCM and this resulted in a much deeper daytime planetary boundary layer and reduced precipitation rates over the continents in SiB-GCM. In the summer simulation, the 200 mb jet stream was slightly weakened in the SiB-GCM relative to the Ctl-GCM results and analyses made from observations.

Transients and the Extratropical Response to El Niño

Abstract: A baroclinic stationary wave model linearized about a zonally symmetric flow is used to interpret the extra-tropical atmospheric response to El Nino produced by a general circulation model. When forced by the anomalous diabatic beating and tendency due to transients, the linear model provides a useful simulation of this response. The direct response to anomalous diabatic heating is found to be small in the extratropics; the dominant term is the response to the anomalous transients, particularly the anomalous upper tropospheric transients in the vorticity equation. These results are complementary to those obtained with a nonlinear barotropic model by Held and Kang, and indicate that the anomalous subtropical convergence which plays a key role in that study is itself primarily forced by the anomalous transients. One can distinguish between two distinct parts of the response of the transients to the tropical heating: the movement of the Pacific storm track associated with the anomalous extratropical...

Vertical Velocity Characteristics of Oceanic Convection

Abstract: Oceanic cumulonimbus updraft and downdraft events observed in the Western Pacific during the TAMEX program by NOAA P-3 research aircraft are analyzed and discussed The basic dataset consists of flight-level data from 10 missions in the Taiwan region during May and June 1987 The 1 Hz time series of vertical velocity is used to define convective updrafts using the criteria that the velocity must be continuously positive for at least 05 km and exceed 05 m s−1 for 1 s A subset of the strongest drafts, termed cores, are defined as events that exceed 1 m s−1 for 05 km Downdrafts and downdraft cores are defined analogously The statistics are from a total of 12 841 km of flight legs and consist of 359 updrafts and 466 downdrafts at altitudes from 150 m to 68 km MSL The populations of average vertical velocity, maximum vertical velocity, diameter, and mass transport for both drafts and cores are approximately log-normally distributed, consistent with the results of previous studies of convective

Climatic Equilibrium of the Atmospheric Convective Boundary Layer over a Tropical Ocean

Abstract: A radiative-convective boundary layer model was developed by coupling a thermodynamic model of a partially mixed convective boundary layer (CBL) with a radiation model, and energy balance constraints were used to study coupled boundary layer (CBL) equilibrium over three timescales (about 1 day, about 10 days, and more than 100 days). It is shown that the variation in cloud top decreases with greater coupling to the atmosphere and the ocean. The slope of the latent heat flux with increasing SST decreases with more tropospheric coupling, and reverses sign with a coupled ocean.

Cirrus crystal nucleation by homogeneous freezing of solution droplets

Abstract: A numerical model consisting of a system of differential equations is used to study cirrus crystal nucleation in a rising parcel containing a distribution of cloud condensation nuclei. The evolution of the particle population and the thermodynamic variables in the parcel are examined. The results suggest that, if homogeneous freezing is not considered, liquid water should be detected below -40 C. If homogeneous freezing is considered, the rapid growth of ice crystals and vapor depletion prevent water saturation from being reached. It is shown that the likelihood of a droplet being frozen is increased by lower temperatures, larger droplet diameter, or lower solution density.

Lightning Rates Relative to Tornadic Storm Evolution on 22 May 1981

Abstract: Lightning and Doppler radar data for two tornadic storms in Oklahoma on May 22, 1981 are used to analyze ground flash rates relative to the time of tornadoes. It is found that the ground flash rates had no obvious relationship with the tornado times, although the stroke rate in both storms was greatest after the tornadic stage ended. The variations in the cyclone shear and the intracloud flash rates within 10 km of the mesocyclone region are examined. The results suggest that most tornadic storms have an increase in total flash rates near the time of the tornado and that this increase is often dominated by intracloud flashes.

A General Equation for the Terminal Fall Speed of Solid Hydrometeors

Abstract: A comprehensive yet simple formula is presented for the terminal fall velocity of solid precipitation particles. It depends on three particle parameters: mass, the mean circumscribed area presented to the flow, and the mean effective projected area presented to the flow. This formula is deduced from a single mean Davies number-Reynolds number relation based on boundary layer theory and therefore includes environmental conditions (air density and temperature). Terminal velocity is predicted with errors ≲10% for a wide variety of particles, e.g., various planar and columnar crystals, rimed and unrimed aggregates, graupel (lump, conical, and hexagonal) and hail up to over 10cm in diameter. In view of its general form and the broad base of examination, the formula is felt to be generally applicable to all kinds of natural solid precipitation particles including shapes not tested in this study.

Modeling Study of a Tropical Squall-Type Convective Line

Abstract: A multidimensional and time-dependent cloud scale model is used to investigate the dynamic and micro-physical processes associated with convective and stratiform regions within a tropical squall-type convective line. The evolution of the total convective and stratiform portions of rainfall is also estimated by using model output. A three-dimensional version of the model covers a horizontal domain about 96 × 96 km2. Frequently, the horizontal extent of an observed stratiform region is over a few hundred kilometers. Therefore, a two-dimensional version of the model with a 512 km horizontal length is also used to incorporate a complete stratiform region. Two-dimensional model result recapture many interesting features as observed. In particular, the fractional portion of stratiform rain as well as its fractional area coverage are in good agreement with observations. A significant amount of ice particles melted to rain near the freezing level in the trailing part of the modeled squall system during i...

MST Radar Observations of a Saturated Gravity Wave Spectrum

Abstract: We present vertical wavenumber spectra of mesoscale wind fluctuations using data observed in the troposphere, lower stratosphere and mesosphere by the MU radar at 35°N in Japan in October 1986 and June 1987, as well as lower stratospheric spectra obtained by the Arecibo UHF radar at 18°N in Puerto Rico in June 1983. These spectra are much more homogeneous than previously available spectra since all of the data were observed by the same radar technique, the data in the different atmospheric regions were taken essentially simultaneously, and all of the spectra were analyzed using very similar methods. In the large-wavenumber ranges of the observed spectra, the asymptomatic slopes and amplitudes agree well with the saturated gravity wave spectral model developed by Dewan and Good (1986) and Smith et al. (1987), which has a slope of −3 and a spectral amplitude proportional to the buoyancy frequency squared. The good agreement between the model spectrum and the observed spectra from different altitude...

Intraseasonal Periodicities in Indian Rainfall

Abstract: Spectral analysis of a 70-year (1901–70) record of daily precipitation from 3700 stations in the country of India is carried out to search for periodicities on subseasonal time scales during the summer monsoon. Two statistically significant spectral peaks are found. A 40–50 day spectral peak corresponding to the Madden-Julian Oscillation is found over most of the portion of India south of 23°N. The phase of the oscillation is such that the precipitation maximum appears first over the relatively dry southeastern portion of the peninsula. Ten to 12 days later the precipitation peaks simultaneously all along the coast west of the Western Ghats and along a line running across India between 20° and 25°N. The precipitation maximum then spreads slowly northward and loses significance. Cross-spectral analysis shows strong coherence between the precipitation patterns and wind oscillations. The zonal wind oscillations at 850 and 200 mb am about 180 degrees out-of-phase equatorward of about 20°N, but in-pha...

External Influences on Hurricane Intensity. Part I: Outflow Layer Eddy Angular Momentum Fluxes.

Abstract: Outflow layer winds were objectively analyzed every 12 h for 6 days during the life cycle of Hurricane Elena (1985). A high correlation was found between angular momentum fluxes by azimuthal eddies at large radii and central pressure changes in the storm 27–33 h later. Momentum flux by eddies exceeded that by the azimuthal mean outside the 800 km radius, while vortex spinup by the eddies reached instantaneous magnitudes as large as 25 m s−1/day. Outflow maxima and minima repeatedly appeared more than 1000 km from the hurricane center and tracked inward with time. The results provide evidence of significant environmental control on the behavior of the storm. After reaching hurricane strength, Elena experienced a major secondary intensification associated with a large inward cyclonic eddy momentum flux produced by the passage of a middle latitude trough north of the hurricane. An outflow maximum appeared radially inside of the eddy momentum source, consistent with balanced vortex theory, and tracke...

Effects of Variable Droplet Growth Histories on Droplet Size Distributions. Part I: Theory

Abstract: A theoretical framework is developed that permits estimation of the effects of fluctuating supersaturation on the development of cloud droplet size spectra. The studies focus on the role of turbulent fluctuations in vertical wind and in the microphysical environments in which droplets grow, and represent the effects of droplets mixing together that have encountered different trajectories through the cloud. It is contended that the effects can be analyzed in terms of two contributions to the variance in supersaturation history, one dependent on the average microphysical environment (specifically, integral radius) of the near environment in which a droplet grows, and the other dependent on the correlation between the integral radius and the updraft along the droplet trajectory. Variations in the possible trajectories that all end at a given point (and so form the droplet spectrum there) are used to estimate the possible widths of droplet spectra, and methods of testing these predictions using exper...

Low-frequency variability in the Northern Hemisphere winter: geographical distribution, structure and time-scale dependence

Abstract: Low-frequency variability in wintertime 500 mb height is examined, with emphasis on its structure, geographical distribution, and frequency dependence. A 39-year record of 500 mb geopotential height fields from the NMC analyses is time filtered to partition the fluctuations into frequency bands corresponding to periods of 10–60 days, 60–180 days and > 180 days. Winter is defined as the six month period November through April. Variance, teleconnectivity, and anisotropy fields, and selected loading vectors derived from orthogonal and oblique rotations of the eigenvectors of the temporal correlation matrix for each band are shown and discussed. The variability in all frequency bands exhibits substantial anistropy, with meridionally elongated features arranged as zonally oriented wave trains prevailing over the continents and zonally elongated features organized in the form of north–south oriented dipole patterns prevailing over the oceanic sectors of the hemisphere. The wave trains are most pronounc...

Implications of Monin–Obukhov Similarity Theory for Scalar Quantities

Abstract: Monin-Obukhov similarity theory of surface-layer turbulence has been extended to include all scalar quantities. The tenets of this theory, as it is presently practiced, are followed to their logical conclusions, which produce some novel results. First, the similarity theory is applied to the variance of a scalar quantity and its correlation with another scalar quantity. For this similarity to apply to all scalar quantities, it is shown that the dimensionless functions of stability are all equal, that the correlation coefficient of any two scalars is +1 or −1, and that the correlation of two scalars has the same sign as the product of their fluxes. These results also apply to structure parameters and cross-structure parameters as well as to the dissipation rates of the scalar's variances and correlations. It is shown that the fluctuations of all the scalar quantities are proportional to one another. On the basis of Monin–Obukhov similarity, the Obukhov–Corrsin constants (i.e., Kolmogorov constants...

Jupiter's Great Red Spot as a Shallow Water System

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.

Solar Radiative Transfer in Cirrus Clouds. Part II: Theory and Computation of Multiple Scattering in an Anisotropic Medium

Abstract: We have developed a theoretical framework for the computation of the transfer of solar radiation in an anisotropic medium with particular application to oriented ice crystals in cirrus clouds. In the theoretical development, the adding principle for radiative transfer has been used with modifications to account for the anisotropy of the phase matrix. The single-scattering properties including the phase function, single-scattering albedo, and extinction cross section, for randomly and horizontally oriented ice crystals are then used in the computation of reflected and transmitted intensifies, planetary albedo, and polarization in multiple scattering. There are significant differences in the reflected and transmitted intensifies between hexagonal ice crystals and equivalent ice spheres. In addition, it is found that ice spheres are inadequate to model the general pattern of reflected intensity. The orientation properties of ice crystals are also significant in the determination of the reflected and...