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NASA NTRS1987

The terminal area simulation system. Volume 1: Theoretical formulation

A three-dimensional numerical cloud model was developed for the general purpose of studying convective phenomena. The model utilizes a time splitting integration procedure in the numerical solution of the compressible nonhydrostatic primitive equations. Turbulence closure is achieved by a conventional first-order diagnostic approximation. Open lateral boundaries are incorporated which minimize wave reflection and which do not induce domain-wide mass trends. Microphysical processes are governed by prognostic equations for potential temperature water vapor, cloud droplets, ice crystals, rain, snow, and hail. Microphysical interactions are computed by numerous Orville-type parameterizations. A diagnostic surface boundary layer is parameterized assuming Monin-Obukhov similarity theory. The governing equation set is approximated on a staggered three-dimensional grid with quadratic-conservative central space differencing. Time differencing is approximated by the second-order Adams-Bashforth method. The vertical grid spacing may be either linear or stretched. The model domain may translate along with a convective cell, even at variable speeds.

Proctor, F. H.↗

NASA NTRS1987

Orbital atmospheric physics and dynamics

There are two ways of modeling the upper atmosphere. One is the empirical model that makes use of experimental data on means and excursions from the mean and fits the data in a self-consistent manner. The other approach is to deal directly with the physical processes. This is difficult since what is happening is extremely complex. Data measured using an interferometer to give Doppler shifts of airglow lines showed 300 to 800 m/sec winds with a complex structure in the upper region of the thermosphere at high latitudes. Ionospheric electric fields, strongly influenced by interaction with the solar wind, drive the ionized component and large neutral winds result due to momentum transfer between the charged particles and the neutrals. Frictional heating results from movement of ions through the neutrals, which also influences the compositional structure. These are examples of the complex interactions involved. The NCAR General Circulation Model (tropospheric) was adapted for use at thermospheric altitudes: the Thermospheric General Circulation Model (TGCM). The model makes use partly of primitive equations and partly of empirical data for some quantities such as electron density, magnetic field, and ion drift.

Roble, Raymond↗

NASA NTRS1987

A study of the adequacy of quasi-geostrophic dynamics for modeling the effect of frontal cyclones on the larger scale flow

The evolution of individual cyclone waves is studied in order to see how well quasi-geostrophic (QG) dynamics can simulate the behavior of primitive equations (PE) dynamics. This work is an extension of a similar study (Mudrick, 1982); emphasis is placed here on adding a frontal zone and other more diverse features to the basic states used. In addition, sets of PE integrations, with and without friction, are used to study the formation of surface occluded fronts within the evolving cyclones. Results of the study are summarized at the beginning of the report.

Mudrick, Stephen↗

NASA NTRS1986

Numerical studies of frontal dynamics

Efforts concentrated on the development of a two dimensional primitive equation (PE) model of frontogenesis that simultaneously incorporates the frontagenetical mechanisms of confluence and horizontal shear. Applying this model to study the effects of upper level frontogenesis, it appeared to be dominated by tilting effects associated with cross front variation of vertical motion, in which subsidence is maximized within and to the warm side of the frontal zone. Results suggest that aspects characteristic of three-dimensional baroclinic waves may be abstracted to a significant extent in a two dimensional framework. They also show that upper-level frontogenesis and tropopause folding can occur in the absence of three-dimensional curvature effects, commonly believed to be necessary for realistic upper-level frontogenesis. An implication of the dominant tilting effects is that they may have to be adequately resolved by numerical weather prediction models, thus requiring better horizontal and vertical resolution.

Keyser, Daniel↗

NASA NTRS1985

A fully implicit scheme for global numerical weather prediction

A fast-slow factored scheme is presented for use with shallow-water primitive equation numerical weather prediction models. The technique was developed to reduce the rotational mode errors which arise when the fast and slow terms of the governing differential equations are treated simultaneously. The method factors out the fast and slow terms along the coordinate directions by means of a modified Crank-Nicolson scheme. A finite-difference spatial discretization is carried out in the zonal and meridional directions to reduce the factorization error to near-zero, and that time steps of 60-90 min can be used to obtain acceptably accurate results, even in the presence of fine spatial structures in the flow.

Augenbaum, J. M.↗

NASA NTRS1985

Sensitivity of a mesoscale model to initial specification of relative humidity, liquid water and vertical motion

The influence of synoptic scale initial conditions on the accuracy of mesoscale precipitation modeling is investigated. Attention is focused on the relative importance of the water vapor, cloud water, rain water, and vertical motion, with the analysis carried out using the Limited Area Mesoscale Prediction System (LAMPS). The fully moist primitive equation model has 15 levels and a terrain-following sigma coordinate system. A K-theory approach was implemented to model the planetary boundary layer. A total of 15 sensitivity simulations were run to investigate the effects of the synoptic initial conditions of the four atmospheric variables. The absence of synoptic cloud and rain water amounts in the initialization caused a 2 hr delay in the onset of precipitation. The delay was increased if synoptic-scale vertical motion was used instead of mesoscale values. Both the delays and a choice of a smoothed moisture field resulted in underestimations of the total rainfall.

Kalb, M. W.↗

NASA NTRS1986

Evaluation of a multivariate variational assimilation of conventional and satellite data for the diagnosis of cyclone systems

A variational data assimilation method for the study of cyclone-scale weather systems is described. The variational data assimilation method is to incorporate primitive equations for a moist, convectively unstable atmosphere and the radiative transfer equation. The variables to be adjusted include the three-dimensional vector wind, height, temperature, and moisture from rawinsonde data, and cloud-wind vectors, moisture, and radiance from satellite data. The development of variational model 1 which contains two nonlinear horizontal momentum equations, an integrated continuity equation, and a hydrostatic equation is examined. Examples applying the assimilation model to rawinsonde and satellite data are presented.

Achtemeier, Gary L.↗

NASA NTRS1986

Transport of atmospheric tracers by planetary waves during a winter stratospheric warming event - A three-dimensional model simulation

In a simple three-dimensional primitive equation model, a wave number 1 major stratospheric warming is simulated. With the aid of two idealized tracers it is shown that the transport during a major warming event is characterized by a small, well-organized tongue of subtropical air flowing around the displaced winter vortex into the polar cap and by a wide area with strong quasi-horizontal mixing (surf zone). The description of these dynamical processes requires a full three-dimensional space resolution.

Kouker, W.↗

NASA NTRS1986

Nongeostrophic theory of zonally averaged circulation. I - Formulation

A nongeostrophic theory of zonally averaged circulation is formulated using the nonlinear primitive equations (mass conservation, thermodynamics, and zonal momentum) on a sphere. The relationship between the mean meridional circulation and diabatic heating rate is studied. Differences between results of nongeostropic theory and the geostrophic formulation concerning the role of eddy forcing of the diabatic circulation and the nonlinear nearly inviscid limit versus the geostrophic limit are discussed. Consideration is given to the Eliassen-Palm flux divergence, the Eliassen-Palm pseudodivergence, the nonacceleration theorem, and the nonlinear nongeostrophic Taylor relationship.

Tung, Ka Kit↗

NASA NTRS1986

Linear simulation of the stationary eddies in a general circulation model. I - The no-mountain model

A linear primitive-equation stationary-wave model is developed to describe Northern Hemisphere winter stationary eddies on a sphere, and simulation results are compared with the predictions of a flat-lower-boundary GCM in extensive graphs and maps. The linear model is shown to reproduce the general behavior of the GCM well, with 10-30-percent underestimation of amplitudes in the Northern Hemisphere extratropical upper troposphere. The response to global heating plus transient eddy flux convergences is then decomposed into responses to total tropical forcing (heating plus transients) and total extratropical forcing (upper and lower tropospheric transients and latent, sensible, and radiative heating). The quality of the simulation is found to deteriorate rapidly if transient forcing is omitted, although somewhat better results are obtained by substituting thermal damping for transient forcing. The importance of low-level-transient parameterization for theories of time-mean low-level flow is emphasized.

Nigam, Sumant↗

NASA NTRS1987

Zonal winds near Venus' cloud top level - A model study of the interaction between the zonal mean circulation and the semidiurnal tide

The Holton (1982) wave-mean flow interaction model's primitive equation is presently adapted in order to clarify the interaction between the semidiurnal tide and the thermally driven mean meridional circulation near cloud top level. The model is found to produce midlatitude jets whose structure is insensitive to vertical shear of the background angular velocity, both above and below cloud top level; a sensitivity to background angular velocity at cloud top level, however, is noted. Agreement between the model tide and either the observed one or that generated by the more detailed calculations of Pechmann and Ingersoll (1984) is found to be greatest when the background angular velocity at the jet level is of the order of 30 percent larger than that which is observed.

Baker, Nancy L.↗

NASA NTRS1986

Effects of eddy initial conditions on nonlinear forcing of planetary scale waves by amplifying baroclinic eddies

The previous study of Young and Villere concerning growth of planetary scale waves forced by wave-wave interactions of amplifying intermediate scale baroclinic eddies is extended to investigate effects of different eddy initial conditions. A global, spectral, primitive equation model is used for the calculations. For every set of eddy initial conditions considered, growth rates of planetary modes are considerably greater than growth rates computed from linear instability theory for a fixed zonally independent basic state. However, values of growth rates ranged over a factor of 3 depending on the particular set of eddy initial conditions used. Nonlinear forcing of planetary modes via wave-wave coupling becomes more important than baroclinic growth on the basic state at small values of the intermediate-scale modal amplitudes. The relative importance of direct transfer of kinetic energy from intermediate scales of motion to a planetary mode, compared to baroclinic conversion of available potential energy to kinetic energy within that planetary mode, depends on the individual case. In all cases, however, the transfer of either kinetic or available potential energy to the planetary modes was accomplished principally by wave-wave transfer from intermediate scale eddies, rather than from the zonally averaged state. The zonal wavenumber 2 planetary mode was prominent in all solutions, even in those for which eddy initial conditions were such that a different planetary mode was selectively forced at the start. General characteristics of the structural evolution of the planetary wave components of total heat and momentum flux, and modal structures themselves, were relatively insensitive to variations in eddy initial conditions, even though quantitative details varied from case to case.

Young, Richard E.↗

NASA NTRS1987

Variational four-dimensional analysis using quasi-geostrophic constraints

A variational four-dimensional analysis technique using quasi-geostrophic models as constraints is examined using gridded fields as data. The analysis method uses a standard iterative nonlinear minimization technique to find the solution to the constraining forecast model which best fits the data as measured by a predefined functional. The minimization algorithm uses the derivative of the functional with respect to each of the initial condition values. This derivative vector is found by inserting the weighted differences between the model solution and the inserted data into a backwards integrating adjoint model. The four-dimensional analysis system was examined by applying it to fields created from a primitive equations model forecast and to fields created from satellite retrievals. The results show that the technique has several interesting characteristics not found in more traditional four-dimensional assimilation techniques. These features include a close fit of the model solution to the observations throughout the analysis interval and an insensitivity to the frequency of data insertion or the amount of data. The four-dimensional analysis technique is very versatile and can be extended to more complex problems with little theoretical difficulty.

Derber, John C.↗

NASA NTRS1988

Application of satellite data in variational analysis for global cyclonic systems

The goal of the research is a variational data assimilation method that incorporates as dynamical constraints, the primitive equations for a moist, convectively unstable atmosphere and the radiative transfer equation. Variables to be adjusted include the three-dimensional vector wind, height, temperature, and moisture from rawinsonde data, and cloud-wind vectors, moisture, and radiance from satellite data. In order to facilitate thorough analysis of each of the model components, four variational models that divide the problem naturally according to increasing complexity were defined. The research performed during the second year fall into four areas: sensitivity studies involving Model 1; evaluation of Model 2; reformation of Model 1 for greater compatibility with Model 2; development of Model 3 (radiative transfer equation); and making the model more responsive to the observations.

Achtemeier, G. L.↗

NASA NTRS1987

The effect of the Hadley circulation on the meridional propagation of stationary waves

The effect of the Hadley circulation on the meridional propagation of stationary planetary waves was investigated using a multilevel linearized steady primitive equation model with an idealized meridional circulation. It was found that a mean meridional circulation in the basic state can change the response of a multilevel model, especially to forcing in the tropics. The idealized model version was altered in several ways and was run with realistic zonal mean conditions of January and July for a variety of forcings, including topographic forcing and idealized tropical heating. In this model, the Hadley circulation changes the response to earth topographic forcing in the subtropics. The inclusion of the Hadley circulation allows interhemispheric connections in the stationary response to tropical forcing comparable to those that observations suggest are forced by the Asian monsoon in July and the anomalous upper-tropospheric divergence during the El Nino in January.

Watterson, Ian G.↗

NASA NTRS1987

Vacillations induced by interference of stationary and traveling planetary waves

The interference pattern produced when a traveling planetary wave propagates over a stationary forced wave is explored, examining the interference signature in a variety of diagnostics. The wave field is first restricted to a diatomic spectrum consisting of two components: a single stationary wave and a single monochromatic traveling wave. A simple barotropic normal mode propagating over a simple stationary plane wave is considered, and closed form solutions are obtained. The wave fields are then restricted spatially, providing more realistic structures without sacrificing the advantages of an analytical solution. Both stationary and traveling wave fields are calculated numerically with the linearized Primitive Equations in a realistic basic state. The mean flow reaction to the fluctuating eddy forcing which results from interference is derived. Synoptic geopotential behavior corresponding to the combined wave and mean flow fields is presented, and the synoptic signature in potential vorticity on isentropic surfaces is examined.

Salby, Murry L.↗

NASA NTRS1987

Numerical simulation of polar lows and comma clouds using simple dry models

Linear and nonlinear numerical channel models are used to simulate polar low/comma cloud evolution. The basic state of the model is idealized and can be specified analytically. It has strong horizontal as well as vertical wind shear and implicitly includes the effect of sensible heat fluxes from the lower boundary. This is done by having a layer of reduced stability present in the lower troposphere. The results of the linear model study are presented and used to provide input for the nonlinear model integration. It is shown that, given sufficient horizontal resolution, many features of polar low/comma clouds can be simulated by the nonlinear primitive equations model and the idealized basic state, in particular a rapidly growing disturbance with a wavelength on the order of 1000 km.

Mudrick, Stephen E.↗

NASA NTRS1988

The GISS global climate-middle atmosphere model. I - Model structure and climatology

A coupled global climate/middle atmosphere model (GCMAM) is developed by extending the Hansen et al. (1983) GISS global climate model to include the middle atmosphere up to 85 km. The model includes numerical solutions of the primitive equations, calculations of the radiative and surface fluxes, and a complete hydrologic cycle with convective and cloud-cover parameterizations. In addition, a parameterized gravity wave drag cycle is incorporated, in which gravity-wave momentum fluxes due to flow over topography, wind shear, and convection are calculated at each grid box, using theoretical relationships between the grid-scale variables and expected source strengths. The results of the GCMAM demonstrate that the model produces a reasonable simulation of the stratosphere. It is shown that the improvements over the previous version were achieved largely through the incorporation of the parameterized gravity wave drag.

Rind, D.↗