The Ocean Mesoscale Regime of the Reduced-Gravity Quasi-Geostrophic Model
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It is shown that the fields of velocity, eddy viscosity, potential temperature, and specific humidity in a planetary boundary layer are decoupled by the introduction of a free parameter, Q, which combines the effects of thermal and humidity stratification. Solutions of the whole system are shown to be obtainable by the method of trial and error on Q. Results show good agreement when both the thermal and humidity stratification are accounted for.
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.
Factors which affect the long term predictability, and also the feasibility of defining an ultimate level of weather predictability, are discussed. It is noted that current models yield a one week forecast at the best. Long range predictability, however, is a restriction on the knowledge of evolutive processes of the atmosphere, and does not characterize the prediction of specific atmospheric quantities. The influences of local phenomena such as cyclones and other nonlinear processes can cause planetary waves which affect the predictability of weather everywhere. It is suggested that any successful prediction model will necessarily account for the evolution of ultralong waves. Although significant differences in predictions have been found between hemispheric and global predictions, the location of the errors in extrapolating the hemispheric to the global scale have been identified.
A finite difference model and an approximate WKB analysis were employed to test the validity of three of the Smagorinsky conclusions (1953) regarding the influence of diabatic heating upon the resultant stationary eddies. The conclusions comprised a necessity of including surface friction to avoid resonance, to account for stratospheric influence to accurately estimate the magnitude of the disturbances in the upper third of the troposphere, and the adequacy of the linear model for describing the gross features of sea-level normals at middle and high latitudes. Results of the WKB analysis of the effects of orography and diabatic heating demonstrate that streamfunctions are produced when orography forces a stationary solution. The surface friction is concluded to have a negligible effect on the solutions when the wind speeds are low. The solutions, however, require the presence of a lid for the middle troposphere to eliminate resonance responses.
The seasonal variation of the alongshore geostropic velocity (AGV) (relative to 500 dbar) over the outer continental slope off Point Sur and Point Conception, California, is investigated statistically on the basis of hydrographic data collected in the California Cooperative Oceanic Fisheries Investigations from 1949 through 1981. Previous observations and theoretical models of the AGV features are reviewed, the data are characterized, and the results are presented graphically and compared with the model predictions. Both locations have coherent mainly annual flow above 100-m depth, north during October-January and south during February-September; below 100 m, the flow is semiannually variable and always northward (with December and June maxima) at Point Conception but annual (with northward maximum in December and weak southward flow from March to May) at Point Sur.
Both zonal mean flow and stationary waves in the stratosphere have large variabilities from month to month and from year to year. One plausible mechanism that can account for these variabilities is the interaction between the forced stationary waves and the mean zonal flow. Given the large energy source contained in the stationary waves which are forced in the lower atmosphere, they are probably responsible for inducing the bulk of the variability in the mean flow in the stratosphere. Variability in the mean flow can in turn produce variability in the stationary wave amplitudes due to the possible sensitivity of wave response in the stratosphere to the configuration of the wave guide determined by the mean flow. The likely causes for the low-frequency variability of the stationary waves-mean flow system in extratropical latitudes are assessed. The causes of variability are divided into internal and external ones. Internal mechanisms include transition between equilibria and vacillation cycles, while mechanisms external to the midlatitude system include eddy heat and momentum fluxes from the tropics and the Hadley circulation forced in the tropics.
Boutko et al., used available satellite radiometer data to estimate 0.1 mb constant pressure heights in the mesosphere and Koshelkov and Kovshova derived, 0.1 to 0.005 mb or 0.1 to 0.001 mb layer thickness from which were compiled height fields of the 0.005 mb and 0.001 mb levels. The close relationship discovered between mean thicknesses and zonal values of atmospheric radiances observed in channel 3000 of the pressure modulated radiometer was used. An analysis of the geopotential height fields in the lower thermosphere of the Southern Hemisphere was carried out by others. The Northern Hemisphere patterns are analyzed herein. The analysis was limited to regions north of 20 N due to poor reliability of the thickness estimates from the radiometer data at low latitudes. These analyses are discussed.
The temperature and the derived winds obtained from the LIMS Map Archival Tape data for the period of October 25, 1978, to May 28, 1979, were compared with corresponding data from the Berin (Tempelhof) radiosonde station at several representative levels in the stratosphere, to assess the quality of the LIMS satellite data for use in dynamics and transport studies. It was found, on the basis of this single-station time series comparison, that the synoptically mapped LIMS temperature and wind analyses are of a sufficiently high quality for investigating large-scale dynamics in the stratosphere in conjunction with high-resolution radiosonde measurements.
The diagnostics of large scale geostrophy in a stratified atmosphere are revisited using a full Coriolis force.
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An in-depth analysis of observed gravity waves and their relationship to precipitation bands over the Montana mesonetwork during the 11-12 July 1981 CCOPE case study indicated two episodes of coherent waves. While geostrophic adjustment, shearing instability, and terrain were all implicated separately or in combination as possible wave generation mechanisms, the lack of upper-air data within the wave genesis region made it difficult to define the genesis processes from observations alone. The first part of this paper, 3D Numerical Modeling Studies of Terrain-Induced Mass/Momentum Perturbations, employs a mesoscale numerical model to help diagnose the intricate early wave generation mechanisms during the first observed gravity wave episode. The meso-beta scale numerical model is used to study various simulations of the role of multiple geostrophic adjustment processes in focusing a region for gravity wave genesis. The second part of this paper, Linear Theory and Theoretical Modeling, investigates the response of non-resting rotating homogeneous and continuously stratified Boussinesq models of the terrestrial atmosphere to temporally impulsive and uniformly propagating three-dimensional localized zonal momentum sources representative of midlatitude jet streaks. The methods of linear perturbation theory applied to the potential vorticity (PV) and wave field equations are used to study the geostrophic adjustment dynamics. The total zonal and meridional wind perturbations are separated into geostrophic and ageostrophic components in order to define and follow the evolution of both the primary and secondary mesocirculations accompanying midlatitude jetogenesis forced by geostrophic adjustment processes. This problem is addressed to help fill the gap in understanding the dynamics and structure of mesoscale inertia-gravity waves forced by geostrophic adjustment processes in simple two-dimensional quiescent current systems and those produced by mesoscale numerical models simulating the orographic and diabatic perturbation of three-dimensional quasi-geostrophically balanced synoptic scale jet streaks associated with complex baroclinic severe storm producing environments.
In rapidly rotating turbulent flows the largest scales of the motion are in approximate geostrophic balance. Single-point turbulence closures, in general, cannot attain a geostrophic balance. This article addresses and resolves the possibility of constitutive relation procedures for single-point second order closures for a specific class of rotating or stratified flows. Physical situations in which the geostrophic balance is attained are described. Closely related issues of frame-indifference, horizontal nondivergence, Taylor-Proudman theorem and two-dimensionality are, in the context of both the instantaneous and averaged equations, discussed. It is shown, in the absence of vortex stretching along the axis of rotation, that turbulence is frame-indifferent. A derivation and discussion of a geostrophic constraint which the prognostic equations for second-order statistics must satisfy for turbulence approaching a frame-indifferent limit is given. These flow situations, which include rotating and nonrotating stratified flows, are slowly evolving flows in which the constitutive relation procedures are useful. A nonlinear non-constant coefficient representation for the rapid-pressure strain covariance appearing in the Reynolds stress and heat flux equations consistent with the geostrophic balance is described. The rapid-pressure strain model coefficients are not constants determined by numerical optimization but are functions of the state of the turbulence as parameterized by the Reynolds stresses and the turbulent heat fluxes. The functions are valid for all states of the turbulence attaining their limiting values only when a limit state is achieved. These issues are relevant to strongly vortical flows as well as flows such as the planetary boundary layers, in which there is a transition from a three-dimensional shear driven turbulence to a geostrophic or horizontal turbulence.
The two-layer system of an atmosphere over water bodies is reduced to a single-layer problem. Values of the interfacial quantities, such as the friction velocity, the surface velocity, the angles, alpha and beta, between the surface shear stress and the geostrophic wind velocity and the surface wind velocity, respectively, and the surface roughness, all of which depend upon external parameters, such as the geostrophic wind and stratifications, are obtained. The geostrophic drag coefficient, the geostrophic wind coefficient, and the angles alpha, and beta, of the turbulent flow at the sea-air interface are functions of a dimensionless number, mfG/kg, with S sub 1 and S sub 2 as two free stratification parameters. The surface roughness is uniquely determined from the geostrophic wind rather than from the wind profile in the boundary layer.
The Charney-Phillips (1953) standard vertical grid for quasi-geostrophic models is compared with the Lorenz (1960) vertical grid (which departs from the standard grid by carrying horizontal velocity and potential temperature at same levels) in the framework of the quasi-geostrophic potential vorticity equation and baroclinic instability. It is demonstrated that the Charney-Phillips grid makes it possible to maintain important dynamical constraints on quasi-geostrophic flow, such as the conservation of quasi-geostrophic potential vorticity through horizontal advection and resulting integral constraints. The Lorenz grid, on the other hand, is not straightforward even to define quasi-geostrophic potential vorticity. Moreover, due to an extra degree of freedom in potential temperature, the Lorenz grid can falsely satisfy the necessary condition for baroclinic instability near the lower and the upper boundaries.
Improvements to the global reference atmospheric model are described. The basic model includes monthly mean values of pressure, density, temperature, and geostrophic winds, as well as quasi-biennial and small and large scale random perturbations. A spherical harmonic wind model for the 25 to 90 km height range is included. Below 25 km and above 90 km, the GRAM program uses the geostrophic wind equations and pressure data to compute the mean wind. In the altitudes where the geostrophic wind relations are used, an interpolation scheme is employed for estimating winds at low latitudes where the geostrophic wind relations being to mesh down. Several sample wind profiles are given, as computed by the spherical harmonic model. User and programmer manuals are presented.
A nongeostrophic theory of zonally averaged circulation is formulated using the nonlinear primitive equations on a sphere, taking advantage of the more direct relationship between the mean meridional circulation and diabatic heating rate which is available in isentropic coordinates. Possible differences between results of nongeostrophic theory and the commonly used geostrophic formulation are discussed concerning: (1) the role of eddy forcing of the diabatic circulation, and (2) the nonlinear nearly inviscid limit vs the geostrophic limit. Problems associated with the traditional Rossby number scaling in quasi-geostrophic formulations are pointed out and an alternate, more general scaling based on the smallness of mean meridional to zonal velocities for a rotating planet is suggested. Such a scaling recovers the geostrophic balanced wind relationship for the mean zonal flow but reveals that the mean meridional velocity is in general ageostrophic.