Isobaric Coordinates Research Articles

Winter Forecast Problems Associated with Light to Moderate Snow Events in the Mid-Atlantic States on 14 and 22 February 1986

Abstract Two cases of light and moderate snow events over the Washington, DC area are presented for 14 and 22 February 1986. These cases were selected since the upper-tropospheric and surface features were quite similar, yet significantly different snowfall patterns occurred in the mid-Atlantic status. The numerical guidance and local forecasters displayed minimal skill in forecasting the amount of snow for each case, especially in the Washington, DC area. Analyses in isobaric and isentropic coordinates are presented which focus on the structure and evolution of the thermal fields and associated temperature advection patterns in the lower troposphere. These analyses reveal that the low-level upslope flow (as derived from vertical motion computations in isentropic coordinates) and the associated warm-air advection patterns (as viewed in isobaric coordinates) were important factors in determining the intensity and spatial distribution of precipitation for each case. Three-hourly soundings from the Genesis o...

Global Diabatic Heating during FGGE SOP-1 and SOP-2

With the increase in the observational data provided by FGGE and the use of global circulation models with full physics for the data assimilation, it is now becoming feasible to attempt to estimate globally the atmospheric diabatic heating. The thermodynamic equation in isobaric coordinates and the data generated by the FGGE III-b analysis of the Goddard Laboratory for Atmospheres (GLA) are employed to serve this purpose. The results of the present study generally agree with other previous investigations. However, some important differences are also revealed. (1) The diabatic heating obtained in the tropics in the present study is larger than that obtained elsewhere; (2) the relatively large heating over the mountainous areas shown in other studies does not appear; (3) no significant negative values of diabatic heating are found in the polar regions; and (4) unlike other studies, cooling is noted over parts of Eurasia in the summer.

Wind‐driven spin‐up in eddy‐resolving ocean models formulated in isopycnic and isobaric coordinates

Wind‐driven spin‐up of the four‐layer, quasi‐isopycnic, eddy‐resolving primitive equation model of Bleck and Boudra (1981) is compared with that obtained with a (numerically dissimilar) “pure” isopycnic coordinate model and an isobaric (i.e., quasi‐Cartesian) coordinate model. In particular, the onset of hydrodynamic instabilities in the flow forced by a double‐gyre wind stress pattern is studied. The spin‐up processes associated with the isopycnic and quasi‐isopycnic model are found to be similar, whereas the flow pattern produced by the quasi‐Cartesian model deviates in the direction of Holland's (1978) and Holland and Lin's (1975a, b) two‐layer solutions.

Wind-driven spin-up in eddy-resolving ocean models formulated in isopycnic and isobaric coordinates: Bleck, Rainer and Douglas Boudra, 1986. J. geophys. Res., 91(C6):7611–7621

Wind-driven spin-up in eddy-resolving ocean models formulated in isopycnic and isobaric coordinates: Bleck, Rainer and Douglas Boudra, 1986. J. geophys. Res., 91(C6):7611–7621

Mass and Angular Momentum Diagnostics of Cyclones within Numerically Simulated Linear Baroclinic Waves

The mass and angular momentum budgets of extratropical cyclones within three numerically simulated adiabatic linear baroclinic waves are investigated through quasi-Lagrangian diagnostics. The waves analyzed, wavenumbers 5, 11 and 17, were chosen to represent a range of baroclinically active horizontal scales observed in the atmosphere within which cyclonic circulations develop. Results are compared with diagnostics of an observed atmospheric cyclone in order to examine the extent to which linear baroclinic instability theory explains extratropical cyclone development in the real atmosphere. Diagnostics are computed in both isobaric and isentropic coordinates. In the isobaric framework, inward mass and angular momentum transport occurs in the lower troposphere of the linear cyclones while the transport is outward in the upper troposphere Upward transport of these quantities throughout the troposphere redistributes these quantities vertically. Within isobaric coordinates the mass and angular momentum budgets of the cyclones within linear waves resemble results from actual cyclones. Analysis of these linear model cyclones in isentropic coordinates shows that the mass and angular momentum transport is inward in upper isentropic layers and outward below. Angular momentum is transferred from upper to lower isentrople layers by pressure and inertial torques within the baroclinic structure. The vertical distribution of transport process and torques within linear baroclinic wave is in general agreement with the results occurring during the dry-baroclinic phase of development in a 1971 Alberta cyclone but differs markedly from the distribution observed during the moist-baroclinic phase. The major dissimilarity between the development of the model cyclones and leeside dry-baroclinic cyclogenesis is the existence of a much stronger eddy component of horizontal angular momentum transport in the model cyclones. A strong eddy transport is required for the cyclones to simultaneously deepen and spin-up over the flat terrain in the linear model, while such a transfer is not necessary for development over sloped topography.

A Comparison of Methods for Computing the Sigma-Coordinate Pressure Gradient Force for Flow over Sloped Terrain in a Hybrid Theta-Sigma Model

Five methods for computing the pressure gradient force within a sigma domain of a hybrid model are compared for flow over a steeply sloped terrain. The comparison includes pressure gradient calculations determined from a direct transformation to sigma coordinates, an application of an atmospheric deviation state to the direct transformation (Phillips, 1974), an evaluation within isobaric coordinates (Janjić, 1977), a flux form (Johnson, 1980), and a flux prime form that applies the Phillips' deviation state to the flux form. The results from a numerical simulation establish that the Janjić, Phillips and flux prime methods reduce truncation errors substantially, and successfully predict the surface anticyclonic circulation that develops within vertically and horizontally sheared baroclinic flow over elevated terrain. A discussion of the generation of kinetic energy and elimination of a spurious kinetic energy source through reduction of the truncation error by the flux prime method is presented.

Diagnostic Equations in Isobaric Coordinates

Diagnostic studies of the general circulation are conducted, almost exclusively, using data and equations where pressure is the vertical coordinate. The complexity of the lower boundary condition in these isobaric coordinates may lead to some ambiguity in the manner of calculating and displaying the pertinent diagnostic statistics and budget terms. A formalism is developed using the unit and delta functions which permits an unambiguous calculation of the appropriate diagnostic terms. Using this formalism, budget equations are derived which display a number of unfamiliar boundary terms. The more familiar budget equations are seen to be approximations to these more complete equations. Examples of some basic general circulation statistics involving temperature are used to illustrate the application of the formalism.

The Forcing of the Meridional Circulation of the Isentropic Zonally Averaged Circumpolar Vortex

Abstract For the axisymmetric general circulation, Eliassen (1951) showed that stable meridional circulations are controlled by large-scale diabatic heating and friction torque. Because the real atmosphere is longitudinally disturbed, a direct meridional response to large-scale diabatic heating is not readily found by conventional zonal averaging in isobaric coordinates. By introducing, the concept of a zonally averaged general circulation in isentropic coordinates, a direct meridional response to diabatic heating is isolated. Using an approach analogous to Eliassen's, this study has extended the concept of diabatically forced isentropic meridional circulations to include the role of angular momentum torques within the circumpolar vortex. The absolute angular momentum torques comprise three terms: divergence of eddy relative momentum transport, friction and zonal pressure torques. The heating is composed of hemispheric-scale diabatic processes. For a hydrodynamically and statically stable atmosphere, a co...

A Reexamination of Limited-Area Available Potential Energy Budget Equations

Abstract Previous formulations of the limited area available potential energy (APE) budget equations in isobaric coordinates are examined based on computations performed on cyclone systems. It is shown that two terms can be two orders of magnitude greater than other APE and kinetic energy budget terms. These two terms are nearly equal in magnitude and opposite in sign. A new formulation of APE budget equations is developed. The advantages of this formulation over previous ones are that several terms have clearer physical interpretations and all terms in the equation have the same order of magnitude. A comparison of the different forms of the equations is given.

Azimuthally Averaged Transport and Budget Equations for Storms: Quasi-Lagrangian Diagnostics

Abstract The azimuthally averaged transport and budget equations for a translating storm volume are derived in generalized coordinates. The mean and eddy lateral modes of transport by rotational and irrotational motion are contrasted in symmetric and asymmetric vortices. By contrasting the transport relations in isobaric, cartesian, and isentropic coordinates, the results establish that hydrostatic-rotational regimes of atmospheric motion are typified by eddy modes of transport in isobaric and cartesian coordinates, while both mean and eddy modes may be present in isentropic coordinates. This requirement for a “handover” from an eddy mode of transport in the hydrostatic-rotational environment of a vortex to a mean mode of transport via irrotational motion within a vortex is discussed. Evidence for the existence of mean meridional circulation in isentropic coordinates for the Midwest extratropical cyclone of 22–24 April 1968 is presented. The inward mass transport in the lower troposphere and outward mass ...

Some further considerations concerning energy budgets of moving systems

Equations for the available potential energy and kinetic energy budgets of a moving open system are developed in isobaric coordinates. Three equations constitute the final set, the first two representing the available potential energy changes due to baroclinic and barotropic processes, referred to as the baroclinic and barotropic contributions after Johnson (1970), and the third representing the kinetic energy changes in the system. The terms in the equations bear a resemblance to those presented by Johnson with the exception that a new term is introduced which explicitly relates the effect of the changing reference state of an individual system to its change in available potential energy. A discussion of the various energy budget terms is given and a method of solving the set of equations is proposed. DOI: 10.1111/j.2153-3490.1973.tb00606.x