Rossby-Ertel Potential Vorticity Research Articles

The diabatic contour‐advective semi‐Lagrangian algorithms for the dynamical core of global models in terrain‐following isentropic and pressure vertical coordinates

AbstractDesign, development and assessment of numerical algorithms based on Rossby–Ertel potential vorticity (PV) for the dynamical core of global models are of particular importance in atmospheric and oceanic modelling for improving representation of both balanced and unbalanced flows. The general circulation models are usually developed in various vertical coordinates and horizontal grids. The Diabatic Contour‐Advective Semi‐Lagrangian (DCASL) algorithm based on contour representation of an approximate form of PV is further developed by (a) inclusion of a form of arbitrary Lagrangian–Eulerian method for the hybrid – vertical coordinate, and (b) extension to the –p vertical coordinate with both Charney–Phillips (CP) and Lorenz (L) grids. Using a baroclinic instability test case, the working of DCASL in the newly developed – is compared with two other forms of DCASL in –p developed with CP and L grids. These comparisons show that the initialisation problem present in – vertical coordinate is removed and the solutions become close to the numerically convergent solutions of four other dynamical cores, within the range of their uncertainties, when the –p vertical coordinate is used. Results also show the usefulness of DCASL in –p, even though the prognostic variable representing vortical flow is less materially conservative than that of the –.

The Relation between Beltrami's Material Vorticity and Rossby–Ertel's Potential Vorticity

Abstract It is shown that there is an exact correspondence between the scalar Rossby–Ertel's potential vorticity (PV) for a field e, and the component of Beltrami's material vorticity along the e-coordinate line (first equivalence theorem). Thus, Rossby–Ertel's PV can be interpreted as a particular case (scalar) of the vectorial Beltrami's material vorticity. The rate of change of Beltrami's vorticity only depends on the curl of the acceleration (or baroclinic–diffusive terms in the rate of change of vorticity) and not on the convective rate of change (involving advection, stretching, and divergence terms). When the motion is circulation preserving (the acceleration is irrotational) Cauchy's vorticity formula states that Beltrami's material vorticity is conserved. However, when the curl of the acceleration is zero only along the direction normal to certain e surfaces, only the e component of Beltrami's material vorticity is conserved. Thus, a second equivalence theorem states that Ertel's PV conservation ...

Small Mesoscale Features at a Meandering Upper-Ocean Front in the Western Ionian Sea (Mediterranean Sea): Vertical Motion and Potential Vorticity Analysis

Abstract Transient mesoscale and submesoscale processes, such as small eddies and filaments, could play a fundamental role in the marine ecosystem, especially in oligotrophic seas like the Mediterranean. However, very little is known about the biological and physical dynamics characterizing such structures. In this work, the 8-km horizontal resolution data collected during the SYMPLEX 1998 survey are analyzed to describe the physical dynamics of small mesoscale features along the Atlantic–Ionian stream (western Ionian Sea). The data were optimally interpolated over a regular grid and used to compute the 3D ageostrophic circulation by solution of the Q-vector formulation of the omega equation. The relative importance of stratification, relative vorticity, and twisting terms in the Rossby–Ertel potential vorticity is thus examined along selected isopycnals, together with the associated vertical motions and vortex stretching. A surface cyclonic eddy ∼15 km of radius was observed near a meander of the Atlanti...

Simulations of the February 1979 Stratospheric Sudden Warming: Model Comparisons and Three-Dimensional Evolution

The evolution of the stratospheric flow during the major stratospheric sudden warming of February 1979 is studied using two primitive equation models of the stratosphere and mesosphere. The United Kingdom Meteorological Office Stratosphere-Mesosphere Model (SMM) uses log pressure as a vertical coordinate. A spectral, entropy coordinate version of the SMM (entropy coordinate model, or ECM) that has recently been developed is also used. Both models produce similar successful simulations through the peak of the warming, capturing the splitting of the vortex and the development of small-scale structures, such as narrow baroclinic zones. The ECM produces a more realistic recombination and recovery of the polar vortex in the midstratosphere after the warming, due mainly to better conservation properties for Rossby-Ertel potential vorticity in this model. Another advantage of the ECM is the automatic increase in vertical resolution near baroclinic zones. Comparison of SMM simulations with forecasts performed using the University of California, Los Angeles general circulation model confirms the previously noted sensitivity of stratospheric forecasts to tropospheric forecast and emphasizes the importance of adequate vertical resolution in modeling the stratosphere. The ECM simulators provide a schematic description of the three-dimensional evolution of the polar vortex and the motion of air through it. During the warming, the two cyclonic vortices till westward and equatorward with height. Strong upward velocities develop in the lower stratosphere on the west (cold) side of a baroclinic zone as it forms over Europe and Asia. Strong downward velocities appear in the upper stratosphere on the east (warm) side, strengthening the temperature gradients. After the peak of the warming, vertical velocities decrease, downward velocities move into the lower stratosphere, and upward velocities move into the upper stratosphere. Transport calculations show that air with high ozone mixing ratios is advected toward the pole from low latitudes during the warming, and air with low ozone mixing ratios is transported to the midstratosphere from both higher and lower altitudes along the baroclinic zone in the polar regions. Trajectories of parcels moving around the vortex oscillate up and down as they move through regions of ascending and descending motions, with an overall increase in pressure in the polar regions. Tracer transport and trajectory calculations show enhanced diabatic descent in the region between cyclone and anticyclone during the warming, consistent with the temperature structure shown.

Towards a PV-<i>θ</i> view of the general circulation

In recent years, there has been a resurgence of interest in using isentropic coordinates and Rossby-Ertel potential vorticity (PV) for diagnosing the behaviour of middle latitude synoptic systems. Such a PV-θ analysis may also prove important in providing insight into the global circulation of the atmosphere. Apart from the isentropic diagnostic of D. Johnson and collaborators, some quasi-geostrophic studies and recent studies of stratospheric behaviour, there has been little work in this area and our present understanding is very limited. The object of the present paper is to stimulate such studies by presenting some initial results from continuing research. A three-fold division of the atmosphere is discussed. The “Overworld” is the region encompassed by isentropic surfaces that are everywhere above the tropopause. In the “Middleworld”, the region with isentropes crossing the tropopause but not striking the Earth’s surface, the isentropic zonal and time mean of PV exhibits interesting regions of enhanced and diminished gradients. The isentropic transient eddy advection of PV exhibits a dipolar distribution about the tropopause, suggestive of PV mixing. The marked PV signature of the Asian summer monsoon on one particular Middleworld isentrope is shown and the mean isentropic advection of PV shows interesting features. For the “Underworld”, in which isentropic surfaces intercept the surface of the Earth, a PV-θ analysis yields a novel constraint linking low-level drag and diabatic heating. This constraint links “westerlies” and “cooling”, and “easterlies” and “heating” in some average sense. The result is discussed in terms of the Southern Hemisphere strong surface westerlies and the circulation associated with the Asian summer and winter monsoons.

Towards a PV-θ view of the general circulation

In recent years, there has been a resurgence of interest in using isentropic coordinates and Rossby-Ertel potential vorticity (PV) for diagnosing the behaviour of middle latitude synoptic systems. Such a PV- θ analysis may also prove important in providing insight into the global circulation of the atmosphere. Apart from the isentropic diagnostic of D. Johnson and collaborators, some quasi-geostrophic studies and recent studies of stratospheric behaviour, there has been little work in this area and our present understanding is very limited. The object of the present paper is to stimulate such studies by presenting some initial results from continuing research. A three-fold division of the atmosphere is discussed. The “Overworld” is the region encompassed by isentropic surfaces that are everywhere above the tropopause. In the “Middleworld”, the region with isentropes crossing the tropopause but not striking the Earth's surface, the isentropic zonal and time mean of PV exhibits interesting regions of enhanced and diminished gradients. The isentropic transient eddy advection of PV exhibits a dipolar distribution about the tropopause, suggestive of PV mixing. The marked PV signature of the Asian summer monsoon on one particular Middleworld isentrope is shown and the mean isentropic advection of PV shows interesting features. For the “Underworld”, in which isentropic surfaces intercept the surface of the Earth, a PV- θ analysis yields a novel constraint linking lowlevel drag and diabatic heating. This constraint links “westerlies” and “cooling”, and “easterlies” and “heating” in some average sense. The result is discussed in terms of the Southern Hemisphere strong surface westerlies and the circulation associated with the Asian summer and winter monsoons. DOI: 10.1034/j.1600-0870.1991.t01-3-00005.x

On the Conservation and Impermeability Theorems for Potential Vorticity

If the partial analogy between the behavior of Rossby-Ertel potential vorticity (PV) and the behavior of chemical tracers is to be correctly used in the general case of diabatic, frictional motion, then certain fundamental differences, as well as similarities, between the behavior of PV and that of chemical tracers must be recognized. These differences stem from the well-known kinematical relationship between PV and isentropic circulation (via Stokes' theorem), which has no counterpart for chemical substances. One way of stating the analogy while recognizing the differences is to say first that PV behaves like the mixing ratio of a peculiar chemical “substance” that has zero source; i.e., is exactly conserved, away from boundaries (conserved not in the material or Lagrangian sense, but in the general sense associated with the idea of an indestructible chemical substance), and second that isentropic surfaces behave exactly as if they were impermeable to this “PV-substance” or “PVS,” even when diabatic heating or cooling, including that associated with turbulent mixing, makes them permeable to mass and chemical substances. In this respect isentropic surfaces can be said to act like semipermeable membranes. The PV itself can of course change, as can the mixing ratio of an exactly conserved chemical substance or decay-corrected radioactive tracer. For instance, all these mixing ratios can change by dilution when cumulonimbus clouds penetrate isentropic surfaces in a tropopause fold. The net flux or transport of PVS along isentropic surfaces can be either up or down any pre-existing isentropic gradient of PV. For instance the typical effect of the small-scale turbulence due to breaking internal gravity waves is to transport PVS along isentropes in a gradient-independent sense, while transporting chemical substances across isentropes in a downgradient sense. It is the turbulent transport of PVS along isentropes that gives rise to the phenomenon of gravity-wave drag. Such a transport is absent from the formulation given in Danielsen (1990), which supposes that PV always behaves like the mixing ratio of a chemical even in three-dimensionally turbulent flow. The latter supposition is demonstrably incorrect.

On the Evolution of Vorticity and Potential Vorticity in the Presence of Diabatic Heating and Frictional or Other Forces

Abstract Some consequences of regarding potential vorticity as a tracer are considered. It is shown that neither diabatic heating, nor frictional forces, nor external forces such as might be used to model gravity-wave drag, can bring about any net transport or Rossby-Ertel potential vorticity (PV) across an isotropic surface—notwithstanding the diabatic, cross-isentropic transport of mass and chemical tracers. Nor can PV be created or destroyed within a layer bounded by two isentropic surface. It can only be transported along the layer. and diluted or concentrated by cross-isentropic mass inflow or outflow. This constitutes a systematic difference between the behavior of PV and that of other tracers, recognition of which simplifies thinking about PV budgets and gives insight into the relationships between dynamical processes, departures from radiatively determined temperatures, and chemical tracer transport including stratosphere-troposphere exchange. The results just stated are true by virtue of the way ...