A vorticity-and-stability diagram as a means to study potential vorticity nonconservation

The study of atmospheric circulation from a potential vorticity (PV) perspective has advanced our mechanistic understanding of the development and propagation of weather systems. The formation of PV anomalies by nonconservative processes can provide additional insight into the diabatic-to-adiabatic coupling in the atmosphere. PV nonconservation can be driven by changes in static stability, vorticity or a combination of both. For example, in the presence of localized latent heating, the static stability increases below the level of maximum heating and decreases above this level. However, the vorticity changes in response to the changes in static stability (and vice versa), making it difficult to disentangle stability from vorticity-driven PV changes. Further diabatic processes, such as friction or turbulent momentum mixing, result in momentum-driven, and hence vorticity-driven, PV changes in the absence of moist diabatic processes. In this study, a vorticity-and-stability diagram is introduced as a means to study and identify periods of stability- and vorticity-driven changes in PV. Potential insights and limitations from such a hyperbolic diagram are investigated based on three case studies. The first case is an idealized warm conveyor belt (WCB) in a baroclinic channel simulation. The simulation allows only condensation and evaporation. In this idealized case, PV along the WCB is first conserved, while stability decreases and vorticity increases as the air parcels move poleward near the surface in the cyclone warm sector. The subsequent PV modification and increase during the strong WCB ascent is, at low levels, dominated by an increase in static stability. However, the following PV decrease at upper levels is due to a decrease in absolute vorticity with only small changes in static stability. The vorticity decrease occurs first at a rate of 0.5 f per hour and later decreases to approximately 0.25 f per hour, while static stability is fairly well conserved throughout the period of PV reduction. One possible explanation for this observation is the combined influence of diabatic and adiabatic processes on vorticity and static stability. At upper levels, large-scale divergence ahead of the trough leads to a negative vorticity tendency and a positive static stability tendency. In a dry atmosphere, the two changes would occur in tandem to conserve PV. In the case of additional diabatic heating in the mid troposphere, the positive static stability tendency caused by the dry dynamics appears to be offset by the diabatic tendency to reduce the static stability above the level of maximum heating. This combination of diabatically and adiabatically driven static stability changes leads to its conservation, while the adiabatically forced negative vorticity tendency continues. Hence, PV is not conserved and reduces along the upper branch of the WCB. Second, in a fullfledged real case study with the Integrated Forecasting System (IFS), the PV changes along the WCB appear to be dominated by vorticity changes throughout the flow of the air. However, accumulated PV tendencies are dominated by latent heat release from the large-scale cloud and convection schemes, which mainly produce temperature tendencies. The absolute vorticity decrease during the period of PV reduction lasts for several hours, and is first in the order of 0.5 f per hour and later decreases to 0.1f per hour when latent heat release becomes small, while static stability reduces moderately. PV and absolute vorticity turn negative after several hours. In a third case study of an air parcel impinging on the warm front of an extratropical cyclone, changes in the horizontal PV components dominate the total PV change along the flow and thereby violate a key approximation of the two-dimensional vorticity-and-stability diagram. In such a situation where the PV change cannot be approximated by its vertical component, a higher-dimensional vorticity-and-stability diagram is required. Nevertheless, the vorticity-and-stability diagram can provide supplementary insights into the nature of diabatic PV changes.

Development Processes of the Explosive Cyclones over the Northwest Pacific: Potential Vorticity Tendency Inversion

A novel method that quantitatively evaluates the development processes of extratropical cyclones is devised and applied to the explosive cyclones over the Northwest Pacific in the cold season (October–April). By inverting the potential vorticity (PV) tendency equation, the contribution of dynamic and thermodynamic processes at different levels to explosive cyclone development is quantified. In terms of geostrophic vorticity tendency at 850 hPa, which is utilized to quantify cyclone development, the leading factors for the explosive cyclone intensification are upper-level PV advection by the mean zonal flow and the PV production from latent heating. However, explosive cyclones are also subject to hindrances from vertical and meridional PV advections. Quantitatively, the sum of thermodynamic contributions by the latent heating, vertical PV advection, and surface temperature tendency is about 1.6 times more important than the dynamical PV redistribution by horizontal advections on the explosive cyclone intensification. This result confirms the dominant role of thermodynamic processes in explosive cyclone development over the Northwest Pacific. It turns out from further analysis that the interactions of lower-level anomalous flows are important for thermodynamic processes, whereas the advections by the upper-level mean flow are primary for dynamic processes.

The Compressional Beta Effect: Analytical Solution, Numerical Benchmark, and Data Analysis

This study derives a complete set of equatorially confined wave solutions from an anelastic equation set with the complete Coriolis terms, which include both the vertical and meridional planetary vorticity. The propagation mechanism can change with the effective static stability. When the effective static stability reduces to neutral, buoyancy ceases, but the role of buoyancy as an eastward-propagation mechanism is replaced by the compressional beta effect (i.e., vertical density-weighted advection of the meridional planetary vorticity). For example, the Kelvin mode becomes a compressional Rossby mode. Compressional Rossby waves are meridional vorticity disturbances that propagate eastward owing to the compressional beta effect. The compressional Rossby wave solutions can serve as a benchmark to validate the implementation of the nontraditional Coriolis terms (NCTs) in numerical models; with an effectively neutral condition and initial large-scale disturbances given a half vertical wavelength spanning the troposphere on Earth, compressional Rossby waves are expected to propagate eastward at a phase speed of 0.24 m s−1. The phase speed increases with the planetary rotation rate and the vertical wavelength and also changes with the density scale height. Besides, the compressional beta effect and the meridional vorticity tendency are reconstructed using reanalysis data and regressed upon tropical precipitation filtered for the Madden–Julian oscillation (MJO). The results suggest that the compressional beta effect contributes 10.8% of the meridional vorticity tendency associated with the MJO in terms of the ratio of the minimum values.

Predictability of the Strong Ural blocking Event in January 2012 in the Subseasonal to Seasonal Models of Europe and Canada

The occurrence of a Ural blocking (UB) event is an important precursor of severe cold air outbreaks in Siberia and East Asia, and thus is significant to accurately predict UB events. Using subseasonal to seasonal (S2S) models of the European Centre for Medium-Range Weather Forecasts (ECMWF) and the Environment and Climate Change Canada (ECCC), we evaluated the predictability of a persistent UB event on 18 to 26 January 2012. Results showed that the ECCC model was superior to the ECMWF model in predicting the development stage of the UB event ten days in advance, while the ECMWF model had better predictions than the ECCC model for more than ten days in advance and the decaying stage of the UB event. By comparing the dynamic and thermodynamic evolution of the UB event predicted by the two models via the geostrophic vorticity tendency equation and temperature tendency equation, we found that the ECCC model better predicted the vertical vorticity advection, ageostrophic vorticity tendency, the tilting effect, horizontal temperature advection, and adiabatic heating during the development stage, whereas the ECMWF model better predicted the three dynamic and the two thermodynamic terms during the decaying stage. In addition, during both the development and decaying stages, the two models were good (bad) at predicting the vortex stretching term (horizontal vorticity advection), with the PCC between both the predictions and the observations larger (smaller) than +0.70 (+0.10) Thus, we suggest that the prediction of the persistent UB event in the S2S model might be improved by the better prediction of the horizontal vorticity advection.

Sensitivity of Tropical Cyclone Track to the Vertical Structure of a Nearby Monsoon Gyre

The impact of different vertical structures of a nearby monsoon gyre (MG) on a tropical cyclone (TC) track is investigated using idealized numerical simulations. In the experiment with a relatively deeper MG, the TC experiences a sharp northward turn at a critical point when its zonal westward-moving speed slows down to zero. At the same time, the total vorticity tendency for the TC wavenumber-1 component nearly vanishes as the vorticity advection by the MG cancels the vorticity advection by the TC. At this point, the TC motion is dominated by the beta effect, as in a no-mean-flow environment, and takes a sharp northward turn. In contrast, the TC does not exhibit a sharp northward turn with a shallower MG nearby. In the case with a deeper MG, a greater relative vorticity gradient of the MG promotes a quicker attraction between the TC and MG through the vorticity segregation process. In addition, a larger outer size of the TC also favors a faster westward propagation from its initial position, thus having more potential to collocate with the MG. Once the coalescence is in place, the Rossby wave energy dispersion associated with the TC and MG together is enhanced and rapidly strengthens the southwesterly flow on the eastern flank of both systems. The steering flow from both the beta gyre and the Rossby wave dispersion leads the TC to take a sharp northward track when the total vorticity tendency is at its minimum. This study indicates the importance of good representations of the TC structure and its nearby environmental flows in order to accurately predict TC motions.

The Role of Convective Heating in Tropical Cyclone Eyewall Ring Evolution

The purpose of this study is to analyze the role of diabatic heating in tropical cyclone ring structure evolution. A full-physics three-dimensional modeling framework is used to compare the results with two-dimensional modeling approaches and to point to limitations of the barotropic instability theory in predicting the storm vorticity structure configuration. A potential vorticity budget analysis reveals that diabatic heating is a leading-order term and that it is largely offset by potential vorticity advection. Sawyer–Eliassen integrations are used to diagnose the secondary circulation (and corresponding vorticity tendency) forced by prescribed heating. These integrations suggest that diabatic heating forces a secondary circulation (and associated vorticity tendency) that helps maintain the original ring structure in a feedback process. Sensitivity experiments of the Sawyer–Eliassen model reveal that the magnitude of the vorticity tendency is proportional to that of the prescribed heating, indicating that diabatic heating plays a critical role in adjusting and maintaining the eyewall ring.

Interactions between Typhoon Megi (2010) and a Low-Frequency Monsoon Gyre

The ARW Model is used to investigate the sharp northward turn of Super Typhoon Megi (2010) after it moved westward and crossed the Philippines. The NCEP analyzed fields during this period are separated into a slowly varying background-flow component, a 10–60-day low-frequency component representing the monsoon gyre, and a 10-day high-pass-filtered component representing Megi and other synoptic-scale motion. It appears that the low-frequency (10–60 day) monsoon gyre interacted with Megi and affected its track. To investigate the effect of the low-frequency mode on Megi, numerical experiments were designed. In the control experiment, the total fields of the analysis are retained in the initial and boundary conditions, and the model is able to simulate Megi’s sharp northward turn. In the second experiment, the 10–60-day monsoon gyre mode is removed from the initial and lateral boundary fields, and Megi moves westward and slightly northwestward without turning north. Tracks of the relative positions between the Megi and the monsoon gyre centers suggest that a Fujiwhara effect may exist between the monsoon gyre and Megi. The northward turning of both Megi and the monsoon gyre occurred when the two centers were close to each other and the beta drift was enhanced. A vorticity budget analysis was conducted. It is noted that the Megi moves toward the maximum wavenumber-1 vorticity tendency. The sharp change of the maximum vorticity tendency direction before and after the track turning point is primarily attributed to the change of the horizontal vorticity advection. A further diagnosis shows that the steering of the vertically integrated low-frequency flow is crucial for the change of the horizontal advection tendency.

The Vorticity Budgets of North Atlantic Winter Extratropical Cyclone Life Cycles in MERRA Reanalysis. Part II: Decaying Phase*

The role of physical forcing mechanisms that contribute to the decay of winter North Atlantic extratropical cyclones during the period 1979–2009 are examined using the Modern-Era Retrospective Analysis for Research and Applications (MERRA). The paired Zwack–Okossi tendency equation and omega equation explained in part I of this paper is employed to investigate the total effects of forcing processes (the direct effect of the forcing mechanisms and the indirect effect of the induced adiabatic cooling) that dissipate the 950-hPa cyclonic geostrophic vorticity at the cyclone center. Composite analyses reveal that the commencement of the decay is associated mainly with the upper-level anticyclonic vorticity advection, cold-air advection, and positive ageostrophic vorticity tendency. The secondary contributor to the dissipation of cyclonic circulation is the lower-tropospheric adiabatic cooling induced mainly by friction and positive ageostrophic vorticity tendency. The dynamics is found to be different at the beginning of the decay than in the later stages. While the negative tilt of troughs aloft and the surface cyclone is required for cyclolysis to occur, low air processes show a greater effect in the termination of the low pressure systems. Further, the total effect of the vorticity advection and temperature advection terms are modest, while the ageostrophic vorticity tendency and friction terms show a greater total negative contribution. This is because the two latter terms decrease the cyclonic geostrophic vorticity at the low center through both their direct and indirect effects. The latent heat release maximizing at 800–700 hPa produces cyclonic circulation, thus reducing the spindown of decaying cyclones.

The Vorticity Budgets of North Atlantic Winter Extratropical Cyclone Life Cycles in MERRA Reanalysis. Part I: Development Phase*

This series of papers (parts I and II) examines the vorticity budgets of winter North Atlantic extratropical cyclones during the period 1979–2009 using the Modern-Era Retrospective Analysis for Research and Application (MERRA). The authors use a new partitioning technique to combine the Zwack–Okossi (Z–O) equation with the omega equation. The combination provides a possibility to partition the adiabatic term in the Z–O equation into its different forcing mechanisms. Thus, both the direct effect of the dynamic and thermodynamic forcings and their indirect effect on the adiabatic term can be calculated to provide the total effect (direct plus indirect) on the 950-hPa geostrophic vorticity tendency. It is demonstrated that the total-effect diagnostic is a suitable tool to identify the dynamically consistent characteristics of cyclone development in midlatitudes because it possesses less case-to-case variability. The authors found that the vorticity advection is the major forcing process, the tendencies attributed to the ageostrophic vorticity tendency term are considerable, and the opposing effect of the friction term in moderating the deepening is significant. In general, the upper-level dynamics drive the deepening of the cyclones, except at the end of development, where a combination of midlevel latent heating, positive ageostrophic vorticity tendency, and positive indirect effect of vorticity advection contribute to the development. Additionally, the total effects of temperature advection and latent heating on the intensification of cyclones are reduced because of the inclusion of counteractive indirect effects, as are their variabilities within the cyclone composite.