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The e-folding time associated with regions of inertial instability at 850 hPa at 1800 UTC 30 Jul 1979 diagnosed with (a) the gradient criterion and (b) the traditional criterion. The e-folding time is given by 1/ ffiffi ffi I p , where I 5 (f 1 2V/R)(z 1 f ) in (a) and I 5 f (z 1 f ) in (b). Streamfunction contours are black with an interval of 2 3 10 6 m 2 s 21. To better resolve these fields on a regional domain, the 0.258 3 0.258 latitude-longitude reanalysis is used.
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A climatology of tropospheric inertial instability is constructed using the European Centre for Medium-Range Weather Forecasts interim reanalysis (ERA-Interim) at 250, 500, and 850 hPa. For each level, two criteria are used. The first criterion is the traditional criterion of absolute vorticity that is opposite in sign to the local Coriolis paramet...
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Citations
... The condition PV < 0 is used here primarily to identify regions of inertial instability (e.g., Kim et al., 2014;Knox & Harvey, 2005;Sato & Dunkerton, 2002;Trier & Sharman, 2016) which may be favorable for the generation of CAT. Inertial instability is primarily generated by negative relative vorticity in strong anticyclonic shear and curvature flows in the NH (e.g., Holton, 1992;Jaeger & Sprenger, 2007;Thompson et al., 2018). However, as with the Ri, PV can be negative when the absolute vorticity is positive and N 2 < 0 as well. ...
Spatial and temporal distributions of Clear‐Air Turbulence (CAT) in the Northern Hemisphere were investigated using 41 years (1979–2019) of the European Centre for Medium‐range Weather Forecast Reanalysis version 5 (ERA5) data. We used two groups of CAT diagnostics to determine occurrence frequencies: (a) commonly used empirical turbulence indices (TI1, TI2, and TI3) and their components [vertical wind shear (VWS), deformation, ‐divergence, and divergence tendency], and (b) theoretical instability indicators [Richardson number (Ri), potential vorticity (PV), and Brunt‐Vӓisӓlӓ frequency]. The empirical indices showed high frequencies of moderate‐or‐greater (MOG)‐level CAT potential over the East Asian, Eastern Pacific, and Northwestern Atlantic regions in winter. Over East Asia, the entrance region of strong upper‐level jets showed the highest frequencies in TI1, TI2, and TI3 due mainly to strong VWS. The Eastern Pacific and Northwestern Atlantic areas near the exit region of jets had relatively high frequencies of these indices and also Ri. PV frequency was high on the southern side of jet primarily due to negative relative vorticity. Long‐term increasing trends of MOG‐level CAT potential also appeared in those three regions mainly due to warming in lower latitudes. The most significant increasing trend was found over East Asia, due to the strengthening of the East Asian jet and increased VWS due to the strong meridional temperature gradients in the mid‐troposphere induced by warming in the tropics and cooling in eastern Eurasia. These trends over East Asia, if continued, are expected to be of importance to efficient aviation operations across the northwestern Pacific Ocean.
... In this study, the e-folding time of the initialized instability is approximately 5 h. Therefore, as no seeded perturbations are specified to trigger the release of the instability, and given that previous studies indicate that regions of inertial instability may be long-lived (e.g., Sato & Dunkerton, 2002;Schultz & Knox, 2007;Thompson et al., 2018), simulations are run for 14 model days to allow sufficient time for the growth of meridional perturbations (i.e., the release of the instability). ...
Plain Language Summary
The jet stream is a narrow region of strong westerly winds above the Earth's surface over the midlatitudes in the Northern and Southern Hemispheres. When winds speeds decrease too sharply laterally on the equatorward side of the jet stream, the flow is said to be in state of inertial instability. How the atmosphere responds to the instability in this situation is not well understood. To gain a better understanding, we used a numerical model to simulate an idealized jet stream with inertial instability against a control jet stream with no instability. We find that the simulation with the instability produced stationary ribbon‐shaped circulations along the jet within the unstable region, in addition to circulations called inertia–gravity waves that propagate several hundred kilometers away from the unstable region. Although these inertia–gravity waves have been suggested to instigate clear‐air turbulence, we find that the ribbon‐shaped regions of enhanced north–south winds themselves instigate light–moderate instances of clear‐air turbulence that can last for up to 12 h. Further research on whether this result is found in the real atmosphere has the potential to improve weather forecasts for the aviation sector.
... This method has been largely applied in the atmospheric field (Brill 2014;Thompson et al. 2018;Cohen et al. 2019). In oceanography, the study of the gradient-wind balance in ocean eddies has been less frequent, but Olson et al. (1985), Chassignet et al. (1990), Olson (1991), and more recently Penven et al. (2014), Douglass and Richman (2015), and Chassignet and Xu (2017), showed that strong, nonlinear eddies in the North Atlantic, the Mozambique Channel, and the Agulhas Current are in gradient-wind balance. ...
The Loop Current (LC) system has long been assumed to be close to geostrophic balance despite its strong flow and the development of large meanders and strong frontal eddies during unstable phases. The region between the LC meanders and its frontal eddies was shown to have high Rossby numbers indicating nonlinearity; however, the effect of the nonlinear term on the flow has not been studied so far. In this study, the ageostrophy of the LC meanders is assessed using a high-resolution numerical model and geostrophic velocities from altimetry. A formula to compute the radius of curvature of the flow from the velocity field is also presented. The results indicate that during strong meandering, especially before and during LC shedding and in the presence of frontal eddies, the centrifugal force becomes as important as the Coriolis force and the pressure-gradient force: LC meanders are in gradient-wind balance. The centrifugal force modulates the balance and modifies the flow speed, resulting in a subgeostrophic flow in the LC meander trough around the LCFE and supergeostrophic flow in the LC meander crest. The same pattern is found when correcting the geostrophic velocities from altimetry to account for the centrifugal force. The ageostrophic percentage in the cyclonic and anticyclonic meanders is 47% ± 1% and 78% ± 8% in the model and 31% ± 3% and 78% ± 29% in the altimetry dataset, respectively. Thus, the ageostrophic velocity is an important component of the LC flow and cannot be neglected when studying the LC system.
... These regions can be hydrostatically, inertially, or symmetrically unstable (e.g., Hoskins, 2015) and can form mesoscale circulations associated with, e.g., frontal rainbands (Bennetts and Hoskins, 1979;Schultz and Schumacher, 1999;Siedersleben and Gohm, 2016), sting jets (Clark et al., 2005;Volonté et al., 2018Volonté et al., , 2019, enhanced stratosphere-troposphere exchange (Rowe and Hitchman, 2015), and local jet accelerations and northward displacements (Rowe and Hitchman, 2016). The adjustment timescales for the release of these instabilities range from minutes for hydrostatic instability to several hours for inertial instability (timescale is proportional to [−f (f + ζ )] −0.5 ) (Schultz and Schumacher, 1999;Thompson et al., 2018). Thus, while hydrostatic instability is rapidly released and near-neutral conditions are established, inertial instability can prevail for several hours and therefore synoptic-scale regions of inertial instability can be found, for instance at the anticyclonic shear side of midlatitude ridges (Thompson et al., 2018). ...
... The adjustment timescales for the release of these instabilities range from minutes for hydrostatic instability to several hours for inertial instability (timescale is proportional to [−f (f + ζ )] −0.5 ) (Schultz and Schumacher, 1999;Thompson et al., 2018). Thus, while hydrostatic instability is rapidly released and near-neutral conditions are established, inertial instability can prevail for several hours and therefore synoptic-scale regions of inertial instability can be found, for instance at the anticyclonic shear side of midlatitude ridges (Thompson et al., 2018). ...
... 4.2 we will see that the negative PV pole, produced by convective WCB trajectories, persists for several hours. This is consistent with adjustment timescales of several hours (e.g., Thompson et al., 2018) in inertially unstable regions where f + ζ < 0. A convectively unstable atmo-sphere (dθ/dz < 0), in contrast, would adjust to stability on a timescale of less than 1 h (Schultz and Schumacher, 1999). ...
Warm conveyor belts (WCBs) are important airstreams in extratropical cyclones. They can influence large-scale flow evolution by modifying the potential vorticity (PV) distribution during their cross-isentropic ascent. Although WCBs are typically described as slantwise-ascending and stratiform-cloud-producing airstreams, recent studies identified convective activity embedded within the large-scale WCB cloud band. However, the impacts of this WCB-embedded convection have not been investigated in detail. In this study, we systematically analyze the influence of embedded convection in an eastern North Atlantic WCB on the cloud and precipitation structure, on the PV distribution, and on larger-scale flow. For this reason, we apply online trajectories in a high-resolution convection-permitting simulation and perform a composite analysis to compare quasi-vertically ascending convective WCB trajectories with typical slantwise-ascending WCB trajectories. We find that the convective WCB ascent leads to substantially stronger surface precipitation and the formation of graupel in the middle to upper troposphere, which is absent for the slantwise WCB category, indicating the key role of WCB-embedded convection for precipitation extremes. Compared to the slantwise WCB trajectories, the initial equivalent potential temperature of the convective WCB trajectories is higher, and the convective WCB trajectories originate from a region of larger potential instability, which gives rise to more intense cloud diabatic heating and stronger cross-isentropic ascent. Moreover, the signature of embedded convection is distinctly imprinted in the PV structure. The diabatically generated low-level positive PV anomalies, associated with a cyclonic circulation anomaly, are substantially stronger for the convective WCB trajectories. The slantwise WCB trajectories lead to the formation of a widespread region of low-PV air (that still have weakly positive PV values) in the upper troposphere, in agreement with previous studies. In contrast, the convective WCB trajectories form mesoscale horizontal PV dipoles at upper levels, with one pole reaching negative PV values. On a larger scale, these individual mesoscale PV anomalies can aggregate to elongated PV dipole bands extending from the convective updraft region, which are associated with coherent larger-scale circulation anomalies. An illustrative example of such a convectively generated PV dipole band shows that within around 10 h the negative PV pole is advected closer to the upper-level waveguide, where it strengthens the isentropic PV gradient and contributes to the formation of a jet streak. This suggests that the mesoscale PV anomalies produced by embedded convection upstream organize and persist for several hours and therefore can influence the synoptic-scale circulation. They thus can be dynamically relevant, influence the jet stream and (potentially) the downstream flow evolution, which are highly relevant aspects for medium-range weather forecast. Finally, our results imply that a distinction between slantwise and convective WCB trajectories is meaningful because the convective WCB trajectories are characterized by distinct properties.
... In section 5 we will see that the negative PV pole, produced by convective WCB trajectories, persists for several hours. This is consistent with adjustment timescales of several hours (e.g., Thompson et al., 2018) in inertially unstable regions where f + ζ < 0. A convectively unstable atmosphere (dθ/dz < 0), in contrast, would adjust to stability on a timescale of less than For both WCB categories static stability is reduced in the upper troposphere near the WCB outflow (Fig. 6e,f, white hatching). The static stability reduction above the convective WCB is stronger (Fig. 6e), but the slantwise WCB leads to a reduced static stability over a larger region (Fig. 6f). ...
Warm conveyor belts (WCBs) are important airstreams in extratropical cyclones. They can influence the large-scale flow evolution due to the modification of the potential vorticity (PV) distribution during their cross-isentropic ascent. Although WCBs are typically described as slantwise ascending and stratiform cloud producing airstreams, recent studies identified convective activity embedded within the large-scale WCB cloud band. Yet, the impacts of this WCB-embedded convection have not been investigated in detail. In this study, we systematically analyse the influence of embedded convection in an eastern North Atlantic WCB on the cloud and precipitation structure, on the PV distribution, and on the larger-scale flow. For this, we apply online trajectories in a high-resolution convection-permitting simulation and perform a composite analysis to compare quasi-vertically ascending convective WCB trajectories with typical slantwise ascending WCB trajectories. We find that the convective WCB ascent leads to stronger surface precipitation including the formation of graupel, which is absent for the slantwise WCB category, indicating the key role of WCB-embedded convection for precipitation extremes. Compared to the slantwise WCB trajectories, the initial equivalent potential temperature of the convective WCB trajectories is higher and they originate from a region of larger potential instability, which gives rise to more intense cloud diabatic processes and stronger cross-isentropic ascent. Moreover, the signature of embedded convection is distinctly imprinted in the PV structure. The diabatically generated low-level positive PV anomalies, associated with a cyclonic circulation anomaly, are substantially stronger for the convective WCB trajectories. While the slantwise WCB trajectories form a wide-spread negative PV anomaly (but still with weakly positive PV values) in the upper troposphere, in agreement with previous studies, the convective WCB trajectories, in contrast, form mesoscale horizontal PV dipoles at upper levels, with one pole reaching negative PV. On the larger-scale, these individual mesoscale PV anomalies can aggregate to elongated PV dipole bands extending from the convective updraft region, which are associated with coherent larger-scale circulation anomalies. An illustrative example of such a convectively generated PV dipole band shows that within around 10 hours the negative PV pole is advected closer to the upper-level waveguide, where it strengthens the isentropic PV gradient and contributes to the formation of a jet streak. This suggests that the mesoscale PV anomalies produced by embedded convection upstream organise and persist for several hours, and therefore can influence the synoptic-scale circulation. They thus can be dynamically relevant. Finally, our results imply that a distinction between slantwise and convective WCB trajectories is meaningful because the convective WCB trajectories are characterized by distinct properties, such as the formation of graupel and of an upper-level PV dipole, which are absent for slantwise WCB trajectories.
... In the troposphere, II is associated with circulations that span the equator and induce cross-equatorial flow, jet structures (Rowe & Hitchman, 2016), and regions where there is large anticyclonic shear and curvature (Fortuin et al., 2003;Thompson et al., 2018). In the stratosphere and mesosphere (where GWs grow to be large-amplitude, break, and deposit momentum to the background flow), II is prevalent in the Tropics when there is meridional shear in the equatorial zonal wind, and when there is cross-equatorial flow during solstice seasons. ...
Rapp, Dörnbrack, and Preusse (2018, https://doi.org/10.1029/2018GL079142) uses radio occultation observations and meteorological data from the European Centre for Medium Range Weather Forecasting to quantify the effect of inertial instability on stratospheric temperature variability. A very interesting by‐product of their study is the take‐away message that inertial instability “pancake structures” may be misidentified as being caused by gravity waves. We place this result in the context of inertial instability research. We concur with Rapp et al.'s caution to researchers to first examine the large‐scale meteorological environment to rule out inertial instability when analyzing temperature fluctuations that appear to be gravity wave signals in vertical profile data.
... We assess its presence (or lack thereof) in the latter by adding the zero contour of low-level (0-3-km-averaged) absolute vorticity z a to Figs. 5d-f. Areas enclosed by the green contours possess z a , 0 and thus satisfy a necessary condition for inertial instability (e.g., Holton 1972;Schultz and Schumacher 1999;Thompson et al. 2018). Our evaluation of z a focuses on lower levels where the z a perturbations are maximized, but the result does not strongly depend on the precise layer chosen for the evaluation (not shown). ...
Elongated and quasi-stationary cloud bands capable of producing heavy precipitation have recently been observed in the lee of midlatitude mountain ridges. Herein, idealized explicit-convection simulations are used to investigate such bands. A methodical sampling of environmental parameter space reveals that the bands are favored by a multilayer upstream static-stability profile, with a conditionally unstable midlevel layer overlying an absolutely stable surface-based layer. Such profiles promote the formation of leeside hydraulic jumps, with deep upright ascent that initiates elevated moist convection. Over smooth ridges, isolated bands develop past each ridge end due to a local superposition of cross-barrier and along-barrier pressure gradients. This superposition enhances leeside vertical displacements compared to parcels traversing the ridge midsection. In the Northern Hemisphere, the Coriolis force favors the left band over the right band (relative to the incoming flow) due to opposite-signed relative-vorticity perturbations past the two ridge ends. Whereas the negative vorticity anomaly past the left end enhances forcing for ascent, the positive vorticity anomaly past the right end suppresses it. For the environmental flows considered herein, the simulated bands are the most persistent over medium-height (1.5-km high) ridges, which force stronger leeside ascent than taller or shorter ridges. Over more rugged terrain, additional bands form past deep gaps or valleys, again due to a local superposition of horizontal pressure gradients. In contrast to some recent studies of orographic cloud bands, these simulated bands owe their existence to the release of moist static instability, indicating that neither slantwise nor inertial instability is required for their formation.
... Besides these very few direct observations, the excitation and properties of II have mainly been studied using numerical models and theory (e.g., Clark & Haynes, 1996;Griffiths, 2003;O'Sullivan & Hitchman, 1992;Rowe & Hitchman, 2015. A stratospheric II climatology based on analyses from the UK Met Office was presented by Knox and Harvey (2005), and the tropospheric II occurrence was documented using ECMWF Re-Analysis-Interim (ERA-Interim) data by Thompson et al. (2018). Importantly, both Knox and Harvey (2005) and Thompson et al. (2018) based their occurrence statistics of II on various instability criteria (see Thompson et al., 2018 for an in-depth discussion of the validity of various criteria) but they did not quantify the impact of the instability on stratospheric temperature variability. ...
... A stratospheric II climatology based on analyses from the UK Met Office was presented by Knox and Harvey (2005), and the tropospheric II occurrence was documented using ECMWF Re-Analysis-Interim (ERA-Interim) data by Thompson et al. (2018). Importantly, both Knox and Harvey (2005) and Thompson et al. (2018) based their occurrence statistics of II on various instability criteria (see Thompson et al., 2018 for an in-depth discussion of the validity of various criteria) but they did not quantify the impact of the instability on stratospheric temperature variability. ...
... A stratospheric II climatology based on analyses from the UK Met Office was presented by Knox and Harvey (2005), and the tropospheric II occurrence was documented using ECMWF Re-Analysis-Interim (ERA-Interim) data by Thompson et al. (2018). Importantly, both Knox and Harvey (2005) and Thompson et al. (2018) based their occurrence statistics of II on various instability criteria (see Thompson et al., 2018 for an in-depth discussion of the validity of various criteria) but they did not quantify the impact of the instability on stratospheric temperature variability. ...
Stratospheric temperature perturbations (TP) that have previousl y been misinterpreted as du e to gravity waves are revisited . The perturbations ob-served by radio occultations during December 2015 had peak-to-peak amplitudes of 10 K extending from t h e Equator to mid-latitud es. The vertically stacked and horizontally flat structures had a vertical wavelength of 12 km.The signs of the TP were 18 0◦ phase shi ft ed between equat o r i al and midlatitudes at fi xed altit u d e levels. High-resolutio n operational analyses reveal that th ese shallow temperature structures were caused by inertial instabil- ity (II) due to the large meridional shear of the polar night jet (PNJ) at ist equatorward flank in combination with Rossby wave breaking. Large stratospheric TP owing to II do frequently occur in th e Northern Hemisphere (South- ern Hemisp h er e) from October to Apri l (April to October) in the 39 years of ERA-Interim data. During 10% of the days, TP exceed 5 K (peak-to -peak) .
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.
