• Agustí-Panareda, A., , S. L. Gray, , and S. E. Belcher, 2009: On the dependence of boundary layer ventilation on frontal type. J. Geophys. Res.,114, D05305, doi:10.1029/2008JD010694.

  • Balasubramanian, G., , and M. K. Yau, 1994: The effects of convection on a simulated marine cyclone. J. Atmos. Sci., 51, 23972417.

  • Balasubramanian, G., , and M. K. Yau, 1996: The life cycle of a simulated marine cyclone: Energetics and PV diagnostics. J. Atmos. Sci., 53, 639653.

    • Search Google Scholar
    • Export Citation
  • Balasubramanian, G., , and S. T. Garner, 1997: The role of momentum fluxes in shaping the life cycle of a baroclinic wave. J. Atmos. Sci., 54, 510533.

    • Search Google Scholar
    • Export Citation
  • Bennets, D. A., , and B. J. Hoskins, 1979: Conditional symmetric instability - A possible explanation for frontal rainbands. Quart. J. Roy. Meteor. Soc., 105, 945962.

    • Search Google Scholar
    • Export Citation
  • Bjerknes, J., 1919: On the structure of moving cyclones. Mon. Wea. Rev., 47, 9599.

  • Boutle, I. A., , S. E. Belcher, , and R. S. Plant, 2011: Moisture transport in midlatitude cyclones. Quart. J. Roy. Meteor. Soc., 137, 360373.

    • Search Google Scholar
    • Export Citation
  • Browning, K. A., 1986: Conceptual models of precipitation systems. Wea. Forecasting, 1, 2341.

  • Browning, K. A., 1990: Organization of clouds and precipitation in extratropical cyclones. Extratropical Cyclones: The Erik Palmén Memorial Volume, C. W. Newton and E. O. Holopainen, Eds., Amer. Meteor. Soc., 129–153.

  • Browning, K. A., 2004: The sting at the end of the tail: Damaging winds associated with extratropical cyclones. Quart. J. Roy. Meteor. Soc., 130, 375399.

    • Search Google Scholar
    • Export Citation
  • Browning, K. A., , and N. M. Roberts, 1994: Structure of a frontal cyclone. Quart. J. Roy. Meteor. Soc., 120, 15351557.

  • Bush, A. B. G., , and W. R. Peltier, 1994: Tropopause folds and synoptic-scale baroclinic wave life cycles. J. Atmos. Sci., 51, 15811604.

    • Search Google Scholar
    • Export Citation
  • Carlson, T. N., 1980: Airflow through midlatitude cyclones and the comma cloud pattern. Mon. Wea. Rev., 108, 14981509.

  • Cooper, I. M., , A. J. Thorpe, , and C. G. Bishop, 1992: The role of diffusive effects on potential vorticity in fronts. Quart. J. Roy. Meteor. Soc., 118, 629647.

    • Search Google Scholar
    • Export Citation
  • Davies, H. C., , C. Schär, , and H. Wernli, 1991: The palette of fronts and cyclones within a baroclinic wave development. J. Atmos. Sci., 48, 16661689.

    • Search Google Scholar
    • Export Citation
  • Davis, C. A., 2010: Simulations of subtropical cyclones in a baroclinic channel model. J. Atmos. Sci., 67, 28712892.

  • Eckhardt, S., , A. Stohl, , H. Wernli, , P. James, , C. Forster, , and N. Spichtinger, 2004: A 15-year climatology of warm conveyor belts. J. Climate, 17, 218237.

    • Search Google Scholar
    • Export Citation
  • Eliassen, A., , and E. Kleinschmidt, 1957: Dynamic meteorology. Handbuch der Physik (Encyclopedia of Physics), S. Flügge, Ed., Springer-Verlag, 1–154.

  • Fantini, M., 2004: Baroclinic instability of a zero-PVE jet: Enhanced effects of moisture on the life cycle of midlatitude cyclones. J. Atmos. Sci., 61, 16631680.

    • Search Google Scholar
    • Export Citation
  • Fehlmann, R., 1997: Dynamics of seminal PV elements. Ph.D. dissertation, Swiss Federal Institute of Technology (ETH), Diss. ETH 12229, 143 pp.

  • Govindasamy, B., , and S. T. Garner, 1997: The equilibration of short baroclinic waves. J. Atmos. Sci., 54, 28502871.

  • Grams, C. M., and Coauthors, 2011: The key role of diabatic processes in modifying the upper-tropospheric wave guide: A North Atlantic case-study. Quart. J. Roy. Meteor. Soc., 137, 21742193.

    • Search Google Scholar
    • Export Citation
  • Harrold, T. W., 1973: Mechanisms influencing distribution of precipitation within baroclinic disturbances. Quart. J. Roy. Meteor. Soc., 99, 232251.

    • Search Google Scholar
    • Export Citation
  • Hoskins, B. J., , and N. V. West, 1979: Baroclinic waves and frontogenesis. Part II: Uniform potential vorticity jet flows—Cold and warm fronts. J. Atmos. Sci., 36, 16631680.

    • Search Google Scholar
    • Export Citation
  • Hoskins, B. J., , M. E. McIntyre, , and A. W. Robertson, 1985: On the use and significance of isentropic potential vorticity maps. Quart. J. Roy. Meteor. Soc., 111, 877946.

    • Search Google Scholar
    • Export Citation
  • Joos, H., , and H. Wernli, 2012: Influence of microphysical processes on the potential vorticity development in a warm conveyor belt: A case-study with the limited-area model COSMO. Quart. J. Roy. Meteor. Soc., 138, 407418.

    • Search Google Scholar
    • Export Citation
  • Kleinschmidt, E., 1950: Über Aufbau und Entstehung von Zyklonen (1. Teil) (On the structure and formation of cyclones, part 1). Meteor. Rundsch., 3, 16.

    • Search Google Scholar
    • Export Citation
  • Massacand, A. C., , H. Wernli, , and H. C. Davies, 2001: Influence of upstream diabatic heating upon an Alpine event of heavy precipitation. Mon. Wea. Rev., 129, 28222828.

    • Search Google Scholar
    • Export Citation
  • Moore, R. W., , and M. T. Montgomery, 2005: Analysis of an idealized, three-dimensional diabatic Rossby vortex: A coherent structure of the moist baroclinic atmosphere. J. Atmos. Sci., 62, 27032725.

    • Search Google Scholar
    • Export Citation
  • Nakamura, N., , and I. M. Held, 1989: Nonlinear equilibrium of two-dimensional Eady waves. J. Atmos. Sci., 46, 30553064.

  • Olson, J. B., , and B. A. Colle, 2007: A modified approach to initialize an idealized extratropical cyclone within a mesoscale model. Mon. Wea. Rev., 135, 16141624.

    • Search Google Scholar
    • Export Citation
  • Orlanski, I., , and J. Katzfey, 1991: The life cycle of a cyclone wave in the Southern Hemisphere. Part I: Eddy energy budget. J. Atmos. Sci., 48, 19721998.

    • Search Google Scholar
    • Export Citation
  • Orlanski, I., , and E. K. M. Chang, 1993: Ageostrophic geopotential fluxes in downstream and upstream development of baroclinic waves. J. Atmos. Sci., 50, 212225.

    • Search Google Scholar
    • Export Citation
  • Orlanski, I., , and J. P. Sheldon, 1995: Stages in the energetics of baroclinic systems. Tellus, 47A, 605628.

  • Pomroy, H. R., , and A. J. Thorpe, 2000: The evolution and dynamical role of reduced upper-tropospheric potential vorticity in intensive observing period one of FASTEX. Mon. Wea. Rev., 128, 18171834.

    • Search Google Scholar
    • Export Citation
  • Schär, C., , and H. Wernli, 1993: Structure and evolution of an isolated semi-geostrophic cyclone. Quart. J. Roy. Meteor. Soc., 119, 5790.

    • Search Google Scholar
    • Export Citation
  • Schultz, D. M., , D. Keyser, , and L. F. Bosart, 1998: The effect of large-scale flow on low-level frontal structure and evolution in midlatitude cyclones. Mon. Wea. Rev., 126, 17671791.

    • Search Google Scholar
    • Export Citation
  • Shapiro, M. A., , and D. A. Keyser, 1990: Fronts, jet streams, and the tropopause. Extratropical Cyclones: The Erik Palmén Memorial Volume, C. W. Newton and E. O. Holopainen, Eds., Amer. Meteor. Soc., 167–191.

  • Shapiro, M. A., and Coauthors, 1999: A planetary-scale to mesoscale perspective of the life cycles of extratropical cyclones: The bridge between theory and observations. The Life Cycles of Extratropical Cyclones, M. A. Shapiro and S. Grønås, Eds., Amer. Meteor. Soc., 139–185.

  • Simmons, A. J., 1994: Numerical simulations of cyclone life cycles. Proceedings of an International Symposium on the Life Cycles of Extratropical Cyclones, E. S. Grønås and M. A. Shapiro, Eds., Vol. 1, Alma Mater Forlag, 149–160.

  • Simmons, A. J., , and B. J. Hoskins, 1979: The downstream and upstream development of unstable baroclinic waves. J. Atmos. Sci., 36, 12391254.

    • Search Google Scholar
    • Export Citation
  • Sinclair, V. A., , S. L. Gray, , and S. E. Belcher, 2008: Boundary-layer ventilation by baroclinic life cycles. Quart. J. Roy. Meteor. Soc., 134, 14091424.

    • Search Google Scholar
    • Export Citation
  • Steppeler, J., , G. Doms, , U. Schäettler, , H. W. Bitzer, , A. Gassmann, , U. Damrath, , and G. Gregoric, 2003: Meso-gamma scale forecasts using the nonhydrostatic model LM. Meteor. Atmos. Phys., 82, 7596.

    • Search Google Scholar
    • Export Citation
  • Stoelinga, M. T., 1996: A potential vorticity-based study of the role of diabatic heating and friction in a numerically simulated baroclinic cyclone. Mon. Wea. Rev., 124, 849874.

    • Search Google Scholar
    • Export Citation
  • Thorncroft, C. D., , B. J. Hoskins, , and M. E. McIntyre, 1993: Two paradigms of baroclinic-wave life-cycle behaviour. Quart. J. Roy. Meteor. Soc., 119, 1755.

    • Search Google Scholar
    • Export Citation
  • Vallis, G. K., 2006: Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation. Cambridge University Press, 745 pp.

  • Wernli, H., 1997: A Lagrangian-based analysis of extratropical cyclones. II: A detailed case-study. Quart. J. Roy. Meteor. Soc., 123, 16771706.

    • Search Google Scholar
    • Export Citation
  • Wernli, H., , and H. C. Davies, 1997: A Lagrangian-based analysis of extratropical cyclones. I: The method and some applications. Quart. J. Roy. Meteor. Soc., 123, 467489.

    • Search Google Scholar
    • Export Citation
  • Wernli, H., , and C. Schwierz, 2006: Surface cyclones in the ERA-40 dataset (1958–2001). Part I: Novel identification method and global climatology. J. Atmos. Sci., 63, 24862507.

    • Search Google Scholar
    • Export Citation
  • Wernli, H., , R. Fehlmann, , and D. Lüthi, 1998: The effect of barotropic shear on upper-level induced cyclogenesis: Semigeostrophic and primitive equation numerical simulations. J. Atmos. Sci., 55, 20802094.

    • Search Google Scholar
    • Export Citation
  • Wernli, H., , M. A. Shapiro, , and J. Schmidli, 1999: Upstream development in idealized baroclinic wave experiments. Tellus, 51A, 574587.

    • Search Google Scholar
    • Export Citation
  • Whitaker, J. S., , and C. A. Davis, 1994: Cyclogenesis in a saturated environment. J. Atmos. Sci., 51, 889907.

  • Young, M. V., , G. A. Monk, , and K. A. Browning, 1987: Interpretation of satellite imagery of a rapidly deepening cyclone. Quart. J. Roy. Meteor. Soc., 113, 10891115.

    • Search Google Scholar
    • Export Citation
  • View in gallery

    Initial conditions. (a) Meridional cross section of basic state. Thin gray lines show potential temperature from 260 K, every 8 K. Zonal wind speed (thin black lines) from 6 to 42 m s−1, every 6 m s−1. Dashed line indicates the 2-PVU tropopause, and potential vorticity is shown in gray shading. (b) Specific humidity of the basic state in gray shading and equivalent potential temperature (thin black lines) from 260 K, every 8 K. (c) Wind perturbation obtained from inversion of upper-level PV anomaly (gray shading) with a magnitude of 2 PVU. Solid (dashed) lines are positive (negative) zonal wind perturbations from −10 to 10 m s−1, every 4 m s−1. Dashed (solid) line shows the tropopause without (with) the upper-level PV anomaly.

  • View in gallery

    Time evolution from days 3 to 6 of surface pressure (dashed contours, every 5 hPa), surface potential temperature (solid contours, every 4 K), and (for the moist simulation only) RH at 900 hPa (colored, %). (a)–(d) Dry simulation, and (e)–(h) moist simulation m60.

  • View in gallery

    Temporal evolution of minimum SLP along the tracks of the primary, upstream, and downstream cyclones in dry and moist simulations.

  • View in gallery

    Time evolution from days 3 to 6 of PV on 316 K (colored, PVU) and low-level PV at 950 hPa (black contour for 1 PVU). (a)–(d) Dry simulation, and (e)–(h) moist simulation m60.

  • View in gallery

    Temporal evolution of various terms in the energy analysis for (a) the primary cyclone and (b) the downstream cyclone. Overall growth rates and individual contributions from terms I [−3 · (EKu)], II [−3 · (pu′)], and III as well as the residual term (Res) of Eq. (9) are shown by black and gray lines for the dry and m60 simulations, respectively. Gray shading represents the sensitivity to the choice of the box in the dry simulation.

  • View in gallery

    WCB of the primary cyclone in the m60 simulation. Shown are trajectories ascending at least 600 hPa during the 48 h between days 3 and 5. Trajectories are colored with pressure. Contours show surface potential temperature from 260 to 300 K, every 2 K. Shown are snapshots from (a) day 3.5, every 12 h, through (d) day 5. Path of the trajectories is added every 12 h.

  • View in gallery

    Vertical section across the warm front of the primary cyclone in the m60 simulation (exact position of the cross section is shown in the insets) at (a) day 4, hour 8; and (b) day 4, hour 14. Thick black lines indicate condensational latent heating from 0.5 to 3 K h−1, every 0.5 K h−1; colors show the diabatic PV tendency in PVU h−1. Intersection of the WCB trajectories with the cross section is shown by black crosses. Also shown are potential temperature (thin black lines, every 4 K), the 2-PVU tropopause (thick dashed line), and the 0.1 g kg−1 isoline (dashed) of cloud water content.

  • View in gallery

    Temporal evolution of key parameters along the primary cyclone’s WCB shown in Fig. 6. Black lines show averaged values for all WCB trajectories, and gray shading indicates the variability (±σ). Shown are (a) pressure (hPa), (b) specific humidity (g kg−1), (c) cloud water content (g kg−1), (d) relative humidity (%), (e) potential temperature (K), and (f) equivalent potential temperature (K).

  • View in gallery

    As Fig. 8, but for (a) potential vorticity (PVU) and (b) absolute (light gray shading) and relative (dark gray shading) vorticity (in units of f).

  • View in gallery

    Three-dimensional visualization of the WCB in the primary cyclone. Shown are isentropes at the surface (black, from 266 to 298 K, every 2 K), cloud water (blue, semitransparent, Qc = 0.15 g kg−1), and isosurface of latent heating (red, 1.25 K h−1) at day 4, hour 12. Shown aloft are 316-K isentropic surface colored with PV, and wind speed contours at 10-km altitude (black, from 15 m s−1 of southernmost contour to max 40 m s−1, every 5 m s−1) at day 5. WCB trajectory path between day 4 and day 5 is shown in yellow.

  • View in gallery

    As Fig. 6, but for the fWCB in the downstream cyclone, every 12 h from (a) day 6.5 through (d) day 8.

  • View in gallery

    As Fig. 11, but for the rWCB in the downstream cyclone.

  • View in gallery

    Temporal evolution of key parameters along the downstream cyclone’s WCBs (light gray shading for fWCB; dark gray shading for rWCB). Black lines show averaged values for all WCB trajectories, and the gray shading indicates the variability (±σ). Shown are (a) pressure (hPa), (b) specific humidity (g kg−1), (c) cloud water content (g kg−1), (d) potential vorticity (PVU), (e) potential temperature (K), and (f) equivalent potential temperature (K).Vertical line marks hour 40.

  • View in gallery

    Three-dimensional visualization of the WCBs in the downstream cyclone. WCB trajectories are colored with PV (PVU). All fields are shown at day 8; WCB trajectory path shown for last 18 h of ascent. Surface isentropes (black, from 266 to 298 K, every 2 K), isosurface of cloud water content (blue transparent shading, for 0.2 g kg−1), and isosurface of PV (brown shades, for 2 PVU between 6.0 and 6.5 km).

  • View in gallery

    Differences between the moist and the dry simulations of PV (colors, PVU), and horizontal wind vectors at the WCB outflow level for (a) the primary cyclone’s WCB on 316 K at day 5 and (b) the downstream cyclone’s WCBs on 319 K at day 8. Green lines indicate the 2-PVU tropopause (solid for m60 simulation, and dashed for dry simulation).

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 82 82 10
PDF Downloads 76 76 10

Warm Conveyor Belts in Idealized Moist Baroclinic Wave Simulations

View More View Less
  • 1 Institute for Atmospheric and Climate Science, ETH Zürich, Zurich, Switzerland
© Get Permissions
Full access

Abstract

This idealized modeling study of moist baroclinic waves addresses the formation of moist ascending airstreams, so-called warm conveyor belts (WCBs), their characteristics, and their significance for the downstream flow evolution. Baroclinic wave simulations are performed on the f plane, growing from a finite-amplitude upper-level potential vorticity (PV) perturbation on a zonally uniform jet stream. This nonmodal approach allows for dispersive upstream and downstream development and for studying WCBs in the primary cyclone and the downstream cyclone. A saturation adjustment scheme is used as the only difference between the dry and moist simulations, which are systematically compared using a cyclone-tracking algorithm, with an eddy kinetic energy budget analysis, and from a PV perspective. Using trajectories and a selection criterion of maximum ascent, forward- and rearward-sloping WCBs in the moist simulation are identified. No WCB is identified in the dry simulation. Forward-sloping WCBs originate in the warm sector, move into the frontal fracture region, and ascend over the bent-back front, where maximum latent heating occurs in this simulation. The outflow of these WCBs is located at altitudes with prevailing zonal winds; they hence flow anticyclonically (“forward”) into the downstream ridge. In case of a slightly weaker ascent, WCBs curve cyclonically (“rearward”) above the cyclone center. A detailed analysis of the PV evolution along the WCBs reveals PV production in the lower troposphere and destruction in the upper troposphere. Consequently, WCBs transport low-PV air into their outflow region, which contributes to the formation of distinct negative PV anomalies. They, in turn, affect the downstream flow and enhance downstream cyclogenesis.

Supplemental information related to this paper is available at the Journals Online website: http://dx.doi.org/10.1175/JAS-D-12-0147.s1.

Corresponding author address: Sebastian Schemm, Institute for Atmospheric and Climate Science, ETH Zürich, Universitätstrasse 16, 8092 Zurich, Switzerland. E-mail: sebastian.schemm@env.ethz.ch

Abstract

This idealized modeling study of moist baroclinic waves addresses the formation of moist ascending airstreams, so-called warm conveyor belts (WCBs), their characteristics, and their significance for the downstream flow evolution. Baroclinic wave simulations are performed on the f plane, growing from a finite-amplitude upper-level potential vorticity (PV) perturbation on a zonally uniform jet stream. This nonmodal approach allows for dispersive upstream and downstream development and for studying WCBs in the primary cyclone and the downstream cyclone. A saturation adjustment scheme is used as the only difference between the dry and moist simulations, which are systematically compared using a cyclone-tracking algorithm, with an eddy kinetic energy budget analysis, and from a PV perspective. Using trajectories and a selection criterion of maximum ascent, forward- and rearward-sloping WCBs in the moist simulation are identified. No WCB is identified in the dry simulation. Forward-sloping WCBs originate in the warm sector, move into the frontal fracture region, and ascend over the bent-back front, where maximum latent heating occurs in this simulation. The outflow of these WCBs is located at altitudes with prevailing zonal winds; they hence flow anticyclonically (“forward”) into the downstream ridge. In case of a slightly weaker ascent, WCBs curve cyclonically (“rearward”) above the cyclone center. A detailed analysis of the PV evolution along the WCBs reveals PV production in the lower troposphere and destruction in the upper troposphere. Consequently, WCBs transport low-PV air into their outflow region, which contributes to the formation of distinct negative PV anomalies. They, in turn, affect the downstream flow and enhance downstream cyclogenesis.

Supplemental information related to this paper is available at the Journals Online website: http://dx.doi.org/10.1175/JAS-D-12-0147.s1.

Corresponding author address: Sebastian Schemm, Institute for Atmospheric and Climate Science, ETH Zürich, Universitätstrasse 16, 8092 Zurich, Switzerland. E-mail: sebastian.schemm@env.ethz.ch

1. Introduction

While the two most prominent conceptual models of extratropical cyclone life cycles, the Norwegian (Bjerknes 1919) and the Shapiro–Keyser (Shapiro and Keyser 1990) models, focus on the surface cyclonic and frontal evolution, respectively, the conveyor belt concept (Harrold 1973; Carlson 1980; Young et al. 1987; Browning 1990; Browning and Roberts 1994) aims to describe the key aspects of the three-dimensional airflow in developing extratropical cyclones. The most intense ascending airstream in extratropical cyclones is the warm conveyor belt (WCB), which typically rises from the boundary layer to the upper troposphere while moving poleward. Browning (1986) identified two types of WCB ascent, characterized by a rearward- and forward-sloping orientation relative to the moving cold front. The two types were shown to occur preferentially with ana (rearward) and kata (forward) cold-frontal configurations. Following Browning and Roberts (1994), WCBs are classified into types W1 and W2, depending on their frontal region of ascent. The WCB ascent is associated with cross-isentropic flow propelled by the release of latent heat due to the condensation of water vapor in the lower troposphere and ice phase processes (mainly depositional growth of snow) in the upper troposphere (Joos and Wernli 2012). This latent heating in turn acts as a source and sink of potential vorticity (PV; e.g., Hoskins et al. 1985), as discussed in more detail below. WCBs are responsible for the major part of precipitation in the extratropical storm-track areas (Browning 1990). Eckhardt et al. (2004) showed that, in the Northern Hemisphere, they most frequently originate in the western North Pacific and North Atlantic, in the latitude band between 25° and 40°N. Sinclair et al. (2008) emphasized the role of WCBs for boundary layer venting, including the potential transport of pollutants into the free atmosphere. Because of their outflow at the level of the upper-tropospheric jet stream, WCBs have the potential to modify the downstream flow evolution. Case study analyses have shown that the WCB outflow can strongly amplify upper-level ridges, which in turn can lead to downstream Rossby wave breaking (Massacand et al. 2001; Grams et al. 2011). This study investigates the structure of WCBs, the associated PV modification, and their downstream impact for the first time within idealized baroclinic wave simulations. The following subsections provide relevant background information about idealized baroclinic wave simulations and the diabatic PV modification in WCBs, before outlining more precisely the specific aims of this study.

a. Idealized dry and moist baroclinic wave simulations

Idealized dry atmosphere numerical modeling studies of extratropical cyclones (Hoskins and West 1979; Davies et al. 1991; Thorncroft et al. 1993) effectually depicted a set of archetypal life cycles of cyclones and their accompanying frontal structures, and highlighted the process of upstream and downstream development (Simmons and Hoskins 1979)—see Simmons (1994) for a comprehensive review on dry baroclinic wave simulations. Simmons and Hoskins (1979) analyzed the formation of upstream and downstream cyclones developing from the primary disturbance with the quasigeostrophic (QG) omega equation. The concept of downstream energy dispersion from the primary cyclone has been further studied in idealized experiments by Orlanski and Chang (1993). Upstream and downstream development occurs naturally in idealized channel model simulations if the simulations are initialized with a localized finite-amplitude perturbation—for instance, in the form of an upper-level positive PV anomaly (Wernli et al. 1999)—an approach that differs from classical normal-mode initializations. This setup with localized initial perturbations will also be used in this study to investigate WCBs in the primary and the first downstream cyclones.

The overall structure of extratropical cyclones can be reasonably well described using idealized dry atmosphere channel model simulations, although they typically do not produce explosive intensification rates. For instance, in a semigeostrophic dry simulation with a finite-amplitude initial perturbation, Schär and Wernli (1993) were able to identify the dry intrusion as a coherently descending airstream, and they emphasized the fundamental importance of moist processes in forming the WCB, which was not found in their dry runs. The surface frontal evolution followed closely the Shapiro–Keyser (Shapiro and Keyser 1990) model, with a frontal fracture separating the cold and warm fronts, a frontal T-bone stage with a bent-back extension of the warm front wrapping around the surface pressure minimum, and a warm-air seclusion in the center of the mature cyclone. Similar surface frontal structures were found later, for example, by Wernli et al. (1998) with a primitive equation model.

Idealized moist baroclinic wave experiments can produce even more realistic cyclone structures and in particular more intense growth rates, but the inclusion of moisture adds substantially to the complexity of these simulations. Balasubramanian and Yau (1994) studied the effect of convection on a marine cyclone and used a PV inversion technique to quantify the influence of diabatically generated PV anomalies to the cyclone evolution. Whitaker and Davis (1994) made the simplifying assumption of all ascending air to be saturated. In their nonlinear cases, they found an increase in maximum surface wind speeds in the moist case and a more rapid and amplified reduction of the surface geopotential height minimum. The rapid growth rate of the moist cyclone in its early stage was linked to an intensification of a positive PV anomaly at lower levels associated with diabatic heating along the warm front. Fantini (2004) studied moist cyclogenesis growing from an idealized jet with initially zero equivalent potential vorticity. He found for moist cyclogenesis, rapid deepening and intense mesoscale updrafts, especially toward the northern side of the initial jet. Recently, idealized moist experiments have been performed to study special categories of cyclones whose evolution is crucially related to moist dynamical processes, namely, diabatic Rossby waves (Moore and Montgomery 2005) and subtropical cyclones (Davis 2010).

Since our experiments aim to study the formation and structure of WCBs and their downstream influence, it will be of key importance to perform moist baroclinic wave experiments. For analyzing the downstream influence of the WCB associated with the primary cyclone and the first downstream cyclone, nonmodal initial conditions will be required to allow for nonperiodic solutions and dispersion of the initially localized disturbance.

b. Latent heating and potential vorticity along WCBs

Potential vorticity and the corresponding “PV thinking” owes its usefulness in the first place to the material conservation property of PV for adiabatic and frictionless flows and to the invertibility principle, which allows diagnosis of the balanced flow field from the PV in the interior of the atmosphere and suitable boundary conditions (Hoskins et al. 1985). In the presence of diabatic effects, entropy is not conserved and PV loses its material conservation property. These diabatic effects comprise a wide range of physical phenomena, among which are radiation, surface fluxes, and phase transitions of water in clouds.

Mathematically, the response of PV to diabatic heating is described by the material PV tendency equation, which was already discussed by Eliassen and Kleinschmidt (1957). In the formulation here we neglect frictional forces:
e1
The notation is mostly standard, with α being the specific volume, u is the three-dimensional wind vector, and is the diabatic heating rate. For WCBs, the vertical component of the scalar product becomes the dominant term and we may write
e2
where ζ denotes the vertical relative vorticity component and f = 2Ω sin(φ) is the Coriolis parameter. Assuming absolute vorticity to be positive, an assumption valid in most synoptic-scale flow situations in the Northern Hemisphere, this equation indicates that below the heating rate maximum where we have a positive vertical heating rate gradient, ascending WCB air parcels experience a material increase of PV (Stoelinga 1996; Wernli and Davies 1997). In contrast, air parcels located above the heating maximum lose PV. This contrasting effect of latent heating on ascending air parcels in the lower and upper troposphere is crucial for understanding the dynamical effects of WCBs from a PV perspective (see next paragraph). Similar arguments hold for a local diabatic cooling rate maximum (e.g., because of evaporation of hydrometeors) with a negative vertical heating gradient below and a positive gradient above. Note that from the invertibility principle it follows that the diabatic modification of PV has an important influence on the balanced flow field also in the surrounding of the anomaly. Generally speaking, in moist synoptic-scale flow situations, the vertical gradient of the heating rate will determine the onset and the sign of the PV tendency, while absolute vorticity can have an influence on its magnitude as shown by Joos and Wernli (2012) and confirmed by our analysis (see below).

Probably the first publications describing the evolution of potential vorticity along an ascending airstream in the presence of diabatic heating within an extratropical cyclone (later referred to as a WCB) are Kleinschmidt (1950) and Eliassen and Kleinschmidt (1957, p. 136). Eliassen and Kleinschmidt noted, “the potential vorticity increases in the lower current and decreases in the upper current.” This characteristic increase and subsequent decrease of PV along the WCB flow due to the changing sign of the vertical gradient of latent heating (see above) was later confirmed by the detailed Lagrangian analysis of extratropical cyclones by Wernli and Davies (1997) and Wernli (1997). As a consequence, WCBs typically arrive with low PV values [0–0.5 PV units (PVU)]1 in the upper troposphere [see also Pomroy and Thorpe (2000)], where they contribute to the formation, intensification, and/or maintenance of negative PV anomalies associated with upper-level ridges. We identify and quantify this effect in idealized baroclinic wave experiments via a comparison of dry and moist runs (i.e., simulations without and with a WCB).

c. Specific aims and structure of this study

In the first part of the study, dry and moist idealized baroclinic wave simulations on the f plane will be presented, initialized with localized finite-amplitude upper-level perturbations in order to investigate also the formation of the first downstream cyclones. The differences of the dry and moist simulations will be analyzed with a focus on cyclone tracks, cyclone intensification, and the PV evolution at low and upper levels. An eddy kinetic energy budget analysis will also be used to provide a detailed description of the enhanced downstream development in the moist runs.

In the second part of this study, we aim to identify WCBs in the primary and first downstream cyclones of the moist simulation and try to categorize them as rearward- or forward-sloping WCBs (rWCB and fWCB, respectively). The idealized simulations will be ideally suited to quantify the PV generation and destruction along the WCB flow due to condensational latent heating. A particular focus will be on the PV values in the WCB outflow at upper levels, and on their effect on the downstream Rossby wave evolution—a particularly important aspect of WCBs that has not been investigated yet in an idealized framework.

The structure of the paper is as follows: Section 2 gives a brief overview of the model setup and a detailed description of the construction of the synthetic initial conditions. In section 3 we systematically assess the differences between dry and moist simulations, including the eddy kinetic energy budgets of the primary cyclone and the downstream cyclone. The formation of WCBs in the primary cyclone and in the downstream cyclone, their PV modification at upper levels, and the impact on the downstream flow are discussed in section 4, before providing conclusions and a short outlook in section 5.

2. Model and simulation setup

For our simulations we use the nonhydrostatic weather prediction model COSMO (Steppeler et al. 2003), which is in operational use at several European weather services. For our needs, the Consortium for Small-Scale Modeling (COSMO) has been modified into a classical channel setup with periodic zonal boundary conditions and relaxation at the meridional walls. The channel has a zonal extension of 16.800 km and a width of 8.400 km, the horizontal resolution is 21 km (0.18°), and 60 vertical levels extend up to 12 km, equidistant at 200-m intervals. At the top we enable Rayleigh damping, while at the bottom no topography is included. Furthermore, all our simulations are performed on an f plane centered at 45°N2 (f ~ 1.03 × 10−4 s−1).

Our idealized configuration uses a saturation adjustment process to convert water vapor into cloud water and vice versa. Other parameterizations are consciously turned off, including boundary layer turbulence (consequently, no surface fluxes), radiation, cloud microphysics, and moist convection. The main reason for this idealization is to keep the moist simulations fairly close to the “purely dynamical” dry simulations, which will allow for diagnosis of the effects of latent heating due to resolved-scale condensation.

Initial conditions

The initial conditions consist of a zonally uniform jetlike basic state in thermal wind balance, a localized finite-amplitude perturbation, and—for the moist simulations—a suitable moisture profile. The baroclinic basic state is constructed following the approach by Olson and Colle (2007, hereafter OC07) with only minor modifications to suit our purposes. Here, we briefly outline the approach of OC07 to design a zonally uniform jetlike basic state. The initialization starts with defining a meridional pressure distribution at a reference level (OC07 showed 4 km to be a good reference level), given by
e3
where the reference pressure P0 at a height of 4 km is chosen to be 607 hPa. The factors p1 and p2 are the small- and large-scale pressure gradient packings, respectively, which allow for a stronger pressure gradient in the domain center. We use values of 1200 and 1800 km, respectively, and the small- and large-scale pressure gradient amplitudes are set to Ay1 = 12 hPa and Ay2 = 17 hPa, respectively.
In the second step, the three-dimensional temperature profile is specified with a similar approach, as follows:
e4
The temperature gradient amplitudes are set to By1 = 10 K and By2 = 12 K. The reference temperature T0 is 281 K, and the vertical lapse rates for the troposphere and the stratosphere are given by
e5
The temperature lapse rate at the domain’s center (y = 0) is chosen to be τt = 5.2 K km−1 in the troposphere and τs = 0.3 K km−1 in the stratosphere. A tropospheric lapse rate of 5.2 K km−1 is a reasonable choice to prevent e/dz becoming negative near the domain center when including moisture (see below).
In the third step, the full three-dimensional pressure field is calculated by hydrostatic integration upward and downward from the reference level, using the previously obtained temperature profile. The geostrophic wind equation is then taken to compute zonal and meridional winds. Tropopause height is explicitly defined by
e6
e7
In the center of the domain, the tropopause height is Z0 = 8.5 km, and Zdiff denotes the total meridional height variation. After calculating the tropospheric temperature field from Eq. (4), the temperature at grid points above the tropopause defined by Eq. (6) is recalculated by upward integration using the stratospheric lapse rate. For a more detailed description of the implementation of the code, we refer to OC07. Figure 1a shows the unperturbed basic-state jet stream with a maximum wind speed of about 40 m s−1 in the core, the potential temperature field, and the associated PV distribution with the 2-PVU dynamical tropopause.
Fig. 1.
Fig. 1.

Initial conditions. (a) Meridional cross section of basic state. Thin gray lines show potential temperature from 260 K, every 8 K. Zonal wind speed (thin black lines) from 6 to 42 m s−1, every 6 m s−1. Dashed line indicates the 2-PVU tropopause, and potential vorticity is shown in gray shading. (b) Specific humidity of the basic state in gray shading and equivalent potential temperature (thin black lines) from 260 K, every 8 K. (c) Wind perturbation obtained from inversion of upper-level PV anomaly (gray shading) with a magnitude of 2 PVU. Solid (dashed) lines are positive (negative) zonal wind perturbations from −10 to 10 m s−1, every 4 m s−1. Dashed (solid) line shows the tropopause without (with) the upper-level PV anomaly.

Citation: Journal of the Atmospheric Sciences 70, 2; 10.1175/JAS-D-12-0147.1

In the next step, atmospheric moisture is initialized, starting from uniform relative humidity (RH) values of 60% at the surface and using a linear vertical decrease of 5% km−1. The corresponding moist simulations will be referred to as m60. We also performed a moist simulation with 40% relative humidity at the surface, referred to as m40. It is then straightforward to calculate the corresponding specific humidity field. Figure 1c shows specific humidity and equivalent potential temperature for the basic state of the m60 simulation. Maximum specific humidity values exceed 10 g kg−1. Note that in the southern part of the domain, the vertical gradient of the equivalent potential temperature becomes negative in the lowest layers; however, no overturning moist isentropes occur in the central and northern parts of the model domain.

The zonally uniform background state is perturbed with a positive upper-level PV anomaly with an amplitude A of 2 PVU, a horizontal extension of Lx = Ly = 1000 km, and a vertical exponential decay length of Lz = 4000 m, comparable to the approach by Wernli et al. (1999) as shown:
e8
The center of the anomaly is located in the center of the channel at a height of zpos = 8 km, that is, in the vicinity of the maximum jet wind speed.

The PV anomaly has been inverted using a quasigeostrophic PV inversion routine by Fehlmann (1997), producing the three-dimensional perturbation fields of geostrophic wind and temperature—for example, a cyclonic wind field with maximum amplitude of 10 m s−1—as shown in Fig. 1b. Also shown in this vertical section across the center of the PV anomaly (gray shading) is the tropopause modulation due to the PV anomaly (cf. solid and dashed thick lines).

3. Moist and dry baroclinic waves

In this section we investigate the development of the cyclones in the dry and moist simulations, and their differences. The analysis of the surface potential temperature and upper-level PV evolution is complemented by a cyclone-tracking analysis (which allows for quantification of the development of the cyclones’ minimum sea level pressure) and an energy budget analysis.

a. Overview of surface cyclone evolution

As a starting point, Fig. 2 shows the evolution of sea level pressure (SLP) and surface potential temperature for the dry simulation (Figs. 2a–d) and the moist simulation m60 (Figs. 2e–h) from day 3 to day 6. For m60, relative humidity at 900 hPa is also shown.

Fig. 2.
Fig. 2.

Time evolution from days 3 to 6 of surface pressure (dashed contours, every 5 hPa), surface potential temperature (solid contours, every 4 K), and (for the moist simulation only) RH at 900 hPa (colored, %). (a)–(d) Dry simulation, and (e)–(h) moist simulation m60.

Citation: Journal of the Atmospheric Sciences 70, 2; 10.1175/JAS-D-12-0147.1

On day 3 (Fig. 2a) frontogenesis starts in the primary cyclone. At this time the horizontal potential temperature gradient is stronger in the warm front compared to the cold front. The warm sector is aligned at its northern end with the pressure minimum (980 hPa) and the warm front wraps around the pressure minimum to its north. Anticyclonic perturbations start to evolve both upstream and downstream of the primary cyclone. The moist cyclone (Fig. 2e) reveals an increase of relative humidity up to 80% in large parts of the warm sector and around the center of the depression. Confined alongside the warm front, small areas of saturation can be found. Both humidifications can be attributed to lifting. Therefore, the differences between the dry and moist cyclones are still very small and are concentrated in the saturated region at the warm front.

On day 4 (Fig. 2b) the cyclone approaches its frontal fracture stage. The warm front elongates and parts of it bend around the cyclone center, while the cold front fractures, that is, it is comparatively weak in its northern part. The dry cyclone (Fig. 2b) intensifies to a central pressure of 970 hPa, and both across-frontal gradients strengthen substantially with the warm-frontal gradient remaining stronger.

Discrepancies between the dry and moist runs can now be clearly seen along the bent-back extension of the warm front (cf. Figs. 2b,f), where in m60 relative humidity exceeds 90% up to saturation (dark blue shading) and the horizontal temperature gradient is considerably stronger. This bent-back part appears as the natural extension of the warm front, and both are from a dynamical perspective inherently linked to each other throughout the life cycle as shown by a Q-vector analysis of Wernli et al. (1998). From a kinematic viewpoint, however, Schultz et al. (1998) showed that cold-air advection can occur along parts of the bent-back fronts and argued that the phrase “warm front” might be misleading. Although we emphasize the dynamical linkage of the bent-back extension and the warm front, for simplicity, we will use the term “bent-back front” throughout this paper. The isobars show a SLP minimum below 965 hPa for the moist cyclone and an enhanced horizontal gradient at the western tip of the bent-back front, indicating the formation of a low-level wind maximum in this region with wind speeds exceeding those of the dry cyclone. In the upstream anticyclone, relative humidity has decreased to about 25% and a minor increase in RH in the downstream cyclone is observable.

On day 5 (Figs. 2c,g) the primary cyclones reach their T-bone stage, when the cold front is oriented almost perpendicularly to the eastern part of the warm front. Farther to the west, in particular in m60, the bent-back front wraps around the cyclone center and intense surface winds occur along this part of the front. The cyclones now reach minimum SLP values of about 965 hPa in the dry simulation and 960 hPa in the moist simulation. In the moist primary cyclone, saturation occurs along the warm and parts of the cold-frontal regions. Accordingly, the structure of the dry and moist cyclones shows significant discrepancies in these regions where latent heating occurs in m60.

In both simulations, upstream and downstream of the primary cyclone two secondary cyclones start forming around day 5. Compared to the downstream cyclone, the upstream cyclone evolves in a region with a very strong surface baroclinicity. Its characteristic “hook” of warm and cold fronts is in good agreement with previous idealized studies of upstream cyclogenesis (Shapiro et al. 1999; Wernli et al. 1999). The downstream cyclone is slightly stronger at this time in the moist simulation. However, its central relative humidity values do not exceed 80% yet, indicating that the higher intensity of the downstream cyclone in m60 cannot be an effect of in situ latent heat release but rather results from enhanced downstream development.

In both simulations, the primary cyclones reach their mature stage around day 6 (Figs. 2d,h). At that time they are both associated with a strong and elongated cold front, a strongly narrowed warm sector, and again an intense bent-back front, which differs most prominently between the dry and moist simulations in the center of the depression. A pronounced warm-air seclusion coincides with the low pressure center. The central SLP value of the primary cyclone is now about 10 hPa lower in m60 compared to the dry run. Also further intensified are the increase and decrease of surface relative humidity in the cyclonic and anticyclonic systems of the m60 simulation, respectively. Meanwhile the downstream cyclone has reached its frontal fracture stage with the cold front being stronger than the bent-back front, which constitutes a notable difference in the primary cyclone. As will become clear (when discussing the further evolution of the downstream cyclone on day 7 and day 8 in section 4b), the downstream cyclone evolution closely resembles the Shapiro–Keyser life cycle as well. Until this time, relative humidity increased fairly uniformly within the downstream cyclone with values above 90% along the bent-back front.

Overall, the baroclinic wave pattern on day 6 of the dry simulation is in good agreement with previous idealized dry baroclinic wave simulations, for example, by Shapiro et al. (1999). In both simulations, the evolution of the primary cyclone is qualitatively in line with the three stages—frontal fracture, T-bone, and mature seclusion state—described by the Shapiro–Keyser model of marine cyclogenesis.

With the given simulation setup, latent heating starts in m60 only a few days after the start of the simulation, and therefore the scale of the baroclinic wave is determined by dry dynamics and consequently is very similar in both runs (compare, e.g., the distance between the centers of the upstream, primary, and downstream cyclones on day 6). Important differences between the dry and moist simulations occur for the intensity of the cyclones, the structure of the bent-back front (where latent heating is most intense in m60), and the speed of the upstream and downstream development.

Note that the nonmodal development of our simulation setup allows for this upstream and downstream development due to the dispersion of the baroclinic wave, which becomes clearly visible on day 6, when the upstream cyclone’s surface frontal gradients are much stronger than those of the downstream cyclone. This is in line with the bottom-up formation of upstream and top-down formation of downstream cyclones as first described by Simmons and Hoskins (1979), who also noted the typically smaller scale of the upstream perturbation. They investigated this development with the QG dynamical concepts and emphasized the role of vortex stretching and shrinking in regions of Q-vector convergence and divergence. Alternative concepts to explain the development of upstream and downstream cyclones are the PV framework Shapiro et al. (1999) and the QG kinetic energy perspective (see section 3c).

Sea level pressure minima evolution

For a more quantitative comparison of the dry and moist simulations, we identify the primary, upstream, and downstream cyclones with the closed SLP contour approach of Wernli and Schwierz (2006); track the SLP minima; and quantify the cyclones’ deepening rates as given by the decrease of the SLP minima. Figure 3 shows the resulting minimum SLP evolutions from day 2 to day 6 for all three cyclones. The primary cyclone in the dry run shows a first phase of rapid deepening between days 2.5 and 4.5, and a second phase with reduced deepening thereafter. The overall behavior is similar in the moist runs with enhanced intensification rates and a slightly earlier transition from stronger to weaker intensification. As shown later, the inflection point in the SLP evolution is preceded by a maximum of the eddy kinetic energy growth rate. The primary cyclone’s SLP evolution qualitatively matches the evolution in Balasubramanian and Yau (1996), with the inflection point in the dry run also around day 4 and slightly earlier in their moist case.

Fig. 3.
Fig. 3.

Temporal evolution of minimum SLP along the tracks of the primary, upstream, and downstream cyclones in dry and moist simulations.

Citation: Journal of the Atmospheric Sciences 70, 2; 10.1175/JAS-D-12-0147.1

Comparing the deepening rates Δ(SLP)/Δ(t) between days 2.5 and 4.5 (Table 1), we find an enhanced deepening by 2 hPa (2 days)−1 for m40 (moist simulation in which the initial surface relative humidity is 40%) compared to the dry run, and for m60 compared to m40, respectively. After the inflection point (Table 2), the minimum SLP decrease weakens but is still larger for the moister simulations. Taking 960 hPa as an arbitrary threshold, the dry primary cyclone reaches it by day 5, while this value is reached in m60 already on day 4.

Table 1.

Central SLP values (hPa) for the primary cyclone from days 2.5 to 4.5.

Table 1.
Table 2.

Central SLP values (hPa) for the primary cyclone from days 4 to 6.

Table 2.

Upstream and downstream cyclones are detected slightly after day 5. With increasing initial humidity the cyclogenesis appears earlier—as an example, the point of initial upstream detection of the dry compared to the m40 upstream cyclone differs by 8 h. Similar to the primary cyclone, the three pressure curves show differences in their slope, with the m60 curve showing the strongest deepening. No cyclone reaches the point of inflection in its SLP before the end of the tracking around day 6.5. By day 6.5 the downstream cyclones reach minimum pressure levels exceeding those of the corresponding upstream cyclone by 5 hPa.

b. Overview on PV evolution at upper and low levels

To investigate the baroclinic life cycles from a PV perspective, Fig. 4 shows the evolution of isentropic PV on 316 K (colors) and of low-level PV at 925 hPa (black contour for 1 PVU), again for days 3–6 and for the dry and moist simulation m60, respectively. Artificially created strong low-level PV values, typically larger than 1 PVU, are produced in idealized dry simulations due to numerical diffusion in the strongly intensifying frontal area (Nakamura and Held 1989; Cooper et al. 1992; Bush and Peltier 1994), as the front encounters scales finer than grid scaling. In the dry simulation, the first indication of low-level PV exceeding 1 PVU occurs on day 4 in the northernmost point of warm front, where the horizontal temperature gradient is strongest. In the moist simulation, of course, latent heating can lead to a diabatic production of low-level PV exceeding 1 PVU, as discussed in the introduction.

Fig. 4.
Fig. 4.

Time evolution from days 3 to 6 of PV on 316 K (colored, PVU) and low-level PV at 950 hPa (black contour for 1 PVU). (a)–(d) Dry simulation, and (e)–(h) moist simulation m60.

Citation: Journal of the Atmospheric Sciences 70, 2; 10.1175/JAS-D-12-0147.1

Until day 3, latent heating is very weak, and the dry and moist simulations reveal no differences in the considered PV fields (Figs. 4a,e). The initially cyclonic upper-level PV anomaly has deformed into a bow-shaped pattern, and a trough–ridge pattern evolved above the surface primary cyclone.

By day 4 differences between the dry (Fig. 4b) and moist (Fig. 4f) simulations emerge, mainly in the region of the upper-level ridge, which extends farther to the northeast in m60. This indicates that the cyclonic wave breaking advances faster in the moist simulation. Strong low-level PV first appears on day 4 in the dry run. In the moist run, the low-level 1-PVU contour already shows a cyclonic wrap-up stretching along most of the bent-back front. The reason for this enlarged region with strong low-level PV is the enhanced frontogenesis and the diabatic PV production due to the condensational heating in the frontal region.

On day 5 (Figs. 4c,g) the onset of the upper-level cyclonic wave breaking becomes visible as low PV values in the ridge extend far to the northeast in both simulations. In contrast, the filament of PV values larger than 3 PVU in the upstream trough forms a complete cyclonic spiral. This wave breaking process is further evolved in the moist simulation. Downstream of the primary cyclone, trough formation proceeds, which leads to the top-down growth of the downstream cyclone, as discussed above. Moreover, the weak undulation of the tropopause upstream of the primary cyclone can be traced back to the circulation induced by the bottom-up developing upstream cyclone. Along the downstream flank of the primary ridge, PV gradients are considerably strengthened compared to the previous day, suggesting an intensification of wind speeds and the formation of a jet streak.

The low-level 1-PVU contour on day 5 (Figs. 4c,g) gives an impression of the intensifying warm front and its bent-back extension in the dry cyclone reaching a stage comparable with the situation along the moist warm front of the previous day. In the moist primary cyclone (Fig. 4g), low-level PV forms a complete spiral around the sea level pressure minimum. The strong low-level PV anomaly along the bent-back front at this stage of the development agrees with the findings of Whitaker and Davis (1994). Again, considering the PV field at upper levels, a most remarkable difference between the dry and moist simulations is the localized region with very low PV values (<0.2 PVU) in the northern part of the ridge in the moist simulation. This anomaly causes an intensification of the ridge and a locally increased isentropic PV gradient. Note, however, that the strongest PV gradient occurs just downstream of this region of very low PV. In section 3c we will investigate in detail the physical mechanisms responsible for the formation of this prominent negative PV anomaly in the upper-level ridge and its dynamical impact on the downstream flow evolution.

Finally, on day 6 (Figs. 4d,h), the upper-level region with very low PV values in the moist wave covers most of the easterly part of the ridge, while the downstream trough elongates farther south compared to the dry wave. From the PV perspective, these two observations can be related to one another. A lowering of the PV upstream induces a stronger anticyclonic upper-level circulation anomaly, which enables a faster intensification and more southward protrusion of the downstream trough. In both simulations, the evolution of the high-PV features reveals an archetypal cyclonic wave breaking in both the primary and downstream waves.

At lower levels (day 6, Figs. 4d,h), enhanced PV generation along the surface cold front becomes visible, extending far more south along the more intense moist cold front. Also in the upstream cyclone, strong low-level PV occurs in the moist simulation at this time, without a prominent undulation of the tropopause. Along the fronts of the top-down-induced downstream cyclone, strong low-level PV will be produced only later in the development, which is consistent with the weaker fronts and lower humidity values in the downstream cyclone (compared to the upstream cyclone) on day 6 as discussed above.

c. Energy perspective

So far our analysis of the evolution of the dry and moist baroclinic waves at the surface and upper levels reveals a more rapid intensification of the primary cyclone and an earlier and strengthened downstream cyclogenesis in the moist simulation. Here, we would like to briefly investigate the physical processes contributing to the intensified life cycle dynamics in the moist simulation with the aid of an eddy kinetic energy analysis, which allows for quantifying the contributions from baroclinic energy conversion, energy advection, and dispersion. Such an analysis can provide valuable insight into the downstream baroclinic wave development, as previously shown for idealized simulations (Orlanski and Chang 1993) and real case studies (Orlanski and Katzfey 1991).

Following Orlanski and Katzfey [1991, their Eqs. (3.14) and (3.16)] but using height instead of pressure as the vertical coordinate, the tendency equation for the eddy kinetic energy (EKE) is given by
e9
The derivation of this equation is given in the appendix. As usual primes denote eddy components, that is, deviations from the zonal mean of the entire channel. In the equation, 3 represents the three-dimensional gradient operator and ρ0 is a reference density depending solely on z. EKE is redistributed by advection (term I) and the convergence of ageostrophic geopotential fluxes (term II) (ageostrophic, since the eddy geostrophic contribution is free of divergence). The baroclinic term (term III) accounts for the conversion of eddy available potential energy into EKE. Contributions from the exchange of energy with the zonal flow are included in the residual term (Res). Note that we stick to the traditional nomenclature of ageostrophic geopotential fluxes; however, in height coordinates, pressure fluxes would be more appropriate.

To obtain the individual energy conversion terms for the primary cyclone and the downstream cyclone, we average over vertically tilted boxes and normalize every term of Eq. (9) by the box-averaged EKE. The boxes are moving with the mean propagation velocity C ≈ 10 m s−1 of the baroclinic wave, determined from the zonal propagation speed of the primary cyclone’s surface pressure minimum. For this reason the advection term (term I) is corrected by the flux of EKE across the box boundaries by −CxEK. The boxes extend over the entire meridional dimension of the channel and have a zonal dimension of 4.200 km. Their initial position and westward tilt are chosen such that the kinetic energy maxima associated with the considered cyclone at the surface and in the upper-level trough are well contained within the box. With this approach we assure that EKE centers belonging to neighboring disturbances do not extend into the considered box. For the primary cyclone, the top of the box extends 840 km to the west of the edge at the surface and for the downstream cyclone by 1890 km. This stronger tilt for the downstream cyclone is chosen in order to capture the upper-level energy dispersion at a relatively early stage. To assess the sensitivity to the choice of the positioning and the size of the box, we consider four additional boxes, which either have a modified zonal extension (±420 km) or are shifted by ±210 km in the zonal direction.

For the primary cyclone, the evolution between days 2 and 7 of the overall EKE growth rate and the individual terms of Eq. (9), normalized by EK, are shown in Fig. 5a for the dry and moist (m60) simulations, respectively. Lines show the results obtained for the standard box, and the sensitivity to the choice of the box is shown by the gray shading, which corresponds to the envelope of the curves for all five boxes. The sensitivity of the box size turned out to be of similar magnitude in the moist and dry runs, and for visibility reasons only the sensitivity of the dry run is shown in Fig. 5. Figure 5b shows the analogous terms for the downstream cyclone. In both cases the sensitivity is small, which allows for robust conclusions from this feature-based energy diagnostic.

Fig. 5.
Fig. 5.

Temporal evolution of various terms in the energy analysis for (a) the primary cyclone and (b) the downstream cyclone. Overall growth rates and individual contributions from terms I [−3 · (EKu)], II [−3 · (pu′)], and III as well as the residual term (Res) of Eq. (9) are shown by black and gray lines for the dry and m60 simulations, respectively. Gray shading represents the sensitivity to the choice of the box in the dry simulation.

Citation: Journal of the Atmospheric Sciences 70, 2; 10.1175/JAS-D-12-0147.1

Baroclinic conversion accounts for most of the primary cyclone’s positive growth rate, whereas ageostrophic geopotential fluxes disperse EKE to incipient secondary disturbances downstream (at upper levels) and upstream (near the surface), and thus reduce the primary cyclone’s EKE. The overall growth rate is therefore smaller than given by baroclinic conversion alone. The peak in the EKE growth rate occurs around day 4, just at the time of the aforementioned inflection point in the evolution of the surface pressure minimum (cf. Fig. 3). In the moist simulation, baroclinic conversion is enhanced after about day 2.5 (i.e., when condensational heating sets in). Since the energy dispersion term is similar until day 5, the increased baroclinic conversion leads to an enhanced growth rate of EKE in the moist simulation.

A different picture emerges for the downstream cyclone. The peak growth rate is roughly 3 times as large as for the primary cyclone. The fact that the growth rate (Fig. 5b) has its maximum 2 days ahead of the onset of the SLP tracking (Fig. 3b), which marks the emergence of a first closed pressure contour at the surface, is a characteristic consequence of the top-down-induced downstream cyclone that starts with the initiation of an eddy kinetic energy maximum at jet stream altitudes (Orlanski and Sheldon 1995). It is the convergence of ageostrophic geopotential fluxes, removing EKE from the primary cyclone, that dominates EKE growth almost until day 5. Afterward baroclinic conversion takes over. This is in agreement with the concept of downstream development by ageostrophic geopotential fluxes, discussed by Orlanski and Sheldon (1995), according to whom baroclinic conversion sets in only after the genesis of a downstream EKE center by the convergence of geopotential fluxes from upstream. The residual term reduces growth during the incipient phase of the downstream cyclone but weakens as the downstream trough deepens. For the moist case, the EKE tendency is still dominated by the convergence of ageostrophic fluxes; however, it is the enhanced EKE advection that makes the growth rate stronger than the dry case prior to day 5 and enhanced flux convergence thereafter. In the moist case, additional baroclinic conversion does not result in a larger baroclinic growth rate, because of the normalization with EKE that is also larger at the time when baroclinic conversion dominates the overall growth. In agreement with the accelerated moist life cycle, the downstream dispersion away from the first downstream cyclone sets in sooner.

4. Warm conveyor belts in moist baroclinic waves

In this section we aim to identify WCBs in the idealized moist baroclinic wave experiment m60. To this end, air parcel trajectories are started from the low troposphere in the entire model domain at different times during the simulation and WCB trajectories are then identified, separately for the primary cyclone and the first downstream cyclone, with the Lagrangian criterion of ascent within 2 days larger than a certain threshold, as introduced by Wernli and Davies (1997). The identified WCBs are classified as forward- or rearward-sloping WCBs, and their Lagrangian evolution of PV and other significant quantities such as (equivalent) potential temperature and specific humidity are quantified. In a final subsection, the downstream flow modification due to the upper-level WCB outflow is analyzed from the PV perspective.

a. WCBs in the primary cyclone

In the m60 simulation, a prominent WCB with ascent larger than 600 hPa occurs during the 48-h period from day 3 to day 5. Note that this period corresponds to the period with the largest EKE growth rate (Fig. 5). Figure 6 shows the selected trajectories (colored with pressure) together with the surface isentropes in order to investigate the WCB ascent relative to the evolution of the surface fronts. At day 3.5 the WCB trajectories are located at low levels in the warm sector (Fig. 6a). During the next 24 h, they remain within the warm sector and move farther poleward at low levels (Fig. 6b). At day 4.5 they arrive at the warm front, where they experience a very rapid ascent to the upper troposphere (Fig. 6c). Within 10 h they rise from about 900 to 400 hPa (see Fig. 8a). Arriving at upper levels on day 5 (Fig. 6d), the WCB forms an S shape and gently slopes forward into the upper-level ridge downstream of the primary cyclone (located within the negative PV anomaly in Fig. 4g). During later time periods no WCB trajectories fulfilling the 600-hPa ascent criterion are found in the m60 simulation.

Fig. 6.
Fig. 6.

WCB of the primary cyclone in the m60 simulation. Shown are trajectories ascending at least 600 hPa during the 48 h between days 3 and 5. Trajectories are colored with pressure. Contours show surface potential temperature from 260 to 300 K, every 2 K. Shown are snapshots from (a) day 3.5, every 12 h, through (d) day 5. Path of the trajectories is added every 12 h.

Citation: Journal of the Atmospheric Sciences 70, 2; 10.1175/JAS-D-12-0147.1

The location of the rapid WCB ascent coincides with the region of strongest latent heating as shown by vertical south–north-oriented cross sections through this area during the period of strongest vertical motion (Fig. 7). At hour 8 on day 4 (Fig. 7a), the WCB trajectories are located near 850 hPa (see black crosses) in the lower part of the vertically extending warm-frontal cloud (dashed contour; see also thick black contours denoting latent heat release). In this area there is a fairly strong positive diabatic PV tendency (up to about 0.5 PVU h−1), indicating that the ascending WCB air parcels gain PV in the lower troposphere. Six hours later (Fig. 7b), the warm-frontal latent heating has intensified and the WCB trajectories are located at about 600 hPa, above the level of maximum diabatic heating where PV tendencies are negative. Qualitatively, this ascent of the WCB from below to above the level of maximum diabatic heating (associated with diabatic PV production and destruction, respectively) is very similar to the real case analyses of Wernli (1997, see their Fig. 5) and Joos and Wernli (2012, see their Fig. 7). Also, the vertical structure of the diabatic PV tendency field with an intense low-level production region and a vertically extending less intense midtropospheric destruction region agrees favorably with the case study by Joos and Wernli (2012, see their Fig. 8)

Fig. 7.
Fig. 7.

Vertical section across the warm front of the primary cyclone in the m60 simulation (exact position of the cross section is shown in the insets) at (a) day 4, hour 8; and (b) day 4, hour 14. Thick black lines indicate condensational latent heating from 0.5 to 3 K h−1, every 0.5 K h−1; colors show the diabatic PV tendency in PVU h−1. Intersection of the WCB trajectories with the cross section is shown by black crosses. Also shown are potential temperature (thin black lines, every 4 K), the 2-PVU tropopause (thick dashed line), and the 0.1 g kg−1 isoline (dashed) of cloud water content.

Citation: Journal of the Atmospheric Sciences 70, 2; 10.1175/JAS-D-12-0147.1

Figure 8 shows the time evolution of further physical quantities along the WCB flow. Until about hour 28 (i.e., day 4 hour 4), the flow is perfectly adiabatic: specific humidity Qυ and potential temperature θ are exactly conserved along the trajectories. During the same time period, the air parcels ascend slowly and RH increases from about 65% to saturation. As saturation is reached, condensation leads to a transfer of water vapor to cloud water Qc, and Qυ decreases from 9 to less than 1 g kg−1 during the following hours. Note that no other cloud microphysical processes are included in these simulations, such that Qc attains unrealistically high values and no precipitation is forming. In the WCB outflow Qc decreases slightly; however; Qυ and RH remain constant.

Fig. 8.
Fig. 8.

Temporal evolution of key parameters along the primary cyclone’s WCB shown in Fig. 6. Black lines show averaged values for all WCB trajectories, and gray shading indicates the variability (±σ). Shown are (a) pressure (hPa), (b) specific humidity (g kg−1), (c) cloud water content (g kg−1), (d) relative humidity (%), (e) potential temperature (K), and (f) equivalent potential temperature (K).

Citation: Journal of the Atmospheric Sciences 70, 2; 10.1175/JAS-D-12-0147.1

A closer analysis of the ambient air in this region (not shown) revealed constant values of Qυ encompassing patches of high and low Qc, including minor areas of slightly negative PV [associated with the occurrence of inertial instability (Bennets and Hoskins 1979), see below]. We consider these to be numerical artifacts of the chosen model setup (no physical parameterizations are included except for saturation adjustment); however, they do not affect our key results. Associated with the water vapor condensation, latent heating leads to a rapid increase of θ from 294 to 316 K. RH remains constant at 100% and equivalent potential temperature θe remains fairly well conserved near 320 K. Overall, the diagnosed Lagrangian changes along this idealized WCB are qualitatively in good agreement with those identified along real WCBs (Wernli 1997; Grams et al. 2011; Joos and Wernli 2012).

The evolutions of PV and relative vorticity along the WCB are shown in Fig. 9. The Lagrangian PV tendency is calculated from the full tendency Eq. (1) under consideration of the f-plane approximation. The diabatic heating tendency due to evaporation or condensation is a direct model output variable of the saturation adjustment procedure. During the first day, parcel motion is completely adiabatic and PV is perfectly conserved (constant value of about 0.36 PVU). As an aside we note that this—together with the perfect material conservation of Qυ and θ—is an excellent quality check for the accuracy of the trajectories. Relative vorticity already increases, pointing to the effects of vortex stretching on the ascending air parcels. At about hour 28, the air parcels reach saturation (as discussed above) and PV first increases rapidly to about 1.4 PVU at hour 33, before decreasing gradually to values close to 0 PVU at the end of the 2-day period.3 The rapid PV increase is due to both the positive vertical gradient of the latent heating (Fig. 7) and the already increased absolute vorticity values [cf. Eq. (2)]. The substantial influence of absolute vorticity on the material change of PV along a WCB is consistent with the findings of Joos and Wernli (2012).

Fig. 9.
Fig. 9.

As Fig. 8, but for (a) potential vorticity (PVU) and (b) absolute (light gray shading) and relative (dark gray shading) vorticity (in units of f).

Citation: Journal of the Atmospheric Sciences 70, 2; 10.1175/JAS-D-12-0147.1

The transition from a PV increase to a PV decrease along the flow occurs approximately at the level of maximum latent heating (not shown). The overall PV evolution is asymmetric with depleted values in the outflow relative to the initial values (Fig. 9), as diagnosed for a real case WCB by Pomroy and Thorpe (2000). Another interesting asymmetry occurs for the evolution of relative vorticity along the flow: for instance, at hour 40, when the PV values are on average very similar to the ones at hour 30, the relative vorticity values are lower by almost 1f. This points to a strong deformation of the ascending air parcel, which is horizontally confined and vertically extended in the lower troposphere at hour 30 (and therefore high PV is mainly associated with increased relative vorticity) and horizontally broad and vertically shallow in the upper troposphere at hour 40 (and therefore high PV is mainly associated with increased static stability). Note that at the end of the WCB ascent, most trajectories are characterized by relative vorticity below −1f (and some with negative PV values). Such regions with negative absolute vorticity have been associated with the occurrence of inertial instability (Bennets and Hoskins 1979).

As a summary, Fig. 10 provides a three-dimensional visualization of the formation of the primary cyclone’s S-shaped WCB. Shown are surface potential temperature (thin black lines), latent heating due to condensation (red isosurface of 1.25 K h−1 above the warm front intersected by the yellow WCB trajectories), and areas with cloud water (light blue isosurface for Qc = 0.15 g kg−1) at hour 12 on day 4. Two upper-level fields are shown, namely, PV on the 316-K isentropic surface (semitransparent colored surface, see color bar) and the jet stream at 10 km (black contours in uppermost panel) on day 5. The transparency of the isentropic surface allows a glance at the underlying structures. Note that the WCB at lower levels intersects the region of strongest latent heating and later at upper levels, the isentropic surface exactly in the region of lowest PV.

Fig. 10.
Fig. 10.

Three-dimensional visualization of the WCB in the primary cyclone. Shown are isentropes at the surface (black, from 266 to 298 K, every 2 K), cloud water (blue, semitransparent, Qc = 0.15 g kg−1), and isosurface of latent heating (red, 1.25 K h−1) at day 4, hour 12. Shown aloft are 316-K isentropic surface colored with PV, and wind speed contours at 10-km altitude (black, from 15 m s−1 of southernmost contour to max 40 m s−1, every 5 m s−1) at day 5. WCB trajectory path between day 4 and day 5 is shown in yellow.

Citation: Journal of the Atmospheric Sciences 70, 2; 10.1175/JAS-D-12-0147.1

b. WCBs in the downstream cyclone

Within the downstream cyclone, the maximum vertical ascent of trajectories in 2 days amounts to 535 hPa between days 6 and 8. Therefore, we used a threshold of 525 hPa to identify WCB trajectories in the downstream cyclone during these 2 days. Interestingly, and in contrast to the primary cyclone, two distinct coherent airstreams are identified, as shown in Figs. 11, 12. (Reducing the threshold in the primary cyclone to 550 hPa increases the number of selected trajectories; however, it does not reveal the existence of a second WCB as in the downstream cyclone. With a further reduction to the threshold used in the downstream cyclone—that is, 525 hPa—an enormous number of air parcels is identified still without any evidence for two clearly separated airstreams.)

Fig. 11.
Fig. 11.

As Fig. 6, but for the fWCB in the downstream cyclone, every 12 h from (a) day 6.5 through (d) day 8.

Citation: Journal of the Atmospheric Sciences 70, 2; 10.1175/JAS-D-12-0147.1

Fig. 12.
Fig. 12.

As Fig. 11, but for the rWCB in the downstream cyclone.

Citation: Journal of the Atmospheric Sciences 70, 2; 10.1175/JAS-D-12-0147.1

Both WCBs in the downstream cyclone have their starting region in the warm sector; however, in the initial phase, at day 6.5, one is located close to the surface cold front (Fig. 12a), whereas the other one is located farther to the northeast in the center of the warm sector (Fig. 11a). Because of their differing region of ascent (relative to the cyclone system), the two WCBs can be classified as rWCB and fWCB. The rWCB moves along the surface cold front into the frontal fracture region and starts ascending already at the cold front (e.g., before day 7, see Fig. 11b). In contrast, the fWCB remains longer in the warm sector at low levels and moves toward the bent-back front, where it ascends very rapidly. At day 7.5 it is located at about 480 hPa just above the bent-back front (Fig. 11c), whereas the rWCB shows a more gradual ascent and is located at about 650 hPa above the narrowing warm sector (Fig. 12c). In harmony with the region of maximum ascent, the fWCB trajectories reach the region of strongest diabatic heating (i.e., the maximum within the entire cyclone from an Eulerian point of view), which is located at the eastern part of the bent-back front (Fig. 11c), while the rWCB passes the area of strongest heating farther south along the cold front. At this time, the latent heat release within the considered fWCB air masses corresponds to the diabatic heating maximum in the entire cyclone; at slightly earlier times, other WCB trajectories (which we did not consider explicitly) have produced the Eulerian latent heat maximum.

At the end of the ascent (Figs. 11d, 12d), the fWCB turns anticyclonically (“forward sloping”) and moves toward the northeast, whereas the rWCB continues to flow cyclonically to the rear of the cyclone center (“rearward sloping”). The direction of the outflow is determined by the wind direction prevailing at the level and location of the WCB outflow. Obviously, for the two WCBs, the wind in their outflow regions differs substantially.

Figure 13 shows the time evolution of several physical quantities along the fWCB and rWCB in the downstream cyclone. As for the WCB in the primary cyclone, the mean values over all trajectories of the fWCB and rWCB are shown by the black lines, while the standard deviation of the variables is shown by light gray shading for the fWCB and darker gray shading for the rWCB. Qualitatively, the evolution of the parameters along the two WCBs is very similar (also to the evolution along the primary cyclone’s WCB), however, with some interesting differences. Compared to the rWCB, the fWCB starts on slightly lower isentropes (~295.5 vs ~297.5 K) and is initially less humid (8.8 vs 9.6 g kg−1), which is consistent with its more poleward origin. Despite the smaller initial moisture, the fWCB reaches about the same altitude of about 420 hPa and a significantly more pronounced cycle of PV production and destruction during the ascent. Peak values of PV after about 30 h differ strongly (~1.1 PVU for the fWCB and ~0.7 PVU for the rWCB); however, at the end of the ascent, both WCBs reach on average PV values of about 0.15 PVU. The strong increase—and subsequent decrease—of PV along the fWCB are due to the particularly intense vertical gradients of latent heating above the bent-back front, supplemented by higher relative vorticity values for the fWCB (not shown). Note that around hour 40—that is, at the time when the fWCB reaches about its final altitude—the rWCB still experiences latent heating at around 550 hPa. This goes in line with a continued conversion of θυ to θc.

Fig. 13.
Fig. 13.

Temporal evolution of key parameters along the downstream cyclone’s WCBs (light gray shading for fWCB; dark gray shading for rWCB). Black lines show averaged values for all WCB trajectories, and the gray shading indicates the variability (±σ). Shown are (a) pressure (hPa), (b) specific humidity (g kg−1), (c) cloud water content (g kg−1), (d) potential vorticity (PVU), (e) potential temperature (K), and (f) equivalent potential temperature (K).Vertical line marks hour 40.

Citation: Journal of the Atmospheric Sciences 70, 2; 10.1175/JAS-D-12-0147.1

To summarize the WCBs in the downstream cyclone, Fig. 14 provides a three-dimensional visualization of the fWCB and rWCB. The trajectories are colored according to their PV value. All fields are shown at day 8—that is, at the time when the WCBs have reached their outflow level—and the air parcels are located at the end of the trajectory path. Shown are surface isentropes (black contours), areas with cloud water (light blue isosurface for Qc = 0.2 g kg−1), and a band with PV equal to 2 PVU between heights of 6.0 and 6.5 km, indicating the dynamical tropopause. The WCB trajectory path is shown for the last 18 h prior to day 8. During the ascent, the fWCB, which is farther to the west, is dark red, corresponding to more than 1 PVU. As discussed above, the rWCB, which is a lighter red during the ascent, does not attain such large PV values. In the upper-level outflow, the two WCBs diverge considerably into a forward- and rearward-sloping component, both with low PV values below 0.3 PVU, as shown in blue. Note here again that the outflow of the rWCB occurs into the hook of tropospheric PV values located above the surface cyclone’s bent-back front, whereas the fWCB outflow is along the jet entering the downstream ridge.

Fig. 14.
Fig. 14.

Three-dimensional visualization of the WCBs in the downstream cyclone. WCB trajectories are colored with PV (PVU). All fields are shown at day 8; WCB trajectory path shown for last 18 h of ascent. Surface isentropes (black, from 266 to 298 K, every 2 K), isosurface of cloud water content (blue transparent shading, for 0.2 g kg−1), and isosurface of PV (brown shades, for 2 PVU between 6.0 and 6.5 km).

Citation: Journal of the Atmospheric Sciences 70, 2; 10.1175/JAS-D-12-0147.1

c. Downstream flow modification

The diabatically modified, very low PV values in the regions of the WCB outflows (both in the primary and downstream cyclones) can significantly perturb the upper-level Rossby waveguide and consequently modify the downstream cyclogenesis, as we show in this subsection. Compared to the basic-state PV field, the low values in the upper-tropospheric WCB outflows (which are even lower than in the low-tropospheric WCB inflow regions) correspond to substantial negative PV anomalies at an altitude of about 350 hPa in the primary and about 420 hPa in the downstream cyclone. To further elucidate the structure and to quantify the potential impact of these upper-level negative PV anomalies, Fig. 15 shows the difference of PV and horizontal wind on the isentrope of the WCB outflow between the dry reference run and the moist m60 simulation at the time of the WCB outflow, both for the primary and the downstream cyclones.

Fig. 15.
Fig. 15.

Differences between the moist and the dry simulations of PV (colors, PVU), and horizontal wind vectors at the WCB outflow level for (a) the primary cyclone’s WCB on 316 K at day 5 and (b) the downstream cyclone’s WCBs on 319 K at day 8. Green lines indicate the 2-PVU tropopause (solid for m60 simulation, and dashed for dry simulation).

Citation: Journal of the Atmospheric Sciences 70, 2; 10.1175/JAS-D-12-0147.1

For the primary cyclone at day 5 (Fig. 15a), the difference pattern on 315 K shows a pronounced negative PV anomaly in the ridge of the moist simulation, that is, in the region of the WCB outflow and its surrounding, and a narrow band with positive PV differences at higher latitudes. More enhanced positive PV differences occur in the downstream trough, which is essential for the more rapid top-down development of the downstream cyclone in the moist simulation. Note that the absolute amplitude of both anomalies exceeds 2 PVU. Also shown are the differences in the isentropic flow field, which clearly reveals the anticyclonic circulation induced by the negative PV anomaly in the ridge of the moist simulation and the cyclonic circulation associated with the positive PV anomaly in the downstream trough. Also visible is the enhanced jet stream (by about 10 m s−1) in the center of the panel just downstream of the WCB outflow.

To analyze whether the substantial PV differences in the upper-level ridge between the two simulations are primarily due to diabatic PV erosion or modified isentropic advection (due to altered winds arising from modified PV), we calculated 2-day backward trajectories for the moist simulation from the blue region shown in Fig. 15a, that is, from the region where the upper-level PV is reduced in the moist simulation compared to the dry one. The evolution of pressure, potential temperature, and PV along these trajectories reveals that most trajectories from the WCB outflow region (and its surrounding) ascend from lower levels and experience latent heating and a significant diabatic PV reduction during the last 12 h (not shown). In contrast, the trajectories from the hooklike region farther to the west move quasi isentropically and are characterized by an almost constant value of PV. Together, this indicates that both diabatic PV erosion and altered isentropic advection are important for understanding the pattern in Fig. 15a, and that the diabatic erosion process is responsible for the largest reduction of upper-level PV in the moist run compared to the dry run.

Also the modified downstream development can conceptually be understood from the PV perspective. The diabatic ridge intensification in the moist simulation goes along with an amplified upper-level anticyclonic circulation, which in turn leads to an intensification of the downstream trough due to enhanced southward advection of high PV values (cf. Wernli et al. 1999; Grams et al. 2011). The idealized simulations show that the effect of the primary cyclone’s WCB on this amplification of the downstream trough is substantial. The analysis of the energetics also revealed a stronger downstream energy dispersion by ageostrophic fluxes in the moist run, confirming the PV perspective.

For the downstream cyclone at day 8 (Fig. 15b), two distinct negative PV anomalies can be seen on 319 K in the vicinity of the cyclone, associated with the outflow of the fWCB and the rWCB, respectively. For the fWCB the picture is comparable to the primary cyclone’s WCB 3 days earlier. Both ascend into the ridge of the upper-level wave pattern and slope anticyclonically forward. Their associated anomalies in the PV and wind fields are comparable, as is the pronounced amplifying impact on the formation of the downstream trough. For the upper-level negative PV anomaly associated with the outflow of the rWCB, the analysis of its impact on the large-scale flow evolution is not as straightforward as for the fWCB. The anomaly occurs to the west of the surface cyclone center, at the “nose” of the cyclonically breaking wave. As positive and negative PV anomalies of similar size tend to move parallel to each other, the rWCB-enhanced negative PV anomaly accelerates the southward motion. From Fig. 15b, which is approximately at the final height of both conveyor belts, no clear signal of a wind anomaly, induced by the rWCB’s PV anomaly, can be found. The influence of this WCB on the large-scale flow seems to be weak compared to well-defined circulations induced by the fWCB’s PV anomalies. A PV inversion technique would help to investigate further the influence of the negative PV anomaly created by the rWCB.

5. Conclusions

a. Key findings

The main objectives of this study have been to analyze the differences between idealized moist and dry baroclinic life cycles, including the formation of a first downstream cyclone, to identify the formation and structure of WCBs in idealized moist baroclinic waves, to analyze the evolution of PV and other physical quantities along the WCB flow, and to study the mechanisms by which the WCBs influence the upper-level downstream flow evolution. In this section we summarize and discuss the main results concerning these aspects.

The comparison of the upper-level-trough-induced primary cyclone in the dry and moist simulation reveals a faster intensification in the moist simulation, mainly due to enhanced baroclinic conversion. The scale of the dry and moist primary cyclones is comparable, but the moist cyclone develops a more intense bent-back front where the strongest latent heating occurs. These results are in very good qualitative agreement with earlier moist baroclinic life cycle studies, for example, by Balasubramanian and Yau (1994) and Whitaker and Davis (1994). With respect to comparing idealized dry and moist baroclinic waves, the novel aspect of this study is the choice of the localized, finite-amplitude upper-level initial perturbation in the long channel, which also allows for studying the evolution of the first upstream and downstream cyclones, respectively. The downstream trough evolves earlier and has a modified structure in the moist simulation. Consequently, the structure at the surface of the downstream cyclone is modified, compared to the dry run, as of its initiation. Discrepancies along the surface cold- and warm-frontal regions are further enhanced as soon as condensation sets in and latent heating contributes to frontogenesis. The shallow upstream cyclone is of smaller scale and associated with a very intense warm front in the moist simulation. Pronounced differences occur between the dry and moist simulations on day 6 in the upper-level isentropic PV field with, in particular, a much more pronounced ridge between the primary cyclone and the downstream cyclone in the moist simulation. Significantly reduced PV values (compared to the initial conditions) occur along the downstream flank of this upper-level ridge.

In the moist idealized baroclinic wave life cycles, we were able to identify two distinct types of WCBs, forward- and rearward-sloping WCB types, using a Lagrangian criteria of maximum ascent within 2 days (as used previously in real case investigations of WCBs). The primary cyclone developed a strong fWCB, whereas the downstream cyclone, which evolves according to the conceptual Shapiro–Keyser life cycle model, revealed the formation of both an fWCB and an rWCB. In the primary cyclone, the fWCB occurs between days 3 and 5, that is, during the period with the maximum overall kinetic energy growth rate. In the downstream cyclone, the WCBs occur between days 6 and 8, that is, during the period with maximum baroclinic energy conversion. In our moist baroclinic life cycle, the following occur:

  1. fWCBs originate in the warm sector, move into the frontal fracture region at low-tropospheric levels, and then ascend over the bent-back front, where maximum latent heat release occurs in the simulations. Because of prevailing zonal winds in the outflow region, fWCBs turn anticyclonically in the downstream ridge, forming an S shape.
  2. The rWCB also starts in the warm sector, to the south of the origin of the fWCB, and therefore with initially slightly larger specific humidity and potential temperature values. It is located close to the surface cold front, where it starts to ascend. Its ascent is less steep than for the fWCB and leads into regions of prevailing cyclonic flow, where it curves cyclonically (“rearward”) above the cyclone center.
    • The Lagrangian PV evolution along both types of identified WCBs has been studied in detail. Along the low-level parts of the WCBs, located in the cyclone’s warm sector, PV remains almost perfectly conserved. As soon as condensational heating occurs in the considered set of ascending WCB air parcels, PV increases intensively because the air parcels are located in areas with a positive vertical gradient of latent heating [Eq. (2)]. This indicates that they are located below other WCB air parcels, which started to ascend earlier and which, at this particular time, release more latent heat. Later, if the considered WCB air parcels are above the level of maximum latent heating, then PV destruction sets in, leading to slightly lower PV values in the WCB outflow compared to the values in the inflow region. This Lagrangian evolution of PV along the WCB flow agrees well with findings of previous real case studies of WCBs (Wernli 1997; Pomroy and Thorpe 2000; Grams et al. 2011; Joos and Wernli 2012). As a consequence of the low PV values in the WCB outflow, the WCBs create negative PV anomalies in their outflow at upper-tropospheric levels. In accordance with stronger latent heating in the bent-back front, the fWCB attains higher PV values in the midtroposphere than the rWCB (which ascends at the cold front), while both create comparably intense negative PV anomalies in their outflow.
    • Finally, these negative PV anomalies in the WCB outflow significantly affected the downstream flow evolution. Difference patterns of upper-level PV and winds between the dry and the moist simulations clearly reveal (cf. Fig. 15):
  3. reduced PV in the upper-level ridge of the moist baroclinic wave in the region of the WCB outflow;
  4. an amplified upper-level ridge and an intensified anticyclonic circulation;
  5. consequently, an earlier formation and intensification of the downstream trough through enhanced advection of stratospheric air from the north
  6. and accordingly, an intensified cyclonic circulation associated with the more pronounced downstream trough, which contributes to an enhanced downstream cyclogenesis.
We conclude that the WCB ascending from the upstream primary cyclone is of key significance for the downstream baroclinic development in the moist simulation. The described mechanism in our key findings (iii)–(vi) has been observed in the case studies of Pomroy and Thorpe (2000) and Grams et al. (2011). In the dry simulation no WCB occurs, the formation of the upper-level ridge is not enhanced through diabatic processes, and the downstream evolution is slowed down. (A video visualization of the primary WCB and its effect on the evolution of the moist baroclinic wave is available as supplemental material at the Journals Online website: http://dx.doi.org/10.1175/JAS-D-12-0147.s1, which helps to further appreciate Fig. 10.)

b. Classification in the framework of conceptual conveyor belt models

Here, we aim at briefly classifying the identified idealized WCBs within the framework of conceptual conveyor belt models. Two classes of WCBs are commonly distinguished (Young et al. 1987; Browning and Roberts 1994). According to Browning (2004, p. 378), WCBs of type W1 are characterized as “cloudy airstreams along the main cold front before rising above the warm front.” In our simulation we do not identify any WCB starting to rise above the cold front and, consequently, the identified WCBs are not of type W1. However, the WCB in the primary cyclone (which is not yet cloudy along the cold front) mainly ascends above the warm front and later turns anticyclonic into the warm-frontal cloud band. It therefore can be regarded as a variant of W1. Since WCBs of type W1 and W2 have been identified with tracer experiments by Agustí-Panareda et al. (2009), the absence of a clear type W1 WCB points to one of the limitations of our specific simulation setup. WCBs of type W2 cross, according to Browning (2004, p. 378), “the dry-slot region at low levels before rising above the bent-back front (WF2). The W2 flow then fans out and forms the upper part of the cloud head.” The WCBs identified in our study in the downstream cyclone indeed rise above the bent-back front and moreover as they turn rearward and forward, respectively, they together reproduce the mentioned “fanning out” and end up in the cloud head (cf. Fig. 8c in Browning and Roberts 1994). Hence, they can be classified as type W2.

c. Contribution of WCBs to baroclinic energy conversion

One of the key findings of our study is the influence of WCBs on the Rossby waveguide and the downstream cyclogenesis. Here, the question about the relative importance of the WCB (compared to all other, i.e., less strongly ascending, air parcels) on the life cycle of the cyclone in which the WCB is emerging, is briefly discussed. To this end, we calculated a large number of forward trajectories from the lower troposphere for the 2-day period of the WCB in our primary cyclone (days 3–5), which ascend at least by 50 hPa. Along these trajectories we accumulated baroclinic conversion as given by term III in Eq. (9). We found that the majority of air parcels ascend between 50 and 300 hPa in this time period and that the number of WCB air parcels (with an ascent exceeding 600 hPa) is low compared to the rest. The relationship between baroclinically created kinetic energy and ascent in terms of pressure change is almost linear (not shown). When considering different categories of ascent and accumulating the total baroclinic energy conversion for all trajectories in the different categories of ascent, it turns out that the largest contribution to the total converted kinetic energy stems from the large number of air parcels rising from the warm sector with medium to moderate changes in pressure (ascent from 50 to 350 hPa). However, when considering individual air parcels, then those forming the WCB contribute most to the kinetic energy production in terms of accumulated baroclinic conversion in these 2 days. This could serve as an alternative WCB selection criterion. In summary, from an energy budget perspective, the contribution from the WCB to the total baroclinic conversion within the cyclone is weak in our simulation (because of the small number of WCB air parcels). The opposite is true from an individual parcel perspective. A more detailed analysis of the role of the WCB—that is, of the strongest ascending trajectories—for the evolution of the cyclone itself (e.g., through the diabatic production of PV in the low to middle troposphere) is a relevant question that merits a closer analysis in future studies.

d. Limitations and outlook

There are several limitations of this idealized study. First, WCBs have been identified for only one particular structure of the basic-state jet and humidity profile. It is known from several dry baroclinic wave simulations (Davies et al. 1991; Thorncroft et al. 1993; Wernli et al. 1998) that relatively small changes in the basic-state jet structure can lead to profound changes in the structure and intensity of the evolving cyclones and their attendant fronts. This, of course, directly influences the location of the regions of maximum ascent, and, in the moist simulations, of latent heating and therefore the occurrence of WCBs; this points to the necessity to investigate the variability of WCB structures and physical characteristics in future experiments with modified basic-state jets. It is conceivable that with differing basic states, cyclones evolve with particularly strong cold fronts, leading to maximum latent heating and WCB ascent near the cold front (in contrast to the strongest WCB ascent in the bent-back frontal region in our simulations). With respect to the initial humidity profile, we briefly mention that we also investigated the existence of WCBs in simulations with uniform initial relative humidity values of 40% and 80%. Besides an increasing (decreasing) number of selected trajectories and a shift in WCB occurrence due to earlier (later) saturation and stronger (weaker) latent heating in the moister (drier) simulation, we did not observe significant qualitative changes to the WCBs analyzed in detail for the m60 simulation.

A second caveat is related to the simplified physics of our simulations. Condensation and evaporation of water vapor are the only sources of latent heat release in the experiments, and effects from the cloud microphysics, embedded convection, and boundary layer turbulence have been neglected. The main justification for such an approach is that we aimed to work with the simplest system that might be able to produce WCBs, which deviates as little as possible from classical dry baroclinic wave experiments. However, the recent study by Joos and Wernli (2012) revealed that other microphysical processes play a significant role in diabatically modifying the PV evolution along WCBs. Especially close to the outflow level, the formation of snow and ice might lead to a further amplification of PV anomalies. In the future, we plan to investigate WCBs in physically more complete simulations of idealized baroclinic waves, as performed, for instance, by Boutle et al. (2011), who analyzed the moisture transport associated with WCBs.

Acknowledgments

We thank B. Colle and J. Olson for their assistance in implementing the initial conditions. We are grateful to Sebastian Limbach (University of Mainz) for introducing us to INSIGHT and helping with creating the 3D visualizations, and to Linda Schlemmer (now at MPI Hamburg) and colleagues at the German Weather Service (DWD) for supporting us with the implementation of periodic boundaries in the COSMO model. This project was funded by the Swiss National Science Foundation (Project 200021-130079). We thank two anonymous reviewers for their detailed and thoughtful comments, which were very helpful for improving our analysis and the first draft of the manuscript.

APPENDIX

Eddy Kinetic Energy Equation

We follow Orlanski and Katzfey (1991), but with height as the vertical coordinate and the basic state defined by the zonal mean over the entire channel. The anelastic horizontal momentum equation in the absence of friction and neglecting curvature terms (Vallis 2006) can be written as
ea1
where is the horizontal gradient operator. Taking the zonal average, denoted by an overbar or an uppercase letter in the case of wind velocity, yields
ea2
We subtract it from Eq. (A1) to obtain the corresponding equation for the horizontal eddy wind, as shown:
ea3
To arrive at the EKE tendency equation, we multiply Eq. (A3) by ρ0v′, recall the definition of the eddy kinetic energy and collect terms
ea4
The second term is obtained by noting that ρ0 is a function of z only and making use of the anelastic continuity equation (Vallis 2006)
ea5
The exchange of energy with the zonal flow is effectuated by the third and the fourth terms of Eq. (A4), which we will absorb within the residual term. Using the eddy part of the continuity equation · v′ + 1/ρ0z(ρ0w′) = 0, the term on the right-hand side is split into
ea6
Combining Eqs. (A4) and (A6) we obtain
ea7

REFERENCES

  • Agustí-Panareda, A., , S. L. Gray, , and S. E. Belcher, 2009: On the dependence of boundary layer ventilation on frontal type. J. Geophys. Res.,114, D05305, doi:10.1029/2008JD010694.

  • Balasubramanian, G., , and M. K. Yau, 1994: The effects of convection on a simulated marine cyclone. J. Atmos. Sci., 51, 23972417.

  • Balasubramanian, G., , and M. K. Yau, 1996: The life cycle of a simulated marine cyclone: Energetics and PV diagnostics. J. Atmos. Sci., 53, 639653.

    • Search Google Scholar
    • Export Citation
  • Balasubramanian, G., , and S. T. Garner, 1997: The role of momentum fluxes in shaping the life cycle of a baroclinic wave. J. Atmos. Sci., 54, 510533.

    • Search Google Scholar
    • Export Citation
  • Bennets, D. A., , and B. J. Hoskins, 1979: Conditional symmetric instability - A possible explanation for frontal rainbands. Quart. J. Roy. Meteor. Soc., 105, 945962.

    • Search Google Scholar
    • Export Citation
  • Bjerknes, J., 1919: On the structure of moving cyclones. Mon. Wea. Rev., 47, 9599.

  • Boutle, I. A., , S. E. Belcher, , and R. S. Plant, 2011: Moisture transport in midlatitude cyclones. Quart. J. Roy. Meteor. Soc., 137, 360373.

    • Search Google Scholar
    • Export Citation
  • Browning, K. A., 1986: Conceptual models of precipitation systems. Wea. Forecasting, 1, 2341.

  • Browning, K. A., 1990: Organization of clouds and precipitation in extratropical cyclones. Extratropical Cyclones: The Erik Palmén Memorial Volume, C. W. Newton and E. O. Holopainen, Eds., Amer. Meteor. Soc., 129–153.

  • Browning, K. A., 2004: The sting at the end of the tail: Damaging winds associated with extratropical cyclones. Quart. J. Roy. Meteor. Soc., 130, 375399.

    • Search Google Scholar
    • Export Citation
  • Browning, K. A., , and N. M. Roberts, 1994: Structure of a frontal cyclone. Quart. J. Roy. Meteor. Soc., 120, 15351557.

  • Bush, A. B. G., , and W. R. Peltier, 1994: Tropopause folds and synoptic-scale baroclinic wave life cycles. J. Atmos. Sci., 51, 15811604.

    • Search Google Scholar
    • Export Citation
  • Carlson, T. N., 1980: Airflow through midlatitude cyclones and the comma cloud pattern. Mon. Wea. Rev., 108, 14981509.

  • Cooper, I. M., , A. J. Thorpe, , and C. G. Bishop, 1992: The role of diffusive effects on potential vorticity in fronts. Quart. J. Roy. Meteor. Soc., 118, 629647.

    • Search Google Scholar
    • Export Citation
  • Davies, H. C., , C. Schär, , and H. Wernli, 1991: The palette of fronts and cyclones within a baroclinic wave development. J. Atmos. Sci., 48, 16661689.

    • Search Google Scholar
    • Export Citation
  • Davis, C. A., 2010: Simulations of subtropical cyclones in a baroclinic channel model. J. Atmos. Sci., 67, 28712892.

  • Eckhardt, S., , A. Stohl, , H. Wernli, , P. James, , C. Forster, , and N. Spichtinger, 2004: A 15-year climatology of warm conveyor belts. J. Climate, 17, 218237.

    • Search Google Scholar
    • Export Citation
  • Eliassen, A., , and E. Kleinschmidt, 1957: Dynamic meteorology. Handbuch der Physik (Encyclopedia of Physics), S. Flügge, Ed., Springer-Verlag, 1–154.

  • Fantini, M., 2004: Baroclinic instability of a zero-PVE jet: Enhanced effects of moisture on the life cycle of midlatitude cyclones. J. Atmos. Sci., 61, 16631680.

    • Search Google Scholar
    • Export Citation
  • Fehlmann, R., 1997: Dynamics of seminal PV elements. Ph.D. dissertation, Swiss Federal Institute of Technology (ETH), Diss. ETH 12229, 143 pp.

  • Govindasamy, B., , and S. T. Garner, 1997: The equilibration of short baroclinic waves. J. Atmos. Sci., 54, 28502871.

  • Grams, C. M., and Coauthors, 2011: The key role of diabatic processes in modifying the upper-tropospheric wave guide: A North Atlantic case-study. Quart. J. Roy. Meteor. Soc., 137, 21742193.

    • Search Google Scholar
    • Export Citation
  • Harrold, T. W., 1973: Mechanisms influencing distribution of precipitation within baroclinic disturbances. Quart. J. Roy. Meteor. Soc., 99, 232251.

    • Search Google Scholar
    • Export Citation
  • Hoskins, B. J., , and N. V. West, 1979: Baroclinic waves and frontogenesis. Part II: Uniform potential vorticity jet flows—Cold and warm fronts. J. Atmos. Sci., 36, 16631680.

    • Search Google Scholar
    • Export Citation
  • Hoskins, B. J., , M. E. McIntyre, , and A. W. Robertson, 1985: On the use and significance of isentropic potential vorticity maps. Quart. J. Roy. Meteor. Soc., 111, 877946.

    • Search Google Scholar
    • Export Citation
  • Joos, H., , and H. Wernli, 2012: Influence of microphysical processes on the potential vorticity development in a warm conveyor belt: A case-study with the limited-area model COSMO. Quart. J. Roy. Meteor. Soc., 138, 407418.

    • Search Google Scholar
    • Export Citation
  • Kleinschmidt, E., 1950: Über Aufbau und Entstehung von Zyklonen (1. Teil) (On the structure and formation of cyclones, part 1). Meteor. Rundsch., 3, 16.

    • Search Google Scholar
    • Export Citation
  • Massacand, A. C., , H. Wernli, , and H. C. Davies, 2001: Influence of upstream diabatic heating upon an Alpine event of heavy precipitation. Mon. Wea. Rev., 129, 28222828.

    • Search Google Scholar
    • Export Citation
  • Moore, R. W., , and M. T. Montgomery, 2005: Analysis of an idealized, three-dimensional diabatic Rossby vortex: A coherent structure of the moist baroclinic atmosphere. J. Atmos. Sci., 62, 27032725.

    • Search Google Scholar
    • Export Citation
  • Nakamura, N., , and I. M. Held, 1989: Nonlinear equilibrium of two-dimensional Eady waves. J. Atmos. Sci., 46, 30553064.

  • Olson, J. B., , and B. A. Colle, 2007: A modified approach to initialize an idealized extratropical cyclone within a mesoscale model. Mon. Wea. Rev., 135, 16141624.

    • Search Google Scholar
    • Export Citation
  • Orlanski, I., , and J. Katzfey, 1991: The life cycle of a cyclone wave in the Southern Hemisphere. Part I: Eddy energy budget. J. Atmos. Sci., 48, 19721998.

    • Search Google Scholar
    • Export Citation
  • Orlanski, I., , and E. K. M. Chang, 1993: Ageostrophic geopotential fluxes in downstream and upstream development of baroclinic waves. J. Atmos. Sci., 50, 212225.

    • Search Google Scholar
    • Export Citation
  • Orlanski, I., , and J. P. Sheldon, 1995: Stages in the energetics of baroclinic systems. Tellus, 47A, 605628.

  • Pomroy, H. R., , and A. J. Thorpe, 2000: The evolution and dynamical role of reduced upper-tropospheric potential vorticity in intensive observing period one of FASTEX. Mon. Wea. Rev., 128, 18171834.

    • Search Google Scholar
    • Export Citation
  • Schär, C., , and H. Wernli, 1993: Structure and evolution of an isolated semi-geostrophic cyclone. Quart. J. Roy. Meteor. Soc., 119, 5790.

    • Search Google Scholar
    • Export Citation
  • Schultz, D. M., , D. Keyser, , and L. F. Bosart, 1998: The effect of large-scale flow on low-level frontal structure and evolution in midlatitude cyclones. Mon. Wea. Rev., 126, 17671791.

    • Search Google Scholar
    • Export Citation
  • Shapiro, M. A., , and D. A. Keyser, 1990: Fronts, jet streams, and the tropopause. Extratropical Cyclones: The Erik Palmén Memorial Volume, C. W. Newton and E. O. Holopainen, Eds., Amer. Meteor. Soc., 167–191.

  • Shapiro, M. A., and Coauthors, 1999: A planetary-scale to mesoscale perspective of the life cycles of extratropical cyclones: The bridge between theory and observations. The Life Cycles of Extratropical Cyclones, M. A. Shapiro and S. Grønås, Eds., Amer. Meteor. Soc., 139–185.

  • Simmons, A. J., 1994: Numerical simulations of cyclone life cycles. Proceedings of an International Symposium on the Life Cycles of Extratropical Cyclones, E. S. Grønås and M. A. Shapiro, Eds., Vol. 1, Alma Mater Forlag, 149–160.

  • Simmons, A. J., , and B. J. Hoskins, 1979: The downstream and upstream development of unstable baroclinic waves. J. Atmos. Sci., 36, 12391254.

    • Search Google Scholar
    • Export Citation
  • Sinclair, V. A., , S. L. Gray, , and S. E. Belcher, 2008: Boundary-layer ventilation by baroclinic life cycles. Quart. J. Roy. Meteor. Soc., 134, 14091424.

    • Search Google Scholar
    • Export Citation
  • Steppeler, J., , G. Doms, , U. Schäettler, , H. W. Bitzer, , A. Gassmann, , U. Damrath, , and G. Gregoric, 2003: Meso-gamma scale forecasts using the nonhydrostatic model LM. Meteor. Atmos. Phys., 82, 7596.

    • Search Google Scholar
    • Export Citation
  • Stoelinga, M. T., 1996: A potential vorticity-based study of the role of diabatic heating and friction in a numerically simulated baroclinic cyclone. Mon. Wea. Rev., 124, 849874.

    • Search Google Scholar
    • Export Citation
  • Thorncroft, C. D., , B. J. Hoskins, , and M. E. McIntyre, 1993: Two paradigms of baroclinic-wave life-cycle behaviour. Quart. J. Roy. Meteor. Soc., 119, 1755.

    • Search Google Scholar
    • Export Citation
  • Vallis, G. K., 2006: Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation. Cambridge University Press, 745 pp.

  • Wernli, H., 1997: A Lagrangian-based analysis of extratropical cyclones. II: A detailed case-study. Quart. J. Roy. Meteor. Soc., 123, 16771706.

    • Search Google Scholar
    • Export Citation
  • Wernli, H., , and H. C. Davies, 1997: A Lagrangian-based analysis of extratropical cyclones. I: The method and some applications. Quart. J. Roy. Meteor. Soc., 123, 467489.

    • Search Google Scholar
    • Export Citation
  • Wernli, H., , and C. Schwierz, 2006: Surface cyclones in the ERA-40 dataset (1958–2001). Part I: Novel identification method and global climatology. J. Atmos. Sci., 63, 24862507.

    • Search Google Scholar
    • Export Citation
  • Wernli, H., , R. Fehlmann, , and D. Lüthi, 1998: The effect of barotropic shear on upper-level induced cyclogenesis: Semigeostrophic and primitive equation numerical simulations. J. Atmos. Sci., 55, 20802094.

    • Search Google Scholar
    • Export Citation
  • Wernli, H., , M. A. Shapiro, , and J. Schmidli, 1999: Upstream development in idealized baroclinic wave experiments. Tellus, 51A, 574587.

    • Search Google Scholar
    • Export Citation
  • Whitaker, J. S., , and C. A. Davis, 1994: Cyclogenesis in a saturated environment. J. Atmos. Sci., 51, 889907.

  • Young, M. V., , G. A. Monk, , and K. A. Browning, 1987: Interpretation of satellite imagery of a rapidly deepening cyclone. Quart. J. Roy. Meteor. Soc., 113, 10891115.

    • Search Google Scholar
    • Export Citation
1

1 PVU = 10−6 m2 s−1 K kg−1.

2

At this point we want to emphasize the influence of the channel geometry on the cyclone evolution. Neglecting metrical terms in the equations of motion leads to deviations from the behavior observed in simulations on the sphere, for example, a perfectly symmetric initial jet on a f plane tends to develop cyclonic wave breaking (Balasubramanian and Garner 1997; Govindasamy and Garner 1997). Therefore, to avoid any ambiguity with life cycles 1 and 2 nomenclature from spherical geometry (Thorncroft et al. 1993), we simply use the terminology of cyclonic and anticyclonic wave breaking.

3

The asymmetry in the gray shading at the onset of the positive PV tendency in Fig. (9) is due to the standard deviation being added symmetrically around the mean value. The PV decreases to values below about 0.36 PVU are a spurious effect of this procedure.

Supplementary Materials

Save