• Allen, R. J., , S. C. Sherwood, , J. R. Norris, , and C. S. Zender, 2012a: Recent Northern Hemisphere tropical expansion primarily driven by black carbon and tropospheric ozone. Nature, 485, 350354, doi:10.1038/nature11097.

    • Search Google Scholar
    • Export Citation
  • Allen, R. J., , S. C. Sherwood, , J. R. Norris, , and C. S. Zender, 2012b: The equilibrium response to idealized thermal forcings in a comprehensive GCM: Implications for recent tropical expansion. Atmos. Chem. Phys., 12, 47954816, doi:10.5194/acp-12-4795-2012.

    • Search Google Scholar
    • Export Citation
  • Barnes, E. A., , and D. L. Hartmann, 2011: Rossby wave scales, propagation, and the variability of eddy-driven jets. J. Atmos. Sci., 68, 28932908, doi:10.1175/JAS-D-11-039.1.

    • Search Google Scholar
    • Export Citation
  • Bordoni, S., , and T. Schneider, 2010: Regime transitions of steady and time-dependent Hadley circulations: Comparisons of axisymmetric and eddy-permitting simulations. J. Atmos. Sci., 67, 16431654, doi:10.1175/2009JAS3294.1.

    • Search Google Scholar
    • Export Citation
  • Ceppi, P., , and D. L. Hartmann, 2013: On the speed of the eddy-driven jet and the width of the Hadley cell in the Southern Hemisphere. J. Climate, 26, 34503465, doi:10.1175/JCLI-D-12-00414.1.

    • Search Google Scholar
    • Export Citation
  • Cordeira, J. M., , and L. F. Bosart, 2010: The antecedent large-scale conditions of the “perfect storms” of late October and early November 1991. Mon. Wea. Rev., 138, 25462569, doi:10.1175/2010MWR3280.1.

    • Search Google Scholar
    • Export Citation
  • Davies, H. C., , and A. M. Rossa, 1998: PV frontogenesis and upper-tropospheric fronts. Mon. Wea. Rev., 126, 15281539, doi:10.1175/1520-0493(1998)126<1528:PFAUTF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Dee, D. P., and et al. , 2011: The ERA-Interim reanalysis: Configuration and performance of the data assimilation system. Quart. J. Roy. Meteor. Soc., 137, 553597, doi:10.1002/qj.828.

    • Search Google Scholar
    • Export Citation
  • Dritschel, D. G., , and M. E. McIntyre, 2008: Multiple jets as PV staircases: The Philips effect and the resilience of eddy-transport barriers. J. Atmos. Sci., 65, 855874, doi:10.1175/2007JAS2227.1.

    • Search Google Scholar
    • Export Citation
  • Eichelberger, S. J., , and D. L. Hartmann, 2007: Zonal jet structure and the leading mode of variability. J. Climate, 20, 51495163, doi:10.1175/JCLI4279.1.

    • Search Google Scholar
    • Export Citation
  • Feldstein, S. B., , and U. Dayan, 2008: Circumglobal teleconnections and wave packets associated with Israeli winter precipitation. Quart. J. Roy. Meteor. Soc., 134, 455467, doi:10.1002/qj.225.

    • Search Google Scholar
    • Export Citation
  • Fueglistaler, S., , H. Wernli, , and T. Peter, 2004: Tropical troposphere-to-stratosphere transport inferred from trajectory calculations. J. Geophys. Res., 109, D03108, doi:10.1029/2003JD004069.

    • Search Google Scholar
    • Export Citation
  • Gill, A. E., 1980: Some simple solutions for heat-induced tropical circulation. Quart. J. Roy. Meteor. Soc., 106, 447462, doi:10.1002/qj.49710644905.

    • Search Google Scholar
    • Export Citation
  • Gill, A. E., 1982: Atmosphere-Ocean Dynamics. Academic Press, 645 pp.

  • Held, I. M., , and A. Y. Hou, 1980: Nonlinear axially symmetric circulations in a nearly inviscid atmosphere. J. Atmos. Sci., 37, 515533, doi:10.1175/1520-0469(1980)037<0515:NASCIA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hoskins, B. J., , and D. J. Karoly, 1981: The steady linear response of a spherical atmosphere to thermal and orographic forcing. J. Atmos. Sci., 38, 11791196, doi:10.1175/1520-0469(1981)038<1179:TSLROA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hoskins, B. J., , and T. Ambrizzi, 1993: Rossby-wave propagation on a realistic longitudinally varying flow. J. Atmos. Sci., 50, 16611671, doi:10.1175/1520-0469(1993)050<1661:RWPOAR>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Isotta, F., , O. Martius, , M. Sprenger, , and C. Schwierz, 2008: Long-term trends of synoptic-scale breaking Rossby waves in the Northern Hemisphere between 1958 and 2001. Int. J. Climatol., 28, 15511562, doi:10.1002/joc.1647.

    • Search Google Scholar
    • Export Citation
  • Kallberg, P., , P. Berrisford, , B. Hoskins, , A. Simmons, , S. Uppala, , S. Lamy-Thépaut, , and R. Hine, 2005: ERA-40 atlas. ERA-40 Project Rep. 19, 191 pp.

  • Kang, S. M., , and L. M. Polvani, 2011: The interannual relationship between the latitude of the eddy-driven jet and the edge of the Hadley cell. J. Climate, 24, 563568, doi:10.1175/2010JCLI4077.1.

    • Search Google Scholar
    • Export Citation
  • Kang, S. M., , L. M. Polvani, , J. C. Fyfe, , and M. Sigmond, 2011: Impact of polar ozone depletion on subtropical precipitation. Science, 332, 951954, doi:10.1126/science.1202131.

    • Search Google Scholar
    • Export Citation
  • Kiladis, G. N., , and K. M. Weickmann, 1992: Extratropical forcing of tropical Pacific convection during northern winter. Mon. Wea. Rev., 120, 19241938, doi:10.1175/1520-0493(1992)120<1924:EFOTPC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Koch, P., , H. Wernli, , and H. C. Davies, 2006: An event-based jet-stream climatology and typology. Int. J. Climatol., 26, 283301, doi:10.1002/joc.1255.

    • Search Google Scholar
    • Export Citation
  • Lee, S., 1997: Maintenance of multiple jets in a baroclinic flow. J. Atmos. Sci., 54, 17261738, doi:10.1175/1520-0469(1997)054<1726:MOMJIA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Madonna, E., , H. Wernli, , H. Joos, , and O. Martius, 2014: Warm conveyor belts in the ERA-Interim dataset (1979–2010). Part I: Climatology and potential vorticity evolution. J. Climate, 27, 326, doi:10.1175/JCLI-D-12-00720.1.

    • Search Google Scholar
    • Export Citation
  • Manney, G. L., et al. , 2011: Jet characterization in the upper troposphere/lower stratosphere (UTLS): Applications to climatology and transport studies. Atmos. Chem. Phys., 11, 61156137, doi:10.5194/acp-11-6115-2011.

    • Search Google Scholar
    • Export Citation
  • Martius, O., , and H. Wernli, 2012: A trajectory-based investigation of physical and dynamical processes that govern the temporal evolution of the subtropical jet streams over Africa. J. Atmos. Sci., 69, 16021616, doi:10.1175/JAS-D-11-0190.1.

    • Search Google Scholar
    • Export Citation
  • Martius, O., , C. Schwierz, , and H. C. Davies, 2010: Tropopause-level waveguides. J. Atmos. Sci., 67, 866879, doi:10.1175/2009JAS2995.1.

    • Search Google Scholar
    • Export Citation
  • Moore, R. W., , O. Martius, , and T. Spengler, 2010: The modulation of the subtropical and extratropical atmosphere in the Pacific basin in response to the Madden–Julian oscillation. Mon. Wea. Rev., 138, 27612779, doi:10.1175/2010MWR3194.1.

    • Search Google Scholar
    • Export Citation
  • Ploeger, F., et al. , 2011: Insight from ozone and water vapour on transport in the tropical tropopause layer (TTL). Atmos. Chem. Phys., 11, 407419, doi:10.5194/acp-11-407-2011.

    • Search Google Scholar
    • Export Citation
  • Schiemann, R., , D. Luthi, , and C. Schar, 2009: Seasonality and interannual variability of the westerly jet in the Tibetan Plateau region. J. Climate, 22, 29402957, doi:10.1175/2008JCLI2625.1.

    • Search Google Scholar
    • Export Citation
  • Schwierz, C., , S. Dirren, , and H. C. Davies, 2004: Forced waves on a zonally aligned jet stream. J. Atmos. Sci., 61, 7387, doi:10.1175/1520-0469(2004)061<0073:FWOAZA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Seidel, D. J., , Q. Fu, , W. J. Randel, , and T. J. Reichler, 2008: Widening of the tropical belt in a changing climate. Nat. Geosci., 1, 2124, doi:10.1038/ngeo.2007.38.

    • 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, doi:10.1002/qj.49712353811.

    • Search Google Scholar
    • Export Citation
  • Woollings, T., , A. Hannachi, , and B. Hoskins, 2010: Variability of the North Atlantic eddy-driven jet stream. Quart. J. Roy. Meteor. Soc., 136, 856868, doi:10.1002/qj.625.

    • Search Google Scholar
    • Export Citation
  • View in gallery

    Mean wind speed on the 345-K isentropic surface in (a) winter, (b) spring, (c) summer, and (d) fall. The regional sectors used for some of the analyses in the paper are indicated by the vertical black lines and are labeled in (a).

  • View in gallery

    Time evolution of various variables along the trajectories started in the winter season (DJF). Shown are (a) the angular momentum (109 m2 s−1), (b) the pressure forcing during 6 h (109 m2 s−1), (c) the height (hPa), (d) the latitude, (e) PV (PVU), and (f) zonal wind speed (m s−1) averaged over all trajectories started from the subtropical jet in the winter season. Error bars indicate plus or minus one standard deviation. The trajectories were grouped according to their PV value at t = 0 (black line: PV < 1 PVU; dark gray: 1 ≤ PV < 2 PVU; medium gray: 2 ≤ PV < 3 PVU; light gray: 3 ≤ PV < 4 PVU; and lightest gray: PV > 4 PVU).

  • View in gallery

    As in Fig. 2, but for the summer months (JJA).

  • View in gallery

    Positions of the example trajectories started on 1800 UTC 19 Dec 2005 for (a) days −1 and −2, (b) days −3 and −4, and (c) days −5 and −6. The colors indicate the time (h) since the start of the trajectories.

  • View in gallery

    Shown is the full 7-day time period for a set of example trajectories started at 1800 UTC 19 Dec 2005. (a) Total wind speed along the trajectories (m s−1, gray shading) and PV = 2 PVU isolines on the 320- (blue), 330- (orange), 340- (red), and 350-K (green) isentropes. (b) PV along the trajectories (PVU, color shading) and wind speed isolines (contours: 40, 65, and 75 m s−1). (c) Pressure along the trajectories (hPa, color shading).

  • View in gallery

    Shown is the full 7-day time period for a set of example trajectories started at 1800 UTC 19 Dec 2005. (a) Angular momentum along the trajectories (109 m2 s−1, shading). (b) Negative pressure gradient forcing (109 m2 s−1, gray shading) and PV = 2 PVU isolines on the 340- (red) and 350-K (green) isentropes. (c) Positive pressure gradient forcing (109 m2 s−1; gray shading) and PV = 2 PVU isolines on the 340- (red) and 350-K (green) isentropes.

  • View in gallery

    Trajectory densities (number of trajectory points per square kilometer) aggregated over 5 yr for the (left) winter months (DJF) and the (right) spring months (MAM) at the time when the back trajectories were initiated (first row) from the jet (t = 0 h), (second row) 1 day earlier (t = −24 h), (third row) 3 days earlier (t = −72 h), (fourth row) 5 days earlier (t = −120 h), and (fifth row) 7 days earlier (t = −168 h).

  • View in gallery

    Trajectory densities (number of trajectory points per square kilometer) aggregated over 5 yr for the (left) summer months (JJA) and the (right) fall months (SON) at the time when the back trajectories were initiated (first row) from the jet (t = 0 h), (second row) 1 day earlier (t = −24 h), (third row) 3 days earlier (t = −72 h), (fourth row) 5 days earlier (t = −120 h), and (fifth row) 7 days earlier (t = −168 h).

  • View in gallery

    Mean height of the trajectories (hPa, color shading) at t = −168 h in winter for trajectories started over (a) Africa, (b) Asia, (c) the Pacific, and (d) North America (shaded). Pressure values are only shown for grid points where the trajectory density exceeds 0.01 count per square kilometer. The black contours indicate trajectory density values of 0.02 and 0.04 count per square kilometer.

  • View in gallery

    Mean height of the trajectories (hPa) at t = −168 h in summer for trajectories started over (a) Africa, (b) Asia, (c) the Pacific, and (d) North America (shaded). Pressure values are only shown for each grid point where the trajectory density exceeds 0.001 count per square kilometer. The black contours indicate density values of 0.005 and 0.01 count per square kilometer.

  • View in gallery

    Relative decrease in angular momentum along the tropospheric trajectories (PV < 2 PVU at t = 0) per season.

  • View in gallery

    Total pressure gradient forcing of the angular momentum (109 m2 s−1 during 6 h, shaded) along tropospheric (PV < 2 PVU) trajectories in (left) winter and (right) summer for areas that exceed a trajectory density of 0.005 count per square kilometer and trajectory counts at t = −12 h (red contours, 0.02, 0.05, 0.1 count per square kilometer).

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A Lagrangian Analysis of the Northern Hemisphere Subtropical Jet

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  • 1 Institute of Geography, Oeschger Centre for Climate Change Research, University of Bern, Bern, Switzerland
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Abstract

This study presents a 5-yr climatology of 7-day back trajectories started from the Northern Hemisphere subtropical jet. These trajectories provide insight into the seasonally and regionally varying angular momentum and potential vorticity characteristics of the air parcels that end up in the subtropical jet. The trajectories reveal preferred pathways of the air parcels that reach the subtropical jet from the tropics and the extratropics and allow estimation of the tropical and extratropical forcing of the subtropical jet.

The back trajectories were calculated 7 days back in time and started every 6 h from December 2005 to November 2010 using the Interim European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-Interim) dataset as a basis. The trajectories were started from the 345-K isentrope in areas where the wind speed exceeded a seasonally varying threshold and where the wind shear was confined to upper levels.

During winter, the South American continent, the Indian Ocean, and the Maritime Continent are preferred areas of ascent into the upper troposphere. From these areas, air parcels follow an anticyclonic pathway into the subtropical jet. During summer, the majority of air parcels ascend over the Himalayas and Southeast Asia.

Angular momentum is overall well conserved for trajectories that reach the subtropical jet from the deep tropics. In winter and spring, the hemispheric-mean angular momentum loss amounts to approximately 6%; in summer, it amounts to approximately 18%; and in fall, it amounts to approximately 13%. This seasonal variability is confirmed using an independent potential vorticity–based method to estimate tropical and extratropical forcing of the subtropical jet.

Denotes Open Access content.

Corresponding author address: Olivia Martius, Institute of Geography, Oeschger Centre for Climate Change Research, University of Bern, Hallerstrasse 12, CH-3012, Bern, Switzerland. E-mail: olivia.martius@giub.unibe.ch

Abstract

This study presents a 5-yr climatology of 7-day back trajectories started from the Northern Hemisphere subtropical jet. These trajectories provide insight into the seasonally and regionally varying angular momentum and potential vorticity characteristics of the air parcels that end up in the subtropical jet. The trajectories reveal preferred pathways of the air parcels that reach the subtropical jet from the tropics and the extratropics and allow estimation of the tropical and extratropical forcing of the subtropical jet.

The back trajectories were calculated 7 days back in time and started every 6 h from December 2005 to November 2010 using the Interim European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-Interim) dataset as a basis. The trajectories were started from the 345-K isentrope in areas where the wind speed exceeded a seasonally varying threshold and where the wind shear was confined to upper levels.

During winter, the South American continent, the Indian Ocean, and the Maritime Continent are preferred areas of ascent into the upper troposphere. From these areas, air parcels follow an anticyclonic pathway into the subtropical jet. During summer, the majority of air parcels ascend over the Himalayas and Southeast Asia.

Angular momentum is overall well conserved for trajectories that reach the subtropical jet from the deep tropics. In winter and spring, the hemispheric-mean angular momentum loss amounts to approximately 6%; in summer, it amounts to approximately 18%; and in fall, it amounts to approximately 13%. This seasonal variability is confirmed using an independent potential vorticity–based method to estimate tropical and extratropical forcing of the subtropical jet.

Denotes Open Access content.

Corresponding author address: Olivia Martius, Institute of Geography, Oeschger Centre for Climate Change Research, University of Bern, Hallerstrasse 12, CH-3012, Bern, Switzerland. E-mail: olivia.martius@giub.unibe.ch

1. Introduction

a. Rationale

The subtropical jet is a salient feature of the subtropical upper-level flow and a key player in the dynamical processes that link the tropics with the subtropics and the extratropics. Of central importance is the role that the subtropical jet (STJ) plays in governing Rossby wave dynamics. The STJ is coaligned with a band of strong potential vorticity (PV) gradients and therefore acts as a waveguide for synoptic-scale Rossby waves (Hoskins and Ambrizzi 1993; Schwierz et al. 2004). As a consequence, Rossby waves triggered by the upper-level outflow of strong tropical convection (e.g., Gill 1980) are trapped by the STJ waveguide. The waves then propagate downstream along the STJ waveguide and influence the weather in the extratropics (e.g., Cordeira and Bosart 2010; Moore et al. 2010). Analogously, synoptic-scale Rossby wave disturbances propagating along the extratropical waveguide can transfer to the STJ waveguide through Rossby wave breaking and then propagate downstream on the STJ waveguide and affect the surface weather in the subtropics (e.g., Feldstein and Dayan 2008; Martius et al. 2010).

The STJ is also a key indicator of changes in the Northern Hemisphere Hadley circulation (Allen 2012a) and may indeed play an important role in this process. Observations show a poleward expansion of the Hadley circulation in recent years (Seidel et al. 2008) in the Northern Hemisphere. This expansion of the Hadley circulation has significant impacts on the surface weather, for example, the precipitation in the subtropics (Kang et al. 2011). This expansion is not zonally symmetric and varies with the season. Using the 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40) dataset, Isotta et al. (2008) analyzed trends in the position and strength of the Northern Hemisphere STJ between 1958 and 2002 and found trends that were not zonally symmetric. In winter and spring, the Pacific basin STJ shifted poleward and the STJ over the Atlantic shifted equatorward in accordance with the positive trend in the North Atlantic Oscillation. In summer, positive trends were strongest over Europe. These positive trends have been linked to changes in black carbon and tropospheric ozone that resulted in tropospheric warming, a poleward shift of the areas of strong upper-level temperature gradients, and, as a consequence, a poleward shift of the STJ (Allen et al. 2012b).

All of these aspects underline the importance of furthering our understanding of the processes that govern the dynamics of the STJ and the role that tropical and extratropical forcing play in determining the characteristics of the STJ.

b. Tropical and extratropical forcing of the subtropical jet

The subtropical jet is affected by tropical, subtropical, and extratropical forcing. To better understand the dynamics of the STJ, it is illuminating to investigate these tropical–subtropical–extratropical interactions from a linear-wave-propagation point of view, from a PV perspective, and from an angular momentum point of view as outlined in the following paragraphs.

1) Angular momentum perspective

The zonal-mean STJ is located at the poleward edge of the Hadley cell and is mainly driven by angular momentum exported from the tropics (Held and Hou 1980; Lee 1997). High–angular momentum air from the tropics reaches the subtropics following the upper, poleward-directed branch of the Hadley cell. The angular momentum is not, however, perfectly conserved: subtropical eddies can modify (decrease or increase) the angular momentum of an air parcel (Gill 1982). This nonconservation of angular momentum is due to the effect of pressure gradients in the zonal direction and in essence describes the subtropical and extratropical forcing of the STJ in an angular momentum framework.

The amplitude of the subtropical forcing varies over the course of the year. Using an idealized dry GCM, Bordoni and Schneider (2010) show that the zonal-mean Hadley circulation is governed by an angular momentum–conserving regime during the winter and shifts into a regime where eddy momentum fluxes become more dominant during spring and fall.

A quantitative analysis of the nonconservation of angular momentum and hence the subtropical forcing of the STJ in a nonzonally averaged framework is so far missing.

2) PV perspective

In a PV framework, the formation of jets is equivalent to the formation of meridionally confined strong PV gradients (e.g., Davies and Rossa 1998). It is therefore important in a PV framework to identify and quantify dynamical processes in the tropics, subtropics, and extratropics that result in a strengthening or weakening of the subtropical PV gradient.

Irreversible mixing of PV by eddies—that is, by Rossby wave breaking, and the attendant formation of a PV staircase—is the classical process that results in jet formation in the extratropics (e.g., Dritschel and McIntyre 2008). Similarly, wave breaking in the subtropics can accelerate the subtropical jet (e.g., Martius and Wernli 2012). In the tropics, the meridional branch of the Hadley circulation ensures the export of very-low- or even negative-PV air from the tropics into the subtropics, thereby contributing to strong PV gradients and hence a strong jet in the subtropics. Hence, the strengthening of the subtropical PV gradient by tropical low-PV air is conceptually the PV-view equivalent of angular momentum export from the tropics by the Hadley circulation.

3) Linear-wave perspective and momentum fluxes

As mentioned previously, the STJ serves as a waveguide for Rossby waves emerging from the tropics and the extratropics (Hoskins and Karoly 1981; Hoskins and Ambrizzi 1993). The role of the STJ is, however, not limited to that of a passive waveguide. The strength, width, and latitudinal position of the STJ all affect the presence and the position of the critical lines in the subtropics and, in consequence, the wave-breaking characteristics of extratropical Rossby waves and the associated momentum fluxes (e.g., Barnes and Hartmann 2011). However, the Southern Hemisphere STJ is in return affected by the latitude of the extratropical jet (Kang and Polvani 2011) via the momentum fluxes associated with breaking extratropical Rossby waves (Ceppi and Hartmann 2013). Harnik et al. (2014, manuscript submitted to J. Climate) illustrate the complex and nonlinear interaction between tropical and extratropical forcing of the subtropical jet for one winter season.

c. Aims and outline

Thus, the dynamics of the STJ are at times significantly affected by extratropical and subtropical forcing. However, where and when the tropical or extratropical forcing is dominant in governing these interactions is currently an open question and a detailed and quantitative understanding of these interactions is currently missing.

The aim of this study is to address the question of tropical versus extratropical forcing of the STJ using a trajectory-based method as outlined in Martius and Wernli (2012). The trajectory-based approach is advantageous because it provides Lagrangian information on the angular momentum and PV characteristics of the air parcels that reach the STJ. Martius and Wernli (2012) used this information to investigate how synoptic-scale features in the extratropics and the subtropics can affect the dynamics of the STJ. Their study focused on one winter season and on the STJ over Africa only. In the current study, the findings of Martius and Wernli (2012) are extended and corroborated for a larger sample of trajectories covering a 5-yr period and the entire Northern Hemisphere. Using these trajectories, it is possible to illuminate and quantify some aspects of tropical–extratropical interactions and their effects on the STJ.

Using the trajectory information allows for the following:

  • the characterization of the three-dimensional pathways of the air that ends up in the STJ for different longitudinal sections of the STJ and for all seasons; and
  • the quantification of the extratropical and the tropical forcing of the STJ for different longitudinal sections and for all seasons using both a PV-perspective-based approach and an angular momentum–based approach.
The paper is organized as follows: Details regarding the trajectory calculations are outlined in the data and methods section (section 2). This is followed by a brief description of the climatological characteristics of the STJ (section 3), an example case (section 4), and a description of the source areas of the trajectories (section 5). The influence that tropical and extratropical forcing have on the jet is discussed in section 6. The paper closes with a discussion and summary of the main findings in section 7.

2. Data and methods

The Interim ECMWF Re-Analysis (ERA-Interim) dataset (Dee et al. 2011) serves as the basis for all analyses presented in this paper. All fields were interpolated from a T255 spherical representation to a regular 1° × 1° grid. Temperature, wind, and moisture fields on 60 model levels were used to compute potential temperature, PV, angular momentum, and wind speed.

a. Trajectory calculations

All analyses in this paper are based on three-dimensional Lagrangian backward trajectories that were started from the subtropical jet. Throughout the text, I refer to time t = 0, that is, when the trajectories are located in the STJ, as the starting point of the trajectories. Backward trajectories were calculated with the Lagranto trajectory tool (Wernli and Davies 1997). The trajectories were started every 6 h from a regular 50 × 50 km2 grid from starting points on the 345-K isentropic surface where the total wind speed exceeded 40 m s−1 during the winter months [December–February (DJF)], 35 m s−1 during spring [March–May (MAM)] and autumn [September–November (SON)], and 30 m s−1 during summer [June–August (JJA)]. The height of the 345-K isentrope varies with the season; however, the latitudinal position of the subtropical jet also varies, and the 345-K isentrope coincides well with the location of the subtropical jet maximum during all four seasons [Fig. 1; see also Kallberg et al. (2005, 162–163)]. The height of the 345-K isentrope varies strongly in the longitudinal direction during the summer season and is significantly lowered to approximately 350 hPa over the Tibetan Plateau.

Fig. 1.
Fig. 1.

Mean wind speed on the 345-K isentropic surface in (a) winter, (b) spring, (c) summer, and (d) fall. The regional sectors used for some of the analyses in the paper are indicated by the vertical black lines and are labeled in (a).

Citation: Journal of the Atmospheric Sciences 71, 7; 10.1175/JAS-D-13-0329.1

The trajectories are calculated back in time for 168 h (7 days). The accuracy of the trajectories in this time range is still reasonably good even in the tropics (Fueglistaler et al. 2004), and this is sufficient time to cover the upper branch of the Hadley circulation. On average, the trajectories emerging from the deep tropics have very low zonal wind speeds at t = −168 h (Figs. 2f, 3f) and undergo ascent (Figs. 2c, 3c).

Fig. 2.
Fig. 2.

Time evolution of various variables along the trajectories started in the winter season (DJF). Shown are (a) the angular momentum (109 m2 s−1), (b) the pressure forcing during 6 h (109 m2 s−1), (c) the height (hPa), (d) the latitude, (e) PV (PVU), and (f) zonal wind speed (m s−1) averaged over all trajectories started from the subtropical jet in the winter season. Error bars indicate plus or minus one standard deviation. The trajectories were grouped according to their PV value at t = 0 (black line: PV < 1 PVU; dark gray: 1 ≤ PV < 2 PVU; medium gray: 2 ≤ PV < 3 PVU; light gray: 3 ≤ PV < 4 PVU; and lightest gray: PV > 4 PVU).

Citation: Journal of the Atmospheric Sciences 71, 7; 10.1175/JAS-D-13-0329.1

Fig. 3.
Fig. 3.

As in Fig. 2, but for the summer months (JJA).

Citation: Journal of the Atmospheric Sciences 71, 7; 10.1175/JAS-D-13-0329.1

An important issue pertains to the accuracy of the trajectories that pass through the tropics and hence potentially through areas of strong convection. Areas of strong vertical motion associated with deep convection are not explicitly resolved in this dataset because the spatial and temporal resolution is comparatively coarse. The trajectories therefore yield a smoothed image in both space and time of the true vertical motion in the tropics. Nevertheless, the ERA-Interim data are reliable for trajectory analysis in the tropics (Ploeger et al. (2011). In addition, a comparison of trajectory pathways through active convection with satellite images confirmed the reliability of the ERA-Interim-based trajectories for individual cases (Martius and Wernli 2012).

The trajectory algorithm traces any atmospheric variable of interest along the three-dimensional pathways of the air parcels. For this study, the following variables were traced: the specific humidity q, the potential temperature θ, PV, the angular momentum per unit mass [, where r is the radius of Earth, φ is the latitude, and Ω is the rotation velocity of Earth], and the pressure gradient forcing in the longitudinal direction [, where ρ is the density, p is the pressure, and λ is the longitude; see also Gill (1982)].

The trajectories were started every 6 h between 1 December 2005 and 31 November 2010. The choice of this 5-yr period is to a certain degree arbitrary, and the restriction to 5 years is due to the high computational demands of the trajectory calculations. During this 5-yr period, several El Niño and La Niña events occurred.

b. Selection of subtropical jet trajectories

The subtropical jet is characterized by strong baroclinicity that is concentrated at upper levels. In contrast, the baroclinic layer of the extratropical, eddy-driven jets extends all the way to the surface. This attribute can be used to distinguish the subtropical or shallow jets from the deep extratropical jets (Koch et al. 2006; Woollings et al. 2010). Subsequently only trajectories that start in jets with their baroclinic zone concentrated at upper levels, that is, subtropical jets, will be analyzed. The selection of the subtropical jet trajectories is based on a criterion developed by Koch et al. (2006), which distinguishes jets with vertical wind shear profiles that are mainly confined to the upper levels from jets with deep vertical shear profiles as follows:
e1
A trajectory is classified as a subtropical jet trajectory if the vertical wind shear at the starting location of the trajectory falls into the shallow shear category (Δvelrel > 0.5). Koch et al. (2006) show that for shear threshold values between 0.3 and 0.7, the results remain qualitatively very similar. The fraction of subtropical jet trajectories, that is, Δvelrel > 0.5, on the 345-K isentropic surface varies between approximately 66% and 72% during the year. This supports the previous statement that the wind speed maxima on the 345-K isentrope are typically part of the subtropical jet throughout the year.

There are two possible limitations of the shear-based approach. (i) Some trajectories starting in the extratropics fall into the shallow, upper-level shear category (see, e.g., Fig. 4 at 65°N, 50°E). In mitigation, I note that their number is small (as can be seen in Fig. 7) and the advantage of a shear-based criterion compared to geographical selection criteria is the direct link to the driving mechanism of the jet. (ii) In areas where the subtropical jet and the extratropical jet are merged into a hybrid jet, as it is often the case over the eastern Pacific (e.g., Eichelberger and Hartmann 2007), the trajectories are classified either as subtropical or extratropical jet trajectories, depending on the vertical shear, but never as trajectories starting from a merged hybrid jet.

Fig. 4.
Fig. 4.

Positions of the example trajectories started on 1800 UTC 19 Dec 2005 for (a) days −1 and −2, (b) days −3 and −4, and (c) days −5 and −6. The colors indicate the time (h) since the start of the trajectories.

Citation: Journal of the Atmospheric Sciences 71, 7; 10.1175/JAS-D-13-0329.1

Tropical easterlies are excluded by the additional requirement that the trajectories starting south of 15°N must start in a region of westerly winds.

The following four areas are defined for regional analyses: Africa, 30°W–39°E; Asia 40°–109°E; Pacific, 110°E–159°W; and North America, 160°–29°W (Fig. 1a).

For the trajectory density calculations, a slight smoothing of the trajectory counts is used with an exponential filter radius of 200 km (Madonna et al. 2014). The average PV and pressure gradient values along the trajectories are calculated without any smoothing.

c. PV-based analyses

The PV value of an air parcel at t = 0 is a good proxy for the origin of the trajectories (tropical vs extratropical and stratospheric vs tropospheric), assuming that the PV is relatively well conserved along the trajectories. This is generally the case (see Figs. 2e and 3e), and, following Martius and Wernli (2012), the trajectories are therefore grouped according to the PV value at the time when the trajectories are started from within the subtropical jet. The trajectories are grouped into the following five categories: PV > 4 potential vorticity units (PVU; 1 PVU ≡ 1 × 10−6 K m2 kg−1 s−1) at t = 0, which are air masses of extratropical origin located in the stratosphere; 4 > PV > 3 PVU, which are extratropical and subtropical trajectories in the stratosphere; 3 > PV > 2 PVU, which are mainly subtropical trajectories in the stratosphere; 2 > PV > 1 PVU, which are subtropical and tropical tropospheric trajectories; and PV < 1 PVU, which are trajectories with origins in the deep tropics and in the troposphere.

3. Climatological jet characteristics

The subtropical jet stream on the 345-K isentrope is located at approximately 30°N over Africa, Asia, and the Pacific during DJF and is characterized by a wind speed maximum of more than 70 m s−1 over East Asia and the western Pacific (Fig. 1a). In spring, two distinct wind speed maxima are present: one over Africa and one over East Asia, extending downstream over the Pacific Ocean. The jet is located farther south over the eastern Pacific, North America, and the western Atlantic in spring than in winter, resulting in an almost single-jet configuration across the entire Northern Hemisphere (Fig. 1b). In summer, the jet is weaker and located farther north at approximately 40°N (Fig. 1c). Over Asia, the jet is located north of the Himalayas in summer (Schiemann et al. 2009). In fall, the jet maximum is located over East Asia and the Pacific Ocean and is still relatively weak over Africa (Fig. 1d). Comparisons with previous jet climatologies (e.g., Manney et al. 2011) show that all the important seasonal variations of the jet are captured using the wind speed on the 345-K isentrope as a basis for the jet definition.

4. Example case

The information that can be gained from the trajectories is illustrated in Figs. 46 for one example day (1800 UTC 19 December 2005).

Fig. 5.
Fig. 5.

Shown is the full 7-day time period for a set of example trajectories started at 1800 UTC 19 Dec 2005. (a) Total wind speed along the trajectories (m s−1, gray shading) and PV = 2 PVU isolines on the 320- (blue), 330- (orange), 340- (red), and 350-K (green) isentropes. (b) PV along the trajectories (PVU, color shading) and wind speed isolines (contours: 40, 65, and 75 m s−1). (c) Pressure along the trajectories (hPa, color shading).

Citation: Journal of the Atmospheric Sciences 71, 7; 10.1175/JAS-D-13-0329.1

Fig. 6.
Fig. 6.

Shown is the full 7-day time period for a set of example trajectories started at 1800 UTC 19 Dec 2005. (a) Angular momentum along the trajectories (109 m2 s−1, shading). (b) Negative pressure gradient forcing (109 m2 s−1, gray shading) and PV = 2 PVU isolines on the 340- (red) and 350-K (green) isentropes. (c) Positive pressure gradient forcing (109 m2 s−1; gray shading) and PV = 2 PVU isolines on the 340- (red) and 350-K (green) isentropes.

Citation: Journal of the Atmospheric Sciences 71, 7; 10.1175/JAS-D-13-0329.1

a. Trajectory positions

The positions of the 168-h (7 days) back trajectories are shown at 24-h intervals in Fig. 4. On this particular day, the air parcels that reached the subtropical jet from the Southern Hemisphere and the deep tropics crossed the equator over South America, the eastern Pacific, the Indian Ocean, and the Maritime Continent (Fig. 4). The air parcels needed about 3–5 days to reach the Northern Hemisphere subtropics. A substantial fraction of air parcels also reached the subtropical jet from the extratropics. These air parcels followed an anticyclonic pathway over the Atlantic and Pacific basins and over the Eurasian continent before joining the subtropical jet (Fig. 4). The majority of the air parcels were located in the subtropics 7 days prior to their arrival in the subtropical jet.

b. PV and wind speed

The air parcels of tropical origin were characterized by very low and partially negative PV values (Fig. 5b), while the parcels that reached the subtropical jet from the extratropics were characterized by relatively high PV values (>4 PVU) (Fig. 5b). Consequently, the convergence of the tropical and extratropical air in the STJ over the Asian continent and the western Pacific resulted in strong PV gradients that were collocated with maxima in the wind speed (Figs. 5a,b). The PV was almost perfectly conserved along the individual trajectories, the exception being a small number of trajectories over the Maritime Continent.

The pressure traced along the air parcels shows that the trajectories that emerged from the deep tropics over the Maritime Continent ascended from the lower troposphere during this 7-day period (Fig. 5c). Similarly, a branch of trajectories located over the tropical Atlantic underwent ascent. The trajectories in these two areas captured both the poleward-directed and the ascending branch of the Hadley cell, while over South America only the poleward branch is captured. All other trajectories remained at upper levels at a height of approximately 200 hPa.

c. Angular momentum

Figure 6a shows the angular momentum of the air parcels along the trajectories and Figs. 6b and 6c show areas where the angular moment was not conserved (angular momentum reduction in Fig. 6b and angular momentum gain in Fig. 6c) along the trajectories. The angular momentum is to first order determined by the latitudinal position of the air parcels and is relatively well conserved in the tropics between approximately 0° and 15°N.

In the Northern Hemisphere and assuming geostrophic balance, an air parcel moving northward along the eastern (western) edge of a subtropical cyclonic (anticyclonic) eddy will experience a negative pressure gradient forcing and, as a consequence, a decrease in angular momentum. The opposite is true of air parcels moving southward along the western (eastern) flank of a cyclonic (anticyclonic) eddy. Indeed, areas of angular momentum reduction in the subtropics and extratropics are generally located along the western flanks of upper-level subtropical and extratropical ridges (Fig. 6b). Areas of angular momentum gain are generally located along the eastern flank of subtropical and extratropical ridges (Fig. 6c).

5. Climatological trajectory pathways

The aggregation of the longitudinal and latitudinal positions of all trajectories every 6 h over the 5-yr period for different time lags results in the trajectory density plots presented in Figs. 7 and 8. The trajectory counts are slightly smoothed (see section 2) and normalized by the area of each 1° × 1° grid cell.

Fig. 7.
Fig. 7.

Trajectory densities (number of trajectory points per square kilometer) aggregated over 5 yr for the (left) winter months (DJF) and the (right) spring months (MAM) at the time when the back trajectories were initiated (first row) from the jet (t = 0 h), (second row) 1 day earlier (t = −24 h), (third row) 3 days earlier (t = −72 h), (fourth row) 5 days earlier (t = −120 h), and (fifth row) 7 days earlier (t = −168 h).

Citation: Journal of the Atmospheric Sciences 71, 7; 10.1175/JAS-D-13-0329.1

Fig. 8.
Fig. 8.

Trajectory densities (number of trajectory points per square kilometer) aggregated over 5 yr for the (left) summer months (JJA) and the (right) fall months (SON) at the time when the back trajectories were initiated (first row) from the jet (t = 0 h), (second row) 1 day earlier (t = −24 h), (third row) 3 days earlier (t = −72 h), (fourth row) 5 days earlier (t = −120 h), and (fifth row) 7 days earlier (t = −168 h).

Citation: Journal of the Atmospheric Sciences 71, 7; 10.1175/JAS-D-13-0329.1

During the winter season (DJF), the starting points of the subtropical jet trajectories are located primarily in a latitudinal belt between 25° and 30°N, with maxima over Africa and continental Asia and minima over the central Atlantic and the western Pacific (Fig. 7, left column). A small number of trajectory starting points are located in the deep tropics (south of 15°N). These trajectory starting points are located over the western Pacific and in the tropical Atlantic in the areas of the westerly ducts. These tropical upper-level westerly wind speeds can arise from wave breaking in the subtropics (e.g., Kiladis and Weickmann 1992). There are air parcels that reach the STJ from the deep tropics, from the subtropics, and from the extratropics.

The air parcels that reach the STJ from the deep tropics or from the Southern Hemisphere in winter are located in relatively well-confined longitudinal bands 7 days prior to their arrival in the jet (Figs. 7, 9). These air parcels follow similar pathways from the tropics to the STJ (Figs. 4, 7, 9). Of all the trajectories located south of 15°N (0°) at t = −168 h, 21.5% (25.5%) are located over eastern South America at t = −168 h, 11% (12%) over southern Africa, 11% (16%) over the Indian Ocean, 18% (21.5%) over the Maritime Continent, and 31% (21%) over the Pacific Ocean. These are instantaneous values, that is, only valid at t = −168 h; however, they did not change significantly between t = −144 and −168 h and can therefore be assumed to be approximately representative.

Fig. 9.
Fig. 9.

Mean height of the trajectories (hPa, color shading) at t = −168 h in winter for trajectories started over (a) Africa, (b) Asia, (c) the Pacific, and (d) North America (shaded). Pressure values are only shown for grid points where the trajectory density exceeds 0.01 count per square kilometer. The black contours indicate trajectory density values of 0.02 and 0.04 count per square kilometer.

Citation: Journal of the Atmospheric Sciences 71, 7; 10.1175/JAS-D-13-0329.1

In general, the air parcels that reach the STJ from the deep tropics follow an anticyclonic pathway. The majority of air parcels that reach the STJ from the Maritime Continent move westward in the tropics before they turn northward toward the subtropical jet over India (Fig. 7), similar to the behavior of the trajectories of the example case presented in Fig. 4. The air parcels that reach the subtropical jet from the South American continent follow a more-direct northward path over South America before turning eastward into the subtropical jet over the Caribbean.

During the investigated 7-day period, a substantial fraction of trajectories remain in the subtropical belt (53% remain north of 15°N and south of 45°N). The air masses that pass through the extratropics before they reach the subtropical jet move equatorward over the eastern Atlantic, Europe, central Asia, and the eastern Pacific along the eastern flanks of the climatological planetary-scale ridges (see Fig. 4).

The situation in spring is quite similar to that in winter, with a slightly larger fraction of tropical trajectories emerging from South America than from Asia as compared to the winter months (Fig. 7).

In summer, the subtropical jet trajectory starting points are located between 30° and 45°N over the Asian continent, at 45°N over the eastern Pacific and North America, and even farther north over the Atlantic (Fig. 8; JJA, 0 h). The starting points over Asia are mainly located to the north of the Himalayas, which is in agreement with the observations of Schiemann et al. (2009). There are two zonally confined maxima of trajectory starting points extending into the tropics: one over the central Pacific and one over the central Atlantic (Fig. 8; JJA, 0 h), both located slightly farther west as compared to the winter season (Fig. 7; DJF, 0 h).

The trajectories remain in the Northern Hemisphere during the investigated 7-day period (Fig. 8), as is expected, when the main heating area and hence the northern branch of the Hadley cell is located in the Northern Hemisphere. Seven days prior to the arrival in the jet, local frequency maxima in the tropics are located over the eastern Indian Ocean and the central Pacific (Fig. 8; JJA −168 h). Overall, the longitudinal distribution of the trajectories located in the tropics at day −7 is much more homogeneous and symmetric than it is during the winter season. There is also a significant fraction of air parcels that reach the subtropical jet from the extratropics (Fig. 8).

The behavior of the trajectories in the spring and fall is not completely symmetric. Compared to spring, very few trajectories reach the subtropical jet from South America during the fall (Fig. 8). This is consistent with a weaker jet over Africa in the fall (Fig. 1).

That the South American continent is indeed an important region of ascent for the air parcels that end up in the subtropical jet over Africa is illustrated in Fig. 9, which shows trajectory densities for trajectories started in the four subregions, as well as the mean pressure level of the trajectories 7 days prior (t = −168 h) to their arrival in the jet.

During winter, each subregion of the jet is linked to a preferential tropical ascent region (Fig. 9). The air parcels that end up in the subtropical jet over Africa ascend into the upper branch of the Hadley cell primarily over South America (Fig. 9a). The air parcels that reach the subtropical jet over Asia are to equal degrees located over South America (6 days before they reach the jet), equatorial Africa (5 days before they reach the jet), and the Indian Ocean (4 days before they reach the jet) (Fig. 9b).

Air parcels that reach the subtropical jet over the Pacific emerge primarily from the Maritime Continent and the Atlantic basin (Fig. 9c). The air parcels that end up in the subtropical jet over the eastern Pacific and North America ascend into the jet primarily over the western and central Pacific (Fig. 9d). The substantial fraction of trajectories that stays in the subtropics at upper levels almost circles the Northern Hemisphere once during the 7-day period (Fig. 9).

Overall, the majority of the trajectories ascend over the South American continent and the Maritime Continent. Next in importance are ascent areas over the African continent, the western Indian Ocean, and the western Pacific. There are very few trajectories that ascend over the southern Atlantic Ocean or the eastern Pacific.

During summer, the main ascent region of air parcels into the subtropical jet during the investigated 7-day time window is located over the eastern Indian Ocean, the southern and southeastern Asian continent, and the Chinese Sea (Fig. 10). A much smaller fraction of trajectories ascend over the Gulf of Mexico and the North American continent (Fig. 10). It is important to keep in mind that Fig. 10 shows the mean altitude averaged over all trajectories located at a specific grid point. And the mean height value of approximately 350 hPa over North America is the mean of a group of trajectories that ascend locally into the subtropical jet and many trajectories that pass this region at upper levels.

Fig. 10.
Fig. 10.

Mean height of the trajectories (hPa) at t = −168 h in summer for trajectories started over (a) Africa, (b) Asia, (c) the Pacific, and (d) North America (shaded). Pressure values are only shown for each grid point where the trajectory density exceeds 0.001 count per square kilometer. The black contours indicate density values of 0.005 and 0.01 count per square kilometer.

Citation: Journal of the Atmospheric Sciences 71, 7; 10.1175/JAS-D-13-0329.1

In summer, the East Asian monsoon seems to be of primary importance for the subtropical jet over Asia and the Pacific (Fig. 10c).

6. Tropical, subtropical, and extratropical forcing of the subtropical jet

From the pathways of the air parcels that end up in the subtropics (Figs. 79), it is evident that a nonnegligible fraction of air reaches the STJ from the extratropics. The magnitude and the temporal and spatial variability of the tropical versus the extratropical forcing of the STJ are discussed in the following section. Two complementary approaches are used: one based on angular momentum conservation and one based on PV.

a. Angular momentum conservation

Tracing the angular momentum along the trajectories that end up in the subtropical jet allows for the quantification of the fraction of angular momentum m that is conserved along tropospheric trajectories that emerge from the tropics (PV < 2 PVU), as well as for the identification of areas where the angular momentum is reduced. The 5-yr mean relative change of angular momentum along the 7-day trajectories reaching the STJ from the tropics, that is, (mmaxmmin)/mmax, for the four seasons and for different regions is shown in Fig. 11. The nonconservation of angular momentum is generally greatest in summer. In summer, it is largest over the Pacific and over the North American sector, where it amounts to almost 20%. The nonconservation of angular momentum along the trajectories started from the jet over the Asian continent is even greater. However, these trajectories are strongly influenced by the very low altitude of the 345-K surface over the Tibetan Plateau, where presumably frictional effects become important.

Fig. 11.
Fig. 11.

Relative decrease in angular momentum along the tropospheric trajectories (PV < 2 PVU at t = 0) per season.

Citation: Journal of the Atmospheric Sciences 71, 7; 10.1175/JAS-D-13-0329.1

In summer, the Northern Hemisphere mean angular momentum nonconservation, without taking into account the trajectories started over Asia, amounts to approximately 14% and is slightly weaker in fall (~13%). The total angular momentum nonconservation in winter and spring is approximately half as strong (~6%; see Table 1).

Table 1.

Decrease in angular momentum averaged over all trajectories and over all tropospheric trajectories (PV < 2 PVU at t = 0). The numbers in parentheses indicate averages excluding the Asian sector.

Table 1.

A possible explanation for this difference is the time that the air parcels spend in the subtropics. In winter, the angular momentum nonconservation mainly occurs during the last 24 h prior to the arrival of the air parcels in the jet (Figs. 2a,b) and during the last 48 h in summer (Figs. 3a,b). The trajectories move more slowly and spend more time in the subtropics during the summer (Figs. 2d, 3d, 7, 8). As a result, they are subjected to angular momentum depletion by subtropical and extratropical eddies for a longer period.

The areas where air parcels of tropospheric tropical origin are preferentially subjected to subtropical eddy forcing are shown in Fig. 12. This figure shows the mean (averaged over all PV < 2 PVU trajectories) angular momentum nonconservation due to longitudinal pressure gradients, that is, eddies. Only grid points where the trajectory density exceeds a threshold are shown, and the subsequent discussion focuses hence on the subtropics where the majority of the PV < 2 PVU trajectories are located at t = −12 h. For the following discussion, it is important to keep in mind that while spatial variability of the pressure gradient forcing term is robust, the uncertainty of the absolute values is quite large (see also Figs. 2b, 3b). The main pattern in winter is an increase in angular momentum nonconservation with latitude, as is to be expected (Fig. 12). There is virtually no change in the angular momentum equatorward of approximately 20°N. Areas with large negative tendencies and relatively high trajectory numbers are located in the subtropics over the western Pacific, North America, and the eastern Mediterranean.

Fig. 12.
Fig. 12.

Total pressure gradient forcing of the angular momentum (109 m2 s−1 during 6 h, shaded) along tropospheric (PV < 2 PVU) trajectories in (left) winter and (right) summer for areas that exceed a trajectory density of 0.005 count per square kilometer and trajectory counts at t = −12 h (red contours, 0.02, 0.05, 0.1 count per square kilometer).

Citation: Journal of the Atmospheric Sciences 71, 7; 10.1175/JAS-D-13-0329.1

In summer, the tendencies are less zonally symmetric. Negative tendencies are strongest over the eastern Mediterranean, the western Pacific, and along the coasts of North America. Trajectories are generally located farther away from the equator and hence in areas with larger-amplitude changes in the angular momentum.

In winter, the extratropical trajectories gain angular momentum during the last 48 h before they arrive in the jet (Figs. 2a,b). At the same time, they move southward (Fig. 2d). This is consistent with the picture that these air parcels follow an anticyclonic pathway and experience a positive pressure gradient forcing when moving southward along the eastern flank of an anticyclone.

b. Correlation between the strength of the jet and the percentage of air with tropical and extratropical origin

The following set of simple assumptions is made to estimate tropical and extratropical forcing of the STJ, that is, the enhancement of the subtropical PV gradient. (i) The extratropical strengthening of the PV gradient corresponds to the fraction of trajectories with PV > 4 PVU at t = 0. (ii) The tropical strengthening of the PV gradient corresponds to the fraction of trajectories with PV < 1 PVU at t = 0. Martius and Wernli (2012) show that on days when the wintertime jet, and hence the PV gradient over Africa, is very strong (uppermost 10%), the fraction of extratropical and tropical trajectories that reach the jet is substantially larger than on days when the jet is very weak. This finding indicates that both extratropical and tropical contributions are potentially important for the strengthening of the PV gradient across the jet and the concomitant jet intensification. The trajectory data available in this study allow us to extend this analysis to other regions and seasons and to quantify the effect of extratropical versus tropical forcing. The hypotheses to be tested are (i) that very strong PV gradients and jets occur when both the extratropical and the tropical forcing are strong, that is, when the sum of fraction of PV < 1 PVU and PV > 4 PVU is large and (ii) that tropical forcing is more relevant than extratropical forcing.

In the following, we first discuss the fraction of tropical and extratropical trajectories, and then we present a regression model to quantify the respective contributions of extratropical and tropical forcing to the regional jet strength. The fraction of air parcels reaching the subtropical jet from the deep tropics, the subtropics and the extratropics varies throughout the year. For the entire Northern Hemisphere, the fraction of trajectories with very low PV values (origin in the deep tropics; PV < 1 PVU) varies between a maximum of 36% during MAM and a minimum of 23% during JJA. Regionally, the strongest seasonal variation occurs in the African sector, with values varying between 43% in DJF and 13% in MAM.

The fraction of trajectories with an extratropical origin (PV > 4 PVU) for the entire Northern Hemisphere varies between 34% during JJA and 28% during MAM. The fraction of deep tropical and extratropical trajectories is largest in winter (65%) and spring (64%), which is consistent with a stronger PV gradient and a stronger jet during these seasons. The combined contribution of deep tropical and extratropical trajectories lies between 57% and 65% in all seasons (Table 2).

Table 2.

Fraction (%) of trajectories separated by PV value at t = 0 and by season.

Table 2.

To quantify the effect of the varying contributions of trajectories from the deep tropics and the extratropics on the jet, a multiple regression model is set up. The model is applied (i) to time-mean values and (ii) to 6-hourly values. In this model, the regional-mean percentage of trajectories from the deep tropics (PV < 1 PVU) and the extratropics (PV > 4 PVU) serve as independent (predictor) variables for regional-mean wind speed (response variable) [Eq. (2)]. Note that these fractions are to first order governed by independent, dynamical processes [see also Martius and Wernli (2012)] and neither fraction ever reaches 100%. The model is applied to data averaged over the entire Northern Hemisphere and over the four regions (Africa, Asia, Pacific, and North America):
e2
Using the time-mean values as input (16 values, one for each season and one for each region), approximately 70% of the wind speed variance is explained by the fraction of tropical and extratropical trajectories (pvalue < 0.001 of the F statistic of the global model and R2 = 0.7; see also Table 3). Both predictor variables have contributions of similar magnitude (β2 = 0.89 m s−1, β3 = 0.75 m s−1) and are statistically significantly different from 0 (pvalue < 0.001). An increase in the fraction of tropical or extratropical trajectories by 1% results hence in an increase in wind speed of approximately 0.9 and 0.75 m s−1, respectively. The explained variance is much lower, if only the fraction of tropical (R2 = 0.4) or extratropical (R2 = 0.03) trajectories is used for the regression. These results point (i) to the importance of both tropical (%PV1) and extratropical (%PV4) contributions to the strength of the STJ since the explained variance decreases substantially when only one variable is used and (ii) to the overall dominant role of the tropical forcing (%PV1). This second finding is in good agreement with the angular momentum–based analyses [see previous section and, e.g., Held and Hou (1980)].
Table 3.

Regression parameters and correlation coefficients obtained from the multiple regression model using the time-mean values (16 values, one for each season and each region). All p values of the F statistics of the global model are above the 99th percentile.

Table 3.

The results are similar when the regression model is applied to the 6-hourly data; however, the explained variance is much lower (R2 = 0.44, β2 = 0.33 m s−1, and β3 = 0.19 m s−1; see also Table 4). The daily data allow for looking into the seasonal and spatial variations in the regression model results. The largest explained variance of the STJ speed due to tropical contributions is found in spring and winter. In summer, the explained variance is very low (R2 = 0.2), and the explained variance due to extratropical contributions exceeds that of the tropical contributions. This is in good qualitative agreement with the findings of the angular momentum analysis.

Table 4.

Regression parameters and correlation coefficients obtained from the multiple regression model using 6-hourly input values. All p values of the F statistics of the global models are above the 99th percentile.

Table 4.

There are also quite substantial regional differences. The explained variance for the African and Asian sectors (R2 = 0.4 and R2 = 0.6) is more than twice as high as for the American sector (R2 = 0.2) (Table 4).

These numbers are only rough approximations, and it is important to keep in mind that only the fraction of PV > 4 PVU and PV < 1 PVU was used for the model. In summer, when the explained variance is very small, this choice is not optimal, since the fraction of trajectories with a value of PV < 1 PVU is only 23% (16% in the American sector). Nevertheless, the main results are in very good agreement with and support the findings of the angular momentum–based analysis.

7. Summary and conclusions

In this paper, tropical, subtropical, and extratropical forcing of the Northern Hemisphere subtropical jet is investigated using back trajectories. For a 5-yr period, trajectories were started every 6 h from the STJ and traced back in time for 7 days. These trajectories provide information about the pathways that air parcels take that end up in the subtropical jet and about the temporal evolution of important dynamical parameters (PV, angular momentum, potential temperature, and wind speed) along the trajectories. Overall, PV is well conserved along the trajectories and the PV values of the air parcels at the time when the trajectories were started can therefore be used to separate the trajectories with a tropical origin from those with a subtropical or extratropical origin. Trajectories with a clear extratropical origin (PV > 4 PVU) constitute 34% of all trajectories in summer and 28% in spring. Trajectories with a tropical origin (PV < 1 PVU) amount to 36% of all trajectories in winter and spring and 23% in summer.

a. Trajectory pathways

The trajectories that reach the subtropical jet from the tropics in the winter season (DJF) follow preferred pathways and ascend into the upper troposphere in geographically distinct areas. The air parcels that end up in the jet over Africa 7 days later ascend to the tropopause in the Southern Hemisphere over the South American continent, then cross the equator, and then follow an anticyclonic pathway across the Atlantic into the STJ over Africa. The air parcels ending up in the STJ over East Asia and the Pacific ascend over the tropical Indian Ocean and the Maritime Continent and follow an anticyclonic path into the jet. Other tropical areas are of secondary importance in terms of the number of trajectories that emerge from this region. In summary, the trajectories illustrate the zonally nonsymmetric nature of the winter hemisphere Hadley circulation and “teleconnections” between zonally confined regions of tropical convection and zonal sections of the subtropical jet.

During the investigated 7-day period, a substantial fraction of trajectories remained in the subtropical belt (53% remained north of 15°N and south of 45°N). The trajectories that stayed in the subtropics almost circle the Northern Hemisphere once during the 7-day period. This means that, if angular momentum is conserved, the momentum that reaches the subtropical jet from a (potentially very local) source of tropical forcing is distributed across the entire Northern Hemisphere within approximately 1 week (Fig. 9). The interesting question regarding how well the momentum is conserved in the subtropics is not addressed in the present study and would require an extension of the trajectories forward in time. Once the trajectories are directed into the extratropics along a planetary-scale ridge, they are subjected to strong pressure gradient forcing and, accordingly, a change in their angular momentum.

The trajectories that reach the jet from the extratropics preferentially enter the STJ at the downstream edge of the climatological ridges over the eastern Pacific and the eastern Atlantic, as well as over central Asia.

During summer (JJA), the majority of air parcels ascend to the tropopause in the Northern Hemisphere over Southeast Asia and the Himalayas indicating that the Southeast Asian monsoon is of central importance for the entire Northern Hemisphere subtropical jet. Trajectories ending over North America also ascend to upper levels over North America and the Caribbean.

b. Tropical and extratropical forcing of the jet

Overall angular momentum is well conserved along the trajectories that reach the jet from the deep tropics. Along the tropical trajectories, the nonconservation of angular momentum due to eddy pressure gradient forcing is strongest in summer, which is consistent with the findings of previous studies (Bordoni and Schneider 2010; Ceppi and Hartmann 2013; Kang and Polvani 2011). In summer, the angular momentum is reduced by approximately 14% (18% if the trajectories started over Asia are included). The reduction is slightly weaker in fall (about 13%). In winter and spring, the total angular momentum reduction is approximately half as strong (~6%; see Table 1). Nonconservation of angular momentum along the trajectories with tropical origin happens in the subtropics, and the negative tendencies exceed the positive tendencies, but both are of the same order of magnitude. The nonconservation happens preferentially in the western Pacific and over the North American continent in summer.

These results are corroborated by a PV-based estimation of tropical and extratropical forcing of the subtropical jet. The results confirm the important role of tropical forcing, that is, export of very-low-PV air into the subtropics, and point to the relevant influence that both tropical and extratropical forcing have on the STJ, with extratropical forcing being most relevant in summer and fall and least important in spring and winter.

Acknowledgments

I thank MeteoSwiss for granting access to ERA-Interim. Two anonymous reviewers are acknowledged for substantially improving the quality of this manuscript.

REFERENCES

  • Allen, R. J., , S. C. Sherwood, , J. R. Norris, , and C. S. Zender, 2012a: Recent Northern Hemisphere tropical expansion primarily driven by black carbon and tropospheric ozone. Nature, 485, 350354, doi:10.1038/nature11097.

    • Search Google Scholar
    • Export Citation
  • Allen, R. J., , S. C. Sherwood, , J. R. Norris, , and C. S. Zender, 2012b: The equilibrium response to idealized thermal forcings in a comprehensive GCM: Implications for recent tropical expansion. Atmos. Chem. Phys., 12, 47954816, doi:10.5194/acp-12-4795-2012.

    • Search Google Scholar
    • Export Citation
  • Barnes, E. A., , and D. L. Hartmann, 2011: Rossby wave scales, propagation, and the variability of eddy-driven jets. J. Atmos. Sci., 68, 28932908, doi:10.1175/JAS-D-11-039.1.

    • Search Google Scholar
    • Export Citation
  • Bordoni, S., , and T. Schneider, 2010: Regime transitions of steady and time-dependent Hadley circulations: Comparisons of axisymmetric and eddy-permitting simulations. J. Atmos. Sci., 67, 16431654, doi:10.1175/2009JAS3294.1.

    • Search Google Scholar
    • Export Citation
  • Ceppi, P., , and D. L. Hartmann, 2013: On the speed of the eddy-driven jet and the width of the Hadley cell in the Southern Hemisphere. J. Climate, 26, 34503465, doi:10.1175/JCLI-D-12-00414.1.

    • Search Google Scholar
    • Export Citation
  • Cordeira, J. M., , and L. F. Bosart, 2010: The antecedent large-scale conditions of the “perfect storms” of late October and early November 1991. Mon. Wea. Rev., 138, 25462569, doi:10.1175/2010MWR3280.1.

    • Search Google Scholar
    • Export Citation
  • Davies, H. C., , and A. M. Rossa, 1998: PV frontogenesis and upper-tropospheric fronts. Mon. Wea. Rev., 126, 15281539, doi:10.1175/1520-0493(1998)126<1528:PFAUTF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Dee, D. P., and et al. , 2011: The ERA-Interim reanalysis: Configuration and performance of the data assimilation system. Quart. J. Roy. Meteor. Soc., 137, 553597, doi:10.1002/qj.828.

    • Search Google Scholar
    • Export Citation
  • Dritschel, D. G., , and M. E. McIntyre, 2008: Multiple jets as PV staircases: The Philips effect and the resilience of eddy-transport barriers. J. Atmos. Sci., 65, 855874, doi:10.1175/2007JAS2227.1.

    • Search Google Scholar
    • Export Citation
  • Eichelberger, S. J., , and D. L. Hartmann, 2007: Zonal jet structure and the leading mode of variability. J. Climate, 20, 51495163, doi:10.1175/JCLI4279.1.

    • Search Google Scholar
    • Export Citation
  • Feldstein, S. B., , and U. Dayan, 2008: Circumglobal teleconnections and wave packets associated with Israeli winter precipitation. Quart. J. Roy. Meteor. Soc., 134, 455467, doi:10.1002/qj.225.

    • Search Google Scholar
    • Export Citation
  • Fueglistaler, S., , H. Wernli, , and T. Peter, 2004: Tropical troposphere-to-stratosphere transport inferred from trajectory calculations. J. Geophys. Res., 109, D03108, doi:10.1029/2003JD004069.

    • Search Google Scholar
    • Export Citation
  • Gill, A. E., 1980: Some simple solutions for heat-induced tropical circulation. Quart. J. Roy. Meteor. Soc., 106, 447462, doi:10.1002/qj.49710644905.

    • Search Google Scholar
    • Export Citation
  • Gill, A. E., 1982: Atmosphere-Ocean Dynamics. Academic Press, 645 pp.

  • Held, I. M., , and A. Y. Hou, 1980: Nonlinear axially symmetric circulations in a nearly inviscid atmosphere. J. Atmos. Sci., 37, 515533, doi:10.1175/1520-0469(1980)037<0515:NASCIA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hoskins, B. J., , and D. J. Karoly, 1981: The steady linear response of a spherical atmosphere to thermal and orographic forcing. J. Atmos. Sci., 38, 11791196, doi:10.1175/1520-0469(1981)038<1179:TSLROA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hoskins, B. J., , and T. Ambrizzi, 1993: Rossby-wave propagation on a realistic longitudinally varying flow. J. Atmos. Sci., 50, 16611671, doi:10.1175/1520-0469(1993)050<1661:RWPOAR>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Isotta, F., , O. Martius, , M. Sprenger, , and C. Schwierz, 2008: Long-term trends of synoptic-scale breaking Rossby waves in the Northern Hemisphere between 1958 and 2001. Int. J. Climatol., 28, 15511562, doi:10.1002/joc.1647.

    • Search Google Scholar
    • Export Citation
  • Kallberg, P., , P. Berrisford, , B. Hoskins, , A. Simmons, , S. Uppala, , S. Lamy-Thépaut, , and R. Hine, 2005: ERA-40 atlas. ERA-40 Project Rep. 19, 191 pp.

  • Kang, S. M., , and L. M. Polvani, 2011: The interannual relationship between the latitude of the eddy-driven jet and the edge of the Hadley cell. J. Climate, 24, 563568, doi:10.1175/2010JCLI4077.1.

    • Search Google Scholar
    • Export Citation
  • Kang, S. M., , L. M. Polvani, , J. C. Fyfe, , and M. Sigmond, 2011: Impact of polar ozone depletion on subtropical precipitation. Science, 332, 951954, doi:10.1126/science.1202131.

    • Search Google Scholar
    • Export Citation
  • Kiladis, G. N., , and K. M. Weickmann, 1992: Extratropical forcing of tropical Pacific convection during northern winter. Mon. Wea. Rev., 120, 19241938, doi:10.1175/1520-0493(1992)120<1924:EFOTPC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Koch, P., , H. Wernli, , and H. C. Davies, 2006: An event-based jet-stream climatology and typology. Int. J. Climatol., 26, 283301, doi:10.1002/joc.1255.

    • Search Google Scholar
    • Export Citation
  • Lee, S., 1997: Maintenance of multiple jets in a baroclinic flow. J. Atmos. Sci., 54, 17261738, doi:10.1175/1520-0469(1997)054<1726:MOMJIA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Madonna, E., , H. Wernli, , H. Joos, , and O. Martius, 2014: Warm conveyor belts in the ERA-Interim dataset (1979–2010). Part I: Climatology and potential vorticity evolution. J. Climate, 27, 326, doi:10.1175/JCLI-D-12-00720.1.

    • Search Google Scholar
    • Export Citation
  • Manney, G. L., et al. , 2011: Jet characterization in the upper troposphere/lower stratosphere (UTLS): Applications to climatology and transport studies. Atmos. Chem. Phys., 11, 61156137, doi:10.5194/acp-11-6115-2011.

    • Search Google Scholar
    • Export Citation
  • Martius, O., , and H. Wernli, 2012: A trajectory-based investigation of physical and dynamical processes that govern the temporal evolution of the subtropical jet streams over Africa. J. Atmos. Sci., 69, 16021616, doi:10.1175/JAS-D-11-0190.1.

    • Search Google Scholar
    • Export Citation
  • Martius, O., , C. Schwierz, , and H. C. Davies, 2010: Tropopause-level waveguides. J. Atmos. Sci., 67, 866879, doi:10.1175/2009JAS2995.1.

    • Search Google Scholar
    • Export Citation
  • Moore, R. W., , O. Martius, , and T. Spengler, 2010: The modulation of the subtropical and extratropical atmosphere in the Pacific basin in response to the Madden–Julian oscillation. Mon. Wea. Rev., 138, 27612779, doi:10.1175/2010MWR3194.1.

    • Search Google Scholar
    • Export Citation
  • Ploeger, F., et al. , 2011: Insight from ozone and water vapour on transport in the tropical tropopause layer (TTL). Atmos. Chem. Phys., 11, 407419, doi:10.5194/acp-11-407-2011.

    • Search Google Scholar
    • Export Citation
  • Schiemann, R., , D. Luthi, , and C. Schar, 2009: Seasonality and interannual variability of the westerly jet in the Tibetan Plateau region. J. Climate, 22, 29402957, doi:10.1175/2008JCLI2625.1.

    • Search Google Scholar
    • Export Citation
  • Schwierz, C., , S. Dirren, , and H. C. Davies, 2004: Forced waves on a zonally aligned jet stream. J. Atmos. Sci., 61, 7387, doi:10.1175/1520-0469(2004)061<0073:FWOAZA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Seidel, D. J., , Q. Fu, , W. J. Randel, , and T. J. Reichler, 2008: Widening of the tropical belt in a changing climate. Nat. Geosci., 1, 2124, doi:10.1038/ngeo.2007.38.

    • 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, doi:10.1002/qj.49712353811.

    • Search Google Scholar
    • Export Citation
  • Woollings, T., , A. Hannachi, , and B. Hoskins, 2010: Variability of the North Atlantic eddy-driven jet stream. Quart. J. Roy. Meteor. Soc., 136, 856868, doi:10.1002/qj.625.

    • Search Google Scholar
    • Export Citation
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