Day Meridional Propagation of Global Circulation Anomalies ( A Global Convection Circulation Paradigm for the Annular Mode) Ming Cai 1 and R-C Ren 1,2 1 Department of Meteorology Florida State University, USA 2 LASG, Institute of Atmospheric Physics, CAS, Beijing, P. R. China Ming Cai 1 and R-C Ren 1,2 1 Department of Meteorology Florida State University, USA 2 LASG, Institute of Atmospheric Physics, CAS, Beijing, P. R. China

2 The objective To provide a physical explanation on the dynamical nature of the annular mode by linking the climate variability of the annular mode to the collective effects of individual weather circulation systems.

3 Global zonal mean (mass) circulation viewed from isentropic coordinate NH winter NH summer Warm air is transported poleward at the upper layer and cold air advances toward the equator near the surface. Speed ~ 1-3 m/s Townsend and Johnson (1985)

4 Palmen and Newton’s cartoon

5 PV Latitudes (or Equivalent Latitudes, Norton 1994) NP 30º 0º For circular contours of PV centered at the pole, PV Latitudes = Latitudes NP 30º 0º Area encircled by a PV contour = Area encircled by a Latitude. 30º #1: The location of the PV contour is assigned to have a PV latitude equal to the latitude. #2: The mapping from PV contours to PV latitudes is done progressively from large PV to small PV till reaching the zero PV contour.

6 Data NCEP/NCAR isentropic reanalysis II ( ) Daily 2.5ºx2.5º gridded data on 11 isentropic surfaces. PV, U, V, W, Temp./pressure, RH, N 2. NH and SH.

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8 Transformation from a 3-D field to 2-D field in the  -PVLAT coordinate NP 30º 0º 30º Zonally averaging a field along PV latitudes (or PV contours), instead of real latitudes, => Mean “meridional” circulation in the  -PVLAT coordinate.

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12 31 positive events 25 negative events

13 Meridional propagation Poleward propagation in the stratosphere Equatorward propagation in troposphere 2 Periods 45 days 72 days

14 Downward propagation at different PV-lat bands 12 days23 days Polar Cap (65-90N) Mid-lat. (40-55N) Sub-Tropics (10-25N)

15 Explanation

16 Relationship between temperature and PV anomalies Generalized PV ( Bretherton, 1966) T’ > 0 near the top boundary => negative PV T’ positive PV T’ > 0 at the lower boundary => Positive PV T’ Negative PV

17 Why do the wind anomalies follow the temperature anomalies of the opposite sign in the stratosphere? T’ > 0 aloft => negative PV anomaly => positive Montgomery potential => u’ 0 T’ positive PV anomaly => negative Montgomery potential => u’ > 0 follows poleward propagating T’ < 0 by a quarter of period. OR (by thermal wind relation) T’ more elevated isentropic surface. T’ > 0 => downwelling of isentropic surface. Poleward propagating T’ > 0 => more sloped isentropic surface at north and less sloped at south => U’ 0 by a quarter period. T’ > 0 aloft => negative PV anomaly => positive Montgomery potential => u’ 0 T’ positive PV anomaly => negative Montgomery potential => u’ > 0 follows poleward propagating T’ < 0 by a quarter of period. OR (by thermal wind relation) T’ more elevated isentropic surface. T’ > 0 => downwelling of isentropic surface. Poleward propagating T’ > 0 => more sloped isentropic surface at north and less sloped at south => U’ 0 by a quarter period.

18 Why do the wind anomalies lead to the temperature anomalies of the same sign in the troposphere? T’ negative PV source => positive Montgomery potential anomaly => u’ < 0; T’ > 0 at low levels => positive PV source => negative Montgomery potential anomaly => u’ > 0; Equatorward propagation => U’ > 0 leads to T’ > 0 by a quarter period and U’ < 0 leads to T’ < 0 by a quarter period. T’ negative PV source => positive Montgomery potential anomaly => u’ < 0; T’ > 0 at low levels => positive PV source => negative Montgomery potential anomaly => u’ > 0; Equatorward propagation => U’ > 0 leads to T’ > 0 by a quarter period and U’ < 0 leads to T’ < 0 by a quarter period.

19 Why do stratospheric anomalies propagate poleward and downward simultaneously and tropospheric anomalies propagate equatorward? A global convection circulation paradigm

20 Semi-geostrophic frontogenesis theory (Hoskins 1972) Due to cross-frontal circulation, the baroclinic zone becomes less vertically sloped => or a more leveled baroclinic zone => upper level frontolysis in the warm air sector and frontogenesis in the cold air sector. (Fig of the book by Bluestein) Col d Warm Col d Warm Cold

21 Application of the semi-geostrophic frontogenesis theory YSYS YNYN P1P1 P2P2 11 22 33 33 22 11 P1P1 P2P2 Before After Easterly anomalies Westerly anomalies

22 Day-29 Day-73 Day_0 Day_50 Day_73 Day_29 Day_0 Day_50

23 Slope of the extratropical baroclinic zone and the annular mode variability P1P1 P2P2 11 22 33 YSYS YNYN 33 22 11 P1P1 P2P2 Steeply sloped isentropic surfaces (a steeply sloped baroclinic zone) => the positive phase of the annular mode=> surface cold air mass remains in the polar region => a much warm SURFACE temperature in mid-latitudes. +NAM More leveled isentropic surfaces (a gently sloped baroclinic zone) => the negative phase of the annular mode. => surface cold air advances southward => cold episodes in mid latitudes.  NAM

24 Troposphere and Stratosphere coupling Minimum U anomalies Tropospheric cold air in high latitudes starts to propagate equatorward as the arrival of the stratosphere warm air => “disruption” of the downward propagation of temperature anomalies into troposphere. T’ > 0 in the stratosphere => negative PV anomalies => U’ < 0 T’ negative PV source => U’<0 wind anomalies APPEARS to propagate downward “continuously”. Tropospheric cold air in high latitudes starts to propagate equatorward as the arrival of the stratosphere warm air => “disruption” of the downward propagation of temperature anomalies into troposphere. T’ > 0 in the stratosphere => negative PV anomalies => U’ < 0 T’ negative PV source => U’<0 wind anomalies APPEARS to propagate downward “continuously”. Polar cap (65-90N) mid-lat (40-55) Sub- tropics 10-25N Montgomery potential anomaly

25 Time Scale Poleward propagation in the stratosphere Equatorward propagation in troposphere 72 days 47 days 45 days => 1.6 m.s => 2.5 m.s Enhanced hemispheric mass circulation is faster due to a stronger meridional temperature gradient => a stronger eddy forcing Weaker hemispheric mass circulation is slower due to a weaker meridional temperature gradient => a weak eddy forcing.

26 Summary The annular mode variability is a manifestation of continuous and endless adjustments of mass, geostrophy, and static stability accompanying with the processes of transporting heat poleward. Global mass adjustment/circulation is carried out by a succession of cross-frontal circulations from the tropics to the pole and from the stratosphere to the troposphere => Stratospheric circulation anomalies propagate poleward and downward whereas tropospheric anomalies propagate equatorward. The leveling of the vertically slopped baroclinic zone results in a reduction (an increase) of the meridional temperature gradient in the warm (cold) air sector. ==> a weakening (strengthening) of the westerly jet in the warm air sector (cold air sector). A more sloped baroclinic zone in the polar area corresponds to the positive phase of the annular mode and a more leveled baroclinic zone corresponds to the negative phase of the annular mode. The propagation time scale is dictated by diabatic heating/cooling of both external thermal forcing and eddy-driven forcing. The annular mode variability is a manifestation of continuous and endless adjustments of mass, geostrophy, and static stability accompanying with the processes of transporting heat poleward. Global mass adjustment/circulation is carried out by a succession of cross-frontal circulations from the tropics to the pole and from the stratosphere to the troposphere => Stratospheric circulation anomalies propagate poleward and downward whereas tropospheric anomalies propagate equatorward. The leveling of the vertically slopped baroclinic zone results in a reduction (an increase) of the meridional temperature gradient in the warm (cold) air sector. ==> a weakening (strengthening) of the westerly jet in the warm air sector (cold air sector). A more sloped baroclinic zone in the polar area corresponds to the positive phase of the annular mode and a more leveled baroclinic zone corresponds to the negative phase of the annular mode. The propagation time scale is dictated by diabatic heating/cooling of both external thermal forcing and eddy-driven forcing.

27 Climate prediction application The long time scale (40-70 days). The systematic poleward propagation from the tropics to the pole. The coupling of stratospheric and tropospheric anomalies. The long time scale (40-70 days). The systematic poleward propagation from the tropics to the pole. The coupling of stratospheric and tropospheric anomalies.