Toshiki  Iwasaki

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Iwasaki, Toshiki

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Diagnostic Tool of Zonally Symmetric Structureof the Global Atmosphere Based on thePressure-Isentrope Hybrid Vertical Coordinates(Extended Abstract)著者 Toshiki  Iwasaki雑誌名 The science reports of the Tohoku University.Fifth series, Tohoku geophysical journal巻 36号 2ページ 213-218発行年 2001-09URL http://hdl.handle.net/10097/45378TOhoku Geophys. Journ. (Sci. Rep.  TOhoku Univ., Ser. 5), Vol. 36, No. 2, pp. 213-218, 2001Diagnostic Tool of the Zonally Symmetric Structure of the Global Atmosphere Based on the Pressure-Isentrope          Hybrid Vertical Coordinates            (Extended  Abstract) TOSHIKI IWASAKI Geophysical Institute, Graduate School of Science, Tohoku University  Arainaki, Aoba-ku , Sendai, 980-8578                (Received January 5, 2001)1. Introduction    A set of zonal mean equations is formulated in the  pressure-isentrope hybrid vertical coordinates, which diagnoses the mean-meridional circulation and wave, mean-flow interaction (Iwasaki, 1989 and 1998, hereafter called as 189 and 198). This is to generalize the  nonaccelera-tion theorem (e.g., Andrews and McIntyre, 1976) toward finite-amplitude and/or nongeostrophic (fully primitive) expression, where the vertical component of the  Eliassen-Palm flux is expressed as the from drag over the isentropic or the ground line. The formulation leads us to a consistent view of the meridional transports of mass, angular momentum, heat and minor constituents. It gives the nondivergent mean-meridional mass circulation and solves the lower boundary  condi-tions. We demonstrate the performance of the scheme as a diagnostic tool of the global atmosphere.    Next, we derive rate equations of potential energy and kinetic energies of zonal means and eddies. We find significant differences from conventional Eulerian mean view (Lorenz, 1955). The zonal mean available potential energy directly transforms with the eddy available potential energy but the zonal mean kinetic energy directly transforms with the eddy available potential energy. Particular attention is paid to the energetics of ideal baroclinic waves based on the above formulation.    Polar vortexes have sharp edges around the polar night jetstream. The thermodynamic structure of the atmosphere suggests large differences in the meridional heat transport between the inside and outside of the polar vortex. Here, we apply the new formulation to the mean meridional circulation and its relation to the maintenance mechanisms of the polar vortex.2. Basic formulations    Isentropic zonal means of pressure  pt _--=  p"are used as the vertical coordinate. The means of arbitrary variables are defined with the mass weight  Op/  Pt  OP   A*  =A  Opt  t and eddies are defined as departures from the mass weighted zonal meanszonal(1)214 TOSHIKI  TWASAKi A* (2) The mass weight is required to satisfy conservation constraints. Cartesian coordinate is chosen for simplicity. The zonal mean zonal momentum equation is written by  (   u* v*  (  du*cos0)au                               + cot-----fv*+DF+ X*, (3)  at ),,a cost aoPt apt where Eliassen-Palm flux and its divergence are  F Fr,)                              1                       acos0(— (dv")*,—(divt')*  a  cos  0  /3(  aail°  )p, and                      1  j 1   D  F=  a  cos  0 a cos ( 00 FØcos0)+                                                        Pt UPt respectively. The  cut is the mean-vertical pt-velocity and others are conventional notations. The vertical component of  Eliassen-Palm flux is expressed as the form drag over isentropes. The thermodynamic equation without any eddy terms           ( .00v*dO_L apt _ Q \* (4)                     dt)13,1a30 )p,("ut—( .11(p) More details are found in  189 and 198.3. Mass stream function    Figure 1 shows the mass stream functions analyzed by the conventional Eulerian mean, TEM and  pt analysis  (189). The  pt analysis is very different from the conventional analysis based on pressure coordinates. The tropospheric circulation consists only of single direct cell with a kink near the subtropical jet stream in contrast with the well-known three cell structure of the conventional Eulerian mean circulation. The stratospheric circulation diagnosed by the new scheme is more consistent with the observation of minor constituents and with trajectory simulations than that by the TEM. These results suggest practical advantages of the scheme as well.4. Energy cycle    The global atmospheric energy cycle is formulated meeting with the context of the non acceleration theorem. As shown in  fig.  2, it is significantly different from the conventional Eulerian mean view (Lorenz, 1955). The zonal mean available potential energy do not directly transforms with the eddy available potential energy but the zonal mean kinetic energy directly transforms with the eddy available potential energy. The latter is contributed to by the vertical divergence of the  Eliassen-Palm flux divergence.    Figure 3 shows the energy flow of the baroclinic instability waves. The zonal mean available potential energy is released to the zonal mean kinetic energy by driving mean meridional  wind. Simultaneously the kinetic energy of mean  zonal wind transforms into the eddy available potential energy through wave, mean-flow interactions. Under the geostrophic equilibriumDIAGNOSTIC TOOL OF THE GLOBAL ATMOSPHERE 2153050   100  Cr.  3 tr) Er 300    5001000 Conventtonal  EuIertan MeanTEM30 50 100  cc  3  U) la/ fr 300    500 E  3 U)tat cc 1000  NEW  30  50  ;  :!-  (00      7a. 3 0 0 r t5o  500  [  "     tooJ t „   90  N  60N 30N 0  30S GOS 905  LATITUDE Fig 1. Mass streamfunctions of the perpetual January simulation by NCAR  CCM1,    diagnosed with the conventional Eulerian mean, the TEM and the  pi analyses    (After Iwasaki, 1989)./0-6.,\If_-9::;-E (A          . ,‘‘,._„,:i...,___:  200 • • 4‹.4vii (3° (  f  1 tDA 1condition, these two transformation rates are almost equal to each other. Geostrophic adjust-ments may assist transformations from the eddy available potential energy into the eddy kinetic energy. All the processes might be the main stream of dynamical energy flows in mid- and high latitudes.216 TOSHIKI IWASAKi PZ PE/Fig. 2KZEnergy cycles of the global atmosphere.Fig. 3 —  —  —  —  )Energy cycle of baroclinic instability waves.5. Mean meridional circulation associated with the polar vortex    The SH polar vortex, which is more axisymmetric than the NH one, is studied by using an annual run of the NCAR CCM1 (Iwasaki, 1992). Figure 4 shows the seasonal variation of stratospheric wind and temperature at 54.1 hPa. In SH winter, the temperature has a local maximum at mid-latitudes and minimum at high latitudes. This agrees well with the observa-tion. The meridional temperature gradient is in thermal wind balance with the polar night jetstream. The stratospheric temperature balance is reached by the radiative cooling and adiabatic heating due to downward motions. Figure 5 shows the mean vertical velocity in the stratosphere. In  SH winter, the fast downward velocity may cause significant adiabatic heating at mid-latitudes. The mid-latitudes are the main passages of downward branch of the  Brewer-Dobson circulation. On the other hand, the downward velocity is so slow that the temperature is close to the radiative equilibrium at high latitudes. The lack of adiabatic heating may be one of the reasons why the temperature becomes very low within the polar vortex.    As is  well-known, the extratropical mean-meridional circulation is driven by wave-meanDIAGNOSTIC TOOL OF THE GLOBAL ATMOSPHERE 217906030 ZONAL  WINO  (M/5EC)  PPRE55UnE=  54.1(HPA) .;nJ  _5.•••••• 5' oTti r 10 0        •••• •••-30•••^•••••••••••••4—.4"-sw11-7-5-RE7471T-;===M====REEMBEENM=1"========Ea========:QW,-60-90•••^•••15901 2  POTENTIAL3  14 5 6  TEMPERATURE  CIO7 8  PP  RESSURE.9    10 11  5t1.1(011)12 6030 0-30-60-90 Fig. 1450 147TOT 5109  :530' —520 148 500 1490 1480  1490 1490510 50 500520510530 1414030 S  1 2 3  LI 5 6 7 8 9  10  11 12 4. Annual variations of mean-zonal wind with a contour interval of 5  m/sec (upper panel) and zonal mean temperature with a contour interval of 10 K (lower panel) at 54.1 hPa. Vertical and horizontal axes indicate latitudes and months, respectively. (After Iwasaki, 1992).flow interactions and the vertical motions are induced by the meridional gradients of the Eliassen-Palm flux divergence above this level (Haynes et al, 1991),                        P   1  a  (  cos q5   (5)                                    DF)clPt.               col                  faa cosf Thus, the different thermodynamic structure between the inside and outside is attributed mainly to wave, mean-flow interactions. Ditailed wave characteristics associated with polar night jet stream will be studied in the future.218 TOSHIKI IWASAKi 30  VERT. VELOCITY  (0.1011/0)  HRH 50 70 100 2 -23 f  —2 •-2 -5.••••••111 60  30 -30 -60 30 VERT. VELOCITY  (0.10H/0)  JJR 50 70 100 --1 .‘"\ 011-3  zl VERT.  VELOCITT  (0.1140/0)-90 30-2SON 90 70too -6 To1  I232 Ll 30  VERT 60 30  0  . VELOCITY  CO.IHH/S) -20 -60 OJF -00 0 50 70 100 4- Zg. • ,732  C  0  160 30  0 -30 -60 -90 90  60 30  0 -30 -60 Fig. 5. Meridional cross section of mean vertical velocity in the stratosphere. Each    panel is averaged over three months, MAM (March, April and May), JJA (June,    July and August), SON (September, October and November) or DJF (December,    January and February). (After  Iwasaki,  1992).-90ReferencesAndrews, D.G., and  M.E. McIntyre,  1976  : Planetary waves in horizontal and vertical  shear  : The generalized  Eliassen-Palm relation and mean-zonal acceleration, J.  Atmos.  Sci., 33, 2031-2048. Haynes,  P.H., C.J. Marks, M.E. McIntyre, T.G. Shepherd, and K.P. Shine,  1991  : On the "downward control" of        the extratropical diabatic circulation, J. Atmos.  Sci., 48, 651-678. Iwasaki, T.,  1989  : A diagnostic formulation for wave-mean flow interactions and Lagrangian-mean  circula-       tion with a hybrid vertical coordinate of pressure and isentropes, J. Meteor. Soc. Japan., 67, 293-312. Iwasaki, T.,  1992: General circulation diagnosis in the pressure-isentrope hybrid vertical coordinate,  J.        Meteor. Soc. Japan., 67, 293-312. Iwasaki , T.,  1998  : A set of zonal mean equations in a pressure-isentrope hybrid vertical coordinate, J. Atmos.  Sci., 55, 300-3002. Lorenz,  E.N.,  1955  : Available potential energy and the maintenance of the general circulation,  Tellus, 7,        157-167.

Diagnostic Tool of Zonally Symmetric Structure of the Global Atmosphere Based on the Pressure-Isentrope Hybrid Vertical Coordinates (Extended Abstract)

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Diagnostic Tool of Zonally Symmetric Structure of the Global Atmosphere Based on the Pressure-Isentrope Hybrid Vertical Coordinates (Extended Abstract)

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