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SUMMARY:Direct Statistical Simulation of a Two-Layer Primitive Equation Mo
 del - Marston\, B (Brown University)
DTSTART:20131204T113000Z
DTEND:20131204T121500Z
UID:TALK49174@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Co-authors: Wanming Qi (Brown University)\, Steve Tobias (Univ
 ersity of Leeds) \n\nLow-order statistics of the large-scale circulation o
 f planetary atmospheres may be directly accessed by solving the equations 
 of motion for the equal-time statistics. We implement such Direct Statisti
 cal Simulation of a two-layer primitive equation model by systematic expan
 sion in the cumulants. The first cumulant is the zonally averaged vorticit
 y\, divergence\, and temperature as a function of latitude and level\, and
  the second cumulant contains information about nonlocal teleconnections. 
 At second order (CE2) the expansion retains the eddy  mean-flow interactio
 n but neglects eddy-eddy interactions and is realizable. Eddy-eddy interac
 tions appear at third (CE3) order\, but care must be taken to maintain rea
 lizability with a non-negative probability distribution function. The cumu
 lant expansion is conservative\, order-by order\, in the total angular mom
 entum\, total energy\, and mean-squared potential temperature. An intermed
 iate approximation\, CE2.5\, is related to the Edd y-Damped Quasi-Normal M
 arkovian (EDQNM) approximation and maintains realizability at the expense 
 of the introduction of a phenomenological timescale for eddy damping. Firs
 t and second cumulants accumulated by time-integration of the two-layer pr
 imitive equations are compared with those obtained at the fixed points fou
 nd at CE2\, CE2.5\, and CE3 levels of approximation\, and against statisti
 cs obtained from reanalysis of the mid-level atmosphere of the Earth. CE2 
 reproduces qualitative features of the zonal mean general circulation such
  as the mid-latitude jets. CE2.5 and CE3 improve quantitative agreement in
  both the zonal means\, and in the teleconnections. \n
LOCATION:Seminar Room 1\, Newton Institute
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