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SUMMARY:A stable treatment of conservative thermodynamic variables for sem
 i-implicit semi-Lagrangian dynamical cores - Kevin Viner\,   (Naval Resear
 ch Laboratory)
DTSTART:20120926T110000Z
DTEND:20120926T112500Z
UID:TALK40147@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Atmospheric motions span a wide array of frequencies\, the slo
 west of which provide us with our day to day weather. In numerical weather
  prediction it is necessary to narrow the focus to these lower frequencies
  for efficiency. The way this is typically done in global modeling is to a
 pply an implicit time-differencing method to terms linked to high frequenc
 y motions while applying an explicit method to terms linked to low frequen
 cy motions like advection\, thereby allowing a larger stable time step. Wh
 ile semi-Lagrangian schemes further increase efficiency by removing the st
 ability restrictions of the standard CFL condition concerning velocity\, t
 hey are still held to a slightly different deformation CFL condition conce
 rning the local variation in velocity. As such\, it is still necessary to 
 slow these fast wave modes in the semi-Lagrangian framework to maintain a 
 stable system. \n\nSemi-Lagrangian systems employing a conservative thermo
 dynamic variable such as potential temperature as a prognostic variable fa
 ce a unique dilemma in applying this standard method because the term resp
 onsible for gravity wave generation is also a vertical advection term whic
 h is absorbed into the total derivative. Application of the scheme in the 
 absence of an explicit gravity wave term results in an unstable system sin
 ce the fast gravity mode frequencies are not properly reduced. Stability c
 an be maintained at the expense of both accuracy and efficiency by way of 
 artificial damping and reduced time steps. \n\nThe modification discussed 
 here defines a basic state potential temperature field which is advected i
 n an Eulerian fashion while the semi-Lagrangian method is applied to the p
 erturbation potential temperature. As the gravity-wave term in question is
  now expressed explicitly through the total derivative of the basic state 
 potential temperature\, gravity mode stability is returned to the system\;
  the semi-implicit treatment of the new term manages stability with respec
 t to the associated CFL condition. Tests of the new scheme in the Navy Glo
 bal Environmental Model (NAVGEM) show that the method allows stable integr
 ation at typical semi-Lagrangian time steps in the absence of artificial d
 amping. \n\n
LOCATION:Seminar Room 1\, Newton Institute
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