skamaroc
commented
6 years ago Dear Dr. Lian,
The moist potential temperature in MPAS, denoted theta_m, is not supposed to be the virtual potential temperature, typically denoted theta_v. The definition of theta_m allows for it to be directly used in the equation of state and the pressure-gradians terms in the MPAS momentum equations, and that is why we have chosen this form. If you examine the paper describing MPAS-Atmosphere,
Skamarock, W. C., KLEMP, J. B., Duda, M., Fowler, L. D., Park, S.-H., & Ringler, T. (2012). A Multiscale Nonhydrostatic Atmospheric Model Using Centroidal Voronoi Tesselations and C-Grid Staggering. Monthly Weather Review, 140(9), 3090–3105. doi:10.1175/MWR-D-11-00215.1
theta_m is defined directly following equation (2) on page 3092, and our MPAS prognostic variable is theta_m multiplied by density (rhotheta_m). The equation of state (8) follows on that same page. As you can see in (8), pressure is proportional to rhotheta_m raised to the power (c_p/c_v), and this leads to casting the pressure gradient terms in the momentum equation directly in terms of rho*theta_m. This last step, and the solution procedure, is described in
KLEMP, J. B., Skamarock, W. C., & Dudhia, J. (2007). Conservative split-explicit time integration methods for the compressible nonhydrostatic equations. Monthly Weather Review, 135, 2897–2913.
See the discussion leading up to the momentum equations (11) and (12) in the Klemp et al paper.
Let me know if you have any other questions.
Regards,
Bill S.
On Wed, Feb 7, 2018 at 12:24 PM, Yuan Lian notifications@github.com wrote:
Hi, I just noticed that the equation calculating the virtual potential temperature has an error in it.
Formula used in current MPAS atmosphere: theta_m = ( 1 + R_v/R_dqv ) theta Correct formula: theta_m = ( 1 + ( R_v / R_d - 1 ) qv ) theta
In above equation: theta_m is virtual potential temperature, theta is potential temperature, R_v is gas constant for vapor, R_d is gas constant for dry air, and qv is relative humidity.
This error spreads everywhere, whenever virtual potential temperature is calculated. There are also hardwired value 1.61 in mpas_init_atm_cases.F. It should be 0.61 instead.
Could anyone take a look? Thanks.
— You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub https://github.com/MPAS-Dev/MPAS-Release/issues/28, or mute the thread https://github.com/notifications/unsubscribe-auth/AD4BLRCQvi96B0hzVXpjd4QiejzI3jEuks5tSfhVgaJpZM4R9QTN .
-- Dr. William C. Skamarock, Senior Scientist National Center for Atmospheric Research Mesoscale and Microscale Meteorology Division P.O. Box 3000 Boulder, Colorado 80307-3000 Phone: (303) 497-8161 Fax: (303) 497-8171 emailskamaroc@ucar.edu http://www2.mmm.ucar.edu/people/skamarock http://www.mmm.ucar.edu/people/skamarock
yuan2lian2
Hi, I just noticed that the equation calculating the virtual potential temperature has an error in it.
Formula used in current MPAS atmosphere: theta_m = ( 1 + R_v/R_dqv ) theta Correct formula: theta_m = ( 1 + ( R_v / R_d - 1 ) qv ) theta
In above equation: theta_m is virtual potential temperature, theta is potential temperature, R_v is gas constant for vapor, R_d is gas constant for dry air, and qv is relative humidity.
This error spreads everywhere, whenever virtual potential temperature is calculated. There are also hardwired value 1.61 in mpas_init_atm_cases.F. It should be 0.61 instead.
Could anyone take a look? Thanks.