What is the exact formula for calculating the potential temperature trend term？

[mirabelle]

Dear Sir or Madam,

As I known, the potential temperature tendency term (∂θ/∂t) include these term:

∂θ/∂t = - V·∇θ +h_diabatic +RTHCUTEN +RTHSHTEN +RTHRATEN +RTHBLTEN （1）

RTHFTEN : the total advective temperature tendency

"h_diabatic": this is from microphsics scheme

"RTHCUTEN": this is from cumulus scheme

"RTHSHTEN": this is from shallow convection

"RTHRATEN": this is from radaition

"RTHBLTEN": this is from boundary layer

My question is： 1. Does this equation right？
2.Does RTHFTEN = - V·∇θ ？
3.The RTHFTEN is only defined when a few cumulus scheme is used. Does this means in other cumulus scheme, the RTHFTEN is equal to 0. ?
4. Is there a paper I can quote for this equation?

 

[William.Hatheway]

WRF Output Variables — WRF Users Guide documentation

This might help answer your question about the variables

As for papers I would query Google Scholar or read the dynamic meteorology textbook like "introduction to dynamic meteorology" - Holten