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


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?
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