When the tropopause is detected, it uses a primary algorithm (WMO based upon Reichler et al. [2003]) and that is TROPP_T. If the primary algorithm fails, then a climatology is used to fill in those gaps. So TROP_T always "finds" a tropopause, sometimes using WMO and sometime using the climatology. The varaibles you mention are the temperature of the tropopause, but you can also get the pressure or altitude of the tropopause (TROP_P and TROP_Z). There are other algorithms that can optinally be used to find the tropopause and added to the output:
! These parameters define and enumeration to be used to define the primary
! and backup algorithms to be used with the tropopause_find() method. The
! backup algorithm is meant to provide a solution when the primary algorithm
! fail. The algorithms that can't fail are: TROP_ALG_ANALYTIC, TROP_ALG_CLIMATE
! and TROP_ALG_STOBIE.
integer, parameter :: TROP_ALG_NONE = 1 ! Don't evaluate
integer, parameter :: TROP_ALG_ANALYTIC = 2 ! Analytic Expression
integer, parameter :: TROP_ALG_CLIMATE = 3 ! Climatology
integer, parameter :: TROP_ALG_STOBIE = 4 ! Stobie Algorithm
integer, parameter :: TROP_ALG_TWMO = 5 ! WMO Definition, Reichler et al. [2003]
integer, parameter :: TROP_ALG_WMO = 6 ! WMO Definition
integer, parameter :: TROP_ALG_HYBSTOB = 7 ! Hybrid Stobie Algorithm
integer, parameter :: TROP_ALG_CPP = 8 ! Cold Point Parabolic
The code is in tropopause.F90 if you want to see how those algorithms work.
Chuck