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If tropical tropopause cirrus lie above convective anvils with tops above about 13km, then net radiative cooling from the cirrus can be produced that is large enough to offset significant subsidence heating, even at the lowest temperatures observed in the tropics. Cirrus clouds near the tropopause are strongly heated by radiation unless they lie above convective anvil clouds. Radiative relaxation in the tropical troposphere is slow above about 14km unless clouds are present. Radiative cooling of tropopause cirrus may be important in processes that dehydrate air before it enters the stratosphere.
Hartmann et al. (Tue,) studied this question.