Slide 11 of 29
The convective scheme needs to take into account latent heat released during condensation. This varies on a diurnal pattern, with maximum instability generally being reached during the night. The numerical weather modelers then have to develop dampers to the convection in order to avoid a convective feedback loop, where a tropical wave violently explodes producing unreasonable amounts of rainfall. This is clearly apparent on the rainfall forecasts, with rainfall maximum concentrating on a single grid point surrounded by numerous contours.
The other challenge is to slow down the development of tropical waves to a reasonable level without affecting warm core convection in areas outside of the Tropics (as is the case over the Mid-Western USA and continental South America)