In the tropics, storms and convection occur intermittently and have a major impact on weather and climate, yet they are sub grid-scale processes for General Circulation Models (GCMs). This talk presents two prototype stochastic models for representing these effects in GCMs. The first model is aimed at precipitation statistics that resemble critical phenomena from statistical physics, including power-law distributions and long-range correlations. The second model is aimed at convective momentum transport due to convective systems, which is intermittent and sometimes extracts energy from the larger-scale flow and sometimes transfers energy to the larger-scale flow. Both models employ stochastic jump processes to represent the intermittent on-off nature of deep convection in the tropics. This is joint work with David Neelin and with Andy Majda.