The observed nonlinear relationship between tropical sea surface temperature (Ts) and precipitation (P) on climate timescales, by which a threshold (Tc) must be exceeded by Ts in order for deep convection to occur, is the basis of a physical-empirical model (PEM) that we fitted to observational data and CMIP5 climate model output and used to show that, with essentially only two constant parameters (Tc and the sensitivity a1 of P to TsCloseSPigtSPi Tc), it provides a useful first-order description of the climatological and interannual variability of the large-scale distribution of tropical P given Ts, as well as of the biases of the Global Climate Models (GCMs). A substantial limitation is its underestimation of the peak P in the convergence zones, as the necessary processes associated with the atmospheric circulation are not considered. The pattern of the intermodel correlation between the mean Ts- Tc for each GCM and the average P distribution is in agreement with the double ITCZ bias, featuring roughly zonally-symmetric off-equatorial maxima, rather than being regionally or hemispherically restricted. The inter-comparison of GCMs indicates a relationship between Tc with the near-equatorial low-level (850 hPa) tropospheric temperature, consistent with the interpretation that it is a measure of the convective inhibition (CIN). The underestimation of Tc is linked to the cold free tropospheric bias in the GCMs. However, the discrepancy among the observational datasets is a limitation for assessing the GCM biases from the PEM framework quantitatively. Under the RCP4.5 climate change scenario, Tc increases slightly more than the mean tropical Ts, implying a stabilizing trend consistent with the amplified free tropospheric warming relative to the surface. However, since a1 increases by 10–50%/∘C with the surface warming, its effect dominates and results in generally positive precipitation change (Δ P) in the equatorial regions. In the equatorial eastern-central Pacific cold tongue, Δ (Ts- Tc) is positive, but the absolute Ts- Tc remains small, which explains the double band pattern of Δ P along the equatorial flanks of the spuriously strong double ITCZs. When the GCM biases are corrected in the PEM, the positive Δ P in the southeast Pacific and Atlantic oceans is substantially reduced.