Simple physical-empirical model of the precipitation distribution based on a tropical sea surface temperature threshold and the effects of climate change

Abstract

The observed nonlinear relationship between tropical sea surface temperature ($T_s$) and precipitation (P) on climate timescales, by which a threshold ($T_c$) must be exceeded by $T_s$ 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 ($T_c$ and the sensitivity $a_1$ of P to $T_s>T_c$), it provides a useful first-order description of the climatological and interannual variability of the large-scale distribution of tropical P given $T_s$, 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 $T_s-T_c$ 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 $T_c$ 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 $T_c$ 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, $T_c$ increases slightly more than the mean tropical $T_s$, implying a stabilizing trend consistent with the amplified free tropospheric warming relative to the surface. However, since $a_1$ increases by 10–50%/$^\circ$C with the surface warming, its effect dominates and results in generally positive precipitation change ($\Delta P$) in the equatorial regions. In the equatorial eastern-central Pacific cold tongue, $\Delta (T_s-T_c)$ is positive, but the absolute $T_s-T_c$ remains small, which explains the double band pattern of $\Delta P$ along the equatorial flanks of the spuriously strong double ITCZs. When the GCM biases are corrected in the PEM, the positive $\Delta P$ in the southeast Pacific and Atlantic oceans is substantially reduced.