Constraints on the Ratio between Tropical Land and Ocean Precipitation Derived from a Conceptual Water Balance Model

Which processes control the mean amounts of precipitation received by tropical land and ocean? Do large-scale constraints exist on the ratio between the two? We address these questions using a conceptual box model based on water balance equations. With empirical but physically motivated parametrizations of the water balance components, we construct a set of coupled differential equations which describe the dynamical behavior of the water vapor content over land and ocean as well as the land’s soil moisture content. For a closed model configuration with one ocean and one land box, we compute equilibrium solutions across the parameter space and analyze their sensitivity to parameter choices. The precipitation ratio χ, defined as the ratio between mean land and ocean precipitation rates, quantifies the land-sea precipitation contrast. We find that χ is bounded between zero and one as long as the presence of land does not affect the relationship between water vapor path and precipitation. However, for the tested parameter values, 95% of the obtained χ values are even larger than 0.75. The sensitivity analysis reveals that χ is primarily controlled by the efficiency of atmospheric moisture transport rather than by land surface parameters. We further investigate under which conditions precipitation enhancement over land (χ > 1) would be possible. An open model configuration with an island between two ocean boxes and nonzero external advection into the domain can yield χ values larger than one, but only for a small subset of parameter choices, characterized by small land fractions and a sufficiently large moisture influx through the windward boundary.