First order controls on the steady state surface energy partitioning and its sensitivity using idealized models

Abstract

The Earth’s surface temperature and the strength of the hydrological cycle are among the most important climatological variables. Their response to natural and anthropogenic forcing is of particular interest in the study of climate change. Climate models of varying degrees of complexity have been used to diagnose their present day magnitudes as well as their projected changes in idealized, and extrapolated emissions trajectories.

Simpler, idealized models offer certain advantages over more complex formulations in first order studies of climate and climate change. For example: 1. The relative transparency of idealized models allows an easier identification of the most important forcings that may influence a particular model outcome, and 2. Their computational efficiency makes them ideal laboratories for rapid hypothesis testing. Here, I adopt such an idealized approach to study the present climate and its response to perturbation. I aim to determine first order controls on the steady state magnitude and partitioning between the emitted flux of longwave radiation and convection at the surface and how this partitioning changes under greenhouse and solar radiative forcings. The reason I do so is because the surface longwave emission is intimately connected to the surface temperature while the convective flux at the surface is the sum of the turbulent sensible and latent heat fluxes. Since the latter drives the hydrological cycle, the partitioning between these surface energy fluxes also determines the magnitude and the response of the two climatological variables of interest.

I use two idealized models in radiative-convective equilibrium with differing parameterizations of convection and radiation. The first is a zero-dimensional energy balance model that treats the surface-atmosphere system as a heat engine that extracts power from the convective heat flux flowing through it. An application of the first and second law of thermodynamics to the heat engine is used to derive a non-trivial thermodynamic constraint to power extraction called the maximum power limit. I use this constraint in conjunction with the surface energy budget to show that it can be used to derive analytic solutions for the convective flux and the surface temperature with a specified surface radiative forcing. I apply this model at the grid scale and compare these solutions with ERA-Interim reanalysis to show that the geographic variation of the data across both land and ocean can be explained very well by this theory. This suggests that the convective flux and surface temperature may indeed organize themselves such that the system operates near the thermodynamic maximum power limit in the long term mean.

I next study the response of the surface energy partitioning, thus of the climatological variables, to perturbations in atmospheric greenhouse gases and aerosols. To this end, I use the second model, which is an analytic one-dimensional model that simulates radiative transfer in a gray atmosphere using "convective adjustment". I derive general driver-response relationships from this idealized approach and show that they are closely obeyed by ERA-Interim reanalysis and global climate model simulation output. I use these relationships to show that certain previous studies that may otherwise appear unrelated, can be understood as specific instances of general relationships among the surface energy components at radiative-convective equilibrium. This includes certain observed historical trends in surface temperature and pan evaporation, and the propagation of biases in global climate model simulations from the radiative drivers to the climatological variables. I show that the differing hydrologic sensitivity to greenhouse and solar forcing can be directly deduced from these expressions. I use this to explain results from solar geoengineering studies and propose a modified scenario, performing a first order study. I also illustrate how these results can be used for simple climate change projections.

These results attest to the utility of simple models to gain insight into the steady state organization of the climatological variables and their response to perturbation. They may also prove useful in studies of other important climate forcings such as land use and land cover change, and cloud and ice albedo feedbacks.