Analysis of the planetary thermal distribution with a simple three-zone maximum-flux model

• Published in: International journal of heat and mass transfer Vol. 160; p. 120185
• Main Authors: Roca, Josep Miquel, Pelegrí, Josep L.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01-10-2020; Elsevier BV
• Subjects: Albedo; Declination; Earth; Greenhouse effect; Greenhouse gases; Heat; Heat distribution; Heat flux; Latitude; Mathematical models; Parameter identification; Steady state models; Temperature
• ISSN: 0017-9310; 1879-2189
• DOI: 10.1016/j.ijheatmasstransfer.2020.120185

•A simple three-zone model reproduces the major feats of the Earth's energy budget.•The model assumes that the latitudinal heat transport is maximized.•We forecast past, present and future conditions for different albedo and greenhouse factors.•Current trends in albedo and greenhouse lead to maximum warming at high latitudes.•These trends compete setting the temperature of other latitudes.
The large uncertainties in the forecasting of future global climatic conditions endorse the need of developing simple yet credible predicting tools. Here we propose a three-zone steady-state radiative model that maximizes latitudinal heat fluxes and considers the potential effect of the Earth's declination. The model is formulated as a set of five equations and six unknowns (zonal temperatures and widths, and the latitudinal heat transport) that requires specifying the reflected (albedo) and back-to-Earth (greenhouse) radiation fractions and obliges turning the low-latitude temperature into an additional parameter. The results do depend on the Earth declination, with changes of 0.5/1.5 K in the intermediate/high zones, which is interpreted as potentially affecting the greenhouse and high-latitude albedo coefficients. Therefore, we focus on identifying the effects of changes in these parameters – properly selected to represent last-glacial-maximum, modern and end-of the-century conditions. The main change is a large rise of the high-latitude temperature, favored both by a decrease in the high-latitude albedo and an increase in the greenhouse factor. For the other variables, the temporal changes in albedo and greenhouse gases compete among them, resulting in one trend from glacial to modern times and a reversal between preindustrial times and the end of the 21st century (currently a warming-narrowing of the intermediate region and the widening of both the low- and high-latitude zones); however, we note that an increase in the low-latitude temperature would tend to alleviate these changes. Despite its simplicity, the model leads to realistic global trends, becoming a useful simple tool for exploring the sensitivity of the Earth's heat distribution to changes in radiative fluxes and endorsing the validity of the maximum latitudinal-heat-transport premise.