A Simple Theoretical Model for Lags and Asymmetries of Surface Temperature

Abstract

Here, we study three fundamental climatic phenomena: The seasonal lag, the diurnal lag, and the asymmetry of daily temperature variation. We write a nonlinear ODE based on an energy balance for surface temperature and humidity. The model focuses on small regions of the Earth’s surface; it reproduces the three phenomena with a reasonable accuracy if a few parameters are chosen according to the climatic type of the regions. The plots in this manuscript compare real climatic data with numerical solutions of the model we propose. The model takes into account the doubly periodic forcing of the solar radiation (annual and daily), IR radiation, the existence of thermodynamic bodies with different thermal inertia (land and oceans), and the effect of humidity on the thermal inertia of the air. We write the equations using astronomical parameters with the possibility of applications to exoplanets in mind. We conclude this article investigating the evolution of temperatures in Catania and Sydney if the Earth was on an orbit around the Sun with the same mean distance but greater eccentricity.