Differences between Seasonal and Mean Annual Energy Balance Model Calculations of Climate and Climate Sensitivity

Abstract

A simple Budyko-Sellers mean annual energy balance climate model with diffusive transport (North, 1975b) is extended to include a seasonal cycle. In the model the latitudinal distribution of the zonal average surface temperature is represented by a series of Legendre polynomials, while its time-dependence is represented by a Fourier sine-cosine series. The model has three parameters which are adjusted so that the observed amplitudes of the Northern Hemisphere's zonal mean surface temperature are recovered. In order to obtain the correct amplitude and phase of the surface temperature's seasonal oscillation, allowance must be made for the disparity between the thermal inertia of the atmosphere over continents and that of the ocean's mixed layer. Although the model parameters are adjusted to recover the surface temperature fields of the Northern Hemisphere, a test of the model's ability to produce the fields of the Southern Hemisphere indicates that the model responds properly to changes in boundary conditions. The seasonal model is used to reveal how the annual mean climate and its sensitivity to changes in incident radiation differ from the predictions obtained with the corresponding mean annual model. Although the zonal temperatures obtained with the seasonal model are 1–3°C higher than those obtained with the mean annual model, the changes in the global average annual mean surface temperatures calculated with the two models are practically identical for a 1% decrease in solar constant. Furthermore, because the albedo changes in them are linked mainly to changes in surface temperature, both models respond in the same manner to changes in the incident solar radiation caused by changes in the earth's orbit. The distribution of the incident solar radiation in the models is shown to be insensitive to changes in the eccentricity and the longitude of perihelion and sensitive only to changes in the obliquity of the earth. For past orbital changes, both the seasonal and the mean annual model fail to produce glacial advances of the magnitude that are thought to have occurred.