Interpretation of Simulated Global Warming Using a Simple Model

Abstract

A simple energy balance model with two parameters, an effective heat capacity and an effective climate sensitivity, is used to interpret six GCM simulations of greenhouse gas?induced global warming. By allowing the parameters to vary in time, the model can be accurately calibrated for each run. It is found that the sensitivity can be approximated as a constant in each case. However, the effective heat capacity clearly varies, and it is important that the energy equation is formulated appropriately, and thus unlike many such models. For simulations with linear forcing and from a cold start, the capacity is in each case close to that of a homogeneous ocean with depth initially 200 m, but increasing some 4.3 m each year, irrespective of the sensitivity and forcing growth rate. Analytic solutions for this linear capacity function are derived, and these reproduce the GCM runs well, even for cases where the forcing is stabilized after a century or so. The formation of a subsurface maximum in the mean ocean temperature anomaly is a significant feature of such cases. A simple model for a GCM run with a realistic forcing scenario starting from 1880 is constructed using component results for forcing segments. Given this, an estimate of the cold start error of a simulation of the warming due to forcing after the present would be given by the negative of the temperature drift of the anomaly due to the past forcing. The simple model can evidently be used to give an indication of likely warming curves, at least for this range of scenarios and GCM sensitivities.