A study of long-term climate change in a simple seasonal nonlinear climate model

Solar radiation cycles, earth-orbital changes, and continental drift drive long to very long term (10³–10⁶ years) climatic changes. Lin and North used the stationary solutions of a simple energy balance model (EBM) to study the equilibrium climatic stages. In this paper, we study time dependent solutions and, in particular, transition processes. We make use of two time scales: a seasonal cycle (fast variation) and a long term time change (slow variation). Variations over short time scales are solved using a Fourier transform in time and long term variations are studied using a 4th order Runge-Kutta method. The energy balance equation is a parabolic type equation and it is well posed. Climate changes depend mainly on external forcing and the state of the climate is determined by the slow time scale forcing. In other words, transitions from one climate stage (snow-covered) to another (snow-free) at bifurcation points are monotonic, despite 20% to 50% shortperiod random fluctuations in the solar energy. This smooth transition is especially noticeable when the land bands lie close to the north pole (70° N to 90° N) or at high latitudes (50° N to 75° N).Now at Applied Physics Laboratory, The Johns Hopkins University, Laurel, MD 20723, USA