ANALYSIS OF TIMESCALES OF RESPONSE OF A SIMPLE CLIMATE MODEL

A detailed analysis is made of various analytic solutions to a OD clim ate model coupled to an upwelling diffusion ocean model. In particular the responses to impulse, step-function, exponential, and linear forc ings are addressed. The coupled climate-ocean model is characterized b y two timescales: a relatively fast timescale, tau(c), associated with the damping of an ocean temperature anomaly by thermal radiation down to the depth of the thermocline, and a slow timescale, tau(u), repres enting the time required for upwelling to balance vertical diffusion i n an uncoupled ocean model. A small parameter, epsilon = tau(c)/tau(u) , is introduced, and it is shown from the analytic solutions that the decay of transients in the complex system is governed by a third times cale resulting from a combination of the first two timescales and writ ten as epsilon tau(c); that is, it is much faster than either of the m ore obvious timescales. The parameter epsilon evidently indicates the ratio of the depth of heating anomaly penetration to the depth of the thermocline. Examples involving forced solutions also indicate that th is is the appropriate timescale for model response provided the forcin g is faster than tau(u). For forcing timescales that are long compared to tau(u),tau(c) becomes the timescale characterizing the lag. The re sponse of the model on the timescale epsilon tau(c) is equivalent to a near balance being reached between the radiative damping of the trans ient temperature anomaly and the downward diffusion of heat into the o cean. Inasmuch as vertical diffusion is an unphysical and questionable characterization of vertical energy exchange processes in the near-su rface ocean, it is concluded that the actual ocean controls of climate response time are still poorly described.