[20] For completeness, we review here the EBCM devised by *Stevens* [1998] in his dissertation. EBCMs have been constructed over the years for two different purposes. The first is to clarify basic conceptual ideas about the climate system. Examples of this are ice cap models [*North*, 1990], studies of the seasonal cycle for paleoclimate purposes [*North et al.*, 1983], small icecap instability [*North*, 1984; *Mengel et al.*, 1988], idealized models of predictability in stochastic versions of the model [*North and Cahalan*, 1981] or in the demonstration that simple stochastic models can be used to simulate natural variability [*Kim and North*, 1991]. A second reason for running EBCMs is to provide simulation models of natural variability for signal processing or other related purposes [e.g., *Stevens and North*, 1996; *North and Stevens*, 1998] and in studies of error assessment in observing systems [*Shen et al.*, 1994]. In the latter class of cases, one fits as closely as possible to the real data using more than a bare minimum of adjustable phenomenological coefficients. Here the idea is similar to the use of autoregressive models in time series analysis: one fits the data to a simplified model whose analytical or numerical properties are easy to study. The result is smooth features such as spectra, etc. The model by Stevens falls in this second category. It is forced as much as possible through parameter adjustment to imitate the present climate. An example of its utility is that it is entirely feasible to make a 10,000-year run on a workstation is a very short time.

[21] The surface temperature is governed by the energy balance equation:

where Independent variables: θ and ϕ are latitude and longitude; *t* is time. Dependent variable: *T*(θ,ϕ,*t*) is surface temperature. *C*(θ,ϕ) is effective heat capacity per unit area. *A* is a radiation parameter, 210.3 W m^{−2}. *B* is the radiative damping coefficient (2.15 W m^{−2} K^{−1}), *C*/*B* is a relaxation time which takes on different values depending on surface type. Over land: 31 days; over ocean 4.3 years; over sea ice 40 days; over snow 26 days. *Q* is the solar constant 1371.75 W m^{−2} ÷ 4. *D*(θ,ϕ) is a macroscopic thermal conductivity coefficient: Over land it has a maximum value of 0.6 at the Equator and tapers toward the poles, going to 0.3 in the NH and 0.2 in the SH. Over ocean, it is also 0.6 at the Equator, tapering toward both poles to a value of 0.4. The asymmetry between hemispheres over land is attributed to the elevation over Antarctica. α(θ,*t*) is set to the observed zonal average value through the seasonal cycle. It is fixed, so there is no snow/ice albedo feedback in this version of the model. *N*(θ,ϕ,*t*) is the noise driving force. It is white noise in space and time modulated by two factors: a constant plus sinusoid differing in each hemisphere, being positive in the NH during NH winter and peaking around 1 February, being small in NH summer. The SH factor is peaked in SH winter at around 1 September. There is also a spatial factor that is the magnitude of the horizontal gradient of the mean seasonal variation of temperature, taken from observations (or the seasonal model data). The three factors make for a noise that is peaked in winter and midlatitudes over land. However, as pointed out by *Kim and North* [1991], the effect gives qualitatively correct answers for the spatial dependence of variance in response if only the white noise factor is retained. The seasonal variation must come from the other factors. *H*(θ,ϕ,*t*) is a heat flux which serves as a “flux correction.” it is proportional to (*T*(θ,ϕ,*t*) − *T*_{0}(θ,ϕ,*t*)) where the second term is the long-term mean for that position and time of year. The proportionality factor differs between the hemispheres. It leads to relaxation times of 44 days in the NH and 55 days in the SH. This term can also be thought of as the horizontal transport by the deeper ocean. This latter is not allowed to change in our simulations. Note that the retoring term does not contribute to static sensitivity (e.g., doubling CO_{2}).