Two versions of a one-dimensional upwelling-diffusion energy balance model coupled with a carbon cycle model are compared. One version has a constant upwelling velocity, whereas in the other model the upwelling velocity depends on the surface temperature change in a nonlinear way. It is assumed that the physical processes leading to diffusion and advection both of energy and carbon dioxide in the deep ocean are identical and can be described with identical parameter values. This reduces the number of degrees of freedom of the coupled models relative to the noncoupled models. The transport parameters of the two versions were fitted simultaneously to both the observed carbon dioxide concentrations in the atmosphere and the observed temperature anomalies from 1860 to 1988 by the least squares method. The sum of squares obtained from the fit of the nonlinear version is significantly smaller than that of the linear version for both the carbon dioxide concentration in the atmosphere and the temperature anomalies from 1860 to 1988, although there are two more parameters in the nonlinear version. Another feature of the nonlinear version is that the climate sensitivity parameter is fixed (in our case to 2.5 K) and cannot be changed over the wide range of 1.5 K to 4.5 K as used in the linear version. Even small changes in this parameter result in large changes of the calculated temperatures. Furthermore, the nonlinear version shows the remarkable feature of calculating nonincreasing temperatures for the period 1940--1980. The nonlinear dependence of advection velocity on surface temperature change enables the upwelling-diffusion energy balance model to oscillate. ¿ American Geophysical Union 1992