Simple one-dimensioinal ocean models have been used to make projections of future temperature trends due to a greenhouse warming, aerosols, or emission reduction. This paper considers the seasonal cycle and the second-moment statistics of a two-dimensional energy balance model with a deep ocean. The surface component, a typical surface energy balance model including the ocean mixed layer, is coupled to an infinite-depth ocean which is characterized by uniform vertical diffusion and upwelling. These processes transport heat energy vertically from the mixed layer to the depth of the ocean and may be important for long-term climatic change of the Earth. The model has an explicit two-dimensional geography. The model reproduces the January and July temperature fields reasonably. The amplitude and phase of the annual and semiannual cycles of the model compare favorably with those of observations. The second-moment statistics of the response field are important measures of the sensitivity of the model. When forced by a noise forcing with spectrum white in space and time, the variance, temporal correlation, and spatial correlation of the surface temperature of the model look similar to those of observations. In the presence of a deep ocean the variance and spatial correlation scale of the model are reduced somewhat over the ocean compared with the mixed layer only case. The temporal correlation scale is shortened by about a month. ¿ American Geophysical Union 1992