Observations from sonar data have suggested enhanced melting of thick, ridged ice relative to level ice. There are several mechanisms that may account for this intensified melting. In this paper, we examine the effects of two-dimensional (2-D) heat conduction and enlarged basal surface area due to the sloping sides of the keel on heat conduction and melt rates. The cross section of the 2-D ridge is taken to be an isosceles triangle with a rounded crest. This is roughly the shape observed and allows a convenient numerical representation in polar coordinates. For comparison, ridges of similar shape are also represented as a collection of 1-D columns of varying thickness, similar to what is implicit in typical ice thickness distribution models. The results show that 2-D ridges inhibit the heat conduction compared to 1-D ridges owing to the dominating effect of weaker temperature gradients. The slope of the keel is the dominant factor in determining the temperature gradient. A size distribution of 2-D ridges reduces heat transfer to the atmosphere by 3 W m-2 compared to a similar distribution of 1-D ridges. Over an annual cycle, basal ablation along the keel is insignificant for 2-D ridges with small slopes, whereas ridges with large slopes show ablation rates determined by the ice-ocean heat flux. These melt rates imply a transition from a triangular to a more rounded shape. The 1-D ridge geometry is not adequate to simulate the net melting at the keel base over an annual cycle. Melt rates are calculated along the ridge keel and for level ice over a 40 day period for comparison with observations. For 1-D ridges, all ice thicker than 5 m melts more slowly than the corresponding level ice. The inclusion of 2-D heat conduction increases the amount of ablation in the thicker ice relative to the 5 m ice, especially for ridges with larger slopes. However, this increase explains only a small fraction of the enhanced basal melting seen in the observations. These results suggest that other mechanisms are important in determining the mass loss from thicker ice. ¿ 2000 American Geophysical Union