Images captured in foggy weather conditions exhibit losses in quality which are dependent on distance. If the depth and atmospheric conditions are known, one can enhance the images (to some degree) by compensating for the effects of the fog. Recently, several investigations have presented methods for recovering depth maps using only the information contained in a single foggy image. Each technique estimates the depth of each pixel independently, and assumes neighbouring pixels will have similar depths. In this work, we employ the fact that images containing fog are captured from outdoor cameras. As a result, the scene geometry is usually dominated by a ground plane. More importantly, objects which appear towards the top of the image are usually further away. We show how this preference (implemented as a soft constraint) is compatible with the alpha-expansion optimization technique and illustrate how it can be used to improve the robustness of any single image dehazing technique.