This paper presents a theoretical study of the stably stratified atmospheric boundary layer (SBL) overlying a uniform shallow slope with a gradient of the order of 1:1000. By relaxing the assumption made in a previous study that the slope-induced drainage force is constant across the boundary layer, analysis has been performed that demonstrates that a realistic functional form for the drainage forcing is a term proportional to (1−zh )1/2, where z is the height above the ground and h is the depth of the boundary layer. Modified expressions for the maximum
sustainable surface buoyancy flux and Zilitinkevich’s ratio are derived
