Horizontal length scale of a rotating system measuring the distance over which the gravitational tendency to render a free surface flat is balanced by a tendency of the Coriolis acceleration to deform the surface. Also called the deformation radius or Rossby radius. In the shallow water approximation, the Rossby deformation radius is R = c/f in which c=(gH)^(1/2) with g the acceleration due to gravity and H the mean depth of the fluid. In stratified fluid, the appropriate length scale is called the internal Rossby deformation radius, and is given by R = ND/f in which N is the buoyancy frequency and D is a characteristic vertical length scale. At the equator, the effect of eta (the meridional gradient of the Coriolis parameter) determines the equatorial Rossby deformation radius R=(c/eta)^(1/2), and the equatorial internal Rossby deformation radius R=(ND/eta)^(1/2).