Abstract Stable boundary layer height h is determined from eddy correlation measurements of the vertical profiles of the buoyancy flux and turbulence energy from a tower over grassland in autumn, a tower over rangeland with variable snow cover during winter, and aircraft data in the stable marine boundary layer generated by warm air advection over a cool ocean surface in summer. A well-defined h within the tower layer at the grass site (lowest 50 m) and the snow site (lowest 30 m) was definable only about 20% of the time. In the remaining stable periods, the buoyancy flux and turbulence energy either (a) remained constant with height, indicating a deep boundary layer, (b) increased with height, or (c) varied erratically with height. Approximately one-half of the tower profiles did not fit the traditional concepts of a boundary layer. The well-defined cases of h are compared with various formulations for the equilibrium depth of the stably stratified boundary layer based on the Richardson number or surface fluxes. The diagnostic models for h have limited success in explaining both the variance and mean magnitude of h at all three sites. The surface bulk Richardson number and gradient Richardson number approaches perform best for the combined data. For the surface bulk Richardson number method, the required critical value varies systematically between sites. The surface bulk Richardson number approach is modified to include a critical value that depends on the surface Rossby number, which incorporates the influence of surface roughness and wind speed on boundary layer depth.