We study the hydrodynamic equilibrium properties of the stably stratified atmospheric boundary layer from measurements obtained in the Snow-Horizontal Array Turbulence Study (SnoHATS) campaign at the Plaine Morte Glacier in the Swiss Alps. Our approach is based on a combination of dynamical systems techniques and statistical analysis. The main idea is to measure the deviations from the behavior expected by a turbulent observable when it is close to a transition between different metastable states. We first assess the performance of our method on the Lorenz attractor, then on a turbulent flow. The results show that the method recognizes subtle differences among different stable boundary layers turbulence regimes and may be used to help characterise their transitions.