Similarity functions for stably stratified atmospheric boundary layers are derived in invariant forms of the underlying system of ensemble averaged equations. Possible nonstationarity and horizontal inhomogeneity of the flows are taken into account. The analysis suggests that nonstationarity and horizontal inhomogeneity are represented through ratios of turbulence statistics. The obtained statistics by MOSAiC data analysis are found to be rather sensitive to the buoyancy frequency, nondimensionalized with the averaging time window. We propose to determine an optimal averaging time by analyzing this frequency.