The conceptual framework for modelling the inertial subrange is strongly influenced by the Richardson cascade, now the subject of various reinterpretations. One apparent departure from the Richardson cascade is attributed to boundary conditions influencing large-scale motion, which in turn, can directly interact with smaller scales thereby destroying the universal statistical scaling attributes of the inertial subrange. Investigating whether boundary conditions and inertial subrange eddies interact continues to be an active research problem in contemporary turbulence research. Using longitudinal (u), lateral (v), and vertical (w) velocities co-located with temperature (T ) time series measurements collected in the atmospheric surface layer (ASL), we evaluate whether the inertial subrange is influenced by different stability regimes. The different stability regimes are proxies for different boundary conditions, as upper boundary condition force the mechanical shear and lower boundary condition force surface heating and buoyancy. The novelty of the present work lies in its combined use of global and local scaling properties (e.g. quasi-Hurst exponent, distributional properties of the wavelet coefficients, and Tsallis’s thermostatic entropy measures) to assess whether atmospheric stability impacts both local and global inertial subrange scaling.