Note on turbulence statistics in z-less stratification

In boundary layer meteorology, surface layer similarity theory plays a critical role in measuring and modeling biospheric fluxes. In stable boundary layer, surface layer similarity called z-less stratification has been one of main research topics for over than two decades and the issue has yet to be settled in micrometeorology. In this scientific discussion on z-less turbulence, different turbulence statistics were used inconsistently and it was argued that z-less turbulence was valid if only any turbulence statistics were constant with different atmospheric stabilities. Consequently, such inconsistently tested turbulence statistics and misconception on z-less turbulence hinder us from correctly understanding turbulence structure in the stable boundary layer. This note revisits z-less turbulence and emphasizes that different dimensionless turbulence statistics generally do not exhibit a common behavior in the limit of z-less stratification.