The vertical temperature structure and scaling relations for heat of the near surface stable boundary layer

Describing the turbulent mixing of heat in the stable boundary layer (SBL) has been a long-standing difficulty for similarity theory. We investigated the connection between turbulent mixing of heat and the thermal structure of the near-surface SBL at three sites impacted by topography using Distributed Temperature Sensing (DTS) and the universal decoupling parameter, which describes the degree of vertical coupling for turbulent eddies. Three categories of thermal structures were found: logarithmic, sublayered, and quasi-logarithmic profiles. The logarithmic type is mostly associated with vertically-coupled turbulence but exists for a range of stability and vertical coupling values, the sublayered types are almost never well-coupled, and the quasi-logarithmic SBL type exhibits a mixed behavior between logarithmic and sublayered. Existing similarity scaling relations are a consequence of aggregating across these SBL types and degree of vertical coupling and, critically, none of the existing similarity scaling relations were physically consistent with the profile types or degree of vertical coupling. Several other frameworks of the SBL were found to be a similar result of aggregating across these SBL types. Similarly, methods for selecting data consistent with similarity theory were only partially successful distinguishing between sublayered, uncoupled and logarithmic, coupled cases. Finally, we show that the universal decoupling parameter may be a more appropriate choice for scaling the turbulent mixing of heat in the SBL than the non-dimensional temperature gradient as it better encodes the physics driving the turbulent mixing processes and has a more robust scaling relationship, without the problem of self-correlation.