Biosphere-atmosphere water vapor and heat fluxes from a forested ecosystem situated on complex terrain: Similarity, anisotropy, and the energy balance closure

Turbulence velocity, water vapor concentration, and temperature fluctuations above a Mediterranean forested canopy from a 2-year experiment whereby variability in mean wind direction interrogates different levels of topographic complexity are analysed and reported.  The overarching goal was to explore how the velocity and scalar statistics are impacted by terrain variability and what are the consequences of such terrain variability on similarity arguments and the energy balance closure (EBc). 

The data were first separated by different wind sectors and analysed for near-neutral conditions.  It was found that the down-slope effective momentum roughness length was smaller than its up-slope counterpart. However, the normalized relation between vertical velocity standard deviation (σ_w) and friction velocity (u_*) was insensitive to the mean wind direction (i.e. σ_w/u_*=Aw - a constant around 1.1-1.2).  The heat flux similarity relations were investigated in two ways: the first uses a conventional flux-variance form whereby the turbulent vertical heat flux <w'T'> was related to u_* and temperature standard deviation (σ_T) using a similarity coefficient (i.e. <w'T'>=C1σ_T u_*). The second evaluates the much less studied relation between the horizontal heat flux <u'T'> and <w'T'> (i.e. <u'T'>=-C2<w'T'>), where C2 was previously reported to vary between 2 and 4 for 'flat-world' near-neutral conditions.  The findings suggest that C1 was close to expectations from flat-world studies but C2 was smaller in magnitude yet independent of mean wind direction. 

When repeating the same analysis for water vapor concentration fluctuations, similarity theory failed on both accounts for almost all mean wind directions.  In fact, for some wind direction sectors, including the upwind sector, no relation between <u'q'> and <w'q'> was found.  Next, EBc was considered.  In this analysis, soil heat flux (Gs) was not measured due to the high rock content at the site. Using literature values, it was assumed that Gs was about 15% of the measured net radiation (Rn).  The EBc did not exhibit appreciable sensitivity to mean wind direction, with sensible and latent heat flux explaining some 80-85% of Rn-Gs across different mean wind directions. 

Guided by recent findings about a connection between the anisotropy in the Reynolds stress tensor and deviations in flux-variance similarity relations, the EBc was re-examined using the anisotropy classification of a barycentric map (isotropic, two-component axisymmetric and one-component turbulence) and the conventional invariance map (or its transformed version to underscore nonlinearities in the return to isotropy in the pressure-strain interaction).   While the down-slope runs were dominated by one-component and isotropic cases, the upslope runs were dominated by two-component axisymmetric cases. For near isotropic cases, the EBc was improved but not significantly.  Other measures that seek to delineate the nonlinearities in the return to isotropy and deviations from isotropic cases were also considered. 
Future work seeks to expand this analysis for diabatic conditions to assess the role of thermal stratification and topography simultaneously on similarity theory, EBc, and invariance analysis of the turbulent stress tensor.  Moreover, the flux variance similarity relation as well as the relations between longitudinal and vertical CO₂ fluxes will also be considered.