Surface heterogeneity and its signature in higher-order scalar similarity relationships

Over the past three decades, a number of field experiments have suggested that land-cover heterogeneity (LCH) impacts Monin and Obukhov (M–O) scaling, when applied to second-order statistics of temperature (T), water vapor (q), and CO2 (c) fluctuations. To further explore how LCH modifies M–O scaling for second-order statistics, 2 years of atmospheric surface layer (ASL) measurements, conducted above a Mediterranean ecosystem in Sardinia, Italy were analyzed. During wet soil moisture states, when grass and trees dominate the ecosystem, M–O scaling was well recovered. For dry soil moisture states, when bare soil and trees dominate the ecosystem, M–O similarity theory predictions significantly underestimated all three scalar variance measurements, consistent with several recent studies. Among the three scalars, q was poorly predicted by M–O scaling despite its ground source/sink similarity with c. A plausible explanation for the de-correlation between q and c is the dissimilarities originating from the top of the boundary layer via entrainment processes. To establish necessary (but not sufficient) conditions that diagnose departures from M–O scaling, the statistical structure of LCH as quantified by its integral length scale (Lx), computed using the NDVI obtained from QuickBird imagery, was employed. When the ecosystem was dominated by grass and trees (wet soil moisture states), Lx ∼ 100 m, and when the ecosystem was dominated by soil and trees (dry soil moisture states), Lx ∼ 10 m. Using the scalar variance budget equation, two canonical time scales connected with the advection–distortion and relaxation time scales were introduced in the absence of flux-transport terms. We showed that M–O scaling is recovered when relaxation time scales of turbulent eddies are much smaller than the advection–distortion time scale by the mean flow (whose length scale was set to Lx). Converting these time scales to approximate length scales, we found that a necessary but not sufficient condition for MOST to be applicable to second-order scalar statistics is whenmmLx≫κzm(u¯/u*), where κ is the von-Karman constant, zm is the measurement height, u¯ is the mean wind speed, and u* is the friction velocity. The term κzm(u¯/u*) did not vary considerably between the two seasons. Its value (on average 20 m) was comparable to Lx for the tree–soil system but an order of magnitude smaller than Lx for the tree–grass system.