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 (L_x), computed using the NDVI obtained from QuickBird imagery, was employed. When the ecosystem was dominated by grass and trees (wet soil moisture states), L_x ∼ 100 m, and when the ecosystem was dominated by soil and trees (dry soil moisture states), L_x ∼ 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 L_x). 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 whenmL_x ≫ κ z_m (over(u, ̄) / u_*), where κ is the von-Karman constant, z_m is the measurement height, over(u, ̄) is the mean wind speed, and u_* is the friction velocity. The term κ z_m (over(u, ̄) / u_*) did not vary considerably between the two seasons. Its value (on average 20 m) was comparable to L_x for the tree-soil system but an order of magnitude smaller than L_x for the tree-grass system.