Law-of-the wall adjustments above the Amazon Forest via Cospectral Budget Model

Measurements collected at two experimental sites, the Amazon Tall Tower Observatory (ATTO) and the tower at the Cuieiras Biological Reserve (ZF2) that was part of the GoAmazon experiment, were considered to study deviations from the law-of-the wall for the roughness sublayer (RSL) above the Amazon Forest. A plethora of physical, chemical, and biological processes are influenced by the flow structure in the RSL. Further, above tall and dense canopies the handshake between the land and the atmosphere in numerical Weather Predictions and Earth Systems Models occurs in the RSL. For the mean velocity, the RSL effects are operationally accommodated using a dimensionless roughness sublayer correction function (φ) to the law-of-the wall. For dense canopies the mixing-layer analogy is assumed, and the correction function φ depends on the vorticity thickness, L_s. φ measures the ratio of the eddy viscosity from attached eddies to a zero-plane displacement (d) and the actual eddy viscosity in the RSL at (z-d), for (z-d)/L_s>>1, φ∼1. However, this formulation remains only plausible for dense forested canopies and its extension to sparse and urban canopies difficult at the least. In the Amazon the experimental determination and modeling of φ may also be challenging for the forest topography that introduce z-dependent mean pressure gradients that then lead to variability in second-order flow velocity statistics with z.  In this work an original formulation of φ is proposed based on a scale-wise co-spectral budget model that balances mechanical production to pressure-decorrelation terms in the co-spectral budget. Because the turbulent kinetic energy dissipation rate (ε) is conserved across the vertical velocity spectrum, the co-spectral budget model reveals a novel link between φ and a macro-scale dissipation length, L_d=u_*³/ε.The friction velocity, u_*, is interpreted from the moving-equilibrium hypothesis to be appropriately defined at the canopy top. The analysis shows that the estimation of φ with the new formulation agrees with independent estimates of φ using measured turbulent momentum flux and mean velocity gradient. Further, L_d emerges as a key length scale in the RSL, being more efficient than the vorticity thickness in the estimation of the peaks of the wind vertical velocity spectra.