Adjustments to the law-of-the wall above an Amazon Forest explained by a spectral link

Modification to the law-of-the wall represented by a dimensionless correction function ?RSL(z/h) is derived using atmospheric turbulence measurements collected at two sites in the Amazon in near-neutral stratification, where z is the distance from the forest floor and h is the mean canopy height. The sites are the Amazon Tall Tower Observatory (ATTO) for z/h ? [1,2.3] and the Green Ocean Amazon (GoAmazon) site for z/h ? [1,1.4]. A link between the vertical velocity spectrum Eww(k) (k is the longitudinal wavenumber) and ?RSL is then established using a co-spectral budget (CSB) model interpreted by the moving-equilibrium hypothesis (MEH). The key finding is that ?RSL is determined by the ratio of two turbulent viscosities and is given as ?t,BL/?t,RSL, where ?t,RSL =(1/A)?0??(k)Eww(k)dk,?t,BL =?(z-d)u*,?(k)is a scale-dependent decorrelation time scale between velocity components, A = CR /(1 - CI ) = 4.5 is predicted from the Rotta constant CR = 1.8 and the isotropization of production constant CI = 3/5 given by Rapid Distortion Theory, ? is the von Kármán constant, u* is the friction velocity at the canopy top, and d is the zero-plane displacement. Because the transfer of energy across scales is conserved in Eww(k) and is determined by the turbulent kinetic energy dissipation rate (?), the CSB model also predicts that ?RSL scales with LBL/Ld, where LBL is the length scale of attached eddies to z = d, Ld = u3*/? is a macro-scale dissipation length.