On the Scaling Laws of the Velocity-Scalar Cospectra in the Canopy Sublayer Above Tall Forests

The scaling laws of the vertical (Fwc) and longitudinal (Fuc) velocity-scalar cospectra within the inertial subrange are explored using dimensional arguments and a simplified cospectral budget in the canopy sublayer above three distinct forested ecosystems. The cospectral budget was shown to be consistent with plausible scaling laws originating from dimensional considerations. Using the analytical solution to the novel cospectral budget, it was shown that Fwc(k) and Fuc(k) are governed by the linear superposition of two terms that scale as k−2/3−α and k−β , where k is the wavenumber, −α is the exponent of the velocity spectrum, and β(≥ 7/3) depends on the ratio of the similarity constants for the pressure-scalar covariance and the flux transport terms. It was also demonstrated that, when the magnitude of the mean scalar concentration gradient is large, the k−2/3−α term dominates the velocity-scalar cospectral budget. For such a case, correcting for biases emerging from high frequency losses in eddy-covariance scalar fluxmeasurements can be readily formulated by using the measured velocity spectral exponent in the inertial subrange.