A practical Lagrangian method for relating scalar concentrations to source distributions in vegetation canopies

The transfer of scalar atmospheric constituents within vegetation canopies cannot be predicted from simple gradient-diffusion theory. To replace gradient-diffusion theory in this context, an analytic Lagrangian theory is developed which predicts the concentration field of a scalar atmospheric constituent emanating from a spatially extensive source in an inhomogeneous turbulent flow. In this ‘localized near-field’ theory, the mean scalar concentration C is expressed as the sum of a diffusive far-field contribution Cf which obeys gradient-diffusion theory, and a non-diffusive near-field contribution Cn which is calculated for each source element by assuming the turbulence to be locally homogeneous. It follows that Cf provides the large-scale background variation and Cn the detailed local structure of the C profile. The theory applies to both non-advective and advective situations. Comparison with random-flight predictions of C shows that the assumptions of the theory (which are exact in homogeneous turbulence) are adequate for inhomogeneous turbulence typical of real canopies. The random-flight predictions also show that vertical velocity skewness (not accounted for in the localized near-field theory but typically of order −0.5 to −1 in canopies) has only a small effect on C.