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

Abstract

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.