The effect of scalar source distribution on eddy diffusivities and bulk transfer coefficients

Although eddy diffusivities are invalid within plant canopies they are widely used to describe transfer above the foliage, for example in Bowen-ratio methods to deduce scalar fluxes. Close to the foliage in the roughness sub-layer however, dimensionless gradients (=-k(z-d)/c* dc/dz, where k is the von Karman constant, c*=scalar flux/u*, and u*c*=area-averaged scalar flux) are observed to depart from standard Monin-Obukhov values. These departures are a result both of the changed nature of turbulent transport in the roughness sub-layer (RSL) and of the proximity of scalar sources to the measurement point.

We have examined the effect of different source distributions and different methods for determining surface concentrations on estimates of eddy diffusivities and bulk transfer coefficients. The Black Forest model plant canopy was constructed of small light globes with distinct crown and trunk regions. Heat was used as a passive scalar that was independently introduced to the flow at ground and crown heights. Four scalar source distributions were generated, ranging from ground-only to canopy-only. Hotwire anemometery with simultaneous coldwire measurements were used to sample flow and scalar characteristics at eleven locations throughout the canopy area. High-resolution infra-red thermography was used to measure surface temperature.

The inverse of the non-dimensional scalar gradient attains the neutral Monin-Obukhov value of 1.0 at heights between 3h and 5h. Below this height the non-dimensional scalar gradient is as large as 1.8 suggesting that the RSL for this sparse canopy is deeper than normally assumed. The lowest values close to h occur for a strong elevated source. We should expect this since the measurements are in the near field of upper canopy sources and Lagrangian theory suggests that effective diffusivities (which are proportional to the non-dimensional gradients) are smaller in the near than in the far field of an isolated source. The non-dimensional gradient for momentum is enhanced below 3h and of similar value to those for the scalar.

Details of transport through the canopy and RSL in simple, single-layer models of vegetated surfaces is often subsumed into a bulk transfer coefficient G(z) where Flux=G(z) [C(0) - C(z)], z is a reference height well above the surface and C(0) is the surface concentration of scalar C. Surface temperatures for the ground and globe surfaces were obtained for each source distribution used in the Black Forest Experiment. In addition, the infra-red data allow estimates of total surface temperature as an integrated value for the surface as a whole. We also calculate a surface temperature for the two mixed source distributions based on linear combinations of ground and canopy surface temperatures weighted by source strength.

When C(0) is set equal to the integrated surface temperature, G(z) is larger for elevated source distributions than when the source is located only on the ground. With as little as 25% of the total source in the crown rather than on the ground G(z) is greatly increased over that determined for the ground-only source. In contrast, if ground-only and canopy-only surface temperatures are used for the ground-only and elevated-only source distributions, the bulk transfer coefficients are very similar.