Particle deposition to forests: An alternative to K-theory

It has been known for some time that flux-gradient closure schemes (or K-theory), widely used to model the aerosol sized particle turbulent diffusivity, are problematic within canopies. Reported momentum transport in a zero- or counter-mean velocity gradient flow within open trunk spaces of forests is prototypical of the failure of K-theory. To circumvent this problem, a multi-layered and size-resolved second-order closure model is developed using the mean particle turbulent flux budget as a primary closure for the particle turbulent flux instead of K-theory. The proposed model is evaluated against the multi-level size-resolved particle fluxes and particle concentration measurements conducted within and above a tall Scots pine forest situated in Hyytiälä, Southern Finland. Conditions promoting the failure of K-theory for different particle sizes and canopy layers and the characteristics of the particle transport processes within the canopy sub-layer (CSL) are discussed. Using the model, it is shown that K-theory may still be plausible for modeling the particle deposition velocity when the particle size range is smaller than 1 μm provided the local particle turbulent diffusivity is estimated from the characteristic turbulent relaxation time scale and the vertical velocity variance. Model calculations suggest that the partitioning of particle deposition onto foliage and forest floor appears insensitive to the friction velocity for particles smaller than 100 nm (ultrafine), but decreases with increasing friction velocity for particles larger than 100 nm (accumulation and coarse modes).