Conventional source area/footprint models for turbulent flux measurements are not directly applicable to forests, where sources and sinks are distributed in a volume rather than on a surface. Thus, a modified concept of a three-dimensional source/sink volume model is presented. This model is based on a Lagrangian particle-trajectory approach for transport and diffusion below, within and above a forest canopy, and uses backward trajectories to estimate the partitioning of an above-canopy flux to sources or sinks in the canopy, the understory, or the soil, respectively. The core of the footprint model is a state-of-the-art Langevin equation model that satisfies the well-mixed condition and is capable of handling moderately inhomogeneous turbulence in three dimensions.
As inputs this model needs information about the distribution of turbulence statistics (means, variances, and skewnesses of the three Cartesian velocity components). This input may take the form of simple analytical (parameterized) profiles, or comprises measured data that are then interpolated to provide values at every point in the domain. To simulate the source/sink distribution of the canopy, additional input is required about the distribution of leaf area and bole area with height (and, potentially, horizontal variations). Again, this input can be based on parameterizations and/or measured profiles of leaf area index.
The backward trajectory model is cycled over a large number of particle runs, to provide an ensemble of source/sink locations throughout the forest canopy and the surface. The distribution of intercepts of particles by leafage, boles, or soil surfaces per unit volume (grid-cells) is then proportional to the volumetric source/sink weight distribution (equivalent to the footprint in two dimensions). Due to its property of a probability density distribution, this source/sink weight distribution is scaled to integrate to unity over space. In analogy to the conventional source area concept, the source volume is defined as the smallest possible volume that contains a given fraction (50%, say) of the total source/sink distribution. It is possible to specify partial source/sink distributions, by considering sources or sinks only in the canopy, or only on the forest floor.
Thus, the utility of this source-volume model is manifold. (i) It allows the estimate of the effective fetch of tower based flux measurements, for experimental design purposes, even for sensors mounted above complex forest canopies. (ii) By comparing the contents of the source volume (in terms of LAI, species composition, etc.) with the corresponding averages in the forest ecosystem, this model serves as a tool to evaluate the spatial representativeness of flux measurements. (iii) It allows the fractionation of measured fluxes to sources/sinks in the canopy, and the forest floor respectively.