Footprint Estimation from Multi-Layered Sources in Forests and Protected Agro-Systems

In recent years, assessing the spatial representativeness of measured turbulent fluxes of carbon dioxide and water vapor within forests and crops (especially in protected environments) is drawing increased attention. This problem is analogous to deriving explicit relations between measured scalar turbulent fluxes and ecosystem sources or sinks. Such activity has been carried out in the last decade for atmospheric flows, in the context of footprint analysis or a corollary problem often referred to as the ‘inverse problem' (i.e. inferring sources and sinks from measured concentration). Although footprint analysis was extensively studied and is widely used, footprint models commonly assume that the sources are at ground-level or some effective displacement height. Since in canopy flows the source (or sink) strength distribution also varies within the canopy volume, it is necessary to develop footprint models that can treat such inhomogeneity.

In this work, a multi-layered footprint model is developed for a heterogeneous canopy problem, which takes into account the vertical distribution of sources and sinks within a canopy. A Lagrangian stochastic method is employed for calculating flux footprints functions, which are then used to assess the effective fetch for forest canopies of various leaf area distributions. In the model, scalar particles are released at all heights of the canopy, and trajectories are calculated based on a flow field which is generated by a second order closure model. A fetch which is height-weighted averaged by the source-sink distribution is then achieved. This effective fetch is studied as a function of the measurement height above the canopy, as well as the diurnal variations in the source-sink distribution.

A superstatistical approach is used to include effects of intermittency of the turbulent kinetic energy (TKE) dissipation-rate in the Lagrangian stochastic model. This intermittent behavior is shown to be significant in turbulent flows, especially within canopies. The genesis of the superstatistical treatment is the Lagrangian time-scale, which is treated as a random variable along the air parcel trajectories. This addition induces intense intermittent ejections of scalar particles from the canopy, generating a heavy tail for the flux footprint.

A footprint analysis is also explored for inhomogeneous environments encountered in a screenhouse. While a screenhouse reduces radiative load and, more importantly, irrigation water use, its presence significantly modifies the flow field and micro-environment in complex ways, which makes footprint modeling a challenge. The effect of the screen and its relative height above the protected crop on the fetch is studied. Eddy-covariance measurements inside a large banana screenhouse are then used to verify the footprint model. Comparisons between measurements and model predictions are carried out for a Lagrangian time scale which is treated either in a conventional way or as a random variable (i.e. superstatistical treatment). It is shown that the model is able to estimate the ratio between a measured flux and the entire canopy source-sink flux, for a case where the measurement location does not satisfy the effective fetch, as commonly found in enclosed structures such as screenhouses.