Footprint estimation for scalar flux measurements in the atmospheric surface layer

Abstract

The flux footprint is the contribution, per unit emission, of each element of a surface area source to the vertical scalar flux measured at height z,; it is equal to the vertical flux from a unit surface point source. The dependence of the flux footprint on crosswind location is shown to be identical to the crosswind concentration distribution for a unit surface point source; an analytic dispersion model is used to estimate the crosswind-integrated flux footprint. Based on the analytic dispersion model, a normalized crosswind-integrated footprint is proposed that principally depends on the single variable Z/Z,,, , where Z is a measure of vertical dispersion from a surface source. The explicit dependence of the crosswind-integrated flux footprint on downwind distance, thermal stability and surface roughness is contained in the dependence of Z on these variables. By also calculating the flux footprint with a Lagrangian stochastic dispersion model, it is shown that the normalized flux footprint is insensitive to the analytic model assumption of a self-similar vertical concentration profile.

Long-term Turbulent Sensible-Heat-Flux Measurements with a Large-Aperture Scintillometer in the Centre of Łódź, Central Poland

“…So far many different footprint models have been developed, e.g. Horst and Weil (1992), Schmid (1994), Leclerc et al (1997), Hsieh et al (2000). In urban areas one of the most commonly used footprint model is the 3D analytical Flux Source Area Model (FSAM) developed by Schmid (1994Schmid ( , 1997, and successfully applied for single-point measurements in cities (e.g.…”

Crop coefficient approaches based on fixed estimates of leaf resistance are not appropriate for estimating water use of citrus

“…In addition, whilst water use of a single tree is determined in a lysimeter, eddy covariance measurements represent a much larger area and a number of trees. The size and the shape of the area sampled are not fixed in time and vary with wind speed and direction (Horst and Weil 1992;Baldocchi 1997). …”

Flux footprint climatology estimated by three analytical models over a subtropical coniferous plantation in Southeast China

“…where A = rΓ(2/r)/Γ(1/r) 2 , B = Γ(2/r)/Γ(1/r), Γ is a gamma function, r is a shape factor (calculation of r was described by Horst and Weil (1992)),z is the mean plume height for dispersion, U is the effective speed of plume advection, dz dx is the gradient ofz with x, z m is measurement height, and u is the mean wind speed profile.…”

“…r r is variable r is constant -a*:z must be calculated numerically (Horst and Weil, 1992). b*: K = 0.4 is von Karman's constant; p = 1.55 is also a constant, and ψ(pz/L) and φ c(pz/L) are the diabatic integrations of the wind profile and stability function of heat.…”