Footprint prediction of scalar fluxes from analytical solutions of the diffusion equation

Abstract

The use of analytical solutions of the diffusion equation for 'footprint prediction' is explored. Quantitative information about the 'footprint', i.e., the upwind area most likely to affect a downwind flux measurement at a given height z, is essential when flux measurements from different platforms, particularly airborne ones, are compared. Analytical predictions are evaluated against numerical Lagrangian trajectory simulations which are detailed in a companion paper (Leclerc and Thurtell, 1990). For neutral stability, the structurally simple solutions proposed by Gash (1986) are shown to be capable of satisfactory approximation to numerical simulations over a wide range of heights, zero displacements and roughness lengths. Until more sophisticated practical solutions become available, it is suggested that apparent limitations in the validity of some assumptions underlying the Gash solutions for the case of very large surface roughness (forests) and tentative application of the solutions to cases of small thermal instability be dealt with by semi-empirical adjustment of the ratio of horizontal wind to friction velocity. An upper limit of validity of these solutions for z has yet to be established.

CO2 exchange between air and water in an Arctic Alaskan and midlatitude Swiss lake: Importance of convective mixing

“…Although the Schmid [1997] model yields similar values for the point of maximum contribution as the Schuepp et al [1990] model, the assumptions for the trailing end of the footprint and thus for the potential contribution of the land surface to fluxes measured over the lake are not identical. Schmid [2002] provides a thorough review of various footprint calculations and addresses their limitations and weaknesses.…”

Monitoring the Multi-Year Carbon Balance of a Subarctic Palsa Mire with Micrometeorological Techniques

“…The size of this footprint is mainly dependent on a combination of atmospheric stability, surface roughness, as well as the measurement height. We analyzed the footprint according to the model presented by Schuepp et al (1990) and used a distance within which 80 % of the measured flux value originates. This distance in our EC setup for the daytime conditions ranged *300 m and for nighttime up to 400-500 m. The mire has a very stable and well-defined easterly-westerly wind direction distribution (95 % of winds are evenly distributed along the Lake Torneträsk Valley) and very rarely winds from north and south.…”

Response of a tundra ecosytem to elevated atmospheric carbon dioxide and CO{sub 2}-induced climate change. Final report

“…These differences maybe due to differences in sampling location and spatial averam@nng (Hope et a)., 1995). For example, eddy correlation flux measurements were taken from a height of 2.5 m, which, depending on the wind speed and temperature profile, corresponds to sampling area that is at least 4 orders of magnitude greater than the chamber sampling area (Schuepp et al 1990 1995;Oechef and1995). Hummock ecosystems at the former IBP Tareya site on the Tiiymyr Peninsula were small net sources of approximately 0.25 gC m-* d-1, while wetter polygonal ecosystems were slight sinks of 0.13 gC m-2 d-1.…”