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.
[1] A wavelet analysis was applied to airborne flux measurements over a boreal ecosystem in Canada to investigate thermally induced mesoscale circulations and turbulent organized structures, which are according to large eddy simulation studies considered as one major reason for the energy balance closure problem. Fluxes of sensible heat, latent heat, carbon dioxide, and ozone were separated into a mesoscale and a small-scale turbulence part to quantify those flux contributions that cannot be captured with singletower measurements. Mesoscale fluxes were comparable in magnitude to the energy balance residuals from ground-based tower measurements close to the flight track. A scale-dependent correlation analysis between the fluxes of different scalar quantities could not justify the common practice of correcting eddy covariance measurements of the sensible and the latent heat flux for the lack of energy balance closure according to the Bowen ratio or of correcting carbon dioxide fluxes according to the energy balance residual.Citation: Mauder, M., R. L. Desjardins, and I. MacPherson (2007), Scale analysis of airborne flux measurements over heterogeneous terrain in a boreal ecosystem,
[1] This analysis uses 40 years of hourly observations of temperature (T), relative humidity (RH), and opaque cloud cover from 14 climate stations across the Canadian Prairies to analyze the diurnal cycle climate, represented by the mean T and RH and their diurnal ranges. From April to October, when incoming shortwave radiation dominates over longwave cooling, maximum temperature and the diurnal ranges of T and RH increase with decreasing opaque cloud cover, while minimum temperature is almost independent of cloud. During the winter period, both maximum and minimum temperatures fall with decreasing cloud, as longwave cooling dominates over the net shortwave flux, which is reduced by the high solar zenith angle and surface reflection by snow. We relate the daily mean opaque cloud cover to the longwave and shortwave cloud forcing and the effective cloud albedo, using multiyear measurements of downward shortwave and longwave fluxes, and longwave fluxes under clear skies from historical weather reanalysis. We provide quadratic fits to compute effective cloud albedo and net longwave fluxes from opaque cloud cover. During the warm season, the daytime rise of temperature is related to the net radiation, and the nighttime fall is related to the net longwave cooling. The diurnal range of T, RH, and all the net radiative fluxes have a quasi-linear dependence on the effective cloud albedo. This gives a seasonal climate perspective on the coupled land-surface system of T, RH, and cloud cover over the Canadian Prairies, and the winter transitions in snowy climates.
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