Highly accurate analytical footprint model for general stratification of the atmosphere

Abstract

<p>The flux footprint (or so-called source area) is the zone of the surface that contributes to a measured vertical flux (e.g. of water vapor or carbon dioxide) between the ground and the atmosphere: Footprint models are then used to derive location and size of the source area and for interpretation of flux-tower measurements, in particular to estimate the contribution of passive scalar sources to these measured fluxes, and to combine measured fluxes with remotely sensed data.</p><p>Existing footprint models are of two types: either they derive from the solution of an advection-diffusion differential equation or they result from a parameterization based on numerical simulations performed with a Lagrangian stochastic particle dispersion model. Models of the first type are essentially based on the hypothesis of power-law profiles of the mean wind speed u(z) and eddy diffusivity K(z). Our objective was to suppress this constraint and to build a footprint model for any type of profile, in particular Monin-Obukhov surface-layer profiles.</p><p>The model was developed in the frame of the K-theory. Homogeneous conditions were assumed in the horizontal plane and the alongwind diffusion term was neglected with respect to the advection term. A semi-analytical tool has been developed to cope with any type of atmosphere stratification. Applying a dedicated quadrupole method, the boundary layer is divided into a series of sublayers and an extended power law model is applied in each of them (10 to 15 sublayers are enough to reach an error of less than 0.1%, whatever the atmosphere stability).</p><p>In the end, a highly accurate estimation of the footprint can be obtained very quickly for any profile of wind speed and eddy diffusivity.</p>