An empirical expression to relate aerodynamic and surface temperatures for use within single-source energy balance models

Single-source energy balance models are simple and particularly suited to assimilate mixed pixel remote sensing data. Mixed pixels are made up of a combination of two main elements, the soil and the vegetation. The use of single-source models implies that the reference temperature for the estimation of convective fluxes, the aerodynamic temperature, is linked to the available remotely sensed surface temperature. There are many relationships relating both temperatures in the literature, but few that try to find objective constraints on this link. These relationships accounts for the difference between both temperatures by dividing the roughness length for thermal turbulent transport by an expression known as “radiometric kB−1”, which depends mostly on Leaf Area Index (LAI). Acknowledging that the two temperatures should be similar for bare soil and high LAI conditions, we propose an empirical relationship between LAI and the ratio of the difference between the aerodynamic and the air temperatures and the difference between the surface and the air temperatures, also known as “β function”. Nine datasets obtained in agricultural areas (four in south western France near Toulouse, four in south eastern France near Avignon, one in Morocco near Marrakech) are used to evaluate this new relationship. They all span the entire cropping season, and LAI values range from 0 to about 5. This new expression of the β function is then compared to the β function retrieved from measured sensible heat flux and in situ radiometric measurements as well as the β function simulated by a two-source SVAT model (ICARE). Its performance in estimating the sensible heat compares well to other empirical or semi-empirical functions, either based on a β function or a radiometric kB−1.