Estimation of sensible heat flux from surface temperature wave and one-time-of-day air temperature observation

By means of the algorithm presented here, the temporal course H(t) and the daily mean H of the sensible heat flux H can be estimated from measurements of the thermodynamic surface temperature (as a function of time) and from a one-time-of-day air temperature observation. In addition to these temperatures, one needs estimates for daily mean wind speed, for the roughness lengths of momentum and heat transfer, and for the displacement height. First, a quite general solution of the equation for heat conductance (equation for the vertical profile of potential temperature Theta(z, t)) in the dynamic sublayer will be presented. The undetermined parameters in this solution will be defined with the aid of the above mentioned measurements. The influence of horizontal advection will be taken into account. After that, the sensible heat flux can be evaluated from the temperature difference between surface and air with the well known resistance formulae. In this paper the algorithm is derived for areas with homogeneous surfaces, i.e., with uniform surface temperatures. Finally, the method will be verified by measurements taken during the field campaigns HIBE 89 (Hildesheimer Borde in Germany) and EFEDA 91 (Spain). The root mean square errors (RMSE) for the comparison between measurement and model with regard to the temperature difference of surface and air amount to one or MO degrees Kelvin, and the error of (H) over bar reaches 10 to 25 per cent. The method can be used to determine the sensible heat flux from measurements of surface temperatures by satellites (e.g., METEOSAT), but can also be applied to ground based measurements. For instance, horizontal temperature advection can be estimated from measurements at a single location, especially if more than one near-surface air temperature is available. The procedure can be generalized for larger areas, which consist of various surface types with different surface temperatures. This generalization of the algorithm is in progress and will be addressed in a subsequent paper. It will allow us to improve the estimates for H(t) by means of temperature measurements from, e.g., NOAA/AVHRR or LANDSAT/TM, taking into account the heterogeneity of the area that is contained in one METEOSAT pixel.