Modelling the effect of optical thickness on diurnal cycles of land surface temperature

Fitting a model to diurnal temperature cycles (DTC) of the land surface yields a set of parameters which summarizes the surfaceʹs thermal dynamics and is more informative and representative of its thermal characteristics than the individual land surface temperatures (LST). Modelling DTC is also useful for temporal compositing and for cloud screening. However, an earlier version of the DTC model presented in this article did not capture the smooth and gradual increase of LST around sunrise: this shortcoming is addressed here. Starting from the energy balance equation of the surface, a DTC model is developed which accounts for atmospheric attenuation of solar irradiation, the land surfaceʹs main heating source. By including total optical thickness (TOT), the new model reproduces the shape of morning rise of LST better, is able to “squash” DTC temporally, and more accurately reproduces the natural variability of DTC width and slope. Three different formulations of relative optical air mass are given and a Levenberg-Marquardt minimisation scheme is used to fit the DTC model to time series of LST, which are obtained from ground based thermal infrared (TIR) data measured at permanent validation stations near “Gobabeb Training and Research Centre”, Namibia, and near the town of Evora, Portugal. For turbid atmospheres (transparency 40%) the new model reduces the average deviation between modelled and measured LST by a factor of around three. Statistical analyses of 154 DTCs collected at the two validation sites show that the new DTC model consistently outperforms the earlier version of the model.