Combined modelling of annual and diurnal land surface temperature cycles

The land surface's thermal dynamics follows annual and diurnal cycles that are to a large extent controlled by solar geometry. Therefore, annual and diurnal variations of land surface temperature (LST) can be modelled with relatively simple functions controlled by a small number of parameters, typically from three to six. The parameter values of the models can be determined by fitting the respective functions to time series of LST observations. Commonly either annual or diurnal LST variations are modelled or they are modelled sequentially in a two-step process. Here, we combine an annual temperature cycle (ATC) model controlled by the solar zenith angle (ATCsza) with a four-parameter version of the diurnal temperature cycle (DTC) model GOT09: this yields a new annual-diurnal temperature cycle (ADTC) model that simultaneously describes the annual and diurnal surface temperature dynamics. The proposed ADTC model is controlled by physically meaningful parameters: annual minimum temperature, annual temperature amplitude, annual maximum of daily temperature amplitude, mean time of thermal noon and time lag of maximum temperature with respect to summer solstice. Thus, the entire annual-diurnal LST dynamics is described with only five parameters. The new model was tested by fitting it to one year of LST observations obtained for five globally representative tiles of the Moderate Resolution Imaging Spectroradiometer (MODIS), onboard EOS - TERRA and EOS - AQUA satellites. For these tiles, the mean of the root mean square error (RMSE) was 4.2 K. ADTC modelled LSTs were also compared against those obtained with the standard ATC model for the four MODIS overpass times at five representative sites: for these, an overall RMSE of 1.2 K between the two models was obtained. The ADTC derived LSTs were validated against insitu measurements from three different sites, which yielded an overall RMSE of 3.4 K. Additional investigations over five areas with different land covers (i.e. urban, lake, forest, mountain area and desert) revealed the potential of the ADTC parameters to describe the corresponding surface and climate properties. Since it is driven by solar geometry, the ADTC model reproduces double LST peaks in the tropics naturally. Furthermore, all available observations are modelled simultaneously, which means that a single set of parameters is obtained for each pixel and year.