Evaluation of the temporal relationship between daily min/max air and land surface temperature

Daily minimum and maximum air temperature (min/max Ta) exhibits a strong linear correlation with remotely sensed land surface temperature (LST). However, LST-based predictions of min/max Ta exhibit a strong seasonal pattern in their errors. This study examines the temporal trends in min/max Ta and LST, and shows that the strongest correlation exhibited by any of these variables is a temporal autocorrelation that is periodic in nature. This study analyses the temporal relationship between min/max Ta and LST, and shows that this results in a temporal trend in the errors of LST-based min/max Ta predictions that can primarily be explained by a phase shift between the seasonal oscillations of min/max Ta and LST. After removing the elevation and periodic temporal trend from the min/max Ta and LST measurements, a weak linear correlation was exhibited between min Ta and LST and a moderate linear correlation was exhibited between max Ta and LST. Fitting models to the detrended min/max Ta and LST measurements resulted in an LST-based model of min/max Ta that no longer exhibited seasonal variability in the model errors, and had a lower mean absolute error (MAE) than either a model based only on the elevation and temporal trends or one based on the elevation and LST trends alone. Thus, the results of this study show that in creating relationships between LST and air temperature, it is important to address the phase shift between the annual oscillations of these variables. This study shows that removing the annual oscillation using a Fourier model of the temporal trend improves the LST-based min/max Ta prediction by 0.6°C to 0.8°C.