Quantifying variability of satellite data in the reflective band for long-term monitoring of the Earth's surface: inference from a multi-temporal relationship between remotely sensed pixels

Reliable long-term monitoring of the Earth's surface is urgently needed for a comprehensive understanding of our environment. However, remotely sensed data is generally affected by a number of temporal factors such as lifetime sensor degradation, Sun-target-satellite geometry and atmospheric conditions. The induced inconsistencies weaken the reliability of satellite-based change studies. A direct method is to remove the inconsistencies through converting the satellite digital number (DN) into a physical quantity using a physically or statistically based model. The associated errors in the conversion are generally hard to trace in the converted quantity, and this leaves questions unanswered. In this study, we propose an alternative approach to quantifying the influences on DN values, based on a multi-temporal relationship in the visible bands. First, we make use of the spectral dependency of aerosol optical thickness on wavelength to expand the validity of the multi-temporal relationship for reflective bands. As an inference of the relationship, a satellite DN value is determined analytically with the temporal influences in terms of a multiplicative and an additive component. In the case of the Landsat-5 Thematic Mapper (TM), we illustrate the variability in DN value in a spatio-temporal context. Lifetime sensor degradation (long-term effect) leads to an increase in the multiplicative effect and a minor change in the additive effect on the DN value. The combined Sun-target-satellite geometry and atmospheric variation induce periodic oscillations in both the multiplicative and additive effects on the DN value. The variation is generally larger for surfaces with a high reflectance than those with a low reflectance. The proposed approach combines sensor calibration and atmospheric correction into one equation, which offers the potential for tracing associated uncertainties propagated into a quantity converted or derived from satellite data, for long-term monitoring of changing surfaces.