Optimal Solar Geometry Definition for Global Long-Term Landsat Time-Series Bidirectional Reflectance Normalization

Abstract

The systematic generation of global Landsat time-series products has been advocated, and studies have suggested the need to minimize Landsat reflectance anisotropy effects. Considering a global year of non-Antarctic Landsat 5 and 7 acquisitions, the scene center solar zenith varied from 22.14° to 89.71°, with a mean of 43.23°. However, a solar zenith angle definition suitable for generation of global bidirectional reflectance normalized Landsat time series has not been considered. In this paper, a solar zenith optimal definition is developed in terms of the following criteria: i) ensuring that it can be modeled for any location and date; ii) ensuring that it is constant or smoothly changing with respect to space and time and has global annual variation no greater than the variation in the observed Landsat solar zenith angles (θ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> ); and iii) minimizing the differences between θ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> and the solar zenith angle used for normalization. Global coverage Landsat data are used to evaluate four solar zenith angle definitions, namely, fixed solar zenith angles, i.e., (O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fixed</sub> ), the solar zenith at local solar noon, i.e., (O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">solar</sub> noon), the solar zenith at the global mean Landsat overpass time, i.e., (O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">mean overpass time</sub> ), and the solar zenith at a latitude-varying local time parameterized by a polynomial function of latitude, i.e., (O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">poly overpass time</sub> ), that effectively provides a model of θ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</sub> . The optimal definition for global and long time-series Landsat bidirectional reflectance normalization is (O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">poly overpass time</sub> ). The polynomial coefficients are provided so that users may implement Landsat bidirectional reflectance normalization algorithms using this optimal solar geometry.