Determination of surface reflectance and estimates of atmospheric optical depth and single scattering albedo from Landsat Thematic Mapper data

Abstract

Ground reflectance data of selected targets for calibration of a Landsat Thematic Mapper (TM) image of Wind River Basin, Wyoming, acquired November 21, 1982, were analysed. The calibration lines, one for each band, are derived from linear regression analysis of scatter plots of ground bidirectional spectral reflectance versus the Thematic Mapper (TM) scanner response. The field-measured reflectances were obtained with a portable spectrometer at 10 nm spectral resolution in November 1983. The empirical equations derived were used to predict the ground reflectance of five unknown targets scattered throughout the Wind River and adjacent Bighorn Basins. Subsequently, in July 1984, field measurements were made over these targets with field spectrometers and with a hand-held radiometer with filters matching those of the TM. The agreement between predicted and measured quantities, mostly within the uncertainties of the field observations, was obtained, suggesting that the ground reflectance properties of the areas studied were approximately the same in November 1982 and July 1984, and that, as suggested by visual inspection of the images themselves, the atmosphere during TM data acquisition was relatively homogeneous from place to place over the area of our field observations. In addition to determining ground reflectance, we also used these field-derived calibration relationships together with current radiometric calibration data for the TM in a simple homogeneous atmospheric model to estimate emergent radiance at the satellite. From the emergent radiance and the atmospheric model, we derived estimates, on a straightforward algebraic inversion scheme, of single scattering albedo (ω₀) and optical depth (τ) for the atmosphere. These relationships follow from the fact that the intercept value of a field calibration line, determined at zero surface reflectance, provides an estimate of the path radiance; the slope is a function of the two-way transmittance. To disentangle the atmospheric properties we assumed the atmosphere to be isotropically scattering. This is the only assumption that can be made considering the essentially single nadir-looking direction of TM surface observations. For this model the slope and intercept provide two functions of ω₀ and τ, whose numerical magnitudes together with the solar spectral irradiances are known. These equations were solved simultaneously, exactly in the single scattering approximation and iteratively with multiple scattering. Uncertainties in the derived quantities were estimated from the standard errors provided by the regression analysis. The results for optical depth variation with wavelength are 20 per cent greater than those predicted from the model of reference, a LOWTRAN 6 simulation of mid-latitude winter conditions. This led to consideration of sources of error in the analysis. All of these lead to overestimates of the optical depth, and include: (1) atmospheric scattering from the surroundings over the standard targets (adjacency effects), (2) contamination of surface targets by other components, e.g., ground by snow and snow by ground, vegetation, or shadows, and (3) the neglect of anisotropic scattering in the atmospheric model.