A modified k-distribution approach applied to narrow band water vapour and oxygen absorption estimates in the near infrared

We apply a modified version of the k-distribution method to derive expressions for the total and in-layer transmission of layered atmospheres in the H2O and O-2 absorption bands around 900 and 762 nm, respectively. The calculations are exemplary performed for the channels settings of the forthcoming Medium Resolution Imaging Spectrometer (MERIS), to be launched onboard ESA's Environmental Satellite in 2000, but apply for other narrow band sensors in the visible and near infrared as well. The modifications of the k-distribution approach are (1) that we do not employ the correlated k-distribution approach to derive weights and averaged;ed absorption coefficients in layered atmospheres. Instead, we define a mapping function on the considered spectral interval so that the relation between the approximated absorption coefficients and the associated wavelengths is explicitly fixed for all layers. (2) we derive a consistent concept of introducing the sensor's spectral response functions and the spectral variation of the solar constant in the derivation of the relative weights of the single terms of the k-distribution fit. We compare line-by-line transmissions with k-distribution results performed for 20 terms and show that the in-layer and at the same time the total atmospheric transmission in the O(2)A-absorption band can be fitted with a relative accuracy of 1% and in the water vapour absorption band with a relative accuracy higher than 0.1%. We compare these results to the correlated k-distribution approach and find improvements of the accuracy of the fit of a factor of 5-10 for the O(2)A-band as well as for the water vapour absorption band. Comparing idealised rectangular and actual spectral response functions, we find that errors in the estimation of the atmospheric transmission induced by an idealised rectangular filter function exceed 40% relative (10% absolute) for the narrow channel covering the O(2)A-band (3.75 nm half-width) and 5% relative error (3% absolute) for the 10 nm channel located at 900 nm. (C), 2000 Elsevier Science Ltd. All rights reserved.