This paper presents a weighted least squares approach to retrieve aerosol layer height from top-of-atmosphere reflectance measurements in the oxygen A band (758-770g nm) over bright surfaces. A property of the measurement error covariance matrix is discussed, due to which photons travelling from the surface are given a higher preference over photons that scatter back from the aerosol layer. This is a potential source of biases in the estimation of aerosol properties over land, which can be mitigated by revisiting the design of the measurement error covariance matrix. The alternative proposed in this paper, which we call the dynamic scaling method, introduces a scene-dependent and wavelength-dependent modification in the measurement signal-to-noise ratio in order to influence this matrix. This method is generally applicable to other retrieval algorithms using weighted least squares. To test this method, synthetic experiments are done in addition to application to GOME-2A and GOME-2B measurements of the oxygen A band over the August 2010 Russian wildfires and the October 2017 Portugal wildfire plume over western Europe.

Retrieving aerosol optical thickness and aerosol layer height over a bright surface from measured top-of-atmosphere reflectance spectrum in the oxygen A band is known to be challenging, often resulting in large errors. In certain atmospheric conditions and viewing geometries, a loss of sensitivity to aerosol optical thickness has been reported in the literature. This loss of sensitivity has been attributed to a phenomenon known as critical surface albedo regime, which is a range of surface albedos for which the top-of-atmosphere reflectance has minimal sensitivity to aerosol optical thickness. This paper extends the concept of critical surface albedo for aerosol layer height retrievals in the oxygen A band, and discusses its implications. The underlying physics are introduced by analysing the top-of-atmosphere reflectance spectrum as a sum of atmospheric path contribution and surface contribution, obtained using a radiative transfer model. Furthermore, error analysis of an aerosol layer height retrieval algorithm is conducted over dark and bright surfaces to show the dependence on surface reflectance. The analysis shows that the derivative with respect to aerosol layer height of the atmospheric path contribution to the top-of-atmosphere reflectance is opposite in sign to that of the surface contribution - an increase in surface brightness results in a decrease in information content. In the case of aerosol optical thickness, these derivatives are anti-correlated, leading to large retrieval errors in high surface albedo regimes. The consequence of this anti-correlation is demonstrated with measured spectra in the oxygen A band from the GOME-2 instrument on board the Metop-A satellite over the 2010 Russian wildfires incident.