We discuss the effect of horizontal fluxes on the accuracy of a conventional plane-parallel radiative transfer calculation for a single pixel, known as the Independent Pixel Approximation (IPA) at absorbing wavelengths. Vertically integrated horizontal fluxes can be represented as a sum of three components; each component is the IPA accuracy on a pixel-by-pixel basis for reflectance, transmittance and absorptance, respectively. We show that IPA accuracy for reflectance always improves with more absorption, while the IPA accuracy for transmittance is less sensitive to the changes in absorption: with respect to the non-absorbing case, it may first deteriorate for weak absorption and then improve again for strongly absorbing wavelengths. EPA accuracy for absorptance always deteriorates with more absorption. As a result, vertically integrated horizontal fluxes, as a sum of IPA accuracies for reflectance, transmittance and absorptance, increase with more absorption. Finally, the question of correlations between horizontal fluxes, IPA uncertainties and radiative smoothing is addressed using wavenumber spectra of radiation fields reflected from or transmitted through fractal clouds
