The benefit of hyperspectral infrared sounders to weather forecasting has been improved with the representation of inter-channel correlations in the observation error model. A further step would be to assimilate these observations in all-sky conditions. However, in cloudy skies, observation errors exhibit much stronger inter-channel correlations, as well as much larger variances, compared to clear-sky conditions. An observation error model is developed to represent these effects, building from the symmetric error models developed for all-sky microwave assimilation. The combination of variational quality control with correlated errors is also introduced. The new error model is tested in all-sky assimilation of seven?water vapour sounding channels from the Infrared Atmospheric Sounding Interferometer (IASI). However, its initial formulation degrades both tropospheric and stratospheric analyses. To explain this, the eigendeparture and eigenjacobian are introduced as a way of understanding the effect of correlated observation errors in data assimilation. The trailing eigenvalues can be problematic because they strongly amplify high-order harmonic combinations of the water vapour channels, which could have at least three consequences. First, if there are small inter-channel biases, these can be greatly amplified. Second, the trailing eigenjacobians map onto features resembling gravity waves that the data assimilation may not be able to handle. Finally, these harmonic combinations can amplify trace sensitivities, for example, revealing a strong upper stratospheric sensitivity over high cloud in what are usually mid- to upper-tropospheric water vapour channels. A likely explanation is the sensitivity to gravity wave features that are present in the observations but hard for the data assimilation to handle. After reducing the sensitivity to the trailing eigenjacobians, the new error covariance matrix gives good results in all-sky infrared assimilation.
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