| 14 Apr 2026
Revisiting error models for the assimilation of all-sky infrared satellite radiances
Abstract. The sensitivity of all-sky infrared radiances to both hydrometeor content and cloud height leads to a very non-Gaussian distribution of first-guess departures. This non-Gaussianity can be mitigated by the application of cloud-dependent error models that normalize departures by an estimate of the cloud-height effect via assigning increased errors in situations with high clouds that can lead to very large departures. In the current study, we systematically evaluate existing error models and propose a revised approach that leads to a better fit to a Gaussian distribution at no additional cost. Furthermore, the revised approach is physically better justified as the cloud effect is estimated by the maximum cloud effect of model and observations, which determines the largest possible departure. Preceding studies, in contrast, used the mean cloud effect of model and observations.
Our study is based on a one-month data set of infrared observations in two water vapor channels (6.2 and 7.3 μm) from the Spinning Enhanced Visible and Infrared Imager (SEVIRI) onboard the Meteosat Second Generation satellite and corresponding simulations from the weather forecast model AROME (Application of Research to Operations at Mesoscale) over central Europe. The evaluation of different approaches revealed that near-Gaussian departures can be achieved with three different approaches for the estimation of the cloud effect: (1) deviation from a climatologically estimated value; (2) deviation from the clear-sky brightness temperature of a window channel; and (3) deviation from the clear-sky brightness temperature of the channel that is assimilated. For the lower-peaking channel (7.3 μm) with a larger cloud effect, best results were achieved with the first two options. For the 6.2 μm channel, the third option led to a slightly more Gaussian distribution. The third option, however, requires a quality control that eliminates about 10 % of the observations.
This manuscript revisited the previous two methods developed by Okamoto et al. and Harnisch et al., and proposed a revised method that replaced the average cloud effect predictor C with the maximum C, and finally evaluated the performances of all methods. The manuscript is within the scope of Atmospheric Measurement Techniques. The manuscript is well-written and easy to follow. However, the universality and reliability of the method require further supporting evidence. Specific comments are as follows.
Major comments:
(1) The authors proposed using the maximum cloud effect instead of the mean cloud effect, but the theoretical justification for this claim is insufficient. It is recommended that the authors provide additional statistical theory or sensitivity experiments (e.g., using different quantiles such as 90% or 95%) to demonstrate that the maximum is the optimal choice.
(2) The study only used a one-month dataset (August), and the generalizability of the methods and findings requires further verification. It is recommended to conduct additional validation across different seasons (e.g., the convectively active summer period and the stably stratified winter season).
(3) This study only examined the Gaussianity of the departure distribution and did not demonstrate the impact of the proposed error model on analysis quality or forecast skill when applied in an actual data assimilation cycle. The authors could appropriately conduct idealized or real data assimilation experiments to illustrate its practical value.
Minor comments:
(1) The terms “Cloud-height effect” and “cloud effect” are used interchangeably in the text, but the two are not entirely equivalent.
(2) Line 107: “Austria in 2023,.” Change to “Austria in 2023.”
(3) Line 121: “for the BTclr calculation” maybe “for the BTcld calculation”?
(4) Figure 1: “BTclr” in caption change to “BTcld”. Please check the correct use of these physical quantities throughout. E.g., Lines 160-165, caption of all the Figs.
(5) Line 161: Delete a “between”
(6) Line 277: What is “CA”?