the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 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.
- Preprint
(2697 KB) - Metadata XML
- BibTeX
- EndNote
Status: final response (author comments only)
- RC1: 'Comment on egusphere-2026-1463', Anonymous Referee #1, 12 May 2026
-
RC2: 'Comment on egusphere-2026-1463', Anonymous Referee #2, 22 Jul 2026
Review of the manuscript “Revisiting error models for the assimilation of all-sky infrared satellite radiances”
Summary
The present manuscript aims to evaluate two error models (Okamoto et al., 2014; Harnisch et al., 2016) for the assimilation of all-sky infrared satellite radiances over a one month dataset above central Europe. The final goal is propose a revised version of the two approach.
The manuscript is very well-written and within the scope of AMT.
In the following pages, the editor and authors can find my recommendations for this manuscript.
Major comments
- Is the use of maximum cloud effect representative and appropriate for all the cases? A statistical analysis to justify this choice would be essential for the improvement of the manuscript.
- The authors use one month (August 2023) of data. Ideally, 4 months (1 per season) or a full year would be more presentative for the outcomes of the study. Is it something possible? If not, some case studies of other months would be necessary to evaluate the methodology.
Minor comments
- Page 2, Line 31: Add the acronym ECMWF & NCEI.
- Page 4, Line 121: “… for the BTcld …” and not BTclr.
- Same comment for Figure’s 1 & 2 captions.
- Page 6, Line 151: Could you justify your choice of bin width equal to 0.1?
- Page 7, Line 165: BTclr both of them? Please make sure that BTclr and BTcld are correct throughout the text
- Page 10, Line 238: Is should be stated where the selection of Cmin=2 is based on.
Citation: https://doi.org/10.5194/egusphere-2026-1463-RC2 -
RC3: 'Comment on egusphere-2026-1463', Anonymous Referee #3, 03 Aug 2026
General Comments:------------------This study investigates several existing approaches to estimate observation error variances for the purpose of all-sky infrared radiance DA, and proposes an interesting revision to those approaches. The manuscript is generally well written, the results largely support the study's findings, and I did not detect any unacknowledged major shortcomings in the study's design. The comments I have for this study are relatively minor. Therefore, I recommend an editorial decision of minor revisions for this manuscript.Specific Comments:------------------Section 1: This study is largely motivated by the nonlinear non-Gaussian effects associated with all-sky IR statistics. Please include the following relevant references on the subject.Lei, L., Ju, H., Fu, K., Anderson, J. L., Zhou, L., & Tan, Z. M. (2026). Quantile-Conserving Ensemble Filters for All-Sky Infrared Radiance Assimilation. Monthly Weather Review, 154(1), 99-117.Zhou, L., Lei, L., Tan, Z. M., Zhang, Y., & Di, D. (2023). Impacts of observation forward operator on infrared radiance data assimilation with fine model resolutions. Monthly Weather Review, 151(1), 163-173.Chan, M. Y. (2026). Improving convection‐permitting all‐sky infrared radiance ensemble data assimilation through mitigating deleterious non‐Gaussian artifacts. Quarterly Journal of the Royal Meteorological Society, 152(774), e70039.Chan, M. Y., Chen, X., & Anderson, J. L. (2023). The potential benefits of handling mixture statistics via a bi‐Gaussian EnKF: Tests with all‐sky satellite infrared radiances. Journal of Advances in Modeling Earth Systems, 15(2), e2022MS003357.Chan, M. Y., Zhang, F., Chen, X., & Leung, L. R. (2020). Potential impacts of assimilating all-sky satellite infrared radiances on convection-permitting analysis and prediction of tropical convection. Monthly Weather Review, 148(8), 3203-3224.2) L47: The sentence beginning with "This method was first proposed..." should be the start of a new paragraph.3) L101: "peak around 350 hPa and 500 hPa" -- please include a reference for this.4) L101: "For Ch10.8, it peaks near..." -> "Ch10.8's weighing function peaks near..."5) L107: "Austria in 2023,. AROME" -> "Austria in 2023. AROME"6) L110: "is still currently" -> "is currently"7) L111: "but the GeoSphere plan to switch to a 1km grid spacing some time in 2026" -- this tidbit does not contribute towards your story. Please eliminate that.8) L134: "which cloud be" -> "which could be"9) L135: "low/medium clouds, or it could be that with less" -> "low/medium clouds. Alternatively, with less"10) L142: "where $\sup_x$ is the" -> "where the $\sup_x$ operator finds the"11) L147: "it's" -> "it is".12) Eq (2): It took me a while to understand how this quantity is a measure of the two distribution's overlap. Am I correct in interpreting this quantity as the ratio of (a) the intersection of two pdf's areas under curve versus (b) the union of the two pdf's areas under curve? I recommend adding a graphical illustration to help readers understand this quantity.13) L160: Add an explicit statement of the purpose for having a threshold BT. My impression is that the threshold BT's purpose to separate clear-sky BTs from cloudy-sky BTs.14) L161: "For deriving BT_lim, we" -> "We"15) L165: "note the logarithmic scaling" -> "note the logarithmic color scale"16) Eq (3): To help readers with this equation, break up the right hand side into two fractions. The first fraction is the model term, and the second fraction is the observaiton term.17) Eq (4): I cannot locate the definitions of $C_{min}$ and $C_{max}$. Did I miss them?18) L193: The term "model error" is vague as it can refer to either model representation errors (epistemic uncertainties) or background uncertainties (aleatoric uncertainties). Please use a more precise term instead of "model error". This term crops up a few times in your paper.19) L206: "the observed profile" -> "the observed BT"?20) Eq (5): Same as comment 16.21) L220: "It produces" -> "$O_{14}$ produces"22) L220: "doesn't" -> "does not"23) L223: "by computing the" -> "by comparing the"24) L225-229: I agree with you that if Std is always equal to 2 C_j for clear-clear situations, then the two-point Bernoulli distribution manifests. However, it is unclear to me why that equivalence exists. Could you elaborate on why that equivalence exists?25) L235-236: Remove the sentence beginning in "For this modification".26) L238: "Here, C_min=2 is set for futher analysis" -> "Here, we set C_min = 2."27) Eq (8): The sheer number of maximum operators make this equation hard to read. Maybe use "{}" instead of "()" for the outer-most maximum operator, and use "[]" for the middle maximum operator? Also, add some spaces here and there to help with reading your equation (this would be the \, command in LaTeX).28) L400: "We are convinced that the revised approach" -> " The revised approach"Citation: https://doi.org/
10.5194/egusphere-2026-1463-RC3 -
RC4: 'Reply on RC3', Anonymous Referee #3, 03 Aug 2026
I just want to mention here that I did think about whether this study needs to have some DA experiments to confirm that their revised methods result in better results than the original methods. This is something that RC1 did note. However, the Acknowledgements suggest that this study was done during the lead author's visit to the U of Vienna. As such, I suspect that DA experiments might be beyond the resource constraints of the lead author. Therefore, I decided against making that a major comment.
Citation: https://doi.org/10.5194/egusphere-2026-1463-RC4
-
RC4: 'Reply on RC3', Anonymous Referee #3, 03 Aug 2026
Viewed
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 299 | 106 | 27 | 432 | 26 | 27 |
- HTML: 299
- PDF: 106
- XML: 27
- Total: 432
- BibTeX: 26
- EndNote: 27
Viewed (geographical distribution)
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
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”?