the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 19 Sep 2025
Methods for validation of random uncertainty estimates and their applications to ozone profiles from limb-viewing satellite instruments
Abstract. For satellite measurements of atmospheric composition, the random uncertainty estimates provided by retrieval algorithms might be imperfect due to various approximations used in the retrievals or presence of unknown error sources. This paper presents an overview of the methods used for validation of random uncertainty estimates. All methods discussed in this study are categorized, and assumptions and limitations of each method are discussed. This overview evaluates these methods in application to ozone profile measurements data from limb and occultation satellite instruments and provides practical illustrations of random uncertainty validation.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Atmospheric Measurement Techniques.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.-
Notice on discussion status
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
-
Preprint
(1349 KB)
-
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(1349 KB) - Metadata XML
- BibTeX
- EndNote
- Final revised paper
Journal article(s) based on this preprint
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2025-2830', Anonymous Referee #1, 03 Nov 2025
- AC1: 'Reply on RC1', Viktoria Sofieva, 15 Jan 2026
-
RC2: 'Comment on egusphere-2025-2830', Anonymous Referee #2, 20 Nov 2025
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-2830/egusphere-2025-2830-RC2-supplement.pdf
- AC2: 'Reply on RC2', Viktoria Sofieva, 15 Jan 2026
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2025-2830', Anonymous Referee #1, 03 Nov 2025
Methods for validation of random uncertainty estimates and their applications
to ozone profiles from limb-viewing satellite instrumentsSofieva et al
Referee comments
The paper discusses various methods for assessing the actual random error
of satellite-derived profiles of atmospheric data, comparing these with
the reported random error, and showing results of various methods of
assessment.I have no objection to the content of the paper, or the analysis, but
I offer some suggestions for improvements and clarifications which the
authors may wish to consider.1) Firstly, There ought to be an initial statement of the meaning of
'random uncertainty' as used in the title of this paper. I think it may be
close to the lab definition at the start of section 3.2 but it should be
at the start, along with some discussion of various alternative interpretationsÂ
that have also been used (eg those briefly listed in Table 1).2) I can think of two further methods which could also at least be
mentioned, if not applied. Â
a) (in addition to methods considered in 3.3)Â
  For continuous limb-scanning instruments retrieving profiles every
  few hundred km along the orbit, one could compare each profile with
  a profile interpolated from the profiles immediately before and
  afterwards along the orbit. While this still has some component of
  natural variability, that would be reduced by the linear interpolation.
  This has an advantage over the method of using orbital intersections since
  the time gap is smaller and all three profiles are likely to be measured
  with the same day or night illumination. However, this would not work forÂ
  tomographic retrievals.
b) (in addition to methods considered in 3.4)
  Measurement of variation about the zonal mean. This seems to be
  partly covered in 3.4.2 but I was thinking of much narrower
  latitude bands. This particularly suits solar-occultation
  instruments which typically make 14 measurements in each of two
  very tightly-constrained latitude bands every 24 hours, and also
  tomographic retrievals since any along-orbit correlation is likely
  to be negligible over half an orbit.  One could then dispense with
  any time (apart from within the same day) or longitudinal
  constraint on matching - hence more comparisons with polar-orbitingÂ
  instruments - and the only additional information required
  is \sigma_nat on c.15deg longitude scale which is, obviously, the
  same for all instruments and, in the summer stratosphere, quite possibly
  negligible3) Although the various methods that are discussed are applied to different
  instruments, there is no summary table or plot comparing the results
  from the different methods applied, eg, to just one instrument, so that
  the methods can be directly compared.Minor points/typographical corrections:
Section 2 - it would be helpful in each subsection to have just an initial
sentence describing the type of instrument/observation.Generally, use 'en' dashes ($--$) to indicate a range of numbers rather than
hyphens (eg Figure captions, P11 L20, P13 L4-5 L18, P17 L15).P5 L9 (&L17): A large chi-squared value seems more likely to indicate theÂ
  presence of residual spectral features, eg systematic errors in theÂ
  forward model, than correctness of the assumed random error.P5 L20: 'em' dashes are required here ($---$ in LaTeX),
P7 L19/20: 'which represent ... is different': sigma^2_0,nat is treated asÂ
  both plural and singular in this sentence.P8 L9: Note that such collocated measurements necessarily involve comparing
  ascending and descending nodes of the orbit, so likely to involve different
  day/night conditions.P8 Eq (5): presumably D(\rho) depends differently on the magnitude of each
  coordinate of \rho (and in any case some scaling is required to convert
  between the time and space coordinates).P9 L11: $S_12$ (upper case here, lower case elsewhere)
P9 Fig 15 caption: '20011' should presumably be '2011'.
P10 L16: "true" - initial pair of double-quote marks show as ",,"
P10 L22: "not dense" - I suggest "sparse"
P10 L32: Here it seems that "a-posteriori" and "ex-post" mean the same thing
  but elsewhere both are used individually so it is less clear that their
  meanings are the same. Also "a posteriori" is sometimes hyphenated,
  sometimes not (P16 L21)
Â
P11 L2: Since it is a direct part of the sentence, I would suggest
  "von Clarmann et al (2020)" rather than "(von Clarmann et al., 2020)"Â
  (also P17 L14)P13 Fig 25: I was initially impressed with the consistency of the \sigma_nat
  values shown in the lower plots, but then I realised that these are
  very similar to the sample SDs shown in the upper plot, somewhatÂ
  contradicting condition (b) mentioned on P14 L2.P14 L23: pedantically it should perhaps be noted that \epsilon_y,z refer
  to random errors scaled to x rather than associated with the original
  measurements (to me it seems more natural to have eg y = c_y t + e_y)P12 L11: I may have missed it, but what is $\sigma^2_0,var$ ?Â
Â
----------Citation: https://doi.org/10.5194/egusphere-2025-2830-RC1 - AC1: 'Reply on RC1', Viktoria Sofieva, 15 Jan 2026
-
RC2: 'Comment on egusphere-2025-2830', Anonymous Referee #2, 20 Nov 2025
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-2830/egusphere-2025-2830-RC2-supplement.pdf
- AC2: 'Reply on RC2', Viktoria Sofieva, 15 Jan 2026
Peer review completion
Journal article(s) based on this preprint
Viewed
| HTML | XML | Total | BibTeX | EndNote | |
|---|---|---|---|---|---|
| 1,377 | 130 | 37 | 1,544 | 36 | 35 |
- HTML: 1,377
- PDF: 130
- XML: 37
- Total: 1,544
- BibTeX: 36
- EndNote: 35
Viewed (geographical distribution)
| Country | # | Views | % |
|---|
| Total: | 0 |
| HTML: | 0 |
| PDF: | 0 |
| XML: | 0 |
- 1
Viktoria F. Sofieva
Alexandra Laeng
Thomas von Clarmann
Gabriele Stiller
Michael Kiefer
Johanna Tamminen
Alexey Rozanov
Carlo Arosio
Nathaniel Livesey
Robert Damadeo
Patrick Sheese
Kaley A. Walker
Doug Degenstein
Daniel Zawada
Natalya A. Kramarova
Arno Keppens
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(1349 KB) - Metadata XML
Methods for validation of random uncertainty estimates and their applications
to ozone profiles from limb-viewing satellite instruments
Sofieva et al
Referee comments
The paper discusses various methods for assessing the actual random error
of satellite-derived profiles of atmospheric data, comparing these with
the reported random error, and showing results of various methods of
assessment.
I have no objection to the content of the paper, or the analysis, but
I offer some suggestions for improvements and clarifications which the
authors may wish to consider.
1) Firstly, There ought to be an initial statement of the meaning of
'random uncertainty' as used in the title of this paper. I think it may be
close to the lab definition at the start of section 3.2 but it should be
at the start, along with some discussion of various alternative interpretationsÂ
that have also been used (eg those briefly listed in Table 1).
2) I can think of two further methods which could also at least be
mentioned, if not applied. Â
a) (in addition to methods considered in 3.3)Â
  For continuous limb-scanning instruments retrieving profiles every
  few hundred km along the orbit, one could compare each profile with
  a profile interpolated from the profiles immediately before and
  afterwards along the orbit. While this still has some component of
  natural variability, that would be reduced by the linear interpolation.
  This has an advantage over the method of using orbital intersections since
  the time gap is smaller and all three profiles are likely to be measured
  with the same day or night illumination. However, this would not work forÂ
  tomographic retrievals.
b) (in addition to methods considered in 3.4)
  Measurement of variation about the zonal mean. This seems to be
  partly covered in 3.4.2 but I was thinking of much narrower
  latitude bands. This particularly suits solar-occultation
  instruments which typically make 14 measurements in each of two
  very tightly-constrained latitude bands every 24 hours, and also
  tomographic retrievals since any along-orbit correlation is likely
  to be negligible over half an orbit.  One could then dispense with
  any time (apart from within the same day) or longitudinal
  constraint on matching - hence more comparisons with polar-orbitingÂ
  instruments - and the only additional information required
  is \sigma_nat on c.15deg longitude scale which is, obviously, the
  same for all instruments and, in the summer stratosphere, quite possibly
  negligible
3) Although the various methods that are discussed are applied to different
  instruments, there is no summary table or plot comparing the results
  from the different methods applied, eg, to just one instrument, so that
  the methods can be directly compared.
Minor points/typographical corrections:
Section 2 - it would be helpful in each subsection to have just an initial
sentence describing the type of instrument/observation.
Generally, use 'en' dashes ($--$) to indicate a range of numbers rather than
hyphens (eg Figure captions, P11 L20, P13 L4-5 L18, P17 L15).
P5 L9 (&L17): A large chi-squared value seems more likely to indicate theÂ
  presence of residual spectral features, eg systematic errors in theÂ
  forward model, than correctness of the assumed random error.
P5 L20: 'em' dashes are required here ($---$ in LaTeX),
P7 L19/20: 'which represent ... is different': sigma^2_0,nat is treated asÂ
  both plural and singular in this sentence.
P8 L9: Note that such collocated measurements necessarily involve comparing
  ascending and descending nodes of the orbit, so likely to involve different
  day/night conditions.
P8 Eq (5): presumably D(\rho) depends differently on the magnitude of each
  coordinate of \rho (and in any case some scaling is required to convert
  between the time and space coordinates).
P9 L11: $S_12$ (upper case here, lower case elsewhere)
P9 Fig 15 caption: '20011' should presumably be '2011'.
P10 L16: "true" - initial pair of double-quote marks show as ",,"
P10 L22: "not dense" - I suggest "sparse"
P10 L32: Here it seems that "a-posteriori" and "ex-post" mean the same thing
  but elsewhere both are used individually so it is less clear that their
  meanings are the same. Also "a posteriori" is sometimes hyphenated,
  sometimes not (P16 L21)
Â
P11 L2: Since it is a direct part of the sentence, I would suggest
  "von Clarmann et al (2020)" rather than "(von Clarmann et al., 2020)"Â
  (also P17 L14)
P13 Fig 25: I was initially impressed with the consistency of the \sigma_nat
  values shown in the lower plots, but then I realised that these are
  very similar to the sample SDs shown in the upper plot, somewhatÂ
  contradicting condition (b) mentioned on P14 L2.
P14 L23: pedantically it should perhaps be noted that \epsilon_y,z refer
  to random errors scaled to x rather than associated with the original
  measurements (to me it seems more natural to have eg y = c_y t + e_y)
P12 L11: I may have missed it, but what is $\sigma^2_0,var$ ?Â
Â
----------