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 interpretations 

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.  

a) (in addition to methods considered in 3.3) 

   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 for 

   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-orbiting 

   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 the 

   presence of residual spectral features, eg systematic errors in the 

   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 as 

   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)

 

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)" 

    (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, somewhat 

    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 $\sigma^2_0,var$ ? 

 

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