Review for Atmospheric boundary layer structure over the Arctic Ocean during MOSAiC

Summary: In this study, the authors performed analyses on data collected during the MOSAiC campaign, focusing on the atmospheric boundary layer height (ABLH). The authors first identified the ABLH manually and then calibrated the critical bulk Richardson number in the bulk Richardson number method for computing ABLH based on the manually labeled ABLH. The relations between ABLH and surface variables were examined, and two cases were examined in detail to investigate the controlling factors of the ABLH variations during the campaign. My overall impression of the paper is that the motivation was justified, the methodology was sound, and the results made sense. I have a few comments on the bulk Richardson number method and also the language needs to be improved (beyond what I pointed out in my comments bleow). 

Major comments:

1, the bulk Richardson number method for computing the ABLH. 

1.1 Some studies also considered a friction velocity in the definition of bulk Richardson number (see e.g., Zhang et al. 2020). It might be worth discussing this. 

1.2 it is not clear whether Eq. 2 is exactly the formula used in the VAP. If so, please state it. 

1.3 the authors mentioned that their results are different from Jozef et al. (2022). It would help the readers understand this by discussing a bit more of how exactly the formulations differ. Which formula did Jozef et al use?

2, an automated algorithm

By looking at Figure 3, why not use an automated algorithm that is based on the bulk Richardson number method for SBL and the Heffter algorithm for CBL?

3, line 318:

If the manually labeled ABLH didn’t include any data in transit, why did the authors think that the calibrated bulk Richardson number method using the manually labeled ABLH could be used to compute ABLH during transit?

Minor comments:

1, line 32: “has” should be “have”, and add “the” before “rapid changing”

2, line 37: “and the essential place for…” can be removed. 

3, line 52: add “the” before “Atmospheric boundary layer height”, “referred to…” should be removed.

4, line 56: replace “literature” with “studies”

5, line 60: replace “surface mixed layer” with “surface layer”. Surface mixed layer is odd. 

6, line 107: remove “special”

7, line 108: remove “fundamental”

8, line 211: I wouldn’t call this “multiple methods”. Maybe change it to “multiple profiles”. 

9, line 161/182/221/260: I would not call this “subjective ABLHs”. Maybe “manually-labeled ABLHs”. 

10, line 223: replace “applied” with “available”

11, line 257: add “a” before “better performance”. 

12, line 302: “the smallest” should be “the best”. R is not the smallest clearly. 

13, line 324-327: these sentences need to be re-worded. 

14, line 382: I would probably not call this “where the annual cycle began”. Please reword. 

15, line 392: how do you know a priori that it is the surface conditions that influence the ABLH, not the other way around? Please re-word. 

16, line 397: I would not say this. The friction velocity and dissipation are affected by both shear and buoyancy. 

17, line 408: turbulence intensity is different from turbulence kinetic energy. Do you mean turbulence intensity or turbulence kinetic energy?

18, line 412: replace “accorded” with “proposed”

19, line 427: add “the” before “highest”

20, line 468: I wonder what features on the figure led the authors to conclude “the cloud-mixed layer aloft does not interact with the near-surface environment”. The relative humidity is closer to saturation than figure 9 where the authors concluded “the near-saturated relative humidity indicates that the cloud-mixed layer couples with the surface-mixed layer, which facilitates the ABL development”. This needs to be clarified. 

21, line 556-558: it’s unclear to me what the authors mean by “Coupling between the cloud mixed layer and surface mixed layer could also be recognized by the Rib algorithm”. Does the Rib method can really distinguish this?

References:

Zhang, Y. J., K. Sun, Z. Q. Gao, Z. T. Pan, M. A. Shook, and D. Li, 2020: Diurnal Climatology of Planetary Boundary Layer Height Over the Contiguous United States Derived From AMDAR and Reanalysis Data. J Geophys Res Atmos, 125.

Review of the manuscript egusphere-2023-347

Atmospheric boundary layer structure over the Arctic Ocean during MOSAiC

by Shijie Peng, Qinghua Yang, Matthew D. Shupe, Xingya Xi, Bo Han, Dake Chen, and Changwei Liu

Summary: In this paper the authors perform an analysis of the boundary-layer height as observed from radio soundings during the MOSAiC field campaign in the Arctic in 2020. These observations are compared to PBL estimates from existing algorithms, and it is concluded that the critical Richardson number should amount to 0.15 rather than the traditional value of 0.25. The analysis has some potential, but at the same time the novelty is limited. My feeling is the paper does not build on the latest and most complete knowledge about PBL height estimation, especially not for the stable boundary layer. More can learnt from this dataset, and I find the controversial result of Ri_crit =0.15 should be discussed in more detail with findings elsewhere.

Recommendation: Major revision required

Major remarks:

1. The paper misses the opportunity to stratify the dataset of the PBL heights in more classes or groups. I.e. for example Zilitinkevich and co workers have been working on PBL types as truly neutral PBLs, nocturnal PBLs, and conventionally neutral PBLs. In addition the analysis can be separated between profiles for cloudy/foggy vs clear sky conditions. I think this can help to reduce the scatter in Fig 3.
2. The study misses some novelty. I understand of course that the dataset at hand is unique and very valuable, but conceptually the paper does not add much in novelty for the PBL height detection. Would it be possible to come up with a completely new approach or PBL height formula for the PBL depth, rather than “just” retuning the Ri_crit again as was done by so many other studies before?
3. The authors have missed a paper by Barten et al. (2023) in the MOSAIC special issue in Elementa in which a similar PBL height analysis was performed. While the main focus of that paper is on the ozone budget in the Arctic PBL, it reports that the critical Richardson number should be 0.40 for MOSAIC for the same set of radio soundings. Hence this is above the typical value of 0.25, while the authors here propose 0.15. This is an obvious contradiction that needs to be discussed.
4. The discussion section of the paper can be deepened in the sense that the Ri_crit value has been widely discussed in other papers before, but I do miss some important ones in the review, e.g. Zilitinkevich and Baklanov (2002, https://link.springer.com/article/10.1023/A:1020376832738 ). Also Basu et al (2014) proposes that the Ri_crit depends on the stability of the SBL as well (https://link.springer.com/article/10.1007/s10546-013-9878-y ). Also, Equation 2 used in the paper has been revised already by Vogelezang and Holtslag for a better score, but it feels this paper does not take benefit from this knowledge. Also, earlier LES studies for the SBL height formula are not mentioned. Hence, the current paper can be embedded more in these earlier works/contributions.
5. I was surprised that the paper never discusses whether a critical Richardson number should exist anyway. In the EFB papers by Zilitinkevich it is analytically derived that the Ri_crit does formally not exist. Though I understand that in practisal applications of Ri_crit still can have some value.

Minor remarks:

Ln 14: hyphenation: boundary layer height -> boundary-layer height. Please check whole document.

Ln 17: perhaps it is good to mention in then abstract before coming up with a new RI_crit how you defined the ABLH in your study. I.e. the level of the largest d_theta/dz, the backscatter level of a ceilometer, the low-level jet height, etc etc.?

Ln 33: Kwok, 2018; Hartfield et al., 2018. I have nothing against these studies but are they still recent?

Ln 42: “various mechanisms and interactions with the surface”: I would say the opposite since turbulent fluxes in the Arctic are usually small so the interaction with the surface is small. In the hierarchy of PBL types by Zilitinkevich et al the Arctic PBL height is characterised as a long-lived stable boundary layer where the PBL height scales more with the stratification in the free atmosphere (and wave activity therein) than with the fluxes at the surface.

Ln 51: The study by Sterk et al (2014) nicely summarizes this (https://doi.org/10.1002/jgrd.50158).

Ln 56: There are many more recent studies that indicate this as well than Deardorff, 1972; Suarez et al., 1983; Holtslag and Nieuwstadt, 1986. Please connect to the recent work!

Ln 109: over the altitude range of 12 m up to 30 km. Please add what is the typical vertical resolution of the sounding measurements in the profile near the surface, this is important to know to what extent the ABLH can be well estimated.

Ln 116: Moreover, we cut off the sounding data observed below 100 m altitude considering the potential contamination of the vessel itself. Please add how many of the launches had to be excluded because of the restriction.

Ln 116: Moreover, we cut off the sounding data observed below 100 m altitude considering the potential contamination of the vessel itself. The ABLH is typically shallow in the Arctic, so is the part that is eliminated not exactly the part you are interested in.

Ln 116: the section should finish with a statement how many soundings are available for analysis after all the correction and control exercises.

Section 2.3: The authors should explain in more detail what is the size of the footprint of these fluxes, and to what extent they are expected to relate to the ABLH.

Ln 169: please add more justification why 2 classes of ABLH types are sufficient. The SBL part was earlier subdivided by many studies by Zilitinkevich in the truly neutral PBL, the nocturnal SBL and the long-lived PBL. These concepts may help to further explain the observations.

Ln 178: theta is used here as measure for stratification. However, above you mention that the PBL driven by turbulence in cloud is an ABLH important archetype. Is it not more appropriate to use a temperature metric that is conserved in moist conditions like the liquid water potential temperature? Please show that this choice does not affect your conclusions!

Ln 180: delta_s is chosen to be 0.2 K. Please relate link this to the measurement accuracy of the sounding. In my view even for a routine AWS the measurement uncertainty is about 0.3K when it includes also representativeness uncertainty.

Ln 226: which an air parcel rising adiabatically from the surface becomes neutrally buoyant... Has an temperature excess been added to the surface parcel and if so with which value?

Ln 227+228: two different estimates of the SBL height are obtained based on stability criteria and wind shear criteria, respectively. Please elaborate in more detail how it has been done, in this way we cannot evaluate the procedure is appropriate.

Ln 239: dimensional number. It is a dimensionLESS number, of course!

Ln 240-246: the paper ignores here the knowledge that was developed in Vogelezang and Holtslag, which was by the way cited, that a better score for the ABLH can be obtained if Equation 2 is not considered from the surface parcel, but a parcel at somewhat above the surface. Hence I feel the latest knowledge is not taken into account here.

Ln 254: 𝐵𝑖𝑎𝑠 is the absolute bias; 𝑆𝐸𝐸 is the standard error. I object against the term bias here. Bias can be either positive or negative, but your formula for bias cannot, so you use the MAE, mean absolute error. Idem for SEE, it is the standard deviation of the error, not the standard deviation of the ABLH.

Ln 257: note that Steeneveld et al. (2007) used the median of the absolute error is evaluation metric in a similar type of study. This is helpful to avoid that the error statistics are determined strongly by one or two outliers. Please consider this as well.

Figure 3: it is unclear whether the error statistics in the left upper corner relate to the CBL or SBL data. It would be interesting to have the statistics for both classes, to underline the score for SBL is much poorer.

Figure 3c and d: I do not understand why the H_obs is different for the SBL and the CBL for the two panels. Please explain, the filtering was done on the observation, wasn’t it? Not on the selected algorithm. Also add the number of samples in the block with error statistics.

Ln 296: Note again that VH96 do use a different definition of Ri.

Ln 302: This result is distinct from that of Jozef et al. (2022). Add how it is distinct....?

Ln 303: might be that ... different... ->Better to figure that out!!! It is related to the key of this paper.

Ln 328: from 13 April through to 24 May 2020. In this period, the convectively thermal structure contributes to ABLH reaching over 610 m for about 6 days, with the maximum ABLH of 1152 m: This is the period with a warm intrusion from the south, so the PBL height is likely strongly governed by the advection of warm air, its turbulent kinetic energy, and its stratification. Equation 2 was not developed for such conditions, so it is fair to evaluate it as such?

Ln 366: I am little surprised that the theta_E appears here in the analysis, while it is not reasoned why we step over from theta to theta_E. I agree that theta_E analysis is valuable, but should theta_E not have been applied to Equation 2?

Figure 7: Add in the legend whether these are the monthly averages of the soundings from 5:00, or 11:00, or 17:00, or 23:00, or all mixed together. It is better to stick to one time slot to avoid that the effects of the diurnal cycle in the summer months are mixed away.

Ln 395: temperature gradient. Better to use (equivalent) potential temperature gradient to remain consistent with the above.

Ln 396: u*, * should be subscripted (twice). And in the rest of the manuscript.

Figure 8a and c: The R value in the plot is an estimate for the LINEAR correlation between the two variables, but obviously the relation is not linear. So better to remove it, or first do a transformation on the data such that the relation between them becomes linear.    

Figure 8b: it is interesting to note that the ABLH is about 700xu*, which was also found/discussed in Vogelezang and Holtslag (1996) and Steeneveld et al. (2007). Both studies also explore ABLH=10u*/N as ABLH estimate, it would be interesting to be tested here as well.

Fig 9, caption: wind speed -> horizontal wind speed

Fig 10: Figure 10 Similar to Fig. 9, but the period is from 15 July 2020 to 30 August 2020. Legend is likely wrong since the x axis goes surely beyond September 1^st.