Summary: This study uses co-planar Doppler lidar observations in an across-valley transect during the CROSSINN campaign to (a) present a new approach for estimating the boundary layer depth and (b) applies these lidar observations along with other contextualizing field observations to describe variations in the MoBL structure and evolution. The new boundary layer depth approach relies on merged co-planar observations of the Doppler spectrum width, which is useful for evaluating CBL turbulence irrespective of the scan angle and thus overcomes limitation with other velocity based approaches that work for single column lidar observation but not RHIs. The analysis of the MoBL evolution reveals a mix of expected and unexpected features including terrain following CBLs, persistent thermalling features, and lowering Foehn flows, to name a few.

Overall comments:

The paper contains a number of useful and fascinating observations and techniques, but also suffers from a mix of focus on (a) a new technique and (b) trying to decipher MoBL physical processes. Broadly speaking I find the following strengths and weaknesses:

Strengths:

• The use of the merged spectrum width to infer spatial variability in turbulent mixing is a strong contribution to the field of mountain boundary layer observations and alone warrants publication of this work. This approach overcomes the limitation of either using (a) single vertical velocity variance profiles above a fixed site, or (b) requiring dual-Doppler retrievals of the vertical wind, which can not yield the same spatially continuous coverage of the valley atmosphere.
• The paper clearly demonstrates that these merged spectrum width data reveal important spatially and temporally varying aspects of the MoBL that are not otherwise possible. The content of the individual figures is stimulating and informative, as is the analysis of them, which gets at many of the complexities of the MoBL as compared to its flat terrain counter part.

Weaknesses:

• The bottom up thresholding approach clearly has limitations, many evidenced in the analyses presented and some discussed by the authors. This is especially true in the presence of elevated turbulence sources. At times the approach seems to work great (e.g., Fig. 9a-f, h) whereas at other critical times it does not (e.g., Fig. 9g). Other examples of it not working well include the jumps in Zi apparent in Fig. 5a where the algorithm couples to the elevated layers aloft. This is not to say the approach isn’t useful, it just adds another approach that suffers from many of the problems we always encounter in defining Zi.
• The approach is not all that well “validated” or “calibrated”. Most of what you present are fairly loose comparisons with other imperfect observations (e.g., radiosondes, Rb, etc). This lack of rigor is somewhat unavoidable, but undermines the efficacy of the paper as a demonstration of technique in that the results are far from universal.
• The paper is long and somewhat sprawling trying to accomplish two things at once (a) a technique demonstration and (b) a process-focused study. It leaves me wondering if splitting it into a technique paper and a process paper would be best. I’ll defer to the authors and input from other reviewers on this, as I understand the motivation to merge the two. I ran a quick word count on this, and I think (could be wrong) that you’re well over 10,000 words (probably 11-12,000). Many Journals try to keep word limits to ~7500. In reading the text I estimate you could probably remove up to ¼ of the total words and significantly improve the readability and conciseness of your manuscript.  

Overall evaluation: I’d recommend minor revisions with a focus on addressing specific points enumerated below and an overall shortening/tightening of the manuscript where possible, or splitting into two if deemed appropriate.

Specific Comments:

• Can you please specify what the units of the spectrum width are? I was assuming this was the Doppler spectrum width, thus representing the ranger of Doppler velocities sampled inside a lidar volume (pencil beam). It looks like your units are a.u.? I apologize for my ignorance, but I’m not familiar with what the a.u. unit is with respect to measured spectrum width. I’d have thought the units would be m/s?
• Lines 173-180: I don’t understand why shear effects are separate from the true or measured value? How are they separable here?
• Line 183: A fundamental question: if the spectrum width is related the range of observed Doppler velocities in a sample time/volume then are there expected to be differences as a function of elevation angle in an RHI for non-isotropic turbulence? In other words if the flow is a convective CBL with positively skewed vertical velocity you probably get a rather different spectrum width for the near horizontal vs near vertical parts of the RHI. Has this been explored? Is it an important consideration in merging the RHI scans?
• Section 2.4: I would recommend changing the title of this subsection to something more like “comparing spectrum width and vertical velocity”. I was expecting some sort of statistical validation, whereas you provide a qualitative comparison (which is certainly still useful and worthwhile).
• Line 233: I don’t understand the meaning of “1 hour intervals shifted forward by 10 minutes can you clarify”? Does this mean you take hour long averages every 10 minutes?
• Line 235: What is a.u.? Here and elsewhere.
• Line 242: errant apostrophe?
• Line 266: This threshold (1100 m) gives me pause. I fully appreciate that these definitions always require range checks and thresholds but 1100 m seems well within the range of potential CBL depths in the MoBL… this approach discards any possibly deeper CBLs and preclude the application of the technique across a broader data set or other locations. I think you’re safe here in that your results are reproducible for this particular study, but it will undermines broadness of the use of this technique.
• 4. These data look promising, but it would be interesting to know how much better or worse the RMSE values were for other combinations? For example was the 12 point theta average not wildly different, or pretty similar? What about 3 points?
• 5a. In panel a, your CBL height ID on the left edge (~-2200 m) jumps up to the elevated spectrum width layers. Is this physical or not? Likewise at 2100 m (to the right) the blue dots jump to the elevated feature despite passing through a minima is spectrum width above the shallower near surface high SW layer. How do you interpret this result? I’m aware how tricky these threshold approaches are, and am supportive of the overall approach, it just seems there are some difficulties in its universal application (as with other approaches, the problem is not unique to you).
• Line 316: I’m not sure that a “mature CBL” is a defined concept, and if it were I probably wouldn’t associate it with being decoupled, but rather strongly coupled. Consider rewording or specifying what you mean by mature?
• Line 318: what allows you to characterize this elevated turbulence as convectively driven. Its decoupled nature would seem to suggest it has a non-surface based origin. Is it possibly mechanically generated? How do you know?
• Line 325: These seem like very broad features to be convectively driven (1.5 km in width). Are they perhaps wave driven? Or waves coupled to the CBL top?
• Line 333-334: But the cross section doesn’t show any coupling to the surface, so it is either not representative of the valley as a whole, or these are a not coupled to the surface? I’m a bit confused here.
• 8. We can again see some of the issues with the bottom-up threshold approach where your algorithm seems to jump to elevated layers (e.g., Fig. 8b at ~1600-1700 UTC), or wherein there are strong elevated sources of spectrum width not driven by CBL processes (e.g. strong winds aloft). This also gets at the issue of the 1100 m height threshold imposed… there seems to be coupling processes at play that *could* produce deeper convectively (or shear and convective) boundary layer depths).
• Line 468: This is a really interesting persistent thermal plume feature. Really underscore how nice the merged RHI data are for examining the MoBL.
• 9. This figure is fantastic and provides all sorts of interesting details about the structure of the MoBL, including both terrain following and non-terrain following components of the MoBL structure, cross valley asymmetries (e.g., Fig. 9d).
• Line 497: I’m a bit confused by the surface following high spectrum width feature and your description. First, just to be clear, is this evidence of a near surface up or down valley flow? Second, this feature is so strongly terrain following I’m almost confused by it. What does a radiosonde wind profile look like at this time? Does it show a low-level jet feature near the surface?
• Lines 540-546: Seems odd to start a conclusions with a bunch of caveats. I’d recommend revising this section and focusing on what you have established. The rest of the paper addresses the nuances.

Overview

This manuscript introduces a novel method to retrieve the convective boundary layer (CBL) height from coplanar Lidar scans. The scan data is availbale from the CROSSINN campaign, which took place in an Alpine Valley to study, among other mountain boundary layer (MoBL) phenomena, the cross-valley wind circulation. The new method to determine the CBL height is described over around 8 pages of the manuscript (excluding Figures) and gives a detailed overview of the necessary assumptions to extract the CBL height information from the measurements, which can be considered as a first part. In the second part (Section 3 onwards), the authors describe the varibility over space and time of selected ABL variables influencing the CBL height. Finally, they identify distinct regimes of MoBL (spatial) evolution determined from four selected intensive observation periods (IOPs). This work substantially contributes to the rich body of boundary-layer research in the Inn Valley and highlights the complexity of mountain boundary layers (again). Unfortunately, the manuscript reads more like a measurement report than a paper manuscript, because the authors leave many questions open, while they could have answered them by extracting more information from the CROSSINN and i-Box datasets.

Major comments

1. The authors try to bridge the gap between introducing a new method to determine the CBL height by analyzing the measurement data to gain new knowledge on the boundary-layer evolution in the Inn Valley, Austria. Since the explanation of the method is complex, this already takes almost half of the entire manuscript, which is very long, as a previous referee already pointed out. The extensive description of a measurement setup is likely out of scope for Weather and Climate Dynamics: The detailed description and proof of concept likely fit better in other Copernicus journals as  Geoscientific Instrumentation, Methods and Data Systems (GI) or Atmospheric Measurement Techniques (AMT). At AMT, there is even a well-fitting special issue open right now: "Profiling the atmospheric boundary layer at a European scale" (https://amt.copernicus.org/articles/special_issue1209.html). Please consider a split of the manuscript, and then you can focus in the current WCD manuscript almost solely on the boundary-layer dynamics part. Henceforth, the major part of my review will focus on the interpretation and results from Section 3 and onwards.
2. The second part is written in an almost chaotic way. The authors assume that the reader already knows a lot about (i) the Inn Valley and surroundings, (ii) the local boundary layer development, and (iii) read all the previous publications of the CROSSINN campaign (e.g., different IOPs are mentioned, but there is no description on which processes were actually at play or that actually happened in  the IOPs). This makes it difficulat to understand the relevant phenomena at play.
3. Furthermore, the authors leave a lot of questions open. On the one hand, they could answer them easily instead of speculating (e.g., using observations of radiosondes or the eddy covariance towers, or aircraft data), and on the other hand, they could extend their comparison to more IOPs (e.g., in Section 3.4) or add a fifth IOP with less synoptic influence (e.g., IOP10). If the authors choose to split their manuscript, this can be easily achieved.
4. Comparison with other work and lack of discussion - the comparison with real-case and idealized simulations is of course valid, especially when there is a lack of previous observations. However, I wonder why the authors complexely omit a comparison with other measurement campaigns, e.g., Hymex (Adler and Kalthoff, 2014, 2016); MAP-Rivera (Rotach et al, 2007, and their previous papers on the topic), T-REX  observations and simulations (Strauss et al, 2015; Babic et al, 2019), and PIANO on foehn flows (Haid et al, 2020, 2021) to put their results into context. 

To make the manuscript fit within the scope of WCD, the following possible questions could be answered:

• Is there such a thing as an "ideal CBL development" in complex terrain?
• (already partly answered) Which processes lead to a non-ideal CBL development? Typical MoBL processes due to the underlying terrain such as up-valley winds, slope flows, and the plain-to-mountain circulation, or other, larger scale influence (e.g., chanelling, foehn flows)?
• Does the new CBL height determination method help us to untangle this complex flow structure, or does it raise new open questions? Is a regime classification with schematic diagrams possible, as in, e.g., Haid et al (2022)?
• Why does a diagnostic of the CBL height give insight on the general dynamics in the Inn Valley? Unfortunately, the diagnostic only seems to work before noon, when buoyancy is the dominant production process for TKE production.
• What is the essential take-away when we can finally diagnose the CBL height not only in the vertical, but also in space?

Minor comments

• line 29: The substantial importance of horizontal shear was also shown by Goger et al (2018).
• line 24: "will lead" [...] "leading" please reformulate
• lines 30-48: This paragraph can easily be shortened towards "MoBLs are complex due to their multi-scale flow strucutre"
• lines 65-76: I am not sure whether the introduction needs this lengthy description on the disadvantages on ceilometers
• Section 3 (or even before): Add a brief summary of the IOPs you are using for this manuscript (parhaps with an overview table of the most relevant information). I know that the IOPs are described extensively in previous publications, but a summary is necessary for the interested reader here to udnestand the rest of the manuscript.
  
  Here would be the opportunity to briefly discuss the differences between the single IOPs. If they are all similar, describe a typical diurnal cycle in the Inn valley (perhaps with a concept graph?) to prepare the reader on what to expect in the next chapters.
• line 345: Which IOPs experience which large-scale forcings? Please elaborate.
• line 355: "the prevalence of downvalley flows at night": Looking at Fig. 7b, only IOP2b shows persistent down-valley flows during the night. Up-valley flows during the night are not typical for days, when the diurnal valley wind circulation dominates in the Inn Valley (e.g, Goger et al 2018, Lehner et al, 2019). 
  
  Follow-up, what are the reasons that there are no down-valley flows in all the other (chosen) IOPs?
• line 357: "synoptic foehn influence": This is the first occasion in the manuscript where you mention foehn winds at all. Please describe them and their potential impact on the Inn vally boundary layer at an earlier opportunity (e.g., beginning of section 3 where you could outline the diurnal cycle in the valley and potential synoptic influcenes). Furthermore, Plavcan's foehn diagnostic applies to the city of Innsbruck, 30km west of the I-Box area. How can you make sure that this diagnostic can be also apllied to the I-Box station? Did you check, e.g., the upstream slope stations Weerberg and Hochhaeuser?
• line 365: Previous studies from the Rivera Valley (Weigel and Rotach, 2004) suggest that sensible heat fluxes (H) from slopes might have a larger impact on the valley boundary layer structure than H from the valley floor. Why do the authors only elaborate on the valley floor H, while there are observations from the other i-Box stations (e.g., Terfens, Eggen, Hochhäuser)?
• line 367: Early turn of sensible heat fluxes: Can this turn of sensible heat fluxes also be connected to advection processes by the valley winds, a similar processes as negative SH fluxes during strong foehn flow (Umek et al (2021), their Figure 4)? How do you argue the influence of local vegetation when this turn of H was already observed 35 years ago at a different location in the Inn Valley (Vergeiner and Dreiseitl (1987), their Figure 8) or from the Rivera Valley (Rotach et al, 2008, their Figure 5)?
• line 375: "assuming H is the sole driver of the CBL": How sure can we be of that assumption in complex topography? On the one hand, the authors wrote a very lengthy introduiction about the complexity of mountain boundary layers, but in the end they use a column approach with H from a single station, although there are more observations available.
• line 400: Subsidence values are compared to idealized simulations - are there no observations from other campaigns available? What about MAP-Rivera (e.g., Weigel et al, 2006)?
• line 407: The influence of the up-valley wind leads to a stabilization of the Inn Valley boundary layer, visible in previous simulation studies and the CROSSINN radiosonde observations. The term "well-mixed" might not be a fitting choice here.
• line 412: "foehn-driven turbulence": What do you mean with this term? Considering the TKE budget equation, TKE can be generated by buoyancy and/or shear. You can check in the i-Box stations, whether the TKE measurements are similar between your convective and foehn days, and can also calculate bouyancy production and the vertical shear to check on the source of turbulence (at least at Kolsass and Terfens). Furthermore, could you determine TKE (and budget) values from your aircraft observations? 
• line 415: "horizontal convergence of upslope flow branches detaching from the slopes": This is true, but slope flows are likely eroded by the up-valley wind after 12 UTC (Rotach et al, 2008, Goger et al, 2018, their Figs 5 and 7). Furthermore, how sure are you on the development of slope flows in this non-ideal boundary layer in the valley with foehn influence?
• line 418: Instead of speculating, you could check your radiosonde measurements whether they give any information on the mountain-to-plain wind circulation, e.g. by a shift in wind direction above crest height?
• line 435: Now IOP3 is also under a strong foehn influence - Please write in the beginning of Sect. 3, which IOPs have considerate synoptic forcing. Then, the question could be raised, why the authors chose these IOPs for CBL height determination. For example, CROSSINN IOP10, has way less disturbance from synoptic flows.
• line 441: "Increase in specturm width": Just curious, how is this an indicator for turbulence?
• line 474: "up to 200 m deeper above the plateau than over the southern sidewall", Why? Is this due to differential heating? Is H at the South-facing sidewalls larger than at the North-facing slopes?
• line 485: "plateau-locked upslope flows": What do you mean and where do you see this?
• line 492: "low-level upvalley flow jet" ... you mean the jet of the up-valley flow? You can determine the jet maximum from your radiosonde observations?
• line 509: "We will focus only on IOP 2a." Why? It would be an excellent improvement for the manuscript if you would show all four IOPs and then discuss the differences again. This would also highlight the different regimes observed.
• lines 535-539: This was already done by Weigel and Rotach (2004). It would be a valueable insight whether this method of applying a different H also works for the Inn Valley.
• line 532: "given the CVV influence": Is this really just the CVV - or just the up-valley flow?

Figures

• All figures: The front size in the figures varies a lot. Please be consistent.
• Figure 1: You could add somewhere in a small box the general location in the Alps (or Europe).
• Figure 2 (and all future cross-sections in that style): Add South (S) and North (N) on the sides of your figure so that orientation is easier.
• Figure 3: Maybe I've missed it, but what unit is a.u.?
• Figure 4: Please add the day of your IOPs, otherwise the reader can not follow your seasonality argument.
• Fig 7d: What's going on with z_i from IOP2a? Please adjust the range of your figure.
• Fig8: Where do you describe the CBL evolution of Fig8c,d? Is this not worth mentioning?

References

• Adler, B. & Kalthoff, N. Multi-scale Transport Processes Observed in the Boundary Layer over a Mountainous Island, Boundary-Layer Meteorol., 2014, 153, 515-537 
• Adler, B. & Kalthoff, N. The Impact of Upstream Flow on the Atmospheric Boundary Layer in a Valley on a Mountainous Island, Boundary-Layer Meteorol., 2016, 158, 429-452
• Babić, N. & De Wekker, S. F. Characteristics of roll and cellular convection in a deep and wide semiarid valley: A large-eddy simulation study, Atmos. Res., 2019, 223, 74 - 87
• Goger, B.; Rotach, M. W.; Gohm, A.; Fuhrer, O.; Stiperski, I. & Holtslag, A. A. M.: The Impact of Three-Dimensional Effects on the Simulation of Turbulence Kinetic Energy in a Major Alpine Valley, Boundary-Layer Meteorol, 2018, 168, 1-27
• Haid, M.; Gohm, A.; Umek, L.; Ward, H. C.; Muschinski, T.; Lehner, L. & Rotach, M. W.: Foehn-cold pool interactions in the Inn Valley during PIANO IOP2 Q. J. R. Meteorol. Soc., 2020, 146, 1232-1263
• Haid, M.; Gohm, A.; Umek, L.; Ward, H. C.; Muschinski, T.; Lehner, L. & Rotach, M. W.
  
  Foehn-cold pool interactions in the Inn Valley during PIANO IOP2, Q. J. R. Meteorol. Soc., 2020, 146, 1232-1263
• Lehner, M.; Rotach, M. W. & Obleitner, F.: A Method to Identify Synoptically Undisturbed, Clear-Sky Conditions for Valley-Wind Analysis, Boundary-Layer Meteorol., 2019, 173, 435–450
• Rotach, M. W. & Zardi, D.: On the boundary-layer structure over highly complex terrain: Key findings from MAP, Q. J. R. Meteorol. Soc., 2007,  937-948
• Rotach, M. W.; Andretta, M.; Calanca, P.; Weigel, A. & Weiss, A.: Boundary layer characteristics and turbulent exchange mechanisms in highly complex terrain, Acta Geophys., 2008, 56, 194-219 
• Strauss, L.; Serafin, S.; Haimov, S. & Grubišić, V.: Turbulence in breaking mountain waves and atmospheric rotors estimated from airborne in situ and Doppler radar measurements, Q. J. R. Meteorol. Soc., 2015, 141, 3207-3225
• Umek, L.; Gohm, A.; Haid, M.; Ward, H. C. & Rotach, M. W.: Large eddy simulation of foehn-cold pool interactions in the Inn Valley during PIANO IOP2, Q. J. R. Meteor. Soc., 2021, 147, 944-982
• Vergeiner, I. & Dreiseitl, E.: Valley winds and slope winds --- Observations and elementary thoughts. Meteorol. Atmos. Phys., 1987, 36, 264-286
• Weigel, A. P. & Rotach, M. W.: Flow structure and turbulence characteristics of the daytime atmosphere in a steep and narrow Alpine valley, Q. J. R. Meteorol. Soc., 2004, 130, 2605-2627
• Weigel, A. P.; Chow, F. K. & Rotach, M. W.: The effect of mountainous topography on moisture exchange between the “surface” and the free atmosphere, Boundary-Layer Meteorol., 2006, 125, 227-244