An LES Exploration of the Assumptions used in Retrieving Entrainment from a Mixing Diagram Approach with Ground-Based Remote Sensors

Rosenberger, Tessa E.; Heus, Thijs; Raghunathan, Girish N.; Turner, David D.; Wagner, Timothy J.; Simonson, Julia M.

doi:https://doi.org/10.5194/egusphere-2024-2894

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https://doi.org/10.5194/egusphere-2024-2894

Preprints

28 Oct 2024

| 28 Oct 2024

An LES Exploration of the Assumptions used in Retrieving Entrainment from a Mixing Diagram Approach with Ground-Based Remote Sensors

Tessa E. Rosenberger, Thijs Heus, Girish N. Raghunathan, David D. Turner, Timothy J. Wagner, and Julia M. Simonson

Abstract. Entrainment is a crucial component of the atmospheric boundary layer (BL) moisture and heat budget. While usually thought of as only entrainment flux, entrainment within the mixed layer budget equation is really composed of two terms: the flux of a property across the boundary separating the BL from the free troposphere and the change in the concentration of a property as the depth of the BL changes. In a recent study, Wakefield et al. (2023) used ground-based remote sensing observations to estimate entrainment flux as the residual of a mixing diagram framework that was applied to the daytime convective boundary layer. This present work uses LES to examine how well this residual assumption for entrainment fluxes alone compares to the actual sum of those two entrainment terms derived from spatial averages of the LES output. We highlight the importance of the second entrainment term in closing the mixed layer budget and show that the residual assumption does not represent entrainment flux only but rather a total entrainment term when the boundary layer depth is changing.

Received: 16 Sep 2024 – Discussion started: 28 Oct 2024

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Journal article(s) based on this preprint

07 Oct 2025

A large-eddy simulation exploration of the assumptions used in retrieving entrainment from a mixing diagram approach with ground-based remote sensors

Tessa E. Rosenberger, Thijs Heus, Girish N. Raghunathan, David D. Turner, Timothy J. Wagner, and Julia M. Simonson

Atmos. Meas. Tech., 18, 5129–5140, https://doi.org/10.5194/amt-18-5129-2025,https://doi.org/10.5194/amt-18-5129-2025, 2025

Short summary

Tessa E. Rosenberger, Thijs Heus, Girish N. Raghunathan, David D. Turner, Timothy J. Wagner, and Julia M. Simonson

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2024-2894', Anonymous Referee #1, 07 Jan 2025

This study investigates the assumptions of the mixing diagram (MD) approach when used to estimate entrainment (ENT) into the boundary layer (BL) from ground-based remote sensing by using LES single columns as proxies for these observations. The main assumption analyzed is that the residual of the MD can be used to represent the entrainment flux across the top of the BL. The authors show that for these simulations, the residual term not only represents the entrainment flux, called ENT1 in the text, but also a second term that takes into account the change in concentration of a given atmospheric property as the BL depth changes, called ENT2. The authors show that this second term, ENT2, is crucial in understanding the contribution of entrainment to mixed layer energy budgets, especially when the BL is in a growth phase (such as during the morning hours). Additionally, the authors analyze three separate approaches for calculating BL depth, and show that the using neutral buoyancy approach in the MDs leads to the most accurate estimation of the domain-mean ENT when just using output from a single column of the LES. Finally, the authors show that the estimation of domain-mean LES properties is improved when averaging over multiple columns when compared to only using a single column. I think the impact of this result could be highlighted more in the conclusions, as it shows that observations of spatial statistics could be much improved by just adding a few more ground-based observation sensors, as opposed to only using one, and could be useful for future observational studies.
After review, I recommend that this document be accepted after undergoing minor revisions. I think the science is looks good and is well-written. It constitutes a valuable addition to the journal, however, there are some points that need to be explained in more detail and with more justification, as well as some reorganizing that could be done to improve readability.
Minor comments
L35-41: There appears to be some inconsistencies in this equation and the definitions of each term that follows. There is a negative sign in front of the ENT1 flux term in eqn. (1), however, in the definition below (L41) this minus sign is absent, which is correct? Furthermore, in the last term in equation one, <φ_bar> is used to represent an averaged mixed layer property, but below, φ_ml is used. I would just pick one and be consistent.
L46-48: I think the end of this paragraph could benefit from a small explanation or example of what ENT2 means physically. ENT1 is explained fairly easily, as simply the flux of one property from the free troposphere into the BL. They explain it further down in L63 as a concentration change as the BL depth changes, but it might aid readability if this explanation was moved up here, or repeated here. I found myself not understanding what ENT2 was until I got to this explanation in L63.
L83-84: The authors state that MDs are usually only used when the BL is well-mixed. In my opinion, this seems to muddle some of the later conclusions which highlight the importance of ENT2 in the morning growth phase. The BL is not always well-mixed, especially early in the morning when growth is fastest. I would add a caveat for this in the conclusions, or provide some justification that for these days, the BL is well-mixed during the analysis period if it is.
L97: I would remove the sentence here about the GPU and its effect on LES runtime. It doesn't seem relevant. I also think it could lead the reader to be skeptical and ask questions like: "If the LES runs so much faster than others, why didn't they do even more runs?"
L108: I know that the lower BCs are prescribed from VARANAL, but are they spatially homogeneous or heterogeneous (i.e. does each grid cell feel the same domain-mean fluxes)? I think this is key to the results, as spatial heterogeneity at the surface can significantly affect BL development over a domain of this size. If the domain is homogeneous, I would also add a caveat to the conclusions stating how they could change if spatial heterogeneity was included at the land-atmosphere interface.
L111: Why was 6400 m domain size chosen? This is a lot smaller than most climate model grid cells. Are you intending to help improve higher resolution models used for numerical weather prediction? Since the LES is used as a proxy over a spatial domain, what is the proxy meant to represent? Maybe I am reading into this too much, but I think you should justify your choices for domain size and resolution more with another sentence or two.
L139: The term "entrainment zone" is used without being defined, I have an idea of what it means, but any reader might not be entirely sure without a solid definition. I would add a sentence to do that.
Figure 5: This figure is a little confusing/overwhelming at first glance, and the key doesn't help much. This is just a suggestion, but I think it would be easier to understand if the days were the variable that was color-coded, and the type of BL depth method used was represented by the different shapes (the reverse of what is used now). That way, you could have a much simpler key which just stated which day was what color, and which method was one of the three chosen shapes, I don't think you need to have a line for each symbol/color combination in the key. This would get rid of the long key used presently, which has many repeated terms and in my opinion only confuses the reader more initially.
L179-181: You say that the cluster around the full z_i method is "tighter", however its hard for me to conclude this based on the figure alone. It might just look tighter because the dots you use for the full method are larger than the "+" signs used for the restricted. I think finding a way to quantify this clustering would strengthen this argument, and help in justifying choosing the full method over the restricted method.
L194: This is nitpicky, but you say that the two averages are "the same", however, in the figure they look very close, but not the same. I would change this wording to reflect this.
L195-199: I don't really understand the point the authors are trying to make here. How do the orange and purple points show that there is "perfect closure" for the latent heat flux in the morning? And the next sentence, how do they show that the "the average single column performs better than the full array"? I think reasoning needs to be explained more or maybe reworded, because as it is right now these two sentences confused me.
L207: This is just for clarity, I would add in the word "multiple" before profilers. So the sentence would read "...using multiple profilers, rather than one..."
Figure 9: Why not differentiate day by color or symbol here? Like in Figure 5.
L233: "The greater amount of sampling error in latent heat is expected because it is more sensitive to the variability at z_i..." I think this needs more explanation. LH is more sensitive to the variability of what? And why is this expected? Why is the LH more sensitive to this variability? Is there a previous study you could cite for this?
L247-249: I think you could highlight this conclusion a little more, and go into more detail on its impact on future observational studies.

Citation: https://doi.org/10.5194/egusphere-2024-2894-RC1
- AC1: 'Reply on RC1', Tessa Rosenberger, 23 Mar 2025
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-2894/egusphere-2024-2894-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2024-2894-AC1
RC2:
'Comment on egusphere-2024-2894', Anonymous Referee #2, 17 Feb 2025

The article is motivated by the need to accurately model the boundary layer entrainment flux and changes in the property concentration due to entrainment in the budget of scalar property equations for use in numerical weather prediction models.
The authors aim to robustly estimate the entrainment fluxes from ground based remote sensing instruments. To this effect, the validity of the residual assumption used by Wakefield et al 2023 (W23) is investigated over the course of the evolving BL using LES framework, and a reinterpretation of the mixing diagram method presented in W23 is offered.
The scientific method, the results, and the discussions that follow are compelling. However, the article suffers from a few minor shortcomings that hamper readability. I recommend that the authors carefully consider below listed minor suggestions/revisions in their resubmission to the journal:
- Line 53-55: "Because of the vertical resolution of the profiling instruments used in W23, they computed the mean of the mixed layer properties only from 0.1zi−0.5zi, where zi is the depth 55 of the BL determined from the TROPoe retrievals using a parcel method". Please clarify what is the instrument vertical resolution. Is this superior to the LES resolution? Do the authors wish to suggest that the data resolution used by W23 is insufficient to resolve the BL? I fail to understand the point of this statement.
- Line 67: MD here is used without defining the abbreviation. The abbreviation is defined in section 2.1. Please move the definition of MD to line 67 instead for clarity.
- The end of section 1 could very much use a breakdown of the article sections to guide the reader through the document.
- A nearly periodic drop in the BL depth is observed when minimum potential temperature flux method is considered for single column (left plot of figure 2). See at times 0930, 1030, 1130, 1230, and 1400 hour time stamps. Is there an obvious explanation for such an observation? Such a systematic trend could potentially affect the relative magnitudes of ENT1 and ENT2 for single column data and brings into question the representativeness of the BL depth estimate using the minimum potential temperature flux method. (Overall, section 2 is well designed to crisply convey the investigation methodology).
- Are ENT1 and ENT2 estimates presented in Figure 5 computed from single-column data, slab averaged data, or average of the equidistantly placed columns? Please specify this upfront when describing figure 5. (If such a detail was already resented in section 2 earlier, ignore this comment).
- Further, in figure 5: There appears to be no systematic trend in the ENT1/(ENT1+ENT2) ratios using the three methods even in the afternoon data when compared across the 5 different days. For instance: for days represented by the square and circles, the BL estimated using the maximum humidity variance seems to provide consistently the smallest ratio of ENT1/(ENT1+ENT2) while the BL depth estimated using level of neutral buoyancy provides the largest ratios. Is there a specific reason as to why such a trend is not observed for the other 3 days?
- Lines 179-181 are vague. "Slightly better job" is purely qualitative here. It is hardly distinguishable from visual inspection of figure 6, especially in the afternoon data. Some effort to quantify such a difference would be more defensible and provide further evidence to the use of full zi as a proxy for the mixed layer.
- I fully concur with RC1's comments that lines 193-196 are confusing and need a revision. This is only clear after reading it numerous times, but not readily intuitive from visual inspection. A brief explanation here is warranted.
- The mean closures presented for August 17th dataset appears as a clear outlier. Is there a specific reason for this?
- In figure 9 it is not possible to differentiate between the different days of the dataset. It would be nice to differentiate the legends of the closure estimates for average of single columns for clarity.
- Lines 221-223: "ENT2 is larger the higher in the entrainment zone the BL depth definition." This sentence doesn't make sense to me. What do the authors intend to say here?
I recommend that the article be published subject to the authors addressing the above mentioned minor suggestions/revisions.

Citation: https://doi.org/10.5194/egusphere-2024-2894-RC2
- AC2: 'Reply on RC2', Tessa Rosenberger, 23 Mar 2025
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-2894/egusphere-2024-2894-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2024-2894-AC2

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2024-2894', Anonymous Referee #1, 07 Jan 2025

This study investigates the assumptions of the mixing diagram (MD) approach when used to estimate entrainment (ENT) into the boundary layer (BL) from ground-based remote sensing by using LES single columns as proxies for these observations. The main assumption analyzed is that the residual of the MD can be used to represent the entrainment flux across the top of the BL. The authors show that for these simulations, the residual term not only represents the entrainment flux, called ENT1 in the text, but also a second term that takes into account the change in concentration of a given atmospheric property as the BL depth changes, called ENT2. The authors show that this second term, ENT2, is crucial in understanding the contribution of entrainment to mixed layer energy budgets, especially when the BL is in a growth phase (such as during the morning hours). Additionally, the authors analyze three separate approaches for calculating BL depth, and show that the using neutral buoyancy approach in the MDs leads to the most accurate estimation of the domain-mean ENT when just using output from a single column of the LES. Finally, the authors show that the estimation of domain-mean LES properties is improved when averaging over multiple columns when compared to only using a single column. I think the impact of this result could be highlighted more in the conclusions, as it shows that observations of spatial statistics could be much improved by just adding a few more ground-based observation sensors, as opposed to only using one, and could be useful for future observational studies.
After review, I recommend that this document be accepted after undergoing minor revisions. I think the science is looks good and is well-written. It constitutes a valuable addition to the journal, however, there are some points that need to be explained in more detail and with more justification, as well as some reorganizing that could be done to improve readability.
Minor comments
L35-41: There appears to be some inconsistencies in this equation and the definitions of each term that follows. There is a negative sign in front of the ENT1 flux term in eqn. (1), however, in the definition below (L41) this minus sign is absent, which is correct? Furthermore, in the last term in equation one, <φ_bar> is used to represent an averaged mixed layer property, but below, φ_ml is used. I would just pick one and be consistent.
L46-48: I think the end of this paragraph could benefit from a small explanation or example of what ENT2 means physically. ENT1 is explained fairly easily, as simply the flux of one property from the free troposphere into the BL. They explain it further down in L63 as a concentration change as the BL depth changes, but it might aid readability if this explanation was moved up here, or repeated here. I found myself not understanding what ENT2 was until I got to this explanation in L63.
L83-84: The authors state that MDs are usually only used when the BL is well-mixed. In my opinion, this seems to muddle some of the later conclusions which highlight the importance of ENT2 in the morning growth phase. The BL is not always well-mixed, especially early in the morning when growth is fastest. I would add a caveat for this in the conclusions, or provide some justification that for these days, the BL is well-mixed during the analysis period if it is.
L97: I would remove the sentence here about the GPU and its effect on LES runtime. It doesn't seem relevant. I also think it could lead the reader to be skeptical and ask questions like: "If the LES runs so much faster than others, why didn't they do even more runs?"
L108: I know that the lower BCs are prescribed from VARANAL, but are they spatially homogeneous or heterogeneous (i.e. does each grid cell feel the same domain-mean fluxes)? I think this is key to the results, as spatial heterogeneity at the surface can significantly affect BL development over a domain of this size. If the domain is homogeneous, I would also add a caveat to the conclusions stating how they could change if spatial heterogeneity was included at the land-atmosphere interface.
L111: Why was 6400 m domain size chosen? This is a lot smaller than most climate model grid cells. Are you intending to help improve higher resolution models used for numerical weather prediction? Since the LES is used as a proxy over a spatial domain, what is the proxy meant to represent? Maybe I am reading into this too much, but I think you should justify your choices for domain size and resolution more with another sentence or two.
L139: The term "entrainment zone" is used without being defined, I have an idea of what it means, but any reader might not be entirely sure without a solid definition. I would add a sentence to do that.
Figure 5: This figure is a little confusing/overwhelming at first glance, and the key doesn't help much. This is just a suggestion, but I think it would be easier to understand if the days were the variable that was color-coded, and the type of BL depth method used was represented by the different shapes (the reverse of what is used now). That way, you could have a much simpler key which just stated which day was what color, and which method was one of the three chosen shapes, I don't think you need to have a line for each symbol/color combination in the key. This would get rid of the long key used presently, which has many repeated terms and in my opinion only confuses the reader more initially.
L179-181: You say that the cluster around the full z_i method is "tighter", however its hard for me to conclude this based on the figure alone. It might just look tighter because the dots you use for the full method are larger than the "+" signs used for the restricted. I think finding a way to quantify this clustering would strengthen this argument, and help in justifying choosing the full method over the restricted method.
L194: This is nitpicky, but you say that the two averages are "the same", however, in the figure they look very close, but not the same. I would change this wording to reflect this.
L195-199: I don't really understand the point the authors are trying to make here. How do the orange and purple points show that there is "perfect closure" for the latent heat flux in the morning? And the next sentence, how do they show that the "the average single column performs better than the full array"? I think reasoning needs to be explained more or maybe reworded, because as it is right now these two sentences confused me.
L207: This is just for clarity, I would add in the word "multiple" before profilers. So the sentence would read "...using multiple profilers, rather than one..."
Figure 9: Why not differentiate day by color or symbol here? Like in Figure 5.
L233: "The greater amount of sampling error in latent heat is expected because it is more sensitive to the variability at z_i..." I think this needs more explanation. LH is more sensitive to the variability of what? And why is this expected? Why is the LH more sensitive to this variability? Is there a previous study you could cite for this?
L247-249: I think you could highlight this conclusion a little more, and go into more detail on its impact on future observational studies.

Citation: https://doi.org/10.5194/egusphere-2024-2894-RC1
- AC1: 'Reply on RC1', Tessa Rosenberger, 23 Mar 2025
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-2894/egusphere-2024-2894-AC1-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2024-2894-AC1
RC2:
'Comment on egusphere-2024-2894', Anonymous Referee #2, 17 Feb 2025

The article is motivated by the need to accurately model the boundary layer entrainment flux and changes in the property concentration due to entrainment in the budget of scalar property equations for use in numerical weather prediction models.
The authors aim to robustly estimate the entrainment fluxes from ground based remote sensing instruments. To this effect, the validity of the residual assumption used by Wakefield et al 2023 (W23) is investigated over the course of the evolving BL using LES framework, and a reinterpretation of the mixing diagram method presented in W23 is offered.
The scientific method, the results, and the discussions that follow are compelling. However, the article suffers from a few minor shortcomings that hamper readability. I recommend that the authors carefully consider below listed minor suggestions/revisions in their resubmission to the journal:
- Line 53-55: "Because of the vertical resolution of the profiling instruments used in W23, they computed the mean of the mixed layer properties only from 0.1zi−0.5zi, where zi is the depth 55 of the BL determined from the TROPoe retrievals using a parcel method". Please clarify what is the instrument vertical resolution. Is this superior to the LES resolution? Do the authors wish to suggest that the data resolution used by W23 is insufficient to resolve the BL? I fail to understand the point of this statement.
- Line 67: MD here is used without defining the abbreviation. The abbreviation is defined in section 2.1. Please move the definition of MD to line 67 instead for clarity.
- The end of section 1 could very much use a breakdown of the article sections to guide the reader through the document.
- A nearly periodic drop in the BL depth is observed when minimum potential temperature flux method is considered for single column (left plot of figure 2). See at times 0930, 1030, 1130, 1230, and 1400 hour time stamps. Is there an obvious explanation for such an observation? Such a systematic trend could potentially affect the relative magnitudes of ENT1 and ENT2 for single column data and brings into question the representativeness of the BL depth estimate using the minimum potential temperature flux method. (Overall, section 2 is well designed to crisply convey the investigation methodology).
- Are ENT1 and ENT2 estimates presented in Figure 5 computed from single-column data, slab averaged data, or average of the equidistantly placed columns? Please specify this upfront when describing figure 5. (If such a detail was already resented in section 2 earlier, ignore this comment).
- Further, in figure 5: There appears to be no systematic trend in the ENT1/(ENT1+ENT2) ratios using the three methods even in the afternoon data when compared across the 5 different days. For instance: for days represented by the square and circles, the BL estimated using the maximum humidity variance seems to provide consistently the smallest ratio of ENT1/(ENT1+ENT2) while the BL depth estimated using level of neutral buoyancy provides the largest ratios. Is there a specific reason as to why such a trend is not observed for the other 3 days?
- Lines 179-181 are vague. "Slightly better job" is purely qualitative here. It is hardly distinguishable from visual inspection of figure 6, especially in the afternoon data. Some effort to quantify such a difference would be more defensible and provide further evidence to the use of full zi as a proxy for the mixed layer.
- I fully concur with RC1's comments that lines 193-196 are confusing and need a revision. This is only clear after reading it numerous times, but not readily intuitive from visual inspection. A brief explanation here is warranted.
- The mean closures presented for August 17th dataset appears as a clear outlier. Is there a specific reason for this?
- In figure 9 it is not possible to differentiate between the different days of the dataset. It would be nice to differentiate the legends of the closure estimates for average of single columns for clarity.
- Lines 221-223: "ENT2 is larger the higher in the entrainment zone the BL depth definition." This sentence doesn't make sense to me. What do the authors intend to say here?
I recommend that the article be published subject to the authors addressing the above mentioned minor suggestions/revisions.

Citation: https://doi.org/10.5194/egusphere-2024-2894-RC2
- AC2: 'Reply on RC2', Tessa Rosenberger, 23 Mar 2025
  
  The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2024/egusphere-2024-2894/egusphere-2024-2894-AC2-supplement.pdf
  
  Citation: https://doi.org/10.5194/egusphere-2024-2894-AC2

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload

AR by Tessa Rosenberger on behalf of the Authors (23 Mar 2025) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (09 Apr 2025) by Marcos Portabella

RR by Anonymous Referee #2 (09 Apr 2025)

ED: Publish as is (29 May 2025) by Marcos Portabella

AR by Tessa Rosenberger on behalf of the Authors (08 Jun 2025)

Journal article(s) based on this preprint

07 Oct 2025

A large-eddy simulation exploration of the assumptions used in retrieving entrainment from a mixing diagram approach with ground-based remote sensors

Tessa E. Rosenberger, Thijs Heus, Girish N. Raghunathan, David D. Turner, Timothy J. Wagner, and Julia M. Simonson

Atmos. Meas. Tech., 18, 5129–5140, https://doi.org/10.5194/amt-18-5129-2025,https://doi.org/10.5194/amt-18-5129-2025, 2025

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Tessa E. Rosenberger, Thijs Heus, Girish N. Raghunathan, David D. Turner, Timothy J. Wagner, and Julia M. Simonson

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Entrainment is key in understanding temperature and moisture changes within the boundary layer, but it is difficult to observe using ground-based observations. This work used simulations to verify an assumption that simplifies entrainment estimations from ground-based observational data, recognizing that entrainment is the combination of the transfer of heat and moisture from above the boundary layer into it and the change in concentration of heat and moisture as boundary layer depth changes.


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An LES Exploration of the Assumptions used in Retrieving Entrainment from a Mixing Diagram Approach with Ground-Based Remote Sensors

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