Energetically Stringent Quantification of Water Vapor Supersaturation at Cloud Base

Braga, Ramon Campos; Harrison, Daniel; Wendisch, Manfred; Albrecht, Rachel

doi:10.5194/egusphere-2026-795

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https://doi.org/10.5194/egusphere-2026-795

Preprints

17 Feb 2026

| 17 Feb 2026

Energetically Stringent Quantification of Water Vapor Supersaturation at Cloud Base

Ramon Campos Braga, Daniel Harrison, Manfred Wendisch, and Rachel Albrecht

Abstract. We quantify water vapor supersaturation (S_v) at warm cloud base by describing the ascent of a saturated (cloudy) air parcel as a reversible cloud-adiabatic process. In this framework, the parcel’s isobaric enthalpy is conserved along the ascent. The latent heat release (Q) during condensational growth of cloud condensation nuclei (CCN) and droplets is internally redistributed according to the first law of thermodynamics, such that the energy balance is partitioned between the parcel’s internal energy (U) and the saturation work of water vapor (W_s). We find that the fraction of Q associated with ∆U and W_s corresponds to liquid-phase supersaturation (S_l) and S_v, respectively. Closure analyses of airborne measurements at cloud bases of growing cumuli over the Amazon Basin demonstrate that the droplet number concentration N_d scales with S_v and agrees within the uncertainty range with the CCN(S_v) activation spectra measured below cloud base. The new methodology allows the calculation of N_d(S_v) spectra from airborne measurements at cloud bases. Our results suggest that adiabatic models assuming full conversion of phase-change energy into condensational growth tend to overestimate the liquid water content. During the cloud parcel ascent, a finite fraction of this energy is expended as vapor expansion work, reducing the amount available for vapor-to-liquid conversion. Neglecting this energetic partition leads to an overestimation of the latent heat released during condensational growth of particles, cloud parcel buoyancy and vertical acceleration.

Received: 09 Feb 2026 – Discussion started: 17 Feb 2026

Competing interests: At least one of the (co-)authors is a member of the editorial board of Atmospheric Chemistry and Physics. The peer-review process was guided by an independent editor, and the authors also have no other competing interests to declare.

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.

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Journal article(s) based on this preprint

20 Oct 2026

A new method to derive water vapor supersaturation at cumulus cloud base from in situ measurements

Ramon C. Braga, Manfred Wendisch, Rachel Albrecht, and Daniel Harrison

Atmos. Chem. Phys., 26, 14769–14791, https://doi.org/10.5194/acp-26-14769-2026,https://doi.org/10.5194/acp-26-14769-2026, 2026

Short summary

Ramon Campos Braga, Daniel Harrison, Manfred Wendisch, and Rachel Albrecht

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2026-795', Anonymous Referee #1, 08 Apr 2026

The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2026-795/egusphere-2026-795-RC1-supplement.pdf

Citation: https://doi.org/10.5194/egusphere-2026-795-RC1
- AC1: 'Reply on RC1', Ramon Braga, 25 Apr 2026
  
  Response is attached.
  
  Citation: https://doi.org/10.5194/egusphere-2026-795-AC1
RC2:
'Comment on egusphere-2026-795', Anonymous Referee #2, 29 Apr 2026
General comments:
The paper presents a new method that employs the energy budget analysis framework to estimate the amount of supersaturation at warm cloud base by assuming the saturated parcel ascent as reversible adiabatic process with conserved isobaric enthalpy. The authors partition the supersaturation of the cloud (S_c) into vapor-phase (S_v) and liquid-phase (S_l) supersaturations to derive magnitudes of S_c, S_v, and S_l in the context of the energy balance defined by the first law of thermodynamics. This method is complemented by a closure analysis conducted using airborne observations of warm cumulus clouds from the ACRIDICON-CHUVA campaign. The analysis demonstrates how droplet number concentration (N_d) scales with S_v and agrees within the uncertainty range of CCN(S_v) spectra measured below cloud base prior to cloud observations.

Overall, the manuscript is well written and easy to follow. However, some analyses require further clarification. It is recommended that the manuscript be reconsidered after a major revision.

Specific Comments:
In section 3.1, please clarify the impact of background buoyant forcing on the estimated values of S_l and S_v using this framework regardless of aerosol regimes. In other words, how do uncertainty in S_l and S_v scales with increasing background buoyant forcing in any given environment?

Cloud passes were considered using a threshold criterion of N_d greater than 20 cm^–3 at initial stage of cloud formation (Lines 260-265). Since such in-cloud measurement thresholds are currently not standardized in our community, please perform sensitivity analysis on the resulting supersaturations with different threshold criteria defined using a combination of both minimum N_d and/or LWC. Additionally, please verify whether such definitions have any significant impact on the correlation coefficients discussed with power-law fits in Figure 4, S10, and S11. Include the analysis in the supporting information document.

The derived correlation coefficients values exhibit inverse correlation with the sample size. Larger sample sizes are associated with lower correlation coefficients and vice versa. Given the extremely limited sample size for this analysis and considering the prior argument, justify whether Nd is well constrained by S_v (Lines 408-409).

The reported uncertainties of 10% for N and LWC at lines 307-309 are applicable only to the ACRIDICON-CHUVA dataset. These uncertainties can be considered as the best-case scenario for measurement uncertainties, given that the Baumgardner et al., 2017 report the uncertainty range for scattering probes for sizing to be 10%-50% and for concentrations to be 10%-30%. Therefore, to extend the energy balance method to be applicable for other datasets from other field campaigns and to account for the worst-case scenario containing the maximum possible range of energy terms and supersaturations, please consider discussing the uncertainty to be defined as both the best-case and worst-case scenarios.

Lines 473-474: Please provide the magnitude of overestimation to better highlight the importance of including the energetic cost of vapor expansion during the ascent of the saturated parcel.

Technical corrections:
The spelling of ‘modeling’ in the manuscript is inconsistent. At Lines 33,36,237, it is spelled as ‘modeling’, whereas at lines 189, 226, 467 it is spelled as ‘modelling’.

Figure 3 and 4: Include a description in the figure captions that indicates that the color choices correspond to different aerosol backgrounds in the Amazon region and list the colors with their corresponding regions.

Reference:
Baumgardner, D., and Coauthors, 2017: Cloud Ice Properties: In Situ Measurement Challenges. Meteor. Monogr., 58, 9.1–9.23, https://doi.org/10.1175/AMSMONOGRAPHS-D-16-0011.1
Citation: https://doi.org/10.5194/egusphere-2026-795-RC2
- AC2: 'Reply on RC2', Ramon Braga, 08 May 2026
  
  The document is attached.
  
  Citation: https://doi.org/10.5194/egusphere-2026-795-AC2

Peer review completion

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

AR by Ramon Braga on behalf of the Authors (25 May 2026) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (01 Jun 2026) by Greg McFarquhar

RR by Anonymous Referee #3 (10 Jun 2026)

RR by Anonymous Referee #2 (12 Jul 2026)

Suggestions for revision or reasons for rejection

General comments:
The paper proposes a novel method to diagnose vapor-phase supersaturation at cloud base by utilizing measured liquid water content (LWC), temperature (T), and pressure (p). The latent heat (Q) is partitioned into changes in internal energy and saturation work. This method was applied to ACRIDICON-CHUVA campaign data, and the derived Nd (Sv) spectra were successfully compared with sub-cloud NCCN(Sv). This revised manuscript adequately addressed the concerns raised during initial review and my concerns are therefore not with the goal, the data or the care taken, but with the theoretical explanation and assumptions. The manuscript had been revised significantly making it extremely difficult to follow with unflattened track-changes and duplicate equation numbers resulting in significant delay.
Since some analysis requires an important clarification, it is recommended that manuscript is reconsidered after a minor revision with cleaner formatting.

Specific Comments:
1. The entire introduction section needs to be revised to ensure a consistent flow. For example, consider moving sentence starting with “In general, …” at lines 67-70 after discussing all the current methods in later part of introduction. Also consider removing the sentence starting with “In this study we introduce…” at line 71 since it is repeated later at line 128.

2. The framework of “conserved isobaric enthalpy” justified by small pressure variability of “0.1-0.3%” (Line 209) is questionable with a physically ascending parcel and the smallness of ∆p cannot defend it, please justify.
Figure 1 and its caption Line 248-262 and lines 225-226 (“undergoes a small upward displacement to slightly lower pressure”) describe a physical displacement. For displacement, the conserved quantity should be moist static energy, not enthalpy. The difference is g.dz and for adiabatic motion -g.dz equals cp.dT. So, the neglected term is the same size as the entire budget Q = Cp,cloud(T0-T) of Eq. 2 (Line 286) at any displacement, however small. So even a small pressure change cannot hold this key approximation. Looking at your data, largest reported cooling of 1.81K for AC17a (Lines 791-792) implies ascent of ~180m considering saturated lapse rate of 4.5 K km-1, which is a pressure change of ~2%, an order of magnitude beyond the 0.1-0.3% invoked at line 209. Several other statements (e.g., AC18, ∆Tc=0.71 ℃, Line 788) exceed the stated bounds as well.

3. Adiabaticity assumption for the sampled clouds may not apply to most of the observations.
Section 3.2, in-cloud RH ranged ~60-102% (Lines 709-710) attributed to sensor wetting and entrainment (Lines 711-716). If entrainment affects 60-90% readings, then the reversible-adiabatic premise (Sec 2.4) fails where the method is applied. The Nd > 20 cm-3 / RWC=0 selection (Line 526-528) does not address this. Consider stratifying Fig. 6, 7 closure by an adiabaticity proxy (LWC/LWCad, or the RH-RHc residual already computed in Fig 4a) to show whether the agreement improves for near adiabatic passes. A positive result will further strengthen the method.

Technical corrections:
Units: Mixing ratio “kg-1kg-1” throughout text should be “kg kg-1”
Line 57: Consider replacing the word "salty" droplets with "solution" droplets.
Line 76: "Clayperon-Clausius relation" should be written as "Clausius-Clapeyron relation"
Line 539-540: Please mention equation number used to calculate RHc and Sc.
Line 1170: Squires (1952) is referenced but I could not find it cited in the text.
Table 1, Line 635: AC19 is dated 20-Sep but is listed after AC18 (28-Sep), please explain.

Hide

RR by Anonymous Referee #4 (07 Aug 2026)

ED: Reconsider after major revisions (08 Aug 2026) by Greg McFarquhar

AR by Ramon Braga on behalf of the Authors (13 Sep 2026) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (14 Sep 2026) by Greg McFarquhar

RR by Anonymous Referee #4 (05 Oct 2026)

ED: Publish subject to minor revisions (review by editor) (05 Oct 2026) by Greg McFarquhar

AR by Ramon Braga on behalf of the Authors (07 Oct 2026) Author's response Author's tracked changes Manuscript

ED: Publish as is (07 Oct 2026) by Greg McFarquhar

AR by Ramon Braga on behalf of the Authors (09 Oct 2026) Manuscript

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2026-795', Anonymous Referee #1, 08 Apr 2026

The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2026/egusphere-2026-795/egusphere-2026-795-RC1-supplement.pdf

Citation: https://doi.org/10.5194/egusphere-2026-795-RC1
- AC1: 'Reply on RC1', Ramon Braga, 25 Apr 2026
  
  Response is attached.
  
  Citation: https://doi.org/10.5194/egusphere-2026-795-AC1
RC2:
'Comment on egusphere-2026-795', Anonymous Referee #2, 29 Apr 2026
General comments:
The paper presents a new method that employs the energy budget analysis framework to estimate the amount of supersaturation at warm cloud base by assuming the saturated parcel ascent as reversible adiabatic process with conserved isobaric enthalpy. The authors partition the supersaturation of the cloud (S_c) into vapor-phase (S_v) and liquid-phase (S_l) supersaturations to derive magnitudes of S_c, S_v, and S_l in the context of the energy balance defined by the first law of thermodynamics. This method is complemented by a closure analysis conducted using airborne observations of warm cumulus clouds from the ACRIDICON-CHUVA campaign. The analysis demonstrates how droplet number concentration (N_d) scales with S_v and agrees within the uncertainty range of CCN(S_v) spectra measured below cloud base prior to cloud observations.

Overall, the manuscript is well written and easy to follow. However, some analyses require further clarification. It is recommended that the manuscript be reconsidered after a major revision.

Specific Comments:
In section 3.1, please clarify the impact of background buoyant forcing on the estimated values of S_l and S_v using this framework regardless of aerosol regimes. In other words, how do uncertainty in S_l and S_v scales with increasing background buoyant forcing in any given environment?

Cloud passes were considered using a threshold criterion of N_d greater than 20 cm^–3 at initial stage of cloud formation (Lines 260-265). Since such in-cloud measurement thresholds are currently not standardized in our community, please perform sensitivity analysis on the resulting supersaturations with different threshold criteria defined using a combination of both minimum N_d and/or LWC. Additionally, please verify whether such definitions have any significant impact on the correlation coefficients discussed with power-law fits in Figure 4, S10, and S11. Include the analysis in the supporting information document.

The derived correlation coefficients values exhibit inverse correlation with the sample size. Larger sample sizes are associated with lower correlation coefficients and vice versa. Given the extremely limited sample size for this analysis and considering the prior argument, justify whether Nd is well constrained by S_v (Lines 408-409).

The reported uncertainties of 10% for N and LWC at lines 307-309 are applicable only to the ACRIDICON-CHUVA dataset. These uncertainties can be considered as the best-case scenario for measurement uncertainties, given that the Baumgardner et al., 2017 report the uncertainty range for scattering probes for sizing to be 10%-50% and for concentrations to be 10%-30%. Therefore, to extend the energy balance method to be applicable for other datasets from other field campaigns and to account for the worst-case scenario containing the maximum possible range of energy terms and supersaturations, please consider discussing the uncertainty to be defined as both the best-case and worst-case scenarios.

Lines 473-474: Please provide the magnitude of overestimation to better highlight the importance of including the energetic cost of vapor expansion during the ascent of the saturated parcel.

Technical corrections:
The spelling of ‘modeling’ in the manuscript is inconsistent. At Lines 33,36,237, it is spelled as ‘modeling’, whereas at lines 189, 226, 467 it is spelled as ‘modelling’.

Figure 3 and 4: Include a description in the figure captions that indicates that the color choices correspond to different aerosol backgrounds in the Amazon region and list the colors with their corresponding regions.

Reference:
Baumgardner, D., and Coauthors, 2017: Cloud Ice Properties: In Situ Measurement Challenges. Meteor. Monogr., 58, 9.1–9.23, https://doi.org/10.1175/AMSMONOGRAPHS-D-16-0011.1
Citation: https://doi.org/10.5194/egusphere-2026-795-RC2
- AC2: 'Reply on RC2', Ramon Braga, 08 May 2026
  
  The document is attached.
  
  Citation: https://doi.org/10.5194/egusphere-2026-795-AC2

Peer review completion

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

AR by Ramon Braga on behalf of the Authors (25 May 2026) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (01 Jun 2026) by Greg McFarquhar

RR by Anonymous Referee #3 (10 Jun 2026)

RR by Anonymous Referee #2 (12 Jul 2026)

Suggestions for revision or reasons for rejection

Hide

RR by Anonymous Referee #4 (07 Aug 2026)

ED: Reconsider after major revisions (08 Aug 2026) by Greg McFarquhar

AR by Ramon Braga on behalf of the Authors (13 Sep 2026) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (14 Sep 2026) by Greg McFarquhar

RR by Anonymous Referee #4 (05 Oct 2026)

ED: Publish subject to minor revisions (review by editor) (05 Oct 2026) by Greg McFarquhar

AR by Ramon Braga on behalf of the Authors (07 Oct 2026) Author's response Author's tracked changes Manuscript

ED: Publish as is (07 Oct 2026) by Greg McFarquhar

AR by Ramon Braga on behalf of the Authors (09 Oct 2026) Manuscript

Journal article(s) based on this preprint

20 Oct 2026

A new method to derive water vapor supersaturation at cumulus cloud base from in situ measurements

Ramon C. Braga, Manfred Wendisch, Rachel Albrecht, and Daniel Harrison

Atmos. Chem. Phys., 26, 14769–14791, https://doi.org/10.5194/acp-26-14769-2026,https://doi.org/10.5194/acp-26-14769-2026, 2026

Short summary

Ramon Campos Braga, Daniel Harrison, Manfred Wendisch, and Rachel Albrecht

Supplement

https://doi.org/10.5194/egusphere-2026-795-supplement

Ramon Campos Braga, Daniel Harrison, Manfred Wendisch, and Rachel Albrecht

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Short summary

We introduce a new thermodynamic method to quantify water vapor supersaturation (S_v) at warm cloud bases by describing the ascent of a cloudy air parcel as a reversible cloud-adiabatic process. This approach enables the calculation of cloud-base droplet number concentration spectra from in situ airborne measurements without reliance on prescribed updraft velocities or empirical parameterizations. The method is validated using CCN measurements from airborne observations over the Amazon Basin.


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