Estimating Vertical Velocity in Convective Updrafts from Temperature, Pressure, and Latent Heating

Amel Derras-Chouk; Andreas F. Prein; Gregory Elsaesser; Jingbo Wu; Toshi Matsui; Zhengzhao Johnny Luo

arxiv: 2508.16750 · v3 · submitted 2025-08-22 · ⚛️ physics.ao-ph

Estimating Vertical Velocity in Convective Updrafts from Temperature, Pressure, and Latent Heating

Amel Derras-Chouk , Gregory Elsaesser , Zhengzhao Johnny Luo , Toshi Matsui , Andreas F. Prein , Jingbo Wu This is my paper

Pith reviewed 2026-05-18 20:55 UTC · model grok-4.3

classification ⚛️ physics.ao-ph

keywords convective cloudsvertical velocitylatent heatingplume modelstropical convectionmid-latitude convectioncloud simulations

0 comments

The pith

A method estimates vertical velocity in convective updrafts from temperature, pressure, and latent heating profiles.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a technique for estimating the vertical velocity within convective updrafts, denoted w_c, based on vertical profiles of in-cloud temperature, pressure, and latent heating rate. This velocity plays a key role in the development of cloud anvils and the transport of moisture globally, which affects the planet's energy budget, yet it has been difficult to measure over long periods from space. The method is grounded in analytical plume models that establish an approximately linear link between the updraft speed and the condensation rate of water vapor. Validation using cloud simulations shows that the estimates have lower uncertainties in tropical environments, achieving accuracy to about 1 m/s for most samples, compared to higher uncertainties in mid-latitudes. Potential uses include integration with future satellite observations to map these velocities worldwide.

Core claim

The authors present a method to estimate convective vertical velocity w_c from in-cloud temperature, pressure, and latent heating rate profiles by leveraging the approximately linear relationship between w_c and the condensation rate derived from both steady-state and non-steady-state plume models, with an additional formulation from supersaturation rate. Assessments against simulations indicate higher precision in the tropics.

What carries the argument

Analytical models establishing the approximately linear relationship between vertical velocity w_c and condensation rate q_vc dot, derived from steady-state and non-steady-state plume models.

If this is right

Enables potential global, long-term estimation of vertical velocities using spaceborne retrievals.
Supports improved understanding of convective anvil development and global moisture transport.
Provides a way to assess cloud simulations across tropical and mid-latitude environments.
Facilitates applications to future satellite missions for mapping updraft strengths.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

This technique could be used to compare updraft strengths across different climate regimes if applied to satellite observations.
Integration into climate models might help refine representations of convection and its effects on moisture.
Field measurements from campaigns could test the method's performance beyond simulations.

Load-bearing premise

The approximately linear relationship between vertical velocity and condensation rate from plume models applies to real convective clouds in various environments.

What would settle it

Direct in-situ measurements of vertical velocity in convective clouds that show deviations larger than approximately 1 m/s from the estimates in tropical regions for a majority of samples.

read the original abstract

The vertical velocity in convective clouds ($w_c$) mediates convective anvil development and global moisture transport, influencing Earth's energy budget, but has yet to be estimated globally over long periods due to the absence of spaceborne retrievals. Here, a method for estimating $w_c$ given vertical profiles of in-cloud temperature, pressure, and latent heating rate is presented and assessed. The method relies on analytical models for the approximately linear relationship between $w_c$ and condensation rate ($\dot{q}_{vc}$) in convective clouds, which we derive from steady-state and non-steady-state plume models. We include in our analysis a version of $\dot{q}_{vc}/w_c$ derived from the supersaturation rate in convective clouds, recently presented in Kukulies et al. (2024). We assess the accuracy of $w_c$ estimates against convective cloud simulations run with different model cores and spatial resolutions in both tropical and mid-latitude environments. The velocity estimates exhibit lower uncertainties and higher precision in the tropics than they do in the mid-latitudes. Vertical velocity is estimated to within $\approx1$ m/s for most samples in the tropics. Potential applications, validation against future satellite mission retrievals, and approaches for improving the estimation are discussed.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper gives a workable way to estimate updraft vertical velocity from temperature, pressure, and latent heating profiles by using linear relations pulled from plume models, with better results shown in tropical simulations than mid-latitude ones, though the tests stay inside the same modeling framework.

read the letter

The main point is a method to estimate convective vertical velocity from vertical profiles of in-cloud temperature, pressure, and latent heating. It draws on analytical derivations from steady-state and non-steady-state plume models for the roughly linear link between vertical velocity and condensation rate, and folds in the supersaturation-based ratio from Kukulies et al. 2024. They then apply the estimator to cloud simulations run with different cores and resolutions in both tropical and mid-latitude cases. The estimates look tighter in the tropics, landing within about 1 m/s for most samples there. This lines up with the long-standing need for a way to get at vertical motions that control anvil formation and moisture transport, and it could feed into satellite validation or model checks later. The work is clear about how the relations are derived and shows the performance difference between environments. The soft spot is that all the accuracy numbers come from applying the estimator back to the same class of simulations whose equations and assumptions match the plume models used to build it. That makes the results more of an internal consistency check than an independent test. If real clouds differ in entrainment or how quickly supersaturation relaxes, the reported precision will not necessarily hold. The abstract also skips sample counts, error bars, and post-processing details, so the 1 m/s figure is hard to weigh fully. The linear relationship itself is taken from the models without separate checks against observations. This is for atmospheric scientists working on convection, remote sensing, or parameterization development. It is worth a serious referee because it fills a real observational gap with a direct method, even if the validation section will need more work to stand up.

Referee Report

2 major / 2 minor

Summary. The manuscript presents a method to estimate convective updraft vertical velocity (w_c) from vertical profiles of in-cloud temperature, pressure, and latent heating rate. The approach derives an approximately linear relationship between w_c and condensation rate (q̇_vc) from steady-state and non-steady-state analytical plume models, incorporates a supersaturation-based ratio from Kukulies et al. (2024), and evaluates the resulting w_c estimates against output from convective cloud simulations run with different dynamical cores and spatial resolutions in both tropical and mid-latitude environments. The abstract reports lower uncertainties and higher precision in the tropics, with w_c estimated to within ≈1 m/s for most samples there.

Significance. If the central accuracy claims hold under independent validation, the method could enable global retrievals of convective vertical velocities from future satellite observations, addressing a long-standing observational gap relevant to anvil development, moisture transport, and the energy budget. The analytical derivations from plume models and the multi-simulation assessment framework represent strengths that could support reproducible applications if the validation concerns are addressed.

major comments (2)

[Abstract] Abstract: the headline claim that vertical velocity is estimated to within ≈1 m/s for most samples in the tropics is presented without error bars, exact sample counts, or details on post-hoc sample selection. This information is load-bearing for assessing whether the reported precision is robust or sensitive to particular simulation subsets.
[Assessment section] Assessment against simulations (throughout §4 and related figures/tables): the linear w_c–q̇_vc relationship is derived from plume models and then evaluated on simulations that solve the same continuity and thermodynamic equations. This creates a risk of circularity; the reported tropical precision may reflect consistency within the modeling framework rather than independent confirmation. A concrete test against observations or simulations with deliberately altered entrainment and microphysics would be needed to support generalization to real clouds.

minor comments (2)

[Abstract] Abstract: clarify whether the Kukulies et al. (2024) supersaturation-based ratio was recomputed inside the present simulation suite or adopted unchanged from the earlier study.
[Throughout] Notation: ensure consistent use of symbols for condensation rate (q̇_vc vs. similar variants) across derivations and results to avoid reader confusion.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed review. We address each major comment below, indicating planned revisions to the manuscript where appropriate.

read point-by-point responses

Referee: [Abstract] Abstract: the headline claim that vertical velocity is estimated to within ≈1 m/s for most samples in the tropics is presented without error bars, exact sample counts, or details on post-hoc sample selection. This information is load-bearing for assessing whether the reported precision is robust or sensitive to particular simulation subsets.

Authors: We agree that the abstract would benefit from greater quantitative detail to support the precision claim. In the revised version, we will specify the total number of samples, the precise error metric underlying the ≈1 m/s figure (e.g., interquartile range or standard deviation), and the sample-selection criteria applied. These additions will make the headline statement more transparent and easier to evaluate. revision: yes
Referee: [Assessment section] Assessment against simulations (throughout §4 and related figures/tables): the linear w_c–q̇_vc relationship is derived from plume models and then evaluated on simulations that solve the same continuity and thermodynamic equations. This creates a risk of circularity; the reported tropical precision may reflect consistency within the modeling framework rather than independent confirmation. A concrete test against observations or simulations with deliberately altered entrainment and microphysics would be needed to support generalization to real clouds.

Authors: We recognize the legitimate concern about potential circularity. Although the plume models are analytical approximations and the simulations employ distinct dynamical cores and resolutions, they do share the same governing equations. We will revise §4 and the discussion section to explicitly acknowledge this limitation, to quantify the differences introduced by the varied numerical setups, and to state that the current results constitute an initial consistency check rather than fully independent validation. We will also add a forward-looking statement that observational tests and sensitivity experiments with modified entrainment or microphysics are important future directions. New simulations of that type lie outside the scope of the present study. revision: partial

Circularity Check

0 steps flagged

Derivation from analytical plume models is independent of simulation assessment

full rationale

The paper derives the approximately linear w_c–condensation rate relationship analytically from steady-state and non-steady-state plume models and augments it with an external supersaturation-based ratio from Kukulies et al. (2024). These steps constitute an independent analytical derivation rather than a fit or self-referential loop. The subsequent assessment applies the derived estimator to output from convective cloud simulations to measure accuracy; this is a test of applicability, not a reduction of the derivation itself to the simulation inputs by construction. No load-bearing self-citation, fitted parameter renamed as prediction, or ansatz smuggled via citation is evident in the provided derivation chain. The method remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Central claim rests on the assumption that plume-model-derived linear relations between vertical velocity and condensation rate apply to real clouds; no explicit free parameters or new entities are introduced in the abstract.

axioms (1)

domain assumption The relationship between vertical velocity and condensation rate is approximately linear in convective clouds.
Stated as derived from steady-state and non-steady-state plume models and used as the basis for the estimation method.

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discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AbsoluteFloorClosure.lean, IndisputableMonolith/Foundation/AlexanderDuality.lean reality_from_one_distinction, alexander_duality_circle_linking unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

We derive expressions to model the proportionality between vertical velocity and condensation rate based on a one-dimensional plume model... conservation of water vapor specific humidity... moist static energy

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