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arxiv: 2606.24593 · v2 · pith:PSNTAX7Anew · submitted 2026-06-23 · ⚛️ physics.flu-dyn

Data-Driven Flux Parameterization for the Atmospheric Boundary Layer

Abed Hammoud , Edriss S. Titi , Mitchell Bushuk , Marc Calaf , Khaled Ghannam , Elie Bou-Zeid This is my paper

Pith reviewed 2026-06-26 05:50 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords turbulent flux parameterizationatmospheric boundary layerdata-driven closurelarge eddy simulationconvolution operatorK-profile closurestability regimessingle-column model
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The pith

A data-driven linearized convolution operator on mean profiles parameterizes ABL turbulent fluxes more accurately than standard K-profile closures while remaining interpretable.

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

The paper trains a closure in which nondimensional fluxes are outputs of a linearized convolution operator applied to nondimensional mean temperature and velocity profiles. Training and testing use large-eddy simulations of idealized flow over homogeneous surfaces across stability regimes. The selected operator improves predictive skill relative to a conventional K-profile closure, exposes the degree of locality in turbulent transport through its kernels, and produces stable, LES-matching profiles when run in single-column mode.

Core claim

Nondimensional turbulent fluxes in the atmospheric boundary layer can be represented by a linearized convolution operator acting on nondimensional mean state profiles; when the operator is learned from LES data spanning multiple stability regimes, the resulting parameterization improves mean-squared error over a standard K-profile closure, retains an interpretable kernel form that distinguishes local and nonlocal transport, and remains stable while reproducing LES state profiles in a posteriori single-column integrations.

What carries the argument

Linearized convolution operator acting on nondimensional mean temperature and velocity profiles to predict heat and momentum fluxes.

If this is right

  • The operator form reveals how locality of momentum and heat transport changes across stability regimes.
  • Single-column integrations remain stable and match LES mean profiles more closely than the baseline K-profile closure.
  • Different combinations of input mean profiles can be tested to isolate the minimal set needed for accurate flux prediction.
  • The closure supplies a transparent, first-order alternative for use inside coarse-resolution weather and climate models.

Where Pith is reading between the lines

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

  • If the operator kernels prove robust, they could be inserted directly into operational boundary-layer schemes without retraining.
  • The same convolution structure might be applied to other scalar fluxes such as moisture once suitable LES training data exist.
  • Discrepancies between learned kernels and classical similarity functions would highlight where nonlocal effects dominate and require explicit treatment.

Load-bearing premise

Idealized LES cases over homogeneous surfaces produce an operator that stays accurate and stable under real-world surface heterogeneity, transient forcing, and subgrid effects.

What would settle it

Running the learned operator in single-column mode on LES cases that include surface heterogeneity or time-varying large-scale forcing and checking whether profile errors remain below those of the K-profile closure would confirm or refute the claim.

Figures

Figures reproduced from arXiv: 2606.24593 by Abed Hammoud, Edriss S. Titi, Elie Bou-Zeid, Khaled Ghannam, Marc Calaf, Mitchell Bushuk.

Figure 1
Figure 1. Figure 1: Linear operators mapping mean profiles to fluxes under (a–c) stable and (d–f) unstable [PITH_FULL_IMAGE:figures/full_fig_p011_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Momentum flux hodographs showing the relation between the turbulent flux components [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: multivariate operators for the stable ABL and their reconstruction skill for the stable [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Multivariate operators for the convective ABL and their reconstruction skill for the [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Time-height plots of (a) temperature, (b) [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Time-height plots of (a) temperature, (b) [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Time-height plots of (a) potential temperature, (b) [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Instantaneous snapshots of temperature, u-velocity and v-velocity profiles at select times [PITH_FULL_IMAGE:figures/full_fig_p020_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Instantaneous snapshots of temperature, u-velocity and v-velocity profiles at select times [PITH_FULL_IMAGE:figures/full_fig_p021_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Time-height plots of temperature, u-, and v-velocity for a posteriori tests initialized from neutral stability. Shown are the cases for (a) transition to a stable ABL with ∂θ/∂t = −1 K h−1 , and (b) transition to an unstable ABL with w′θ ′ = 150 W m−2 . 22 [PITH_FULL_IMAGE:figures/full_fig_p022_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Snapshots of potential temperature and mean [PITH_FULL_IMAGE:figures/full_fig_p024_11.png] view at source ↗
read the original abstract

Turbulent fluxes in the atmospheric boundary layer (ABL) govern exchanges of momentum, heat, and mass between the surface and atmosphere, shaping boundary layer structure and influencing weather, climate, and engineering applications. Yet their representation in coarse resolution models remains challenging, particularly under unstable conditions with strongly nonlocal transport and stable conditions with intermittent turbulence. Here, we develop a data driven turbulent flux parameterization in which nondimensional fluxes are represented by a linearized convolution operator acting on nondimensional mean state profiles. We train and evaluate the closure using high resolution large eddy simulations (LES) of idealized flow over homogeneous surfaces spanning multiple stability regimes. Several first order closure variants are constructed from different combinations of mean temperature and velocity profiles to predict heat and momentum fluxes, and the best model is selected by minimizing mean squared error across training and unseen test cases. The resulting parameterization improves predictive skill relative to a standard K-profile closure while retaining an interpretable operator form. Its learned kernels expose the locality and nonlocality of turbulent transport across stability regimes, linking empirical performance to physically inspectable flux--profile relationships. In a posteriori single column simulations, the closure remains stable and produces state profiles that closely match LES, demonstrating its potential as an accurate and transparent ABL flux parameterization.

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.

Referee Report

3 major / 2 minor

Summary. The manuscript develops a data-driven parameterization for turbulent fluxes in the atmospheric boundary layer, representing nondimensional fluxes via a linearized convolution operator acting on nondimensional mean temperature and velocity profiles. Multiple first-order closure variants are constructed, trained by minimizing mean squared error on large-eddy simulation (LES) data from idealized flows over homogeneous surfaces spanning stability regimes, and evaluated on unseen test cases from the same ensemble. The selected model is reported to outperform a standard K-profile closure in predictive skill, with learned kernels exposing locality and nonlocality of transport; a posteriori single-column simulations are shown to remain stable and match LES state profiles.

Significance. If the central results hold within the tested regime, the work supplies an interpretable operator-based alternative to traditional closures that links data-driven performance to inspectable flux-profile relationships across stabilities. The retention of an explicit convolution form and the demonstration of a posteriori stability constitute concrete strengths that could aid adoption in coarse-resolution models, provided the approach can be shown to extend beyond the idealized homogeneous cases used for training and testing.

major comments (3)
  1. [Abstract] Abstract: the claim that the parameterization improves predictive skill relative to a standard K-profile closure while demonstrating potential for broader ABL use rests exclusively on MSE reductions and stable single-column matches for unseen cases drawn from the same idealized homogeneous-surface LES ensemble. No tests are reported on surface heterogeneity, intermittent turbulence, or transient forcing—regimes the abstract itself identifies as those where standard closures fail—making the generalization assumption load-bearing for the stated significance.
  2. [Abstract] Abstract and evaluation description: the kernels are obtained by fitting to the LES data (with held-out test cases drawn from the identical ensemble of homogeneous-surface simulations). This constitutes a within-distribution held-out fit rather than an independent derivation or out-of-sample validation, which directly limits the strength of the claim that the learned operator form will remain accurate under the broader range of conditions encountered in operational models.
  3. [Abstract] Abstract: the a posteriori single-column tests are described only for the same idealized cases used in training/evaluation. Without additional off-distribution single-column or LES configurations, it is not possible to assess whether the learned convolution kernels retain stability or accuracy when surface heterogeneity or transient forcing is present.
minor comments (2)
  1. [Methods] The description of how the best model variant is selected (minimizing MSE across training and test cases) would benefit from an explicit statement of the cross-validation procedure and any safeguards against post-hoc exclusion of cases.
  2. [Methods] Notation for the nondimensionalization of profiles and fluxes, as well as the precise definition of the convolution operator, should be consolidated in one location with a clear reference to the relevant equations.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed review. The comments correctly identify that the current validation is restricted to idealized homogeneous-surface LES cases. We address each major comment below and agree to revise the abstract and evaluation sections to more precisely delineate the scope of the present study.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that the parameterization improves predictive skill relative to a standard K-profile closure while demonstrating potential for broader ABL use rests exclusively on MSE reductions and stable single-column matches for unseen cases drawn from the same idealized homogeneous-surface LES ensemble. No tests are reported on surface heterogeneity, intermittent turbulence, or transient forcing—regimes the abstract itself identifies as those where standard closures fail—making the generalization assumption load-bearing for the stated significance.

    Authors: We agree that the reported results are confined to the idealized homogeneous-surface ensemble and that the abstract's phrasing of 'potential for broader ABL use' could be read as implying stronger generalization than the evidence supports. We will revise the abstract to explicitly state that the training, testing, and a-posteriori evaluations are performed within this ensemble and to replace the broader-use language with a statement that future work is required to assess performance under surface heterogeneity and transient forcing. revision: yes

  2. Referee: [Abstract] Abstract and evaluation description: the kernels are obtained by fitting to the LES data (with held-out test cases drawn from the identical ensemble of homogeneous-surface simulations). This constitutes a within-distribution held-out fit rather than an independent derivation or out-of-sample validation, which directly limits the strength of the claim that the learned operator form will remain accurate under the broader range of conditions encountered in operational models.

    Authors: The held-out cases are drawn from the same ensemble of homogeneous-surface simulations, constituting within-distribution evaluation. This is standard practice for assessing interpolation within the trained regime but does not constitute out-of-distribution testing. We will revise the manuscript to clarify the nature of the train/test split and to qualify any statements about accuracy under broader conditions. revision: yes

  3. Referee: [Abstract] Abstract: the a posteriori single-column tests are described only for the same idealized cases used in training/evaluation. Without additional off-distribution single-column or LES configurations, it is not possible to assess whether the learned convolution kernels retain stability or accuracy when surface heterogeneity or transient forcing is present.

    Authors: The single-column tests were performed on the same class of idealized cases to verify numerical stability and profile fidelity inside the validated regime. We acknowledge that these tests do not address off-distribution behavior. We will revise the relevant sections to emphasize the scope of the a-posteriori experiments and to note that stability under heterogeneous or transient conditions remains to be demonstrated. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is explicitly empirical fitting with held-out validation

full rationale

The paper explicitly constructs a data-driven parameterization by fitting linearized convolution kernels to nondimensional fluxes from a set of idealized LES cases over homogeneous surfaces, then selects the best variant by MSE on both training and unseen test cases drawn from the same ensemble. This process is standard supervised learning and does not reduce any claimed result to an input by construction; the test-case 'predictions' are out-of-sample evaluations rather than tautological. No self-citation chains, uniqueness theorems, or ansatzes imported from prior author work are invoked as load-bearing steps. The central claim of improved skill versus K-profile closure is an empirical comparison on held-out data and remains independent of the fitting procedure itself.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the modeling assumption that a linear convolution suffices and on the empirical kernels fitted to LES; no new physical entities are postulated.

free parameters (1)
  • convolution kernel weights
    Learned by minimizing mean squared error on LES flux predictions; these are the primary fitted quantities that define the operator.
axioms (1)
  • domain assumption Nondimensional fluxes can be represented by a linearized convolution operator acting on nondimensional mean state profiles.
    Invoked as the functional form of the closure in the abstract.

pith-pipeline@v0.9.1-grok · 5768 in / 1182 out tokens · 25313 ms · 2026-06-26T05:50:28.350359+00:00 · methodology

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Works this paper leans on

90 extracted references · 46 canonical work pages

  1. [1]

    and Giometto, Marco G

    Calaf, Marc and Vercauteren, Nikki and Katul, Gabriel G. and Giometto, Marco G. and Morrison, Travis J. and Margairaz, Fabien and Boyko, Vyacheslav and Pardyjak, Eric R. , title=. Boundary-Layer Meteorology , year=. doi:10.1007/s10546-022-00742-5 , url=

    work page doi:10.1007/s10546-022-00742-5

  2. [2]

    2012 , publisher=

    An Introduction to Boundary Layer Meteorology , author=. 2012 , publisher=

    2012

  3. [3]

    and Cohen, Y

    Lopez-Gomez, I. and Cohen, Y. and He, J. and Jaruga, A. and Schneider, T. , title =. Journal of Advances in Modeling Earth Systems , year =

  4. [4]

    Sauer, J. A. and Mu. The FastEddy. Journal of Advances in Modeling Earth Systems , year =

  5. [5]

    and Lemari

    Perrot, M. and Lemari. Energetically consistent eddy-diffusivity mass-flux convective schemes: 1. Theory and models , journal =. 2025 , volume =

    2025

  6. [6]

    and Bretherton, C

    Han, J. and Bretherton, C. S. , title =. Weather and Forecasting , year =

  7. [7]

    Soares, P. M. M. and Miranda, P. M. A. and Siebesma, A. P. and Teixeira, J. , title =. Quarterly Journal of the Royal Meteorological Society , year =

  8. [8]

    Eddy diffusivity/mass flux and shallow cumulus boundary layer: An updraft PDF multiple mass flux scheme , journal =

    Su. Eddy diffusivity/mass flux and shallow cumulus boundary layer: An updraft PDF multiple mass flux scheme , journal =. 2012 , volume =

    2012

  9. [9]

    A unified eddy-diffusivity/mass-flux approach for modeling atmospheric convection , journal =

    Su. A unified eddy-diffusivity/mass-flux approach for modeling atmospheric convection , journal =. 2019 , volume =

    2019

  10. [10]

    On the factors controlling the development of shallow convection in eddy-diffusivity/mass-flux models , journal =

    Su. On the factors controlling the development of shallow convection in eddy-diffusivity/mass-flux models , journal =. 2019 , volume =

    2019

  11. [11]

    and Mahrt, L

    Troen, I. and Mahrt, L. , title =. Boundary-Layer Meteorology , year =

  12. [12]

    Holtslag, A. A. M. and Boville, B. A. , title =. Journal of Climate , year =

  13. [13]

    Large, W. G. and McWilliams, J. C. and Doney, S. C. , title =. Reviews of Geophysics , year =

  14. [14]

    Taylor, G. I. , title =. Philosophical Transactions of the Royal Society A , year =

  15. [15]

    , title =

    Prandtl, L. , title =. 1925 , volume =

    1925

  16. [16]

    Deardorff, J. W. , title =. Journal of Fluid Mechanics , year =

  17. [17]

    , title =

    Moeng, C.-H. , title =. Journal of the Atmospheric Sciences , year =

  18. [18]

    Nieuwstadt, F. T. M. and Mason, P. J. and Moeng, C.-H. and Schumann, U. , title =. Turbulent Shear Flows , year =

  19. [19]

    Holtslag, A. A. M. and Boville, B. A. and Moeng, C.-H. , title =. Boundary-Layer Meteorology , year =

  20. [20]

    Siebesma, A. P. and Soares, P. M. M. and Teixeira, J. , title =. Journal of the Atmospheric Sciences , year =

  21. [21]

    Shin, H. H. and Hong, S.-Y. , title =. Monthly Weather Review , year =

  22. [22]

    Sullivan, P. P. and Moeng, C.-H. and Stevens, B. and Lenschow, D. H. and Mayor, S. D. , title =. Journal of the Atmospheric Sciences , year =

  23. [23]

    Journal of Advances in Modeling Earth Systems , volume =

    Bolton, Thomas and Zanna, Laure , title =. Journal of Advances in Modeling Earth Systems , volume =. doi:https://doi.org/10.1029/2018MS001472 , url =. https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2018MS001472 , abstract =

    work page doi:10.1029/2018ms001472

  24. [24]

    Geophysical Research Letters , volume =

    Zanna, Laure and Bolton, Thomas , title =. Geophysical Research Letters , volume =. doi:https://doi.org/10.1029/2020GL088376 , url =. https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2020GL088376 , note =

    work page doi:10.1029/2020gl088376

  25. [25]

    2025 , eprint=

    A Framework for Hybrid Physics-AI Coupled Ocean Models , author=. 2025 , eprint=

    2025

  26. [26]

    and Hallberg, R

    Adcroft, A. and Hallberg, R. and Dunne, J. P. and et al. , title =. Journal of Advances in Modeling Earth Systems , year =

  27. [27]

    and Meneveau, C

    Bou-Zeid, E. and Meneveau, C. and Parlange, M. B. , title =. Water Resources Research , volume =. 2004 , doi =

    2004

  28. [28]

    and Meneveau, C

    Bou-Zeid, E. and Meneveau, C. and Parlange, M. B. , title =. Physics of Fluids , volume =. 2005 , doi =

    2005

  29. [29]

    and Bou-Zeid, E

    Momen, M. and Bou-Zeid, E. , title =. Journal of Fluid Mechanics , volume =. 2017 , doi =

    2017

  30. [30]

    and Bou-Zeid, E

    Fogarty, J. and Bou-Zeid, E. , title =. Boundary-Layer Meteorology , year =

  31. [31]

    Turbulence and Vertical Fluxes in the Stable Atmospheric Boundary Layer

    Huang, Jing and Bou-Zeid, Elie , year =. Turbulence and Vertical Fluxes in the Stable Atmospheric Boundary Layer. Part I: A Large-Eddy Simulation Study , volume =. Journal of the Atmospheric Sciences , publisher =. doi:10.1175/jas-d-12-0167.1 , number =

    work page doi:10.1175/jas-d-12-0167.1

  32. [32]

    , title =

    Blackadar, Alfred K. , title =. Journal of Geophysical Research (1896-1977) , volume =. doi:https://doi.org/10.1029/JZ067i008p03095 , url =. https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/JZ067i008p03095 , abstract =

    work page doi:10.1029/jz067i008p03095 1977

  33. [33]

    Williams and Clarence W

    Matthew O. Williams and Clarence W. Rowley and Ioannis G. Kevrekidis , keywords =. A kernel-based method for data-driven. Journal of Computational Dynamics , volume =. 2015 , issn =. doi:10.3934/jcd.2015005 , url =

    work page doi:10.3934/jcd.2015005 2015

  34. [34]

    and Budi

    Brunton, Steven L. and Budi. Modern. SIAM Review , volume =. 2022 , doi =

    2022

  35. [35]

    International Conference on Learning Representations , year=

    Fourier Neural Operator for Parametric Partial Differential Equations , author=. International Conference on Learning Representations , year=

  36. [36]

    Schmid, Peter J. , year=. Dynamic mode decomposition of numerical and experimental data , volume=. doi:10.1017/S0022112010001217 , journal=

    work page doi:10.1017/s0022112010001217

  37. [37]

    Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators https://doi.org/10.1038/s42256-021-00302-5

    Lu, Lu and Jin, Pengzhan and Pang, Guofei and Zhang, Zhongqiang and Karniadakis, George Em , title=. Nature Machine Intelligence , year=. doi:10.1038/s42256-021-00302-5 , url=

    work page doi:10.1038/s42256-021-00302-5

  38. [38]

    González-García and R

    R. González-García and R. Rico-Martínez and I.G. Kevrekidis , keywords =. Identification of distributed parameter systems: A neural net based approach , journal =. 1998 , note =. doi:https://doi.org/10.1016/S0098-1354(98)00191-4 , url =

    work page doi:10.1016/s0098-1354(98)00191-4 1998

  39. [39]

    Nonlocality and nonlinearity implies universality in operator learning

    Lanthaler, Samuel and Li, Zongyi and Stuart, Andrew M. Nonlocality and nonlinearity implies universality in operator learning. Constr. Approx

  40. [40]

    , title =

    Kumar, Vijayant and Kleissl, Jan and Meneveau, Charles and Parlange, Marc B. , title =. Water Resources Research , volume =. doi:https://doi.org/10.1029/2005WR004651 , url =

    work page doi:10.1029/2005wr004651

  41. [41]

    Synergistic Interactions between Urban Heat Islands and Heat Waves: The Impact in Cities Is Larger than the Sum of Its Parts , volume =

    Li, Dan and Bou-Zeid, Elie , year =. Synergistic Interactions between Urban Heat Islands and Heat Waves: The Impact in Cities Is Larger than the Sum of Its Parts , volume =. Journal of Applied Meteorology and Climatology , publisher =. doi:10.1175/jamc-d-13-02.1 , number =

    work page doi:10.1175/jamc-d-13-02.1

  42. [42]

    Chorin , title =

    Alexandre J. Chorin , title =. Mathematics of Computation , year =. doi:10.2307/2004575 , publisher =

    work page doi:10.2307/2004575

  43. [43]

    Terra Incognita

    Wyngaard, John C. , year =. Toward Numerical Modeling in the “Terra Incognita” , volume =. Journal of the Atmospheric Sciences , publisher =. doi:10.1175/1520-0469(2004)061<1816:tnmitt>2.0.co;2 , number =

    work page doi:10.1175/1520-0469(2004)061 2004

  44. [44]

    Open questions in atmospheric turbulence: A synthesis from the centenary workshop “100 years of turbulence: Innsbruck 1922 -2022

    Stiperski, Ivana and Rotach, Mathias W. and Ansorge, Cedrick and Baklanov, Alexander and Belušić, Danijel and Bou-Zeid, Elie and Brun, Christophe and Christen, Andreas and Dias, Nelson Luís and D\". Open questions in atmospheric turbulence: A synthesis from the centenary workshop “100 years of turbulence: Innsbruck 1922 -2022” , volume =. 2025 , month = d...

    work page doi:10.1016/j.jemets.2025.100022 1922

  45. [45]

    Scale-Invariance and Turbulence Models for Large-Eddy Simulation , volume =

    Meneveau, Charles and Katz, Joseph , year =. Scale-Invariance and Turbulence Models for Large-Eddy Simulation , volume =. Annual Review of Fluid Mechanics , publisher =. doi:10.1146/annurev.fluid.32.1.1 , number =

    work page doi:10.1146/annurev.fluid.32.1.1

  46. [46]

    Challenging the large eddy simulation technique with advanced a posteriori tests , volume =

    Bou-Zeid, Elie , year =. Challenging the large eddy simulation technique with advanced a posteriori tests , volume =. doi:10.1017/jfm.2014.616 , journal =

    work page doi:10.1017/jfm.2014.616 2014

  47. [47]

    Turbulence and Vertical Fluxes in the Stable Atmospheric Boundary Layer

    Huang, Jing and Bou-Zeid, Elie and Golaz, Jean-Christophe , year =. Turbulence and Vertical Fluxes in the Stable Atmospheric Boundary Layer. Part II: A Novel Mixing-Length Model , volume =. Journal of the Atmospheric Sciences , publisher =. doi:10.1175/jas-d-12-0168.1 , number =

    work page doi:10.1175/jas-d-12-0168.1

  48. [48]

    Quality and reliability of

    Li, Qi and Bou-Zeid, Elie and Anderson, William and Grimmond, Sue and Hultmark, Marcus , year =. Quality and reliability of. doi:10.1016/j.ijheatmasstransfer.2016.06.093 , journal =

    work page doi:10.1016/j.ijheatmasstransfer.2016.06.093 2016

  49. [49]

    , year =

    Bou-Zeid, Elie and Higgins, Chad and Huwald, Hendrik and Meneveau, Charles and Parlange, Marc B. , year =. Field study of the dynamics and modelling of subgrid-scale turbulence in a stable atmospheric surface layer over a glacier , volume =. doi:10.1017/s0022112010004015 , journal =

    work page doi:10.1017/s0022112010004015

  50. [50]

    A First Course in Turbulence

    Tennekes, Henk and Lumley, John L. A First Course in Turbulence

  51. [51]

    and Lustig, M

    Kim, Seung-Jean and Koh, K. and Lustig, M. and Boyd, Stephen and Gorinevsky, Dimitry , journal=. An Interior-Point Method for Large-Scale l1-Regularized Least Squares , year=

  52. [52]

    Boundary-Layer Meteorology , volume=

    Large-eddy simulation of the atmospheric boundary layer , author=. Boundary-Layer Meteorology , volume=. 2020 , publisher=

    2020

  53. [53]

    Journal of computational physics , volume=

    On the effect of numerical errors in large eddy simulations of turbulent flows , author=. Journal of computational physics , volume=. 1997 , publisher=

    1997

  54. [54]

    Journal of Geophysical Research: Atmospheres , volume=

    Unsteady land-sea breeze circulations in the presence of a synoptic pressure forcing , author=. Journal of Geophysical Research: Atmospheres , volume=. 2025 , publisher=

    2025

  55. [55]

    Authorea Preprints , year=

    Numerical Simulations of Satellite-Sensed Surface Maps in the Marginal Ice Zone , author=. Authorea Preprints , year=

  56. [56]

    Quarterly Journal of the Royal Meteorological Society , volume=

    Baroclinicity and directional shear explain departures from the logarithmic wind profile , author=. Quarterly Journal of the Royal Meteorological Society , volume=. 2021 , publisher=

    2021

  57. [57]

    Journal of the Atmospheric Sciences , volume=

    Modulation of mean wind and turbulence in the atmospheric boundary layer by baroclinicity , author=. Journal of the Atmospheric Sciences , volume=

  58. [58]

    Encyclopedia of atmospheric sciences , volume=

    Large-eddy simulation , author=. Encyclopedia of atmospheric sciences , volume=. 2015 , publisher=

    2015

  59. [59]

    and Smith, Katherine and Robey, Rachel and Li, Qing and Pearson, Brodie and Van Roekel, Luke , year =

    Garanaik, Amrapalli and Pereira, Filipe S. and Smith, Katherine and Robey, Rachel and Li, Qing and Pearson, Brodie and Van Roekel, Luke , year =. A New Hybrid Mass‐Flux/High‐Order Turbulence Closure for Ocean Vertical Mixing , volume =. Journal of Advances in Modeling Earth Systems , publisher =. doi:10.1029/2023ms003846 , number =

    work page doi:10.1029/2023ms003846

  60. [60]

    and Zavala‐Romero, Olmo and Wan, Xiaoliang and Cronin, Meghan F

    Yuan, Jianguo and Liang, Jun‐Hong and Chassignet, Eric P. and Zavala‐Romero, Olmo and Wan, Xiaoliang and Cronin, Meghan F. , year =. The. Journal of Advances in Modeling Earth Systems , publisher =. doi:10.1029/2024ms004405 , number =

    work page doi:10.1029/2024ms004405

  61. [61]

    Strobach

    Edward J. Strobach. A Single-Column Model Evaluation of Mixing Length Formulations and Constraints for the sa-TKE-EDMF Planetary Boundary Layer Parameterization. Weather and Forecasting. 2022. doi:10.1175/WAF-D-21-0059.1

    work page doi:10.1175/waf-d-21-0059.1 2022

  62. [62]

    and Hoteit, Ibrahim and Knio, Omar , title =

    Hammoud, Mohamad Abed El Rahman and Titi, Edriss S. and Hoteit, Ibrahim and Knio, Omar , title =. Journal of Advances in Modeling Earth Systems , volume =. doi:https://doi.org/10.1029/2022MS003051 , url =. https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2022MS003051 , note =

    work page doi:10.1029/2022ms003051

  63. [63]

    and Schneider, Tapio , year =

    Cohen, Yair and Lopez‐Gomez, Ignacio and Jaruga, Anna and He, Jia and Kaul, Colleen M. and Schneider, Tapio , year =. Unified Entrainment and Detrainment Closures for Extended Eddy‐Diffusivity Mass‐Flux Schemes , volume =. Journal of Advances in Modeling Earth Systems , publisher =. doi:10.1029/2020ms002162 , number =

    work page doi:10.1029/2020ms002162

  64. [64]

    and Pressel, Kyle G

    Tan, Zhihong and Kaul, Colleen M. and Pressel, Kyle G. and Cohen, Yair and Schneider, Tapio and Teixeira, João , year =. An Extended Eddy‐Diffusivity Mass‐Flux Scheme for Unified Representation of Subgrid‐Scale Turbulence and Convection , volume =. Journal of Advances in Modeling Earth Systems , publisher =. doi:10.1002/2017ms001162 , number =

    work page doi:10.1002/2017ms001162

  65. [65]

    , year =

    Tseng, Yu-Heng and Meneveau, Charles and Parlange, Marc B. , year =. Modeling Flow around Bluff Bodies and Predicting Urban Dispersion Using Large Eddy Simulation , volume =. Environmental Science and; Technology , publisher =. doi:10.1021/es051708m , number =

    work page doi:10.1021/es051708m

  66. [66]

    Part I: Scheme description and single-column model tests , author=

    A new boundary layer mixing scheme. Part I: Scheme description and single-column model tests , author=. Monthly weather review , volume=

  67. [67]

    Quarterly Journal of the Royal Meteorological Society , volume=

    The non-local character of turbulence asymmetry in the convective atmospheric boundary layer , author=. Quarterly Journal of the Royal Meteorological Society , volume=. 2017 , publisher=

    2017

  68. [68]

    Coupling subgrid-scale surface heterogeneity to the convective boundary layer in the GFDL global model (AM4. 0-LM4. 0): Parameterization development and climate impacts , author=. Journal of Advances in Modeling Earth Systems , volume=. 2026 , publisher=

    2026

  69. [69]

    and Ackerley, Duncan and Xavier, Prince and Franklin, Charmaine and Senior, Catherine A

    Tomassini, Lorenzo and Willett, Martin and Sellar, Alistair and Lock, Adrian and Walters, David and Whitall, Michael and Sanchez, Claudio and Heming, Julian and Earnshaw, Paul and Rodriguez, José M. and Ackerley, Duncan and Xavier, Prince and Franklin, Charmaine and Senior, Catherine A. , title =. Journal of Advances in Modeling Earth Systems , volume =. ...

    work page doi:10.1029/2022ms003418

  70. [70]

    Journal of Advances in Modeling Earth Systems , volume =

    Tan, Zhihong and Zhao, Ming , title =. Journal of Advances in Modeling Earth Systems , volume =. doi:https://doi.org/10.1029/2025MS005168 , url =. https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2025MS005168 , note =

    work page doi:10.1029/2025ms005168

  71. [71]

    and Zanna, Laure , title =

    Guillaumin, Arthur P. and Zanna, Laure , title =. Journal of Advances in Modeling Earth Systems , volume =. doi:https://doi.org/10.1029/2021MS002534 , url =. https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2021MS002534 , note =

    work page doi:10.1029/2021ms002534

  72. [72]

    Journal of Advances in Modeling Earth Systems , volume =

    Zhang, Cheng and Perezhogin, Pavel and Gultekin, Cem and Adcroft, Alistair and Fernandez-Granda, Carlos and Zanna, Laure , title =. Journal of Advances in Modeling Earth Systems , volume =. doi:https://doi.org/10.1029/2023MS003697 , url =. https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2023MS003697 , note =

    work page doi:10.1029/2023ms003697

  73. [73]

    Journal of Advances in Modeling Earth Systems , volume =

    Perezhogin, Pavel and Zhang, Cheng and Adcroft, Alistair and Fernandez-Granda, Carlos and Zanna, Laure , title =. Journal of Advances in Modeling Earth Systems , volume =. doi:https://doi.org/10.1029/2023MS004104 , url =. https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2023MS004104 , note =

    work page doi:10.1029/2023ms004104

  74. [74]

    and Adcroft, Alistair and Zanna, Laure , title =

    Sane, Aakash and Reichl, Brandon G. and Adcroft, Alistair and Zanna, Laure , title =. Journal of Advances in Modeling Earth Systems , volume =. doi:https://doi.org/10.1029/2023MS003890 , url =. https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2023MS003890 , note =

    work page doi:10.1029/2023ms003890

  75. [75]

    Geophysical Research Letters , author =

    Schneider, Tapio and Lan, Shiwei and Stuart, Andrew and Teixeira, João , title =. Geophysical Research Letters , volume =. doi:https://doi.org/10.1002/2017GL076101 , url =. https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/2017GL076101 , abstract =

    work page doi:10.1002/2017gl076101

  76. [76]

    Lopez-Gomez, Ignacio and Christopoulos, Costa and Langeland Ervik, Haakon Ludvig and Dunbar, Oliver R. A. and Cohen, Yair and Schneider, Tapio , title =. Journal of Advances in Modeling Earth Systems , volume =. doi:https://doi.org/10.1029/2022MS003105 , url =. https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2022MS003105 , note =

    work page doi:10.1029/2022ms003105

  77. [77]

    Christopoulos, Costa and Lopez-Gomez, Ignacio and Beucler, Tom and Cohen, Yair and Kawczynski, Charles and Dunbar, Oliver R. A. and Schneider, Tapio , title =. Journal of Advances in Modeling Earth Systems , volume =. doi:https://doi.org/10.1029/2024MS004485 , url =. https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2024MS004485 , note =

    work page doi:10.1029/2024ms004485

  78. [78]

    Geophysical Research Letters , volume =

    Perezhogin, Pavel and Adcroft, Alistair and Zanna, Laure , title =. Geophysical Research Letters , volume =. doi:https://doi.org/10.1029/2025GL117046 , url =. https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2025GL117046 , note =

    work page doi:10.1029/2025gl117046

  79. [79]

    and Clark, Spencer K

    Watt-Meyer, Oliver and Brenowitz, Noah D. and Clark, Spencer K. and Henn, Brian and Kwa, Anna and McGibbon, Jeremy and Perkins, W. Andre and Harris, Lucas and Bretherton, Christopher S. , title =. Journal of Advances in Modeling Earth Systems , volume =. doi:https://doi.org/10.1029/2023MS003668 , url =. https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1...

    work page doi:10.1029/2023ms003668

  80. [80]

    and Han, Y

    Wang, X. and Han, Y. and Xue, W. and Yang, G. and Zhang, G. J. , TITLE =. Geoscientific Model Development , VOLUME =. 2022 , NUMBER =

    2022

Showing first 80 references.