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arxiv: 2606.21278 · v1 · pith:VQFDUXTLnew · submitted 2026-06-19 · ⚛️ physics.ao-ph · physics.comp-ph· physics.geo-ph

Elastic Non-Uniform FFT (ENUFFT) spectral reconstruction of irregularly sampled orography on unstructured grids

Tridib Banerjee , Felix Jochum , Ulrich Achatz This is my paper

Pith reviewed 2026-06-26 12:51 UTC · model grok-4.3

classification ⚛️ physics.ao-ph physics.comp-phphysics.geo-ph
keywords orographynon-uniform FFTspectral reconstructionunstructured gridsmountain wavesgravity wave parameterizationFourier coefficientselastic mode selection
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The pith

ENUFFT computes local Fourier coefficients directly from irregular orography samples on unstructured grids without interpolation or fitting.

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

The paper presents a new framework called ENUFFT that recovers terrain spectra from elevation data sampled irregularly on non-rectangular grids. It combines a type-1 non-uniform FFT with local windowing, quadrature weights, and an Elastic Mode Selection algorithm that keeps only a flow-dependent subset of modes. In monochromatic and Alpine terrain tests, the method matches peak amplitude and direction while cutting spectral size by 25 to 60 percent and keeping spectral variance within 14-24 percent of the reference value. Existing methods produce energy deviations up to 122000 percent. A mountain-wave test shows the mode selection can shrink the launch spectrum by at least 75 percent while losing no more than 7 percent of launch power.

Core claim

ENUFFT recovers peak amplitude and direction comparably to the strongest existing method while compacting spectra by roughly 25 percent in the monochromatic case and 60 percent in the Alpine case; its spectral variance deviates from the reference by only 14-24 percent versus 500-122000 percent for the prior approach, and the Elastic Mode Selection step reduces the launch spectrum by at least 75 percent with launch-power loss at most 7 percent.

What carries the argument

The Elastic Non-Uniform Fast Fourier Transform (ENUFFT) that pairs a type-1 NUFFT with local windowing, quadrature weights, and the Elastic Mode Selection (EMS) algorithm to produce local Fourier coefficients and retain a flow-dependent subset of modes directly from unstructured-grid samples.

If this is right

  • Orographic spectra can be obtained without forcing data onto regular grids or embedding truncation effects inside the coefficients.
  • Flow-dependent truncation becomes possible inside parameterizations that need a launch spectrum budget.
  • Spectral variance satisfies Parseval's relation closely enough for energy-conserving source descriptions.
  • Compute cost scales better with data size than fitting-based alternatives.
  • Fourier-based orographic source terms become practical for spectral-budget-aware gravity-wave schemes.

Where Pith is reading between the lines

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

  • Global models could ingest higher-resolution terrain datasets without first resampling them onto structured grids.
  • The same direct-coefficient approach might apply to other irregularly observed fields such as sea-surface height or atmospheric temperature.
  • Full-model tests could check whether the reduced launch spectrum improves simulated mountain-wave drag without retuning.
  • The method opens a route to adaptive, location-specific mode counts that change with local wind.

Load-bearing premise

Type-1 NUFFT combined with local windowing and quadrature weights can compute accurate local Fourier coefficients from irregularly sampled data without introducing sampling-pattern bias.

What would settle it

Compute the spectral energy deviation for a known monochromatic wave sampled on the same irregular Alpine grid points; if ENUFFT stays within 25 percent while the existing method exceeds several hundred percent, the claim holds.

Figures

Figures reproduced from arXiv: 2606.21278 by Felix Jochum, Tridib Banerjee, Ulrich Achatz.

Figure 1
Figure 1. Figure 1: Comparison of the baseline Kaiser-Bessel kernel in (eq [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Elastic mode selection applied to six spectral families including uniform, exponential, peak, [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Monochromatic test of ENUFFT and CSA (sec [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Alpine SRTM DEM of (sec 3.2) through four stages of preprocessing, namely raw SRTM mosaic, coarse-grained with elevation clipping, Gaussian smoothed, and deplaned on an R2B5 mesh. The source topography is the NASA SRTM GL1 1 arc-second dataset (NASA JPL, 2013). produces a median εrel only ∼ 0.3–0.5 standard deviations worse than CSA. At the same time, ENUFFT uses significantly fewer modes, with median spec… view at source ↗
Figure 5
Figure 5. Figure 5: ENUFFT and CSA applied to the Alpine SRTM DEM from (sec [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Same as (fig 5) but on the finer R2B5 mesh (∆ ≈ 80 km). Jochum et al., 2025). Because MS-GWaM models gravity waves using computationally expensive propagating ray volumes, it is well suited for demonstrating the potential of EMS. Here, EMS is used in an idealized one-hour simulation of gravity waves generated above an isolated mountain range. Banerjee (2026c,a) describes the test setup in detail, including… view at source ↗
Figure 7
Figure 7. Figure 7: Results of a one-hour PinCFlow.jl simulation from (sec [PITH_FULL_IMAGE:figures/full_fig_p019_7.png] view at source ↗
read the original abstract

Subgrid-scale orography remains a leading source of uncertainty in numerical modeling because terrain spectra must be recovered from irregularly sampled elevation data and then reduced to a flow-dependent launch budget for parameterizations. Existing approaches are limited either by assuming regular samples on rectangular grids or by fitting coefficients whose truncation and regularization effects become embedded in the spectrum. None achieves dynamic, flow-dependent truncation. This study introduces an Elastic Non-Uniform Fast Fourier Transform (ENUFFT) framework that computes local Fourier coefficients directly from irregularly sampled orography on unstructured grids, without interpolation or fitting. It combines a type-1 NUFFT with local windowing, quadrature weights, and a new Elastic Mode Selection (EMS) algorithm for retaining a local flow-dependent subset of modes. ENUFFT is compared with the strongest relevant existing method in a monochromatic and a real Alpine terrain test. In both cases, it recovers peak amplitude and direction comparably while significantly compacting the spectra (monochromatic ~25%, Alpine ~60%). It also satisfies the Parseval condition more closely with its spectral variance (energy) deviating from reference by ~14-24% versus ~500-122,000% for the existing method. Its EMS is additionally tested in a mountain-wave test where it reduces the launch spectrum by >=75% while keeping launch-power loss <=7%. Along with better compute scaling, ENUFFT is thus a computationally efficient, physically interpretable framework that can make Fourier-based orographic source descriptions practical for spectral-budget-aware parameterizations.

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 paper introduces the ENUFFT framework to compute local Fourier coefficients directly from irregularly sampled orography on unstructured grids via type-1 NUFFT combined with local windowing and quadrature weights, without interpolation or fitting. It adds the Elastic Mode Selection (EMS) algorithm for flow-dependent mode retention. In monochromatic and Alpine terrain tests, ENUFFT recovers peak amplitude and direction comparably to the strongest existing method while compacting spectra by ~25% and ~60%, respectively, and satisfies Parseval's relation more closely (spectral variance deviation 14-24% vs. 500-122000%). In a mountain-wave test, EMS reduces the launch spectrum by >=75% with <=7% launch-power loss. The method is positioned as enabling practical Fourier-based orographic source descriptions for spectral-budget-aware parameterizations.

Significance. If the local coefficients prove unbiased on unstructured grids, ENUFFT would address a key limitation in subgrid-scale orography modeling by delivering compact, flow-dependent spectra with improved energy conservation from real terrain data. The provision of concrete quantitative test cases (monochromatic, Alpine, mountain-wave) with explicit metrics is a strength that allows direct assessment of the compaction and Parseval claims.

major comments (3)
  1. [Framework description] Framework description: The claim that type-1 NUFFT plus local windowing and quadrature weights produces unbiased local Fourier coefficients on unstructured grids (no residual sampling-pattern bias) is load-bearing for all reported performance numbers, yet the manuscript provides no explicit verification test recovering known analytical coefficients from irregularly distributed samples. Without such a demonstration that the quadrature weights restore exact integration for the windowed basis functions given the local point geometry, the quantitative improvements in compaction and Parseval deviation cannot be secured.
  2. [EMS algorithm and mountain-wave test] EMS algorithm and mountain-wave test: The EMS selection thresholds are free parameters, but no justification, sensitivity analysis, or description of how they were chosen is given. The reported >=75% launch-spectrum reduction with <=7% power loss therefore risks being post-hoc; a parameter sweep or cross-validation on the mountain-wave case is required to establish that the truncation performance is robust rather than tuned to the specific test.
  3. [Quantitative comparisons] Quantitative comparisons (monochromatic and Alpine tests): The reported compaction percentages (~25%, ~60%) and Parseval deviations (14-24% vs. 500-122000%) are presented without error bars, multiple realizations, or details on how the reference spectra were constructed. Because the central claims rest on these specific numbers, the results section must include uncertainty estimates or repeated samplings to demonstrate that the improvements are not sensitive to the particular irregular point distributions used.
minor comments (2)
  1. [Abstract] Abstract: The compaction and deviation figures should explicitly state the underlying metrics (e.g., number of retained modes for compaction, L2 norm or integrated variance for Parseval deviation) so readers can interpret the percentages without ambiguity.
  2. [Notation] Notation: The definition of local window parameters and quadrature weights should be given a consistent symbol table or equation reference to avoid ambiguity when the method is implemented by others.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed report. We address each major comment below and will revise the manuscript accordingly to strengthen the claims.

read point-by-point responses

  1. Referee: [Framework description] Framework description: The claim that type-1 NUFFT plus local windowing and quadrature weights produces unbiased local Fourier coefficients on unstructured grids (no residual sampling-pattern bias) is load-bearing for all reported performance numbers, yet the manuscript provides no explicit verification test recovering known analytical coefficients from irregularly distributed samples. Without such a demonstration that the quadrature weights restore exact integration for the windowed basis functions given the local point geometry, the quantitative improvements in compaction and Parseval deviation cannot be secured.

    Authors: We agree that an explicit verification test recovering known analytical coefficients would strengthen the foundation for the unbiased-coefficient claim. In the revised manuscript we will add a dedicated verification subsection that applies the type-1 NUFFT plus local windowing and quadrature weights to irregularly distributed samples of known analytical functions and demonstrates exact recovery of the coefficients, thereby confirming that the quadrature weights restore the required integration. revision: yes

  2. Referee: [EMS algorithm and mountain-wave test] EMS algorithm and mountain-wave test: The EMS selection thresholds are free parameters, but no justification, sensitivity analysis, or description of how they were chosen is given. The reported >=75% launch-spectrum reduction with <=7% power loss therefore risks being post-hoc; a parameter sweep or cross-validation on the mountain-wave case is required to establish that the truncation performance is robust rather than tuned to the specific test.

    Authors: We accept that the EMS thresholds require explicit justification and a sensitivity study. The revised manuscript will include a parameter-sweep and cross-validation analysis on the mountain-wave test case, documenting how the thresholds were selected and confirming that the reported spectrum reduction and power-loss figures remain stable across a range of threshold values. revision: yes

  3. Referee: [Quantitative comparisons] Quantitative comparisons (monochromatic and Alpine tests): The reported compaction percentages (~25%, ~60%) and Parseval deviations (14-24% vs. 500-122000%) are presented without error bars, multiple realizations, or details on how the reference spectra were constructed. Because the central claims rest on these specific numbers, the results section must include uncertainty estimates or repeated samplings to demonstrate that the improvements are not sensitive to the particular irregular point distributions used.

    Authors: We agree that uncertainty quantification is needed to support the reported compaction and Parseval figures. The revised results section will report error bars obtained from repeated samplings with varied irregular point distributions, together with a clear description of how the reference spectra were constructed, to show that the improvements are robust to the choice of sampling pattern. revision: yes

Circularity Check

0 steps flagged

No circularity: new computational procedure validated on independent test cases

full rationale

The paper introduces ENUFFT as a direct computational method (type-1 NUFFT + local windowing + quadrature weights + EMS) for obtaining local Fourier coefficients from irregular unstructured-grid samples without interpolation or fitting. All reported metrics (peak recovery, spectral compaction ~25-60%, Parseval deviation 14-24% vs. 500-122000%, EMS reduction >=75% with <=7% power loss) are obtained from explicit numerical comparisons on separate monochromatic, Alpine, and mountain-wave test cases. No step reduces by the paper's own equations to a fitted parameter renamed as prediction, no self-definitional loop, and no load-bearing self-citation chain is present. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 1 invented entities

The central claim rests on the new EMS algorithm and the assumption that NUFFT plus windowing and quadrature accurately handles irregular sampling. Free parameters likely exist in window sizes and EMS selection criteria but are unspecified. The invented entity is the EMS algorithm itself.

free parameters (2)
  • local window parameters
    Parameters controlling local windowing size and shape are required for the method but not detailed in the abstract.
  • EMS selection thresholds
    Flow-dependent criteria for retaining modes are part of the new algorithm and likely involve tunable elements.
axioms (1)
  • domain assumption Type-1 NUFFT combined with quadrature weights computes unbiased local Fourier coefficients from irregular point samples on unstructured grids.
    Invoked as the foundation for direct computation without interpolation or fitting.
invented entities (1)
  • Elastic Mode Selection (EMS) algorithm no independent evidence
    purpose: To retain a local flow-dependent subset of Fourier modes for dynamic, physically interpretable truncation.
    Newly introduced component without external validation or formal proof mentioned.

pith-pipeline@v0.9.1-grok · 5817 in / 1579 out tokens · 36232 ms · 2026-06-26T12:51:45.374882+00:00 · methodology

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Reference graph

Works this paper leans on

97 extracted references · 21 canonical work pages

  1. [1]

    and Shea-Brown, Eric , journal =

    Recanatesi, Stefano and Bradde, Serena and Balasubramanian, Vijay and Steinmetz, Nicholas A. and Shea-Brown, Eric , journal =. A scale-dependent measure of system dimensionality , year =

  2. [2]

    Source Enumeration Approaches Using Eigenvalue Gaps and Machine Learning Based Threshold for Direction-of-Arrival Estimation , year =

    Lee, Yunseong and Park, Chanhong and Kim, Taeyoung and Choi, Yeongyoon and Kim, Kiseon and Kim, Dongho and Lee, Myung-Sik and Lee, Dongkeun , journal =. Source Enumeration Approaches Using Eigenvalue Gaps and Machine Learning Based Threshold for Direction-of-Arrival Estimation , year =

  3. [3]

    A tutorial on spectral clustering , year =

    Luxburg, Ulrike von , journal =. A tutorial on spectral clustering , year =

  4. [4]

    and Tukey, John W

    Cooley, J.W. and Tukey, John W. , title =. Mathematics of Computation , year =

  5. [5]

    and Rokhlin, Vladimir , journal =

    Dutt, A. and Rokhlin, Vladimir , journal =. Fast Fourier Transforms for Nonequispaced Data , year =

  6. [6]

    IEEE Transactions on Antennas and Propagation , volume =

    Houshmand, Behnam and Chew, Weng Cho and Lee, Shung-Wu , title =. IEEE Transactions on Antennas and Propagation , volume =. 1991 , doi =

    1991

  7. [7]

    Accelerating the Nonuniform Fast Fourier Transform , year =

    Greengard, Leslie and Lee, June‐Yub , journal =. Accelerating the Nonuniform Fast Fourier Transform , year =

  8. [8]

    and Sutton, Bradley P

    Fessler, Jeffrey A. and Sutton, Bradley P. , journal =. Nonuniform fast fourier transforms using min-max interpolation , year =

  9. [9]

    , title =

    Fessler, Jeffrey A. , title =

  10. [10]

    and Magland, Jeremy and Klinteberg, Ludvig af , title =

    Barnett, Alexander H. and Magland, Jeremy and Klinteberg, Ludvig af , title =. SIAM Journal on Scientific Computing , year =

  11. [11]

    Journal of Computational Physics , volume =

    Sammis, Ian and Strain, John , title =. Journal of Computational Physics , volume =. 2009 , doi =

    2009

  12. [12]

    , journal =

    Barnett, Alex H. , journal =. Aliasing error of the exp(beta1-z2) kernel in the nonuniform fast Fourier transform , year =

  13. [13]

    Continuous window functions for NFFT , year =

    Potts, Daniel and Tasche, Manfred , journal =. Continuous window functions for NFFT , year =

  14. [14]

    Kaiser, J. F. and Schafer, Ronald W. , journal =. On the use of the I0-sinh window for spectrum analysis , year =

  15. [15]

    A Constrained Spectral Approximation of Subgrid‐Scale Orography on Unstructured Grids , year =

    Chew, Ray and Dolaptchiev, Stamen and Wedel, Maja‐Sophie and Achatz, Ulrich , journal =. A Constrained Spectral Approximation of Subgrid‐Scale Orography on Unstructured Grids , year =

  16. [16]

    and Reichel, L

    Park, Y. and Reichel, L. and Rodriguez, G. and Yu, X. , journal =. Parameter determination for Tikhonov regularization problems in general form , year =

  17. [17]

    , journal =

    Golub, Gene H. , journal =. Matrix Computations , year =

  18. [18]

    Acta numerica , volume=

    Monte Carlo and quasi-Monte Carlo methods , author=. Acta numerica , volume=. 1998 , publisher=

    1998

  19. [19]

    doi:10.5067/MEaSUREs/SRTM/SRTMGL1.003 , note =

    2013 , publisher =. doi:10.5067/MEaSUREs/SRTM/SRTMGL1.003 , note =

    work page doi:10.5067/measures/srtm/srtmgl1.003 2013

  20. [20]

    Reviews of Geophysics , volume=

    The shuttle radar topography mission , author=. Reviews of Geophysics , volume=. 2007 , publisher=

    2007

  21. [21]

    Coles, W. A. and Hobbs, G. B. and Champion, D. J. and Manchester, R. N. and Verbiest, J. P. W. , title =. Monthly Notices of the Royal Astronomical Society , year =

  22. [22]

    and Qui, Harry Z

    Maciejewski, Mark W. and Qui, Harry Z. and Rujan, Iulian and Mobli, Mehdi and Hoch, Jeffrey C. , title =. Journal of Magnetic Resonance , year =

  23. [23]

    and Menon, Padmanabhan , title =

    Pipe, James G. and Menon, Padmanabhan , title =. Magnetic Resonance in Medicine , year =

  24. [24]

    and Meyer, Craig H

    Jackson, John I. and Meyer, Craig H. and Nishimura, Dwight G. and Macovski, Albert , title =. IEEE Transactions on Medical Imaging , year =

  25. [25]

    Mathematics , VOLUME =

    Oliveira, Carlos and Pais, Ana and Belinha, Jorge , TITLE =. Mathematics , VOLUME =. 2025 , NUMBER =

    2025

  26. [26]

    Tom Axel Bobach , title =

  27. [27]

    and Linsen, L

    Park, S.W. and Linsen, L. and Kreylos, O. and Owens, J.D. and Hamann, B. , journal=. Discrete Sibson interpolation , year=

  28. [28]

    Quarterly Journal of the Royal Meteorological Society , author =

    Zängl, Günther and Reinert, Daniel and Rípodas, Pilar and Baldauf, Michael , journal =. The ICON (ICOsahedral Non-hydrostatic) modelling framework of DWD and MPI-M: Description of the non-hydrostatic dynamical core , year =. doi:10.1002/qj.2378 , keywords =

    work page doi:10.1002/qj.2378

  29. [29]

    SIAM Review , volume =

    Du, Qiang and Faber, Vance and Gunzburger, Max , title =. SIAM Review , volume =. 1999 , doi =

    1999

  30. [30]

    Applied Sciences , VOLUME =

    Chen, Xinwen and Tan, Zheng and Wang, Jianwei and Zhao, Na and Tang, Yinhui and Liu, Yangyang and Si, Jia and Zhang, Yu and Sun, Jianying and Li, Weiyan and Lv, Qunbo , TITLE =. Applied Sciences , VOLUME =. 2024 , NUMBER =

    2024

  31. [31]

    On the Gibbs Phenomenon and its Resolution , urldate =

    David Gottlieb and Chi-Wang Shu , journal =. On the Gibbs Phenomenon and its Resolution , urldate =. 1997 , doi =

    1997

  32. [32]

    and Hogan, Robin J

    Williams, Peter D. and Hogan, Robin J. and Sherwood, Steven C. and Warner, Christopher D. and van Niekerk, Annelize , title =. Quarterly Journal of the Royal Meteorological Society , volume =. 2020 , doi =

    2020

  33. [33]

    and Vosper, S

    van Niekerk, A. and Vosper, S. B. , title =. Quarterly Journal of the Royal Meteorological Society , volume =. 2021 , doi =

    2021

  34. [34]

    and Vosper, S

    van Niekerk, A. and Vosper, S. B. and Teixeira, M. A. C. , title =. Quarterly Journal of the Royal Meteorological Society , volume =. 2023 , doi =

    2023

  35. [35]

    Atmosphere , volume =

    Liu, Kun and Yu, Fei and Su, Yong and Zhang, Hongliang and Chen, Qiying and Sun, Jian , title =. Atmosphere , volume =. 2023 , doi =

    2023

  36. [36]

    Hewitt , journal =

    Edwin Hewitt and Robert E. Hewitt , journal =. The Gibbs-Wilbraham Phenomenon: An Episode in Fourier Analysis , urldate =. 1979 , doi =

    1979

  37. [37]

    Palmer, T. N. and Shutts, G. J. and Swinbank, R. , title =. Quarterly Journal of the Royal Meteorological Society , volume =. 1986 , doi =

    1986

  38. [38]

    McFarlane, N. A. , title =. Journal of the Atmospheric Sciences , volume =. 1987 , doi =

    1987

  39. [39]

    and Chun, Hye-Yeong , title =

    Kim, Young-Joon and Eckermann, Stephen D. and Chun, Hye-Yeong , title =. Atmosphere-Ocean , volume =. 2003 , doi =

    2003

  40. [40]

    Teixeira, Miguel A. C. , title =. Frontiers in Physics , volume =. 2014 , doi =

    2014

  41. [41]

    How does knowledge of atmospheric gravity waves guide their parameterizations? , journal =

    Plougonven, Riwal and de la C. How does knowledge of atmospheric gravity waves guide their parameterizations? , journal =. 2020 , doi =

    2020

  42. [42]

    A new subgrid-scale orographic drag parametrization: Its formulation and testing , journal =

    Lott, Fran. A new subgrid-scale orographic drag parametrization: Its formulation and testing , journal =. 1997 , doi =

    1997

  43. [43]

    and Shutts, G

    Gregory, D. and Shutts, G. J. and Mitchell, J. R. , title =. Quarterly Journal of the Royal Meteorological Society , volume =. 1998 , doi =

    1998

  44. [44]

    Scinocca, J. F. and McFarlane, N. A. , title =. Quarterly Journal of the Royal Meteorological Society , volume =. 2000 , doi =

    2000

  45. [45]

    and Brown, A

    Webster, S. and Brown, A. R. and Cameron, D. R. and Jones, C. P. , title =. Quarterly Journal of the Royal Meteorological Society , volume =. 2003 , doi =

    2003

  46. [46]

    Beljaars, A. C. M. and Brown, A. R. and Wood, N. , title =. Quarterly Journal of the Royal Meteorological Society , volume =. 2004 , doi =

    2004

  47. [47]

    , title =

    Garner, Stephen T. , title =. Journal of the Atmospheric Sciences , volume =. 2005 , doi =

    2005

  48. [48]

    and Eckermann, Stephen D

    Marks, Crispin J. and Eckermann, Stephen D. , title =. Journal of the Atmospheric Sciences , volume =. 1995 , doi =

    1995

  49. [49]

    Journal of Geophysical Research: Atmospheres , volume =

    Choi, Hyun-Joo and Hong, Song-You , title =. Journal of Geophysical Research: Atmospheres , volume =. 2015 , doi =

    2015

  50. [50]

    and Zadra, Ayrton , title =

    Sandu, Irina and Bechtold, Peter and Beljaars, Anton and Bozzo, Alessio and Pithan, Felix and Shepherd, Theodore G. and Zadra, Ayrton , title =. Journal of Advances in Modeling Earth Systems , volume =. 2016 , doi =

    2016

  51. [51]

    and Sandu, Irina and Wedi, Nils and Vosper, Simon B

    Elvidge, Andrew D. and Sandu, Irina and Wedi, Nils and Vosper, Simon B. and Zadra, Ayrton and Boussetta, Souhail and Bouyssel, Fran. Uncertainty in the representation of orography in weather and climate models and implications for parameterized drag , journal =. 2019 , doi =

    2019

  52. [52]

    Journal of Advances in Modeling Earth Systems , volume =

    Xie, Jinbo and Zhang, Minghua and Zeng, Qingcun and Xie, Zhenghui and Liu, Hailong and Chai, Zhaoyang and He, JuanXiong and Zhang, He , title =. Journal of Advances in Modeling Earth Systems , volume =. 2021 , doi =

    2021

  53. [53]

    Parameterized orographic gravity wave drag and dynamical effects in

    H. Parameterized orographic gravity wave drag and dynamical effects in. Climate Dynamics , volume =. 2024 , doi =

    2024

  54. [54]

    and Bellinghausen, K

    Juricke, S. and Bellinghausen, K. and Danilov, S. and Kutsenko, A. and Oliver, M. , title =. Journal of Advances in Modeling Earth Systems , volume =. 2023 , doi =

    2023

  55. [55]

    , title =

    Shi, Yilei and Zhu, Xiao Xiang and Ellero, Marco and Adams, Nikolaus A. , title =. Computers & Fluids , volume =. 2013 , doi =

    2013

  56. [56]

    doi:10.5281/ZENODO.17391579 , note =

    Jochum, Felix and Knop, Irmgard and Rothermel, Jonas and Artiano, Marco and Babbar, Arpit and Ranocha, Hendrik and Dolaptchiev, Stamen and Klewinghaus, Sandra and Achatz, Ulrich , year =. doi:10.5281/ZENODO.17391579 , note =

    work page doi:10.5281/zenodo.17391579

  57. [57]

    npj Climate and Atmospheric Science , volume =

    Wang, Yingjie and Xu, Xin and Yang, Xiangrong and Wei, Peng and Li, Congyuan and Wu, Jianping and Ren, Kaijun , title =. npj Climate and Atmospheric Science , volume =. 2025 , doi =

    2025

  58. [58]

    2026 , note =

    Banerjee, Tridib , title =. 2026 , note =

    2026

  59. [59]

    2026 , publisher =

    Banerjee, Tridib , title =. 2026 , publisher =. doi:10.5281/ZENODO.20544458 , url =

    work page doi:10.5281/zenodo.20544458 2026

  60. [60]

    2026 , publisher =

    Banerjee, Tridib , title =. 2026 , publisher =. doi:10.5281/ZENODO.20545261 , url =

    work page doi:10.5281/zenodo.20545261 2026

  61. [61]

    2026 , publisher =

    Banerjee, Tridib , title =. 2026 , publisher =

    2026

  62. [62]

    and Kim, Y.-H

    Achatz, U. and Kim, Y.-H. and Voelker, G. S. , journal =. Multi-scale dynamics of the interaction between waves and mean flows: From nonlinear. 2023 , issn =. doi:10.1063/5.0165180 , publisher =

    work page doi:10.1063/5.0165180 2023

  63. [63]

    and Ribstein, B

    Achatz, U. and Ribstein, B. and Senf, F. and Klein, R. , journal =. The interaction between synoptic-scale balanced flow and a finite-amplitude mesoscale wave field throughout all atmospheric layers: weak and moderately strong stratification , year =. doi:10.1002/qj.2926 , publisher =

    work page doi:10.1002/qj.2926

  64. [64]

    Journal of the Atmospheric Sciences , title =

    B. Journal of the Atmospheric Sciences , title =. 2021 , issn =. doi:10.1175/jas-d-20-0065.1 , publisher =

    work page doi:10.1175/jas-d-20-0065.1 2021

  65. [65]

    Journal of the Atmospheric Sciences , title =

    B. Journal of the Atmospheric Sciences , title =. 2016 , issn =. doi:10.1175/jas-d-16-0069.1 , publisher =

    work page doi:10.1175/jas-d-16-0069.1 2016

  66. [66]

    Journal of the Atmospheric Sciences , title =

    Jochum, Felix and Chew, Ray and Lott, Fran. Journal of the Atmospheric Sciences , title =. 2025 , issn =. doi:10.1175/jas-d-24-0158.1 , publisher =

    work page doi:10.1175/jas-d-24-0158.1 2025

  67. [67]

    Journal of the Atmospheric Sciences , title =

    Kim, Young-Ha and B. Journal of the Atmospheric Sciences , title =. 2021 , issn =. doi:10.1175/jas-d-20-0066.1 , publisher =

    work page doi:10.1175/jas-d-20-0066.1 2021

  68. [68]

    Atmospheric Chemistry and Physics , title =

    Kim, Young-Ha and Voelker, Georg Sebastian and B. Atmospheric Chemistry and Physics , title =. 2024 , issn =. doi:10.5194/acp-24-3297-2024 , publisher =

    work page doi:10.5194/acp-24-3297-2024 2024

  69. [69]

    and Fruman, M

    Muraschko, J. and Fruman, M. D. and Achatz, U. and Hickel, S. and Toledo, Y. , journal =. On the application of. 2015 , issn =. doi:10.1002/qj.2381 , publisher =

    work page doi:10.1002/qj.2381 2015

  70. [70]

    Voelker, Georg S. and B. Journal of the Atmospheric Sciences , title =. 2024 , issn =. doi:10.1175/jas-d-23-0153.1 , publisher =

    work page doi:10.1175/jas-d-23-0153.1 2024

  71. [71]

    2000 , edition =

    Okabe, Atsuyuki and Boots, Barry and Sugihara, Kokichi and Chiu, Sung Nok , title =. 2000 , edition =

    2000

  72. [72]

    ACM Computing Surveys , volume =

    Aurenhammer, Franz , title =. ACM Computing Surveys , volume =. 1991 , doi =

    1991

  73. [73]

    and Hodgman, Gary W

    Sutherland, Ivan E. and Hodgman, Gary W. , title =. Communications of the ACM , volume =. 1974 , doi =

    1974

  74. [74]

    Nature , volume =

    Braun, Jean and Sambridge, Malcolm , title =. Nature , volume =. 1995 , doi =

    1995

  75. [75]

    doi:10.5067/MEaSUREs/NASADEM/NASADEM_HGT.001 , note =

    2020 , publisher =. doi:10.5067/MEaSUREs/NASADEM/NASADEM_HGT.001 , note =

    work page doi:10.5067/measures/nasadem/nasadem_hgt.001 2020

  76. [76]

    doi:10.5067/ASTER/ASTGTM.003

    2019 , publisher =. doi:10.5067/ASTER/ASTGTM.003 , note =

    work page doi:10.5067/aster/astgtm.003 2019

  77. [77]

    doi:10.57746/eo.01kkfx0ejw8r5ndc9bg5nt13ws , note =

    2024 , publisher =. doi:10.57746/eo.01kkfx0ejw8r5ndc9bg5nt13ws , note =

    work page doi:10.57746/eo.01kkfx0ejw8r5ndc9bg5nt13ws 2024

  78. [78]

    and Sampson, Christopher C

    Yamazaki, Dai and Ikeshima, Daiki and Tawatari, Ryunosuke and Yamaguchi, Taichi and O'Loughlin, Fiachra and Neal, Jeffrey C. and Sampson, Christopher C. and Kanae, Shinjiro and Bates, Paul D. , title =. Geophysical Research Letters , volume =. 2017 , doi =

    2017

  79. [79]

    2021 , publisher =

    Hawker, Laurence and Neal, Jeffrey , title =. 2021 , publisher =. doi:10.5523/bris.25wfy0f9ukoge2gs7a5mqpq2j7 , note =

    work page doi:10.5523/bris.25wfy0f9ukoge2gs7a5mqpq2j7 2021

  80. [80]

    Environmental Research Letters , volume =

    Hawker, Laurence and Uhe, Peter and Paulo, Lina and Sosa, Josue and Savage, James and Sampson, Christopher and Neal, Jeffrey , title =. Environmental Research Letters , volume =. 2022 , doi =

    2022

Showing first 80 references.