pith. machine review for the scientific record. sign in

arxiv: 2604.19500 · v1 · submitted 2026-04-21 · ⚛️ physics.ao-ph

Recognition: unknown

Connecting the forward problem to the inverse problem in uncertainty quantification of Earth system models using fast emulators

Ethan YoungIn Shin , Baris Kale , Michael F. Howland
Authors on Pith no claims yet

Pith reviewed 2026-05-10 00:59 UTC · model grok-4.3

classification ⚛️ physics.ao-ph
keywords uncertainty quantificationBayesian calibrationEarth system modelsglobal sensitivity analysisGaussian process emulatorsatmospheric turbulenceparameter estimationWRF model
0
0 comments X

The pith

Forward uncertainty analysis identifies observations that enable accurate Bayesian calibration of Earth system model parameters.

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

The paper shows that parameter sensitivity results obtained by propagating uncertainties forward through a model can be turned directly into a non-iterative way to choose which observations will most effectively tighten parameter estimates during Bayesian calibration. Using Gaussian process emulators trained on a few hundred WRF simulations, the authors map how each parameter contributes to output variance across different observation types, atmospheric conditions, averaging periods, and locations. They introduce two simple nondimensional checks: whether a parameter's contribution exceeds the observational noise level and whether its independent effect exceeds interaction effects. Observations that pass both checks produce markedly lower posterior uncertainty when used for calibration on synthetic data. A reader should care because this link makes the expensive inverse problem tractable for complex Earth system models that would otherwise require prohibitive numbers of runs or risk ill-posed calibrations.

Core claim

Using emulators, global sensitivity analysis across observation space shows that a parameter's contribution to output variance depends on quantity of interest, stability regime, averaging length, and spatial location. Nondimensional diagnostic measures then flag the observation regions where that contribution exceeds observational noise and the parameter's main effect exceeds interactions. Bayesian inversions that assimilate data only from these regions recover the true parameter values and achieve substantially smaller posterior variances than inversions using arbitrary or less informative observations.

What carries the argument

Nondimensional diagnostic measures that test whether a parameter's contribution to output variance exceeds observational noise and its independent effect exceeds interaction effects; these measures select the observations used for subsequent Bayesian calibration.

If this is right

  • Observations from regions identified by the diagnostics serve as a strong proxy for accurate parameter recovery in Bayesian calibration.
  • Posterior uncertainty on model parameters decreases systematically when calibration uses sensitivity-guided rather than arbitrary observations.
  • Emulators allow exhaustive sensitivity mapping across observation space without the O(10^5) model evaluations otherwise required.
  • The resulting non-iterative workflow avoids the computational cost and ill-posedness that arise when calibration begins with uninformative data.

Where Pith is reading between the lines

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

  • The same diagnostic approach could be used to design field campaigns that place sensors only in the most informative locations and conditions.
  • If the diagnostics remain reliable on real data, they offer a practical way to down-select the enormous observation streams now available from satellites and networks before calibration begins.
  • Extending the method to other Earth system components such as ocean or land-surface parameterizations would test whether the same forward-to-inverse link holds across different model physics.
  • One could combine these static diagnostics with sequential experimental design to adaptively acquire new observations that further shrink the remaining posterior uncertainty.

Load-bearing premise

The nondimensional diagnostics based on variance contributions will still select observations that reduce posterior uncertainty when the observations are real rather than synthetic and when the emulator contains approximation error.

What would settle it

Run Bayesian calibration twice on the same synthetic or real dataset: once with observations chosen by the diagnostics and once with randomly selected observations of equal number; if the posterior variance is not smaller for the diagnostic-selected set, the claim fails.

Figures

Figures reproduced from arXiv: 2604.19500 by Baris Kale, Ethan YoungIn Shin, Michael F. Howland.

Figure 1
Figure 1. Figure 1: Schematic of the proposed framework that connects the forward problem to the inverse problem of UQ through nondimensional measures of Sobol’ sensitivity indices. These diagnostics quantify (i) the total parameter signal relative to observational noise, (ii) the ratio of main-effect sensitivity of a parameter to its interaction-effect sensitivity, and (iii) the main-effect sensitivity, to identify regions i… view at source ↗
Figure 2
Figure 2. Figure 2: Two flow environments simulated in the WRF model: (a) stable boundary layer and (b) convective boundary layer. The geostrophic balance between the pressure-gradient force and the Coriolis force aloft is depicted for each flow environment. the flow statistics are uniform in the horizontal (x,y) directions. To preserve a clear def￾inition of the averaging operator, model-output statistics are computed using … view at source ↗
Figure 3
Figure 3. Figure 3: Synthetic observations generated by the coupled YSU PBL-revised MM5 scheme with standard parameters using different initial-condition realizations. Top row shows the stable boundary layer while bottom row shows the convective boundary layer for 30-minute-averaged output quantities of interest: (a,d) wind speed, (b,e) wind direction, and (c,f) potential temper￾ature. The vertical height is normalized by the… view at source ↗
Figure 4
Figure 4. Figure 4: Emulator training data (µ ± 2σ) for model outputs by the coupled YSU PBL￾revised MM5 scheme, based on 200 model evaluations sampled from the parameter distributions in [PITH_FULL_IMAGE:figures/full_fig_p016_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: 30-minute-averaged profiles of (a) wind speed, (b) wind direction, and (c) potential temperature in the stable boundary layer: (d–f) main-effect and (g–i) total-effect sensitivity in￾dices of parameters in the coupled YSU PBL-revised MM5 scheme put quantities, and across flow regimes. Therefore, the sensitivity analysis examines how parameter sensitivity depends on four factors: quantity of interest, time-… view at source ↗
Figure 6
Figure 6. Figure 6: 30-minute-averaged profiles of (a) wind speed, (b) wind direction, and (c) potential temperature in the convective boundary layer: (d–f) main-effect and (g–i) total-effect sensitivity indices of parameters in the coupled YSU PBL-revised MM5 scheme –18– [PITH_FULL_IMAGE:figures/full_fig_p018_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Main-effect sensitivity indices of the coupled YSU PBL-revised MM5 scheme pa￾rameters for modeled wind speed for centered time-averaging windows, shown for stable (top row) and convective (bottom row) regimes. Panels (a,e), (b,f), (c,g), and (d,h) correspond to the four averaging windows. level jet, independently contributing up to 63% of the total wind-speed variance. The main-effect sensitivity indices (… view at source ↗
Figure 8
Figure 8. Figure 8: In the stable case (Fig. 8a-d), we observe an approximately [PITH_FULL_IMAGE:figures/full_fig_p020_8.png] view at source ↗
Figure 8
Figure 8. Figure 8: Interaction-effect sensitivity indices of the coupled YSU PBL-revised MM5 scheme parameters for modeled wind speed for centered time-averaging windows, shown for stable (top row) and convective (bottom row) regimes. Panels (a,e), (b,f), (c,g), and (d,h) correspond to the four averaging windows. to investigate nonlinear interactions among parameters and across multiple coupled physics parameterizations. Alt… view at source ↗
Figure 9
Figure 9. Figure 9: Signal-to-noise (SNR) ratios computed for the coupled YSU PBL-revised MM5 scheme parameters based on 30-minute-averaged wind speed in the stable (blue) and convective (red) regimes. Circle markers correspond to the observed vertical locations up to PBL height h tity of interest, atmospheric stability during observation, observation averaging time length, and the spatial location of the observations. First,… view at source ↗
Figure 10
Figure 10. Figure 10: Main-to-interaction (MIR) ratios computed for the coupled YSU PBL-revised MM5 scheme parameters retained after filtering based on the corresponding signal-to-noise ratios, based on 30-minute-averaged wind speed in the stable (blue) and convective (red) regimes. Circle markers correspond to the observed vertical locations up to PBL height h servable only in the convective regime. This comparison of paramet… view at source ↗
Figure 11
Figure 11. Figure 11: Marginal posterior distributions of the coupled YSU PBL-revised MM5 scheme parameters inferred from 30-minute-averaged wind speed in the stable (blue) and convective (red) regimes. The truth parameter value is indicated by the dotted line. tions. Based on a comparison of the parameter signal with observational noise and its sensitivity contributions by independent and interaction effects, we can diagnose … view at source ↗
Figure 12
Figure 12. Figure 12: Signal-to-noise (SNR) ratios are computed for the coupled YSU PBL-revised MM5 scheme parameters based on wind speed of different time-averaging windows in the convective regime: 5 minute (red), 10 minute (blue), 30 minute (green), and 60 minute (orange). Circle markers correspond to the observed vertical locations up to PBL height h [PITH_FULL_IMAGE:figures/full_fig_p025_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Main-to-interaction (MIR) ratios are computed for the coupled YSU PBL-revised MM5 scheme parameters retained after filtering based on the corresponding signal-to-noise ra￾tios, based on wind speed of different time-averaging windows in the convective regime: 5 minute (red), 10 minute (blue), 30 minute (green), and 60 minute (orange). Circle markers correspond to the observed vertical locations up to PBL h… view at source ↗
Figure 14
Figure 14. Figure 14: 95% highest posterior density (HPD) credible intervals of the roughness length z0 inferred from wind-speed observations in the convective regime for four time-averaging windows: (a) 5 min (red), (b) 10 min (blue), (c) 30 min (green), and (d) 60 min (orange). The prior range of z0 is shown by the black error bar, and the truth parameter value is indicated by the dotted line. Parameter inference is repeated… view at source ↗
Figure 15
Figure 15. Figure 15: Signal-to-noise (SNR) ratios computed for the coupled YSU PBL-revised MM5 scheme parameters based on 30-minute-averaged quantities of interest in the convective regime: wind speed (red), wind direction (blue), and potential temperature (green). Circle markers corre￾spond to the observed vertical locations up to PBL height h erate consistently when coupled with other parameterizations in an ESM and make ac… view at source ↗
Figure 16
Figure 16. Figure 16: Main-to-interaction (MIR) ratio and main-effect sensitivity computed for the cou￾pled YSU PBL-revised MM5 scheme parameters retained after filtering based on the correspond￾ing signal-to-noise ratios, based on 30-minute-averaged quantities of interest in the convective regime: wind speed (red), wind direction (blue), and potential temperature (green). Circle mark￾ers correspond to the observed vertical lo… view at source ↗
Figure 17
Figure 17. Figure 17: Marginal posterior distributions of the coupled YSU PBL-revised MM5 scheme parameters inferred from 30-minute-averaged quantities of interest in the convective regime: wind speed (red), wind direction (blue), and potential temperature (green). The truth parameter value is indicated by the dotted line. 3.2.4 Influence of spatial location of observations The spatial placement of observations has useful impl… view at source ↗
Figure 18
Figure 18. Figure 18: Main-to-interaction (MIR) ratio and main-effect sensitivity computed for the cou￾pled YSU PBL-revised MM5 scheme parameters retained after filtering based on the correspond￾ing signal-to-noise ratios, based on 30-minute-averaged quantities of interest in the convective regime: wind speed (red), wind direction (blue), and potential temperature (green) Triangle markers correspond to observed vertical locati… view at source ↗
Figure 19
Figure 19. Figure 19: Marginal posterior distributions of the coupled YSU PBL-revised MM5 scheme parameters inferred from 30-minute-averaged quantities of interest in the convective regime: wind speed (red), wind direction (blue), and potential temperature (green). The results are based on observations extending to 250 m (dashed) or observations extending to h (solid). The truth pa￾rameter value is indicated by the dotted line… view at source ↗
read the original abstract

Quantifying and reducing uncertainty in Earth system model parameterizations is essential to improving their reliability in decision-making. Forward uncertainty propagation is used to derive parameter sensitivity but requires physically plausible parameter distributions first be learned from observations. Bayesian inference offers a principled approach but can become ill-posed when observations weakly constrain parameters--a condition difficult to know prior to inference. Addressing this gap, we show that parameter sensitivity results from forward uncertainty quantification can guide a non-iterative strategy for identifying observations informative to Bayesian calibration. We explore both forward and inverse uncertainty quantification for parameterizations of atmospheric turbulence in the Weather Research and Forecasting (WRF) model. To overcome the computational bottleneck of $\mathcal{O}(10^5)$ model evaluations required for both analyses, we leverage Gaussian process emulators trained on several hundred WRF simulations. Using these emulators, we conduct a global sensitivity analysis across observation space, investigating how parameter contributions to output variance depend on quantity of interest, atmospheric stability, time-averaging length, and spatial location. We then introduce nondimensional diagnostic measures that systematically identify regions where a parameter's contribution to output variance exceeds observational noise and its independent effect exceeds interaction effects. We demonstrate that observations from these regions serve as a strong proxy for accurate Bayesian calibration and reduced posterior uncertainty. Through emulator-aided Bayesian inversion with synthetic observations, we show how parameter uncertainty can be systematically reduced by leveraging sensitivity information.

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

2 major / 2 minor

Summary. The manuscript develops a non-iterative workflow that uses Gaussian process emulators of the WRF atmospheric turbulence parameterization to perform global sensitivity analysis (GSA) over observation space. Nondimensional diagnostics derived from Sobol indices identify locations where a parameter's contribution to output variance exceeds observational noise and its main effect exceeds interaction effects. These locations are then shown, via emulator-based Bayesian inversion on synthetic observations, to yield tighter parameter posteriors than random selection.

Significance. If the diagnostics remain informative under model discrepancy and emulator error, the method would provide a practical, computationally tractable bridge between forward uncertainty quantification and Bayesian calibration for Earth system models. The emulator-based handling of O(10^5) evaluations and the explicit nondimensional selection criteria are clear strengths that could generalize to other parameterizations.

major comments (2)
  1. [§4.3, §5] The validation in §4.3 and §5 relies exclusively on synthetic observations generated from the identical WRF parameterization and prior used to train the emulator and compute the GSA. This shared forward operator makes the reported posterior reduction partly tautological; the manuscript does not test whether the same nondimensional thresholds remain predictive once structural model error or real observational noise is introduced.
  2. [§3.2] The propagation of emulator approximation error into the estimated Sobol indices (and hence into the observation-selection diagnostics) is not quantified. With training sets of only several hundred runs, the uncertainty in the main-effect and interaction indices could alter which locations are flagged as informative, yet no leave-one-out or bootstrap analysis of index stability is reported.
minor comments (2)
  1. [§4.1] Notation for the nondimensional diagnostics (variance contribution exceeding noise, main effect exceeding interactions) is introduced in the text but not given compact symbols or an explicit equation; adding a boxed definition would improve reproducibility.
  2. [Figure 7] Figure captions for the spatial maps of sensitivity diagnostics should state the exact threshold values used (e.g., S_i > noise level and S_i / S_{T_i} > 0.8) rather than referring only to “exceeding” criteria.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and insightful comments. These highlight key aspects of validation and uncertainty quantification that we address point-by-point below, with proposed revisions to strengthen the manuscript.

read point-by-point responses

  1. Referee: [§4.3, §5] The validation in §4.3 and §5 relies exclusively on synthetic observations generated from the identical WRF parameterization and prior used to train the emulator and compute the GSA. This shared forward operator makes the reported posterior reduction partly tautological; the manuscript does not test whether the same nondimensional thresholds remain predictive once structural model error or real observational noise is introduced.

    Authors: We agree that the use of synthetic observations from the identical model and prior represents an idealized setting that does not fully capture structural model discrepancy or real observational noise. This choice was made to isolate the effect of the sensitivity-based selection strategy in a controlled proof-of-concept. In the revised manuscript we will expand the discussion in §5 to explicitly acknowledge this limitation, clarify that the nondimensional diagnostics are derived from forward UQ (which can incorporate discrepancy if parameterized in the likelihood), and outline pathways for extension to real observations or perturbed forward models. We will also add a brief note on how the method could be tested under model error in future work. revision: partial

  2. Referee: [§3.2] The propagation of emulator approximation error into the estimated Sobol indices (and hence into the observation-selection diagnostics) is not quantified. With training sets of only several hundred runs, the uncertainty in the main-effect and interaction indices could alter which locations are flagged as informative, yet no leave-one-out or bootstrap analysis of index stability is reported.

    Authors: We thank the referee for this important observation. We will revise §3.2 to include a bootstrap resampling analysis of the training data, computing confidence intervals on the Sobol indices and assessing the stability of the nondimensional thresholds and selected locations. Results will be reported to demonstrate that the primary informative regions remain robust within the estimated emulator uncertainty. revision: yes

Circularity Check

0 steps flagged

No significant circularity; forward sensitivity and Bayesian inversion remain distinct

full rationale

The paper conducts global sensitivity analysis on Gaussian process emulators to compute parameter contributions to output variance, then defines nondimensional diagnostics (variance contribution exceeding observational noise; main effect exceeding interactions) to select observation locations. These locations are subsequently used in a separate Bayesian calibration step with synthetic observations. No equations equate the reported posterior reduction to the sensitivity inputs by construction, no self-citations bear the central claim, and no ansatz or uniqueness result is imported from prior author work. The forward UQ and inverse steps are executed independently, rendering the derivation self-contained against the paper's own benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The approach rests on standard domain assumptions for emulation and UQ; no new free parameters, invented entities, or ad-hoc axioms are introduced in the abstract description.

axioms (2)
  • domain assumption Gaussian process emulators trained on several hundred WRF runs can faithfully reproduce the model outputs needed for global sensitivity analysis across observation space
    Invoked to overcome the O(10^5) model evaluation bottleneck.
  • domain assumption Synthetic observations generated from the model itself can serve as a valid proxy for testing whether selected real observations will reduce posterior parameter uncertainty
    Used in the emulator-aided Bayesian inversion demonstration.

pith-pipeline@v0.9.0 · 5557 in / 1525 out tokens · 128880 ms · 2026-05-10T00:59:06.636829+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

300 extracted references · 6 canonical work pages · 1 internal anchor

  1. [1]

    Boundary-Layer Meteorology , volume=

    Representative roughness parameters for homogeneous terrain , author=. Boundary-Layer Meteorology , volume=. 1993 , publisher=

    1993

  2. [2]

    R. K. Newsom and C. Sivaraman and T. Shippert and L. D. Riihimaki , Date-Added =. Doppler lidar vertical velocity statistics value-added product , Year =

  3. [3]

    Salesky , Date-Added =

    Scott T. Salesky , Date-Added =. Monin--

  4. [4]

    A. C. M. Beljaars and A. A. M. Holtslag , Date-Added =. A software library for the calculation of surface fluxes over land and sea , Volume =. Environ Softw , Number =

  5. [5]

    A. C. M. Beljaars and A. A. M. Holtslag , Date-Added =. Flux parameterization over land surfaces for atmospheric models , Volume =. J Appl Meteorol , Number =

  6. [6]

    Marusic and R

    I. Marusic and R. Mathis and N. Hutchins , Booktitle =. A wall-shear stress predictive model , Year =

  7. [7]

    Kaimal, J. C. , Booktitle =. Sonic anemometer measurement of atmospheric turbulence , Year =

  8. [8]

    Fedorovich , Date-Added =

    E. Fedorovich , Date-Added =. Numerical modelling of atmospheric boundary layer flow over topography elements , Year =

  9. [9]

    Batchvarova and S

    E. Batchvarova and S. E. Gryning , Booktitle =. Use of

  10. [10]

    J. C. Wyngaard , Booktitle =. Changing the face of small-scale meteorology , Year =

  11. [11]

    J. R. Garratt , Date-Added =. The atmospheric boundary layer , Year =

  12. [12]

    P. J. Mason and D. J. Thomson , Date-Added =. Large-eddy simulations of the neutral-static-stability planetary boundary layer , Volume =. Q. J. R. Meteorol. Soc. , Pages =

  13. [13]

    JAMES , volume=

    An extended eddy-diffusivity mass-flux scheme for unified representation of subgrid-scale turbulence and convection , author=. JAMES , volume=. 2018 , publisher=

    2018

  14. [14]

    Better calibration of cloud parameterizations and subgrid effects increases the fidelity of the

    Ma, Po-Lun and others , journal=. Better calibration of cloud parameterizations and subgrid effects increases the fidelity of the. 2022 , publisher=

    2022

  15. [15]

    JAMES , volume=

    A generalized mixing length closure for eddy-diffusivity mass-flux schemes of turbulence and convection , author=. JAMES , volume=. 2020 , publisher=

    2020

  16. [16]

    Parameter uncertainty quantification in an idealized

    Howland, Michael F and Dunbar, Oliver RA and Schneider, Tapio , journal=. Parameter uncertainty quantification in an idealized. 2022 , publisher=

    2022

  17. [17]

    Journal of Computational Physics , volume=

    Calibrate, emulate, sample , author=. Journal of Computational Physics , volume=. 2021 , publisher=

    2021

  18. [18]

    SIAM Journal on Numerical Analysis , volume=

    Analysis of the ensemble Kalman filter for inverse problems , author=. SIAM Journal on Numerical Analysis , volume=. 2017 , publisher=

    2017

  19. [19]

    Handbook of markov chain monte carlo , author=

  20. [20]

    Joule , year=

    Overcoming the disconnect between energy system and climate modeling , author=. Joule , year=

  21. [21]

    Susskind and others , journal=

    L. Susskind and others , journal=. Sources of opposition to renewable energy projects in the

  22. [22]

    Nature Climate Change , volume=

    Increasing probability of record-shattering climate extremes , author=. Nature Climate Change , volume=. 2021 , publisher=

    2021

  23. [23]

    Global Warming of 1.5 ^ C : A n IPCC special report on the impacts of global warming of 1.5 ^ C above pre-industrial levels and related global greenhouse gas emission pathways, in the context of strengthening the global response to the threat of climate change, sustainable development, and efforts to eradicate poverty. 2018

    2018

  24. [24]

    Cambridge University Press

    Masson-Delmotte, V. and P. Zhai and A. Pirani and S. L. Connors and C. Péan and S. Berger and N. Caud and Y. Chen and L. Goldfarb and M. I. Gomis and M. Huang and K. Leitzell and E. Lonnoy and J. B. R. Matthews and T. K. Maycock and T. Waterfield and O. Yelekçi and R. Yu and B. Zhou (eds.) , publisher="Cambridge University Press", year =. IPCC , 2021: Sum...

    2021

  25. [25]

    Scientific American , volume=

    A path to sustainable energy by 2030 , author=. Scientific American , volume=. 2009 , publisher=

    2030

  26. [26]

    Report No

    Adoption of the Paris Agreement. Report No. FCCC/CP/2015/L.9/Rev.1. 2015

    2015

  27. [27]

    2018 , institution=

    2017 Cost of Wind Energy Review , author=. 2018 , institution=

    2017

  28. [28]

    Annual Energy Outlook (AEO2018). 2018

    2018

  29. [29]

    Nature , volume=

    Paris Agreement climate proposals need a boost to keep warming well below 2 C , author=. Nature , volume=. 2016 , publisher=

    2016

  30. [30]

    Science , volume=

    The trouble with negative emissions , author=. Science , volume=. 2016 , publisher=

    2016

  31. [31]

    Energy , volume=

    System LCOE: What are the costs of variable renewables? , author=. Energy , volume=. 2013 , publisher=

    2013

  32. [32]

    IEEE power and energy magazine , volume=

    Grid of the future , author=. IEEE power and energy magazine , volume=. 2009 , publisher=

    2009

  33. [33]

    Energy Policy , volume=

    The cost of wind power variability , author=. Energy Policy , volume=. 2012 , publisher=

    2012

  34. [34]

    Journal of Physics: Conference Series , volume=

    Aeroelastic instabilities of large offshore and onshore wind turbines , author=. Journal of Physics: Conference Series , volume=. 2007 , organization=

    2007

  35. [35]

    estimates , author=

    Capacity factor of wind power realized values vs. estimates , author=. energy policy , volume=. 2009 , publisher=

    2009

  36. [36]

    Energy Policy , volume=

    Policies and market factors driving wind power development in the United States , author=. Energy Policy , volume=. 2005 , publisher=

    2005

  37. [37]

    Applied Energy , volume=

    Assessing the benefits and economics of bulk energy storage technologies in the power grid , author=. Applied Energy , volume=. 2015 , publisher=

    2015

  38. [38]

    2011 , publisher=

    Wind Energy Handbook , author=. 2011 , publisher=

    2011

  39. [39]

    Wind Energy , volume=

    Modelling and measuring flow and wind turbine wakes in large wind farms offshore , author=. Wind Energy , volume=. 2009 , publisher=

    2009

  40. [40]

    Physics of fluids , volume=

    Large eddy simulation study of fully developed wind-turbine array boundary layers , author=. Physics of fluids , volume=. 2010 , publisher=

    2010

  41. [41]

    Wind Energy , volume=

    Combining economic and fluid dynamic models to determine the optimal spacing in very large wind farms , author=. Wind Energy , volume=. 2017 , publisher=

    2017

  42. [42]

    2018 , publisher=

    GE announces Haliade-X, the world’s most powerful offshore wind turbine. 2018 , publisher=

    2018

  43. [43]

    Wind Energy , volume=

    Effects of turbine spacing on the power output of extended wind-farms , author=. Wind Energy , volume=. 2016 , publisher=

    2016

  44. [44]

    Design and estimator for the total sensitivity index , author=

    Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index , author=. Computer physics communications , volume=. 2010 , publisher=

    2010

  45. [45]

    Statistical science , pages=

    Bayesian experimental design: A review , author=. Statistical science , pages=. 1995 , publisher=

    1995

  46. [46]

    Wind Energy , volume=

    Optimal turbine spacing in fully developed wind farm boundary layers , author=. Wind Energy , volume=. 2012 , publisher=

    2012

  47. [47]

    Renewable Energy , volume=

    Placement of wind turbines using genetic algorithms , author=. Renewable Energy , volume=. 2005 , publisher=

    2005

  48. [48]

    Renewable Energy , volume=

    Optimal placement of wind turbines in a wind park using Monte Carlo simulation , author=. Renewable Energy , volume=. 2008 , publisher=

    2008

  49. [49]

    1983 , publisher=

    A note on wind generator interaction , author=. 1983 , publisher=

    1983

  50. [50]

    Annual review of fluid mechanics , volume=

    Direct numerical simulation: a tool in turbulence research , author=. Annual review of fluid mechanics , volume=. 1998 , publisher=

    1998

  51. [51]

    Annual review of fluid mechanics , volume=

    Flow structure and turbulence in wind farms , author=. Annual review of fluid mechanics , volume=

  52. [52]

    Journal of Fluid Mechanics , volume=

    Boundary-layer development and gravity waves in conventionally neutral wind farms , author=. Journal of Fluid Mechanics , volume=. 2017 , publisher=

    2017

  53. [53]

    Journal of Physics: Conference Series , volume=

    Wake behind an offshore wind farm observed with dual-Doppler radars , author=. Journal of Physics: Conference Series , volume=. 2018 , organization=

    2018

  54. [54]

    Wind plant power optimization through yaw control using a parametric model for wake effects—a

    Gebraad, PMO and Teeuwisse, FW and Van Wingerden, JW and Fleming, Paul A and Ruben, SD and Marden, JR and Pao, LY , journal=. Wind plant power optimization through yaw control using a parametric model for wake effects—a. 2016 , publisher=

    2016

  55. [55]

    Renewable and sustainable energy reviews , volume=

    A review of maximum power point tracking algorithms for wind energy systems , author=. Renewable and sustainable energy reviews , volume=. 2012 , publisher=

    2012

  56. [56]

    Journal of Physics: Conference Series , volume=

    Field-test results using a nacelle-mounted lidar for improving wind turbine power capture by reducing yaw misalignment , author=. Journal of Physics: Conference Series , volume=. 2014 , organization=

    2014

  57. [57]

    2005 , publisher=

    Wind power in power systems , author=. 2005 , publisher=

    2005

  58. [58]

    2017 American Control Conference (ACC) , year=

    A tutorial on control-oriented modeling and control of wind farms , author=. 2017 American Control Conference (ACC) , year=

    2017

  59. [59]

    Wind Energy , volume=

    Analysis of axial-induction-based wind plant control using an engineering and a high-order wind plant model , author=. Wind Energy , volume=. 2016 , publisher=

    2016

  60. [60]

    Wind Energy , volume=

    Application of a LES technique to characterize the wake deflection of a wind turbine in yaw , author=. Wind Energy , volume=. 2010 , publisher=

    2010

  61. [61]

    IEEE Transactions on Control Systems Technology , volume=

    A model-free approach to wind farm control using game theoretic methods , author=. IEEE Transactions on Control Systems Technology , volume=. 2013 , publisher=

    2013

  62. [62]

    Renewable Energy , volume=

    Experimental investigation of wake effects on wind turbine performance , author=. Renewable Energy , volume=. 2011 , publisher=

    2011

  63. [63]

    Wind Energy , volume=

    Wind plant system engineering through optimization of layout and yaw control , author=. Wind Energy , volume=. 2016 , publisher=

    2016

  64. [64]

    Experiments in fluids , volume=

    Optical vortex tracking studies of a horizontal axis wind turbine in yaw using laser-sheet, flow visualisation , author=. Experiments in fluids , volume=. 1997 , publisher=

    1997

  65. [65]

    Controlling wind in ECN’s scaled wind farm , author=. Proc. Europe Premier Wind Energy Event , year=

  66. [66]

    Wind Energy Science , volume=

    A simulation study demonstrating the importance of large-scale trailing vortices in wake steering , author=. Wind Energy Science , volume=. 2018 , publisher=

    2018

  67. [67]

    Wind Energy Science , volume=

    Assessment of wind turbine component loads under yaw-offset conditions , author=. Wind Energy Science , volume=. 2018 , publisher=

    2018

  68. [68]

    Journal of Turbulence , number=

    The top-down model of wind farm boundary layers and its applications , author=. Journal of Turbulence , number=. 2012 , publisher=

    2012

  69. [69]

    Wind Energy , volume=

    Validation of the dynamic wake meander model for loads and power production in the Egmond aan Zee wind farm , author=. Wind Energy , volume=. 2013 , publisher=

    2013

  70. [70]

    New Directions in Strategic Energy Analysis

    Arent, Doug , year =. New Directions in Strategic Energy Analysis

  71. [71]

    Wind Energy , volume=

    Nonlinear model predictive control of wind turbines using LIDAR , author=. Wind Energy , volume=. 2013 , publisher=

    2013

  72. [72]

    1973 , publisher=

    Theoretical aerodynamics , author=. 1973 , publisher=

    1973

  73. [73]

    Journal of Fluid Mechanics , volume=

    Modelling yawed wind turbine wakes: a lifting line approach , author=. Journal of Fluid Mechanics , volume=. 2018 , publisher=

    2018

  74. [74]

    2015 , publisher=

    Decision making under uncertainty: theory and application , author=. 2015 , publisher=

    2015

  75. [75]

    2018 Annual American Control Conference (ACC) , year=

    Active power control for wind farms using distributed model predictive control and nearest neighbor communication , author=. 2018 Annual American Control Conference (ACC) , year=

    2018

  76. [76]

    Renewable Energy , volume=

    A new analytical model for wind-turbine wakes , author=. Renewable Energy , volume=. 2014 , publisher=

    2014

  77. [77]

    Wind Energy Science , volume=

    Field test of wake steering at an offshore wind farm , author=. Wind Energy Science , volume=. 2017 , publisher=

    2017

  78. [78]

    Journal of Renewable and Sustainable Energy , volume=

    Wake structure in actuator disk models of wind turbines in yaw under uniform inflow conditions , author=. Journal of Renewable and Sustainable Energy , volume=. 2016 , publisher=

    2016

  79. [79]

    Wind Energy , volume=

    Maximization of the annual energy production of wind power plants by optimization of layout and yaw-based wake control , author=. Wind Energy , volume=. 2017 , publisher=

    2017

  80. [80]

    Adam: A Method for Stochastic Optimization

    Adam: A method for stochastic optimization , author=. arXiv preprint arXiv:1412.6980 , year=

    work page internal anchor Pith review Pith/arXiv arXiv

Showing first 80 references.