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Ensembles in Urban Large Eddy Simulations with Changing Wind Direction

T0 review · 2 major / 4 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read When the wind direction turns during a simulation, plain time averaging of urban large-eddy simulations can severely distort both the mean wind and its variance, so ensemble averaging with a short time window is needed.

desk verdict The paper delivers a useful practical message about ensemble design for urban LES with changing wind direction, but the specific 10–50 member recommendation rests on pseudo-replicated members and a self-referential reference, so the quantitative core needs revision. read the letter →

arxiv 2502.04836 v2 pith:WGAI3RLD submitted 2025-02-07 physics.flu-dyn

Jukka-Pekka Keskinen , Antti Hellsten This is my paper · ORCID
classification physics.flu-dyn
keywords largeeddysimulationensembleaveragingtimenonstationaryurbanflowturningwinddirectionstaggeredcubearraybuildingwakesTaylordiagram
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Urban wind simulations at metre-scale resolution are increasingly used for flows whose forcing changes over time, and when the wind direction turns, a simple time average is not a valid substitute for an average over many independent realizations. This paper establishes, from large-eddy simulations of a staggered cube array and of a real city district, that plain time averaging can seriously contaminate both the mean wind and its variance once the averaging window is comparable to the turning time scale of the driving pressure gradient. The errors are largest for the weaker horizontal velocity component and inside building wakes, which are precisely the regions used for pollutant-dispersion and pedestrian-comfort assessments. The paper shows that a practical remedy is to combine ensemble averaging with a short time average, about 13% of the turning time scale, so that ensembles of 10–50 members reproduce the statistics of a much larger reference ensemble.

What carries the argument

The load-bearing construction is a set of large-eddy simulations branched off a fully developed, constant-direction flow at intervals larger than the integral time scale, so each member begins from a distinct turbulent state. For the cube array, the 648 repeating spatial units of each of five runs are counted as additional members, giving 3,240 in total; for the real city, 50 runs provide one member each. The driving force is a pressure gradient of constant magnitude rotating at $\Omega = 15^\circ\,\mathrm{h}^{-1}$, defining $T_\Omega = 1/\Omega \approx 230$ minutes and a modified Rossby number of about 210 (the ratio of the turning time scale to the bulk-flow time scale). Agreement between time-averaged and ensemble-averaged fields is quantified with Taylor diagrams, normalized standard deviation, correlation, normalized RMSE, and fractional bias, and bootstrap resampling is used to test convergence with ensemble size. The decisive comparison is among averaging windows from $0.0438\,T_\Omega$ to $0.920\,T_\Omega$; the $0.131\,T_\Omega$ window is adopted for the final recommendation.

What would settle it

Run the same turning-pressure-gradient cube-array case twice: once with the repeating-unit construction and once with roughly 20 fully independent simulations started from uncorrelated turbulent fields, and compare member-to-member variance and ensemble means at $t = 0.526\,T_\Omega$. Substantially larger spread or a shifted mean in the independent ensemble would show that the 3,240-member reference is not unbiased, and the recommended ensemble sizes would need revision.

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Extended reading notes

Core claim

The paper's central claim is that with a pressure gradient rotating at rate $\Omega$, the characteristic turning time $T_\Omega = 1/\Omega$ controls how long a time average can be before it corrupts the statistics. Plain time averaging over windows of order $T_\Omega$ folds the changing wind direction into the mean and, more severely, into the variance, inflating the variance of the weaker lateral component and displacing mean winds; the damage is concentrated in building wakes. Against a reference ensemble of 3,240 members for the cube array and a 50-member ensemble for a real urban district, the paper shows that time averaging over roughly $0.13\,T_\Omega$ improves agreement with the ensemble statistics, while longer windows degrade it, and that 10–50 ensemble members then suffice in the roughness sublayer. The conclusion is that plain time averaging should be avoided for nonstationary urban LES, and that short-time-averaged ensembles offer an accurate, affordable compromise.

Load-bearing premise

The reference 'true' ensemble for the cube array assumes the 648 repeating spatial units of each of five simulations behave as independent members, and the paper's expectation that temporal separation of initial conditions keeps spatial correlation negligible is the load-bearing premise; if that correlation is not small, the quoted errors and the 10–50-member recommendation are biased toward spatially homogeneous statistics.

Editorial extensions

If this is right

  • Plain time averages over long windows should be treated as unreliable for nonstationary urban LES, particularly for variances of the weaker horizontal velocity component.
  • Combining ensemble averaging with a time window of about $0.13\,T_\Omega$ makes 10–50 ensemble members sufficient to approximate the statistics of far larger ensembles.
  • Building wakes are the regions where time-averaging errors concentrate, so wake-sensitive applications such as pollutant dispersion and pedestrian-level wind studies should use ensemble statistics.
  • Above the roughness sublayer, horizontal spatial averaging can replace ensemble and time averaging when the flow is horizontally homogeneous.
  • The turning time scale $T_\Omega = 1/\Omega$ provides a practical rule for choosing the averaging window before a nonstationary urban LES campaign begins.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A testable extension is to check whether the same ratio of averaging window to forcing time scale governs other nonstationary forcings, such as a changing pressure-gradient magnitude; the paper does not simulate that case.
  • The repeating-unit ensemble's independence assumption could be validated directly by comparing its member variance with fully independent realizations; if spatial correlation is sizable, 10–50 members may be optimistic.
  • Since errors concentrate in building wakes, pollutant-concentration statistics from a single time-averaged run would be biased in exactly the locations where exposure estimates matter, so dispersion studies should report ensemble spread rather than time-mean fields.
  • An implicit engineering rule follows: record the characteristic forcing time scale, keep averaging windows an order of magnitude below it, and size the ensemble by bootstrap convergence rather than defaulting to large member counts.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. The paper studies how plain time averaging distorts ensemble statistics in large-eddy simulations of urban flows when the wind direction changes. The authors simulate a staggered cube array with a temporally turning pressure gradient, constructing a 3,240-member ensemble by combining five branched simulations with 648 repeating spatial units, and also simulate a realistic urban area around Turku with a 50-member ensemble. Using vertical profiles, Taylor diagrams, RMSE, and fractional bias, they show that time averaging over intervals comparable to the turning time scale T_Omega severely degrades the variance, especially of the weaker horizontal component, and that shorter averaging (chosen as 0.131 T_Omega) can be combined with modest ensemble sizes of 10-50 members. They further identify building wakes as the regions most affected by long time averaging.

Significance. If the quantitative recommendation holds, the paper provides useful practical guidance for a growing class of nonstationary urban LES studies, and the openly available data set with 50 realistic-urban ensemble members is a valuable resource. The qualitative finding that long time averaging contaminates variances, not only means, is convincingly supported by consistent signals in both the cube-array and Turku cases. The central quantitative claim of the paper, however, rests on two fragile pillars: the treatment of 648 spatially correlated cube-array units as independent ensemble members, and the use of the recommended 0.131 T_Omega averaging window as the reference in the realistic-urban evaluation. Both are acknowledged in the manuscript, but neither is resolved, so the 10-50 member recommendation should be treated as conditional until the independence and circularity concerns are addressed.

major comments (2)
  1. [Sections 2.4 and 3.1 (Figs. 7-8, Table 1)] The 3,240-member 'ensemble' is not a set of 3,240 independent realizations: it consists of five turning simulations, each expanded into 648 members by treating the repeating spatial units as separate ensemble members. The statement in Section 2.4 that 'time separation between initial conditions mitigates the effect' addresses decorrelation of the five branched simulations, not of the 648 units within a single simulation; in a periodic cube array with coherent large-scale structures, these units are positively correlated, and the shifted periodic boundaries in Section 2.3.1 were introduced precisely to weaken such structures. The bootstrap convergence statement, the reference ensemble statistics used throughout Section 3.1, and the resampling experiment in Fig. 8 and Table 1 all treat the 3,240 units as carrying 3,240 independent pieces of information. If the effective number of independent samples is much smaller, the reference ensemble variance may understate the true between-realization spread and the reported convergence of 10-50 member ensembles is optimistic. Please quantify the spatial correlation among repeating-unit fluctuations (for example, via correlation functions or by repeating the convergence analysis using only the five independent simulations) and, if the correlation is non-negligible, revise the quantitative recommendation accordingly.
  2. [Section 3.2 (Fig. 14, Table 2)] The realistic-urban evaluation is circular to a degree that affects the transferability of the central recommendation. The reference against which all time-averaging intervals are scored is the ensemble mean computed with 0.131 T_Omega time averaging, which is exactly the averaging window recommended in Section 3.1; the text itself acknowledges that this 'can be expected to result in improved performance for at least the 0.131T_Omega averaging time.' The urban case therefore independently demonstrates only that long averaging (0.657-0.920 T_Omega) performs worse than shorter averaging, not that 0.131 T_Omega is the correct threshold or that 10-50 members suffice in a realistic geometry. Please provide an independent reference, for example the instantaneous 50-member ensemble with its sampling noise explicitly characterized, or a subset of members averaged over a window different from the one used in the reference, and state clearly which aspects of the cube-array recommendation the urban case can actually confirm.
minor comments (4)
  1. [Section 2.5, Eq. (11)] The correlation coefficient formula has an unmatched parenthesis in the numerator: it reads (Co - <Co>)(Cp - <Cp>> and should be (Co - <Co>)(Cp - <Cp>).
  2. [Section 3.2 and Fig. 14 caption] The text discussing Table 2 refers to 'the Taylor diagram in Fig. 8,' but the relevant figure for the realistic urban case is Fig. 14; please correct the cross-reference.
  3. [Figure 4 caption] Panel d) in the caption is labeled 'd) b)' and should be 'd)'; several other typos appear in the text, including 'avaraging', 'chaning', 'waske', 'beheviour', and 'fractioanl'.
  4. [Section 3.1, Fig. 7 discussion] The statement that averaging up to 0.219 T_Omega improves results is not uniformly true across quantities; for example, the mean u component still improves at 0.394 T_Omega in Fig. 7, and the degradation onset differs between means and variances. Please phrase the threshold as quantity-dependent or provide a more granular summary.

Circularity Check

1 steps flagged · score 4.0 of 10

Urban-section Taylor diagram uses the recommended 0.131T averaging as its own reference, making the urban accuracy claim partly self-referential; the core cube-array recommendation is evaluated against an independent instantaneous reference.

  1. self definitional [Section 3.2, Taylor diagram for realistic urban environment (Fig. 14 and accompanying text)]
    "As a reference we value, we use the ensemble mean calculated with the 0 .131TΩ time average. ... One has to keep in mind that the Taylor diagram was created using a small ensemble that was calculated with 0.131TΩ averages as the reference value. This can be expected to result in improved performance for at least the 0.131TΩ averaging time."

    The recommended averaging time (0.131T) is simultaneously the treatment being evaluated and the basis for the reference ensemble in the urban Taylor diagram. The 0.131T points in Fig. 14 therefore measure each member's deviation from the mean of the same 0.131T-averaged fields rather than from an independent ensemble truth; the favorable placement of these points is partly guaranteed by the least-squares property of the mean. The paper explicitly acknowledges this expected improvement, but the acknowledgment does not remove the circularity: the urban 'accuracy' of the recommended recipe is, to a degree, an artifact of the reference definition.

full rationale

This paper's central claim is not globally circular. The staggered cube-array study constructs a 3,240-member ensemble and evaluates time-averaged and resampled ensembles against the instantaneous full ensemble mean, which is an independent reference. The 10-50 member recommendation, based on Fig. 8 and Table 1, is therefore a genuine empirical finding rather than a tautology. The main circular step is confined to the realistic urban section: the Taylor diagram of Fig. 14 and the associated fractional-bias table use the 0.131T time-averaged ensemble mean as the reference while also endorsing 0.131T as the recommended averaging interval. That makes the apparent good performance of 0.131T in the urban case partially self-referential, a point the authors themselves concede in the quoted passage. A second concern raised by the construction — treating 648 spatially repeating cube-array units as independent ensemble members atop only five simulations — is an acknowledged statistical-validity risk rather than a circular reduction, so it does not contribute to the circularity score under the rules. Weighing the independent core against the explicitly acknowledged self-referential urban comparison yields a moderate partial-circularity score.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claim rests on three fitted or hand-chosen parameters: the post hoc averaging window of 0.131T, the branching sampling interval of 0.0876T, and the recommended ensemble size of 10 to 50 members. The most load-bearing axiom is the treatment of repeating cube units as quasi-independent ensemble members, and the main domain assumptions are the fidelity of PALM LES and the transferability from one turning scenario to general urban practice. No new physical entities are introduced.

free parameters (3)
  • Temporal averaging window T = 0.131 T = 0.131 T (about 30 minutes in physical time)
    Chosen post hoc from the cube-array Taylor diagrams and fractional-bias tables as a 'conservative' interval that improves convergence while avoiding the deterioration seen in the variance of v. It is then used as the basis for the 10 to 50 member recommendation and as the reference in the realistic urban case.
  • Ensemble branching sampling interval = 0.0876 T
    Chosen to balance member independence: about 1.5 flow-through times for the cube array and about 0.5 flow-through time for the outermost urban domain. Since the urban members are branched more frequently than one flow-through time, consecutive members may be correlated, reducing the effective ensemble size. Location: Section 2.4.
  • Recommended ensemble size = 10 to 50 members
    Inferred visually from the convergence of Taylor diagrams in Figure 8 and from the fractional-bias interquartile ranges in Table 1. No formal error threshold or cost function is stated, and the recommendation directly drives the choice of 50 members in the realistic urban case. Location: Section 3.1 and Section 3.2.
assumptions (5)
  • ad hoc to paper The 648 repeating units of the staggered cube array can be treated as quasi-independent ensemble members.
    This assumption makes the 3,240-member reference ensemble possible. The authors explicitly state in Section 2.4 that spatial correlation is expected and assumed to be mitigated by time separation between the five simulations. If the correlation is large, all reference statistics are biased.
  • domain assumption PALM 6.0 with Deardorff's SGS closure produces urban flow statistics accurate enough for the conclusions.
    The paper uses a standard LES model and SGS scheme, but all accuracy statements are relative to the LES ensemble mean, not to field or wind-tunnel data. The practical relevance assumes the model faithfully represents the real flow. Location: Sections 2.1 and 2.2.
  • domain assumption Branching from a single spinup simulation at fixed time intervals produces statistically equivalent ensemble members without altering the underlying statistics.
    This is the standard CMIP6-style ensemble construction described in Section 2.4. The validity depends on sampling intervals exceeding the relevant integral and flow-through timescales, which is only marginally satisfied in the urban outer domain.
  • standard math Cellwise error measures spatially averaged over the roughness sublayer provide a meaningful summary of model performance.
    The Taylor diagram and fractional-bias methods are standard, but the spatial averaging can hide localized error structure. The paper partially compensates by showing spatial error maps in Figures 6 and 13. Location: Section 2.5.
  • domain assumption Neutral stratification, no Coriolis force, no buoyancy, and a single turning rate are sufficient to generalize the qualitative findings.
    The authors acknowledge in the Conclusions that these simplifications limit applicability to near-neutral, short-distance urban roughness-layer flows. The quantitative recommendation is derived from a single Rossby number, Ro about 210.

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Cite this review

Pith. "Pith review of Ensembles in Urban Large Eddy Simulations with Changing Wind Direction." pith.science (2026). https://pith.science/paper/WGAI3RLD

@misc{pith2026250204836,
  author       = {Pith},
  title        = {Pith review of: Ensembles in Urban Large Eddy Simulations with Changing Wind Direction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WGAI3RLD}},
  note         = {Machine review of arXiv:2502.04836}
}
read the original abstract

Differences between time-averaged and ensemble-averaged wind are studied for the case of changing wind direction. We consider a flow driven by a temporally turning pressure gradient in both an idealized case of a staggered cube array and a realistic urban environment. The repeating structure of the idealized case allows us to construct a large ensemble of 3 240 members with a reasonable compute time. The results indicate that the use of plain time averaging instead of an ensemble average can severely reduce the accuracy of both the mean and variance. These errors are the largest when the averaging time is of the same order as the time scale associated with the turning. Utilizing Taylor diagrams, we show that a reasonable compromise between ensemble size and accuracy can be achieved by calculating the ensemble statistics from temporally averaged results with an averaging time that is clearly smaller than the characteristic time scale. This allows the use of reasonably-sized ensembles with 10-50 members. By applying this approach to the realistic urban geometry, we identify building wakes as the regions most severely affected by the incorrectly use of time averaging.

Figures

Figures reproduced from arXiv: 2502.04836 by the authors.

Figure 1
Figure 1. Staggered cube array as viewed from top. All cubes are of the same size, and with equal separation. The repeating pattern, consisting of a cube and its adjoining empty space, is used for calculating averages and is indicated for each cube using a dashed line. In every second column, the repeating pattern is wrapped from top to bottom due to cyclic boundary conditions. The full extent of the computational domain is s… view at source ↗
Figure 2
Figure 2. Topography height in the simulated area. The green colour bar indicates areas with vegetation, the gray colour bar the areas with buildings, and the multi￾coloured bar indicates terrain only. The outlines of the intermediate and the innermost domain are indicated with red. Buildings and vegetation are not included in the largest domain. North is up. The coordinates indicate the distance to local origin at 60°22’27”N… view at source ↗
Figure 3
Figure 3. Volume average of the resolved kinetic energy of the simulations with the staggered cube array. a) The spinup simulation (black dashed line) and the simulations with a turning pressure gradient (coloured lines). The nth turning pressure gradient simulation branches off from the spinup at time tn/TΩ = 4.73 + 0.0876(n − 1). b) All turning pressure gradient simulations shown using time since start of pressure gradient … view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: Vertical wind profiles in the case of the staggered cube array. The mean and variances for all quantities have been accumulated over the horizontal directions and the possible statistical accumulation over time is indicated with different lines. In time, all quantities…
Figure 5
Figure 5. Figure 5: Ensemble statistics in the case of the staggered cube array at time 0.526TΩ. Two different planes of a single repeating element are shown. One is horizontal through the roughness elements at z/H = 0.0825 (panels on the first, third, and fifth rows from the top) and the…
Figure 6
Figure 6. Figure 6: RMSE between the ensemble velocity and the long (t/TΩ = 0.920) time average. Two different planes of a single repeating element are show, one horizontal through the roughness elements at z/H = 0.0825 (panels on the first, third, and fifth rows from the top) and one ver…
Figure 7
Figure 7. Figure 7: Taylor diagrams for the mean (a–c, g) and variance (d–f, h) of u, v, w, and U components of velocity with different averaging intervals in roughness sublayer (z/H < 0.660) for the case of the staggered cube array. The ensemble mean calculated with instantaneous values …
Figure 8
Figure 8. Figure 8: Taylor diagrams for ensembles with different sizes calculated using 0.131TΩ (a–c, g) and variance (d–f, h) of u, v, w, and U components of velocity for the case of staggered cube-array. The ensemble mean calculated with instantaneous values is used as the reference. Th…
Figure 9
Figure 9. Figure 9: The volume-averaged, resolved kinetic energy of the realistic urban envi￾ronment simulations. The nth turning pressure gradient simulation branches off from the spinup at time tn/TΩ = 4.20+ 0.0876(n−1). a) The spinup simulation (black) and the simulations with a turnin…
Figure 10
Figure 10. Figure 10: Vertical wind profiles in the innermost domain in the case of the realistic urban flow. The mean and variances for all quantities have been accumulated over the horizontal directions and statistical accumulation over time is indicated with different lines. In time, al…
Figure 11
Figure 11. Figure 11: Ensemble-averaged velocity component u calculated using instantaneous values for a horizontal plane through the roughness elements at z = 40 m for the innermost domain in the case of the realistic urban flow. The coordinate axis indicate the relative distance in metre…
Figure 12
Figure 12. Figure 12: Ensemble-averaged velocity, calculated with 0.131TΩ time averages) for a horizontal plane through the topography at z = 40 m for the innermost domain in the case of the realistic urban flow. The coordinate axis indicate the relative distance in metres to the domain or…
Figure 13
Figure 13. Figure 13: RMSE between the ensemble velocity calculated using 0.131TΩ time aver￾age and the plain time average calculated over 0.920TΩ for a horizontal plane through the roughness elements at z = 40 m for the innermost domain in the case of the re￾alistic urban flow. The coordi…
Figure 14
Figure 14. Figure 14: Taylor diagrams for the mean (a–c, g) and variance (d–f, h) of u, v, w, and U components of velocity with different averaging intervals for z < 4havg = 84 m in the innermost domain in the case of the realistic urban flow. The ensemble mean calculated with 0.131TΩ time…

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Reviewed August 8, 2026 · model on record in the stance chip above.