The LES data used in this study originate from precursor simulations by .

The precursor simulates a neutral atmospheric boundary layer driven by a steady pressure gradient over flat terrain. It is performed using the EllipSys3D flow solver , which solves the Navier–Stokes equations in general curvilinear coordinates using a finite-volume method on a block-structured and collocated grid.

The computational domain spans 2880m×1440m×700.8m, discretized into 576×288×320 cells, with uniform grid spacing of 5m in the longitudinal and lateral directions and 2.19m vertically. To avoid spanwise locking of turbulent structures, a lateral shift is applied to the periodic boundaries in the longitudinal direction, following . The simulation assumes a surface roughness of z0org=0.05m and a friction velocity of u*org=0.4545ms-1. It runs for 82 600 s (approximately 22.94 h) to ensure statistical convergence before collecting 28 800 s of inflow data.

As described by , neutral atmospheric boundary flows can be rescaled to generate multiple inflow conditions. We apply this rescaling following : 1unew=u*newuorgu*org+1κln⁡z0orgz0new, where κ=0.41 is the von Kármán constant, and the superscript “new” refers to the inflow condition to be generated, where unew∈[8.0,12.0,15.0,18.0]ms-1, obtaining four inflow wind speeds. All inflows have an average TI of approximately 11 %.

The LES datasets (sets A and B) are taken from two different locations within the LES domain and have distinct spatial dimensions in the lateral and vertical directions. Set A consists of 28800×1×61×138 grid points (t×x×y×z), while set B includes 28800×1×39×91 grid points. Both datasets cover a 4 h period at a temporal resolution of dt=0.5 s, with spatial resolutions of 5 m in the lateral (y) direction and 2.19 m in the vertical (z) direction. An illustration of the locations in the LES domains is given in Fig.  in the Appendix for clarity. For each inflow wind speed, the three turbulent velocity components (u, v, w) are extracted and rescaled following the method described in Sect. .

To ensure that the global POD basis characterizes the coherent turbulent structures over the rotor area, the spatial domain of set B is reduced and centered accordingly, spanning 190.3m×197.1m (y×z). In contrast, set A retains a larger spatial extent of 300.5m×300.0m (y×z), providing sufficient coverage for aeroelastic simulation and lidar probe volume modeling.

From set A, 16 non-overlapping 900 s segments are extracted to generate 16 independent 3D turbulent inflow fields. These are transformed into spatial boxes under Taylor's frozen turbulence hypothesis , which assumes that turbulent structures are convected downstream at a constant advection velocity U¯o – the average wind speed at hub height – without evolving over time. Under this transformation, the time and longitudinal directions are combined to define the longitudinal coordinate x, with a spatial resolution given by dx=U¯oTsimNx, where Nx=Tsimdt=1800,Tsim=900s.

The resulting reference turbulence boxes have dimensions of 1800×61×138 grid points (x×y×z), enabling accurate 15 min HAWC2 simulations and ensuring full inclusion of lidar probe volume effects.

To account for HAWC2's transient effects, lidar initialization, and boundary effects, the first 250 s and the last 50 s of the simulation are discarded – beyond the conventional 100 s warm-up typically used in HAWC2 – yielding the final reconstructed wind fields of 600 s, with dimensions of 1200×39×91 grid points (t×y×z), with a time step dt=0.5 s.

POD decomposes turbulent flow into orthogonal spatial modes that optimally capture the variance of the fluctuations . Typically, POD is applied to a single flow case, yielding an orthogonal basis optimized for that specific dataset.

To enable generalization across different flow conditions, utilized a “global” POD basis, which is derived by combining multiple cases, providing a more general representation across a broader parameter space. As the global POD modes are derived from multiple flow conditions, they are not optimized for any single case but instead capture generalized flow structures across the parameter space. However, as shown by , the global basis is still very effective, and the suboptimality of a global basis compared to a “local” basis is at least an order of magnitude smaller than the truncation error.

To compute the basis, we first calculate the fluctuating component of the longitudinal velocity field by subtracting the temporal mean, U¯(y,z), from the full velocity field: U′(y,z,t)=U(y,z,t)-U¯(y,z). These fluctuations are then reshaped into column vectors over Nt time steps for each of Nc flow cases, forming the matrix M=[U1,1′,…,U1,Nt′,…,UNc,1′,…,UNc,Nt′], which is used to compute the POD modes using the randomized singular value decomposition (SVD) following the method of .

The decomposition yields a set of orthonormal spatial modes G=[g1,…,gNt-1]. A visualization of the first 10 global POD modes is provided in Appendix .

The corresponding modal time series are obtained by projecting the fluctuating flow onto the spatial POD modes using an inner product ϕi(t)=U′(t),gi.

A reduced-order approximation of the flow field can then be constructed as 2U(y,z,t)=∑i=1Kgi(y,z)ϕi(t)+U¯(y,z), where K<Nt-1 is the number of retained modes, and ϕi(t) is the modal time coefficient. This approach provides a low-dimensional representation of the flow, retaining dominant coherent structures while reducing computational complexity.

Although accurate representation of the flow physics in POD requires all three velocity components (u,v,w) , in this study we only extract the global POD modes using the longitudinal component (u) from the LES dataset set B (see Sect. ). This choice reflects the focus on reconstructing the longitudinal wind speed, which is the primary quantity of interest for LAC applications. The simplification is motivated by both methodological and practical considerations. First, u component fluctuations dominate turbine loads , whereas lateral (v) and vertical (w) components have a negligible impact . Additionally, only the longitudinal u component can be estimated from the LOS. This limitation arises because the lidar does not measure the full 3D velocity vector; instead, it senses only the component projected along the beam direction (the “cyclops dilemma”) . Recovering individual velocity components from LOS measurements therefore requires additional assumptions. One option is to combine multiple beams under an assumption of local flow homogeneity , which enables estimation of multiple velocity components (e.g., u, v, and/or w) but relies on limited spatial variability across the rotor. A second approach is to assume a known wind direction (e.g., align with the u component) and neglect the lateral and vertical components . Because this study aims to resolve wind speed variations across the full rotor plane, we adopt the latter assumption and thus estimate only the longitudinal component u from the LOS measurements.

To avoid data leakage and promote generalization, the POD basis is computed from LES domains that are spatially offset from the reconstruction region (Appendix ).

A numerical model of a hub-mounted pulsed lidar sensor is available in HAWC2 v13.1 to simulate realistic LOS wind measurements based on user-defined parameters for a single-beam lidar. This section outlines the sensor used in this study, including lidar parameters, coordinate system, and estimation of longitudinal wind speed.

The hub lidar consists of a pulsed single-beam sensor installed on the spinner and constrained to the wind turbine model, meaning that the lidar beams moves with the turbine structure and is affected by tower motion, including yaw, pitch, roll, and structural vibrations. As the spinner rotates, the beam sweeps the rotor area, measuring LOS wind speeds by projecting the local u, v, and w components onto the LOS direction (Fig. ). Tower motion together with rotor rotation influences the measurements by introducing a relative-velocity contribution to the measured wind speed. However, in the current HAWC2 hub-lidar sensor implementation, rotor rotation does not introduce an additional translational velocity component into the measured wind speed. Motion-induced fluctuations are therefore dominated by tower motion and can be mitigated using frequency-domain filtering, which preserves the integrity of the estimated wind field without introducing bias . In practical deployments, such pre-processing should be applied before reconstructed inflow fields are used for load assessment or LAC because uncorrected motion artifacts can excite structural dynamics; inflate fatigue loads; and, in control applications, provoke undesirable actuator responses . Nevertheless, no motion correction or filtering has been applied in the present analysis because the study focuses on inflow reconstruction accuracy under multiple uncertainty sources.

Probe volume effects are simulated by HAWC2 using the weighting function and system parameters described in for pulsed lidar systems. HAWC2 provides the following as outputs: (i) the probe-volume-averaged LOS velocity VLOS, wgh; (ii) the nominal LOS velocity VLOS, nom, without volume averaging; and (iii) the corresponding measurement locations in X,Y, and Z.

The lidar beam unit directional vector, n(θ,ψ,ω(t)), can be defined in a left-handed Cartesian coordinate system, with X downwind and Z vertical directions as n(θ,ψ,ω(t))=(-cos⁡(θ),-sin⁡(θ)sin⁡(ψ+ω(t)),3sin⁡(θ)cos⁡(ψ+ω(t))), where θ is the half-cone angle, ψ is the azimuthal offset from blade 1 where the lidar beam is located (clockwise viewed downwind), and ω(t) is the azimuthal angle of blade 1 (origin aligned with the Z axis upward, rotation clockwise viewed downwind).

The LOS velocity (also called radial velocity) can be mathematically expressed as 4VLOS(θ,ψ,ω(t),P)=n(θ,ψ,ω(t))⋅U(P), where U(P)=[u(P),v(P),w(P)]T is the wind vector, and P represents the location in space (x,y,z) where the measurement is taken as a function of the instantaneous hub location, the lidar beam unit vector, and the range length fd.

Figure  illustrates the beam configuration from three perspectives for a beam with θ=20° and ψ=30° and a range length fd=200 m, where the spatial location of the measurement point P is expressed as P(θ,ψ,ω(t),β,ν,γ,fd)=Rhub(β,ν,γ)⋅-Ls005+00Zhub+Rhub(β,ν,γ)⋅fd⋅n(θ,ψ,ω(t)), where Ls is the shaft length, Zhub is the hub height, and Rhub(β,ν,γ) is the rotation matrix accounting for tilt (β), roll (ν), and yaw (γ) of the wind turbine model for a left-handed coordinate system. For this study, β=5.0° and ν=γ=0.

Therefore, the LOS velocity accounting for beam orientation and tilt can finally be expressed as VLOS(θ,ψ,ω(t),β,P)=[cos⁡(β)cos⁡(θ)-sin⁡(β)sin⁡(θ)cos⁡(ψ+ω(t))]⋅u(P)+[sin⁡(θ)sin⁡(ψ+ω(t))]⋅v(P)6+[sin⁡(β)cos⁡(θ)+cos⁡(β)sin⁡(θ)cos⁡(ψ+ω(t))]⋅w(P). The longitudinal wind speed is estimated by projecting VLOS onto the x axis. This projection assumes negligible lateral and vertical components (v and w) when the rotor is perfectly aligned with the wind , which introduces cross-contamination errors . The final equation to project the LOS velocity to the longitudinal direction is thus as follows: ulidar(θ,ψ,ω(t),β,P)=7VLOS(θ,ψ,ω(t),P)cos⁡(β)cos⁡(θ)-sin⁡(β)sin⁡(θ)cos⁡(ψ+ω(t)). Note that the projection is performed from the lidar origin O, placed at (-Ls,0,Zhub), and therefore the projection is only affected by the rotation matrix Rhub.

Effects related to optics, internal signal processing, and lidar-specific smearing are not considered in this study.

The HAWC2 hub-lidar sensor supports flexible scanning configurations, allowing multiple beams with user-defined half-cone angles (θ), azimuthal angles (ψ), and range lengths (fd). In this study, a six-beam configuration is employed, with each beam sampled sequentially at 5 Hz and no switching delay. The lidar records 29 fixed range gates spaced every 10 m, covering distances from 70 to 350 m – consistent with common pulsed lidar practice . During post-processing, the beam sequence, sampling frequency, and switching delay can be customized.

Preliminary analysis (not shown for brevity) revealed that reconstruction accuracy improves when all six lidar beams are angled away from the central axis, rather than having a central beam pointing directly upwind. Although each beam samples multiple range gates, a beam aligned with the wind direction collects data along a nearly straight line, with only a slight vertical shift due to turbine tilt. As a result, many measurements overlap and map into the same grid location, providing only a small number of central points in the fixed spatial grid. In contrast, angled beams increase their spatial coverage and provide more data for the estimation across the rotor plane. Similar results have been reported by , where optimal scan radii were found to be approximately 70 %–75 % of the rotor span.

The half-cone angle selection affects both projection errors – due to the assumption of negligible v and w components – and the spatial coverage of the rotor. Increasing the preview distance reduces cross-contamination and induction effects but increases errors due to wind evolution . Since HAWC2 does not model induction in the lidar sensor or temporal evolution of inflow, their impact is therefore not considered in this study.

The azimuthal angle defines each beam's angular separation from blade 1 in the rotating frame (Fig. ), with allowable values in this study, ψ∈[0°,120°,240°], based on practical installation constraints. Specifically, for many multi-megawatt wind turbines, manufacturers provide access to the hub through service hatches positioned every 120°. Aligning the lidar beams with these access points simplifies both the installation and the maintenance processes.

The goal is to optimize the beam sequence to maximize rotor plane coverage over a given number of scans, where a “scan” is defined as the time needed to sample all six beams. At 5 Hz per beam, a single scan takes tscan=1.2 s.

Figure  illustrates the final six-beam hub-lidar configuration, which was found with an exhaustive search through iteration at fixed rotor speed Ω=9.6 rpm (rated speed of the DTU 10 MW turbine), yielding the following optimal beam sequence: ψ=[0°,240°,120°,240°,120°,0°]. Panel (a) shows the initial mounting azimuthal angles (YZ view), (b) the scanning trajectory over one scan (non-rotating frame), and (c) beam locations onto the XZ plane. This azimuthal configuration ensures optimal coverage of the rotor area above rated wind speed, since this is the operational range where LAC is used for load reduction.

Synthetic lidar measurements are extracted from the reference inflow fields (Sect. ) using the hub-lidar sensor. During post-processing, the 20 Hz HAWC2 lidar output is downsampled to a 5 Hz sampling rate per beam, with no switching delay.

Measurements used for the reconstruction are selected through a spatial filtering process. In the lateral and vertical directions, the filter dimensions match those of the turbulence box from set A (refer to Sect. ). In the longitudinal direction, the filter spans a distance dspan=U¯onscantscan, where nscan is the selected number of scans, and tscan=1.2s is the duration of a single full scan. This longitudinal span is centered around the target reconstruction plane, located at Xtarget=U¯ots, where ts denotes the time step at which the reconstruction is evaluated. As a result, only measurements satisfying the condition Xtarget-12U¯onscantscan<x<Xtarget+12U¯onscantscan are selected for the reconstruction. Additionally, we imposed a constraint requiring all selected measurements to be located at least 1 s upstream of the rotor plane to ensure preview time.

This process is illustrated in Fig. , where (a) shows lidar data advancing towards the rotor with the cuboid centered around Xtarget, representing the spatial filtering region, and (b) maps selected measurements inside the cuboid onto the fixed YZ grid. If multiple measurements fall into the same grid cell, only the one closest to Xtarget is retained. Panel (c) shows the resulting fluctuations after subtracting the known shear profile (U¯(y,z)) from the LES dataset set A (refer to Sect. ).

All data used in this study are gather in a publicly available dataset .

This section presents the methodologies used to reconstruct the longitudinal wind component (u) from synthetic lidar measurements obtained from the hub-lidar database (Sect. ). Reconstructions are performed on a fixed 39×91 grid (y×z), consistent with the global POD modes (Sect. ). A total of 1200 time steps (600 s) are reconstructed with a sampling interval of dt=0.5 s.

All four methods use lidar-derived wind speed fluctuations as input, defined as ulidar′(t,y,z)=ulidar(t,y,z)-U¯(y,z), where U¯(y,z) is the known mean vertical wind speed profile (i.e., shear) from LES set A. This step standardizes the input across methods. After reconstructing the fluctuating component, the known shear is readded to obtain the full wind field for evaluation.

The four reconstruction techniques evaluated in this study are described below.

Several parameters influence the accuracy of wind field reconstruction. To quantify the performance of the methods described in Sect. , we use the mean absolute error (MAE) computed within an area around the rotor, denoted as AR (see Sect. ). The MAE is computed over the 10 min simulation period (Nt=1200, dt=0.5 s) as MAErotor,i,m(θ,nscan,K)=1Nt12×∑t=1Nt1N∑(y,z)∈ARuref,i(t,y,z)-ui,m(t,y,z), where N is the number of spatial grid points within the rotor area AR, and uref,i denotes the reference wind field for inflow case i. The index i∈{1,…,Ncases} spans the set of inflow cases, with Ncases=64 representing 16 independent 10 min realizations across four wind speeds U¯o∈{8.0,12.0,15.0,20.0}ms-1. The subscript m represents each reconstruction method described in Sect. , with m∈{Baseline, POD-LSQ, IDW, and POD-IDW}.

To enable fair comparison across different wind speeds, all reconstruction errors are normalized by the corresponding inflow mean wind speed U¯o,i. The global performance metric for a given method m is defined as MAEglobal,m(θ,nscan,K)=1Ncases13×∑i=1NcasesMAErotor,i,m(θ,nscan,K)U¯o,i.

The global reconstruction performance depends on several key parameters. First, the half-cone opening angle θ directly influences the spatial distribution and availability of lidar measurements across the rotor, as well as potential cross-contamination effects. In this study, we evaluate θ values in the range θ∈{10.0°,12.5°,…,50.0°}, using the same angle for all six beams.

Second, the number of lidar measurements per time step, nmeas, depends on the selected number of lidar scans, nscan∈{1,2,…,8} (see Sect. ). Increasing nscan provides higher data availability, but it can degrade reconstruction due to higher spatial filtering.

For POD-based methods, the number of retained modes K is another important parameter. A higher K allows for finer-scale flow reconstruction but can increase sensitivity to measurement sparsity and lead to overfitting. We evaluate K∈{10,20,30,40,50,75,100,125,150,200}.

The optimal parameter combination for each method, (θopt,m,nscan,opt,m,Kopt,m), is defined as the one that minimizes the global normalized reconstruction error: (θopt,m,nscan,opt,m,Kopt,m)=14arg⁡min⁡θ,nscan,KMAEglobal,m(θ,nscan,K), where the search spans all 1360 (17×8×10) combinations in the discrete parameter space.

In real-time applications, reconstructing wind fields at each time step using global POD modes requires estimating the corresponding modal amplitudes, ϕ̃(t). This estimation is carried out using the POD-LSQ approach described in Sect. . In this section, we evaluate how wind speed quantity selection affects the accuracy of these modal amplitude estimations.

Figure  presents the first five modal amplitudes for a representative 10 min inflow case with a mean wind speed of U¯o=15.35ms-1. The reference modal amplitudes (solid black lines) are compared against those estimated by POD-LSQ (dashed orange lines), using K=50 global POD modes, nscan=7 scans, and a half-cone angle of θ=22.5°. The top row of Fig.  shows results obtained using the true wind speed as input, while the second row uses the nominal lidar estimate (without volume averaging), and the bottom row uses the volume-averaged lidar estimate. This comparison allows us to isolate and quantify the impact of measurement errors on the estimation of modal amplitudes. Each subplot also reports the normalized MAE, defined as MAE/σ, where σ is the standard deviation of the corresponding reference amplitude.

As expected, the estimation error MAE/σ increases with mode number. Lower-order modes (e.g., modes 1–3), which represent dominant large-scale structures, are reconstructed more accurately than higher-order modes (e.g., modes 4–5), which correspond to finer-scale features. Furthermore, the use of the lidar-based estimates leads to consistently higher reconstruction errors compared to using the true wind speed. For mode 1, MAE/σ increases by 55 % when using the nominal lidar estimate compared to the true wind speed, while an increase of 41 % is observed for the volume-averaged lidar estimate. For mode 5, these differences become more pronounced, with increases of 119 % and 114 %, respectively. These results highlight the sensitivity of modal amplitude estimation to measurement-related uncertainties – such as cross-contamination, spatial offsets resulting from the fixed-grid filtering approach used for multi-distance lidar measurements, and tower-induced motion. Higher-order modes are particularly affected by these effects. Notably, probe volume averaging helps to reduce such errors, as reflected in the consistently lower MAE/σ values compared to the nominal case.

To assess how the number of scans and modes affects the reconstruction of turbulent inflow fields, we analyze the power spectral density (PSD) of the u velocity fluctuations for a representative case with U¯o=15.35ms-1 over a 10 min simulation. The PSD is estimated using Welch's method with a Hamming window, six segments, and 50 % overlap. To characterize the spectral energy content across the full rotor plane rather than just the rotor-averaged wind speed, the PSD is computed point-wise and subsequently averaged over all grid points within the area AR (refer to Sect. ): 15PSDavg(f)=1Ngrid∑i=1NgridSii(f), where Sii(f) is the power spectrum estimated at grid point i∈AR, and Ngrid is the total number of grid points inside AR.

The selection of the half-cone angle, θ, affects reconstruction accuracy in two main ways: (1) by influencing the number and spatial distribution of lidar measurements across the rotor plane and (2) by increasing cross-contamination in the volume-averaged lidar estimate derived from LOS measurements.

Figure  illustrates these effects at a representative time step across the YZ rotor plane. Each column corresponds to a half-cone angle θ∈{10.0°,17.5°,20.0°,22.5°,35.0°,50.0°} using K=200 modes and nscan=4 for all reconstructions. Row (a) shows the location of the lidar measurements, and each point's color represents the difference between the true wind speed (ufw) and the volume-averaged lidar estimate (ulidar, wgh), while rows (b)–(e) present reconstruction errors relative to the LES reference for (b) baseline, (c) POD-LSQ, (d) IDW, and (e) POD-IDW. MAE values are reported above each case.

As shown in Fig. a, at θ=10.0°, measurements concentrate near the upper center of the rotor due to turbine tilt, yielding nmeas=457. With increasing θ, spatial coverage improves as measurements spread more broadly across the rotor plane. However, beyond a certain point, outer beams extend beyond the rotor, reducing central coverage. For example, at θ=50.0°, only 182 valid measurements remain as outer range gates extend beyond the rotor area due to beam inclination. Additionally, larger θ values increase cross-contamination – indicated by the more intense coloring of the points – due to increased misalignment with the line of sight and the longitudinal turbulence.

Figure b–e show how each method responds to changes in θ. The baseline method is relatively insensitive, exhibiting consistent performance across all angles. POD-LSQ, in contrast, is highly sensitive, as accuracy depends on both the number and the spatial distribution of measurements. At θ=10.0°, performance degrades despite a high measurement count due to poor spatial coverage and localized overfitting. At θ=50.0°, the number of measurements is too low (nmeas=182) to support fitting K=200 modes, yielding an underdetermined system and degraded accuracy. These results highlight that, for POD-based methods, ensuring nmeas≥K is necessary but not sufficient – broad spatial coverage is equally critical. Notably, although θ=10.0° yields more measurements than θ=35.0°, POD-LSQ performs worse, underscoring the importance of spatial distribution over raw measurement count.

The sensitivity of IDW and POD-IDW to θ is less significant than for POD-LSQ. However, both methods exhibit increased reconstruction error at θ=50.0°, consistent with greater cross-contamination in the LOS-derived wind speed (Fig. a). POD-IDW inherits interpolation errors from the IDW field, so spatial inaccuracies propagate into the final reconstruction. Still, applying POD over the IDW field reduces spatial inconsistencies, resulting in smoother fields and improved performance over IDW alone – though the improvement in MAE is limited (Fig. d and e).

Careful selection of the half-cone angle is therefore essential, particularly for POD-based methods. The angle must balance spatial coverage with minimal contamination from v and w components in the LOS signal. This selection depends on lidar geometry, turbine tilt, and alignment between beam orientation and the rotor plane. It is also critical to ensure that nmeas≥K and that measurements are sufficiently distributed to avoid overfitting in POD-LSQ. The baseline method, by contrast, remains largely insensitive to θ, provided enough data are collected across the scan radius .

To assess how lidar-induced measurement errors affects reconstruction accuracy, we evaluate each method using the three wind speed inputs: (i) true wind speed (ufw), (ii) nominal lidar estimate without volume averaging (ulidar, nom), and (iii) volume-averaged lidar estimate (ulidar, wgh).

Figure  shows the global reconstruction error, MAEglobal (defined in Sect. ), as a function of the half-cone angle θ for each method using its optimal configuration, nscan,opt and Kopt, determined as shown in Fig.  and listed in Table . Results are presented for four methods – (a) baseline, (b) POD-LSQ, (c) IDW, and (d) POD-IDW – under all three wind speed inputs. The performance spread across these inputs reflects the influence of measurement errors and volume averaging. A more comprehensive sensitivity analysis over θ, nscan, and (where applicable) K, including the full set of heat maps used to identify the method-specific optima, is provided in Appendix .

Consistent with Sect. , the baseline method (Fig. a) shows almost identical results regardless of input type due to its rotor-averaging approach that inherently smooths spatial uncertainties. Overall, the baseline yields larger reconstruction errors than the spatial reconstruction methods across most of the parameter space; however, for extreme half-cone angles, POD-LSQ can perform worse than the baseline. Among the other methods, POD-LSQ remains the most sensitive to half-cone angle selection, with errors increasing sharply as θ deviates from the optimum due to overfitting and cross-contamination, which impair modal amplitude estimation (see also Sect.  and ). In contrast, IDW and POD-IDW show less sensitivity to θ, with errors remaining relatively stable even as measurement distribution deteriorates. For POD-IDW, this robustness is partly inherited from IDW, as it uses the interpolated IDW field for modal fitting and thus avoids overfitting (see Sect. ).

IDW shows the largest performance gap between ufw and lidar-based inputs, highlighting its strong sensitivity to uncertainties, particularly the multi-distance fixed-plane mapping error and cross-contamination. POD-IDW performs slightly better, as the modal decomposition enforces spatial coherence, mitigating some interpolation-related errors. POD-LSQ also benefits from modal constraints, reducing sensitivity to input uncertainty, though it remains highly dependent on θ.

Across all methods, reconstructions using the true wind speed ufw significantly outperform those from the two line-of-sight quantities, but the volume-averaged input (ulidar, wgh) outperforms the nominal lidar estimates (ulidar, nom). In other words, there is a significant increase in error caused by measurement inaccuracies, but adding volume averaging actually reduces the error. This demonstrates the benefit of modeling the probe volume, as volume averaging reduces cross-contamination and improves reconstruction quality – a trend especially evident for POD-LSQ and consistent with the findings reported in .

In summary, reconstruction accuracy is significantly influenced by measurement quantity. IDW is the most affected, followed by POD-IDW, which inherits interpolation errors. POD-LSQ shows better resilience but depends strongly on appropriate angle selection. The baseline, though robust to measurement variations, performs worst overall. These results emphasize the importance of tuning method-specific parameters for reliable lidar-based wind field reconstruction.

The ultimate conclusion we would like to draw is which of the investigated methods performs “best”. The optimal parameter sets – half-cone angle θopt, number of scans nscan,opt, and number of POD modes Kopt – are those that minimize the global mean absolute error MAEglobal for each reconstruction method (Sect. ). These values are summarized in Table  for both the true wind speed input (ufw) and the volume-averaged lidar estimate (ulidar, wgh), with corresponding performance trends shown in Fig. .

Using lidar-based input, POD-IDW achieves the lowest reconstruction error, with a 45.4 % reduction in MAEglobal compared to the baseline. IDW performs nearly as well (44.9 % reduction), followed by POD-LSQ (39.4 %). With true wind input, IDW achieves the best accuracy (74.5 % reduction), followed by POD-IDW (65.6 %) and POD-LSQ (58.8 %). For the baseline, only a negligible 0.04 % difference exists between input types – reflecting its robustness to uncertainty but also its limited resolution, which results in the highest reconstruction error overall. Note that the baseline method achieves its best performance with nscan=8, although using fewer scans results in nearly identical accuracy. This insensitivity to scan count reflects the inherent spatial averaging of the baseline approach.

Measurement errors – including probe volume averaging, cross-contamination, multi-distance fixed-plane mapping error, and tower motion – degrade reconstruction accuracy for all methods except the baseline. This effect is most pronounced for IDW (Sect. –), where the error reduction drops from 74.5 % (with ufw) to 44.9 % (with ulidar, wgh), and the optimal number of scans decreases from eight to three. These shifts reflect IDW's strong sensitivity to the assumption that all selected measurements lie on the same plane, neglecting their actual longitudinal location in space. For all methods, using true wind input generally shifts the optimal half-cone angle θ upward by 2.5–5°, as cross-contamination is no longer a limiting factor. POD-LSQ, in particular, improves its performance by increasing the number of modes from 50 to 200 with only one additional scan, highlighting the impact of measurement uncertainty on modal amplitude estimation (Sect. ).

Overall, POD-IDW offers the best reconstruction accuracy with lidar-based inputs but comes with a higher computational cost. IDW is simpler and moderately expensive but does not capture spatial correlations and assumes isotropic flow variations, leading to unrealistic estimates under certain conditions. POD-LSQ provides a good balance between accuracy and efficiency but requires careful tuning of lidar configuration and POD parameters. The baseline method is the fastest and most robust to measurement uncertainty, yet consistently delivers the poorest reconstruction quality. Ultimately, reliable wind field reconstruction depends on accounting for measurement uncertainty and appropriately tuning method-specific parameters.