Tower-Constrained Post-Processing of WRF Hub-Height Wind Speed for Regional Wind-Resource Screening in Hami, Xinjiang, China

Abstract

We evaluate WRF 90 m wind speeds over Hami, China, using hourly observations from 12 towers during June 2016–May 2017. The study combines a tower-point seasonal hindcast, a four-model comparison at six WRF anchors, a bidirectional cross-farm evaluation, and monthly residual interpolation with 2016–2018 wind-power-density (WPD) scenarios. The March–May 2017 hindcast uses causal feature construction and training-period-only fitting on 26,367 matched tower-hour samples. Its two-stage ExtraTrees correction reduces central error relative to its power-law baseline but detects none of the 128 observed hours at or above 25 m⁻¹, revealing substantial loss of the high-wind tail. In a separate leave-one-WRF-anchor-out comparison, ET, DLinear, TCN, and CVAE use identical 48 h power-law wind histories at the six anchors; their unweighted anchor mean RMSE values span 3.521–3.540 m⁻¹ and all strongly underdetect 25 m⁻¹ h. In the cross-farm evaluation, shared-anchor observations were excluded from fitting: all models predict zero of 223 YW exceedance hours when trained with BLK observations, while the reverse direction gives low and variable POD values. For the monthly product, all towers at a held WRF coordinate were excluded from IDW donors. Across six anchors and 72 anchor-month comparisons, the unweighted mean RMSE decreases from 1.04 to 0.77 m⁻¹. The published power-2, fixed-density central WPD remains 726.7 W m⁻²; across 162 sensitivity cases varying IDW power, residual, cubic factor, density, and penalty weight, fixed-density and ISA means span 457.3–1102.5 and 411.0–988.5 W m⁻², respectively. Only 8.36% of product cells lie inside the six-anchor convex hull. Together, these analyses distinguish tower-point prediction, monthly interpolation, and regional WPD comparison. The maps support regional comparison and identify locations for follow-up measurement within the one-year tower record and six-anchor network.

1. Introduction

Wind energy has become an important component of power-system decarbonization [1]. Recent renewable-energy deployment also makes regional infrastructure planning increasingly dependent on resource screening [2]. In inland wind corridors, a first-order comparison of where stronger and weaker wind-resource conditions are likely to occur can guide the next measurement step. This requirement is especially sensitive at turbine hub height because even modest wind-speed errors can propagate strongly into wind power density (WPD) through the cubic wind-speed relationship [3]. In regions where long hub-height observation records are sparse, regional screening commonly relies on mesoscale modeling to provide spatial continuity and temporal coverage beyond the footprint of the available towers [4].

Among mesoscale tools, the Weather Research and Forecasting (WRF) model is widely used for wind-energy meteorology because it can represent boundary-layer evolution and terrain-modulated wind patterns at kilometer-scale resolution [5]. The ARW core and standard WRF modeling framework are documented by Skamarock et al. [6]. Yet direct use of WRF hub-height wind remains challenging in complex inland terrain. Model errors can arise from boundary-layer parameterization [7], wind-shear and planetary-boundary-layer scheme choices [8], surface-layer formulation [9], and topographic representation [10]. Additional difficulties include low-level-jet representation [11], sensitivity to physics parameterization choices [12], dependence on forcing data for wind-energy estimates [13], and terrain-related parameterization effects in other complex regions [14]. In practice, these errors are rarely a single constant offset. They may vary with month, location, and wind-speed range, so a correction that improves average conditions may still misrepresent strong-wind occurrence, seasonal amplitude, or relative spatial gradients among candidate areas. Regional screening therefore requires diagnosis and constraint of structured hub-height bias before comparative resource analysis.

Statistical and machine-learning post-processing offers one route from biased numerical guidance to wind-resource applications. Model output statistics provide an early statistical foundation for numerical-weather post-processing [15]. Kalman-filter and analog approaches show how dynamic correction can be applied to numerical forecasts [16], while probabilistic calibration addresses distributional forecast reliability [17]. In wind-energy applications, local quantile regression has been used for probabilistic wind-power forecasting [18], support-vector approaches are part of the broader renewable-resource forecasting literature [19], and ensemble machine-learning methods have been reviewed as a major family of wind and solar forecasting tools [20]. Wind-resource extrapolation methods [21] and turbine-power machine learning [22] provide related examples of observation-constrained statistical models. Performance under same-site or mixed random splits may not transfer to held towers, and a tower-to-tower test does not establish performance at every unsampled grid cell [23]. A held-out period within one year assesses only the specified season within the same network and does not validate a multi-year corrected climatology [24]. These distinctions call for separate spatial, seasonal-hindcast, and monthly product evidence [25].

Measure-correlate-predict (MCP) methods commonly transfer a short target-site record to a longer reference series through a fitted relationship [23]. Instead, this study tests tower-point correction at held WRF-anchor groups and evaluates a separate monthly residual field. The grouped-anchor design follows the logic of spatially blocked cross-validation [26] but is adapted to the predictor geometry, because towers sharing one WRF coordinate are excluded together. It strengthens within-network independence; external spatial assessment requires an independent tower network. Similarly, forecast calibration and long-term bias-corrected reanalysis provide related uncertainty and temporal-extension frameworks [17,24]. The present WPD analysis uses deterministic sensitivity cases because no calibrated regional error distribution is available.

This problem is particularly relevant in Hami, Xinjiang, an important inland wind-energy region where the tower record spans one common year from 2016-06 to 2017-05. This overlap reveals structured WRF bias and supports observation-constrained correction models. Interannual bias stationarity and the suitability of the 2016–2018 corrected fields for project-level location selection and energy-yield estimation require longer independent observations. The multi-year WRF archive provides the spatial and monthly continuity for regional screening. The study therefore uses the limited hub-height observations to constrain WRF output while limiting interpretation to what a one-year tower record supports.

This study evaluates tower-constrained WRF post-processing in Hami. We ask: (1) whether raw WRF 90 m wind-speed error is structured across month, tower context, and wind-speed range; (2) how a causally constructed correction behaves in the March-May 2017 seasonal hindcast, including its high-wind behavior; and (3) whether a monthly additive IDW correction improves wind speed at held anchors and how its WPD rankings vary across stated sensitivity cases. The first two questions evaluate tower-point behavior, whereas the third evaluates monthly interpolation and regional WPD scenarios. These analyses link hindcast diagnostics, six-anchor interpolation results, and locations for follow-up measurement while retaining their distinct targets.

2. Materials and Methods

2.1. Study Area and Observational Data

The study area is the Hami wind-energy region in eastern Xinjiang, China, an arid inland corridor with mountain-fringe terrain, sparse vegetation, and strong wind resources. The observational constraint comes from 12 meteorological towers distributed across two wind-farm clusters: BLK-04, BLK-07, BLK-12, BLK-14, BLK-15, BLK-17, BLK-19, YW-02, YW-05, YW-06, YW-09, and YW-10. The existing wind-farm and tower corridor is located at approximately 1000–1500 m elevation. Terrain above 2000 m includes higher mountainous areas with forested and glacier-influenced surfaces. We used 2000 m to exclude these surfaces from the ranking mask; it is a terrain threshold, not a wind-resource criterion. The 12 towers occupy six unique nearest-WRF coordinates (anchors): A01 contains BLK-14, BLK-19, YW-06, and YW-09; A02 contains YW-02, YW-05, and YW-10; A03 contains BLK-04 and BLK-15; and A04, A05, and A06 contain BLK-07, BLK-12, and BLK-17, respectively. Figure 1 and Supplementary Table S2 identify these groups because co-located towers share the same WRF spatial test unit.

Hourly observations were paired with WRF tower extractions by timestamp using an inner join. Valid paired hours require non-missing obs_ws90, wrf_ws90, and wrf_ws10. Completeness was calculated relative to the 8760 hourly records expected over 2016-06-01 00:00 to 2017-05-31 23:00. Across the 12 towers, valid paired rows range from 8129 to 8748, corresponding to completeness fractions from 0.928 to 0.999.

Table 1. Tower metadata, processed observation completeness, and paired raw-WRF summary statistics for the 12-tower overlap dataset.

Tower_Id	Farm	Valid_Paired_Hourly_Rows	Completeness_Fraction	obs_ws90_mean_ms	wrf_ws90_bias_ms	wrf_ws90_rmse_ms
BLK-04	BLK	8746	0.998	8.14	−0.76	4.22
BLK-07	BLK	8600	0.982	7.43	0.17	4.17
BLK-12	BLK	8129	0.928	7.84	−0.10	4.93
BLK-14	BLK	8748	0.999	7.99	−1.04	4.79
BLK-15	BLK	8748	0.999	7.89	−0.52	4.31
BLK-17	BLK	8748	0.999	8.25	−1.19	3.92
BLK-19	BLK	8700	0.993	8.55	−1.59	4.86
YW-02	YW	8748	0.999	8.50	−1.16	4.80
YW-05	YW	8748	0.999	7.54	−0.20	4.58
YW-06	YW	8748	0.999	8.52	−1.56	5.37
YW-09	YW	8747	0.999	7.42	−0.46	4.81
YW-10	YW	8700	0.993	7.52	−0.18	4.86

reports tower metadata, processed completeness, paired-row counts, and raw WRF summary statistics for the tower-overlap year.

2.2. WRF Configuration and Data

The Weather Research and Forecasting (WRF) model with the ARW core was configured with three two-way nested domains of 150 × 150 grid points at horizontal resolutions of 9 km, 3 km, and 1 km, centered near 93 degrees E over Hami. The vertical grid comprised 40 levels. Simulations were driven by NCEP FNL reanalysis data at 0.25 degrees × 0.25 degrees and 6-hourly resolution for initial and lateral boundary conditions. The active manuscript baseline identifies the YSU planetary boundary-layer scheme, Revised MM5 Monin-Obukhov surface-layer scheme, Noah land-surface model, RRTMG longwave and shortwave radiation schemes, Thompson microphysics, and Tiedtke cumulus parameterization on the outermost domain only.

2.3. Wind-Speed Correction Methods and Evaluation Design

The study uses two complementary analyses. The hourly analysis characterizes raw WRF bias and evaluates tower-point correction in the March–May 2017 seasonal hindcast, leave-one-anchor-out comparison, and two-direction cross-farm transfer. It uses a fixed 1/7-power-law 90 m WRF baseline and causal WRF-only histories; its two-stage form combines monthly linear and hourly ExtraTrees residual correction. Separately, tower-derived monthly residuals are interpolated by power-2 inverse-distance weighting (IDW), evaluated at held anchors, and applied to the 2016–2018 WPD sensitivity cases. Earlier multi-model results used heterogeneous inputs and tuning and are provided in Appendix A as supplementary diagnostics.

Performance is assessed using RMSE, MAE, bias, and high-wind diagnostics on matched records common to each comparison. The predeclared 25 m s⁻¹ threshold diagnoses the study tail. We report observed and predicted exceedances, probability of detection, false-alarm ratio, critical success index, and conditional event errors. Matched-sample E(V³) characterizes distributional agreement in the tower-point evaluations.

2.4. Monthly IDW Product and Grouped-Anchor Validation

The regional WPD scenarios use the published monthly additive-bias product and are evaluated separately from the tower-point ExtraTrees model. For each tower i and calendar month m, hourly overlap-period residuals were defined as (r_i,t = obsws90_i,t − wrfws90_i,t). The monthly additive correction parameter was then

$$b_{i,m}={\mathrm{mean}}_t\left(r_{i,t}\right),$$

And the corresponding tower-month residual spread was

$$s_{i,m}={\mathrm{sd}}_t\left(r_{i,t}\right).$$

Both fields were interpolated to the grid by planar-coordinate, power-2 inverse-distance weighting (IDW). Using (w_i(x)) for the IDW weight of tower i at grid cell x, the monthly correction field was

$$b_m\left(x\right)=\mathrm{IDW}(b_{i,m};w_i(x\left)\right),$$

And the gridded interpolated residual-spread field was

$$S_m\left(x\right)=\mathrm{IDW}(s_{i,m};w_i(x\left)\right).$$

We evaluated the monthly correction using six leave-one-anchor-out folds. For every held WRF coordinate and calendar month, all towers sharing that coordinate were excluded from IDW donors. Member-tower errors were averaged within each held anchor-month, yielding 72 repeated anchor-month diagnostics (six anchors times 12 months). The primary summary is the unweighted mean over the six anchor-level metrics; repeated calendar months therefore contribute within each of six locations. The field (S_m(x)), termed interpolated historical residual spread, supplies the residual component of the sensitivity cases. The monthly additive product applies (b_m(x)) to the 2016–2018 monthly WRF archive. The one-year tower overlap provides the observational basis for these monthly screening cases.

2.5. Wind Power Density Calculation and Regional Comparison

WPD was computed as a monthly regional product from the corrected monthly 90 m wind-speed fields. The fixed-density case uses ($\rho$ = 1.225 kg m⁻³); a static ISA density calculated from DEM elevation is a separate sensitivity case. To reduce the underestimation that would result from cubing monthly mean wind speed directly, the product uses observed monthly cubic factors derived from the overlap-tower data together with the corrected monthly wind-speed field. The resulting formulation can be written as

$$P_m=0.5\rho C_m{V}_m^3,$$

where P_m is WPD and V_m is the corrected monthly 90 m wind speed at grid cell x and month m; C_m is the observed monthly cubic factor. The cubic factors are held fixed across the domain and the 2016–2018 archive, so their spatial and interannual transfer is assumed. The resulting fields are monthly energy-density estimates.

3. Results

3.1. Baseline Bias Characterization and Climatological Diagnostics

Figure A1 summarizes the one-year tower-overlap baseline for June 2016 to May 2017. Across the 12 towers, raw WRF 90 m wind speed captures the seasonal phase but underestimates amplitude at most sites. The observed mean wind speed is 7.97 m s⁻¹, compared with 7.25 m s⁻¹ from raw WRF, giving a mean bias of 0.72 m s⁻¹ and an RMSE of 4.65 m s⁻¹. The monthly means peak in April and reach their minimum in December in both datasets, but the size of the bias is not constant through the year: the domain-mean underestimation is largest in February (+1.79 m s⁻¹) and much smaller in April (+0.25 m s⁻¹). The main message from the overlap-year baseline is therefore phase agreement with a structured amplitude error; tower-by-tower monthly extremes are better reported in Table 1 than in dense caption text.

Figure 2 uses direct wrf_ws90 diagnostics for the farm-level distribution check. At BLK, directly interpolated WRF 90 m wind speed has a mean of 7.29 m s⁻¹ versus 8.02 m s⁻¹ observed, with (r = 0.65), RMSE = 4.47 m s⁻¹, and bias = −0.73 m s⁻¹. At YW, the corresponding values are 7.19 versus 7.90 m s⁻¹, with (r = 0.65), RMSE = 4.89 m s⁻¹, and bias = −0.71 m s⁻¹. The farm-level distributions retain their broad shape, but the upper tail remains too weak in raw WRF: the q95 decreases from 17.99 to 16.96 m s⁻¹ at BLK and from 19.41 to 17.98 m s⁻¹ at YW, while the frequency of wind speeds at or above 20 m s⁻¹ drops from 2.31% to 1.38% at BLK and from 4.23% to 2.28% at YW. The direct WRF 90 m baseline therefore preserves moderate hourly association while still suppressing strong-wind occurrence.

Figure 3 shows that the bias is also farm- and month-dependent. The mean bias is +0.74 m s⁻¹ at BLK and +0.72 m s⁻¹ at YW over the overlap year, but the largest monthly underestimation occurs in February at both farms (+1.95 m s⁻¹ at BLK and +1.63 m s⁻¹ at YW). In contrast, BLK biases are close to zero in April and May, and YW shows slight overestimation in December. Because monthly sample sizes remain stable, these contrasts indicate structured model error rather than sampling artifacts. Taken together, Figure A1, Figure 2 and Figure 3 show that the raw WRF 90 m bias varies by season, farm context, and wind-speed range.

3.2. Causal March–May 2017 Seasonal Hindcast and High-Wind Behavior

The controlled two-stage correction was evaluated on 26,367 matched tower-hour samples from March–May 2017. The power-law baseline has RMSE 5.070 m s⁻¹; the monthly linear stage has RMSE 4.409 m s⁻¹; and adding hourly ExtraTrees gives RMSE 3.638 m s⁻¹. The two-stage route therefore improves central error in the seasonal hindcast.

High-wind behavior gives a different result. At the predeclared 25 m s⁻¹ threshold, 128 observed tower-hours occur in the hindcast sample. The raw power-law baseline detects 35 (POD = 0.273), whereas the two-stage ExtraTrees prediction has no values at or above the threshold (POD and CSI = 0.000) and a conditional-event bias of −5.847 m s⁻¹. Its matched-sample mean V³ is 14.4% below the observed value. The added hourly correction therefore improves central error while suppressing the high-wind tail in this test, as shown in

Table 2. March–May 2017 seasonal-hindcast central and high-wind diagnostics (26,367 matched tower-hour samples).

Candidate	RMSE (m s−1)	Observed/Predicted ≥25 m s−1	POD	CSI	Conditional-Event Bias (m s−1)	E(V3) Difference (%)
Raw 1/7 power-law	5.070	128/472	0.273	0.062	−2.540	+27.4
Monthly linear	4.409	128/0	0.000	0.000	−8.883	−39.5
Monthly linear plus hourly ExtraTrees	3.638	128/0	0.000	0.000	−5.847	−14.4

.

Full speed-bin, tail, and processed-sequence QC diagnostics are provided in Supplementary Tables S1 and S3–S5. The earlier 14-model comparison, the impurity-based feature-importance diagnostic (Figure A2), and selected high-wind cases (Figure A7) are shown in Appendix A. Tower-wise and earlier cross-farm analyses use different input variables, tuning histories, or spatial test units.

3.3. Hourly Wind-Speed Correction at Held WRF Anchors

The four hourly models were evaluated at the six WRF anchors. At each anchor, all associated towers were excluded from model fitting, and ET, DLinear, TCN, and CVAE used identical 48 h 1/7-power-law WRF histories. The unweighted mean anchor RMSE was 3.521 ± 0.005 m s⁻¹ for TCN, 3.522 ± 0.001 m s⁻¹ for ET, 3.531 ± 0.008 m s⁻¹ for CVAE, and 3.540 ± 0.003 m s⁻¹ for DLinear; values after the plus/minus sign are the standard deviations across three random seeds. The four models therefore had similar central-error performance at the held anchors.

High-wind diagnostics qualify the central-error comparison. Each seed has 248 observed tower-hour exceedances at 25 m s⁻¹ across the six held anchors. ET and DLinear predicted no threshold exceedance in any seed. TCN detected 2, 10, and 11 h in seeds 43, 41, and 42, respectively, while CVAE detected 2, 3, and 3 h. The unweighted six-anchor mean POD was 0.000 for ET and DLinear, 0.009 ± 0.006 for TCN, and 0.003 ± 0.001 for CVAE; the corresponding mean CSI values were 0.000, 0.000, 0.008 ± 0.005, and 0.003 ± 0.001. The upper quantiles of matched hourly prediction-minus-observation errors were positive: six-anchor mean q99 error ranged from +7.511 to +7.656 m s⁻¹ across models. Relative V³ error ranged from −21.5% to −21.1%, so the similar central RMSE values coexist with weak high-wind and third-moment performance, as summarized in

Table 3. Hourly model performance at held WRF anchors. Metrics are unweighted means across six anchors, followed by the standard deviation across three random seeds; all models use the same 48 h ws_power_law_90m history.

Model	RMSE (m s−1)	MAE (m s−1)	POD at 25 m s−1	CSI at 25 m s−1	Relative V3 Error (%)
ET	3.522 ± 0.001	2.781 ± 0.001	0.000 ± 0.000	0.000 ± 0.000	−21.32 ± 0.05
DLinear	3.540 ± 0.003	2.792 ± 0.004	0.000 ± 0.000	0.000 ± 0.000	−21.08 ± 0.29
TCN	3.521 ± 0.005	2.764 ± 0.004	0.009 ± 0.006	0.008 ± 0.005	−21.07 ± 0.54
CVAE	3.531 ± 0.008	2.781 ± 0.002	0.003 ± 0.001	0.003 ± 0.001	−21.50 ± 1.65

. Per-anchor/seed threshold, episode, quantile, and third-moment diagnostics are reported in Supplementary Tables S6–S8.

3.4. Monthly IDW Correction at Held WRF Anchors

The monthly additive product was evaluated separately from the tower-point hindcast. With all towers at each WRF anchor excluded jointly, the unweighted mean anchor-level monthly RMSE decreases from 1.039 to 0.774 m s⁻¹ and mean MAE from 0.866 to 0.644 m s⁻¹ across six anchors. The corrected RMSE varies among anchors (SD 0.317 m s⁻¹); at A04, it increases from 0.498 to 0.819 m s⁻¹. The 72 anchor-month values comprise 12 calendar months at each of six locations. The correction therefore lowers the mean monthly error but performs differently across anchors, as shown in

Table 4. Monthly IDW correction evaluated at held WRF anchors. Each row combines 12 calendar-month errors at one anchor.

Anchor	Held Towers	Raw RMSE	Corrected RMSE	Raw MAE	Corrected MAE
A01	4	1.325	0.772	1.177	0.662
A02	3	0.698	0.594	0.607	0.482
A03	2	0.773	0.616	0.695	0.537
A04	1	0.498	0.819	0.442	0.711
A05	1	1.609	1.369	1.075	1.109
A06	1	1.330	0.474	1.197	0.360
Mean across six anchors	–	1.039	0.774	0.866	0.644

.

3.5. Cross-Farm Transfer Evaluation

The cross-farm evaluation was separate from the six-anchor comparison. BLK-to-YW evaluated all YW towers at A01–A02 after fitting models with BLK observations at A03–A06 (40,687 matched hours per seed); YW-to-BLK evaluated BLK towers at A01 and A03–A06 after fitting models with YW observations at A02 (56,307 matched hours per seed). Observations at the shared A01 anchor were excluded from fitting. The two directions differ in the number and location of their training and test towers and are reported separately.

Table 5. Central-error metrics for cross-farm transfer. Each entry is the mean ± SD across three random seeds within the stated direction; directions are not pooled.

Direction (Test Farm; Training Anchors)	Model	N Matched Hours	RMSE (m s−1)	MAE (m s−1)	Bias (m s−1)	R2	Correlation
BLK2YW (YW; BLK A03–A06)	ET	40,687	3.567 ± 0.002	2.761 ± 0.002	−0.046 ± 0.002	0.626 ± 0.000	0.796 ± 0.000
BLK2YW (YW; BLK A03–A06)	DLinear	40,687	3.530 ± 0.005	2.727 ± 0.010	−0.082 ± 0.015	0.634 ± 0.001	0.799 ± 0.000
BLK2YW (YW; BLK A03–A06)	TCN	40,687	3.570 ± 0.013	2.738 ± 0.033	−0.191 ± 0.101	0.625 ± 0.003	0.795 ± 0.002
BLK2YW (YW; BLK A03–A06)	CVAE	40,687	3.554 ± 0.013	2.738 ± 0.010	−0.279 ± 0.053	0.629 ± 0.003	0.798 ± 0.001
YW2BLK (BLK; YW A02)	ET	56,307	3.520 ± 0.001	2.723 ± 0.001	−0.270 ± 0.002	0.559 ± 0.000	0.754 ± 0.000
YW2BLK (BLK; YW A02)	DLinear	56,307	3.545 ± 0.006	2.739 ± 0.001	−0.277 ± 0.047	0.553 ± 0.001	0.754 ± 0.000
YW2BLK (BLK; YW A02)	TCN	56,307	3.530 ± 0.030	2.738 ± 0.024	−0.160 ± 0.064	0.556 ± 0.008	0.752 ± 0.005
YW2BLK (BLK; YW A02)	CVAE	56,307	3.536 ± 0.029	2.739 ± 0.016	−0.206 ± 0.089	0.555 ± 0.007	0.753 ± 0.003

reports the central-error metrics for both directions.

High-wind events were poorly represented in both directions. In BLK2YW, every model predicted zero threshold exceedances despite 223 observed 25 m s⁻¹ h and 85 observed same-tower episodes per seed. In YW2BLK, there were 25 observed hours and 17 observed episodes per seed: ET predicted none; DLinear had POD 0.040 and CSI 0.025 across seeds; TCN had POD 0.200 ± 0.040 and CSI 0.061 ± 0.007; and CVAE had POD 0.213 ± 0.140 and CSI 0.064 ± 0.041, with false-alarm ratios near 0.92 for the latter three models. The differing directions reveal weak and variable high-wind transfer within the current tower network.

Threshold, episode, quantile, and third-moment diagnostics by direction and seed are reported in Supplementary Tables S10 and S11. Earlier cross-farm results based on heterogeneous inputs are shown in Appendix A.

3.6. Sensitivity of WPD Patterns and Rankings

The WPD sensitivity analysis uses the monthly IDW product and its grouped-anchor errors. The published power-2, published-factor, fixed-density, median-residual, weight-0.25 case is reproduced at 726.7275 W m⁻², or 726.7 W m⁻² after reporting rounding, over 2788 grid cells. In the IDW-power comparison, unweighted six-anchor RMSE is 0.767, 0.774, and 0.819 m s⁻¹ for powers 1, 2, and 3, respectively; power 2 remains the published definition. Across 162 sensitivity cases, fixed-density means span 457.3–1102.5 W m⁻² and ISA-density means span 411.0–988.5 W m⁻² over the DEM-supported subset. These ranges reflect the effects of IDW power, residual, cubic factor, density, and ranking weight, as summarized in

Table 6. Sensitivity of mean WPD and the ten highest-ranked cells relative to the published power-2, published-factor, median-residual, fixed-density, weight-0.25 case.

Density Treatment	Domain Support	Mean WPD Range (W m−2)	Top-10 Overlap Range	Sources of Variation
Fixed density, 81 cases	2788 cells	457.3–1102.5	6–10	IDW power, residual, cubic factor, and ranking weight
ISA elevation density, 81 cases	2448 cells	411.0–988.5	6–10	IDW power, residual, cubic factor, density, and ranking weight

.

Of the 2788 product cells, 233 (8.36%) lie inside the convex hull of the six anchors; the other cells lie beyond the tower network. Across the 162 cases, overlap of the ten highest-ranked cells with the reference is 6–10 cells (Jaccard 0.429–1.000; Spearman rank correlation 0.920–1.000). Two cells occur among the ten highest-ranked cells in all 162 cases. Supplementary Tables S12 and S13 give the full sensitivity results.

4. Discussion

The March-May 2017 hindcast, the four-model evaluation at held anchors, and the cross-farm evaluation describe tower-point central errors, high-wind behavior, and wind-speed distributions. The held-anchor monthly analysis evaluates the separate IDW correction, and the WPD calculation applies that monthly product under the stated assumptions. Across the tower-point analyses, lower central errors coincide with weak high-wind performance: the two-stage ExtraTrees correction misses every observed 25 m s⁻¹ exceedance in the seasonal hindcast, the four models have six-anchor mean POD values no higher than 0.009, and the BLK-to-YW evaluation predicts none of 223 observed exceedance hours for any model. Negative matched-sample V³ errors likewise indicate underrepresentation of the high-wind tail and third moment despite similar central RMSE values.

The held-anchor hourly evaluation excludes all towers at the test anchor. The cross-farm evaluation also excludes same-anchor source-farm observations. Its two directions have unequal numbers of training and test towers, so they are interpreted separately. The held-anchor monthly analysis excludes every co-located tower from the IDW donor set. The monthly improvement from 1.039 to 0.774 m s⁻¹ in mean anchor-level RMSE shows lower average error at the held anchors, although performance varies across them and deteriorates at A04. Only 233 of 2788 product cells fall inside the anchor convex hull; the maps consequently extend well beyond the sampled-anchor hull. Independent tower networks are needed to assess transfer to other terrain and wind regimes.

The WPD values follow the monthly formula and stated sensitivity factors. The central 726.7 W m⁻² value changes to 411.0–1102.5 W m⁻² across the cases, with differing spatial denominators for fixed and ISA density. Selection frequency shows the recurrence of a cell among the ten highest-ranked locations in 162 cases. Kriging or terrain-aware interpolation, interannual cubic-factor variation, and calibrated predictive uncertainty require additional data and analysis. The maps support regional comparison and follow-up measurement. Site-specific energy-yield assessment, location selection, and engineering design require dedicated observations.

The study covers one year of tower-WRF overlap and a March–May holdout, so interannual and all-season behavior require further testing. It uses one WRF physics configuration and processed tower records. The supplied records do not include calibration, maintenance, boom-orientation, icing, or instrument-status information. The sequence-level QC flags characterize the processed time series; field records, multi-physics WRF experiments, and independent tower networks would extend the assessment.

5. Conclusions

This one-year Hami tower-WRF case study evaluates tower-point correction, monthly interpolation, and regional WPD comparison as distinct analyses.

• Raw WRF 90 m error varies by month, tower context, and wind-speed range. A causal two-stage correction reduces central error in the March–May 2017 hindcast from 5.070 to 3.638 m s⁻¹, while detecting none of the 128 observed 25 m s⁻¹ exceedances. Central-error improvement and high-wind behavior therefore need to be assessed together.
• In the held-anchor hourly comparison, ET, DLinear, TCN, and CVAE have similar six-anchor mean RMSE values (3.521–3.540 m s⁻¹ across three random seeds) but strongly underdetect 25 m s⁻¹ h and underestimate matched-sample V³ by about 21%. The cross-farm evaluation excludes same-anchor source-farm observations and again shows direction-dependent failure to represent high-wind hours within the current tower network.
• The separately evaluated monthly, power-2 IDW correction reduces unweighted mean anchor-level monthly RMSE from 1.039 to 0.774 m s⁻¹ across six held WRF anchors. Its performance differs among anchors, including deterioration at A04, and the regional fields extend beyond the six-anchor hull.
• The 2016–2018 WPD maps provide regional comparison under the stated sensitivity factors. The published central fixed-density case has a mean WPD of 726.7 W m⁻²; the 162 cases span 457.3–1102.5 W m⁻² for fixed density and 411.0–988.5 W m⁻² for ISA density across their stated supports. Selection frequency identifies cells that recur among the ten highest-ranked locations and guides follow-up measurement.
• The results represent a one-year overlap, a March–May seasonal hindcast, one WRF configuration, and six spatial anchors. The WPD fields extend beyond the anchor hull, and field-instrument records are incomplete. Independent tower networks, multi-physics WRF experiments, kriging or terrain-aware interpolation tests, interannual cubic-factor observations, calibrated uncertainty, and documented instrument calibration and maintenance would extend these results.