Detecting and calibrating large biases in global onshore wind power assessment across temporal scales

Domain: earth_science
Published: 2025-04-22
Editorial outcome: major_revision

Abstract
The global capacity for wind power has grown rapidly in recent years, yet uncertainties in wind power density (WPD) assessments still hinder effective climate change mitigation efforts. One major challenge is the significant underestimation of WPD when using coarser temporal resolutions (Δt) of wind speed data. Here, we show that using daily Δt results in an average underestimation of 35.6% in global onshore WPD compared to hourly Δt. This discrepancy arises from the exponential decay of WPD with increasing Δt, reflecting the intrinsic properties of wind speed distributions, particularly in regions with weaker winds. To address this, we propose a calibration method that introduces a correction coefficient to reduce biases and harmonize WPD estimates across temporal resolutions. Applying this method to future wind energy projections under the Shared Socioeconomic Pathway 585 scenario increases global onshore WPD estimates by 25% by 2100, compared to uncorrected daily data. These findings highlight the effectiveness of calibration in reducing uncertainties, enhancing WPD assessments, and facilitating robust policy action toward carbon neutrality.

Introduction
In recent years, wind power has emerged as a leading renewable energy source for electricity generation, offering significant potential to mitigate climate change by offsetting greenhouse gas emissions1,2. Global onshore and offshore wind power installations reached a record 117 Gigawatt (GW) in 2023, according to the Global Wind Energy Council3. However, achieving the targets outlined by the United Nations Climate Change Conference and Sustainable Development Goals will still require accelerating this growth to at least 320 GW annually by 2030.

Wind power density (WPD), proportional to the cube of wind speed, is a widely used metric for quantifying the potential wind energy available at a given location4–6. It provides a standardized measure for comparing wind resources, independent of turbine size or technical specifications, and serves as the quantitative foundation for wind energy assessments and resource classification7. Factors influencing WPD assessments include spatial resolution8,9, temporal resolution (Δt) of wind data10,11, and air density12,13. Among these, temporal resolution has a particularly pronounced effect due to the cubic relationship between wind speed and WPD14. High-speed wind events, characterized by short-term variability and disproportionately large contributions to WPD, are often smoothed or lost with coarser Δt data15. This leads to substantial underestimations in wind power calculations and related environmental impact assessments10. For example, monthly averaged wind speeds have been shown to underestimate total wind power by up to 48% compared to hourly measurements from a wind tower in Boulder, CO, USA16. Similarly, daily wind speed data from the fifth-generation atmospheric reanalysis of the global climate produced by the European Centre for Medium-Range Weather Forecasts (ERA5) underestimates global offshore wind power by 10–30% relative to hourly estimates17.

High-resolution data are therefore critical to accurately capturing wind speed variability and improving WPD estimates. However, such data are often challenging to obtain and computationally demanding to process11. Practical applications in global and regional wind power assessments often rely on coarser Δt data (Supplementary Table 1), such as daily or even monthly averages, due to accessibility and resource constraints18,19. Early global wind power assessments, for instance, employed 6-hour or daily wind speed data20,21, while analyses of historical changes in wind energy potential often depend on archived low-resolution data. State-of-the-art global climate models (GCMs) in the Coupled Model Intercomparison Project Phase 6 (CMIP6) typically provide daily wind speed data, exacerbating uncertainties in WPD projections16,22.

Addressing these challenges requires a systematic evaluation of Δt-induced bias, allowing us to balance the trade-offs between accuracy and practical efficiency. To develop robust calibration methods to harmonize WPD estimates across resolutions is also critical but remains unresolved10,16. Furthermore, most research has focused on regional analyses17, leaving the global implications—essential for international policy frameworks—largely underexplored. If a robust relationship between WPD and Δt exists, it would be possible to correct the bias and yield accurate WPD estimates even with coarser Δt, reducing computational demands.

This study investigates the impact of Δt on WPD calculations at a global scale using wind speed data from multiple sources, including high-resolution observations (Supplementary Fig. 1), climate reanalyses (ERA5, and reanalysis datasets from the National Centers for Environmental Prediction/National Centers for Atmospheric Research (NCEP/NCAR) and the NCEP-US Department of Energy (NCEP-DOE)), and climate model simulations from CMIP6. A robust statistical relationship between WPD and Δt is identified, providing a foundation for a calibration method to standardize WPD estimates across temporal resolutions. This approach offers a practical solution for reducing uncertainties in WPD assessments, facilitating wind energy resource planning, and informing policymaking for sustainable energy development.

Results
Underestimation of WPD using coarse temporal resolutions
To demonstrate the effects of temporal resolution on wind speed variability and WPD estimates, a rural station in southern Canada (52.3°N, 111.8°W) was chosen from stations with high-resolution wind speed observational data, ensuring representation of diverse wind conditions. Hourly observational data at this site during May 2021 capture frequent fluctuations and wind gusts exceeding 15 ms−1, with a standard deviation of 3.9 ms-1 (Supplementary Fig. 2a). In contrast, daily data smooth these variations, reducing the standard deviation to 2.9 ms-1 and diminishing the frequency and magnitude of strong gusts. Similar patterns are observed in ERA5 reanalysis data at the same location, where standard deviations decrease from 3.2 ms-1 (1-hour) to 2.6 ms-1 (daily) (Supplementary Fig. 2b). This smoothing effect of coarse Δt eliminates high-frequency variability and suppresses the upper percentiles of wind speeds, which dominate WPD calculations. Consequently, WPD estimates are underestimated by 24.5% (observations) and 18.3% (ERA5 reanalysis) at this site.

Globally, observational data reveal consistent spatial patterns for WPD(daily) and WPD(1-hour) (Fig. 1a, b), both aligning well with prior global wind power assessments16,20,21. However, coarse Δt introduces substantial underestimation. On average, WPD(daily) underestimates WPD(1-hour) by 35.6%, with relative biases ranging from 20–40% at most sites (Fig. 1c). Spatial variations are evident: high-WPD regions (e.g., northern Europe, central USA, central Asia, and southwestern Australia) exhibit low biases, while low-WPD regions (e.g., southern Europe, eastern USA, Brazil, the Middle East, East Asia, and northern Australia) can experience biases of up to 60% (Fig. 1c).

ERA5 reanalysis similarly highlights distinctive regional patterns (Fig. 1d, e) consistent with observations. Mid- to high-latitude regions and subtropical deserts exhibit relatively high WPD (>200 W m-2), whereas tropical regions generally have low WPD (<50 W m-2). However, ERA5 reinforces the underestimation trend with daily data (Fig. 1f). Similar findings are evident in both NCEP/NCAR and NCEP-DOE reanalysis datasets (Supplementary Fig. 3). Across global terrestrial areas, the average WPD bias between hourly and daily ERA5 data is approximately 20%, with biases exceeding 60% in tropical and mountainous regions where wind speeds are generally low. These consistent patterns across observations and reanalyses underscore that Δt effects are less (more) pronounced in strong (weak) wind environments.

Moreover, Δt significantly affects actual electrical power production (AEP) calculations. Using a General Electric GE 1.5s wind turbine as an example (Supplementary Fig. 4), AEP estimates derived from daily wind speed data differ markedly from those based on hourly data (Supplementary Fig. 5), emphasizing the critical role of temporal resolution in accurately evaluating wind energy potential.

Intrinsic dependence of WPD decay on temporal resolutions
To explore why WPD calculations differ across wind speed data with varying Δt, we analyzed the statistical characteristics of their distributions. Using the rural station in southern Canada as an example, the wind speed data were fitted to a Weibull probability density function (PDF). Though the Weibull PDF has been shown to give a good fit to observed wind speed distributions in most cases10, here it was used solely for fitting the distribution, while WPD calculations were performed using the statistical method described in the Methods section.

In this case, the Weibull distribution provides a good fit for the hourly wind speed series, with a shape parameter k = 1.93 and a scale parameter c = 6.53 (Fig. 2a). However, as Δt coarsens, the wind speed distribution becomes increasingly constricted, with a notable shortening of the tail representing high wind speeds. This results in an increase in k and a decrease in c, shifting the distribution toward a more normal shape. Notably, wind speed data with daily or coarser Δt cannot be accurately represented by the Weibull distribution, as k exceeds the theoretical threshold of 3.04223.

This shift in the wind speed distribution due to coarser Δt directly impacts WPD calculations. To quantify this, we calculated WPD across different Δt values using global observations. As illustrated by four representative sites in Figs. 2b, c, the relationship between WPD and Δt follows an exponential function as Eq. (1)

WPD(Δt) = a exp(−bΔt) (1)

Here, a represents the theoretical maximum WPD (WPDmax) associated with the finest Δt, and b quantifies the rate of WPD decline with increasing Δt. Larger b values indicate a more rapid reduction in WPD with coarser Δt (Fig. 2b). The fitting results indicate that a 6-hour Δt reduces WPD to approximately 80–90% of WPDmax, whereas daily averaging can lower it to as little as 55% of WPDmax in certain cases (Fig. 2c). Moreover, although WPD (equal to a) may be slightly lower than the WPD calculated from finer Δt values (e.g., 1-hour or even higher resolutions), a exhibits a strong positive correlation with WPD(1-hour) (Fig. 2d), indicating that WPD(1-hour) is a reasonable approximation of a, the theoretical maximum WPD.

Unlike the stretched exponential model proposed by a previous study10, our exponential function reveals significant negative correlations between a and b, and between b and WPD(1-hour). As shown in Fig. 2e, f, regions with smaller a and lower WPD(1-hour) exhibit larger b values, indicating a steeper WPD decline with coarser Δt. Conversely, in regions with higher a and WPD(1-hour), the decline is less pronounced. These results align with previous findings17 and confirm that WPD underestimation due to coarse Δt is more pronounced in regions with lower wind power potential. Indeed, the ratio of WPD(Δt) to WPD(1-hour) diminishes exponentially as Δt increases, with the decline rate being steeper for lower WPD(1-hour), as shown by site 4 with the smallest a (Fig. 2c).

Globally, the spatial distribution of parameters a and b highlights distinct regional patterns (Fig. 2g, h), and most sites (>95.8%) exhibit robust exponential fits, with coefficients of determination (R2) exceeding 0.7 (Fig. 2i). Regions with higher a—indicative of strong wind speeds and high wind power potential—include northern Europe, central USA, central Asia, southwestern Australia, southern South America, and some coastal areas. These regions typically have lower b values (<0.01), indicating minimal WPD decline with coarser Δt. Conversely, regions with lower a, such as southern Europe, eastern USA, Brazil, the Middle East, and East Asia, exhibit higher b values, suggesting that WPD calculations in these areas are more sensitive to coarse Δt.

Finally, the decay relationship between WPD and Δt is evident not only in observational data but also in ERA5 reanalysis (Supplementary Fig. 6), demonstrating that Δt effect on WPD calculations is independent of data source. The strong correlation between parameters a and b suggests that this effect is likely an intrinsic property of the wind speed distribution itself, rather than a site-specific attribute. The parameter b, which governs the exponential decay of WPD with respect to Δt, is intrinsically linked to general wind-energy conditions represented by parameter a.

Calibration of WPD bias across temporal scales
The robust relationship between parameters a and b indicates that sites with distinct a values—derivable from WPD(1-hour)—exhibit varying decay characteristics, providing a foundation for rectifying WPD estimates derived from coarser Δt. To address this, we propose a calibration coefficient, K(Δt-1hour), which quantifies the relative bias between WPD(Δt) and WPD(1-hour). This coefficient enables the alignment of WPD estimates from varying Δt values to WPD(1-hour). Details of K(Δt-1hour) definition, calculation, and the rationale for using WPD(1-hour) as the “target” for rectification are provided in the Methods section.

The global distribution of K(daily-1hour) based on observations (Fig. 3a) shows that regions with lower K values generally correspond with high wind-energy areas, such as northern Europe, central Asia, central USA, southwestern Australia, southern South America, and certain coastal zones. In contrast, higher K values—indicating significant discrepancies between WPD(daily) and WPD(1-hour)—are observed in relatively flat inland terrains such as East Asia, southern Europe, eastern USA, and Brazil, where wind power generation is already widely implemented. Furthermore, K(daily-1hour) derived from ERA5 reanalysis (Fig. 3b) aligns well with observations, supporting the applicability of the calibration approach across diverse datasets.

Statistical analysis reveals a moderate but significant negative correlation between WPD(daily) and K(daily-1hour) (R = −0.49, p < 0.001; Fig. 3c). Regions with lower WPD(daily) exhibit higher K values; for instance, K can reach 5.0 when WPD(daily) falls below 10 W m-2, while K approximates 1.5 when WPD(daily) exceeds 400 W m-2. As most sites fall within the WPD(daily) range of 10 and 400 W m-2 (Fig. 1a), calibrations using K values of 1.5–2 are particularly relevant. Interestingly, sites with WPD(daily) exceeding about 1000 W m-2 have K values below 1.0 (Fig. 3c), consistent with the positive relative bias in Fig. 1c. This phenomenon is actually attributed to deceptive high-speed wind events arising from averaging wind speeds above the cut-out threshold (Supplementary Fig. 7), which are unsuitable for electricity production.

To facilitate practical use, K values were categorized by WPD levels (Fig. 3d). For WPD Level I (0–50 W m-2), the median K value is 2.12, albeit with substantial variation, while for WPD Level VI (>400 W m-2), the median K value is 1.21, with much narrower variability. These categorized K values can be directly used to adjust WPD across different grades. Additionally, a global gridded dataset of K values at 1°×1° resolution was generated (Supplementary Fig. 8). This dataset preserves large-scale spatial features, enabling straightforward correction of WPD at specific locations with present conditions by referencing the nearest grid point’s K value.

Calibration coefficients K(Δt-1hour) were also derived for 6-hour and 3-hour resolutions, commonly used in previous studies (Supplementary Table 1). As shown in Supplementary Fig. 9, the relationship between WPD and K at these resolutions mirrors that of daily Δt, with slightly lower K values. Applying the same methodology, WPD and K values were calculated from ERA5, NCEP/NCAR, and NCEP-DOE reanalysis datasets across various Δt values (Supplementary Fig. 10). In all cases, K maintained a significant negative correlation with WPD, reinforcing the robustness of the calibration method (Supplementary Fig. 11).

Taken together, these findings suggest that the statistical relationship between K and WPD, derived from diverse datasets, can effectively rectify WPD estimates across different Δt ranges. This calibration approach not only aligns WPD(daily) with WPD(1-hour) but also extends to WPD(3-hour) where applicable, offering a practical solution for harmonizing global wind power assessments and minimizing uncertainties in policy-relevant decisions.

Implications for future wind power assessment
To illustrate the uncertainties in assessing future wind power potential using coarse-resolution wind speed data, and to demonstrate the utility of the proposed calibration coefficient K, we provide an example based on the Earth system model (EC-Earth3) from CMIP6. The global distribution of WPD derived from daily wind speed data in the EC-Earth3 model under the Shared Socioeconomic Pathway 585 (SSP585) scenario for 2100 (Fig. 4a) shows spatial patterns similar to those observed during the historical period in ERA5 (Fig. 1d). According to the model, the average global onshore WPD(daily) is projected to be approximately 120 W m-2 by 2100 (SSP585 scenario; Fig. 4g). However, analysis of 3-hour wind speed data reveals a substantial underestimation when comparing WPD(daily) with WPD(3-hour) (Fig. 4d), despite similar spatial distributions. This discrepancy results in an average deviation of -30.7% for future WPD across global land (Fig. 4f), aligning closely with the -35.6% bias observed historically in the observational data (Fig. 1c). Regions such as East Asia, southern Europe, and USA—where wind power generation is extensively implemented—exhibit particularly pronounced biases.

Applying the calibration coefficient K(daily-3hour) significantly improves WPD estimates (Fig. 4b). The calibrated WPD(3-hour) reduces the relative bias between WPD(3-hour) and WPD(daily) (Fig. 4e), decreasing the average deviation from −30.7% to −15.0% (Fig. 4f). By applying K(daily-1hour), the global average onshore WPD increases to >150 W m-2, representing a 25% enhancement relative to daily data (120 W m-2, Fig. 4g).

These results emphasize the practicality of calibrating WPD using K in scenarios where high-resolution wind speed data are unavailable. This calibration method is especially valuable given that publicly accessible CMIP6 model outputs typically offer wind speed data at resolutions no finer than 3 hours, with most models providing only daily data11. The simplicity of the K-based approach enables accurate assessments without requiring computationally intensive high-resolution data, making it particularly advantageous in resource-constrained settings.

It is important to note that this study focuses on the impact of Δt on absolute future global onshore WPD rather than changes relative to the present. As shown in Supplementary Fig. 12, the CMIP6 multi-model mean indicates statistically insignificant decreasing trends in global onshore WPD over the period 2015–2100. Furthermore, the relative changes in WPD remain largely unaffected by the application of K across different greenhouse gas emission scenarios. It may imply that Δt has a minimal impact on WPD trend estimation, whether for historical periods (Supplementary Fig. 13) or future projections (Supplementary Fig. 12; Supplementary Note 1). While uncertainties persist in GCMs regarding wind speed projections, including discrepancies in simulated magnitude and trends16,22, one certainty is that using daily data to compute wind energy resources consistently results in at least a 30% negative bias on global onshore WPD. Consequently, while calibration may not critically affect assessments of relative changes in WPD—provided both historical and future simulations share consistent biases—it is indispensable for minimizing errors in absolute WPD estimates.

Methods
Wind datasets
This study utilizes global high temporal-resolution wind speed data, including 20-min, 30-min, and 1-hour observations, sourced from the National Climatic Data Center (NCDC). To ensure data quality and sufficient sample sizes for reliable statistical analyses10, only stations with >80% valid records spanning 1973–2021 were included in the analysis, as illustrated in Supplementary Fig. 1. Climate reanalysis datasets, such as ERA5, NCEP/NCAR, and NCEP-DOE, were also employed to analyze 10 m and hub-height (100 m) wind speeds35–37. Reanalysis datasets are widely recognized for their consistency and high-fidelity in wind speed estimates38,39. WPD was calculated across multiple temporal resolutions (e.g., 20-min, 1-hour, 6-hour, daily) for both observational and reanalysis datasets to quantify the effect of Δt.

For future wind power assessments, this study used outputs from EC-Earth3 model in CMIP6 as a representative example. This model was selected because it provides 3-hour wind speed data, which meets the requirements of this analysis40. Previous studies show that EC-Earth3 closely aligns with other CMIP6 models in capturing wind speed trends41. Additional CMIP6 models with coarser temporal resolutions (e.g., BCC-CSM2-MR, CMCC-ESM2, CNRM-CM6-1, INM-CM4-8, IPSL-CM6A-LR, MIROC6, MRI-ESM2-0) were used to evaluate relative changes in WPD under future scenarios (Supplementary Fig. 12).

Extrapolating wind speed at hub height
Wind speed at turbine hub height, typically 100 meters above ground level, was extrapolated from 10 m using a stability-corrected logarithmic wind profile42, as described in Eq. (2)

U(z) = (u*/κ) * ln(z/z0) + Ψ(z/L) (2)

where U(z) is the wind speed at height z, u* is friction velocity, κ = 0.4 (von Karman constant), z0 is the surface roughness length, Ψ(z/L) is the stability correction term, and L is the Monin-Obukhov length. For neutrally stability conditions43,44, this equation simplifies to Eq. (3)

U(z) = (u*/κ) * ln(z/z0) (3)

When height z1 and z2 are known, friction velocities cancel out, yielding Eq. (4)

U(z2) = U(z1) * ln(z2/z0) / ln(z1/z0) (4)

This logarithmic wind profile equation (Eq. (4)) is widely used to extrapolate hub-height wind speed from the observations20,45–47. While previous studies often assumed a constant z0 value, surface roughness varies with land-use and land-cover (LULC)48. To improve the accuracy of WPD calculation, this study applied z0 values specific to LULC types48–51, as summarized in Supplementary Table 2. LULC types were determined using global land cover data from European Space Agency (ESA) WorldCover52.

ERA5 provides 100 m wind speed data directly, eliminating the need for extrapolation. These data have been widely used in WPD assessments due to their reliability and consistency38,46,53. Furthermore, z0 was calculated globally using ERA5 wind speed data at 10 m and 100 m, based on Eq. (4)54,55. The global z0 map derived from ERA5 (Supplementary Fig. 18) aligns well with the LULC-specific z0 values (Supplementary Table 2). This global z0 map derived from ERA5 was applied to extrapolate hub-height wind speeds in CMIP6 outputs.

Calculation of wind power density and actual electrical power production
WPD, a widely used metric for assessing wind energy potential4–6, was calculated using the statistical approach described in Eq. (5)

WPD = (1/2n) * Σ ρUi^3 (5)

where n is the number of observations over a given time period, Ui is the hub-height wind speed (restricted to 3–25 ms-1, corresponding to cut-in and cut-out speeds of wind turbines), and ρ is the air density, assumed to be 1.225 kg m-3 (standard value). While air density varies spatially and temporally due to geographic and seasonal factors, a constant ρ was used here to isolate the effects of Δt on WPD. The 3–25 ms-1 range represents the operational limits for most turbines, where wind speeds outside this range contribute no electrical power14.

To estimate actual electrical power production (AEP), we used the General Electric GE 1.5s wind turbine as an example56. The turbine-specific power curve, shown in Supplementary Fig. 4, includes the following parameters: rated power (1500 kW), cut-in wind speed (3.5 ms-1), rated wind speed (12.0 ms-1), cut-out wind speed (25 ms-1), diameter (70.5 m), swept area (3904.0 m2), and hub height (100 m). Hourly and daily hub-height wind speed data were applied to this power curve to calculate AEP.

Examination of wind speed probability distribution function
The Weibull probability distribution function (PDF) has been widely used to fit wind speed distributions due to its reliability in capturing observed patterns23,27,57. The Weibull PDF is expressed in Eq. (6)

f(U) = (k/c) * (U/c)^(k-1) * exp(-(U/c)^k) (6)

where U is wind speed (ms-1), k is the shape parameter (dimensionless), and c is the scale parameter (ms-1). These parameters can be estimated using methods such as maximum likelihood estimation or least squares fitting58.

WPD derived from Weibull distributions is calculated using Eq. (7)

WPD = (1/2) * ρ * c^3 * Γ(1 + 3/k) (7)

where Γ is the gamma function and can be calculated using the method of factorial.

However, our findings reveal substantial discrepancies between WPD estimates derived using the Weibull method and those calculated via the statistical method (Eq. (5)), irrespective of whether hourly or daily data were utilized (Supplementary Figs. 19, 20). These discrepancies are particularly pronounced at low WPD levels (<50 W m-2) or high levels (>400 W m-2) (Supplementary Fig. 20). Previous studies have also highlighted uncertainties in Weibull-based WPD estimates for coarse temporal resolutions23,29. Thus, to ensure consistency across different Δt values, we adopted the statistical method (Eq. (5)) for WPD calculations in this study.

Definition and calculation of calibration coefficient K
The relative bias (RB) of WPD calculated from different Δt values, relative to WPD(1-hour), is defined by Eq. (8)

RB = (WPD(Δt) / WPD(1-hour) - 1) * 100% (8)

This relationship can be reformulated to express the relationship between WPD(1-hour) and WPD(Δt) as shown in Eq. (9)

WPD(1-hour) = WPD(Δt) / (RB + 100%) (9)

The calibration coefficient K(Δt-1hour), defined as the ratio of WPD(1-hour) to WPD(Δt), is expressed in Eq. (10)

K(Δt-1hour) = WPD(1-hour) / WPD(Δt) (10)

K values directly correspond to RB (e.g., K = 5.0 for RB = -80%; K = 2.0 for RB = -50%). WPD(1-hour) was chosen as the target for rectification due to several reasons. First, as shown in Fig. 2d, WPD(1-hour) closely approximates parameter a, which represents the theoretical maximum WPD. This makes it a useful benchmark for wind power assessments. Second, while higher temporal resolution data, such as 10-minute intervals, may offer more precise WPD estimates29, such data are often unavailable or computationally prohibitive. In contrast, 1-hour resolution data are widely accessible and statistically comparable to 10-minute data10,59. Third, practical considerations, such as data availability and computational efficiency, often necessitate the use of even coarser resolutions (e.g., 3-hour, 6-hour, daily, monthly) in WPD calculations (Supplementary Table 1). Using WPD(1-hour) as the standard enables K(Δt-1hour) to reliably correct biases introduced by coarse resolutions, ensuring robust adjustments while maintaining computational feasibility.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The paper “Large bias in global wind power assessment across temporal scales and the calibration method” examines the effect of temporal aggregation of wind speed on the calculation of wind power density (WPD), a commonly used metric for assessing wind power potential, in observations, reanalysis data, and climate model output. The authors propose that the use of longer (daily) averaging periods significantly underestimates the resulting WPD compared to the results of using higher-frequency (hourly) wind speed data, and that this underestimation can have large effects on the long-term climate change mitigation strategies. The study also points out that this underestimation is stronger in weak-wind environments. The study gives a detailed insight into the regional differences of wind speed distributions and best-fitting parameters to approximate WPD, and develops a robust statistical relationship between averaging period and WPD. The authors then develop a calibration factor which is region-specific and can be used to convert a WPD that was derived from low-frequency wind speed records to one much closer to actually observed values. They demonstrate that the correction of WPD with the calibration factor reduces the relative bias of daily-based WPD estimates considerably and represents a more cost-effective alternative to relying on high-frequency wind speed data, which – especially in climate models – is not always available.\nThe methodology is sound, well described, and generally reproducible. However, some of the data sources described in the method section should be moved to the reference list and provided with a last access date.\nAll in all, I feel the study constitutes an important contribution to the research community and is likely to spark further research towards a more accurate and comparable assessment of current and future wind power potential.\nOverall, I strongly suggest publication of this study in Nature Communications after addressing minor comments and suggestions, which I will elaborate on in the section below.\nGeneral: I already like the discussion of the results and also the description of limitations and challenges that arise with WPD assessment and calibration. Regarding the application to future WPD estimates, I would like to see a little more differentiation between assessing changes in WPD and assessing future absolute WPD. While assessing future relative changes in WPD does not critically depend on the calibration as long as the climate model and the historical analysis are “equally biased”, having an accurate calibration factor is essential to the estimation of future absolute WPD. While reading I felt that this core implication and strength of the paper is a slight bit undersold, and should be moved from the supplement to the main discussion section.\nL1-2: This really comes down to personal taste, but I believe the second part of the current title sounds a bit clunky. I would suggest renaming the paper to something like “Detecting and calibrating large biases in global wind power assessment across temporal scales”.\nL92: Is there a specific reason why you chose this location in rural Canada as an example?\nL149-156: Here, you jump from globally valid results (L111-148) to results that are valid for the exemplary location in Canada only, without mentioning that you do so. During the first reading, I was a tad confused as it sounds like the Weibull shape and scale parameters you mention in this section are valid for the whole globe, which of course would not make sense. I suggest adding that you now focus on the example from earlier on again.\nL261-275: I personally don’t see the added value in repeating the analysis for the six WPD levels. The information that is contained in Fig. 3d) can also be extracted from Fig. 3c) (same for Fig. S9/S11 b,d,f compared to S9/S11 a,c,e). Furthermore, your gridded 2x2° K-value dataset which you present earlier in the manuscript (Fig. S12) already provides an excellent lookup table for the practical application of WPD calibration, arguably even with much higher accuracy and spatial resolution.\nL283: I believe this should refer to Fig. 1d) instead of 1c).\nL317-321: I would argue that wind gustiness is definitely a factor in the decay of WPD with increasing aggregation period length, however not at the timescales investigated in this study. While gusts occur at a second to sub-second scale, the biggest point here in my opinion is that the characteristic timescale of synoptic-scale high-wind features (e.g., the strongest part of an extratropical cyclone) lies somewhere between an hour and a day. You demonstrate very nicely that increasing the temporal resolution can resolve most of the biases and strong underestimation of WPD arising from daily-mean wind speed data. Gusts, however, are already averaged out, both in hourly and daily-resolved time series.\nL345-347: I would call this a similarity instead of a coincidence, as the high correlation between 10-minute and 1-hour wind speed averages is not coincidental, but rather caused by variability on timescales longer than 1 hour that is present in both time series.\nL367-368: This sentence reads like a repetition of L349-350.\nL390-391: The link to the dataset should appear in the reference list and/or in a data availability statement at the end of the manuscript, along with the date of last access. The main body of the text should just contain the short citation. Same suggestion for L408.\nL404: You specify it in the next sentence, but I still would not use the plural form “models” here if you only took data from EC-Earth3. It is perfectly valid to use one model only as a representative for the larger cohort, but I would not recommend introducing this paragraph by creating the expectation of a multi-model study.\nL408: The link should be in the reference list, see my comment to L390-391.\nL446: Please indicate the meaning of the gamma function in Eq. (4) in the text.\nFigs. 2, S8, possibly also S5/S6: Could you mark the locations of the selected stations on any of the maps?\nFigs. 2a & S2: The color of the curves in Fig. 2a) suggest a WPD level of somewhere between 100 and 200 W/m² for daily data, using the colorbar in Fig. 2g). However, in Fig. S2a), the observed WPD(daily) is 310 W/m² for the same location. Could you please explain the disparity between the two plots? Maybe I am missing something here. For WPD(hourly), both figures seem to agree on >400 W/m².\nFig. 3c: On first glance, it appears counterintuitive why the seemingly sparse scatter points in the lower left part of the plot are colored yellow, indicating a high point density. I assume this is because you calculate the density in linear WPD space, not in log(WPD) space, and the logarithmic x-axis distorts the densities, correct?\nFig. 4: The uppercase roman numerals in subplots 4f) and 4g) might be confused with the WPD levels (I through VI) that you introduced in Figure 3. I suggest to consider choosing another label here, for example lowercase roman numerals (i, ii, iii) or uppercase letters.\nSupplementary Text L7-10: Please specify that study by Li et al. (2022) focuses on China only, contrary to Vautard et al. (2010). Thus, the statement on declining WPD trends in most regions should also be constrained to China.\nSupplementary Figures: Would it be possible to order the supplementary figures by their appearance in the main text? For instance, currently Figure S7 is mentioned before S5 and directly after S2.", "reviewer_2": "This paper proposes a calibration method to reduce the biases in global wind power assessment across different temporal and spatial scales. As such, it could be a highly relevant and important contribution to the literature on this topic, potentially provides insight into the common underestimation of wind potential in large-scale studies and fits well in the scope of Nature Communications. The methodology is straightforward and the obtained result provides a good overview of the magnitudes of biases in wind power assessment.\nBut in its current form, the manuscript falls short in many respects, especially for Nature Communications, as outlined in detail below. Our main criticism is that the paper is written rather like a standard research paper, it contains a lot of repetition and does not deliver a concise, clear and powerful analysis that is expected from this journal. The ultimate problem that is addressed, that of the bias due to low/different data resolutions, is the result of a trade-off between accuracy and efforts. But the authors do not raise this important trade-off in their paper, instead only focusing on the point of the bias. If a method is 20% off but uses 50% fewer resources, then for some applications it may suffice, whereas others may need the extra effort to attain 10% or lower errors. This means that the method is not systematic in deriving a bias for a specific resolution, which is generalizable and thus useful to decide what resolution is required based on the above considerations.\nThe style contains a lot of long, nested sentences, which does not aid readability, for example on p.4 and p. 16. More importantly, the “so what?” question is not answered by the majority of the paper, in other words it is written in a rather conventional style that does not push the main implications / takeaways to the forefront and present them in a convincing way. So the relevance, importance and wider context for the main outcomes of the paper is missing or not well communicated.\nOverall, then we consider this topic interesting for analysis but this current version of the manuscript cannot be considered for publication in the current form. A complete rewrite of the paper is required that goes beyond major revisions. We leave it at the editor’s discretion which overall decision this results in.\nBelow are some more detailed comments on the paper:\n1. The introduction is too long, waffling and contains much repetition of the same content. Instead the authors are advised to introduce a clear structure to break their article down into digestible and logical chunks.\n2. A proper definition of wind power density (WPD) is not given. WPD can be easily confused with wind farm power density, which depends on turbines’ technical characteristics, as explored by other studies such as: https://doi.org/10.1016/j.enpol.2018.08.023.\n3. The dependence of WPD calculations on ∆t: Figure 1 shows clearly the underestimation of WPD at lower temporal resolutions, but Figure 2 (b) and (c) are unclear due to missing color legend, (e) and (f) have unclear message: are they to show a weak or intermediate correlation?\n4. Calibration of WPD across temporal scales: When R < 0.7, the correlation is moderate instead of “pronounced”, although it passed the statistical significance test.\n5. The m in Equation (1) should be called the shear exponent in the power law. The power law is in general less accurate than logarithmic wind profile equation. Since there is already available global land cover data (WorldCover: https://esa-worldcover.org/en), it would be valuable to use logarithmic law based on the land cover (e.g. https://www.researchgate.net/publication/228474930), which also aligns with the goal of the paper to improve the accuracy of WPD calculation.\n6. Implications for future wind power assessment: findings are clearly presented but figures can be improved to aid readability and interpretation, both in the figure itself and in the caption.\n7. Discussion and summary: In Figure S14, the numbers at the top are not clearly defined.\n8. Supplementary text, figs and tables: whilst reference is made to some of these figures in the article, it is not clear what purpose the whole collection of supplementary material serves and this should be clarified in the main article.", "reviewer_3": "While it is well-known that there is an influence of temporal resolution on WPD, there has been no systematic global quantification of this effect to date. This article closes this research gap. In addition, the calibration factors presented are also very useful for use in future studies. However, some aspects of this investigation need to be clarified. I hope the comments will help the authors to optimize the manuscript.\nP1L22: Please cite the latest Global Wind Report 2024.\nP3L82: Does the data set also include data from buoys? If not, what about the transferability of the study to offshore regions? Since the article deals with onshore wind energy, the term “onshore“ should be mentioned in the title.\nFigure 1: What is the white bar for the ERA5 wind speed? Is it the prime meridian?\nP1L20-25: Do the values in the first section refer to the combined offshore and onshore wind energy?\nP17L312: “asΔt“ --> Please correct the typo.\nP19L357: However, wind turbines are also sometimes installed in other forms of land use. It would be interesting if the authors could also subdivide their analysis into different types of land use.\nP20L379: It should already be mentioned in the first section (Main) that the time issue is only one of many uncertainty factors. The article partly gives the impression that this is the main problem of wind resource assessment.\nP20L393: What is the rationale behind the 80% threshold?\nP21L406: The general uncertainty of climate models should be mentioned even more clearly.\nP21L421: The surface roughness coefficient depends on the land-use. It is also variable in terms of time. The authors should consider the use of more accurate methods for extrapolating wind speed. Otherwise, it is essential to quantify the possible error magnitudes.\nP22L434: Instead of equation 2, it would make sense to use a real wind turbine power curve and calculate the actual power output.\nP22L436: Air density is not a constant. Especially in regions with high elevation, it is usually significantly lower than the specified 1.225 kg/m3. Although this fact has no influence on the research question of this study, it should nevertheless be mentioned.\nP22L441: Although the Weibull distribution is indeed used in most cases, it does not appear to be suitable for all wind regimes in the world. The use of other, more flexible distributions should be examined.", "reviewer_4": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": "Dear Reviewers,\nWe sincerely thank you for your thoughtful and constructive comments on our manuscript.\nYour detailed feedback has significantly helped us enhance the quality, clarity, and impact of\nour work. We have revised the manuscript accordingly, and below we provide point-by-point\nresponses to each of your comments, outlining the specific changes made to address your\nconcerns.\nTo facilitate readability, the reviewers’ original comments are in blue, and our responses are in\ndark color.\nReviewer #1 (Remarks to the Author):\n[...]\nReply: Thank you very much for recognizing the significance and value of our work. We\nsincerely thank you for the thoughtful comments and constructive feedback. Your suggestions\nhave been instrumental in improving the clarity and robustness of our manuscript. Below, we\naddress each of your comments point by point:\nGeneral: I already like the discussion of the results and also the description of limitations and\nchallenges that arise with WPD assessment and calibration. Regarding the application to future\nWPD estimates, I would like to see a little more differentiation between assessing changes in\nWPD and assessing future absolute WPD. While assessing future relative changes in WPD\ndoes not critically depend on the calibration as long as the climate model and the historical\nanalysis are “equally biased”, having an accurate calibration factor is essential to the estimation\nof future absolute WPD. While reading I felt that this core implication and strength of the paper\nis a slight bit undersold, and should be moved from the supplement to the main discussion\nsection.\nReply: Thank you for this valuable suggestion. We have revised the Results and Discussion\nsections to more clearly differentiate between assessing relative changes in WPD and\nestimating absolute future WPD. Specifically, we have emphasized the critical role of accurate\ncalibration in projecting absolute WPD values under future climate change scenarios, which is\nessential for wind power planning and policymaking.\nWe also clarified that the study focuses on the impact of Δt on absolute future global onshore\nWPD (as shown in Fig. 4) rather than relative changes to the present. Importantly, relative\nchanges in WPD remain largely unaffected by applying the calibration coefficient 𝐾 across\ndifferent greenhouse gas emission scenarios (Supplementary Fig. 12). These revisions are\ndetailed in the updated Results section (Pages 13-14, Lines 236-243).\n1. L1-2: This really comes down to personal taste, but I believe the second part of the current\ntitle sounds a bit clunky. I would suggest renaming the paper to something like “Detecting and\ncalibrating large biases in global wind power assessment across temporal scales”.\nReply: Thank you for this great suggestion. We have revised the title to:“Detecting and\nCalibrating Large Biases in Global Onshore Wind Power Assessment Across Temporal Scales” .\nThe addition of \"onshore\" aligns with Reviewer #3’s suggestion to clarify the study's focus on\nland-based wind energy.\n2. L92: Is there a specific reason why you chose this location in rural Canada as an example?\nReply: The location was chosen from stations with high-resolution wind speed observational\ndata, ensuring representation of diverse wind conditions. This site serves as an illustrative\nexample to demonstrate the effects of temporal resolutions on WPD calculations. We have\nclarified this rationale in the revised manuscript (Page 3, Lines 72-74).\n3. L149-156: Here, you jump from globally valid results (L111-148) to results that are valid\nfor the exemplary location in Canada only, without mentioning that you do so. During the first\nreading, I was a tad confused as it sounds like the Weibull shape and scale parameters you\nmention in this section are valid for the whole globe, which of course would not make sense. I\nsuggest adding that you now focus on the example from earlier on again.\nReply: Thank you for identifying this issue. We have revised the text to explicitly state the\ntransition to the example in rural Canada. The updated section clarifies that the analysis now\nfocuses on a specific site to explore statistical characteristics of wind speed distributions. Please\nrefer to Page 6, Lines 110-111 in the revised manuscript.\n4. L261-275: I personally don’t see the added value in repeating the analysis for the six WPD\nlevels. The information that is contained in Fig. 3d) can also be extracted from Fig. 3c) (same\nfor Fig. S9/S11 b,d,f compared to S9/S11 a,c,e).\nFurthermore, your gridded 2x2° K-value dataset which you present earlier in the manuscript\n(Fig. S12) already provides an excellent lookup table for the practical application of WPD\ncalibration, arguably even with much higher accuracy and spatial resolution.\nReply: Thank you for this insightful observation. We have carefully considered this suggestion,\nand we recognize that the necessity of analyzing the six WPD levels might not have been fully\nexplained in the original submission. While Fig. 3c serves as the foundation for Fig. 3d, the\nlatter provides a simplified classification scheme for applying K-values in different wind\nenergy environments. This approach is particularly useful in scenarios where future wind\nenergy conditions may change significantly due to climate change. For example, regions\ntransitioning from one wind power class to another, as defined by the National Renewable\nEnergy Laboratory (Elliott, 1986), can refer to Fig. 3d for appropriate K-values across WPD\nlevels.\nAdditionally, we would like to clarify the complementary roles of Fig. 3d and the gridded 1°x1°\n𝐾-value dataset (Fig. S12, now Supplementary Fig. 8 in the revision). Supplementary Fig. 8\noffers a gridded 1°x1° K-value dataset, which is ideal for calibrating WPD under current or\nstable wind conditions with high spatial resolution. However, for regions experiencing\nsubstantial changes in wind conditions under global warming scenarios, recalibrating WPD\nwould require insights from both Fig. 3 and Supplementary Fig. 8.\nTo ensure clarity, we have included a detailed explanation of the practical applications of both\nFig. 3 and Supplementary Fig. 8 in the revised manuscript. Additionally, we have made the\ndatasets from Fig. 3 and Supplementary Fig. 8 available in the source data file for easy access\nand practical use.\n5. L283: I believe this should refer to Fig. 1d) instead of 1c).\nReply: Thank you for catching this error. The figure reference has been corrected in the revision.\n6. L317-321: I would argue that wind gustiness is definitely a factor in the decay of WPD with\nincreasing aggregation period length, however not at the timescales investigated in this study.\nWhile gusts occur at a second to sub-second scale, the biggest point here in my opinion is that\nthe characteristic timescale of synoptic-scale high-wind features (e.g., the strongest part of an\nextratropical cyclone) lies somewhere between an hour and a day. You demonstrate very nicely\nthat increasing the temporal resolution can resolve most of the biases and strong\nunderestimation of WPD arising from daily-mean wind speed data. Gusts, however, are already\naveraged out, both in hourly and daily-resolved time series.\nReply: Thank you for this insightful clarification. We fully agree with your assessment. In the\nrevised manuscript, we explicitly state that the decay in WPD is primarily driven by the\nresolution of synoptic-scale high-wind features, rather than gustiness. This distinction is now\nclearly articulated in the revised manuscript (Page 16, Lines 258-259).\n7. L345-347: I would call this a similarity instead of a coincidence, as the high correlation\nbetween 10-minute and 1-hour wind speed averages is not coincidental, but rather caused by\nvariability on timescales longer than 1 hour that is present in both time series.\nReply: We agree with this clarification. The term \"coincidence\" has been replaced with\n\"similar\" in the revised manuscript. The updated text appears on Page 16, Line 275.\n8. L367-368: This sentence reads like a repetition of L349-350.\nReply: We have removed the repetitive sentence to improve conciseness and avoid redundancy.\n9. L390-391: The link to the dataset should appear in the reference list and/or in a data\navailability statement at the end of the manuscript, along with the date of last access. The main\nbody of the text should just contain the short citation. Same suggestion for L408.\nReply: Thank you for this suggestion. The dataset links have been moved to the Data\nAvailability statement, which now includes last access dates. The main text contains only brief\ncitations. Please refer to the updated Data Availability statement in the revised manuscript.\n10. L404: You specify it in the next sentence, but I still would not use the plural form “models”\nhere if you only took data from EC-Earth3. It is perfectly valid to use one model only as a\nrepresentative for the larger cohort, but I would not recommend introducing this paragraph by\ncreating the expectation of a multi-model study.\nReply: Thank you for pointing this out. The text has been revised to clarify that only EC-Earth3\ndata were used as a representative model output. This model was selected because it provides\n3-hourly wind speed data, which meets the requirements of this analysis. The revised wording\nappears on Page 18, Lines 324-326.\n11. L408: The link should be in the reference list, see my comment to L390-391.\nReply: Corrected as suggested.\n12. L446: Please indicate the meaning of the gamma function in Eq. (4) in the text.\nReply: Added as suggested.\n13. Figs. 2, S8, possibly also S5/S6: Could you mark the locations of the selected stations on\nany of the maps?\nReply: Thank you for this suggestion. We have updated Fig. 2 to include markers indicating the\nselected station locations for better clarity. For supplementary figures (e.g., Fig. S8, now\nSupplementary Fig. 6), where displaying station locations on the map is less effective, the\nlocations have been explicitly described in the captions.\n14. Figs. 2a & S2: The color of the curves in Fig. 2a) suggest a WPD level of somewhere\nbetween 100 and 200 W/m² for daily data, using the colorbar in Fig. 2g). However, in Fig. S2a),\nthe observed WPD(daily) is 310 W/m² for the same location. Could you please explain the\ndisparity between the two plots? Maybe I am missing something here. For WPD(hourly), both\nfigures seem to agree on >400 W/m².\nReply: Thank you for pointing this out. The disparity arises because Fig. 2a) represents WPD\nvalues based on annual averages (2014–2021), while Fig. S2a) corresponds to data for May\n2021 only. This distinction has been clarified in the captions. To avoid misunderstanding, we\nhave used different color bars for subplots. The color bars in Fig. 2a) has been adjusted to\ndistinguish them more clearly from Fig. 2g).\n15. Fig. 3c: On first glance, it appears counterintuitive why the seemingly sparse scatter points\nin the lower left part of the plot are colored yellow, indicating a high point density. I assume\nthis is because you calculate the density in linear WPD space, not in log(WPD) space, and the\nlogarithmic x-axis distorts the densities, correct?\nReply: Yes, the density was calculated in linear WPD space. A clarification has been added to\nthe figure caption.\n16. Fig. 4: The uppercase roman numerals in subplots 4f) and 4g) might be confused with the\nWPD levels (I through VI) that you introduced in Figure 3. I suggest to consider choosing\nanother label here, for example lowercase roman numerals (i, ii, iii) or uppercase letters.\nReply: Thank you for this suggestion. We have revised the labeling to lowercase Roman\nnumerals (i, ii, iii) to avoid confusion.\n17. Supplementary Text L7-10: Please specify that study by Li et al. (2022) focuses on China\nonly, contrary to Vautard et al. (2010). Thus, the statement on declining WPD trends in most\nregions should also be constrained to China.\nReply: Thank you for this important suggestion. We have revised the statement to specify that\nLi et al. (2022) focuses on China, and this adjustment has been reflected in the revised\nSupplementary Note 1.\n18. Supplementary Figures: Would it be possible to order the supplementary figures by their\nappearance in the main text? For instance, currently Figure S7 is mentioned before S5 and\ndirectly after S2.\nReply: We appreciate this suggestion. The supplementary figures have been reordered to align\nwith their sequence in the main text for improved consistency and readability.\nWe sincerely thank Reviewer #1 for the thoughtful feedback and constructive suggestions. We\nbelieve the revisions have addressed all concerns and enhanced the clarity and impact of our\nmanuscript. We hope we have addressed all your concerns. Please let us know if there are any\nfurther questions or suggestions.\nReviewer #2 (Remarks to the Author):\n[...]\nReply: We sincerely appreciate your detailed feedback and critical comments on our manuscript.\nYour insights and suggestions have been invaluable in improving the quality, clarity, and\noverall impact of this work. Below, we address each of your comments in detail and describe\nthe corresponding revisions made to the manuscript.\nBut in its current form, the manuscript falls short in many respects, especially for Nature\nCommunications, as outlined in detail below. Our main criticism is that the paper is written\nrather like a standard research paper, it contains a lot of repetition and does not deliver a concise,\nclear and powerful analysis that is expected from this journal. The ultimate problem that is\naddressed, that of the bias due to low/different data resolutions, is the result of a trade-off\nbetween accuracy and efforts. But the authors do not raise this important trade-off in their paper,\ninstead only focusing on the point of the bias. If a method is 20% off but uses 50% fewer\nresources, then for some applications it may suffice, whereas others may need the extra effort\nto attain 10% or lower errors. This means that the method is not systematic in deriving a bias\nfor a specific resolution, which is generalizable and thus useful to decide what resolution is\nrequired based on the above considerations.\nThe style contains a lot of long, nested sentences, which does not aid readability, for example\non p.4 and p. 16. More importantly, the “so what?” question is not answered by the majority of\nthe paper, in other words it is written in a rather conventional style that does not push the main\nimplications / takeaways to the forefront and present them in a convincing way. So the\nrelevance, importance and wider context for the main outcomes of the paper is missing or not\nwell communicated.\nOverall, then we consider this topic interesting for analysis but this current version of the\nmanuscript cannot be considered for publication in the current form. A complete rewrite of the\npaper is required that goes beyond major revisions. We leave it at the editor’s discretion which\noverall decision this results in.\nReply: Thank you for your detailed feedback and constructive criticism. In response, we have\nmade the following major revisions to address these concerns:\n1. Revised structure and writing: We have rewritten the manuscript to emphasize key takeaways,\nimprove readability, and remove redundancy. Long and nested sentences have been simplified\nto enhance clarity and engagement. The structure has been refined to ensure logical flow and\nto bring the main implications of the study to the forefront.\n2. Trade-off Between Accuracy and Effort: We fully agree with the importance of emphasizing\nthe trade-off between accuracy and resource requirements in WPD assessment. To address this,\nwe have incorporated detailed discussions in the revised manuscript, focusing on the balance\nbetween bias reduction and computational efficiency. This highlights the utility of the proposed\ncalibration method, particularly in resource-limited scenarios. Please refer to Page 2, Lines 44-\n46; Page 3, Lines 60-62; Page 13, Lines 233-235; Page 16, Lines 271-277 in the revised\nmanuscript. The rationale for using WPD(1-hour) as the \"target\" for rectification has been\nexplained in details in the Methods section (Part 5, Pages 21-22, Lines 407-417).\nWe would also like to take this opportunity to clarify further. While high-resolution data\nundoubtedly provides more precise results when resources allow, as reviewers have recognized,\nour calibration method significantly reduces the relative bias of WPD estimates derived from\ncoarse-resolution data. This offers a cost-effective alternative to relying solely on high-\nfrequency wind speed data, which—especially in climate models—is not always available.\nMoreover, this new method enables cross-resolution comparisons of WPD estimates, which is\nnot only crucial for future projections but also highly beneficial for historical data analysis.\nMany sites only retain records with coarse resolutions from past periods.\nIn the revised version, we have emphasized the practical value of this calibration method in\nenabling more accurate WPD assessments, balancing accuracy with computational cost, and\nfacilitating comparisons across temporal resolutions. We have revised and streamlined the text\nto improve readability and ensure clearer communication of these key points.\n3. Conciseness: Non-essential details and redundant content have been removed, particularly\nin the Introduction and Results sections. The title has been revised according to the reviewers’\ncomments, for clarity and conciseness to better reflect the study's focus.\nOverall, we have carefully gone through the manuscript and done our best to improve the\nwriting throughout, tightening the prose to facilitate readers’ ability to grasp the big picture.\nThus, we believe these revisions address the core concerns and improve the manuscript's\nreadability, relevance, and impact.\nBelow are some more detailed comments on the paper:\n1. The introduction is too long, waffling and contains much repetition of the same content.\nInstead the authors are advised to introduce a clear structure to break their article down into\ndigestible and logical chunks.\nReply: Thank you for this suggestion. The Introduction has been significantly shortened and\nstreamlined to eliminate redundancy and improve clarity. The revised version focuses on three\nmain points: 1. Background on WPD and its importance. 2. Challenges in assessing WPD\nacross temporal scales. 3. Objectives and contributions of this study.\nThe revised Introduction provides a concise and focused overview, setting the stage for the\nsubsequent sections.\n2. A proper definition of wind power density (WPD) is not given. WPD can be easily confused\nwith wind farm power density, which depends on turbines’ technical characteristics, as explored\nby other studies such as: https://doi.org/10.1016/j.enpol.2018.08.023.\nReply: We fully agree. In the revised manuscript, we have provided a clear and precise\ndefinition of WPD early in the Introduction (Page 2, Lines 27-31). Additionally, the detailed\ncalculation method for WPD is now explicitly described in the Methods section for clarity.\n3. The dependence of WPD calculations on ∆t: Figure 1 shows clearly the underestimation of\nWPD at lower temporal resolutions, but Figure 2 (b) and (c) are unclear due to missing color\nlegend, (e) and (f) have unclear message: are they to show a weak or intermediate correlation?\nReply: Thank you for pointing this out. We have made the following clarifications and revisions:\nFigures 2b and 2c: Each site’s fitted curve is now differentiated by distinct colors, which have\nbeen explained in the figure caption for clarity.\nFigures 2e and 2f: These panels highlight the significant correlations between parameters 𝑎 and\n𝑏, and between 𝑏 and WPD(1-hour). We have clarified in the caption that these correlations are\nstatistically significant and regions with higher WPD (larger 𝑎) exhibit slower decay rates\n(smaller 𝑏) with increasing ∆t.\n4. Calibration of WPD across temporal scales: When R < 0.7, the correlation is moderate\ninstead of “pronounced”, although it passed the statistical significance test.\nReply: Thank you for pointing this out. We have revised the wording to describe correlations\nwith 𝑅<0.7 as “moderate.” The updated text appears on Page 10, Lines 179-180.\n5. The m in Equation (1) should be called the shear exponent in the power law. The power law\nis in general less accurate than logarithmic wind profile equation. Since there is already\navailable global land cover data (WorldCover: https://esa-worldcover.org/en), it would be\nvaluable to use logarithmic law based on the land cover (e.g.\nhttps://www.researchgate.net/publication/228474930), which also aligns with the goal of the\npaper to improve the accuracy of WPD calculation.\nReply: Thanks for this great suggestion. We have carefully considered your suggestion. In many\nprevious studies, the shear exponent m (representing surface roughness coefficient) is often\nassumed as a value of 1/7 for open land (Elliott, 1986; Tian et al., 2019; Zeng et al., 2019), and\nthe equation of wind profile power law is commonly referred to as the one-seventh power law\n(Elliott, 1986).\nHowever, we fully agree with you that the logarithmic wind profile law is more accurate for\nextrapolating hub-height wind speeds, especially when paired with land-use-specific surface\nroughness lengths (𝑧 ). Previous studies have also addressed the error in global wind power\n0\nassessments arising from applying a constant value (1/7) of power law exponent (Jung and\nSchindler, 2021). Therefore, following your suggestions, we have replaced the power law with\nthe logarithmic wind profile equation for hub-height wind speed extrapolation. In the revised\nmanuscript, we have used the global land cover data (ESA WorldCover) to determine land-use-\nspecific surface roughness lengths (𝑧 ).\nbeen updated accordingly. Details are provided in the revised Methods Section (Part 2, Page\n19, Lines 333-357) and Supplementary Note 2.\n6. Implications for future wind power assessment: findings are clearly presented but figures\ncan be improved to aid readability and interpretation, both in the figure itself and in the caption.\nReply: Thank you for this suggestion. We have revised the figures to improve readability. The\nlegends, annotations, and axis labels (e.g., in Fig. 4d,e,f,g) have been clarified or revised where\nnecessary. Figure captions now provide more detailed explanations of the content and purpose\nof each panel.\n7. Discussion and summary: In Figure S14, the numbers at the top are not clearly defined.\nReply: Thank you for this suggestion. We have clarified the numbers in the figure caption of\nFigure S14 (now Supplementary Fig. 12). These numbers represent trends in WPD changes\nacross different scenarios.\n8. Supplementary text, figs and tables: whilst reference is made to some of these figures in the\narticle, it is not clear what purpose the whole collection of supplementary material serves and\nthis should be clarified in the main article.\nReply: Thank you for this suggestion. We have ensured that each supplementary figure and\ntable is explicitly referenced. Their purpose in supporting the main findings is now clarified in\nthe main text.\nWe sincerely thank Reviewer #2 for these detailed and constructive comments. Your insights\nhave greatly improved the manuscript’s clarity, structure, and scientific rigor of the manuscript.\nWe hope the revisions adequately address all your concerns, and we welcome any further\nfeedback.\nReviewer #3 (Remarks to the Author):\n[...]\nReply: Thank you very much for recognizing the significance and value of our work. We\ngreatly appreciate your thoughtful and constructive comments, which have been instrumental in\nimproving the manuscript. Below, we provide point-by-point responses to your comments and\ndetail the corresponding revisions. We hope we have adequately addressed your concerns.\n1. P1L22: Please cite the latest Global Wind Report 2024.\nReply: Thank you for pointing this out. We have updated the manuscript to include the latest\nGlobal Wind Report 2024 in the references. Please refer to Page 1, Lines 22-24 in the revised\nmanuscript.\n2. P3L82: Does the data set also include data from buoys? If not, what about the transferability\nof the study to offshore regions? Since the article deals with onshore wind energy, the term\n“onshore“ should be mentioned in the title.\nReply: The dataset used in this study does not include buoy data, as it focuses primarily on\nonshore observations and reanalysis products. However, our findings suggest that the\ncalibration methods and conclusions may also be applicable to offshore regions. The decay of\nWPD with increasing Δt reflects intrinsic properties of wind speed distributions, which are\nrelated to general wind energy conditions.\nOffshore wind speeds are generally higher, and thus WPD over the ocean may be less affected\nby Δt compared to onshore regions. Our supplementary analysis (Supplementary Figs. 3 and\n10) shows that offshore areas exhibit smaller parameter b values (indicating weaker Δt effects)\nand lower K values across reanalysis datasets (ERA5, NCEP/NCAR, and NCEP-DOE).\nNevertheless, we acknowledge that further validation using offshore-specific datasets is\nnecessary to confirm the transferability of our findings.\nTo clarify the study’s scope, we have revised the title to explicitly include the term \"onshore.\"\n3. Figure 1: What is the white bar for the ERA5 wind speed? Is it the prime meridian?\nReply: Yes, the white bar in Figure 1 corresponds to the prime meridian, an artifact of the\nplotting procedure. We have corrected this issue in the revised figure, which no longer includes\nthe white bar.\n4. P1L20-25: Do the values in the first section refer to the combined offshore and onshore wind\nenergy?\nReply: Yes, the values in this section refer to the combined offshore and onshore wind energy\ncapacity. We have clarified this in the revised text (Page 1, Lines 22-24).\n5. P17L312: “asΔt“ --> Please correct the typo.\nReply: Thank you for identifying this typo. It has been corrected in the revised manuscript.\n6. P19L357: However, wind turbines are also sometimes installed in other forms of land use.\nIt would be interesting if the authors could also subdivide their analysis into different types of\nland use.\nReply: Thank you for this great suggestion. In the revised manuscript, we have subdivided our\nanalysis by land-use and land-cover (LULC) types, such as tree cover, built-up, grassland, and\ncropland, as specified in the ESA WorldCover dataset.\nOur analysis shows that the decay of WPD with Δt is consistent across different LULC\ncategories (Supplementary Figs. 15 and 16), further confirming that this decay is an intrinsic\nproperty of wind speed distributions rather than a site-specific characteristic.\nTo improve accuracy of WPD calculation, we used the logarithmic wind profile equation and\nLULC-specific surface roughness length (z₀) values to extrapolate hub-height wind speeds.\nWhile the recalculated spatial patterns of WPD using this method are similar to those derived\nfrom the one-seventh power law in previous submission, the logarithmic profile equation\nprovides more accurate results. Corresponding figures and discussions have been updated in\nthe revised manuscript (Discussion and Methods Sections, and Supplementary Note 2).\n7. P20L379: It should already be mentioned in the first section (Main) that the time issue is\nonly one of many uncertainty factors. The article partly gives the impression that this is the\nmain problem of wind resource assessment.\nReply: We agree that a broader perspective on uncertainties in wind resource assessments is\nnecessary. The revised Introduction now acknowledges that temporal resolution is one of\nseveral factors, alongside spatial resolution and air density variability, that influence WPD\ncalculations (Page 2, Lines 31-34).\n8. P20L393: What is the rationale behind the 80% threshold?\nReply: The 80% threshold ensures data quality while maintaining sufficient sample sizes for\nreliable statistical analysis. This threshold has also been used in previous studies (e.g., Yizhaq\net al., 2020) and is now explicitly stated in the revised manuscript.\n9. P21L406: The general uncertainty of climate models should be mentioned even more clearly.\nReply: Thank you for this suggestion. We have expanded the discussion in the “Implications\nfor future wind power assessment” Section to explicitly address the general uncertainties of\nclimate models. These include biases in wind speed magnitude and temporal variability, which\ncan influence WPD projections. Please refer to Page 14, Lines 243-244; Pages 17-18, Lines\n300-306 in the revised manuscript.\n10. P21L421: The surface roughness coefficient depends on the land-use. It is also variable in\nterms of time. The authors should consider the use of more accurate methods for extrapolating\nwind speed. Otherwise, it is essential to quantify the possible error magnitudes.\nReply: We fully agree with this great suggestion. We acknowledge that surface roughness (𝑧 )\n0\nvaries with land-use and land-cover (LULC). In the revision, we used the logarithmic wind\nprofile equation, incorporating LULC-specific z₀ values, to extrapolate hub-height wind speeds.\nThis approach improves accuracy of WPD calculations compared to using a constant z₀ value.\nHowever, we also would like to emphasize that the decay relationship of WPD with Δt, and the\ncalibration coefficient K, are minimally affected by LULC types (Supplementary Note 2). This\nreinforces our conclusion that the bias is an intrinsic property of wind speed distributions rather\nthan site-specific attributes. Nevertheless, incorporating LULC-specific z₀ values enhances the\nreliability of absolute WPD estimates. Details are provided in the revised Methods Section\n(Part 2, Page 19, Lines 333-357) and further explained in Supplementary Note 2. Relevant\nfigures have been updated accordingly.\n11. P22L434: Instead of equation 2, it would make sense to use a real wind turbine power curve\nand calculate the actual power output.\nReply: Thank you for this excellent suggestion. In the revised manuscript, we incorporated the\npower curve of a General Electric GE 1.5s wind turbine (Supplementary Fig. 4) to calculate\nactual electrical power production (AEP). This analysis highlights discrepancies between daily\nand 1-hour AEP estimates (Supplementary Figs. 4 and 5), consistent with observed WPD biases.\nUpdated results are described in the revised Results Section (Page 4, Lines 101-105). The\ncalculation of AEP has been added in the revised Methods Section (Part 3, Page 20, Lines 369-\n374).\n12. P22L436: Air density is not a constant. Especially in regions with high elevation, it is\nusually significantly lower than the specified 1.225 kg/m3. Although this fact has no influence\non the research question of this study, it should nevertheless be mentioned.\nReply: We agree. While air density was assumed constant in this study to isolate Δt effects, we\nhave added a note acknowledging its variability, especially in high-elevation regions. This is\nnow mentioned in the revised manuscript (Page 20, Lines 365-367).\n13. P22L441: Although the Weibull distribution is indeed used in most cases, it does not appear\nto be suitable for all wind regimes in the world. The use of other, more flexible distributions\nshould be examined.\nReply: Thank you for this insightful comment. While the Weibull distribution is widely used\n(e.g., Justus et al., 1978; Jamil et al., 1995; Pryor et al., 2004; Pryor and Barthelmie, 2010), our\nanalysis highlights significant discrepancies between Weibull-derived and statistically\ncalculated WPD estimates, particularly in extreme wind regimes (Supplementary Figs. 19 and\n20). These discrepancies align with findings from prior studies (Pryor et al., 2004; Gil Ruiz et\nal., 2021), which also note uncertainties in Weibull-based WPD estimates for coarse temporal\nresolutions. To ensure consistency across Δt values, we adopted the statistical method (Eq. 5)\nfor WPD calculations, as detailed in the revised Methods Section (Part 4, Page 21, Lines 387-\n394).\nWe sincerely thank Reviewer #3 for these valuable comments, which have greatly improved\nthe manuscript. We hope the revisions address all concerns, and please let us know if there are\nany further feedback or suggestions.\nReviewer #4 (Remarks to the Author):\n[...]\nReply: Thank you very much for participating in the review process for our manuscript and for\nsupporting this collaborative initiative to involve Early Career Researchers in peer review. The\ncomments and suggestions from the reviewers have greatly helped us to improve the quality of\nour manuscript.\nWe have carefully revised the manuscript based on all the constructive comments provided by\nthe reviewers. These changes have enhanced the clarity, structure, and scientific impact of the\nwork. We hope that you find the updated version satisfactory. Please feel free to reach out with\nany further suggestions or questions."}, {"round": 2, "reviewer_comments": {"reviewer_1": "I thank the author for the revised version of their manuscript “Detecting and Calibrating Large Biases in Global Onshore Wind Power Assessment Across Temporal Scales”, along with their response to my comments, which was detailed and concise. My previously raised comments and issues were addressed and answered in a satisfactory manner. The changes made to the manuscript, including those in response to the comments of the other referees, have improved the quality, conciseness, and scientific impact considerably. I can therefore recommend the publication of the manuscript in Nature Communications.", "reviewer_2": "Thank you for carefully addressing the comments and implementing the suggested changes. The updated manuscript clearly describes the methodology and interprets the results. We are satisfied with this version and suggest that it be accepted for publication.\nIt is nice to see the surface roughness lengths based on WorldCover are considered for using logarithmic law. This could provide nice inputs for any large-scale onshore wind resource assessment.\nSupplementary Figure 7: Interesting finding on overestimation cases of using daily resolution. The explanation was clear, but why is it only a “likely” cause? It should be easy to check whether the RB changes to negative if you remove the cutout to “confirm” your explanation.", "reviewer_4": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts."}, "author_response": "Once again, we sincerely thank the reviewers for their thoughtful and constructive comments\non this work. Below, we provide our responses to the remaining comments from the last round\nof review. The reviewers' original comments are in blue, and our responses are in black.\nReviewer #1 (Remarks to the Author):\nI thank the author for the revised version of their manuscript “Detecting and Calibrating Large\nBiases in Global Onshore Wind Power Assessment Across Temporal Scales”, along with their\nresponse to my comments, which was detailed and concise. My previously raised comments\nand issues were addressed and answered in a satisfactory manner. The changes made to the\nmanuscript, including those in response to the comments of the other referees, have improved\nthe quality, conciseness, and scientific impact considerably. I can therefore recommend the\npublication of the manuscript in Nature Communications.\nReply: Thank you once again for your constructive comments in the previous round of review.\nWe are very pleased to see that we have successfully addressed your concerns and that you find\nthe revised manuscript improved in quality and impact.\nReviewer #2 (Remarks to the Author):\nThank you for carefully addressing the comments and implementing the suggested changes.\nThe updated manuscript clearly describes the methodology and interprets the results. We are\nsatisfied with this version and suggest that it be accepted for publication.\nIt is nice to see the surface roughness lengths based on WorldCover are considered for using\nlogarithmic law. This could provide nice inputs for any large-scale onshore wind resource\nassessment.\nSupplementary Figure 7: Interesting finding on overestimation cases of using daily resolution.\nThe explanation was clear, but why is it only a “likely” cause? It should be easy to check\nwhether the RB changes to negative if you remove the cutout to “confirm” your explanation.\nReply: Thank you once again for your constructive comments in the previous round of review.\nWe are very pleased to see that we have successfully addressed your concerns.\nRegarding the last comment, as you suggested, we have checked and confirmed that this is\nindeed the cause. The relevant wording has been revised accordingly in the manuscript.\nReviewer #4 (Remarks to the Author):\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports. This\nis part of the Nature Communications initiative to facilitate training in peer review and to\nprovide appropriate recognition for Early Career Researchers who co-review manuscripts.\nReply: Thank you once again for participating in the review process for our manuscript and for\nsupporting this collaborative initiative to involve Early Career Researchers in peer review. We\ntruly appreciate your contributions to improving our work."}]

Decision letter