2.1 Overview

The goal of the KEBA model is to provide a simple and transparent yet physically based approach to estimate wind energy potentials for a given region across scales that can reproduce the wind speed reductions found in much more complex numerical simulation models. It uses an observed record of wind speeds, dimensions of the region, and turbine characteristics as well as the number of turbines as an input. It predicts the reduction in wind speeds as well as the generated yields as output. The simplicity of the approach allows for it to be implemented in a spreadsheet, which is provided in the Supplement.

KEBA derives an effective wind speed within a region of wind turbines from the different fluxes that add, remove, or dissipate kinetic energy within the associated atmospheric air volume that encloses the region (Fig. 1). For this, KEBA uses information of the unaffected wind speed, v_in, of the region in combination with a few meteorological parameters (the drag coefficient C_d and a typical boundary layer height H) as well as turbine characteristics (number of turbines, N, rated capacity, P_el,max, rotor-swept area, A_rotor, and power coefficient, η, as well as cut-in and cut-out velocities, v_min and v_max). The enclosing atmospheric volume is described by the dimensions of the cross section perpendicular to the wind direction (height H and width W) and the downwind depth L of the considered region. The variables are summarized in Table 1.

The effective wind speed v within the region is derived from the kinetic energy budget of the enclosing atmospheric volume. The influx of kinetic energy, J_in,h, through the upwind cross section (HW) and the vertical downward mixing J_in,v over the area (WL) of the region add kinetic energy (dark and light blue arrows in Fig. 1), while the electricity generation, or yield, of the wind turbines, P_el,tot (yellow arrow), the outflux of kinetic energy, J_out,h, downwind of the region (purple arrow), and dissipative losses by surface friction, D_fric (red arrow), and wake turbulence, D_wake (orange arrow), remove or dissipate kinetic energy. We neglect changes in kinetic energy within the region and dissipative losses by mixing taking place above the wind farms but inside the air volume. The balance of these fluxes is given by

Table 1Overview of KEBA variables and how these are specified or computed.

Download Print Version | Download XLSX

2.2 Energy fluxes

The total influx of kinetic energy, J_in,tot, is described in terms of the upwind wind speed v_in by the horizontal influx of kinetic energy by the wind through the cross-sectional area WH,

and by the vertical mixing due to surface friction over the surface area WL,

where C_d is the drag coefficient of the surface. The use of the surface drag coefficient is used here as an approximation.

The loss terms of kinetic energy are described with respect to an effective wind speed, v, within the region. For simplicity, we derive an effective velocity v that is representative of the mean generation of wind turbines, neglecting variations of wind speed within the region, particularly in the downwind direction.

For the electricity generation, or yield, P_el,tot, N wind turbines of the same characteristics are being considered, with each turbine having a rated capacity of P_el,max. The turbines have a rotor-swept cross-sectional area A_rotor and a power coefficient η. The yield, P_el,tot, is then described by

with ρ being the air density and v the effective wind speed. The minimum function is being used with the two arguments inside the parentheses to distinguish the case when the turbines operate below or at their capacity. In the case that the wind speed is below the cut-in velocity (v_in≤v_min) or above the cut-out velocity (v_in≥v_max), no generation is assumed ($P_{\mathrm{el},\mathrm{tot}}=\mathrm{0}$), resulting in no effect on the wind speed.

The outflux of kinetic energy, J_out,h, downwind of the region is described by

Dissipation by surface friction, D_fric, is described by a typical surface drag parameterization of the form

where C_d is the drag coefficient of the surface, which can be calculated for neutral conditions using the roughness length, z₀, of the surface by $C_{\mathrm{d}}={\mathit{\kappa }}^{\mathrm{2}}/{\ln }^{\mathrm{2}}(z/z_{\mathrm{0}})$, where κ≈0.4 is the von Kármán constant and z the reference height at which the wind speed is being measured.

Dissipation of kinetic energy by wake turbulence, D_wake, caused by the wind turbines is assumed to be half of the generated electricity:

This simple approximation is based on theoretical work by Corten (2001). Dissipative losses by the downward mixing of kinetic energy are neglected.

2.3 Estimation of wind speed and yields

The Eqs. (1)–(7) are combined to derive an expression for the effective wind speed, v:

where f_red is a reduction factor that depends on the characteristics of the enclosing air volume and the installed capacity of the region. In the case in which the turbines of the region operate below their rated capacity, this reduction factor is given by

where $n=(N-\mathrm{1})/\left(WL\right)$ is the turbine number density.

The yield of the wind farm, P_el,tot, is then given by

which is the same as Eq. (4), except for the use of f_red and v_in instead of v. In other words, the reduction in yield in this formulation is captured entirely by the factor f_red. A value of f_red=1 represents the case of an isolated wind turbine in which wind speeds are unaffected. The lower the value of f_red is, the greater the reduction in effective wind speed and in yield. The primary factor that results in a reduction is the number of turbines, N, combined with rotor cross-sectional area, A_rotor, as this reduces the value of f_red in Eq. (9).

In the case in which the wind farm operates at its rated capacity (v_in≥v_rated), the reduction factor takes a different form of

where the last fraction on the right-hand side is the ratio of total installed capacity in the region divided by the total horizontal influx of kinetic energy. The electricity generation simply takes the form of

2.4 Diagnostic energy fluxes

To link and visualize reductions in yield and wind speeds, it is instructive to explicitly look at the fluxes that shape the kinetic energy balance. The influxes of kinetic energy, J_in,h and J_in,v, are given by Eqs. (2) and (3), respectively. The yield of the wind turbines is given by the flux P_el,tot (Eqs. 10 or 12, depending whether v_in<v_rated or v_in≥v_rated), with dissipation D_wake by wake turbulence given by Eq. (7). The remaining two terms, dissipation by surface friction, D_fric, and the outflux of kinetic energy, J_out,h, can then be obtained from the energy balance, Eq. (1), and take the simplified forms of

and

These two equations are a reformulation of Eqs. (5) and (6). They simplify the calculation of the budget because these can be directly derived from the forcing, J_in,tot, and the rate of electricity generation, P_el, and no distinction needs to be made whether turbines operate below or at capacity as this is already accounted for in P_el,tot.

2.5 Model implementation

Equations (8)–(12) describe the KEBA approach. These equations describe the lower wind speed within the region (Eq. 8) as a function of the reduction factor f_red (given by either Eq. 9 or 11) and the meteorological forcing given by v_in. The generated yield within the region is then described by Eq. (10) or (12). Note that these expressions are very similar to well-established formulations, particularly regarding the yield. However, instead of a fixed reduction factor to account for wake effects in wind farms, the reduction factor in Eq. (10) is not a fixed value and it is also not empirically determined. Instead, the reduction factor depends explicitly on the size of the region (width W and downwind length L of the region) as well as on the number of wind turbines and their characteristics (rated capacity P_el,max, power coefficient η, number of turbines N, rotor-swept area A_rotor, cut-in and cut-out velocities) but also on meteorological characteristics (boundary layer height H, drag coefficient C_d). The KEBA approach is thus mostly based on the physical concept of a kinetic energy balance and it requires comparatively little empirical parameters to infer the magnitude of wind speed and yield reduction with certain installed capacities at the regional scale.

To estimate wind energy yields, KEBA needs meteorological input in form of wind speeds, v_in, the height of the boundary layer, H, and the drag coefficient, C_d, as well as a specification of the size of the wind farm region (specified in terms of W and L), the number of turbines, N, and their characteristics (power coefficient η, cut-in and cut-out velocities, and rotor-swept area A_rotor).

The implementation of KEBA as well as the evaluations shown in the following section is provided in the Supplement as an Excel spreadsheet.

3.1 Forcing and scenario setup

The wind speed histograms of the three regions considered are shown in Fig. 2a, with median wind speeds of 7.4, 9.1, and 13.1 m s⁻¹ for the three regions. The histograms are represented by Weibull distributions of the form

with values k=3.1 and λ=8.33 for region A, k=2.4 and λ=10.6 for region B, and k=3.1 and λ=14.7 for region C. These distributions were created to closely resemble those shown in Fig. 1 of Volker et al. (2017) and have the same medians. These velocities are taken here as being representative of hub-height wind speeds.

Each scenario considered a set of 2 MW Vestas V-80 turbines ($P_{\mathrm{el},\max }=\mathrm{2}$ MW), with a rotor diameter of D=80 m (yielding a rotor-swept area of A_rotor=5027 m²), a cut-in velocity of v_min=4 m s⁻¹, a cut-out velocity of v_max=25 m s⁻¹, and a power coefficient of η=0.44 when the turbines operate below their capacity. These turbine properties are typically provided by the manufacturer or can be obtained from other data providers such as http://www.thewindpower.net (last access: 20 March 2020) or http://www.wind-turbine-models.com (last access: 20 March 2020). The power curve of the turbine we use here is shown in Fig. 2c and was obtained by fitting the power coefficient η to the values provided at http://www.thewindpower.net (last access: 20 March 2020).

The scenarios consider four different sizes of wind farms arranged in a square, ranging from about 5 to 337 km, with three turbine spacings of 5.25D, 7D, and 10.5D, yielding a range of installed capacities in the scenarios from 72 MW to 1293 GW. We evaluated each scenario with KEBA and compare the resulting yields to the reported yields of the WRF simulations. The wind speed histograms shown in Fig. 2b are sufficient as inputs for v_in; that is, these histograms already encapsulate the climatological information of the wind speeds that are needed to evaluate KEBA. As the wind farms are arranged in a square configuration, we did not consider effects of wind direction. The height H is not derived from the WRF simulations of Volker et al. (2017), but we use typical heights for the boundary layer instead. We use a height of about 2000 m as being representative of region A (land) and 700 m for the marine setting of regions B and C (see, e.g. Seidel et al., 2010, von Engeln and Teixeira, 2013, and Peña et al., 2013 for observed climatological boundary layer heights). For the drag coefficient, we used a value of C_d≈0.001, which is representative of a relatively smooth surface with a low roughness (such as grassland or an ocean surface) and a reference height of about 100 m.

We compare the KEBA estimates also to an estimate in which no wind speed reductions are considered (“isolated” case), so that each turbine operates as if it were an isolated wind turbine. This case is represented in KEBA by a reduction factor of f_red=1.

Table 2Scenarios used to evaluate KEBA, as defined in Volker et al. (2017) for three regions (A, B, and C) and three turbine spacings: wide (10.5D), intermediate (7D), and narrow (5.25D). The yields are taken from Table 3 of Volker et al. (2017) and are shown in units of TWh a⁻¹ as well as W m⁻².

Download Print Version | Download XLSX

Table 3KEBA parameters used to evaluate the scenarios of Volker et al. (2017).

Download Print Version | Download XLSX

3.2 Comparison to Volker et al. (2017) simulations

The comparison of KEBA estimates to the estimates by Volker et al. (2017) is shown in Fig. 3 as well as in Table 4. Figure 3 compares yield estimates in absolute terms (Fig. 3a) and in terms of the relative reduction in yield (Fig. 3b) compared to the “isolated” case of what would be expected from turbines that do not experience loss effects due to reduced wind speeds. The comparison shows that KEBA estimates the annual yields very well. The more detailed comparison in terms of the relative yield reduction in Fig. 3b shows that KEBA seems to be better suited at estimating the effect for larger farms, where it shows closer agreement to the estimates of Volker et al. (2017), while for small wind farms, the yields show a bias towards lower reductions. Using the n=36 simulations as the sample size, a linear regression between KEBA estimates and Volker et al. (2017) yields a correlation of r²=0.822 and a slope near 1, reflecting the close agreement between the two methods.

Figure 3(a) Comparison of yields for the scenarios of Table 2 estimated by KEBA and as reported by Volker et al. (2017). The open circles represent wind energy estimates that do not take wind speed reductions into account (“isolated”, with f_red=1). (b) Relative yield reductions compared to the case of isolated turbines without the wind speed reduction effect. The dotted line reflects a linear regression between the two estimates, with the regression equation provided in the figure.

Download

Table 4Mean yields estimated for the case of isolated wind turbines (without wind speed reductions) and yield estimates with wind speed reductions by KEBA and by Volker et al. (2017) for three regions (A, B, and C). “CF” stands for capacity factor ($P_{\mathrm{el},\mathrm{tot}}/N{P}_{\mathrm{el},\max }$). The ranges for the “KEBA” and “Volker et al. (2017)” cases refer to the different sizes of the wind farms (small, medium, large, X-large), with lowest CFs and yields representing the estimates of the largest wind farms.

Download Print Version | Download XLSX

The key variable that describes the effect of the kinetic energy removal by the wind turbines is the reduction factor, f_red, which is given by Eq. (9) for conditions in which the wind turbines operate above the cut-in velocity but below their rated velocity. This reduction factor is shown in Fig. 4 for the different scenarios, together with the implied reduction in wind speeds (see Eq. 8) and yields (cf. Eq. 10). While this reduction factor does not describe all conditions (only those shaded in blue in Fig. 2), as it does not consider the velocities below the cut-in wind speed or the conditions in which the turbines operate at their rated capacity, it captures the reductions of the different scenarios very well, so that this factor can be used for the interpretation.

Figure 4 shows how the reduction in effective wind speed becomes greater the larger and denser the wind farm is. Mathematically, this can be seen in the expression for f_red (Eq. 9), which decreases with increasing downwind length L of the wind farm. The reduced wind speed is then associated with a reduction factor f_red that deviates more and more from the “isolated” case that is represented by f_red=1. Note that the actual yield is not always affected by the reduction in wind speed as there are some situations in which wind speeds are above the rated wind speed at which the turbines would operate at their capacity despite the reduction in wind speeds. This can be seen in the estimated yields for region C, which has a substantial fraction of wind speeds above the rated velocity (above the blue-shaded region in Fig. 2). Hence, the simulated yields for region C are typically less than what is described by this simplified interpretation of Eq. (9).

Figure 4The value of the reduction factor f_red for the case in which v<v_rated (Eq. 9) for the different scenarios as well as the implied relative reduction in wind speed, $f_{\mathrm{red}}^{\mathrm{1}/\mathrm{3}}-\mathrm{1}$, and the relative reduction of yield, f_red−1, derived directly from the value of f_red. The circles in the right panel refer to the actual estimates that include the information of the wind speed histograms (open circles: KEBA; full circles: Volker et al., 2017), with the colour coding as in Fig. 3.

Download

Figure 5Diagnosed terms of the kinetic energy budget, with the relative contributions to the influxes of kinetic energy (KE) shown in the left column and the conversion to electricity, dissipation, and outflux of kinetic energy shown in the three right columns (for three different turbine spacings: W: wide; I: intermediate; N: narrow). The horizontal and vertical contributions to the KE influx are shown by dark and light blue, respectively. The yield (conversion to electricity) is shown in yellow and the dissipation by surface friction (red) and wake turbulence (orange) and outflux of kinetic energy (purple). The plots show the KE budgets for the scenarios of wind farms of four different areas (S, M, L, and XL) for region A (central US, land, a) and for regions B and C (North Sea and Straight of Magellan, ocean, b). The colours of the bars match the arrows shown in Fig. 1.

Download

3.3 Kinetic energy balance diagnostics

Since KEBA is explicitly based on the budgeting of kinetic energy, we can further analyse these scenarios in terms of changes in the energy fluxes within this budget. These terms are approximated here using the mean kinetic energy fluxes (with the densities given by $(\mathit{\rho }/\mathrm{2})v_{\mathrm{in}}^{\mathrm{3}}$, region A: 313.6 W m⁻²; region B: 742.5 W m⁻²; region C: 1738.2 W m⁻²) into the regions. The resulting budgets are displayed in Fig. 5 and Table 5. The fluxes are grouped into two terms: the terms that gain kinetic energy by the influx of kinetic energy from upwind areas and from above, and the loss terms, the outflux of kinetic energy, the conversion of kinetic energy into electricity by the wind turbines, as well as the dissipation of kinetic energy within wakes and at the surface. The fluxes are shown in Fig. 5 as relative contributions to the total, so that they are normalized and comparable. The relative contributions depend only on the dimensions of the wind farm volume (H, L), as well as the drag coefficient (C_d) and turbine characteristics (N, η, A_rotor) but not on the wind climatology of the region. Hence, regions B and C show the same relative contributions and are combined.

Table 5Estimated kinetic energy influxes for the different scenarios and wind farm sizes in comparison to the estimated yields. The ranges for the “KEBA” and “Volker et al. (2017)” cases refer to the different turbine spacings (narrow, intermediate, wide) with lowest CFs and yields corresponding to the narrowest spacing and highest turbine densities.

Download Print Version | Download XLSX

The analysis of the kinetic energy budget illustrates how an increasing share of the kinetic energy influx is taken by the turbines and converted into electricity, resulting in less kinetic energy outflux and reduced wind speeds. For the scenarios of small wind farms, essentially all of the kinetic energy supply is provided by the horizontal influx, and the wind farm removes an insignificant fraction of it. The larger the wind farm region, the more the vertical influx of kinetic energy contributes to the supply of kinetic energy, and wind farms remove an increasingly significant fraction of this supply (yellow bars in Fig. 5). This results in less kinetic energy in the outflux (purple bars in Fig. 5), associated with the unavoidable reduction of wind speeds, which, in turn, is reflected in lower average yields by the turbines.

It is hence this constrained nature of the fluxes that feed the kinetic energy budget of the regional lower atmosphere that encloses the wind farm that results in the diagnosed magnitude of yield reductions. As the estimates by KEBA match those derived from much more complex model simulations by Volker et al. (2017) very well, it is very likely that the same interpretation holds for these simulations, and they are thus a realistic representation of the actual dynamics of large wind farms.

3.4 Sensitivity to boundary layer height H and drag coefficient C_d

We next evaluated the sensitivity of the KEBA estimates to the height of the boundary layer H and the drag coefficient C_d. Both of these meteorological parameters are quite uncertain, yet they determine how much kinetic energy enters the air volume budgeted by KEBA either in the horizontal or vertical direction. To quantify this sensitivity, we evaluated by how much the yield estimates changed when these two model parameters are varied by ±50 % and determined the linear regressions, as shown in Fig. 3b. The estimates changed systematically and yielded weaker (stronger) reductions with greater (smaller) values for H and C_d. The regression slopes reflected this change, with the slope being reduced to 0.91 and 0.96 when the values of H and C_d were increased, indicating that KEBA would underestimate the yield reduction compared to Volker et al. (2017). When the values for H and C_d decreased, the slope increased to 1.17 and 1.10, reflecting an overestimation of the yield reduction. Yet, the slope changed substantially less than the imposed change of 50 % to H and C_d, indicating that the KEBA estimates are relatively insensitive to these two parameters.

Figure 6KEBA sensitivity to downwind length L for region B (North Sea). The panels show (a) the KEBA reduction factor f_red as a function of downwind length for three turbine spacings, (b) the associated reduction in capacity factor ($P_{\mathrm{el}}/N{P}_{\mathrm{el},\max }$), and (c) the supply of kinetic energy by the horizontal influx from upwind areas (dark blue) and by vertical mixing (light blue) as well as the yields by the wind farms (lines). The circles represent the different sizes of wind farms considered in the comparison with Volker et al. (2017).

Download

3.5 Sensitivity to downwind length L

The sensitivity to downwind length L is more of scientific interest, as it does not reflect a model uncertainty because it is specified by the evaluated scenario. This sensitivity is of interest because it links the high yields and efficiencies of individual turbines and small wind farms to the low, large-scale wind energy potential of less than 1 W m⁻².

To evaluate this sensitivity, we use the meteorological forcing of region B (North Sea) and evaluate how the KEBA reduction factor, f_red, the capacity factor (i.e. the average yield of a turbine divided by its capacity, $P_{\mathrm{el}}/N{P}_{\mathrm{el},\max }$), as well as the kinetic energy influx per surface area of the wind farm change with L. This sensitivity is shown in Fig. 6 for the three installed capacity densities considered above. Note that a downwind length of L=0 represents the case of an isolated wind turbine. In this case, the reduction factor in KEBA is f_red=1. In the specified meteorological forcing, a wind turbine would achieve a capacity factor of 54.1 %, which would be provided solely from the horizontal influx of kinetic energy.

As L increases and the horizontal influx of kinetic energy gets depleted by the wind turbines, the reduction factor drops, and so does the capacity factor. The drop of the reduction factor is relatively fast, being reduced to a value of 0.5 within 260, 82, or 42 km for an installed capacity density of 2.8, 6.4, or 11.3 MW km⁻² for the cases of wide, intermediate, and narrow turbine spacings. This spatial scale is linked to the length scale, L_d, associated with an exponential decay of the horizontal kinetic energy input and is described by $L_{\mathrm{d}}=H/(\mathrm{2}{C}_{\mathrm{d}}+n\mathit{\eta }{A}_{\mathrm{rotor}})$.

For very long downwind lengths (L→∞), the yield per surface area in KEBA reaches a limiting value of $\left(n\mathit{\eta }{A}_{\mathrm{rotor}}\right)/(\mathrm{2}{C}_{\mathrm{d}}+\mathrm{3}/\mathrm{2}n\mathit{\eta }{A}_{\mathrm{rotor}})\cdot C_{\mathrm{d}}\mathit{\rho }{v}_{\mathrm{in}}^{\mathrm{3}}$, which is less than two-thirds of the natural frictional dissipation rate of the region. This limit is then again consistent with the global-scale energetics of the large-scale atmospheric circulation, which generates about 2 W m⁻² of kinetic energy and dissipates about 1 W m⁻² within the boundary layer. The North Sea region is windier than the global mean with a frictional dissipation of about 2 W m⁻², so that KEBA would yield a maximum generation of 1.33 W m⁻². The drop in yields of wind farms from small to very large scales thus reflects the transition from the dominant contribution by a high local horizontal kinetic energy flux to a low global generation and dissipation rate of kinetic energy.

3.6 Limitations

The KEBA approach is, clearly, extremely simple and neglects many complicating factors, such as the role of stability, different drag coefficients, variations in boundary layer height, or the wind direction. KEBA can nevertheless reproduce the wind energy yields and their reductions in large wind farms simulated by the much more complex WRF simulations of Volker et al. (2017). As we deal with climatological estimates, it would seem that the effects of stable and unstable conditions may average out. It therefore suggests that KEBA works well because the most relevant factor is the depletion of the horizontal flow of kinetic energy. This horizontal flow is prescribed by the wind conditions and is thus insensitive to stability and the value of the drag coefficient. Variations in boundary layer height, captured in our approach by the height H, play a more prominent role as these directly affect the total horizontal inflow of kinetic energy. Wind direction in our evaluations probably did not play a large role because we considered simple, artificial square layouts of wind farms. In future applications, it would be insightful and potentially necessary to evaluate the effects of these aspects on simulated wind speed reductions and yields. The estimate by KEBA could help to set a baseline for such evaluations.

Our KEBA approach also only crudely describes the wakes that develop directly behind wind turbines through the wake dissipation term, D_wake (Eq. 7) and does not resolve differences in yields within the same wind park. For these wake effects, approaches are already available to capture these (e.g. Frandsen et al., 2006; Barthelmie et al., 2010; Emeis, 2010). Future extensions could aim to combine such approaches to yield a model that cannot estimate only regional wind energy potentials but also variations within wind farms. On the other hand, it would seem that more complex numerical simulations of wind farm effects would benefit from an analysis of the kinetic energy budget.

In its present form, KEBA can adequately capture wind energy resource estimates at the regional scale and, as such, can inform the planning and policy development regarding the future expansions of wind energy. By being implemented in a spreadsheet, it can quickly estimate the yields of different scenarios in a transparent and reproducible way, given the prescribed wind conditions of the region. What are the likely cases where KEBA would provide useful insights? Current wind farms on land typically have installed capacity densities of less than 3 MW km⁻², covering less than 500 km² (e.g. using data from the US; see Miller and Keith, 2018). These settings are similar to the “small” and “medium” wind farm sizes using a “wide” spacing (cf. Table 2), for which the wind speed reduction effects should be comparatively small, if wind farms are separated sufficiently well to be considered as isolated farms. For these settings, KEBA would not add novel insights because regional wind speed reductions would not necessarily need to be taken into account. The effects become more relevant at larger scales (cf. Fig. 6 and length scale L_d described above) or when larger capacity densities are being considered. This is, for instance, the case when German wind energy scenarios for offshore wind energy in the North Sea are being evaluated, where the KEBA model was used (Agora Energiewende et al., 2020). In these scenarios, installed capacity densities in the range of 5 to 20 MW km⁻² were considered to be installed over an area of 2800 to 7200 km², which falls between the “medium” and “large” areas considered here, with “intermediate”, “narrow”, and even denser spacings. For these settings, KEBA estimates considerable reductions in yield that are consistent with WRF-based estimates (Agora Energiewende et al., 2020). When wind resource potentials are evaluated for whole continents, as it was done recently for Europe by Enevoldsen et al. (2019), who considered 10 MW km⁻² being installed over 45 % of Europe, such reduction effects would clearly matter, would need to be accounted for, and would reduce the resource potential rather substantially. It would thus seem that KEBA can provide useful estimates particularly for large-scale resource assessments and scenarios for the future expansion of wind energy.