Chapter 5 An Introduction to Meteorology for Airborne … Library/Research/Wind Power... · An...

Chapter 5An Introduction to Meteorology for AirborneWind Energy

Cristina L. Archer

Abstract Airborne wind energy systems (AWES) are devices that effectively extractenergy from the air fl ow, more specifi cally kinetic energy, and convert it to electric-ity. Wind is the manifestation of the kinetic energy present in the atmosphere. Un-derstanding wind, its properties and power, as well as other atmospheric propertiesthat can affect AWES, is the goal of this chapter.

5.1 Power in the wind

Generally speaking, wind is simply air in movement. Wind is represented by a vec-tor because it has a magnitude, the wind speed, and a direction. Of the two, winddirection is relatively un-important for AWE resource assessments. Since any tur-bine is most effi cient when facing the wind perpendicularly, as the maximum airfl ux can go through a unit of rotor area, all turbines, whether conventional or air-borne, are designed to face the wind perpendicularly in real-time (e.g., via the yawmechanism in conventional wind turbines). As such, wind direction is not the focusof this chapter.

Wind speed, on the other hand, is extremely important because kinetic energyis a function of wind speed squared. This means that any change in wind speed,whether towards higher or lower values, will translate into amplifi ed changes inkinetic energy and therefore changes in the electricity generated. Let us explore thelinks between wind speed and wind power next.

If an air parcel of mass m (kg) is moving with velocity vw (a 3-dimensionalvector), then the wind speed is vw (m s−1) and the kinetic energy of the air parcel(kg m2 s−2 or J) is:

Cristina L. Archer ()College of Earth, Ocean, and Environment, University of Delaware, Newark, DE, USA, e-mail:[email protected]

81 81U. Ahrens et al. (eds.), Airborne Wind Energy, Green Energy and Technology,DOI: 10.1007/978-3-642-39965-7_ Springer-Verlag Berlin Heidelberg 20135,

82 Cristina L. Archer

KE =12

mv2w. (5.1)

Eq. (5.1) implies that, to calculate KE, it is necessary to calculate the mass m ofeach air parcel going through the area swept by the blades, a very unpractical task.Air density is a more useful property than mass in this case. Air density ρ (kg m−3)is the mass of air contained in a volume V. Consider a volume V given by the areaswept by the blades (A, m2) times the distance covered by the wind vw during thetime interval ∆ t:

V = vwA∆ t. (5.2)

The mass of air that went though the swept area A during the time interval ∆ t is:

m = ρvwA∆ t. (5.3)

Since kinetic energy per unit time is power, Eq. (5.1) can be divided by ∆ t afterreplacing m with Eq. (5.3) to obtain the power available in the wind P (J s−1 or W):

P =12

ρAv3w. (5.4)

Note that A is equal to πL2, where L is the blade length (m), and it is perpendicularto the wind vector vw by design. Measuring or calculating available power is mucheasier than calculating KE because air density is an intensive property, thus inde-pendent on the system size, whereas KE depends on mass, which is extensive. Also,ρ is easy to measure and it varies little horizontally and vertically near the rotor.

Not all the power available in the wind can actually be converted to electricity.The fraction of power that is extracted by the turbine rotor (PR) divided by the poweravailable in the wind (P) is the coefficient of performance CP, which is essentiallyan efficiency:

CP =PR

P=

PR12 ρAv3

w. (5.5)

Momentum theory shows that CP at most can reach a value of 16/27=0.593, knownas the “Betz limit” from the German aerodynamicist Albert Betz who first identifiedit [3]. No conventional wind turbine is capable of reaching the Betz limit; typicalCPs of conventional turbines are about half of the Betz limit, with a few multi-megawatt turbines reaching CPs of 0.45-0.5. The CP of AWES is currently unknown andeven the relevance of the Betz limit for AWES is questionable because the veryconcept of a disc-like swept area is not applicable.

As shown in Eq. (5.4), the power available in the wind P is a function of A,which depends on the turbine design and size. A more useful property is wind powerdensity δ (W m−2), defined as the wind power per unit area as follows:

δ =PA=

12

ρv3w. (5.6)

Wind power density δ is possibly the most useful wind property for conventionaland AWE applications because it truly accounts for the two most important vari-

5 Introduction to Meteorology 83

ables that directly affect wind power generation: wind speed and air density. Thedependence on wind speed is not linear but cubic, thus wind power is very sensitiveto wind speed. A consequence of this cubic relationship is that wind power can fluc-tuate more than wind speed. For example, if wind speed doubles, power in the winddoes not just double, but becomes 8 times higher; vice versa, if wind speed decreasesto a half, wind power decreases to 1/8. As such, errors in wind speed forecasting,even small, can cause large errors in wind power forecasting. The other variable thatdefines wind power density, air density ρ , impacts wind power linearly. Intuitively,as air density increases, more air molecules hit the turbine blades and transmit theirmomentum to the turbine, thus wind power increases proportionally. Let us explorehow wind speed, air density, and wind power density vary in the atmosphere.

5.2 The governing equations

A set of four equations describe the atmospheric dynamics and thermodynamics ofthe atmosphere and are needed to predict the vertical profiles of vw, ρ , and δ . Theseequations are: the continuity equation, the thermodynamic equation, the momentumequation, and the equation of state [4, 6, 8]. This system of four equations in fourunknowns (ρ , T, p, and vw) is non-linear, cannot be solved analytically, and requiresnumerical methods for its solution (except in a few highly simplified cases describedlater).

The continuity equation expresses the principle of conservation of mass for afluid, such as air, as follows:

1ρ

dρdt

=1ρ

∂ρ∂ t

+1ρ

vw ·∇ρ =−∇ ·vw =−(∂u∂x

+∂v∂y

+∂w∂ z

), (5.7)

where p is air pressure (hPa or mb), T is air temperature (K), and the wind vector isdecomposed into its three components:

vw = (u,v,w). (5.8)

The coordinate system is Cartesian orthogonal with x aligned along East-West, yalong North-South, and z along the vertical (plumb line). The term ∇ · vw is called“wind divergence”. Eq. (5.7) states that, if the wind divergence is positive, the righthand side becomes negative and therefore air density must decrease, whereas if winddivergence is negative (i.e., wind convergence), air density must increase. Eq. (5.7)also uses the relationship between total (or Lagrangian) derivative d

dt and partial (orEulerian) derivative ∂

∂ t given by:

ddt

=∂∂ t

+∇ ·vw. (5.9)


By definition, the density of an incompressible fluid does not change following themotion of the fluid parcel and the Lagrangian derivative on the left hand side ofEq. (5.7) is null. Thus the divergence term on the right hand side must be null too.Therefore all incompressible flows are also non-divergent. Water is always treatedas an incompressible fluid; air can be assumed to be incompressible in most at-mospheric applications. However, compressibility effects are not negligible whenabrupt changes in vertical velocity occur, such as over steep topography. For mostAWE applications, the incompressible assumption can be adopted.

The thermodynamic equation, or energy equation, represents the principle ofconservation of energy via the first law of thermodynamics:

cVdTdt

+ pdαdt

= JH , (5.10)

where cV is the specific heat at constant volume (717 J kg−1 K−1), α=ρ−1, and JH isthe rate of heating per unit mass due to radiation, conduction, and latent heat release(J kg−1 s−1). Although this equation does not contain the velocity vector explicitlyand therefore may appear to be valid only for a fluid in equilibrium, it is actuallyvalid also for a fluid in motion in this exact form [4]. It states that the change inan air parcel’s temperature is due to the rate of work by the pressure field and toexternal heat exchanges. Heat generated by frictional dissipation is not accountedfor here.

The equation of motion, or momentum equation, expresses the principle of con-servation of momentum via Newton’s second law of motion. Because it predictsthe rate of change of the wind vector prognostically, it is possibly the most usefulequation for AWE applications. For a rotating reference system, such as the Earth,and for a Cartesian coordinate system in x, y, and z, the equation of motion (ormomentum equation) is:

∂vw∂ t +(vw ·∇)vw = - 1

ρ ∇p Pressure Gradient−2Ω ×vw Coriolis-gk Gravity+ 1

ρ (∇ ·ρK∇)vw Turbulence Flux Divergence+ µ

ρ ∇2vw Viscous Diffusion

(5.11)

where Ω is the Earth’s angular velocity (Ω=7.292x10−5 s−1), k is the unit vector inthe z-direction, K is the eddy viscosity tensor (m2 s−1), and µ is dynamic viscosity(kg m−1 s−1). The left hand side of Eq. (5.11) is the sum of the local acceleration andthe advection of momentum by the velocity field itself. This form of the momentumequation was obtained after performing so-called “Reynolds averages” to isolateturbulent components.

The pressure gradient force (PGF) pushes an air parcel from high to low pressureareas. The PGF has a minus sign because it points towards the lowest values of pres-sure, whereas the gradient alone would point towards the highest values of pressure.On a 2D map of constant height above sea level, contours of constant pressure are


called isobars. The PGF is always perpendicular to the isobars and points towardslow pressure values.

The Coriolis force arises because the Earth is rotating around its axis and there-fore air parcels moving in the atmosphere experience an apparent acceleration tothe right in the northern hemisphere and to the left in the southern. The Coriolisforce is proportional to wind speed vw and it points 90 degrees to right of the winddirection in the northern hemisphere (to the left in the southern). It also depends onthe latitude of the air parcel: for large-scale, horizontal-only, upper-level flows, theCoriolis force is zero at the Equator and strongest at the Poles.

The gravity term includes the effect of the true gravitational force, which actstowards the center of the Earth, and the apparent centrifugal force, which pointsaway from the axis of rotation of the Earth. The resulting term acts therefore normalto the Earth’s surface (parallel and opposite to unit vector k) but not towards itscenter. Although its magnitude g varies slightly with latitude and longitude, it isgenerally assumed to be constant and equal to 9.81 m s−2.

The turbulence flux divergence term represents the effect of eddies, which arerotating air motions caused by wind shear or buoyancy at scales that cannot be re-solved explicitly in the numerical model. Turbulence is the combination of manyeddies of different sizes, smaller than the grid resolution, acting together in whatappears to be a random fashion. Because eddies interacting with one another ex-change momentum and heat among each other, they affect the momentum equation.The turbulence flux divergence term can be expressed in several forms dependingon which “parameterization”, or set of simplifying assumptions, is adopted. The for-mulation adopted here uses the 9-term tensor of eddy diffusion coefficients basedon the K-theory [6].

The viscous term represents molecular viscous processes. Viscosity is a fluidproperty that generally slows the fluid motion. When air molecules collide with oneanother, momentum is exchanged and generally little net energy dissipation occurs,except near the ground. Since the ground does not move, the air flow loses energywhen air molecules in motion hit the ground. The viscous term is generally smalland acts in such a way as to diffuse momentum from faster to slower air parcels.

These last two terms, the turbulence flux divergence and the viscous force, areimportant mainly in the boundary layer, which is the ∼500-m thick layer near theEarth’s surface where shear and buoyancy are strong and a net loss of energy to theground occurs. These two terms are negligible at the upper levels. The next sec-tion will focus on winds at the upper levels, broadly defined as those above ∼500m, where frictional and turbulent effects can be considered small enough to be ne-glected.

The equation of state links pressure, temperature, and air density of an ideal gas,such as air, as follows:

p = ρRT, (5.12)

where R is the gas constant for dry air (287.04 m2 s−2 K−1 or 0.287 m3 hPa kg−1

K−1).


With the exception of the equation of state (Eq. (5.12)), which is diagnostic,the other three equations that describe the state of the atmosphere are prognos-tic and contain partial derivatives in time and/or space. This four-equation sys-tem cannot be solved analytically. Numerical Weather Prediction (NWP) modelshave thus been developed, which usually discretize time and spatial derivatives withfinite-difference, spectral, finite-element, or semi-Lagrangian schemes of variousorders. Such models need initial conditions over the entire spatial domain at timet=0 as well as boundary conditions at all times t>0, for all variables. Once theseare provided, NWP models can provide forecasts of wind and other meteorologi-cal variables over the entire spatial domain at fixed forecast times. Details of theNWP models used in the US by the National Weather Service can be found athttp://www.nco.ncep.noaa.gov/pmb/products/.

5.3 Winds in the upper atmosphere

PGF and Coriolis are the dominant forces that govern the wind at high altitudes,away from the Earth’s surface. When the flow is in equilibrium (thus the left handside of Eq. (5.11) is null) at a given height above the boundary layer, PGF andCoriolis balance each other out and the flow is called “geostrophic”. In such flow,the other terms in Eq. (5.11) are negligible and the wind vector is perpendicular toboth PGF and Coriolis (with the Coriolis vector always to the right of the wind inthe northern hemisphere, and to the left in the southern).

The geostrophic wind vector vG is:

vG =1f ρ

k×∇h p, (5.13)

where f is the Coriolis parameter (s−1), equal to 2ω sinφ , φ is the latitude, and ∇his the horizontal gradient operator on a constant-height surface (thus any derivativewith respect to z is zero). Although the geostrophic flow is a simplification, thisassumption works well in the upper levels of the atmosphere, above the boundarylayer. At those levels, to a first approximation, wind speed and direction can bepredicted by Eq. (5.13) from the pressure distribution at each desired height abovethe ground. The geostrophic wind is relevant only for AWES that can fly near thetop or above the boundary layer.

Pressure is measured in the upper atmosphere with radiosondes mounted on bal-loons that are released into the atmosphere every 12 hours at 0 and 12 UTC si-multaneously at selected locations worldwide. These so-called soundings1 includemeasurements of wind speed, wind direction, temperature, and dew point tempera-ture at mandatory pressure levels2, such as 1000 mb, 850 mb, etc., as well as height

1 Examples of real-time and archived soundings can be found at http://www.esrl.noaa.gov/raobs/2 The definition of mandatory levels can be found in the online Glossary of Meteorology, availableat http://amsglossary.allenpress.com


above ground at which such measurements were taken. Therefore, measurement ofpressure at fixed heights above the ground are generally not available, but the heightsof fixed pressure surfaces are (Fig. 5.1). As such, it is common in meteorology touse pressure, rather than height above ground, as the vertical coordinate.

0

2

4

6

8

10

12

0 10 20 30 40 50 60 70 80

Hei

ght a

bove

gro

und

(km

)

Wind speed (m/s)

WIND SPEED PROFILE BEIJING (2009)

1000-mb level: 4.07 m/s at 102 m

925-mb level: 7.3 m/s at 735 m

850-mb level: 8.6 m/s at 1,432 m

AWES

Conventional

Fig. 5.1 Wind speed measurements (blue dots) by sounding balloons in Beijing (China) in 2009every 12 hours at specified pressure levels, such as 1000, 925, or 850 mb. The average wind speedand height of each pressure level is indicated by a cross mark. For example, the average heightof the 1000-mb pressure level was 102 m, which is the hub height of modern conventional windturbines, with an average wind speed of 4.07 m s−1, generally considered too low for conventionalwind. At 925 mb, the average height was 735 m, close to the target altitudes of several AWES, witha much higher average wind speed of 7.3 m s−1.

In pressure coordinate, the geostrophic wind is:

vG =− gf

k×∇ph, (5.14)

where h is the height of the pressure level under consideration (m) and ∇p is thehorizontal gradient operator on a constant-pressure surface (thus any derivative withrespect to pressure is null).

The pressure coordinate is common in meteorology and most variables predictedby numerical models are presented on constant-pressure surfaces at mandatory lev-els. Typical plots of the upper atmosphere show contours of the height of mandatorypressure levels above mean sea level. Examples of height distributions (and other


variables) on constant-pressure surfaces as predicted by NWP models can be foundat these links:

1. The GFS and RAP models at the National Center for Atmospheric Research,http://weather.rap.ucar.edu/model/;

2. The ECMWF model at Unisys, http://weather.unisys.com/ecmwf/;3. The Rapid Refresh (RAP) Model by the National Oceanic and Atmospheric Ad-

ministration, http://rapidrefresh.noaa.gov.

Where the isolines of constant height, or isopleths, are straight, the wind isgeostrophic. The geostrophic wind blows parallel to the isopleths with the lowerheights to its left in the northern hemisphere (and to its right in the southern). Know-ing the distance across two isopleths, it is possible to calculate the geostrophic windspeed using Eq. (5.14). When the isopleths are not straight but have a curvature, theupper-level flow is called gradient flow and Eq. (5.14) needs to be corrected to ac-count for centrifugal acceleration. The resulting gradient wind (equation not shown)still blows parallel to the curved isopleths with lower height values to its left in thenorthern hemisphere. Isopleths can also be closed around regions of localized low orhigh heights. The upper-level flow around a low is counterclockwise and it is clock-wise around a high in the northern hemisphere (vice versa in the southern). Notethat the actual wind at the upper levels is neither exactly geostrophic nor gradient,but the error is of the order of ∼10−1.

5.4 Winds near the Earth’s surface

Near the Earth’s surface, frictional and turbulent effects are important and cannot beneglected in the equation of motion (Eq. (5.11)). Thus, the wind cannot be treatedas either geostrophic or gradient in the boundary layer. In general, the combinedeffect of frictional and turbulent processes is such that the wind vector crosses -rather than being parallel to - the isobars (or isopleths on a constant-pressure map).Around a low-pressure center near the surface, the isobars are closed and the windvector turns counter-clockwise (in the northern hemisphere, clockwise in the south-ern) and points towards the center, where the pressure is lowest. Vice versa, arounda high-pressure center, the wind is clockwise (in the northern hemisphere, counter-clockwise in the southern) and points away from the center. Although an accurateprediction of wind at a given point near the surface requires solving all four equa-tions described in the previous section, some approximations have been developed,described next.

A vertical profile shows how an atmospheric variable, such as wind speed, varieswith height above the ground (z, in m). Although weather conditions affect verti-cal profiles of any variable at any place and time, this section will focus on typicalprofiles that are observed under average conditions near the Earth’s surface, startingwith air density. A common approximation for understanding how air density varieswith height is to use the so-called standard atmosphere, which is an idealized atmo-


sphere in hydrostatic balance and with a constant adiabatic temperature lapse rate[6]. In the standard atmosphere, air density decreases almost linearly with height(Fig. 5.2, blue line) as follows:

ρ(z) =p0

RT0

(T0−Γ z

T0

)( gΓ R−1)

, (5.15)

where p0 and T0 are pressure and temperature measured at the surface (1013.25 mbor hPa and 288.15 K respectively, in the standard atmosphere), g is gravity (9.81 ms−2), and Γ is the average lapse rate in the atmosphere (6.5 K km−1).

0

100

200

300

400

500

Typical vertical profiles in the boundary layer

Hei

ght a

bove

gro

und

(m)

Air density

AWES

Conventional wind

Wind speed

Wind powerdensity

x

x

x

x

1.18 1.2 1.22 Air density (kg m-3)

2 4 6 Wind speed (m s-1) 30 60 90 Wind power

density (W m-2)

Fig. 5.2 Vertical profiles of: air density (kg m−3, blue) in the standard atmosphere, wind speed (ms−1) derived using the power law (green solid) and the log law (green dashed), and wind powerdensity (W m−2) obtained with both wind speed laws (black lines). At the typical heights of con-ventional wind turbines (80 m), wind speed is 4.3 m s−1 (green cross) and wind power density is50 W m2 (black cross), whereas at the typical heights of AWES (400 m) wind power density isalmost double (93 W m−2, black cross).


For conventional and AWE systems, since wind power density is linearly propor-tional to air density (Eq. (5.6)), it may appear that low altitudes are more favorablethan high altitudes. However, this conclusion does not hold true once wind speed istaken into consideration.

Wind speed in general increases with height above the ground, although severalexceptions to this general behavior are found, such as turbulence fluctuations, low-level jets, or fronts. Two common equations are used to describe analytically thevariation of vw with z. The first one is the log-law:

vw(z) = vw(zREF)log(

zz0

)log(

zREFz0

) , (5.16)

and the second is the power law:

vw(z) = vw(zREF)

(z

zREF

)α, (5.17)

where zREF is a reference height at which a measurement of wind speed vw(zREF)is available, typically 10 m; z0 is surface roughness (m); and α is the friction coeffi-cient (unitless). Both z0 and α represent the effect of obstacles protruding from thesurface and are higher for taller obstacles. For example, z0 varies from 10−5 m oversmooth ice to 5 m over tall buildings in a city, with an average value of 0.1 m; overthe same surface types, α varies from 0.1 to 0.4, with an average value of 1

7 or 0.14[2]. Typical values of z0 and α are listed in Table 5.1 and 5.2. Note that all powerlaw profiles are zero at the surface, whereas log-law profiles are zero at z0.

Table 5.1 Roughness length z0 for various terrain types [10].

Terrain characteristics Roughness length z0 (m)Water surface 0.0002Open areas with a few windbreaks 0.03Farm land with some windbreaks more than 1 km apart 0.1Urban districts and farm land with many windbreaks 0.4Dense urban or forest 1.6

Whereas the log-law in Eq. (5.16) has a theoretical justification near walls underneutral conditions [2], the power law in Eq. (5.17) has been found to approximatewind profiles well empirically. Both equations, however, should not be used abovethe boundary layer, broadly defined here as the lowest layer in the atmosphere, typ-ically below 500 m, in which the frictional effects of the Earth’s surface are impor-tant.

Figure 5.2 (green solid and green dashed lines) shows two vertical profiles ofwind speed obtained for the same v(zREF ) of 3 m s−1 using z0=0.1 m and α=0.15


Table 5.2 Friction coefficient α for various terrain types [10].

Terrain characteristics Friction coefficient αSmooth hard ground, calm water 0.10Tall grass on level ground 0.15High crops, hedges and shrubs 0.20Wooded countryside, many trees 0.25Small town with trees and shrubs 0.30Large city with tall buildings 0.40

(corresponding to crop fields). Because wind speed increases with height in generaland wind power density is a cubic function of wind speed, it is apparent now whyhigher wind power densities are found at higher elevations (Fig. 5.2, black lines).

Measurements of wind speed and wind power density at altitudes of interest forAWES are almost never available, whereas measurements of wind speeds near thesurface, typically at zREF =10 m, are often available. If the flying altitudes are withinthe boundary layer (z<500 m), an estimate of wind speed vw at those altitudes canbe obtained from either Eq. (5.16) or Eq. (5.17) based on measurements of vw(zREF)and an estimate of wind power density δ from Eq. (5.6) after replacing ρ with Eq.(5.15) and vw with the value just calculated. For flying altitudes well above theboundary layer (z>1000 m), either balloon measurements from near-by soundingsor the output of NWP models can be used, as described in Sect. 5.3.

The region between 500 and 1000 m, of interest to AWE, is somewhat “transi-tional” between the near-surface regime, in which the log and power laws apply,and the free-atmosphere regime, where the geostrophic assumption can be made.To make matters worse, very few measurements are available in this transitionalregion, and almost none at the high temporal frequency needed for AWES. On av-erage, wind power density has modest increases with height between 500 and 2000m above ground [1], although exceptions are common, for example where low-leveljets form. Also, hourly, daily, and seasonal effects often cause the boundary layerheight and the vertical profile of δ to deviate from that generally uniform behavior.It is recommended that future funds be devoted to acquiring more measurements inthis transitional region, for example via Light Detection and Ranging (LIDAR) andradar- or sound-based wind profilers.

5.5 Global resource maps

Resource maps show relevant statistics (i.e., mean or selected percentiles) of atmo-spheric variables of interest, such as wind speed or wind power density. Such mapsare useful to identify locations that are particularly promising for AWE installationsand to quantify roughly the expected output at those locations over several years.Examples of the 50th, 68th, and 95th percentiles of wind power density for the entire


globe at heights of 500 m, 750 m, 1000 m, and 1500 m above ground are shown inFig. 5.5. These were obtained by Archer and Caldeira [1] using so-called “reanaly-ses” of wind speed, temperature, pressure, and specific humidity from 1979 to 2009.Reanalyses are a blend of gridded output from NWP models and actual observationsfrom routine meteorological networks, including soundings, satellite, surface, andship reports with a temporal frequency of 6-hours, from the National Centers forEnvironmental Prediction (NCEP) and the Department of Energy (DOE). These re-analyses have 192 x 94 grid points in the horizontal, with spacing of ∼ 1.9 degrees,and are among the most reliable source of gridded upper level winds available [7].

Figure 5.5 shows several of the advantages of AWE. The 80-m height can betaken as representative of conventional wind energy. Only a few locations over landexperience median wind power densities greater than 0.3 W m−2 at 80 m: the south-ern tip of Patagonia, Mongolia, and a few locations in Canada. However, areas withmedian wind power densities greater than 0.3 W m−2 expand as height increases andat 1500 m above ground half of the world can guarantee such wind power densitieshalf of the time or more. A proxy for wind power reliability is the 95th percentile ofwind power density. At 80 m, no location over land can guarantee any power 95% ofthe time, whereas at 750-1500 m above ground the northeast of South America andthe horn of Africa stand out as reliable wind power regions if AWES were imple-mented. Similar maps for all seasons and for additional vertical levels are availableat http://www.mdpi.com/1996-1073/2/2/307.

The resource maps suggest that AWE has the potential to supply a significant por-tion of humanity’s electricity needs. The AWE potential is large not only becauseof the high wind power densities, but also because regions with sufficient AWE re-sources are widespread at the global scale. Extracting even large amounts of kineticenergy from the atmosphere via AWES, on the order of half of our global electricityneeds, is not expected to cause significant climatic effects [1, 5, 9].


Fig. 5.3 Percentiles of global wind power density (W m−2) at selected heights above the groundof interest to AWE, reproduced with permission from Archer and Caldeira [1].


References

1. Archer, C. L., Caldeira, K.: Global Assessment of High-Altitude Wind Power. Energies 2(2),307–319 (2009). doi: 10.3390/en20200307

2. Arya, S. P.: Introduction to Micrometeorology. International Geophysics Series. AcademicPress, San Diego (1988)

3. Burton, T., Sharpe, D., Jenkins, N., Bossanyi, E.: Wind Energy Handbook. John Wiley & Sons,Ltd, Chichester (2001). doi: 10.1002/0470846062

4. Holton, J. R.: An Introduction to Dynamic Meteorology. 3rd ed. Academic Press, San Diego(1992)

5. Jacobson, M. Z., Archer, C. L.: Saturation wind power potential and its implications for windenergy. Proceedings of the National Academy of Sciences 109(39), 15679–15684 (2012). doi:10.1073/pnas.1208993109

6. Jacobson, M. Z.: Fundamentals of Atmospheric Modeling. 2nd ed. Cambridge UniversityPress, New York (2005)

7. Kistler, R., Kalnay, E., Collins, W., Saha, S., White, G., Woollen, J., Chelliah, M., Ebisuzaki,W., Kanamitsu, M., Kously, V., Van den Dool, H., Jenne, R., Fiorino, M.: The NCEP–NCAR50–Year Reanalysis: Monthly Means CD–ROM and Documentation. Bulletin of the AmericanMeteorological Society 82(2), 247–267 (2001). doi: 10 .1175/1520- 0477(2001)082〈0247:TNNYRM〉2.3.CO;2

8. Kundu, P. K., Cohen, I. M., Dowling, D. R.: Fluid Mechanics. Academic Press, San Diego(2012)

9. Marvel, K., Kravitz, B., Caldeira, K.: Geophysical limits to global wind power. Nature ClimateChange 2(9), 1–4 (2012). doi: 10.1038/nclimate1683

10. Masters, G. M.: Renewable and Efficient Electric Power Systems. Wiley-IEEE Press, NewYork (2005)

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