Editing Planetary boundary layer (section)

==Cause of surface wind gradient==
[[File:Light pollution and the planetary boundary layer over Berlin.jpg|thumb|The difference in the amount of aerosols below and above the boundary layer is easy to see in this aerial photograph. Light pollution from the city of Berlin is strongly scattered below the layer, but above the layer it mostly propagates out into space.]]

{{see also|Wind shear|Wind gradient|Wind engineering|Ekman layer}}
Typically, due to [[aerodynamic]] [[drag (force)|drag]], there is a wind gradient in the wind flow ~100 meters above the Earth's surface—the [[surface layer]] of the planetary boundary layer. Wind speed increases with increasing height above the ground, starting from zero<ref name=Wizelius>{{cite book | last = Wizelius | first = Tore | title = Developing Wind Power Projects | url = https://archive.org/details/developingwindpo0000wize | url-access = registration | publisher = Earthscan Publications Ltd. | location = London | year = 2007 | isbn = 978-1-84407-262-0 | quote = The relation between wind speed and height is called the wind profile or wind gradient. | page = [https://archive.org/details/developingwindpo0000wize/page/40 40]}}</ref> due to the [[no-slip condition]].<ref name=Brown>{{cite book | last = Brown | first = G. Z. |author2=DeKay, Mark |title = Sun, Wind & Light | publisher = Wiley | location = New York | year = 2001 | isbn = 0-471-34877-5 | page = 18 }}</ref> Flow near the surface encounters obstacles that reduce the wind speed, and introduce random vertical and horizontal velocity components at right angles to the main direction of flow.<ref>{{cite journal
 |title         = CBD-28. Wind on Buildings
 |author1       = Dalgliesh, W. A.
 |author2       = D. W. Boyd
 |name-list-style = amp
 |journal       = Canadian Building Digest
 |url           = http://irc.nrc-cnrc.gc.ca/pubs/cbd/cbd028_e.html
 |date          = 1962-04-01
 |quote         = Flow near the surface encounters small obstacles that change the wind speed and introduce random vertical and horizontal velocity components at right angles to the main direction of flow.
 |access-date   = 2007-06-30
 |archive-url   = https://web.archive.org/web/20071112203930/http://irc.nrc-cnrc.gc.ca/pubs/cbd/cbd028_e.html
 |archive-date  = 2007-11-12
 |url-status    = dead
}}</ref>
This [[turbulence]] causes vertical [[Mixing (physics)|mixing]] between the air moving horizontally at one level and the air at those levels immediately above and below it, which is important in dispersion of [[pollutants]]<ref name=Hadlock>{{cite book | last = Hadlock | first = Charles |author-link=Charles Robert Hadlock |title = Mathematical Modeling in the Environment | url = https://archive.org/details/supplementarymat0000hadl | url-access = registration | publisher = Mathematical Association of America | location = Washington | year = 1998 | isbn = 0-88385-709-X }}</ref> and in [[soil erosion]].<ref name=Lal/>

The reduction in velocity near the surface is a function of surface roughness, so wind velocity profiles are quite different for different terrain types.<ref name=Brown/> Rough, irregular ground, and man-made obstructions on the ground can reduce the [[geostrophic wind]] speed by 40% to 50%.<ref name=Oke>{{cite book | last = Oke | first = Timothy R. | title = Boundary Layer Climates | publisher = Methuen | location = London | year = 1987 | isbn = 0-415-04319-0 | quote = Therefore the vertical gradient of mean wind speed (dū/dz) is greatest over smooth terrain, and least over rough surfaces. |page = 54}}</ref><ref name=Crawley>{{cite book | last = Crawley | first = Stanley | title = Steel Buildings | publisher = Wiley | location = New York | year = 1993 | isbn = 0-471-84298-2 | page = 272 }}</ref> Over open water or ice, the reduction may be only 20% to 30%.<ref>{{cite book | last = Harrison | first = Roy | title = Understanding Our Environment | url = https://archive.org/details/understandingour00harr_090 | url-access = limited | publisher = Royal Society of Chemistry | location = Cambridge | year = 1999 | isbn = 0-85404-584-8 | page = [https://archive.org/details/understandingour00harr_090/page/n25 11]}}</ref><ref name=Russell>{{cite book | last = Thompson | first = Russell | title = Atmospheric Processes and Systems | url = https://archive.org/details/atmosphericproce00thom | url-access = limited | publisher = Routledge | location = New York | year = 1998 | isbn = 0-415-17145-8 | pages = [https://archive.org/details/atmosphericproce00thom/page/n124 102]–103 }}</ref>  These effects are taken into account when siting [[wind turbine]]s.<ref>Maeda, Takao, Shuichiro Homma, and Yoshiki Ito. [http://www.ingentaconnect.com/content/mscp/wind/2004/00000028/00000006/art00004 Effect of Complex Terrain on Vertical Wind Profile Measured by SODAR Technique.] Retrieved on 2008-07-04.</ref><ref name=Lubosny>{{cite book | last = Lubosny | first = Zbigniew | title = Wind Turbine Operation in Electric Power Systems: Advanced Modeling | publisher = Springer | location = Berlin | year = 2003 | isbn = 3-540-40340-X | page = 17}}</ref>

For [[engineering]] purposes, the wind gradient is modeled as a [[simple shear]] exhibiting a vertical velocity profile varying according to a [[power law]] with a constant [[exponent]]ial coefficient based on surface type. The height above ground where surface friction has a negligible effect on wind speed is called the "gradient height" and the wind speed above this height is assumed to be a constant called the "gradient wind speed".<ref name=Crawley/><ref name=Gupta>{{cite book | last = Gupta | first = Ajaya | title = Guidelines for Design of Low-Rise Buildings Subjected to Lateral Forces | publisher = CRC Press | location = Boca Raton | year = 1993 | isbn = 0-8493-8969-0 | page = 49}}</ref><ref>{{cite book | last = Stoltman | first = Joseph | title = International Perspectives on Natural Disasters: Occurrence, Mitigation, and Consequences | publisher = Springer | location = Berlin | year = 2005 | isbn = 1-4020-2850-4 | page = 73 }}</ref> For example, typical values for the predicted gradient height are 457 m for large cities, 366 m for suburbs, 274 m for open terrain, and 213 m for open sea.<ref>{{cite book | last = Chen | first = Wai-Fah | title = Handbook of Structural Engineering | url = https://archive.org/details/handbookstructur00chen | url-access = limited | publisher = CRC Press | location = Boca Raton | year = 1997 | isbn = 0-8493-2674-5 | pages = [https://archive.org/details/handbookstructur00chen/page/n30 12]–50}}</ref>

Although the power law exponent approximation is convenient, it has no theoretical basis.<ref>{{cite book | last = Ghosal | first = M. | title = Renewable Energy Resources | chapter = 7.8.5 Vertical Wind Speed Gradient | publisher = Alpha Science International, Ltd. | location = City | year = 2005 | isbn = 978-1-84265-125-4 | pages = 378–379}}</ref> When the temperature profile is adiabatic, the wind speed should vary [[logarithm]]ically with height.<ref>{{cite book | last = Stull | first = Roland | title = An Introduction to Boundary Layer Meteorology | publisher = Kluwer Academic Publishers | location = Boston | year = 1997 | isbn = 90-277-2768-6 | quote = ...both the wind gradient and the mean wind profile itself can usually be described diagnostically by the log wind profile. | page = 442}}</ref> Measurements over open terrain in 1961 showed good agreement with the [[log wind profile|logarithmic fit]] up to 100 m or so (within the [[surface layer]]), with near constant average wind speed up through 1000 m.<ref name=Thuillier>{{cite journal
 | author = Thuillier, R.H.
 | author2 = Lappe, U.O.
 | year = 1964
 | title = Wind and Temperature Profile Characteristics from Observations on a 1400 ft Tower
 | journal = [[Journal of Applied Meteorology]]
 | publisher= [[American Meteorological Society]]
 | volume = 3
 | issue = 3
 | pages = 299–306
 | doi = 10.1175/1520-0450(1964)003<0299:WATPCF>2.0.CO;2
 | issn = 1520-0450
 | bibcode=1964JApMe...3..299T
 | doi-access = free
 }}</ref>

The [[shearing (physics)|shearing]] of the wind is usually three-dimensional,<ref>{{cite book | last = McIlveen | first = J. F. Robin | title = Fundamentals of Weather and Climate | publisher = Chapman & Hall | location = London | year = 1992 | isbn = 0-412-41160-1 | page = [https://archive.org/details/fundamentalsofwe0000mcil/page/184 184] | url = https://archive.org/details/fundamentalsofwe0000mcil/page/184 }}</ref> that is, there is also a change in direction between the 'free' pressure gradient-driven geostrophic wind and the wind close to the ground.<ref>{{cite book | last = Burton | first = Tony | title = Wind Energy Handbook | url = https://archive.org/details/handbookwindener00burt | url-access = limited | publisher = J. Wiley | location = London | year = 2001 | isbn = 0-471-48997-2 | page = [https://archive.org/details/handbookwindener00burt/page/n45 20] }}</ref> This is related to the [[Ekman spiral]] effect. 
The cross-isobar angle of the diverted ageostrophic flow near the surface ranges from 10° over open water, to 30° over rough hilly terrain, and can increase to 40°-50° over land at night when the wind speed is very low.<ref name=Russell/>

After sundown the wind gradient near the surface increases, with the increasing stability.<ref name="Köpp">{{cite journal
 | author = Köpp, F.
 | author2 = Schwiesow, R.L.
 | author3 = Werner, C.
 |date=January 1984
 | title = Remote Measurements of Boundary-Layer Wind Profiles Using a CW Doppler Lidar
 | journal = [[Journal of Applied Meteorology and Climatology]]
 | publisher = [[American Meteorological Society]]
 | volume = 23
 | issue = 1
 | pages = 153
 | doi = 10.1175/1520-0450(1984)023<0148:RMOBLW>2.0.CO;2
 | issn = 1520-0450
 | bibcode=1984JApMe..23..148K
 | doi-access = free
 }}</ref>
[[Atmospheric instability|Atmospheric stability]] occurring at night with [[radiative cooling]] tends to vertically constrain turbulent [[Eddy (fluid dynamics)|eddies]], thus increasing the wind gradient.<ref name=Lal>{{cite book | last = Lal | first = Rattan |author-link=Rattan Lal |title = Encyclopedia of Soil Science | publisher = Marcel Dekker | location = New York | year = 2005 | isbn = 0-8493-5053-0 | page= 618}}</ref> The magnitude of the wind gradient is largely influenced by the [[weather]], principally atmospheric stability and the height of any convective boundary layer or [[capping inversion]]. This effect is even larger over the sea, where there is much less diurnal variation of the height of the boundary layer than over land.<ref name=Johansson2002>{{cite conference
 | author = Johansson, C. |author2=Uppsala, S. |author3=Smedman, A.S.
 | year = 2002
 | title = Does the height of the boundary layer influence the turbulence structure near the surface over the Baltic Sea?
 | book-title = 15th Conference on Boundary Layer and Turbulence
 | publisher = [[American Meteorological Society]]
 | url = http://ams.confex.com/ams/BLT/techprogram/paper_43332.htm
 | conference-url = http://ams.confex.com/ams/BLT/techprogram/program_117.htm
 | conference=15th Conference on Boundary Layer and Turbulence
 }}</ref>
In the convective boundary layer, strong mixing diminishes vertical wind gradient.<ref>{{cite book | last = Shao | first = Yaping | title = Physics and Modelling of Wind Erosion | publisher = Kluwer Academic | location = City | year = 2000 | isbn = 978-0-7923-6657-7 |page = 69 | quote = In the bulk of the convective boundary layer, strong mixing diminishes vertical wind gradient...}}</ref>