UBC Faculty Research and Publications

MITACS Project Technical Report : Atmospheric stability and wind profiles at a prospective wind energy… Crawford, Ben; Matangi, Adrian; Griffiths, James; Christen, Andreas; Black, Andrew T. Mar 11, 2015

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	  	  	  	   MITACS	  Project	  Technical	  Report:	  	  Atmospheric	  stability	  and	  wind	  profiles	  at	  a	  prospective	  wind	  energy	  production	  site	  	  	  	  Ben	  Crawford1,2,	  Adrian	  Matangi2,	  James	  Griffiths2,	  Andreas	  Christen1,	  Andy	  Black3	  	  1	  University	  of	  British	  Columbia,	  Department	  of	  Geography	  2	  Sea	  Breeze	  Power	  Corp.	  3	  University	  of	  British	  Columbia,	  Faculty	  of	  Land	  and	  Food	  Systems	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	   	  	   2	  	  	  	  	  	  Abstract	  	  Atmospheric	   stability	   influences	   turbulence	   and	  wind	   speeds	   at	  wind	   turbine	  hub	  heights,	   yet	   it	   is	   seldom	   measured	   or	   explicitly	   considered	   during	   wind	   energy	  resource	   assessment.	   In	   this	   study,	   twelve	   months	   of	   data	   from	   a	   3-­‐d	   sonic	  anemometer	  mounted	  at	  58	  m	  on	  a	  60	  m	  wind	  resource	  assessment	  tower	  are	  used	  to	  characterize	  atmospheric	  stability	  at	  a	  prospective	  wind	  energy	  production	  site.	  	  	  At	   this	   site,	   three	   distinct	   stability	   classes	   (unstable,	   neutral,	   and	   stable)	   are	  identified	  that	  follow	  diurnal	  and	  seasonal	  distributions.	  	  These	  stability	  classes	  are	  distinguished	   by	   unique	   wind	   speed	   distributions,	   vertical	   wind	   speed	   shear	  profiles,	  and	  turbulence	  characteristics.	  A	  comparison	  is	  performed	  to	  test	  whether	  including	   stability	   parameters	   from	   the	   sonic	   anemometer	   improves	   modeled	  predictions	   of	   vertical	   wind	   speed	   profiles.	   Results	   show	   that	   including	   stability	  does	  not	  improve	  results	  at	  this	  site,	  likely	  because	  specific	  assumptions	  underlying	  wind	  profile	  models	  are	  not	  met.	  	  	  Recommendations	   from	  this	  work	  are:	  1)	   future	  wind	  resource	  assessment	  should	  include	   analysis	   of	   stability,	   2)	   bulk	   stability	   can	   be	   classified	   using	   measured	  vertical	   temperature	   gradient	   or	   the	   wind	   shear	   exponent,	   and	   3)	   future	   wind	  resource	   assessment	   should	   include	   at	   least	   two	   temperature	   measurements	   at	  different	   heights.	   Finally,	   as	   turbines	   grow	   in	   height	   and	   are	   placed	   in	   complex	  terrain,	  we	  are	  approaching	  the	  limits	  of	  tower-­‐based	  measurements	  and	  traditional	  shear	  models	  to	  accurately	  model	  conditions	  across	  the	  turbine	  rotor	  plane.	  	  Future	  wind	  resource	  assessments	  are	  recommended	  to	  also	  include	  remotely	  sensed	  wind	  measurements	  (e.g.	  Lidar	  or	  Sodar)	  and	  high-­‐resolution	  non-­‐linear	  models.	  	  	  	  	  	  	  	  	  	  	  	  	  	  	   	  	   3	  Table	  of	  Contents	  	   	   	   	   	   	   	   	   	   Page	  	  1.	  Introduction	   4	  2.	  Methods	   4	  2.1	  Site	  Description	   4	  2.2	  Meteorological	  Instrumentation	   5	  2.3	  Cup	  anemometer	  and	  vane	  quality	  control	   6	  2.4	  Sonic	  anemometer	  quality	  control	  and	  data	  processing	   6	  2.5	  Stability	  parameter	   8	  2.6	  Vertical	  wind	  profile	  calculations	   8	  3.	  Results	  and	  Discussion	   11	  3.1	  Stability	  characteristics	   11	  3.2	  Which	  method	  best	  predicts	  measured	  59	  m	  wind	  speeds?	   18	  3.3	  Effect	  of	  stability	  on	  vertical	  wind	  profiles	   19	  4.	  Conclusions	   21	  5.	  References	   23	  	  List	  of	  Figures	  	   	   	   	   	   	   	   	   	   Page	  	  1.	  Tower	  location	  map.	   5	  2.	  Tower	  instrumentation	  schematic.	   7	  3.	  Hourly	  ensemble	  means	  of	  stability	  and	  sensible	  heat	  flux	  by	  season.	   12	  4.	  Seasonal	  distribution	  of	  stability.	   13	  5.	  Distribution	  of	  stability	  by	  wind	  direction.	   14	  6.	  Wind	  speed	  distribution	  by	  stability.	   15	  7.	  Stability	  and	  turbulence	  intensity.	   16	  8.	  Stability,	  shear	  exponent,	  and	  air	  temperature	  gradient.	   17	  9.	  Vertical	  wind	  profile	  by	  stability.	   20	  	  List	  of	  Tables	   	   	   	   	   	   	   	   	   Page	  	  1.	  Wind	  profile	  models	  used	  in	  this	  study.	   10	  2.	  Seasonal	  frequency	  of	  stability.	   13	  3.	  Mean	  atmospheric	  characteristics	  by	  stability.	   15	  4.	  Wind	  profile	  model	  results	  comparison.	   18	  5.	  Roughness	  length	  and	  friction	  velocity	  differences.	   19	  6.	  Rotor	  equivalent	  wind	  speed.	   21	  	  	  	  	  	  	  	  	  	  	   4	  1.Introduction	  	  Installed	  wind	  energy	  capacity	  in	  Canada	  has	  grown	  by	  more	  than	  20%	  annually	  in	  recent	  years	  and	  is	  forecast	  to	  supply	  20%	  of	  Canada’s	  electricity	  by	  2025	  (CANWEA	  2013).	   Accurate	  wind	   resource	   assessment	   at	   potential	   energy	  production	   sites	   is	  essential	  for	  future	  wind	  energy	  development.	  In	  particular,	  atmospheric	  stability	  is	  important	   to	   consider	   because	   of	   its	   role	   in	   modifying	   mean	   wind	   speeds,	   wind	  speed	  and	  directional	  shear,	   turbulence,	  and	  turbine	  wake	  dissipation.	  Research	  at	  operational	  wind	  parks	  has	  shown	  that	  changes	  in	  stability	  can	  lead	  to	  power	  output	  differences	  of	  up	  to	  15%	  (Wharton	  and	  Lundquist,	  2011).	  However,	  stability	  is	  not	  normally	   considered	   during	   wind	   resource	   assessment	   due	   to	   a	   lack	   of	  instrumentation	   to	   measure	   surface	   heat	   and	   momentum	   exchanges	   (Probst	   and	  Cardenas,	  2010).	  	  The	  objective	  of	  this	  report	  is	  to	  describe	  diurnal	  and	  seasonal	  patterns	  of	  stability	  at	   a	   prospective	   wind	   energy	   production	   site	   in	   a	   mountainous	   area	   of	   British	  Columbia.	   This	   is	   accomplished	   through	   analysis	   of	   data	  measured	   by	   a	   3-­‐d	   sonic	  anemometer	  mounted	  on	  a	  60	  m	  meteorological	   tower.	  The	   impact	  of	   stability	  on	  vertical	   wind	   speed	   profile	   calculations	   is	   then	   assessed	   by	   directly	   comparing	  results	   from	  6	  methods	   to	   extrapolate	  wind	   speeds	   against	  measurements	   from	  a	  wind	  speed	  profile.	  	  	  2.	  Methods	  	  2.1	  Site	  description	  	  The	  study	  site	  is	  located	  in	  a	  mountainous	  region	  in	  the	  interior	  of	  British	  Columbia,	  Canada.	   The	   exact	   location	   is	   withheld	   from	   this	   report	   due	   to	   the	   ongoing	  wind	  energy	  business	  development	  process.	  A	  60	  m	  meteorological	   tower	   is	   located	  on	  top	  of	  a	  ~500	  x	  800	  m	  rise	  (tower	  base	  elevation	  =	  1705	  m	  a.s.l.)	  that	  rises	  ~80	  m	  above	   the	   surrounding	   landscape	   (Figure	   1).	   	   Within	   100	   m	   of	   the	   tower	   base,	  terrain	  is	  generally	   level	  and	  landcover	  is	  primarily	  re-­‐planted	  vegetation	  (<	  1.0	  m	  height)	  with	   interspersed	  standings	  of	  coniferous	  trees	  up	  to	  3	  m	  height.	  Within	  1	  km	  of	   the	   tower,	   landcover	   is	   composed	  of	   clear-­‐cut	   and	   secondary	   growth	   forest	  with	  tree	  heights	  up	  to	  25	  m.	  Terrain	  within	  1	  km	  of	  the	  tower	  ranges	  from	  1610	  m	  a.s.l.	  to	  1720	  m	  a.s.l.	  and	  generally	  slopes	  downward	  to	  the	  NW.	  	  For	  this	  study,	  12	  months	  of	  data	  (December	  2013	  –	  November	  2014)	  are	  used	  for	  analysis.	  The	  area	  was	  covered	  in	  snow	  from	  December	  2013	  –	  mid-­‐April	  2014.	  	   5	  	  Figure	   1.	   Map	   of	   meteorological	   tower	   location.	   Vegetation	   heights	   and	   30	   m	  elevation	   contours	   are	   from	   DataBC	   VRI	   dataset	   (DataBC,	   2014).	   Elevation	   data	  within	  the	  licence	  polygon	  are	  from	  a	  ground	  LiDAR	  dataset	  at	  10	  m	  resolution.	  	  	  	  2.2	  Meteorological	  instrumentation	  	  Wind	  instrumentation	  on	  the	  meteorological	  tower	  consists	  of:	  4	  cup	  anemometers	  (Class	  1,	  Renewable	  NRG	  Systems,	  Vermont,	  USA),	  2	  NRG	  40C	  cup	  anemometers,	  1	  NRG	  heated	  cup	  anemometer,	  1	  model	  NRG	  heated	  vane,	  2	  NRG	  200P	  wind	  vanes,	  1	  heated	  NRG	  wind	  vane,	  and	  1	  3-­‐d	  sonic	  anemometer	  (81000,	  RM	  Young,	  Michigan,	  USA)	  (Figure	  2).	  There	  are	  also	  shielded,	  aspirated	   thermocouple	  (T-­‐type)	  sensors	  at	  three	  heights	  (58	  m,	  33	  m,	  2	  m)	  to	  measure	  air	  temperature.	   	  All	  sensors	  except	  the	   sonic	   anemometer	   sample	   at	   1	   s	   frequency	   and	  dataloggers	   record	  10	  minute	  averaged	   data	   and	   statistics	   (maximum,	  minimum,	   standard	   deviation).	   The	   sonic	  anemometer	   samples	   instantaneous	   3-­‐dimensional	   wind	   velocities	   (u,	   v,	   w)	   and	  virtual	  acoustic	  temperature	  (T)	  at	  10	  Hz	  resolution.	  	  	  	  	  	  	  	   6	  	  	  2.3	  Cup	  anemometer	  and	  vane	  quality	  control	  	  	  Before	   analysis,	   all	   meteorological	   data	   are	   subject	   to	   a	   series	   of	   quality	   control	  filters	   to	   screen	   faulty	   or	   low-­‐quality	   data.	   All	   quality	   control	   procedures	   for	   cup	  anemometers	   and	   vanes	   were	   performed	   using	   industry	   standard	   wind	   analysis	  software	   (Windographer	   Professional	   Edition,	   Version	   3.3,	   Mistaya	   Engineering	  Inc.).	  	  Individual	  datapoints	  are	  flagged	  and	  withheld	  from	  further	  analysis	  if:	  	  i) The	  10-­‐minute	  average	  wind	  speed	  or	  direction	  values	  fall	  outside	  physically	  plausible	  maximum/minimum	  thresholds.	  ii) There	  is	  evidence	  of	  sensor	  icing.	  This	  flag	  is	  triggered	  if	  10-­‐minute	  standard	  deviation	  is	  equal	  to	  0	  m	  s-­‐1	  and	  air	  temperature	  is	  below	  0°	  C.	  iii) The	   10-­‐minute	   wind	   speed	   averages	   are	   influenced	   by	   tower	  distortion.	  Tower	  distortion	  is	  determined	  by	  analysis	  of	  the	  ratio	  of	   10-­‐minute	   averages	   from	   sensors	   co-­‐located	   at	   the	   same	  measurement	  height.	  	  2.4 Sonic	  anemometer	  quality	  control	  and	  data	  processing	  	  Three-­‐dimensional	  wind	  velocities	  (u,	  v,	  w)	  and	  virtual	  acoustic	  air	  temperature	  (T)	  from	   the	   RMY	   sonic	   anemometer	   mounted	   at	   58	   m	   a.g.l.	   are	   recorded	   at	   10	   Hz.	  Individual	   datapoints	   are	   passed	   through	   several	   quality	   control	   filters	   (spike	  detection,	   physically	   plausible	   maximum/minimum	   thresholds)	   and	   are	   withheld	  from	  further	  analysis	  when	  flagged.	  The	  10	  Hz	  data	  are	  then	  block-­‐averaged	  into	  30-­‐min	  periods	  and	  a	  2-­‐d	  coordinate	  rotation	  is	  performed	  to	  orient	  measurements	  into	  a	  streamline	  coordinate	  system	  aligned	  with	  the	  mean	  wind	  direction.	  The	  30-­‐min	  averages	   are	   withheld	   from	   analysis	   when	   wind	   directions	   are	   from	   behind	   the	  meteorological	  tower	  (105	  –	  120°)	  and	  wind	  vectors	  may	  be	  distorted.	  	  	  	  The	  vertical	  heat	  flux	  (QH	  with	  units	  of	  W	  m-­‐2)	  is	  calculated	  as:	  	  	   	   	   	   	   (1)	  	  where	  ρ	  is	  air	  density	  (kg	  m-­‐3),	  cp	  is	  the	  specific	  heat	  capacity	  of	  air	  (J	  kg-­‐1	  K-­‐1),	  and	  	   (K	   m	   s-­‐1)	   is	   the	   covariance	   between	   vertical	   wind	   velocity	   (w′)	   and	   air	  temperature	   (T′)	   fluctuations	   from	  the	  block-­‐averaged,	  2D	  rotated,	  30-­‐min	  means.	  The	   ρ	   and	   cp	   values	   are	   calculated	   based	   on	   air	   temperature	   and	   humidity	  measurements	  at	  the	  tower	  (58	  m).	  	  ! QH= "cpw'T '! w'T '	   7	  	  	   Figure	  2.	  Meteorological	  tower	  instrumentation	  schematic.	  Figure	  is	  not	  drawn	  to	  scale.	  	  	  	   8	  	  2.5	  Stability	  parameter	  	  To	   assess	   atmospheric	   stability	   at	   the	   site,	   the	   Obukhov	   length	   (L)	   surface	   layer	  scaling	   parameter	   is	   calculated	   from	   the	   sonic	   anemometer	   data.	   A	   physical	  interpretation	  of	  L	  is	  that	  it	  is	  proportional	  to	  the	  height	  above	  the	  surface	  at	  which	  buoyant	   factors	   dominate	   over	   shear	   production	   of	   turbulence	   (Stull,	   1988).	   The	  Obukhov	  length	  (in	  m	  units)	  is	  calculated	  as	  (Grimmond,	  1998):	  € L = −u*3Tkgw'T '	  	  	   	   	   	   	   (2)	  	  where	  k	  is	  the	  von	  Karman	  constant	  (0.4),	  g	  is	  gravitational	  acceleration	  (9.8	  m	  s-­‐2),	  € w'T ' 	  is	  the	  covariance	  between	  vertical	  wind	  velocity	  and	  acoustic	  air	  temperature,	  T	  (K)	  is	  virtual	  acoustic	  air	  temperature	  measured	  by	  the	  sonic	  anemometer,	  and	  u*	  (m	  s-­‐1)	  is	  the	  friction	  velocity.	  Friction	  velocity	  is	  calculated	  as	  (Stull,	  1988):	  € u*= (u'w'2+ v 'w'2)1/ 4 	  	  	   	   	   	   	  	  	  	  (3)	  	  where	  € u'w' 	  and	  € v'w'	  are	  covariances	  calculated	  from	  the	  10	  Hz	  sonic	  anemometer	  data	   at	   58	  m.	   The	   friction	   velocity	   is	   a	   surface	   layer	   velocity	   scale	   related	   to	   the	  surface-­‐atmosphere	  momentum	  flux	  and	  horizontal	  shear	  stress	  (Stull,	  1988).	  	  The	   Obukhov	   length	   is	   then	   used	   to	   determine	   the	   dimensionless	   stability	  parameter	  z’/L,	  where	  z’	  =	  z	  –	  zd.	  The	  displacement	  length	  (zd)	  is	  the	  height	  at	  which	  wind	   speeds	   are	   reduced	   to	   zero	   because	   of	   an	   elevated	   canopy	   surface.	   At	   this	  location,	   zd	   is	   set	   to	   0	  m	  because	   the	   surface	   vegetation	   has	   been	   clear-­‐cut	   in	   the	  immediate	  vicinity	  of	  the	  tower	  and	  there	  is	  no	  continuous	  canopy.	  Therefore,	  z’	   is	  equal	   to	   the	   measurement	   height	   (z)	   of	   58	   m.	   Negative	   values	   of	   z’/L	   represent	  unstable	  conditions,	  positive	  values	  represent	  stable	  conditions,	  and	  values	  at	  0	  are	  neutrally	  stable.	  	  2.6	  Vertical	  wind	  profile	  calculations	  	  Six	   variations	  of	   vertical	  wind	  profile	  models	   are	   compared	  and	  assessed	  by	   their	  ability	   to	   predict	   measured	   wind	   speeds	   at	   59	   m	   during	   different	   atmospheric	  stability	   conditions	   (Table	   1).	   Individual	   observations	   are	   sorted	   by	   the	   stability	  parameter	   z’/L	   and	   classified	   as	   stable	   (z’/L>0.1),	   neutral	   (-­‐0.1<z’/L<0.1),	   or	  unstable	   (z’/L	   <	   -­‐0.1).	   Sonic	   anemometer	   variables	   (u*,	   z0,	   z’/L)	   and	   wind	   speed	  measurements	  from	  33	  m	  (sensor	  U5)	  and	  48	  m	  (sensor	  U3)	  are	  averaged	  for	  each	  stability	  class	  and	  used	  to	  predict	  mean	  measured	  wind	  speed	  at	  59	  m	  (sensor	  U1).	  	  	  	  	  	  	   9	  The	  first	  method	  uses	  a	  shear	  exponent	  power	  law	  expressed	  as	  (NYSERDA,	  2010):	  	  € u(z) = βzα 	   	   	   	   	   	  	  	  	  	  	  	  	  	  (4)	  	  where	   β	   and	  α	   parameters	   are	   determined	   with	  measured	   wind	   speeds	   at	   33	  m	  (sensor	  U5)	  and	  48	  m	  (sensor	  U3)	  using	  a	  non-­‐linear	  least	  squares	  fit	  algorithm.	  This	  is	   a	   model	   widely	   used	   in	   the	   wind	   energy	   industry	   that	   relies	   on	   an	   empirical	  exponential	   fit	   with	   wind	   profile	   measurements	   and	   does	   not	   explicitly	   include	  atmospheric	  stability.	  	  	  The	  second	  method	  uses	  a	  formulation	  of	  the	  log	  wind	  profile	  law:	  € u(z) =u*klnzz0⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 	  	   	   	   	   	  	  	  	  	  	  	  	  	  	  (5)	  	  The	   surface	   roughness	   length	   (z0)	   and	   friction	   velocity	   are	   unknown	   parameters	  determined	   by	   a	   non-­‐linear	   least	   squares	   fit	   algorithm	   fit	   to	   wind	   speed	  measurements	  at	  33	  m	  and	  48	  m.	  This	  method	  is	  also	  commonly	  used	  during	  wind	  resource	  assessment	  and	  uses	  the	  assumption	  of	  a	  logarithmic	  profile	  shape	  that	  is	  technically	  valid	  only	  during	  neutral	  conditions.	  This	  results	  in	  a	  dynamic	  roughness	  length	   (z0)	   that	   is	   variable	  with	   stability,	   when	   z0	   is	   usually	   considered	   a	   surface	  property	  that	  is	  fixed	  (Stull,	  1988).	  	  The	  third	  method	  uses	  a	  log	  law	  formulation	  that	  has	  an	  additional	  linear	  term,	  € ψ z'L⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ,	  to	  account	  for	  stability	  changes	  to	  the	  neutral	  logarithmic	  profile	  shape	  (Stull,	  1988):	  € u(z) =u*klnzz0⎛ ⎝ ⎜ ⎞ ⎠ ⎟ −ψ z'L⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ 	  	   	   	   	   	  	  	  	  	  (6)	  	  In	  this	  variation,	  u*	  and	  z0	  are	  calculated	  from	  sonic	  anemometer	  measurements	  and	  the	  € ψ z'L⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 	  term	  is	  empirically	  determined	  using	  wind	  profile	  measurements	  at	  33	  m	  and	  48	  m.	  	  	  Friction	  velocity	  (u*)	  is	  calculated	  according	  to	  Eq.	  3	  and	  roughness	  length	  (z0)	  is	  calculated	  for	  each	  30-­‐minute	  interval	  from	  sonic	  anemometer	  data	  as	  (Grimmond	  1998):	  € z0= z'exp −uku*⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 	  	   	  	  	  	  	  	  	  	  	  	  	  	  	  	  	   	   	   (7)	  	  where	  u	  is	  the	  mean	  wind	  speed	  measured	  by	  the	  sonic	  anemometer	  at	  58	  m.	  A	  constant	  z0	  is	  determined	  as	  the	  mean	  of	  individual	  z0	  values	  during	  near-­‐neutral	  stability	  conditions	  (-­‐0.1<z’/L<0.1).	  	   10	  	  The	  fourth	  method	  is	  identical	  to	  the	  third,	  except	  z0	  is	  calculated	  from	  the	  wind	  profile	  measurements.	  Roughness	  length	  (z0)	  is	  determined	  as	  the	  y-­‐intercept	  on	  a	  semi-­‐log	  plot	  of	  wind	  speed	  versus	  height	  during	  near-­‐neutral	  conditions.	  The	  u*	  value	  is	  calculated	  as	  (Stull,	  1988):	  € u*=uklnzz0⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 	  	   	   	   	   	   	  	  	  	  	  	  (8)	  using	  z0	  from	  the	  profile	  measurements	  and	  mean	  wind	  speed	  (u)	  at	  a	  height	  (z)	  of	  48	  m.	  This	  is	  performed	  during	  all	  stability	  conditions,	  though	  u*	  is	  technically	  proportional	  to	  z0	  only	  during	  neutral	  conditions	  (Stull,	  1988).	  	  The	  fifth	  method	  uses	  Eq.	  6	  and	  the	  Businger-­‐Dyer	  formulations	  for	  € ψ z'L⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 	  (Stull,	  1988).	  During	  stable	  conditions	  (z’/L	  >	  0):	  	  € ψ z'L⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = 4.7z'L	  	  	   	   	   	   	  	  	  (9)	  	  and	  during	  unstable	  conditions	  (z’/L	  <0):	  € ψ z'L⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = −2ln1+ φ2⎛ ⎝ ⎜ ⎞ ⎠ ⎟ − ln1+ φ 22⎛ ⎝ ⎜ ⎞ ⎠ ⎟ + 2tan−1(φ) − π2	  	   	   (10)	  	  where:	  € φ = 1−15 z'L⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 1/ 4 	  	   	   	   	   (11)	  	  During	  neutral	  conditions	  € ψ z'L⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 	  =	  0.	  The	  sixth	  method	  is	  identical	  to	  the	  fifth,	  except	  u*	  and	  z0	  are	  calculated	  from	  the	  wind	  profile	  (Eq.	  8).	  	   Table	  1.	  Summary	  of	  wind	  profile	  models	  used	  to	  predict	  measured	  wind	  speed	  at	  59	  m.	  Method	   Description	  1	   Power	  shear	  exponent	  law.	  2	   Log	  law	  with	  no	  stability	  term.	  3	   Log	  law	  with	  forced-­‐fit	  stability	  term	  and	  sonic	  u*	  and	  z0.	  4	   Log	  law	  with	  forced-­‐fit	  stability	  term	  and	  profile	  u*	  and	  z0.	  5	   Log	  law	  with	  Businger-­‐Dyer	  stability	  term	  and	  sonic	  u*	  and	  z0.	  6	   Log	  law	  with	  Businger-­‐Dyer	  stability	  term	  and	  profile	  u*	  and	  z0.	  	  	   11	  3.	  Results	  and	  discussion	  	  3.1	  Stability	  characteristics	  	  The	  atmospheric	   stability	  parameter	  z’/L	   varies	  according	   to	  diurnal	  and	  seasonal	  cycles	  (Figure	  3a).	  In	  winter	  months	  (DJF),	  mean	  conditions	  are	  stable	  (0<z’/L<0.5)	  throughout	   most	   of	   the	   24-­‐hour	   cycle,	   except	   for	   near-­‐neutral	   conditions	   during	  mid-­‐day	   (1000-­‐1400	   h).	   During	   spring	   (MAM)	   and	   fall	   (SON),	   mean	   overnight	  conditions	   are	   stable	   (0<z’/L<0.5)	   and	   transition	   through	   neutral	   to	   unstable,	   on	  average,	   from	   0800-­‐1800	   h.	   During	   summer	   (JJA),	   overnight	   conditions	   remain	  stable	   (0<z’/L<0.5)	  and	   the	  atmosphere	   is	  unstable	   (mean	  z’/L	  <	   -­‐0.5)	   from	  0800-­‐1800.	  	  Static	  stability	   in	   the	  surface	   layer	   is	  driven	  by	  vertical	  density	  gradients	  resulting	  from	  diurnal	  and	  seasonal	  cycles	  of	  surface	  heating	  and	  sensible	  heat	  transfer	  (QH)	  between	  the	  surface	  and	  atmosphere	  (Figure	  3b).	  In	  winter,	  the	  surface	  on	  average	  experiences	  energy	  loss	  (negative	  QH)	  throughout	  the	  24-­‐hour	  period.	  The	  air	  near	  the	   surface	  becomes	   cooler	   and	  denser	   than	  air	   aloft,	   resulting	   in	   a	   stable	   surface	  layer.	  Increased	  solar	  heating	  leads	  to	  positive	  QH	  (energy	  transfer	  from	  the	  surface	  to	   the	   atmosphere)	   during	   spring	   and	   summer	   daytime	   periods.	   This	   results	   in	  buoyant	  thermal	  plumes	  and	  unstable,	  convective	  conditions.	  	  	  During	   winter,	   stable	   conditions	   are	   observed	   at	   this	   site	   during	   62.6%	   of	   all	  available	  30-­‐minute	  time	  periods,	  neutral	  conditions	  24.3%,	  and	  unstable	  conditions	  13.1%	  (Table	  2,	  Figure	  4).	  During	   summer,	  unstable	   conditions	  are	  most	   common	  (45.0%),	  compared	  to	  neutral	  (22.1%)	  and	  stable	  (32.9%).	  	  	  	   12	  	  Figure	  3.	  Diurnal	  course	  of	  z’/L	  (a)	  and	  sensible	  heat	  flux	  (QH)	  (b)	  during	  winter	  (DJF),	  spring	  (MAM),	  summer	  (JJA),	  and	  fall	  (SON)	  periods.	  	   13	  	  	  	  Figure	  4.	  Distribution	  of	  z’/L	  during	  winter	  (DJF),	  spring	  (MAM),	  summer	  (JJA),	  and	  fall	  (SON).	  The	  z’/L	  values	  are	  binned	  in	  increments	  of	  0.2	  and	  the	  x-­‐axis	  is	  magnified	  on	  the	  range	  from	  -­‐2.0	  to	  2.0.	  	  The	  inset	  figure	  shows	  the	  cumulative	  distribution	  over	  the	  same	  interval.	  	  	   Table	  2.	  Seasonal	  frequency	  of	  unstable,	  neutral,	  and	  stable	  conditions.	  	  Season	   Unstable	  (z’/L	  <	  -­0.1)	   Neutral	  (-­0.1<z’/L	  <0.1)	   Stable	  (0.1<z’/L)	  	  Winter	  (%)	   13.1	   24.3	   62.6	  Spring	  (%)	   30.7	  	   30.4	   38.9	  Summer	  (%)	   45.0	   22.1	   32.9	  Fall	  (%)	   25.0	   28.6	   46.4	  	  	  	  	  	   14	  Winds	  at	  this	  site	  are	  predominantly	  from	  the	  SW	  (220°-­‐240°)	  (Figure	  5).	  Unstable	  conditions	  (z’/L	  <	  0.1)	  occur	  most	  frequently	  when	  winds	  are	  from	  the	  NE	  (30-­‐70°)	  (65.2%	  of	  time	  periods	  when	  winds	  are	  from	  this	  direction).	  Stable	  conditions	  occur	  most	  frequently	  (52.5%)	  when	  winds	  are	  from	  the	  SW	  (205°-­‐215°).	  	  	  	  	  Figure	  5.	  Stability	  parameter	  z’/L	  by	  wind	  direction.	  Wind	  directions	  are	  binned	  in	  10°	  increments.	  	  Observed	  wind	  speed	  distributions	  at	  59	  m	  differ	  between	  stability	  classes	  (Table	  3,	  Figure	  6).	  Mean	  wind	  speeds	  range	  from	  5.0	  m	  s-­‐1	  during	  unstable	  conditions,	  to	  6.5	  m	  s-­‐1	  during	  neutral	  conditions,	  and	  7.3	  m	  s-­‐1	  during	  stable	  conditions	  (Table	  4).	  The	  different	   stability	   regimes	   are	   also	   characterized	   by	   distinct	   values	   of	   turbulence.	  Highest	  turbulence	  intensity	  (wind	  speed	  standard	  deviation	  /	  mean	  wind	  speed)	  is	  observed	  during	  unstable	  conditions	  (0.17),	  compared	  to	  neutral	  (0.13)	  and	  stable	  conditions	  (0.11)	  (Figure	  7).	  Additionally,	  the	  vertical	  wind	  shear	  exponent	  (α	  from	  three	  profile	   levels,	  Eq.	  4)	   is	  greatest	  during	  stable	  conditions	  (0.19),	  compared	  to	  neutral	  (0.13),	  and	  unstable	  conditions	  (0.09).	  	   15	  	  Figure	  6.	  Wind	  speed	  distributions	  during	  different	  stability	  conditions.	  Wind	  speeds	  are	  binned	  in	  1	  m	  s-­‐1	  increments	  and	  the	  inset	  figure	  shows	  the	  cumulative	  distribution	  of	  wind	  speeds.	  Weibull-­‐curve	  parameter	  values	  are	  listed	  in	  Table	  4.	  	  	  Table	  3.	  Mean	  wind	  speed	  distribution	  and	  turbulence	  during	  different	  stability	  classifications.	  	  Variable	   Unstable	  (z’/L	  <	  -­0.1)	   Neutral	  (-­0.1<z’/L	  <0.1)	   Stable	  (0.1<z’/L)	  	  Mean	  59	  m	  wind	  speed	  (m	  s-­‐1)	   5.0	   6.5	   7.3	  Weibull	  c	  parameter	   4.9	   6.81	   8.01	  Weibull	  k	  parameter	   1.67	   1.70	   2.17	  Mean	  turbulence	  intensity	   0.17	   0.13	   0.11	  Shear	  exponent	   0.09	   0.13	   0.19	  ∆T/∆z	  (K	  m-­‐1)*100	   -­‐2.78	   -­‐0.64	   0.70	  	  	   16	  	  Figure	   7.	   Stability	   parameter	   z’/L	   calculated	   from	   sonic	   anemometer	   data	   and	  turbulence	   intensity	   at	   58	  m.	   Horizontal	   turbulence	   intensity	   is	   calculated	   as	   the	  standard	  deviation	  of	  horizontal	  wind	  speed	  (€ σU)	  divided	  by	  mean	  horizontal	  wind	  speed	  (U).	  Vertical	   turbulence	   intensity	   is	  calculated	  as	  € σW/U,	  where	  € σWis	  vertical	  wind	  speed	  standard	  deviation.	  	  	  The	  shear	  exponent	  (α,	  Eq.	  4)	  is	  associated	  with	  z’/L	  at	  this	  site,	  though	  the	  relation	  is	   not	   linear	   (Figure	   8a).	   For	   this	   site,	   α<~0.15	   is	   associated	   with	   unstable	  conditions	  (negative	  z’/L)	  and	  α>~0.15	  is	  stable	  (positive	  z’/L).	  	  The	   vertical	   temperature	   gradient	   (∆T/∆z,	   units	   of	   K	   m-­‐1)	   is	   also	   related	   to	   z’/L	  (Table	  3,	  Figure	  8b).	  The	  gradient	  ∆T/∆z	  is	  calculated	  as	  (T58m	  –	  T33m)	  /	  25	  m,	  where	  T	   is	   measured	   by	   shielded,	   aspirated	   thermocouple	   sensors	   mounted	   on	   the	  meteorological	   tower	   (Figure	   2).	   Negative	   temperature	   gradients	   (temperature	  decreases	   with	   height)	   are	   associated	   with	   unstable	   conditions	   and	   positive	  temperature	   gradients	   (temperature	   increases	   with	   height)	   favor	   a	   stable	  atmosphere.	  	   17	  	  Figure	  8.	  Stability	  parameter	  z’/L	  calculated	  from	  sonic	  anemometer	  data	  at	  58	  m	  and	  shear	  exponent	  α	  from	  wind	  speed	  profile	  measurements	  at	  33	  m,	  48,	  and	  59	  m.	  	   18	  3.2	  Which	  method	  best	  predicts	  measured	  59	  m	  wind	  speeds?	  	  A	  comparison	  was	  conducted	  to	  determine	  if	  explicitly	  including	  stability	  (z’/L)	  and	  surface	   parameters	   (z0	   and	   u*)	   improves	   calculations	   of	   the	   vertical	   wind	   speed	  profile.	  In	  total,	  six	  variations	  of	  vertical	  wind	  profile	  models	  were	  tested	  (Table	  2).	  These	  models	  used	  data	  from	  the	  sonic	  anemometer	  and	  wind	  speed	  measurements	  at	   33	  m	   and	   48	  m	   to	   predict	  mean	  wind	   speed	   at	   59	  m	   under	   different	   stability	  conditions.	   The	   predictions	   are	   compared	   against	   measured	   wind	   speed	   at	   59	  m	  (Table	  4).	  	   Table	  4.	  Percentage	  difference,	  relative	  to	  measurements,	  between	  model	  predictions	  and	  measurements	  of	  mean	  59	  m	  wind	  speed.	  	  Method	   Unstable	  (z’/L	  <	  -­0.1)	   Neutral	  (-­0.1<z’/L	  <0.1)	   Stable	  (0.1<z’/L)	  	  1	   0.75	   1.03	   1.06	  2	   0.68	   0.88	   0.78	  3	   4.00	   -­‐1.70	   -­‐3.21	  4	   2.15	   0.61	   -­‐1.71	  5	   -­‐26.73	   -­‐1.70	   -­‐32.96	  6	   -­‐9.23	   0.61	   26.58	  	  The	   best	   performance	   in	   non-­‐neutral	   stability	   conditions	   is	   Method	   2,	   the	  logarithmic	   law	   fit	   to	   wind	   profile	   measurements	   at	   33	   m	   and	   48	   m	   with	   no	  additional	   stability	   information.	   The	   next	   best	   model	   in	   non-­‐neutral	   stability	  conditions	  is	  Method	  1,	  the	  shear	  exponent	  power	  law.	  	  Methods	  3-­‐4	  use	  a	  stability	  correction	  parameter	  whose	  value	  is	  determined	  based	  on	   wind	   speed	   measurements	   at	   33	   m	   and	   48	   m.	   Both	   variations	   underestimate	  wind	  speed	  during	  stable	  conditions	  and	  overestimate	  during	  unstable	  conditions.	  Method	  4	  performs	  on	  average	  better	  than	  Method	  3,	  suggesting	  profile-­‐determined	  values	  of	  z0	   and	  u*	   are	  more	  accurate	  over	   the	  entire	  wind	  profile	   than	   the	  values	  calculated	  from	  measurements	  at	  a	  single	  height	  by	  the	  sonic	  anemometer	  (Table	  5).	  	  Methods	   5-­‐6	   use	   the	   Businger-­‐Dyer	   formulations	   for	   the	   stability	   correction	  parameter.	  Errors	  are	  large	  during	  stable	  and	  unstable	  conditions	  for	  both	  methods,	  though	  Method	  6	  has	  smaller	  error	  values	  and	  performs	  slightly	  better	  overall.	  This	  also	  suggests	  the	  profile-­‐determined	  values	  of	  z0	  and	  u*	  are	  more	  appropriate	  at	  this	  site.	  	  	  	  	  	  	  	   19	  Table	  5.	  	  Differences	  in	  z0	  and	  u*	  calculated	  from	  sonic	  anemometer	  data	  and	  wind	  profile	  data.	  Variable	   Sonic	  anemometer	   Wind	  profile	  z0	  (m)	  (neutral)	   0.61	   0.05	  u*	  (m	  s-­‐1)	  (unstable)	   0.43	   0.32	  u*	  (m	  s-­‐1)	  (neutral)	   0.59	   0.39	  u*	  (m	  s-­‐1)	  (stable)	   0.31	   0.42	  	  	  Overall,	   the	  failure	  of	  the	  Methods	  3-­‐6	  that	  use	  additional	  stability	  information	  are	  likely	   because	   of	   surface	   layer	   similarity	   assumptions	   that	   do	   not	   hold	   in	   this	  environment.	   During	   stable	   conditions,	   it	   is	   likely	   that	   the	   sonic	   anemometer	  measurement	   height	   is	   above	   the	   surface	   layer	   and	   measurements	   represent	  conditions	   that	   are	   decoupled	   from	   surface	   friction	   and	   heat	   flux.	   Thus,	   surface	  scaling	   parameters	   and	   variables,	   such	   as	   u*	   or	  € w'T ' ,	   measured	   by	   a	   single	  anemometer	   at	   58	   m	   are	   likely	   to	   be	   invalid	   for	   surface	   layer	   similarity	   theory	  applications.	  	  	  Another	   standard	   assumption	   is	   of	   a	   horizontally	   homogeneous	   surface	   and	  wind	  field.	  Sonic	  anemometer	  measurements	  at	  58	  m	  a.g.l.	  are	  representative	  of	  a	  source	  area	   extending	   several	   kilometers	   upwind.	   This	   source	   area	   may	   be	   different	   in	  terms	  of	  surface	  thermal	  and	  roughness	  properties	  compared	  to	  local-­‐scale	  surface	  conditions	   that	   drive	   local	   buoyancy	   production.	   The	   z0	   calculated	   by	   the	   sonic	  anemometer	   (0.61	   m)	   suggests	   a	   surface	   that	   is	   rougher	   than	   the	   profile-­‐based	  calculation	   of	   z0	   (0.05	  m).	   The	   sonic-­‐based	   value	   likely	   is	   more	   representative	   of	  second-­‐growth	   forest	   surface	   cover	   found	   several	   kilometers	   around	   the	   tower,	  while	  the	  profile-­‐based	  value	  represents	  clear-­‐cut	  areas	  in	  the	  immediate	  vicinity	  of	  the	   tower.	   Also,	   topographic	   influences	   could	   distort	   wind	   flow	   (e.g.	   acceleration	  over	   a	  hill)	   and	   introduce	  horizontal	  heterogeneity	   to	   the	  wind	   field	   and	   result	   in	  non-­‐standard	  wind	  speed	  profiles.	  	  	  	  3.3	  Effect	  of	  stability	  on	  vertical	  wind	  profiles	  	  A	  primary	  objective	  of	  wind	  resource	  assessment	  is	  prediction	  of	  mean	  wind	  speeds	  across	  the	  rotor	  plane	  of	  wind	  turbines.	  	  This	  is	  becoming	  more	  challenging	  as	  wind	  turbine	   heights	   grow	   to	   be	   above	   the	   surface	   layer	   and	   turbines	   are	   increasingly	  located	   in	   areas	   of	   complex	   terrain	   (Emeis,	   2014).	   Above	   the	   surface	   layer,	  assumptions	   of	   exponential	   or	   logarithmic	  wind	   profile	   shapes	  may	   no	   longer	   be	  valid	   and	   wind	   fields	   are	  modified	   in	   complex	   ways	   by	   topography.	   Nonetheless,	  vertical	  wind	  profiles	  are	  calculated	  up	  to	  180	  m	  at	  1	  m	  resolution	  using	  the	  shear	  exponent	  power	  law	  (Method	  1)	  and	  log	  law	  (Method	  2)	  based	  on	  mean	  measured	  wind	  speeds	  at	  33	  m,	  48	  m,	  and	  59	  m	  during	  unstable,	  neutral,	  and	  stable	  conditions	  (Figure	  9).	  	  	  	   20	  Figure	  9.	  Vertical	  wind	  profiles	  based	  on	  measurements	  at	  33	  m,	  48	  m,	  and	  59	  m.	  Gray	  shaded	  area	  is	  the	  height	  of	  a	  turbine	  rotor	  with	  hub	  height	  of	  120	  m	  and	  rotor	  diameter	  of	  50	  m.	  	  A	  rotor-­‐equivalent	  wind	  speed	  (ur)	  that	  takes	  into	  account	  vertical	  shear	  across	  the	  turbine	  rotor	  diameter	  is	  calculated	  as	  (Wharton	  and	  Lundquist):	  	  € ur=2ATuzz=h−rz=h+r∑(r2− h2+ 2hz − z2)1/ 2	  	  where	  AT	  is	  the	  turbine	  rotor	  area,	  h	  is	  turbine	  hub	  height,	  r	  is	  turbine	  rotor	  radius,	  and	  z	  is	  the	  height	  level	  of	  the	  wind	  speed	  value	  (uz).	  	  The	   ur	   was	   calculated	   assuming	   a	   turbine	   with	   a	   hub	   height	   of	   120	  m	   and	   rotor	  diameter	  of	  50	  m.	  Differences	  in	  ur	  between	  the	  shear	  exponent	  power	  law	  (Method	  1)	   and	   log	   law	   (Method	   2)	   calculations	   are	  minimal	   (<2%)	   in	   all	   stability	   classes	  used	  in	  this	  study	  (Table	  6).	  	  	  	   21	  Table	  6.	  Differences	  in	  rotor-­‐equivalent	  wind	  speed	  between	  wind	  profile	  calculation	  methods	  under	  different	  atmospheric	  stabilities.	  ur	   Unstable	  (z’/L	  <	  -­0.1)	   Neutral	  (-­0.1<z’/L	  <0.1)	   Stable	  (0.1<z’/L)	  	  Power	  law	  (m	  s-­‐1)	   5.96	   7.66	   8.59	  Log	  law	  (m	  s-­‐1)	   5.94	   7.59	   8.44	  Difference	  (%,	  relative	  to	  log	  law)	   0.43	   0.95	   1.77	  	  	  	  4.	  Conclusions	  	  This	   study	   uses	   data	   from	   a	   3-­‐d	   sonic	   anemometer	   at	   58	   m	   height	   on	   a	  meteorological	   tower	   to	   calculate	   the	   atmospheric	   stability	   parameter	   z’/L.	   The	  central	  findings	  of	  this	  work	  are:	  	   1. There	   are	   at	   least	   three	   distinct	   atmospheric	   stability	   classes	   (unstable,	  neutral,	   stable)	   that	   follow	   seasonal	   and	   diurnal	   patterns.	   These	   stability	  classes	   have	   unique	   wind	   speed,	   vertical	   shear,	   and	   turbulence	  characteristics.	  	  2. It	   is	   recommended	   that	   future	   wind	   resource	   assessment	   reports	   should	  attempt	   to	   differentiate	   between	   stability	   classes.	  When	   sonic	   anemometer	  data	   are	   not	   available,	   the	   shear	   exponent	   is	   related	   to	   the	   stability	  parameter	   z’/L	   and	   can	   be	   used	   instead,	   though	   the	   relation	   is	   not	   linear.	  Temperature	   differences	   at	   two	   heights	   can	   also	   be	   used	   to	   classify	   bulk	  stability	  across	  the	  layer.	  Therefore,	   it	   is	  also	  recommended	  to	  have	  at	  least	  two	  air	  temperature	  measurements	  at	  different	  heights.	  	  	  3. Empirical	  industry-­‐standard	  wind	  profile	  models	  (shear	  exponent	  power	  law	  and	  log	  law)	  	  using	  the	  2	  lower	  wind	  speed	  measurements	  (33	  m	  and	  48	  m)	  perform	  better	  at	  predicting	  top-­‐level	  wind	  speeds	  (59	  m)	  than	  methods	  that	  explicity	  incorporate	  stability	  and	  surface	  parameters	  measured	  by	  the	  sonic	  anemometer	  at	  tower	  top.	  4. Failure	  of	  the	  models	  that	  explicitly	  include	  stability	  and	  surface	  parameters	  is	   likely	   due	   to	   breakdown	   of	   specific	   theoretical	   assumptions	   used	   in	   the	  models.	  A	  single	  measurement	  at	  58	  m	  may	  not	  always	  be	  coupled	  with	  the	  surface	   layer	   and	   is	   likely	   more	   representative	   of	   regional-­‐scale	   surface	  conditions	  than	  local-­‐scale	  conditions.	  5. Rotor	   equivalent	   wind	   speeds	   calculated	   using	   the	   two	   industry-­‐standard	  wind	   profile	  models	   (shear	   exponent	   power	   law	   and	   log	   law)	   vary	   by	   less	  than	  2%.	  6. Future	   research	   to	   assess	   stability	   would	   be	   improved	   with	   additional	  measurement	   levels	   of	   instrumentation.	   An	   additional	   sonic	   anemometer	  closer	  to	  the	  surface	  (e.g.	  20-­‐30	  m)	  would	  better	  represent	  surface	  fluxes	  and	  vertical	  variations	  in	  turbulence	  and	  wind	  speed.	  	   22	  7. In	   general,	   there	   still	   remains	   uncertainty	   with	   extrapolating	   wind	   speeds	  above	   the	   surface	   layer	   and	   in	   complex	   terrain	   using	   current	   tower-­‐based	  measurements	   and	   exponential	   or	   logarithmic	   modeling	   methods.	   As	  turbines	   grow	   larger	   and	   are	   placed	   in	   more	   complex	   terrain,	   it	   is	  recommended	   to	   include	   remotely	   sensed	   observations	   from	  wind	   lidar	   or	  sodar	   systems	  and	  non-­‐linear	   computational	   fluid	  dynamic	   (CFD)	  modeling	  tools	  in	  wind	  resource	  assessment.	  	  	  	  Acknowledgements	  This	  project	  was	  supported	  by	  a	  MITACS-­‐Accelerate	  Fellowship	  (project	  #IT02901)	  and	  would	  not	  have	  been	  possible	  without	  the	  support	  of	  Paul	  Manson,	  CEO	  of	  Sea	  Breeze	  Power	  Corp.,	  Sam	  Chow,	  or	  technical	  contributions	  from	  Nahum	  Robertson	  and	  Mo	  Vahedifar.	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	   23	  References:	  	  CANWEA	  (2013),	  Canadian	  Wind	  Energy	  Association.	  http://www.canwea.ca/pdf/canwea-­‐factsheet-­‐economic-­‐web-­‐final.pdf.	  accessed	  March	  22,	  2013.	  	  DataBC,	  (2014).	  http://apps.gov.bc.ca/pub/dwds/home.so.	  Downloaded	  February,	  2014.	  	  	  Emeis,	  S.	  (2014).	  ‘Current	  issues	  in	  wind	  energy	  meteorology’,	  Meteorological	  Applications,	  DOI:	  10.1002/met.1472	  	  Grimmond,	  C.S.B.,	  T.S.	  King,	  M.	  Roth,	  T.R.	  Oke.	  (1998).	  ‘Aerodynamic	  roughness	  of	  urban	  areas	  derived	  from	  wind	  observations.’	  Boundary	  Layer	  Meteorology,	  89,	  1-­‐24.	  	  NYSERDA	  (2010),	  ‘Wind	  Resource	  Assessment	  Handbook,	  Final	  Report	  10-­‐30.’	  New	  York	  State	  Energy	  Research	  and	  Development	  Authority.	  	  Probst,	  Oliver,	  and	  Diego	  Cárdenas.	  "State	  of	  the	  art	  and	  trends	  in	  wind	  resource	  assessment."	  Energies	  3.6	  (2010):	  1087-­‐1141.	  	  Stull,	  Roland	  B.	  An	  introduction	  to	  boundary	  layer	  meteorology.	  Vol.	  13.	  Springer,	  1988.	  	  Wharton,	  Sonia,	  and	  Julie	  K.	  Lundquist.	  ‘Assessing	  atmospheric	  stability	  and	  its	  impacts	  on	  rotor-­‐disk	  wind	  characteristics	  at	  an	  onshore	  wind	  farm.’	  Wind	  Energy	  15.4	  (2011):	  525-­‐546.	  	  	  	  


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