Meteorology 505: Environmental Biophysics
Dan Rajewski, Post-Doc. drajewsk@iastate.edu
February 5, 2015

• What is turbulence and how does it relate to wind speed?
• How do you measure fluxes and interpret the data
• What is the influence of wind farms on canopy fluxes of energy?

LST [hours]

DAY NIGHT sunrise
LST [hours]
DAY
NIGHT sunrise

• These terms are representing the vertical flux of momentum between the surface (e.g. crop canopy) and the layer of air above the canopy
(boundary layer) up (w>0)
• Wind is 3-dimensional
WEST (u<0)
SOUTH (v<0)
NORTH (v>0)
EAST (u>0)
Horizontal wind speed is a magnitude u
2 v
2 and vector of components <u,v> down (w<0)

Mean Kinetic energy (MKE) = ½ mv 2
For a unit mass MKE~ 0.5 v 2 so  then  TKE  =  0.5  v’ 2 is the Turbulence Kinetic Energy
These terms explain the vertical exchange of momentum above the surface

NIGHT DAY
Take 1-hr subset of 10-minute averaged wind speed and vertical velocity to get u’w’ sunrise
LST [hours]
DAY NIGHT sunrise

• Start with a time series of u and w: u wind speed vs. Time
WEST
U i
EAST u u i u
UP
Time (20 Hz) vertical velocity vs. Time w w i w
Determine the mean and perturbation around the mean for both quantities
This data shows sampling of wind speed at 20 times per second!
DOWN
Time (20 Hz)

• For any variable X : determine the mean and perturbation components to find the variance
•
2
2
X
X
1 n
1 n i i n n
1
1
( X i
2
X x
) 2
2 statistical variance
X x
2
1
2 standard deviation of mean = square root of variance
2
X x
2
TKE
1
2 u
2 v
2 w
2

• For any variables X and Y : determine the mean and perturbation components to find the covariance x y
1 n
1 n i n n i 1
1
( X i
X ) Y i
Y y i x y statistical co-variance co-variance determines the common relationship between two variables u w , v w , u v

Height
2
1
Wind speed
What happens if the air at (1) is displaced upward and displaced downward at (2)?
THINK of mixing a fluid: How does it respond?

Height
1
2
(1)  is  being  carried  up  by  a  turbulent  eddy  (w’  >  0),  but  because it has lower wind speed, it is bringing upward a negative perturbation
(u’  <  0)
(2)  is  brought  down  by  a  turbulent  eddy  (w’  <  0),  and  has  a  higher  wind  than at  (1)  so  it  has  a  positive  perturbation  (u’  >  0)
Net downward flux of momentum
In BOTH cases the product of u’w’  is  (>  0)  (<  0)   negative (downward)
Physical interpretation: The turbulence ‘feeds’   off of the gradient in wind speed
Wind speed is non-zero
The ‘supply’   of turbulence comes from the wind speed above the surface
Wind speed
Energy of mean momentum = Energy of turbulence (fluctuations in momentum)
MKE TKE

DAY NIGHT
Why is turbulence low at night? sunrise
NIGHT sunrise
DAY
At night turbulence is generated by the gradient in wind speed close to the surface

DAY NIGHT sunrise
How is the turbulence sunrise
DAY
This case is for a windy day therefore there is more production of turbulence to the wind speed gradient (shear) than for buoyancy (heating)

Turbulence generated by wind speed
Stull, Introduction to Boundary Layer Meteorology, 1988
Turbulence generated by heating (buoyancy)

DAY NIGHT sunrise
What do you notice about the vertical flux of momentum
(cov uw) vs. cov (vw)?
NIGHT DAY Southerly wind is feeding the turbulent flux to the surface
(flux <0) sunrise
LST [hours]

• http://www.mesonet.agron.iastate.edu/timemachine/#KCCI-
016.201301161330
• January 16 7:15 AM to 4:45 PM (LST)
• What did you notice about the snap shots of smoke?
• How did it change throughout the course of the day?
• What does that indicate about the turbulence?

up up up north north west south north east u’w’
Net transfer is downward down west v’w’ east south Net transfer is downward down west south east u’v’
Net transfer is lateral down

Each axis of the sonic anemometer sends brief pulses of ultrasonic signals in opposite directions. The time of flight of the first signal (out) is given by: and the time of flight of the second signal (back) is given by:
The wind speed, u a
, along any axis can be found by inverting the above relationships, then subtracting the second equation from the first and solving for u a
:
The wind speed is measured on all three non-orthogonal axis to give u a
, u b
, and u c
, where the subscripts a, b, and c refer to the nonorthogonal sonic axis.
The non-orthogonal wind speed components are then transformed into orthogonal wind speed components, u , v , and w , with the following: u v w u a
A u b u c
A is a 3X3 transformation coordinate matrix

• sonic  anemometer  conversion  of  coordinates  from  ‘instrument’  to
‘meteorological’  coordinates
Uz>0 w>0
Uy>0
X
Ux>0 v>0 (south)
• sonic  tilt  correction  so  that  all  measured  fluxes  are  for  true  ‘vertical’,
‘north’,  and  ‘west’ u>0 (west) sensor  sags  due  to  the  weight  or  may  not  point  directly  ‘North’

• Lidar (laser-beam radar) measures
Picture by: Russell Doorenbos vertical profile of wind speed and turbulence
• Data output is every 2 min from composite scans every 2 sec from 40 to 220 m at 20 m intervals every 2 sec
• Measures standard deviations of 3-D wind field
• SoDAR measures wind in the same way as a LiDAR except that it uses sound waves
• LiDAR and SoDAR CANNOT measure covariances (turbulence fluxes)
23

• Sonic anemometers measure: Image taken from LiCOR Biosciences u u , v v , w w , u w , v w , '
• but also heat fluxes: u T , v T , w T , T T
• With an additional sensor to measure gas concentrations of H2O and
CO2, moisture and carbon fluxes can be estimated u H O , v H O , w H O , H O
2
Gas analyzer u CO
2
, v CO
2
, w CO
2
, CO
2
2

2
H c w T
Sensible heat flux
E w C v
F c
C w c g
Latent heat flux
Carbon Dioxide flux

• Spectral analysis shows how to relate the size of the turbulence (xaxis) to the intensity of energy (y-axis)
Low frequency — large eddies
High frequency — small eddies
The area under the curve is equal to the variance or co-variance for that averaging period
This represents the energy cascade

CWEX (Crop/Wind-energy Experiment): measurements of crop microclimate conditions within wind farms
27

Dan Rajewski 2 , Gene Takle 1,2, ,
Tom Horst 3 , Steve Oncley 3 , ,
Julie Lundquist 4 , Mike Rhodes 5 ,
John Prueger 6 , Richard Pfieffer 6 ,
Jerry Hatfield 6 ,
Samantha Irvin 2 , Kris Spoth 2
Russell Doorenbos 2 ,
1 Geological & Atmospheric Sciences, 2 Agronomy
Iowa State University, Ames, IA
3 National Center for Atmospheric Research
4 Atmospheric and Oceanic Sciences, 5 Aerospace Engineering Sciences
University of Colorado, Boulder, CO
6 National Laboratory for Agriculture and the Environment, Ames, IA
28

• Convergence of two unlike energy industries in the same geographical area presents an interaction
• (I): Wind turbine/wind farm influences on crop microclimate and overall yield
• (II): Crop and field management impacts on wind power
• Can strategies of optimization be
developed by studying this interaction?
29

Discussions with Agronomists
• Reduce daytime max temps: avoid summer moisture stress
• Increase nighttime temps : decrease grain fill (respiration) , extend growing season (avoid late spring freeze, avoid early fall frost)
• Enhance evaporation: reduce dew duration (reduce favorable conditions for pests and pathogens; accelerate fall crop dry-down)
• Enhance evaporation: accelerate spring soil drying; accelerate moisture loss during drought
• Enhance atmospheric CO
2
exchange with the crop: enhance daytime photosynthesis; enhance nighttime respiration
• Enhance CO
2
pumping from soil: enhance photosynthesis
• Reduce mean wind speed at top of the canopy: reduce potential for lodging and green snap in corn
• Enhance plant movement through increased turbulence: increase light penetration into canopy and enhance photosynthesis
• Modify mesoscale-scale convergence/divergence patterns: altered/ enhanced rainfall patterns (??
??
??
??)
30
Green = favorable , Red =unfavorable

• Do turbines create a measureable influence on the microclimate over crops?
• If so, does this influence create measureable biophysical changes?
• And if this is so, does this influence affect yield?
Agricultural shelterbelts have a positive effect on crop growth and yield.
Will wind turbines also have a positive effect?
31

Conceptual model of Turbine-crop Interaction via mean wind and turbulence fields, adapted from Wang and Takle (1995) over-speeding zone turbine wake wind-ward
H reduction zone
L
H L leeward  ‘bleed’  through  and speed up-zone
Heat day night
H
2
O CO
2 night day
Speed recovery
32

Heterogeneities of wind turbine wakes offshore of Denmark wake  ‘sheet’  from  several  lines  of  merging    wakes
Diffuse patches of wakes reaching the surface
‘double  wake ’
‘far    wake ’
‘near  wake ’ wake overhead but not reaching the surface
Wake structure differences appear in 2 nd line of turbines
Source: UniFly A/S
Horns Rev 1 owned by Vattenfall. Photographer Christian Steiness 2008.

• Central Iowa wind farm (~200 1.5-MW turbines with 80-m hub height and 77 m and 82.5-m rotor diameter (D) )
• 2010-2012 Measurements taken on southern edge of a wind farm according to prevailing winds at nearby airports, 2013 measurements at northwest edge of the farm
• surface flux and LiDAR measurements above corn : 2010,2011; above soybean : 2012-3013
January July
CWEX-13
CWEX-10/11/12 http://mesonet.agron.iastate.edu/sites/dyn_windrose.phtml?station=DSM&network=IA_ASOS

Hot, high humidity with southerly flow
Cloudy, north wind measuring over corn cup anemometer
2 m above the canopy thermocouples at 1.5, 1.0, 0.5 m above the soybeans wind speed and temperature measured every 0.5 s at upwind and downwind masts

Picture by: Russell Doorenbos
N CWEX-10 : Flux tower measurements
• Cup anemometer at 9.1 m
• T & RH at 9.1 m and 5.3 m
• Sonic anemometer at 6.45 m
• Tipping bucket at 3.75 m
• Two towers (reference and near-wake location) additionally contained
• Net radiometer (net long wave and short wave radiation) at 5.3 m
• Open path CO
2
/H
2
0 IRGA LI-7500 gas analyzer
• Sonic anemometer and gas analyzer sampled at 20 Hz w/ 5 min averages
• T, RH, cup anemometer, rain gage output archived at 5 min
All sensors are connected to a data-logger
Systems are powered with solar panels and deep cycle batteries
36

CWEX-11: Instrumentation of towers
NCAR ISU
NOT SHOWN IN PHOTO:
10 m wind speed, direction
Temp/RH
S
8 m Temp/RH wind speed net radiation probe
2 m above canopy rain gauge at canopy leaf wetness probe at 2/3 canopy height
1 m Temp/RH
Soil temp, moisture, soil heat flux (ISU1)
4.5 m Temp, wind, turbulence
CO
2 and H
2
O (ISU1)
4.5 m Temp/H2O, wind, turbulence
(NCAR 1 -4 )
CO
2
(NCAR 1,3 only)
2 m Temp/RH
2 m Air Pressure
E
3 m Temp/RH wind speed
Picture by: Russell Doorenbos Picture by: Russell Doorenbos
37

Directional shear (change in wind direction with height) can be a complicating factor in wake impacts within the rotor depth vs. near the crop surface
Rajewski et al., Bull Am Meteorol Soc , 2013 38

Downwind-upwind station differences in friction velocity and TKE u
*
200 m downwind of
1 st turbine line
Turbines enhance
1.3 km downwind of
1 st turbine line
2.6 km downwind of
1 st turbine line canopy mixing mostly at night
TKE
200 m downwind of
1 st turbine line
South to North
1.3 km downwind of
1 st turbine line
Higher nighttime turbulence farther into the wind farm
South to North
2.6 km downwind of
1 st turbine line

Station north of two turbine lines has 2-3X ambient TKE and Heat flux before/after the OFF period
80-m wind direction vector
Return to reference flow conditions during the shut down (lightning nearby)

South North Turbines ON
W-power spectra
South North Turbines OFF
ON : Increase in vertical velocity variance of: 2.0X downwind of first line of turbines
5.0X downwind of two lines of turbines
OFF : Similar intensity of variance for all flux stations south and north of two turbine lines
(Modified from Rajewski et al. Agric and For Meteorol ., 2014)

South North Turbines ON
VW-power spectra
South North Turbines OFF
ON : Increase in stream-wise co-variance of 2.0X downwind of first line of turbines
4.0X downwind of two lines of turbines
OFF : Similar intensity of covariance for all flux stations south and north of two turbine lines
(Modified from Rajewski et al. Agric and For Meteorol ., 2014)

Detection of wind turbine impacts on H , E, and CO
2
fluxes: wind direction
Case direction category
Turbine wake
Indicator
Sample size
(N)
DAY
94
Sample size
(N)
NIGHT
98
OFF (combination turbines offline)
333 529
(combination turbines operating) ON
35 60
W
WSW [B1]
(Westerly no-wake, turbines on and off )
B1 (5.3 D to turbine)
25
31
43
19
SW [B12G]
SSW [B2] gap between B1 and B2 (3.8 D to line)
B2 (2.7 D to turbine)
79
198
51
416
S-SSE [B23G] gap between B2 and B3 (2.6 D to line)
(Modified from Rajewski et al. Agric and For Meteorol ., 2014)
Most of these categories have a relevant sample size for testing the statistical significance of the differences
43

u
*
(NLAE 2-NLAE 1)
Means and accumulated differences
Daytime differences are negligible, similar justification as sensible heat flux for a 30-minute average
Nighttime: 50-75% higher mixing at NLAE 2 at 2-5 D downstream of a turbine
(Modified from Rajewski et al. Agric and For Meteorol ., 2014)
44

DAY: Projection of wake influence on surface
B2 B1
Site A Site B
Site 1
H
2
O
Site 3
CO
2
H
2
O
Site 2
CO
2
Daytime H
2
O and CO
2
flux increased by turbine mixing
(response lag in time)
Downward (counter-gradient) heat flux is reported on edge of turbine wake (indicating wake rotation
45

NIGHT: Projection of wake influence on surface
B2 B1
Site A Site B
Site 1
Heat
Site 3
Heat
Site 2
CO
2
CO
2
Nighttime Heat and CO
2
fluxes increased by turbine mixing (via u
*
and TKE)
2X of ambient downward heat flux at wake edges
Stable stratification suppresses upward motion of turbine wake
46

NIGHT: ALIGNED DOUBLE WAKE Projection
A1
B2
L H
Heat
Site 4
Heat
Site 3
Site 2B
Heat
Site 2A
L H
Site 1
<25% higher Heat
<0.25 ° C warmer
<25% increase U,TKE
2X ambient heat flux
0.5-1.5 ° C warmer
1.5X increase U,TKE
50-75% higher heat flux
0.25-0.5 ° C warmer
25-50% increase U,TKE
Wake structure from 1 st turbine dependent on ambient wind speed, direction thermal stability, and thrust specification of turbine
25-50% higher Heat
<0.5 ° C warmer
50-75% increase U,TKE
47

NIGHT: MERGED WAKE Projection
A5 B6
C12
D5
C4
C1
D1
Site 5 A1 Site 4 Site 3 Site 2 B2 Site 1
Turbine eddies become smaller and smaller after passing through additional turbine lines
Merged wakes dissipate energy therein and are unable to change surface fluxes
Negligible downwind-upwind differences in fluxes
Surface – wake interaction resumes several turbine lines downstream when a wake-boundary layer sheet has developed?
48

• Rajewski, D. A., Takle E.S., Lundquist J.K., et al., Crop Wind Energy
Experiment (CWEX): Observations of Surface-Layer, Boundary Layer, and
Mesoscale Interactions with a Wind Farm. Bull. Am. Meteorol. Soc.
94,
655 – 672 (2013). doi: 10.1175/BAMS-D-11-00240
• Rajewski D.A., Takle E.S., Lundquist J.K., et al., Changes in fluxes of heat,
H2O, and CO2 caused by a large wind farm. Agric For Meteorol . 194,
175 – 187 (2014). doi: 10.1016/j.agrformet.2014.03.023
• Stull, R., 1988: An Introduction to Boundary Layer Meteorology . Kluwer
Academic Publishers, 666 pp.
• Wang, H., E. S. Takle, and J. Shen, 2001: Shelterbelts and windbreaks:
Mathematical modeling and computer simulation of turbulent flows.
Ann. Rev. Fluid Mech., 33 , 549-586.

Thank you
“frozen  turbulence”  after  a  blizzard
50