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January 2012

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Supplementary information for: Subsidies for new technologies and knowledge spillovers from learning by doing Methodology for estimating wind power available at California wind farms 1985-2003

Gregory Nemet1 La Follette School of Public Affairs and Nelson Institute Center for Sustainability and the Global Environment (SAGE), University of Wisconsin, Madison, WI USA

1 Extracting Winds from NARR Data

The North American Regional Reanalysis (NARR) data was used for getting the winds at the wind farm locations for the period of 1985 – 2003. It was downloaded from the providers at the National Centers for Environmental Prediction (NCEP) and the National Center for Atmospheric Research (NCAR). The NARR project is a fairly recent undertaking, being completed in 2004. The data was obtained in the form of monthly means and each file included both u and v components of wind. The NARR system is based off the NCEP Eta model and its corresponding 3D-Var Data Assimilation System (EDAS). The resolution is 32km in the horizontal and is comprised of 45 discrete layers, the same as the Eta model prior to 2000. (Mesinger, et. al, 2006) The NARR data that was used incorporates most of the observations from the Global Reanalysis updated version GR2. The only satellite data that was used in the NARR project was from NESDIS for temperature and precipitable water over the oceans within the NARR grid domain and for vegetation parameterizations. (Mesinger, et. al, 2006)

2 The NARR Grid

To extract the winds at the wind farm locations an NCAR Command Language (NCL) Fortran based program was used. A script that takes an input of latitude and longitude coordinates would output a corresponding NARR grid point nearest to the inputted location. A separate NCL script was then utilized to output the wind magnitude from the u and v components at the specified NARR grid point and pressure level in the form of an ASCII text file. The table below lists the grid point from which the data was extracted.

1 I am grateful to D.J. Rasmussen for developing the methodology for providing wind speed estimates for each site using the NARR satellite data.

Supplementary information for `` Subsidies for new technologies and knowledge spillovers” G. Nemet

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The map of California overlaid with the NARR 221 grid visually indicates the location of the wind farms and their corresponding grid points. (Mesinger, et. al, 2006)

Wind Farm NARR Grid Point Location

Altamont 104, 133 San Gorgonio 93, 141 Tehachapi 88, 145

The numerical assimilation techniques used in NARR are made possible by finite difference approximations, which substitute spatial derivatives with a finite-difference approximations. The NARR grid-point array at any level has its grid points made up of indices (i,j) indicating their positions in the grid. All calculations in the NARR data were done at the grid points.


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Every point not on the boundaries on a square one dimensional grid is made up of a five-point stencil pattern that includes the point itself and its four “neighboring” points, which are used to calculate derivatives at the points themselves. The distance between the grid points, known as the grid length, is 32km for the NARR data set. In the equation below, an example derivative,

!

"u"x , at a the grid point (i, j) is given by (Atkinson, 1981):

!

"u"x#

$ %

&

' ( i, j

=ui+1, j ) ui)1, j

2a

Where a is the distance between grid points.

(Atkinson, 1981)

From basic knowledge of calculus and derivatives, it can be said that the equation above is averaging the data that is within the grid box domain. (Bouttier and Courtier)


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3 Converting between geometric and isobaric heights for use in extracting NARR u and v wind components

To account for the various heights of the wind farms above sea level, the geometric heights of the wind farms were converted to isobaric pressure levels. This allows for u and v wind components to be extracted at levels above 10m above sea level, the assimilation level that was used for the NARR winds. The conversion between the two ways of measuring altitude was done with the hypsometric equation. The hypsometric equation relates atmospheric pressure to geometric thickness under constant temperature and gravity and is derived from the hydrostatic equation and the ideal gas law.

!

Rd Tgln p1

p2

"

# $

%

& ' = (z (Martin, 2006)

Solved for

!

p2, and using

!

p1 as a reference pressure of 1013mb, the equation can give the equivalent pressure for an altitude,

!

"z . Both gravity and temperature were held constant and temperature was assumed to be 293.15K or 20 degrees Celsius, a fair approximation of a yearly mean temperature for the three Californian wind farms. Wind Farm Elevation (ft)

Calculated Equivalent

Pressure (mb) Nearest NARR

Equivalent Pressure (mb)

Altamont 755 985 975 San Gorgonio 1591 957 950 Tehachapi 3799 885 875 Elevations from USGS.

4 Using Available Observed Wind Speed Data

In verifying the effectiveness of the NARR wind data, wind observations from locations near the wind farms was used. The source of the wind data was from ASOS, AWOS, and RAWS measurements at airports and automated weather stations. The data was converted to monthly means and then to quarterly means if its original form was hourly and daily data. The source of the data was the National Climatic Data Center (NCDC) and the Western Regional Climate Center (WRCC). The table below lists the locations that the observations were taken from for each wind farm:


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Wind Farm Coordinates Observation Site Coordinates Altamont Pass 37.732°N -

121.652°E Livermore Mun. Airport 37.70°'N -

121.816°E San Gorgonio 33.916°N -

116.600°E Palm Springs Intl. Airport

33.83°N -116.500°E

Tehachapi 35.102°N -118.282°E

Jawbone, CA (RAWS) 35.28°N -118.216° E

Wind Farm Coordinates from USGS Interpolating 10 meter wind speeds to turbine hub heights at 50 meters in an

unstable surface layer Monin-Obukov length for a moderately unstable atmosphere (Pasquill Stability Class B) from Golder (1972) is given by:

!

1L

= ".037 + .029log10(z0)

Where a roughness parameter,

!

z0, corresponds to hilly or mountainous terrain at the wind farm locations and some of the observation sites with the exception of observations from Palm Springs International Airport, which uses a roughness parameter that is typical of an urban area. (Stoll, 1988). The logarithmic wind profile equation with parameters for a diabatic surface layer is given by:

!

uu*

=1"

#

$ % &

' ( ln

zz0

#

$ %

&

' ( + )

zL#

$ % &

' (

*

+ ,

-

. / (Stoll, 1988)

Where

!

u is the mean wind speed at height z,

!

u* is the friction shear velocity, κ is the von

Karman constant, determined to be .35,

!

z0 is the surface roughness parameter, and

!

"zL#

$ % &

' (

is the stability parameter adjustment to the logarithmic wind profile equation.

The stability parameter for unstable conditions

!

zL

< 0"

# $

%

& ' is given by Paulson (1970) and

includes the following Businger-Dyer relationship determined empirically, Businger, et al., (1971) and Dyer (1974):

!

"M = 1# 15zL

$

% &

'

( )

*

+ ,

-

. /

#1/ 4

for

!

zL

< 0"

# $

%

& '

!

"MzL#

$ % &

' ( = )2ln

1+ *M( )2

+

, -

.

/ 0 ) ln

1+ *M2( )

2

+

,

- -

.

/

0 0 + 2tan)1 *M( ) ) 1

2


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To interpolate mean wind speeds,

!

u1 , to a geometric height,

!

z2, from a geometric height,

!

z1, the following equation was derived:

!

u2 = u1

ln z2z0

"

# $

%

& ' + (M

zL"

# $ %

& '

)

* +

,

- .

ln z1z0

"

# $

%

& ' + (M

zL"

# $ %

& '

)

* +

,

- .

Where

!

"z is the difference in height between

!

z2 and

!

z1, in this case 40 meters.

5 Calculating wind power available Using these wind speeds, I then developed an estimate of the energy available at each site in each quarter. The first principles equation for calculating the power available in the wind is:

!

P =12"V 3

where ρ is the density of air. However, the cubic function tends to be highly sensitive to the windiest periods, which is an overstatement of the potential available since turbines typically have cut-out speeds at which they no longer operate in order to protect the equipment. To calculate an estimate of the realistic potential energy available I estimate how much electricity could be extracted from the wind if using equipment at the technological frontier. I use a power curve for a General Electric 2.5 MW turbine that determines the relationship between wind speed and electrical output (Lu, McElroy et al. 2009).


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Finally, I address the issue of quarterly averaging, which tends to underweight the importance of windy periods due to the cubic relationship between speed and power. I apply a Rayleigh distribution to the average wind speed calculated over the quarter to account for the non-linear relationship in the power curve and the observed frequency of above mean periods (Randolph and Masters 2008). This measure of potential wind power available (in kWh/quarter) is calculated as:

!

Wit = F GE2.5(R(Vit)[ ] " h where R is a Rayleigh distribution with mean, Vit , h is the number of hours in a quarter, 2192, and F(GE2.5) is the power curve for the wind turbine at the technological frontier. The figure below shows the calculated values for V for each quarter at the three locations. The strong seasonality that can be observed in the figure leads to the creation of a binary time variable for the windy season, U = 1 for quarters 2 and 3 (April–September).


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1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 20040

2

4

6

8

10

12

Mete

rs/s

econd

Altamont

Tehachapi

San Gorgonio


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References: Atkinson, B.W., 1981: Dynamical Meteorology: An Introductory Selection., 198. Businger, J.A., J.C. Wyngaard, Y. Izumi and E.F. Bradley, 1971: Flux profile relationships in the atmospheric surface layer. J. Atmos. Sci., 28, 181-189. Bouttier, F., P. Courtier, 1999: Data Assimilation concepts and methods, ECMWF lecture notes., 5. Dyer, A.J., 1974: A review of flux-profile relations, Boundary Layer Meteorology., 1, 363-372. Golder, D., 1972: Table 12.4: Coefficients for Straight Line Approximation to Figure 12.8 as a Function of Stability Classes, Boundary Layer Meteorology., 3. Lu, X., M. B. McElroy, et al. (2009). "Global potential for wind-generated electricity." Proceedings of the National Academy of Sciences 106(27): 10933-10938. Martin, J., 2006: Equation 3.6, Mid-Latitude Atmospheric Dynamics., 46. Mesinger, F., G. DiMego, E. Kalnay, K. Mitchell, P.C. Shafran, W. Ebisuzaki, D. Jović, J. Woollen, E. Rogers, E.H. Berbery, M.B. Ek, Y. Fan, R. Grumbine, W. Higgins, H. Li, Y. Lin, G. Manikin, D. Parrish, and W. Shi, 2006: North American Regional Reanalysis. Bull. Amer. Meteor. Soc., 1-42. Paulson, C.A., 1970: The mathematical representation of wind speed and temperature in the unstable atmospheric surface layer. J. Appl. Meteor., 9, 857-861. Randolph, J. and G. M. Masters (2008). Energy for sustainability: technology, planning, policy. Washington, Island Press. Stoll, R.B., 1988: Aerodynamic roughness lengths for typical terrain types, and Equation 9.7.5g, An Introduction to Boundary Layer Meteorology, 380, 385. USGS National Map Viewer. United States Geological Survey. 2 July 2009 <http://nmviewogc.cr.usgs.gov/view.htm>.

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