Modeling of Low-Level Jets Over the Great Plains: Implications for Wind Energy by Brandon A. Storm, B.S., M.S. a Dissertation In

Modeling of Low-Level Jets over the Great Plains: Implications for Wind Energy

Brandon A. Storm, B.S., M.S.

A Dissertation

Wind Science and Engineering

Submitted to the Graduate Faculty of Texas Tech University in Partial Fulﬁllment of the Requirements for the Degree of

DOCTOR OF PHILOSOPHY

Approved:

Dr. Sukanta Basu, Chair

Dr. Christopher C. Weiss

Dr. Andrew H.P. Swift

Dr. Jimy Dudhia

Dr. Fred Hartmeister Dean of the Graduate School

To my Peach and our little Cherry Texas Tech University, Brandon A. Storm, August 2008

ACKNOWLEDGEMENTS

Funding for myself was provided by the National Science Foundation under Grant DGE- 0221688. I would like to acknowledge several people and organizations that were essential in helping me complete this project. NCAR was a large contributor of just not data, but provided many resources and guidance. Jimy Dudhia’s leadership during my internship at NCAR played a large factor in me understanding and running the WRF model. Cindy Bruyere from NCAR was also very helpful in trouble shooting problems with WRF, AR- Wpost, and GrADS. Thanks also needs to be extended to Dennis Elliot and Marc Schwartz from NREL for providing the locations of the tall towers used in this dissertation. David Carr, and the Alternative Energy Institute also needs to be acknowledged for collecting and providing the Sweetwater tall tower data. I would also like to extend my thankfulness to my committee members for input into this report. A special thanks is extended to Sukanta Basu, for without his guidance and knowledge this project would not have been completed. A very special thanks is in order to my wife, who has endured many painful hours of discussion about LLJs and WRF. Without her support I would not have been able to accomplish my studies.

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TABLE OF CONTENTS

Page ACKNOWLEDGMENTS ...... ii ABSTRACT ...... vi LISTOFTABLES ...... viii LISTOFFIGURES...... xii Chapter 1 Introduction and Motivation ...... 1 2 Background...... 8 2.1 Powerfromthewind ...... 8 2.2 Windprofiles ...... 10 2.3 Nocturnal boundary layers ...... 13 2.4 Low-leveljets...... 14 a Forcingmechanisms ...... 14 b Low-level jet observation studies over the Great Plains ...... 17 c Relevant numerical studies of the Great Plains low-level jet ..... 21 3 Description of Observational Data Utilized ...... 24 3.1 ARMprofiler ...... 24 3.2 WestTexasMesonetfieldsite...... 26 3.3 Sweetwater100mtalltower ...... 27 3.4 TalltowerdatafromNREL...... 27 3.5 NWSsurfaceobservations ...... 28 4 TheWeatherResearchandForecasting(WRF)Model ...... 30 4.1 WRFoverview ...... 30 4.2 WRFPreprocessingSystem(WPS)...... 32 4.3 WRFdetails...... 33

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a YSUPBL...... 36 b MYJPBL...... 37 5 OverviewofWAsP ...... 39 5.1 WAsPbasics...... 39 5.2 WAsPmodulespecifics ...... 42 a Topography...... 42 b Stability...... 43 c Surfaceroughness ...... 46 d Obstacles ...... 47 6 EvaluationofWRF’SLLJClimatology ...... 48 6.1 Introduction...... 48 6.2 Classificationmethods ...... 49 6.3 Results...... 55 a Categoryfrequencies ...... 56 b Forecastperformance...... 60 c Height distributions ...... 61 6.4 Concludingremarks...... 62 7 Evaluation of WRF’S Low-Level Shear Climatology ...... 66 7.1 Introduction and motivation ...... 66 7.2 Dataandmethodology ...... 66 7.3 Results...... 68 a WRF’s speed and directional shear performance ...... 68 b Impact on wind speed and power estimates ...... 73 c Average shear exponent and 10 meter wind relationship ...... 74 7.4 Concludingremarks...... 75 8 WRF’s Sensitivity in Forecasting Specific LLJ Events ...... 79 8.1 Introduction...... 79 8.2 Dataandmethodology ...... 79 iv Texas Tech University, Brandon A. Storm, August 2008

8.3 Results...... 81 a WestTexascase...... 81 b SouthernKansascase...... 91 8.4 Concludingremarks...... 92 9 Downscaling WRF with WAsP: Framework and Evaluation ...... 96 9.1 Introduction and motivation ...... 96 9.2 Methodology ...... 98 a Previous coupling methods ...... 98 b WRF downscaling and veriﬁcation methods ...... 100 9.3 WRFDownscalingResults ...... 101 a Windatlas ...... 101 b Wind speed and power density comparison ...... 104 9.4 Discussion...... 106 9.5 FutureConsiderations...... 107 10SummaryandFutureWork ...... 111 REFERENCES ...... 115 Appendices ...... 126 A JacksonandHuntTheory...... 126 B WAsPWindAtlases...... 129 C WAsP Estimated Wind Speed and Power Density ...... 132

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ABSTRACT

Low-level jets (LLJs), wind maximums centered 100 - 1000 m above the ground, are common features observed over the Great Plains of the United States. An accurate understanding of LLJs has many implications for the wind power industry. For example, LLJs can increase wind speeds at turbine heights, which in turn leads to an increase in energy. However, these same high speed winds created by LLJs can create large amounts of stress on the turbines, causing fatigue issues over time. Without a proper understanding of the LLJ, accurate estimates of the wind speeds at hub height, which are essential for wind resource assessment and forecasting projects, are very difficult to obtain. When assessing a particular location for placement of a wind farm, it is common within the wind power industry to use towers that do not reach the height of the turbine hubs to estimate the hub height wind speeds. Therefore, the hub height wind speeds are estimated by using lower-level wind speed measurements (60 m or lower) and assuming a simple power law relationship. However, to obtain an accurate estimate of the hub height and higher wind speeds, one has to know what shear exponent value to assume. The presence of LLJs causes the shear exponent to be significantly higher than what the industry currently assumes. The Weather Research and Forecasting (WRF) model simulates the low-level wind speed over a majority of the Great Plains in a manner that could be used to estimate the shear exponent over the Great Plains. However, a comparative investigation between LLJ climatologies developed from WRF model output and observed profiler data indicates that the WRF model struggles in forecasting the frequency, speed and height of LLJs. For regions with strong and frequent LLJs (e.g., southern Kansas), the underestimation in LLJs results in lower predicted shear exponents than observed. Detailed investigations of two LLJ events reveal similar problems in accurately forecasting the heights and speeds of LLJs, as well as sensitivity to boundary layer parameterizations. To determine if accurate WRF based wind power resource assessments can be accom-

vi Texas Tech University, Brandon A. Storm, August 2008 plished, a framework was developed to downscale the coarse WRF model output with a wind resource analysis tool commonly used within the industry, the Wind Atlas Analysis and Application Program (WAsP). The dynamic downscaling accounts for fine scale topography and surface roughness features that can have a large impact on low-level wind fields. It was found that the WRF model can be used as input into WAsP, and in the future could possibly be a replacement to tower observations when completing preliminary resource assessment projects. This would allow the wind power industry to complete site assessment projects in a timely and economically efficient manner.

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LIST OF TABLES

1.1 Characteristics of selected wind turbines commonly found on the Great Plains, including power capacity (MW), rotor diameter (m), hub height (m), and height extent of blades (m)...... 2

3.1 Site locations, heights of measurements, and dates analyzed by Schwartz and Elliot (2006). Heights in parentheses were not used by Schwartz and Elliot(2006)...... 28

6.1 LLJ occurrences using Bonner’s classification method and maximum jet in a night to classify the night from Song et al. (2005), operational WRF forecasts,andARMprofiler...... 58 6.2 LLJ occurrences using Bonner’s classification method and averaging the LLJs in a night to classify the night from operational WRF forecasts and ARMprofiler...... 58 6.3 LLJ occurrences using max/min classification method and the maximum LLJ in a night to classify the time period from operational WRF forecasts andARMprofiler...... 59 6.4 LLJ occurrences using max/min classification method and averaging the LLJs over a night to classify the night from operational WRF forecasts and ARMprofiler...... 59 6.5 Forecast performance statistics for WRF’s 3 – 12 and 27 – 36 hour forecasts using the ARM profiler for verification...... 60

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7.1 Site names and tower heights used by Schwartz and Elliot (2006). The WRF model heights from the grid points corresponding to the tower locations are given. Also reported are various statistics for observed (Schwartz and Elliot 2006) and WRF simulated annual shear exponents (α) and an-

nual directional shear magnitude (β, degrees). αq and αa are averages based on quenched and annealed, respectively. Spatial location of sites canbefoundinFig.7.2...... 70 7.2 Yearly averaged 100 m extrapolated wind speed m s−1 for three locations, Sumner, KS, Lamar, CO, and Washburn, TX. The wind speed is extrapolated using the wind speed from the ﬁrst corresponding model level height in WRF over a year period, up to 100 m using three different shear exponents. The 1/7 method assumes a constant shear exponent of 1/7, while the WRF_const methods takes the average shear exponent from the WRF model, and Obs_const uses the shear exponent observed by Schwartz and Elliot (2006) at that location to extrapolate all of the wind speeds up. The estimated annual energy output (MWh/yr) are computed based on a GE 1.5 MW machine (1.5s) and energy estimate data provided by GE (available at www.gepower.com/prod_serv/products/wind_turbines/en/15mw/index.htm). These estimates assume a constant air density...... 74

8.1 WRF parameters varying in model comparisons...... 81

9.1 Wind atlas created from 100 m tower data...... 103 9.2 Windatlascreatedfrom100mWRFdata...... 104 9.3 Estimated 100 m average wind speeds (ms−1) and power densities (Wm−2) at the location of the Sweetwater tall tower using various methods. “Raw” methods have not been corrected through WAsP. The 100m tower/WAsP method is “self-predicting.” ...... 106 9.4 SameasTable9.3exceptfor50m...... 106

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9.5 Wind atlas created from 100 m tower data assuming a surface roughness of 0.15m...... 110

B.1 Wind Atlas created from 100 m tower data...... 129 B.2 Wind Atlas created from 100 m WRF data...... 129 B.3 Wind Atlas created from 50 m tower data...... 130 B.4 WindAtlascreatedfrom50mWRFdata...... 130 B.5 Wind Atlas created from 10 m Sweetwater ASOS data...... 131 B.6 WindAtlascreatedfrom10mWRFdata...... 131

C.1 Frequency distribution of directional sectors, as well as Weibull parameters, mean wind speed, and power density analyzed from the 100 m level wind speed from the tall tower. Statistics are produced from the observed wind climate, and have not been processed through WAsP’s site correction routines...... 132 C.2 Same as Table C.1 except representing 100 m level WRF data. ∆ P is the difference between the raw 100 m WRF estimated wind power and the estimated wind power from the 100 m level of the tall tower (Table C.1). . 133 C.3 WAsP frequency distribution of directional sectors, as well as Weibull parameters, mean wind speed, and power density with 100 m level wind data from the tall tower as input. ∆ P is the difference between the estimated wind power as reported in Table C.1. Note, this table represents how well WAsP is self-predicting the site of interest, as it is given data for the same height and location as it is being asked to reproduce...... 133 C.4 Same as Table C.3 except 100 m WRF data is used as input into WAsP. . . 134 C.5 Same as Table C.3 except 50 m tower data is used as input into WAsP. . . . 134 C.6 Same as Table C.3 except 50 m WRF data is used as input into WAsP. . . . 135 C.7 Same as Table C.3 except 10 m ASOS wind data is used as input into WAsP. 135 C.8 Same as Table C.3 except 10 m WRF data is used as input into WAsP. . . . 136

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C.9 Frequency distribution of directional sectors, as well as Weibull parameters, mean wind speed, and power density analyzed from the 50 m level wind speed from the tall tower. Statistics are produced from the observed wind climate, and have not been processed through WAsP’s site correction routines...... 136 C.10 Same as Table C.9 except representing 50 m level WRF data. ∆ P is the difference between the raw 50 m WRF estimated wind power and the estimated wind power from the 50 m level of the tall tower (Table C.9). . . . . 137 C.11 WAsP frequency distribution of directional sectors, as well as Weibull parameters, mean wind speed, and power density with 50 m level wind data from the tall tower as input. ∆ P is the difference between the estimated wind power as reported in Table C.9. Note, this table represents how well WAsP is self-predicting the site of interest, as it is given data for the same height and location as it is being asked to reproduce...... 137 C.12 Same as Table C.11 except 50 m WRF data is used as input into WAsP. . . 138 C.13 Same as Table C.11 except 10 m ASOS wind data is used as input into WAsP.138 C.14 Same as Table C.11 except 10 m WRF data is used as input into WAsP. . . 139

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LIST OF FIGURES

1.1 Average diurnal wind speed variation at Sumner, KS from the WRF model. (left panel): Diurnal trend of yearly average wind speeds at given levels. (right panel) Yearly average wind speed proﬁles at speciﬁed times...... 3 1.2 Wind velocities averaged every half hour at heights of 10, 20, 40, 80, 140 and 200 m (bottom to top; 80 m is in bold) for seasons in 1987 at the Cabauw tower in the Netherlands (Van den Berg 2008)...... 4 1.3 Diurnal variation of WRF simulated (30 -100 m) and observed (40 - 80 m) averaged wind shear exponents along with turbine fault occurrences from Big Spring, Texas. The fault times and observed shear exponent are reproduced from Smith et al. (2002) using Engauge Digitizer 4.1...... 6

2.1 Velocity distribution in smooth pipes over a range of Renyold numbers (Nikuradse1932)...... 11 2.2 Typical boundary layer regions over land with relative times of occurrence (Stull1988)...... 13 2.3 Diurnal oscillation of the LLJ due to thermal wind (T.W. in the ﬁgure) forcings over sloping terrain (Stull 1988)...... 16 2.4 Number of LLJ observations from January 1959 – December 1960 at 1200 and 0000 UTC (Bonner 1968)...... 18 2.5 Scatter diagrams of LLJ speed versus height for LLJs below 300 m. Middle line represents best-ﬁt linear regression (R = 0.50) and upper and lower lines are for 1 standard deviation (Banta et al. 2002)...... 20 ±

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2.6 (a) TKE and (c) the vertical ﬂux of TKE for the night of 20–21 October 1999. (b) TKE and (d) the vertical ﬂux of TKE for the night of 24–25 October 1999. In (c) and (d) negative values imply downward mixing of TKE(Bantaetal.2002)...... 21

3.1 Location of the ARM SGP CART and topography of the Walnut River Wa- tershed along with the relative location of the 915-MHz radar wind profiler near Beaumont (BE) Kansas (Song et al. 2005)...... 25 3.2 Locations of all of the observational data used in this study. Stars denote locations of Schwartz and Elliot (2006) tall towers, the square denotes the location of the ARM profiler, the airplane represents the location of the Sweetwater ASOS station, and the circle is the location of the WTM field site...... 29

4.1 WRF framework ﬂowchart (Wang et al. 2005)...... 31 4.2 Horizontal and veritcal grids of the ARW WRF (Skamarock et al. 2005). . 34 4.3 WRF η levels (Skamarock et al. 2005)...... 35

5.1 WAsP ﬂow chart (Troen and Petersen 1989) ...... 40

6.1 Examples of Chebyshev polynomial fits (black lines) for: (a) – (c) ARM profiler’s U and V wind components (blue circles), and (d) WRF’s V component. Since the Chebyshev polynomial fit requires a vertical scale between 0 – 1, heights are normalized as z/2 km...... 52 6.2 Examples of vertical wind speed (m s−1 ) profiles. Blue circles are wind speeds estimated from the ARM profiler, black line is the Chebyshev polynomial fit computed from the U and V components, green dots are local minimums, and red squares are local maximums...... 55

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6.3 Vertical distributions of southerly LLJs that are averaged over the night from: (a) ARM profiler using Bonner’s classification, (b) WRF’s 3–12 hour forecast using Bonner’s classification, (c) WRF’s 27–36 hour forecast using Bonner’s classification, (d) ARM profiler using lowest max/min classification, (e) WRF’s 3–12 hour forecast using lowest max/min classification, (f) WRF’s 27–36 hour forecast using lowest max/min classification...... 64 6.4 Vertical distributions of maximum southerly LLJs in a night from: (a) ARM profiler using Bonner’s classification, (b) WRF’s 3–12 hour forecast using Bonner’s classification, (c) WRF’s 27–36 hour forecast using Bonner’s classification, (d) ARM profiler using lowest max/min classification, (e) WRF’s 3–12 hour forecast using lowest max/min classification, (f) WRF’s 27–36 hour forecast using lowest max/min classification...... 65

7.1 Diurnal variation of yearly averaged wind shear exponent ( α , left panel) h qi and yearly averaged magnitude of directional shear in degrees ( β , right h i panel). Observed shear exponents are reproduced from Schwartz and Elliot (2006) using Engauge Digitizer 4.1...... 71 7.2 WRF simulated yearly averaged shear exponents (left panel) and yearly averaged magnitude of directional shear (right panel). Stars indicate location of tower locations. The dashed box corresponds to the area used in Fig. 7.4. 71 7.3 12 km resolution of WRF terrain elevation (left panel) above mean sea level (m) and USGS land use categories WRF assigns to the grid points (right panel). For details on the land use categories visit: http://www.mmm.ucar.edu /mm5/mm5v2/landuse-usgs-tbl.html...... 72 7.4 Relationship between 10 m wind speed (m s−1) grouped in 1 m s−1 bins (centered around the listed values) and α based on data in the dashed box in Fig. 7.2. The results are presented using standard boxplot notation with marks at 95, 75, 50, 25, and 5 percentile of an empirical distribution. . . . 76

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8.1 0000 UTC, 2 June 2004 analysis of: (a) surface (MSL pressures contoured every 4 hPa); (b) 850 hPa (heights contoured every 30 m); (c) 500 hPa (heights contoured every 60 m), and (d) visible satellite. Panels a-c show standard station models, with temperatures and dewpoint temperatures in degrees Celsius, heights in m, and wind barbs: barb = 10 m s−1, half barb =5ms−1. Fronts in (a) are subjectively analyzed but based on the National Center for Environmental Prediction (NCEP) analysis. The X denotes the approximate location of the WISE field site...... 83 8.2 Simulated and observed wind speed and wind direction for 0400 UTC - 1200 UTC on 02 June 2004. The left column shows wind speed time- height plots (unit: m s−1) of: (a) hourly output from the YSU_rrtm_TX run; (c) hourly output from the MYJ_rrtm_TX run; and (e) half-hourly averages from the Texas Tech boundary layer wind profiler. The right column shows wind direction time-height plots (unit: meteorological degrees) of: (b) hourly output from the YSU_rrtm_TX run; (d) hourly output from the MYJ_rrtm_TX run; and (f) half-hourly averages from the Texas Tech boundarylayerprofiler...... 84 8.3 Vertical shear exponent (α) time series calculated from the YSU_rrtm_TX (dotted line) and MYJ_rrtm_TX (dashed line) runs (utilizing wind speed time series at the 113 m grid-level and at the 10 m level) between 0300 - 1200 UTC on 2 June 2004. The Texas Tech boundary layer profiler’s 124 m wind speed and the Reese WTM station’s 10 m wind speed time series were utilized to estimate the observed α time series (solid line). The 1/7 power law exponent is also shown for comparison (dashed-dotted line). . . 85

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8.4 Vertical wind speed (m s−1) profiles from the YSU_rrtm_TX (dotted lines in gray) and MYJ_rrtm_TX (dashed lines in black) runs at 0500 UTC (left) and 0600 UTC (right) on 2 June 2004. Observed wind speed profiles from Texas Tech boundary layer profiler are depicted as solid gray lines. Note that the profiler observations are not available below 124 m. In order to facilitate the comparisons, 10 m Reese WTM and 124 m profiler wind speed values are joined using the power law relationship (Eq. 8.1) and the observed α values (long-dashed lines in gray). The extrapolated wind speed profiles utilizing the observed 10 m Reese WTM wind speed and the conventional 1/7 power law are also shown as reference (dashed-dotted lines inblack)...... 86 8.5 Wind speed (m s−1) fields from the YSU_rrtm_TX run at 0600 UTC, 2 June 2004. The cross-sections are taken (a) at 1.3 km MSL height; (b) at 0.955 Sigma level ( 350 m AGL); (c) along 33.3o N latitude (line 1 shown ∼ in (a)); and (d) along 102o W longitude (line 2 shown in (a)). The X marks the approximate location of the WISE field site in (c) and (d). The field site is approximately at the intersection of the two white lines in (a). Reference arrow for wind vector is given on the right...... 88 8.6 Observed (5 min. resolution) 10 meter wind speed (m s−1) from WISE mesonet station (solid) and WRF corresponding grid point 10 meter wind speed (m s−1) outputted every hour, valid through 0300 UTC - 1200 UTC, 02June2004...... 89 8.7 (a) Calculated (5 min. resolution) friction velocity (m s−1) and (b) Monin- Obukhov length (L), from WISE mesonet station (solid) and WRF corresponding grid point friction velocity (m s−1) outputted every 30 minutes. Valid through 0300 UTC - 1200 UTC, 02 June 2004...... 89

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8.8 Potential temperature (θ) profiles 0500 UTC - 0900 UTC, 02 June 2004, from (a)YSU_rrtm_TX and (b) MYJ_rrtm_TX for the grid point corre- spondingtotheWISEfieldsite...... 90 8.9 TKE (m2 s−2) profile from MYJ_rrtm_TX between 0300 - 1200 UTC, 02 June2004...... 91 8.10 Simulated and observed wind speed and wind direction for 0000 UTC - 1200 UTC on 02 October 2006. The left column shows wind speed time- height plots (unit: ms−1) of: (a) hourly output from the YSU_rrtm_KS run; and (c) hourly averages from the Beaumont ARM profiler. The right column shows wind direction time-height plots (unit: meteorological degrees) of: (b) hourly output from the YSU_rrtm_KS run; and (d) hourly averages from the Beaumont ARM profiler...... 93

9.1 Top plots represent 12 km terrain elevation (MSL in meters) used for WRF simulations. Lower blowout is 30 m NED used in WAsP. Note the scale for the top plots is not the same as for the lower blowout. The star represents the location of the 100 m tower...... 102 9.2 Yearly 1 km average surface roughness determined from 30 second land use data processed by WPS. The star denotes the location of the 100 m tower. Red squares represent the high surface roughness associated with thecityofSweetwater,TX...... 103 9.3 a) Power density (W m−2) at 100 m AGL estimated with 100 m tower data as input into WAsP, b) estimated power density (W m−2) at 100 m AGL with 100 m WRF data as input into WAsP...... 105 9.4 Top plots are yearly average wind speeds (m s−1) from WRF’s second grid level ( 100 m AGL). Lower blowout is estimated yearly wind speed from ∼ WAsP as 100 m WRF data as input. The star represents the location of the 100mtower...... 108

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9.5 30 m 2001 NLCD land use categories surrounding the 100 m Sweetwa- ter tall tower. Green areas represent shrub land , red represents urban or developed regions, and tan depicts crop land and pasture areas...... 109

A.1 For ﬂow regimes for turbulent ﬂow over a hill (Jackson and Hunt 1975). . . 126

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Chapter 1

Introduction and Motivation

Wind energy in recent years has become a valuable source of energy in the United States (U.S.), especially throughout the Great Plains (i.e., central states such as Texas) and along the west coast. As of early 2008, nearly 17,000 MW of capacity have been installed in the U.S., with a majority of that located in the Great Plains (AWEA 2008). For wind energy to be economically advantageous, accurate predictions and characteristics of the wind speed at turbine hub heights are needed. Accurate predictions and representations would improve site assessment projects, short term forecasting, and adequate turbine designs. A recent event that strengthens the need for accurate forecasting and understanding of the upper-level winds occurred on 26 February 2008. On this day, a sudden decrease in wind generation and higher than anticipated demand due to cool temperatures, all corresponding to the high evening electric demand, forced grid operators within Texas to implement the second stage of an emergency plan (limit power to interruptible customers in order to reduce the power demand by 1,100 MW). The sudden decrease in wind production was unexpected, as multiple power suppliers (both wind based and conventional sources) fell below the amount of power they were scheduled to produce that day. The wind production fell from more than 1,700 MW to 300 MW (80 MW less than scheduled) when the emergency was declared (Rueters 2008). If the wind production had been adequately forecasted on this day, the emergency could have lessened by bringing other power sources online sooner. Obviously other factors such as predicting the demand and availability of non-wind sources are also key factors in implementing a seamless power supply. Wind turbines commonly found in the Great Plains can have blades extending up to 150 m (Table 1.1) above ground level (AGL), with new turbines extending up to 200 m and higher. As seen in Fig. 1.1, the wind speed over the Great Plains in the lowest 200 m has a strong diurnal trend, with large amounts of speed shear during the stable night time hours (i.e., 0000 - 1200 UTC) due to the out-of-phase relationship of the wind speeds near surface and at higher heights (e.g., Crawford and Hudson 1973; Holtslag 1984; Lange and Focken 2005). The anti-phase relationship has also been observed in the Netherlands, as

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data from the Cabauw tower in Fig. 1.2 shows. One reason for the characteristics of the wind proﬁles seen in Fig 1.1, are phenomena referred to as low-level jets (LLJ). LLJs are wind maxima typically centered around 100 m to 1000 m above ground level (AGL) and are frequently observed during nighttime (stable) hours in the Great Plains (e.g., Bonner 1968; Mitchell et al. 1995; Whiteman et al. 1997; Song et al. 2005). While LLJs help make the Great Plains a favorable location for wind power production, they can make it difﬁcult to get an estimate of hub height wind speeds, which is essential for wind resource assessment projects and determining stresses the turbines will be subjected to. As wind turbines continue to grow in height, the impact of low-level wind shear will become more important for not just wind power predictions, but as well for turbine designs.

TABLE 1.1. Characteristics of selected wind turbines commonly found on the Great Plains, including power capacity (MW), rotor diameter (m), hub height (m), and height extent of blades (m).

Turbine Energy Diameter Hub Maximum Manufacturer Capacity of rotors (m) Height (m) elevation of blades (m) Mitsubishi 1 MW 57 – 61.4 45 – 69 99.7 Suzlon 1.25 MW 64 – 66 56 – 74 107 GE 1.5 MW 70.5 –77 61 – 100 138.5 Vestas 1.8 MW 80 60 – 78 118 Gamesa 2 MW 80 – 90 60 – 100 145 Siemens 2.3 MW 93 70 – 80 126.5 Vestas 3 MW 90 100 145

To estimate wind speeds at essential heights aloft for wind energy purposes, it is common practice to use instrumented towers. Since it is unlikely measurements are available at the desired heights, a logarithmic wind proﬁle or power law relationship is assumed to extrapolate measured wind speeds from lower heights up to the hub height and extent of the turbine blades. A method commonly used in wind energy to estimate the upper wind speeds when a wind speed record at a lower height exists is:

z α U(z)= U , (1.1) r z r where Ur is the reference wind speed at a given height, zr, and U(z) is the estimated wind speed at height z. The only unknown in Eq. 1.1 is the shear exponent (α). For α, 1/7 (0.14) is commonly used in wind resource site assessment projects (Archer

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1000 10 m 0000 UTC 14 900 30 m 0600 UTC 100 m 800 1200 UTC 12 192 m 1800 UTC 312 m 700 464 m 10 600 (m)

d (m/s) 500 8 ht AGL Spee 400 nd nd Heig

Wi 6 300

200 4 100

2 0 0 3 6 9 12 15 18 21 24 2 4 6 8 10 12 Time (UTC) Wind Speed (m/s)

FIG. 1.1. Average diurnal wind speed variation at Sumner, KS from the WRF model. (left panel): Diurnal trend of yearly average wind speeds at given levels. (right panel) Yearly average wind speed profiles at specified times. and Jacobson 2003), while a value of 0.2 is used for turbine designs (IEC 2005). For a neutral boundary layer the shear exponent is typically near the value of 1/7. However, it is well known that the boundary layer is rarely neutral, thus the shear exponent will vary over time. The shear exponent is dependent on the atmospheric stability, surface roughness, and the height of the levels under evaluation (e.g., Frost 1947; Sisterson and Frenzen 1978; Irwin 1979; Sisterson et al. 1983). Some wind resource assessors have used the knowledge that α varies and have adapted using values near 0.2 for α. This may be appropriate for some locations, but due to the spatial and temporal variability of the shear exponent (with a large dependence on the strength and frequency of LLJs), this assumption could still be grossly inaccurate. Solely based on short tower measurements ( 60 m and lower), it is difficult to know ∼ what shear exponents to assume when doing site specific resource assessments, short-term predictions, or turbine designs. The main reason for the shear exponent uncertainty is the limited knowledge of how strong and frequent LLJs are at a location. Previous studies have utilized tall towers, typically communication towers, instrumented with anemometers to determine the shear exponent (e.g., Smith et al. 2002; Schwartz and Elliot 2006). As expected, these studies have found that large shear exponents exist during the nighttime hours. However, these studies are limited due to their spatial coverage, and do not provide information of any spatial variability (possibly due to terrain and land use) over the Great 3 Texas Tech University, Brandon A. Storm, August 2008

FIG. 1.2. Wind velocities averaged every half hour at heights of 10, 20, 40, 80, 140 and 200 m (bottom to top; 80 m is in bold) for seasons in 1987 at the Cabauw tower in the Netherlands (Van den Berg 2008).

Plains. A spatial representation of the shear exponent would allow wind resource assessors to use site speciﬁc exponents, improving the estimate of wind speeds at higher heights. If the correct average shear exponent is known, reference wind speeds from short towers can be used to estimate hub height wind speeds by a power law relationship. As mentioned, LLJs are common features over the Great Plains. The high wind speeds associated with LLJs typically make the Great Plains’ wind resources more favorable for 4 Texas Tech University, Brandon A. Storm, August 2008

wind energy production (Sisterson and Frenzen 1978; Kelley et al. 2005). However, the presence of LLJs can significantly increase the vertical shear and nighttime turbulence in the vicinity of the wind turbine hub height, thus have detrimental effects on rotors (Kelley et al. 2004). For example, LLJs can lead to Kelvin-Helmholtz instability due to intense vertical wind shear and temperature gradients below the height of the wind maxima. This instability can generate bursts of turbulence in a relatively quiescent nighttime boundary layer. It is important to emphasize that the existing codes (e.g., the International Electrical Commissions Normal Turbulence Models (IEC 2005)), which traditionally provide inflow conditions for wind turbine design, represent neither strong wind shear nor bursting events associated with stable boundary layers and LLJs. Thus, it is not surprising that suboptimal wind energy generation and turbine failures due to nighttime turbulence have been repeatedly reported in several Great Plains’ wind farms (Kelley et al. 2005; Hand 2003). According to Smith et al. (2002), it is not clear if there is a direct correlation between the high shear at night (associated with LLJs) and the high frequency of fault times (times the wind turbines are intentionally shut down due to a fault indication). However, Fig. 1.3 shows that the highest occurrence of fault times does correspond to times with high shear exponents (well above 1/7). These results are determined dually by tower data from Smith et al. (2002) and output from a mesoscale numerical weather prediction (NWP) model, the Weather Research and Forecasting Model (WRF). Due to LLJs’ significant impact on wind energy, a detailed understanding of the frequency and characteristics of LLJs, and the subsequent low-level shear, is essential for the wind energy community. At present, NWP models face a challenge in forecasting the development, magnitude, and location of LLJs with precision (Banta et al. 2002). This could be partially attributed to our limited understanding and modeling capability of nocturnal stable boundary layers. Recently, a next generation NWP model, the WRF model, was developed by a collaborative effort (Skamarock et al. 2005). Several studies have demonstrated the competence of this model in forecasting severe weather events (Jankov et al. 2005; Kain et al. 2005). However, to date, the capability of this state-of-the-art model in forecasting LLJs is largely undocumented. The present study attempts to fill this void. Once the modeling deficiencies in predicting the LLJs are known, improvements to current modeling approaches can begin. Apart from their role in wind energy generation, LLJs strongly assist in initiation and sustenance of convective weather (e.g., Maddox 1983), pollutant dispersion (e.g., Banta

5 Texas Tech University, Brandon A. Storm, August 2008

0.35 700

0.3 600 s) α) 0.25 500 our

0.2 400 (h

0.15 300 Times ar Exponent ( ar Exponent

Big Springs WRF Fault She 0.1 200 Big Springs Obs. Fault Time 0.05 100

0 0 0 3 6 9 12 15 18 21 24 Hour (UTC)

FIG. 1.3. Diurnal variation of WRF simulated (30 -100 m) and observed (40 - 80 m) averaged wind shear exponents along with turbine fault occurrences from Big Spring, Texas. The fault times and observed shear exponent are reproduced from Smith et al. (2002) using Engauge Digitizer 4.1. et al. 1998), and migrations of birds and insects (e.g., Liechti and Schaller 1999). In the literature, LLJs have also been linked to widespread flooding events (e.g., Arrit et al. 1997). In theory, a LLJ can even cause premature touch-down of an aircraft during landing (e.g., Wittich et al. 1986). Researchers across multiple disciplines are interested in the prospect of having improved modeling capabilities of LLJs. This dissertation attempts to determine if the WRF model can be successful in predicting and simulating low-level wind characteristics for use in wind energy. If the WRF model is found to be reliable in forecasting LLJs and their morphological characteristics, as well as the low-level wind shear, it could potentially reduce (or even replace if the WRF data were dynamically downscaled) the need for expensive observational tall towers in a variety of forthcoming wind energy projects. WRF output could also be used as input into computational fluid dynamics models as well as large eddy simulation models. These models produce fine scale results that might be appropriate to determine fine scale wind patterns in wind farms as well as flow around individual wind turbines. Others are testing the capabilities of running WRF at fine scales

6 Texas Tech University, Brandon A. Storm, August 2008

(100 m and less). These fine scale WRF simulations could adequately provide information needed for the wind energy community if this technique is found to perform well. The next chapter discusses relevant background material. Details about the observational data utilized, as well as the WRF and the Wind Atlas Analysis and Application Program (WAsP) models are presented in Chapters 3, 4, and 5 respectively. Studies determining how well the WRF model predicts LLJs and low-level (0-200 m) speed and directional shear from a climatological standpoint are presented in Chapters 6 and 7. A comparison of various methods to get hub height wind speeds is also presented in Chapter 7 to determine the impact of model output from WRF on wind speed predictions for wind power systems. Two specific LLJ cases are investigated to evaluate the sensitivity of various WRF configurations in Chapter 8. Finally in Chapter 9, outlined and tested is a method of downscaling WRF model output with WAsP, a tool commonly used within the wind energy industry to do resource assessment. If any improvements from the WRF/WAsP combination are obvious compared to current resource assessment techniques and the WRF model alone, this new method could improve wind resource assessment estimates. Parts of Chapter 6 have been submitted to Renewable Energy, while sections of Chapter 8 have been submitted to the journal Wind Energy.

7 Texas Tech University, Brandon A. Storm, August 2008

Chapter 2

Background

In this chapter, relationships describing wind speed and direction proﬁles within the boundary layer will be discussed, as well as how wind speed is related to power. Since large magnitudes of wind speed shear and LLJs are frequently observed over the Great Plains during the nighttime (stable) hours, this chapter will discuss the nocturnal boundary layer and common wind characteristics in this regime. LLJ forcing mechanisms, as well as previous LLJ climatology and modeling studies, are also discussed.

2.1. Power from the wind

Since this study emphasizes the need for accurate wind speeds to get a reliable estimate of the power that a turbine could produce from the wind, the basic fundamentals of converting wind into power are presented. Power that can be removed from the wind is related to the cube of the wind speed, which makes an accurate assessment of wind speeds for wind energy purposes even more important. The power equation in terms of wind speed can be derived from the kinetic energy (E) of ﬂow:

1 E = mu2, (2.1) 2

where m is the mass of the air in a control volume. Power (P ) is deﬁned as energy per dE unit time ( dt ), therefore Eq. 2.1 can be expanded as:

1 dm P = u2, (2.2) 2 dt where u is assumed to be constant and uniform within the control volume. The mass of the volume is equal to the air density times the volume (m = ρ(AL)), where L is the length of the control volume of air, and A is equal to the area of the incoming air (or the area swept out by the turbine blades). If we divide the length of the control volume by unit dm time, L translates into u. From this, it can be concluded that dt = ρAu. Substituting this

8 Texas Tech University, Brandon A. Storm, August 2008

relationship into Eq. 2.2 results in:

1 P = ρAu3. (2.3) 2

This equation gives the power available from the wind given the density of the air and the wind speed. The wind industry commonly uses wind power density (P/A) to categorize the power available at a location. Wind power density is power normalized by one unit area, thus is independent of the size of turbine rotors. Eq. 2.3 however is not the maximum power that can be withdrawn from the wind by turbines. The maximum amount of power that can be withdrawn by a turbine is limited by what is known as the Betz limit, which is based on momentum theory of propellers (Rohatgi and Nelson 1994). The following is based on the discussion presented in Rohatgi and Nelson (1994). The conservation of momentum implies that the mass ﬂow upstream, down stream, and at the turbine would be all the same. Therefore:

ρu0A0 = ρAu = ρA1u1, (2.4)

where u0, u, and u1 denote the wind speed upstream of the turbine, at the turbine, and downstream from the turbine, respectively. It is also assumed that the air density stays constant. Since the turbines extract energy from the wind, slowing the wind down, A1 has to be the largest of these volumes. Based off of the thrust force, it can be concluded that:

u + u u = 0 1 . (2.5) 2

To derive the Betz limit, what is referred to as the axial induction factor needs to be deﬁned: v a = , (2.6) u0 where v is the velocity induced by the disk, or v = u u. The velocity after the turbine 0 − can be written as u = u (1 2a), as the velocity at the turbine is u = u (1 a). To 1 0 − 0 − determine the power that is extracted from the wind by the turbine (Pe), the wind speeds before, at, and after the turbine can be used:

1 P = ρAu(u2 u2). (2.7) e 2 0 − 1

9 Texas Tech University, Brandon A. Storm, August 2008

If the new forms of u and u1 are substituted into Eq. 2.7:

1 P = ρAu3 4a(1 a)2 . (2.8) e 2 0 − Deﬁning the power coefﬁcient (CP ) as:

P C = e , (2.9) P P

2 it can be concluded that Cp = 4a(1 a) . The power coefﬁcient is maximized when dCp dCp − da = 0. Solutions for da = 0 are a = 0 (meaning no power was removed) and a = 1/3. Since 1/3 is the maximizing solution, CP = 0.593. This means the maximum amount of energy that can be extracted from the wind by a turbine is around 60%, also known as the Betz limit. The efﬁciency of actual turbines, however, are not great enough to reach this theoretical limit, with values of 0.5 being the current state of the art. ∼

2.2. Wind proﬁles

As mentioned in Chapter 1, there are logarithmic and power law relationships that can describe the wind speed proﬁle within the surface layer, which is needed to get an estimate of the power available. A formulation that is widely accepted to help describe the wind speed within the surface layer is based on the Monin-Obukov similarity theory, and can be written as: u z z U(z)= ∗ ln Ψ ( ) . (2.10) κ z − m L o u∗ is the friction velocity, zo describes the aerodynamic roughness, Ψm is the stability function, L is the Obukhov length, and κ is the van Karman constant (0.4). While this relationship can provide accurate estimates of wind speeds within the surface layer, knowledge about the stability, which requires data not readily available to those conducting wind resource analysis projects (e.g., turbulence measurements or gradient information), is needed. Since stability data are not readily available in most instances, a simple power law relationship has been accepted as shown in Chapter 1 and repeated here:

z α U(z)= U . (2.11) r z r 10 Texas Tech University, Brandon A. Storm, August 2008

As mentioned in Chapter 1, 1/7 has been accepted as the value that describes the wind profile in neutral conditions for α. The basis of the 1/7 power law is traced back to flow experiments through smooth pipes conducted by Nikuradse (1932). Nikuradse (1932) found the empirical relationship for flow through smooth pipes (Fig. 2.1) over a large range of Reynold numbers (R) to be:

1 u y n = , (2.12) U r where n varies with the Reynolds number, and U is the free stream velocity. It was found for R = 105, that n = 7, arising to the 1/7 power law.

FIG. 2.1. Velocity distribution in smooth pipes over a range of Renyold numbers (Nikuradse 1932).

Expanding on Nikuradse’s empirical relationship, Schlichting (1968) presents theoretical explanations for why the wind profile would have a shear exponent of 1/7 within the inner layer by using a combination of Nikuradse’s (1932) results and Blasius’ resistance formula (Blasius 1913). To derive the inner layer’s 1/7 power law, the shear stress in the pipe is defined as: 1 τ = λρu¯2, (2.13) o 8 where u¯ is the mean velocity and λ, the dimensionless coefficient of resistance, which is based on Blasius’ emperical equation for smooth pipes, is:

ud¯ −0.25 λ = 0.3164 . (2.14) ν 11 Texas Tech University, Brandon A. Storm, August 2008

ud¯ Here, ν is the kinematic viscosity, d is the diameter of the pipe, and ν is the Reynolds number. By substituting Eq. 2.14 into Eq. 2.13 and replacing d with the radius (r), τo becomes: 7/4 1/4 −1/4 τo = 0.03325ρu¯ ν r . (2.15)

2 2 7/4 Using the knowledge that u∗ = τo/ρ, Eq. 2.15 is equal to ρu∗. Splitting u∗ into u∗ and 1/4 u∗ the following is true: p u¯ u r 1/7 = 6.99 ∗ . (2.16) u ν ∗ 1 u y n Schlichting (1968) then eliminates u¯ by using, U = r , the relationship empirically found by Nikuradse (1932). This can be expanded to: u¯ 2n2 = , (2.17) U (n + 1)(2n + 1)

5 u¯ where n = 7 for R = 10 , as shown earlier. Using this relationship, we know U = 0.8, so Eq 2.16 can be rewritten as: U u r 1/7 = 8.74 ∗ . (2.18) u∗ ν Schlichting (1968) then assumes that Eq. 2.18 is valid for any wall distance y, so Eq. 2.18 simpliﬁes to: u yu 1/7 = 8.74 ∗ . (2.19) u∗ ν Using Eq. 2.19, one can then derive the popular form of the power law. Consider

having two heights, y1 and y2. The ratio of the two wind speeds that correspond to these heights would simplify to: u y 1/7 2 = 2 , (2.20) u y 1 1 assuming ν and u∗ are constant with height. While Schlichting (1968) uses ﬂow that would be described as neutral, it should be noted that this derivation is using ﬂow through smooth pipes, which is not representative of the atmospheric boundary layer since the drag forces from roughness elements would dominate over viscous forces.

12 Texas Tech University, Brandon A. Storm, August 2008

2.3. Nocturnal boundary layers

The nocturnal planetary boundary layer (PBL) over land, which is often stable, plays a vital role in the development of large amounts of wind shear, such as that seen in LLJs. A stable boundary layer develops when the surface cools faster than the overlying air at sunset. This results in a negative heat flux, which transports the heat of the atmosphere downward toward the surface. This decreases the temperature of the lower atmosphere, creating a temperature inversion. Since an inversion is present, large vertical motions that were present earlier in the day are suppressed, leading to a stratified boundary layer (Stull 1988). Above the stable boundary layer is the residual layer, which shares turbulent characteristics of the convective mixed layer (Fig. 2.2). Typically, the stable boundary layer remains turbulent and weakly stratified if significant shear is present. On the other hand, if little shear is present, the boundary layer will have very weak (patchy) turbulence (Mahrt and Vickers 2006). Since no significant vertical mixing is present, the upper portion of the boundary layer can decouple from the frictional effects at the surface. The decoupling effect allows outer layer wind speeds to accelerate and become unbalanced (e.g., possibly supergeostrophic).

FIG. 2.2. Typical boundary layer regions over land with relative times of occurrence (Stull 1988).

13 Texas Tech University, Brandon A. Storm, August 2008

2.4. Low-level jets

Since LLJs are a large source of speed and directional shear, as well as increasing low-level wind speeds, discussions about forcing mechanisms and previous observational studies are highlighted. a. Forcing mechanisms

Over the past ﬁfty years, several physical mechanisms were proposed in the literature to explain the development and intrinsic characteristics of LLJs. They include: inertial oscillations (Blackadar 1957), baroclinicity generated by sloping terrain (Bleeker and Andre 1951; Holton 1967; Lettau 1967), and large scale coupling (Reiter 1963). One mechanism proposed by Blackadar (1957) is based on varying eddy viscosity and is referred to as the inertial oscillation. Decoupling of the outer boundary layer from the friction layer allows the ageostrophic wind in the friction layer to rotate due to the Coriolis force, while the geostrophic portion stays the same. This inertial oscillation induced by the Coriolis force then leads to supergeostrophic wind speed. The supergeostrophic wind speed can be described by solving the momentum equations for a deviation in the geostrophic wind (Blackadar 1957). Solving these equations for the nighttime components of the wind speed result in (Stull 1988):

U = U + F sin(f t) F cos(f t) (2.21) night g uday c − vday c

V = V + F cos(f t) F sin(f t). (2.22) night g uday c − vday c

Fuday and Fvday represent the initial departure of the wind from geostrophic balance (due to friction and the Coriolis force), and fc is the Coriolis parameter. According to Blackadar (1957), this departure will remain constant but rotate clockwise with time in the northern hemisphere. The observed jet will have a speed equal to the vector sum of the oscillation and mean wind. While inertial oscillations have been believed to be dominant during the stable hours over the Great Plains, based on proﬁler data in southern Kansas, Lundquist (2003) found that inertial motions do not have a strong diurnal variability or have a preference for the lower levels. Lundquist (2003) states that Coriolis inﬂuenced accelerations probably do occur during and after the evening transition, but inertial motions at this time rarely occur

14 Texas Tech University, Brandon A. Storm, August 2008

in layers resolved by boundary layer wind profilers (i.e., 60 m and lower). The motions would also be required to have a duration longer than an hour to be depicted by the profilers since the profiler was based off of hourly averages. Sloping terrain can also force LLJs due to the effects of baroclinicity, as proposed by Bleeker and Andre (1951) and further analyzed by Holton (1967) and Lettau (1967). Over sloping terrain, horizontal temperature gradients will form due to the effects of diurnal heating (Stull 1988). The air near the surface over the high terrain is warmer than the air well above the surface over the lower terrain at midday due to the adiabatic lapse rate (Fig. 2.3a). So for any plane at a constant height above sea level, a temperature gradient will be present. Once radiation cooling begins at sunset, air near the surface over the high terrain is cooler than than the air well above the surface over lower terrain (Fig. 2.3b). Such a horizontal temperature gradient can cause a change in the geostrophic wind with height due to the thermal wind relationship as given by Holton (1972):

∂U g ∂T g = (2.23) ∂z −fcT ∂y ∂V g ∂T g =+ , (2.24) ∂z fcT ∂x where Ug and Vg are the geostrophic wind components, g is gravity, and T is the temperature. Assuming a southerly geostrophic wind, and warmer air to the west over higher terrain during the daytime hours, the southerly geostrophic wind decreases with height. Including the frictional effects, a subgeostrophic LLJ can form. The forcing of the daytime LLJ from sloping terrain is not very common since vigorous mixing in the convective boundary layer tends to mix out the LLJ cores with adjacent layers (Stull 1988). The nighttime temperature gradient results in a reversal of the thermal wind shear at low levels in the stable boundary layer, while the thermal wind shear aloft is unchanged. If a southerly surface geostrophic wind is assumed, a jet like feature will occur since the thermal wind shear in the low-levels is also southerly (Fig. 2.3), while aloft the thermal wind shear is unchanged and from the north (Stull 1988). Synoptic weather patterns have also been linked to the formation of LLJs (e.g., Chen and Kpaeyah 1993; Djuric and Damiani 1980; Djuric and Ladwig 1983; Uccellini and Johnson 1979; Uccellini 1980). A relationship between upper-level jet streaks and LLJs was proposed by Reiter (1963). The importance of the lee trough has also been mentioned as a key factor, which can be a response to an upper level jet streak. Several studies have 15 Texas Tech University, Brandon A. Storm, August 2008

FIG. 2.3. Diurnal oscillation of the LLJ due to thermal wind (T.W. in the ﬁgure) forcings over sloping terrain (Stull 1988). mentioned the importance of the isallobaric wind, which would be in response to the development of the lee trough. LLJs that are forced from synoptic conditions would have a minimal diurnal oscillation, and the depth of the jet tends to extend above the top of the PBL since the wind maxima are associated with non-boundary layer features. LLJs can also have a northerly direction, compared to the southerly direction of the LLJs forced by the sloping terrain and intertial oscillation. The northerly direction LLJs are typically associated with cold fronts, with a domination during the winter months (Song et al. 2005). While no one forcing mechanism can explain every LLJ occurrence, each mechanism mentioned has merit and contributes to the formation of LLJs. The various forcing

16 Texas Tech University, Brandon A. Storm, August 2008 mechanisms may also play a role in the height of the LLJ. This is an area that needs to be further investigated. In most instances, the Great Plains’ LLJs can be explained by the following summary. Over the United States’ Great Plains, LLJs are quite common during nighttime stably stratiﬁed conditions. Under stable stratiﬁcation, turbulence is usually generated by shear, but destroyed by negative buoyancy and viscosity. Because of this competition between shear and buoyancy effects, the strength of mixing in nighttime stable boundary layer is typically weak. Lack of vertical mixing sometime leads to decoupling of the outer (Ekman) boundary layer (Garratt 1992) from the inner (surface) layer. This decoupling allows the outer layer wind speed to accelerate, since no surface friction is felt, and to become a (supergeostrophic) low-level jet. The existence of mild sloping terrain over the Great Plains further increases the strength of these jets, as well as the synoptic scale lee trough. b. Low-level jet observation studies over the Great Plains

Several studies have attempted to construct a climatology of LLJs over the Great Plains (e.g., Bonner 1968; Whiteman et al. 1997; Song et al. 2005; Mitchell et al. 1995). Knowledge of the frequency of LLJs is important for the wind energy industry to take into consideration during the design process of turbines, as well as their placement. However, reasonably large discrepancies exist between these observational studies when comparing the frequency and the average strength and heights of the LLJs. Some of these inconsistencies are due to the differences in the observational platforms utilized in the studies. Bonner (1968) used two years of rawinsonde data from 47 stations with wind speeds reported two times a day, 0000 UTC and 1200 UTC (eight of the stations reported four times a day). LLJs were classified based on three different speed profile critera with height constraints. The first category (LLJ1) Bonner (1968) classified must have a maximum −1 wind speed (Vmax) equal to or greater than 12 m s with a wind speed decrease (∆V ) of at least 6 ms−1 that occurs at the next higher minimum. The LLJ2 category must have a −1 −1 Vmax of 16 m s and ∆V of at least 8 ms . It should be noted that a LLJ classified as a LLJ2, would also be classified as a LLJ1, meaning the classification method is cumulative. −1 −1 Finally, a LLJ3 must have a Vmax of 20 m s and ∆V of at least 10 ms . It should be noted that while Bonner (1968) stated that ∆V should be calculated from

17 Texas Tech University, Brandon A. Storm, August 2008

the next higher minimum, subsequent studies adapted Bonner’s method to calculate ∆V from the lowest wind speed above the jet maximum but below 2 or 3 km, which is not necessarily the next higher minimum. This point will be discussed more in Chapter 6. Bonner (1968) found that a majority of events classiﬁed as LLJs were in the southern Great Plains (i.e., Texas, Oklahoma, and Kansas), as well as many events in the northern Great Plains (Fig. 2.4). He also discovered that 55-60% of the LLJs observed in the Great Plains were during the summer months, with a maximum occuring during August through September. LLJs common in the Great Plains during the summer months typically had a southerly component, were observed during the nighttime hours, and were centered around 800 m AGL (Bonner 1968). The observational frequency in Bonner’s study is of concern given that several LLJ events might have been missed since only two or four soundings per day were used.

FIG. 2.4. Number of LLJ observations from January 1959 – December 1960 at 1200 and 0000 UTC (Bonner 1968).

18 Texas Tech University, Brandon A. Storm, August 2008

Mitchell et al. (1995) used a wind profiler network in their investigation of the Great Plains jet characteristics. They analyzed data during the warm seasons (April -– September) of 1991 and 1992. Mitchell et al. (1995) also found that the predominant direction of the LLJ found over the Great Plains was southerly, with the strongest wind speed locations ranging from northern Oklahoma to Nebraska. Similar to Bonner (1968), they found that LLJs were more common during September than any other warm-season month. It was also found that most of the LLJs formed during 0600 - 0900 UTC, with an average duration of four hours. It is noteworthy that Mitchell et al. (1995) used the 404-MHz profiler system. The vertical resolution of this system is approximately 250 m, fairly coarse, with the lowest useful data reported at 750 m AGL. Since LLJs occur frequently below this height, several LLJ events would have been missed or misrepresented. It is speculated that the coarse vertical resolution could be behind the comparably high ( 1000 m AGL) average jet altitude reported by Mitchell et al. (1995). ∼ Whiteman et al. (1997) investigated the LLJ climatology using high resolution (10 m) soundings released from the U.S. Department of Energy’s (DOE) Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) Cloud and Radiation Testbed (CART) site in northern Oklahoma. The soundings were released either every three or six hours, with two years of data (April 1994 – April 1996) being utilized. Whiteman et al. (1997) found that LLJs were present in 46% of the soundings, with no strong preference to either warm or cold season months (northerly jets are frequently observed during the winter months). It is believed that most of the northerly LLJs are synoptically forced, and are a result of frontal passages (Song et al. 2005). The heights of the jet maxima in the Whiteman et al. (1997) study were most commonly between 300 and 600 m AGL. Song et al. (2005) took advantage of six years of hourly wind profiler data from Atmospheric Boundary Layer Experiment (ABLE) located in southern Kansas to determine the climatology of the LLJ over that region. Investigating the nighttime hours (0200 — 1200 UTC) over the six year period, LLJs were found to have an occurrence rate of 63%, with 72% of those jets being southerly. They found that the average jet speed for the cold season was stronger for both the northerly and southerly jets in comparison to the warm season. An average of 20 and 18 m s−1 for the southerly jet were found for the cold and warm season, respectively. The southerly LLJ was observed most frequently in July, though Song et al. (2005) noted that both the mean altitude and mean wind speed decreased during July through September. Song et al. (2005), in line with previous

19 Texas Tech University, Brandon A. Storm, August 2008

studies, found that LLJs were more common during the nighttime hours, with occurence times increasing after sunset, reaching the maximum wind speed at 0500 UTC, and then starting to decrease after 0800 UTC. Song et al. (2005) also found a correlation between jet height and speed. A stronger LLJ was most likely to occur between 300 — 400 m AGL, while a weaker jet often forms between 200 — 300 m AGL. Banta et al. (2002) found similar results as well (Fig. 2.5).

FIG. 2.5. Scatter diagrams of LLJ speed versus height for LLJs below 300 m. Middle line represents best-ﬁt linear regression (R = 0.50) and upper and lower lines are for 1 standard deviation (Banta et al. 2002). ±

Being able to use three different proﬁlers arranged in a triangle with 60 km sides, as well as the data set from Whiteman et al. (1997), Song et al. (2005) determined that the mean LLJ altitude was roughly equipotential (not terrain following) rather than parallel to the terrain elevation, corroborating ﬁndings by Banta et al. (2002). LLJs have also been investigated from the stand point of limited case studies, or relatively short time periods. For example, several studies have investigated turbulence characteristics that correspond to LLJ events, and rely heavily on Cooperative Atmosphere-Surface Exchange Study (CASES) data (e.g., Banta et al. 2002, 2003, 2006, 2007). Banta et al. (2002) showed that LLJs can create turbulent kinetic energy (TKE) and 20 Texas Tech University, Brandon A. Storm, August 2008

FIG. 2.6. (a) TKE and (c) the vertical flux of TKE for the night of 20–21 October 1999. (b) TKE and (d) the vertical flux of TKE for the night of 24–25 October 1999. In (c) and (d) negative values imply downward mixing of TKE (Banta et al. 2002). result in a downward transport of this energy (Fig. 2.6). This TKE could have implication for wind turbine designs and performance as indicated in Kelley et al. (2004). Arrit et al. (1997) and Wu and Raman (1998) also investigated LLJ’s impact on the widespread flooding that occurred within the Midwest during the summer of 1993. They found that LLJs were a major contributor in the transport of water vapor and thunderstorm initiation. c. Relevant numerical studies of the Great Plains low-level jet

Most of the previous modeling works have focused on investigating the forcing mechanisms of LLJs (e.g., Fast and McCorcle 1990; McCorcle 1988; McNider and Pielke

21 Texas Tech University, Brandon A. Storm, August 2008

1981; Zhong et al. 1996; Wu and Raman 1997). Some of these numerical studies further investigated the sensitivities of LLJ evolution to topography, land-surface heterogeneity, soil moisture, etc. Zhong et al. (1996) studied the sensitivities of the LLJ evolution to topography, soil moisture, and other effects by utilizing the Regional Atmospheric Modeling System (RAMS). They compared a 48 hour RAMS forecast of a LLJ over Oklahoma and Kansas centered between 700 - 1000 m AGL to the National Oceanic and Atmospheric Administration (NOAA) wind profiler network and nearby soundings. RAMS was able to simulate the LLJ using a 25 km nested domain and a vertical resolution of 30 - 200 m in the lowest 1km of the atmosphere. Since the LLJ being simulated was predominantly synoptically forced, it is not surprising that such a coarse grid resolution could represent the major features of the LLJ. Zhong et al. (1996) did not find a significant difference between using a 25 km resolution topography data set compared to a 100 km resolution set. At these resolutions, the fine scale variability of the topography that can influence LLJ heights and strength is most likely not being represented. These coarse model grids to represent the LLJ are valuable to evaluate the theoretical forcing mechanisms for the LLJ, but not very useful for wind energy purposes which need fine scale details and variabilities. Others have studied the ability of NCEP-NCAR reanalysis data (Kalnay and Coauthors 1996) and global climate models to simulate the LLJ climatology (e.g., Helfand and Schubert 1995; Ghan et al. 1996; Higgins et al. 1996; Anderson and Arrit 2001). Anderson and Arrit (2001) used the NCEP-NCAR reanalysis data, which have a 210 km horizontal grid spacing, 10 levels below 3 km, and output available every 6 hours. This data were compared to the national profiler network (NPN) of 404-MHz Doppler profilers within the central U.S.. Anderson and Arrit (2001) utilized data from June, July, and August over 7 years (1992-1998). It should be noted that the resolution of both the profiler and the model used in this study were coarse and had grid spacings that would cause low altitude LLJs (such as those observed in Song et al. (2005)) to be missed, making this data set unconducive to wind energy applications. Anderson and Arrit (2001) found that the reanalysis data reproduced the same spatial extent of the LLJs in the central U.S. as compared to that found in the NPN. However, the spatial representation in the lee of the Rocky Mountains by the reanalysis data was slightly less extensive compared to what was observed. While the reanalysis data showed promise in reproducing the spatial extent of LLJs, the frequency of LLJ1 was lower than what was found in the NPN dataset and

22 Texas Tech University, Brandon A. Storm, August 2008 nearly no occurrences of LLJ3.

23 Texas Tech University, Brandon A. Storm, August 2008

Chapter 3

Description of Observational Data Utilized

Various sources of observational data are used to validate numerical modeling results. The main sources are: the Department of Energy (DOE) Atmospheric Radiation Measurement (ARM) program proﬁler near Beaumont, Kansas, the Reese West Texas Mesonet (WTM) ﬁeld site located west of Lubbock, Texas, a 100 m tall tower (part of Texas tall tower project) near Sweetwater, Texas, various tall tower data throughout the Southern Great Plains analyzed by Schwartz and Elliot (2006), and surface observations provided by the National Weather Service (NWS). Details about each data source are presented in the following sections.

3.1. ARM proﬁler

The ARM program has been collecting data essential for improving cloud and radiative models and parameterizations at the SGP CART in south-central Kansas and north-central Oklahoma since 1997. In addition, ARM has measurement sites that are part of the ABLE facility, which is located in the Walnut River watershed (Fig. 3.1 and 3.2). The purpose of the ABLE facility is to provide essential data to further the knowledge of atmospheric boundary layer processes. Several field campaigns have been centered in this region, including CASES in both 1997 and 1999. The ABLE site includes several 915 MHz wind profilers, though the profiler located near Beaumont, Kansas is the only one utilized in this study. The Beaumont profiler was selected for analysis in Chapter 6 since it was the same location Song et al. (2005) used. Though not utilized in this study, the 915 MHz wind radar profiler is also equipped with a radio acoustic sounding system (RASS) that measures virtual temperature profiles. The profiling system at Beaumont measures the wind speed by transmitting electromagnetic energy upward, and measuring the strength and frequency of the backscattered energy. The backscattered energy varies due to fluctuations in the refractive index, primarily due to perturbations in water vapor concentration that move with the mean wind. The wind velocity can then be determined from the Doppler shift in the

24 Texas Tech University, Brandon A. Storm, August 2008

FIG. 3.1. Location of the ARM SGP CART and topography of the Walnut River Watershed along with the relative location of the 915-MHz radar wind profiler near Beaumont (BE) Kansas (Song et al. 2005). frequency of the backscattered energy, with an accuracy of 1 ms−1 (Coulter et al. 1999). To determine the three dimensions of the wind field (i.e., u, v, and w), the radial components of motion are determined from one vertical beam, and four offset beams (tilted at 14 degrees from vertical that measure to the south, north, east, and west). Since the radial components of motion are determined sequentially (30-45 seconds for each direction), and it cycles through two power phases (low and high power), around five minutes are required for each phase. Each phase is then averaged over one hour periods, with data from the last 50 minutes of the hour being used to form the wind speed profile averages, and the first 10 minutes are used to determine the temperature profile (Coulter 2005). As mentioned, two different power outputs are transmitted, and are referred to as low-power and high-power. These different power levels result in different range gate spacing and heights available for analysis. The low-power mode (used in Chapter 6 and 8) has a vertical resolution of 60 m between 150–2,000 m AGL. The first level is reported around 90 m, but due to the quality and unreliability of these data, it is normally discarded. The high-power mode has a range gate of 200 m, and operates between

25 Texas Tech University, Brandon A. Storm, August 2008

200–5,000 m. Unlike Song et al. (2005), no mini Sodar data were available during the time period of interest (April 2006 – March 2007) to supplement the 915 MHz profiler and get data in the lowest 150 m (Coulter 2005). Even though no wind data below 150 m AGL are available from 915 MHz radar profilers, the resolution is significantly improved over the NPN’s 404 MHz wind profilers. Another benefit of the 915 MHz profiler over the 404 MHz is that there is less signal contamination (e.g., migrating birds). This is due to the smaller beamwidth and pulse volume of the 915 MHz profiler (Song et al. 2005). When precipitation is present, neither profiling system can accurately provide wind speed estimates.

3.2. West Texas Mesonet ﬁeld site

Chapter 8 uses data from the WTM to validate numerical modeling results. The WTM consist of over 50 automated surface meteorological stations, as well as the field site located at the former Reese Air Force Base. The WTM field site includes an instrumented 200 meter tower, a boundary layer profiler, and the Reese Mesonet station (Fig. 3.2). Due to questions regarding the quality of the 200 meter tower data during periods of interest, these data were not rigorously compared to the model results and will not be presented. The WTM boundary layer profiler, a Vaisala LAP-3000 915 MHz Doppler radar vertical profiler (Schroeder et al. 2005), has a vertical resolution of 55 meters, with the first level reported at 124 m AGL, and an output of 30 minute averaged data. The WTM profiler operates under the same principles as the ARM 915 MHz profiler discussed in the previous section. Data below 1 km AGL were mainly utilized in this study due to loss of data above this level. Unfortunately the RASS system used to determine temperature profiles was not functioning during the time of interest. The 50+ automated surface meteorological stations (10 m tall towers) have an average spacing of 35 km. Each surface station measures up to 15 meteorological (e.g., wind speed, wind direction, temperature, humidity, barometric pressure, precipitation and solar radiation) and 10 agricultural (e.g., soil moisture and soil temperature) variables every 5 and 15 min, respectively (Schroeder et al. 2005). Utilized in Chapter 8 are 5 minute averaged values from the temperature sensors (Campbell Scientific 107 temperature probes) at both 2 and 9 meters AGL, along with wind monitors at 2 and 10 meters AGL (R.M. Young 030103 Wind Sentry and R.M. Young 05103 Wind Monitor, respectively), and a barometric pressure sensor (Vaisala PTB220 Class B digital barometer). The 26 Texas Tech University, Brandon A. Storm, August 2008 temperature and wind data were used to calculate upward sensible heat flux, friction velocity, and Monin-Obukhov length based on similarity theory.

3.3. Sweetwater 100 m tall tower

Tall tower data acquired from West Texas A&M University’s Alternative Energy Institute (AEI) is used in Chapter 9 to determine the performance of proposed numerical modeling techniques. The AEI data consists of wind speeds and wind directions at 50 and 100 m, as well as wind speed at 75 m, from a tower located near Sweetwater, Texas (Fig. 3.2). Two wind speed measurements, captured from NRG # 40 3-cup anemometers, are provided at each level. It is assumed multiple sensors were placed on the tower to mitigate interferences from the tower. Since no information is available on the tower conﬁguration and it is not known which sensor to use for which direction, the two wind speeds at the same level were averaged together. The wind direction is measured from a NRG 200P wind direction vane. The raw data ﬁles include 10 minute averages, though hourly averages computed by AEI using NRG’s Symphonie Data Retriever were used.

3.4. Tall tower data from NREL

Data analyzed by Schwartz and Elliot (2006) are used for comparison to modeling results in Chapter 7. Average shear exponents (diurnal and yearly) from 13 towers throughout the the southern Great Plains, as well as one location in both South Dakota and North Dakota, were presented by Schwartz and Elliot (2006). The data from the towers in South Dakota and North Dakota were not used for comparison, and will not be discussed in any more detail. Geographical locations of each tower were provided personally by Schwartz and Elliot (Fig. 3.2), which allows accurate comparison of modeling results. The towers Schwartz and Elliot (2006) used were typically pre-existing communication towers, all over 70 m. The time period and level of measurements varied and can be found in Table 3.1. Details about instruments installed on each of these towers are not available, though it is assumed that appropriate quality control and assurance techniques were implemented. The authors also noted that the reporting times of the instruments were not all the same, though most of them reported 10 minute average values (Schwartz and Elliot 2008, personal communication). It should be noted that one of the towers utilized by Schwartz and Elliot (2006) is the same tall tower located near

27 Texas Tech University, Brandon A. Storm, August 2008

Sweetwater previously discussed, though the times analyzed differ.

TABLE 3.1. Site locations, heights of measurements, and dates analyzed by Schwartz and Elliot (2006). Heights in parentheses were not used by Schwartz and Elliot (2006).

Site Name Anemometer Heights From To Lamar, CO (3) 52 113 10/5/2001 9/16/2003 Ellsworth, KS 50 (80) 110 4/18/2003 9/2/2005 Kearny, KS 50 80 (110) 4/29/2003 9/2/2005 Sumner, KS 50 80 (110) 6/11/2003 9/2/2005 Jewell, KS 50 (80) 110 4/23/2003 9/4/2005 Ness, KS 50 (80) 110 6/4/2003 9/3/2005 Logan, KS 50 80 (110) 5/1/2003 9/3/2005 Hobart, OK 40 70 (100) 4/1/2002 12/31/2003 Elk City, OK (10) 40 70 (100) 10/30/2003 8/31/2005 Sweetwater, TX 50 (75) 100 5/17/2003 3/2/2005 Washburn, TX 50 75 (100) 9/5/2003 10/3/2005

3.5. NWS surface observations

Wind speed measurements at 10 m at the Sweetwater Airport (32.467o N latitude and 100.500o W longitude) (Fig. 3.2) were obtained from NWS Automated Surface Observing System (ASOS). These data were used as an input into WAsP. Sweetwater ASOS 20-minute data were obtained from the National Climatic Data Center (NCDC). Data from ASOS stations are subjected to rigorous data quality control and assurance algorithms (Lott et al. 2001), and are considered to be of high quality.

28 Texas Tech University, Brandon A. Storm, August 2008

o 42 N

40 oN Jewell Logan Ellsworth 38 o Ness N Lamar ARM Profiler Kearny Sumner

36 oN Elk City Washburn Hobart o 34 N WTM Field Site Sweetwater ASOS o 32 N Sweetwater

o o o o 104 W 102 W 100oW 98 oW 96 W 94 W

FIG. 3.2. Locations of all of the observational data used in this study. Stars denote locations of Schwartz and Elliot (2006) tall towers, the square denotes the location of the ARM proﬁler, the airplane represents the location of the Sweetwater ASOS station, and the circle is the location of the WTM ﬁeld site.

29 Texas Tech University, Brandon A. Storm, August 2008

Chapter 4

The Weather Research and Forecasting (WRF) Model

Note that the material covered in this chapter is heavily based on Skamarock et al. (2005) and the ARW Users Guide (Wang et al. 2005).

4.1. WRF overview

The WRF model was developed by a collaborative effort, including the National Center for Atmospheric Research (NCAR) Mesoscale and Microscale Meteorology (MMM) Division, NOAA’s National Centers for Environmental Prediction (NCEP) and Earth System Research Laboratory (ESRL), the Department of Defense’s Air Force Weather Agency (AFWA) and Naval Research Laboratory (NRL), the Center for Analysis and Prediction of Storms (CAPS) at the University of Oklahoma, the Federal Aviation Administration (FAA), along with the participation of a number of university scientists (Skamarock et al. 2005). Two different dynamical cores are available for use, the Advance Research WRF (ARW) and the Nonhydrostatic Mesoscale Model (NMM) WRF. In this study the ARW WRF, which is primarily developed at NCAR, is utilized and will be discussed in more detail. It will be referred to simply as the WRF model throughout this dissertation. Several versions of WRF have been issued since WRF’s first release, with version 2.2 being analyzed and discussed herein. The WRF model was developed with several applications in mind, including: idealized simulations, parameterization research, data assimilation research, forecast research, coupled-model applications, and real-time NWP. The WRF model is also unique in its module design. This allows easy combination of various physics packages independent of the core. The WRF model is also designed to be efficient, and work well in parallel computing environments. This high efficiency allows for fine scale model grids to be computed within relatively small amounts of time. The overall WRF code maintained by MMM includes several components, which includes the WRF Software Framework (WSF), the ARW solver, the WRF Preprocessing System (WPS), WRF Variational Data Assimilation (WRF-Var), and numerous physics packages contributed by WRF partners

30 Texas Tech University, Brandon A. Storm, August 2008 and the research community (Fig. 4.1) (Skamarock et al. 2005; Wang et al. 2005). Once the WRF model has created the output ﬁles, various options exist post for viewing and analyzing the data. Popular options include using ARWpost (GrADS), NCL graphics, RIP-4, or any other software capable of reading Netcdf ﬁles (e.g., Matlab or IDL). ARWpost combined with GrADS, along with Matlab was used to view and analyze the WRF output in this study. While WRF has the capabilities to perform idealized simulations, this discussion will be focused on WRF’s real data abilities.

FIG. 4.1. WRF framework ﬂowchart (Wang et al. 2005).

31 Texas Tech University, Brandon A. Storm, August 2008

4.2. WRF Preprocessing System (WPS)

The WPS is responsible for defining the location and grid spacing of the desired model domain (including nests), interpolating static data (i.e., terrain, landuse, soil types) to the desired grid spacing, and degribbing and horizontally interpolating meteorological data from another model or data set (i.e., NARR, GFS, NAM) onto the domain. These processes are accomplished through three steps referred to as geogrid.exe, ungrib.exe, and metgrid.exe. Grids with decreasing resolutions, referred to as nests, can be placed within the coarse grids, either with or without feedback to the coarse grids. The static fields typically have a resolution of 10’, 2’, or 30”, though these are interpolated by geogrid.exe onto the user’s selected grid spacing. Therefore, if the model domain has a resolution of 12 km, there is no benefit of selecting 30” over the 2’ data since the higher details of the 30” will be smoothed out. On the other hand, if the horizontal resolution of the domain is a fine scale (e.g., 1 km and less), the static high resolution data is beneficial. If a nested high resolution domain exists inside a coarser grid, different static resolution data sets can be used appropriately. The preexisting meteorological data used by the ungrib.exe and metgrid.exe programs to make the files that will be processed further by real.exe can vary in resolution and time availability. This study uses 40 km Eta grib data produced by NCEP, available every 6 hours to create the boundary condition files. The WPS is essentially responsible for preparing the input data for the real.exe program, or the real data initialization program. The real.exe program vertically interpolates the meteorological fields produced by metgrid.exe to the defined eta levels within WRF. More discussion about WRF’s model heights will be presented later in this chapter. The real.exe program creates the initial and boundary condition files needed for the WRF model itself. The time frequency of the boundary condition files are based on the availability of the input data, but is typically set to either every 3 or 6 hours. Once all of the input and static data has been processed by the WPS system and real.exe, the ARW solver is implemented. Specific details about the techniques and options within the ARW solver will be discussed next.

32 Texas Tech University, Brandon A. Storm, August 2008

4.3. WRF details

WRF is an fully compressible Euler non-hydrostatic (with a hydrostatic option) model. The time integration is a 3rd order Runge-Kutta, with smaller time steps for the acoustic and gravity-wave modes. The spatial discretization in horizontal and vertical can be selected anywhere between a 2nd to 6th order advection option (Skamarock et al. 2005). The WRF model also has turbulent mixing filters. This includes the subgrid scale turbulence formulation in both coordinate and physical space. Divergence damping, external-mode filtering, vertically implicit acoustic step off-centering, with an explicit filter option are also available. The diffusion options select how the derivatives used in terms of diffusion are calculated. This is accomplished by selecting two parameters within WRF, the “diffusion” and “K” option. Two different approaches have been undertaken in this paper, turning off the diffusion options (Chapter 8), and selecting the diffusion to be evaluated as a 2nd order (Chapters 6, 7, and 9). If the diffusion option is not turned off, the K option selects how the diffusivity coefficients are calculated. Since a PBL scheme is utilized throughout this study, the K option only evaluates the horizontal diffusion, as the vertical diffusion is performed by the PBL scheme. For the WRF simulations that used the diffusion option, a horizontal Smagorinsky first order closure was used. There are 3-D diffusion options available if no PBL scheme is selected. The WRF model uses an Arakawa C-grid, which is a staggered grid (Fig. 4.2). The mass variables are defined in the middle of the grid, while the wind components are defined on the edge of the grids. To compute the wind speeds for the center of the grid points (where the 10 meter wind and 2 m temperature, etc. variables are defined), the U and V variables are interpolated onto the center of the grid. The vertical grid also uses the staggered grid (Fig. 4.2). The WRF model uses a terrain-following hydrostatic-pressure vertical coordinate denoted by η (Fig. 4.3). The coordinates are defined as:

(P P ) η = h − ht , (4.1) µ where µ = P P and P is the hydrostatic pressure at the surface and P is the hs − ht hs ht hydrostatic pressure at the top of the model domain. The heights selected to be used can either be speciﬁed by giving the desired η levels or by selecting how many vertical levels the user wants. If the user does not specify the η levels, then an automated algorithm is

33 Texas Tech University, Brandon A. Storm, August 2008

FIG. 4.2. Horizontal and veritcal grids of the ARW WRF (Skamarock et al. 2005). used to select the placement of these levels. This algorithm will not place more than 7 levels within the lowest 2 km. Since the model output is reported on the η levels, the ground relative heights are calculated from the geopotential heights. The grid spacing of the vertical levels is also not constant; rather, it stretches with height. The WRF model also has several options for various physics needs, including microphysics, cumulus, land-surface, PBL physics, and radiation parameterizations. Since the PBL schemes in WRF have the largest impact on the wind speed within the lowest 1 km AGL, a discussion about the purpose of the PBL schemes, as well as details about two common schemes are presented. According to Skamarock et al. (2005), the PBL schemes in WRF represent the vertical subgrid-scale fluxes due to eddy transports in both the boundary layer and the free atmosphere overlying it. How this is represented can vary from scheme to scheme, and will be discussed in more detail later in the following subsections. In general, the PBL schemes are responsible for determining the flux profiles within the boundary layer, while the surface fluxes are determined by the surface layer and land-surface schemes. The flux profiles provide the atmospheric tendencies of temperature, moisture, and horizontal momentum (Skamarock et al. 2005). PBL schemes in WRF are one-dimensional and assume a clear scale separation between subgrid eddies and resolved eddies. Once the grid

34 Texas Tech University, Brandon A. Storm, August 2008

FIG. 4.3. WRF η levels (Skamarock et al. 2005). spacing becomes small enough, boundary layer eddies can be resolved (few hundred meters), and the above assumption may not be valid. When using a ﬁne grid, a fully three-dimensional local subgrid turbulence scheme may be more appropriate (Skamarock et al. 2005). Two PBL schemes in the latest version of WRF are supported, Yonsei University (YSU) PBL (Hong et al. 2006) and Mellor-Yamada-Janic (MYJ) PBL (Janjic 1990, 1996, 2001; Mellor and Yamada 1974, 1982). Another PBL scheme available in WRF is the Medium Range Forecast Model (MRF) PBL. The YSU PBL is the latest revision of the MRF, thus thought superior over the MRF. The YSU and MYJ PBL models also use slightly different surface-layer schemes, but both are based on Monin-Obukhov similarity theory (Skamarock et al. 2005). The YSU and MYJ PBL schemes will be discussed in detail in the next two subsections.

35 Texas Tech University, Brandon A. Storm, August 2008

a. YSU PBL

The YSU PBL uses a parabolic non-local-K mixing in the dry convective boundary layer (Skamarock et al. 2005). With unstable and neutral conditions, the depth of the PBL is defined using a critical bulk Richardson number of zero. This means the PBL depth is dependent on the buoyancy profile and is determined by the thermal profile. Skamarock et al. (2005) states that this method typically lowers the calculated PBL top compared to the MRF since the MRF uses a bulk Richardson number of 0.5 instead of 0. The YSU also has an explicit treatment of the entrainment process at the PBL top, which is proportional to the surface buoyancy flux. This entrainment process is to account for the MRF’s over-mixing. However, in the stable conditions typically found during the nighttime hours when LLJs are common, the YSU uses the same formulas for the boundary layer as it uses for the free atmosphere, a local diffusion scheme (Hong et al. 2006). Therefore, it sets the PBL height to 0, though it is not implying the actual PBL top is at the surface. In the free atmosphere, the vertical diffusion depends on the local value of the Richardson number

(Rig). The local vertical diffusivity coefficients for momentum (m) and heat (t) are represented by: ∂U K = l2f (Ri ) , (4.2) m_loc,t_loc m,t g ∂z where l is the mixing length, and fm,t(Rig) are the stability functions. The stability functions for stably stratified free atmosphere are defined as

1 (4.3) fm,t(Rig)= 2 , (1+5Rig)

where Rig in a noncloudy layer is given as

g ∂θ /∂z Ri = v . (4.4) g θ (∂U/∂z)2 v The Prandtl number for stably stratiﬁed free atmosphere is deﬁned as:

P r = 1.0 + 2.1 Ri . (4.5) ∗ g Slight modiﬁcations to the YSU scheme will be implemented in the next release of WRF (version 3). The modiﬁcations will help address problems of too little mixing seen 36 Texas Tech University, Brandon A. Storm, August 2008

at night when there is strong enough wind and the Richardson number is low.

b. MYJ PBL

The MYJ PBL is a local 1.5-order Mellor - Yamada Level 2.5 turbulence closure model (Janjic 1990, 1996, 2001; Mellor and Yamada 1974, 1982). The upper limit

imposed on the master length scale lM is dependent on the turbulent kinetic energy (TKE), buoyancy, and shear. TKE is represented by e in Equation 4.6.

1 e = (u′)2 +(v′)2 +(w′)2 (4.6) 2 Here the prime variables represent the turbulent perturbations. Typically when discussing the MYJ PBL scheme, TKE is represented by:

q2 q = √2eore = . (4.7) 2

TKE is then governed by the following equation (Mellor and Yamada 1982; Janjic 2001):

d q2 ∂ ∂ q2 l qS = P + P ǫ. (4.8) dt 2 − ∂z M q ∂z 2 s b −

Sq is a constant of 0.2, while Ps and Pb represent the production of TKE via shear and the production/dissipation by buoyancy respectively. ǫ represents the dissipation due to viscosity. These values are expressed by:

∂u ∂v P = u′w′ v′w′ , (4.9) s − ∂z − ∂z ′ ′ Pb = βg w θv , and (4.10) q3 ǫ = . (4.11) B1lM

B1 is a constant determined empirically, while β is a constant of 1/273 and g is the gravitational acceleration (9.8 m s−2). The ﬂuxes in Eq. 4.9 are represented by:

∂u u′w′ = K , (4.12) − m ∂z

37 Texas Tech University, Brandon A. Storm, August 2008

∂v v′w′ = K , and (4.13) − m ∂z ∂θ θ′w′ = K . (4.14) − H ∂z Additionally, the eddy diffusivity coefﬁcients for momentum and heat (same for moisture too) are represented respectively by:

Km = lM Smq, (4.15)

Kh = lM Shq. (4.16)

Here Sm and Sh are the coefﬁcients that modify lM as a function of wind shear and buoyancy. These coefﬁcients are governed by:

S (6A A G )+ S (1 3A B G 12A A G )= A (4.17) m 1 2 m h − 2 2 h − 1 2 h 2

S (1+6A2G 9A A G ) S (12A2G + 9A A G )= A (1 3C ), (4.18) m 1 m − 1 2 h − h 1 h 1 2 h 1 − 1 where A1, A2, B2, and C1 are determined from experimental data. Also, Gm and Gh represent the shear turbulence production and buoyancy production/dissipation term respectively. They are represented by the following:

l2 ∂u 2 ∂v 2 G = M + , (4.19) m q2 ∂z ∂z " #

l2 ∂θ G = M βg v . (4.20) h − q2 ∂z For stable environments, the upper limit length scale is based on the premise that the ratio of the variance of the vertical velocity ﬂuctuations and TKE cannot be smaller than that corresponding to the regime of vanishing turbulence (Skamarock et al. 2005).

38 Texas Tech University, Brandon A. Storm, August 2008

Chapter 5

Overview of WAsP

The Wind Atlas Analysis and Application Program (WAsP), whose sub-models were first developed by the Risø National Laboratory in 1987, is commonly used throughout the world in the wind energy industry to get an estimate of available regional wind resources, to site turbines at specific locations, and to estimate wind farm production (the program incorporates wake losses) (Mortensen et al. 2004). The actual implementation of the sub-models is known as WAsP, which is the software package (Troen and Petersen 1989) that bundles all of the sub-models together. Details about the WAsP model are presented since it is used in Chapter 9 to downscale operational WRF output. WAsP, which is based on the physical principles of flows in the boundary layer and attempts to solve the Navier-Stokes momentum equations, estimates the regional wind climate, as well as the wind speed at any specific location and height. This is done by horizontally and vertically extrapolating a record of wind data within the region using steps that take into consideration elevation or topography changes, land use or classification / surface roughness, and local obstacles (Troen and Petersen 1989). WAsP also attempts to take into consideration stability effects on the wind profile. A discussion about the general concepts incorporated into WAsP and details of how WAsP takes into consideration the effects mentioned before are presented in the remaining parts of this chapter.

5.1. WAsP basics

As mentioned, WAsP can be used to estimate the regional wind climate as well as site specific location of wind turbines. This is accomplished in two main steps: the development of the regional wind climate or wind atlas and the creation of site specific wind climatology (Fig. 5.1). Once the site specific wind climatology is created, characteristics of desired wind turbines (i.e., the power curve) can be used to get estimates of the annual mean energy production. A wind farm can also be simulated, giving the estimated annual energy production of all of the turbines together or separate, taking into

39 Texas Tech University, Brandon A. Storm, August 2008 consideration wake losses upon the turbines (Mortensen et al. 2004).

FIG. 5.1. WAsP ﬂow chart (Troen and Petersen 1989)

The wind atlas is typically created by using a reference wind speed within the general location of the site of interest. The reference wind data can either originate from 10 m

40 Texas Tech University, Brandon A. Storm, August 2008

wind speed and directional data from NWS ASOS stations or other preexisting surface observations as well as data from towers erected by the interested investors. The height of these towers can vary, but they are normally 60 m or shorter. A time period of at least a year of measurements is also desired. According to Frank et al. (2001), WAsP is a linear flow model for neutrally stratified flow that does not account for Coriolis accelerations. WAsP can only simulate flow over weak to moderately steep terrain on scales of less than a few kilometers distance. This is one reason why it is important to have a wind record within a relatively close proximity to the site of interest. The observed data are processed with what is called the “observed wind climate (OWC) wizard.” The output from the OWC wizard is a wind rose with information about the wind speed distributions in different sectors (12 sectors is the default). The OWC also computes the Weibull distribution parameters for each sector. The Wiebull distribution is expressed as (Troen and Petersen 1989):

k u u f(u)= ( )k−1exp ( )k . (5.1) A A − A Here f(u) is the frequency of occurrence for the wind speed u, A is the scaling factor, and k is the shaping factor. Once the observed wind climate has been generated, it needs to be “cleaned” of local conditions in order to generate the regional wind climate. This is when the techniques that take into consideration sheltering effects from obstacles, surface roughness, topography, and stability are incorporated. The regional wind climate represents standard conditions (ﬂat terrain with no obstacles and given surface roughnesses) in terms of the A and k parameters (as well as mean wind speed and power density) for 12 azimuth sectors with 4 standard roughnesses and 5 standard heights. This data set can then be used to estimate the wind speed and power density distribution for any location and height within the vicinity of the regional wind climate. This is accomplished by taking the inverse technique used to generate the regional wind climate. To do so, detailed descriptions of the local terrain, surface roughness, and obstacles are needed for the region around the site of interest. Considering the relatively simplistic approach in estimating the wind speed for a speciﬁc site, WAsP does well in predicting the annual energy of turbines. It is reported that the typical errors in terms of annual energy prediction for WAsP are about 10% (Frank et al. 2001). Though, due to the methods used to account for topography, larger errors should be expected for regions that have complex terrain, which will be discussed 41 Texas Tech University, Brandon A. Storm, August 2008

more later in this chapter. When WAsP uses the generated wind atlas to predict for the same location where the original data were measured (known as self-prediction), errors of less than 2% have been reported as common (Frank et al. 2001).

5.2. WAsP module speciﬁcs

As mentioned before, WAsP calculates the local wind climate or atlas by taking into consideration the local topography, surface roughness, obstacles, and atmospheric stability. Details on how WAsP creates the regional and site speciﬁc wind climates based on these principals is now presented. The details rely mainly on material presented in the European Wind Atlas (Troen and Petersen 1989).

a. Topography

A general expression for the relative speed-up at the crest of a hill is

u u ∆S = 2 − 1 , (5.2) u1 where u1 and u2 are the wind speeds at the same height AGL at the top of the hill and over ﬂat terrain upstream of the hill. Jensen et al. (1984) says that ∆S can be estimated by:

h ∆S 2 , (5.3) ≈ L where L is the half-width of the hill and h is the height above the ground. The height of the maximum speed-up is: L 0.67 l 0.3z0 . (5.4) ≈ z0 These expressions are not valid for complex terrain (i.e., topography with 30% or greater change in elevation). While the above expressions can give a general idea the inﬂuence a hill can have on the wind speed, WAsP accounts for topography effects by implementing a linear theory described in Jackson and Hunt (1975). This theory attempts to conserve momentum and mass, while attempting to solve the linearized Navier Stokes equations. This theory is based on assuming a logarithmic wind proﬁle in regions with no disturbances due to topography, and then solving for perturbations induced by elevation changes. To solve for

42 Texas Tech University, Brandon A. Storm, August 2008 these perturbations, the lower atmosphere is divided into an inner and outer layer. Solutions for both the inner and outer layers are linked to one another, as the outer-layer solution provides the perturbation pressure field which drives the elevation-induced flow perturbations within the inner layer (Jackson and Hunt 1975). Once the perturbations are solved, they are added to the vertically displaced logarithmic profile to determine the new wind profile. More details on this theory can be found in Appendix A. Revisions to the original Jackson and Hunt (1975) theory have been suggested by Mason and Sykes (1979). The main addition was making the original two-dimensional Jackson and Hunt (1975) implementation to be three-dimensional. Further modifications have been provided by Walmsley et al. (1982), who replaced the surface pressure forcing by height-dependent pressure forcing as well as the first application to real terrain. Taylor et al. (1983) then added a blending of the inner and outer-layer solutions. In 1986, Walmsley et al. (1986) incorporated variable surface roughness to the original Jackson and Hunt (1975) theory. These implantations are referred to as MS3DJH/3R, or MS-Micro. While WAsP uses a combination of the original Jackson and Hunt (1975) theory, Mason and Sykes (1979) modifications, and MS3DJH/3R, the actual topography correction within WAsP is call the BZ (Bessel Expansion on a Zooming Grid) model. Instead of using a rectangular grid for the computations, the BZ model uses a polar computational grid and can calculate the wind perturbation at the center point, saving computational time when appropriate. According to the European Wind Atlas (1989), the BZ model computes the coefficients of a Fourier-Bessel expansion of the potential flow perturbation on the polar grid instead of calculating Fourier coefficients. b. Stability

Even though the WAsP application is based on a neutral boundary layer, it attempts to take into account variations in the atmospheric stability. This is done so by the user selecting the climatological average and root-mean-square (RMS) of the surface heat flux (Giebel and Gryning 2004). The default values within WAsP are -40 W m−2 and 100 W m−2, respectively. Even though most texts refer to the average heat flux, it is more appropriately referred to as the heat flux offset. Giebel and Gryning (2004) noted that for stable conditions, a more negative number (i.e., -100 W m−2) for the heat flux offset and 10 W m−2 is appropriate They further suggested for unstable conditions a value 0 W m−2 for the heat flux offset. According to the European Wind Atlas, the effects of non-neutral

43 Texas Tech University, Brandon A. Storm, August 2008 stabilities are modeled through their effects on the vertical proﬁle of the climatological mean value and standard deviation of wind speed using the following expressions. The fundamental basis of the stability correction in WAsP is based on the neutral condition Geostrophic Drag law and surface-layer similarity laws. The Geostrophic Drag law for neutral conditions is:

u u 2 G = ∗ ln ∗ A + B2, (5.5) κ fz − s 0 where f is the coriolis force, u∗ is the friction velocity, κ is von Karman constant, A = 1.8, and B = 4.5. The Geostrophic Drag law can be simpliﬁed assuming neutral conditions to (Jensen et al. 1984):

0.5G u∗ = . (5.6) ln G A |f|z0 − The similarity expression that is commonly used to describe general wind proﬁles is:

u u(z)= ∗ [ln(z/z ) ψ(z/L)], (5.7) κ 0 − where ψ is an empirical function that corrects for stability effects. WAsP assumes for the stability function that:

(1 16 z )1/4 for unstable conditions − L ψ(z/L)=  (5.8)  4.7 z for stable conditions. − L  The Monin-Obukhov length, L, is deﬁned as:

T ρc u3 L = 0 p ∗ , (5.9) κg H0 where T0 is the surface absolute temperature, ρ is air density, cp is the speciﬁc heat, g is gravity, and H0 is the heat ﬂux. Differentiating G by taking into consideration L, neutral conditions, and keeping

44 Texas Tech University, Brandon A. Storm, August 2008

G, z0, and f constant, as well as ignoring the small terms, one can arrive at:

du cg ∗ dH, (5.10) u ≈ fT c ρG2 ∗ 0 p where c = 2.5. This accounts for the stability effect on the friction velocity, and will be used later. The differential of Eq. 5.7 is:

du u dψ dL du(z)= ∗ [ln(z/z ) ψ(z/L)] ∗ dH. (5.11) κ 0 − − κ dL dH Using this relationship, as well as again assuming neutral conditions and the neutral drag law as described by Eq. 5.6, one can determine a relationship that describes the height where the heat ﬂux modulations vanish (zm). This relationship is:

z G β m α , (5.12) z ≈ f z 0 | | 0 with α = 0.002 and β = 0.9. At the height of minimum variance, the relative deviation from the neutral value of the mean speed is determined as a sum of the deviation caused by an average heat ﬂux offset

(∆Hoff ) and the varying heat ﬂux (∆Hrms). The wind-speed offset relative to neutral conditions is estimated by:

∆u(z ) ∆u ψ(z /L )+ ψ(z /L ) m = ∗ m off m rms , (5.13) u0(zm) u∗0 − ln(zm/z0)

where Loff corresponds to ∆Hoff and Lrms corresponds to ∆Hrms.

To evaluate the stability correction at heights other than zm, the following is done:

∆u(z ) ∆u u(z)= u (z) 1+ m (1 f(z)) + ∗off , (5.14) 0 u (z ) − u o m ∗0 where z ln(z /z ) f(z) = 1 m 0 . (5.15) − zm ln(z/z0) Though WAsP is based on neutral assumptions, it has been shown that there are parameters a user can vary to correct for stability factors.

45 Texas Tech University, Brandon A. Storm, August 2008

c. Surface roughness

The logarithmic wind proﬁle (Eq. 5.7) is applicable if the terrain is either completely or somewhat homogeneous upwind of the location of interest. To account for instances where it is not, an effective roughness length implicitly deﬁned by the geostrophic drag law should be used. Since the surface wind speed only depends on surface conditions to a certain upstream distance, WAsP only considers surface conditions out to around 10 km. According to the European Wind Atlas (Troen and Petersen 1989), when the wind is

ﬂowing from one surface that has a roughness z01 to a surface with roughness z02, the internal boundary layer grows downwind from the roughness change to a depth denoted as h. This depth is deﬁned as

h h x ln 1 = 0.9 , (5.16) z z − ∗ z 0m 0m 0m

where x is the distance downwind from the surface change, and z0m is the maximum

between z01 and z02. Based on experiments and numerical models, the perturbed proﬁle downstream can be estimated with three logarithmic parts.

u′ ln(z/z01) z c h ln(c1h/z01) ≥ 1   ln(z/c2h) u(z)=  u′′ +(u′ u′′) c h z c h (5.17)  ln(c1/c2) 2 1  − ≤ ≤  u′′ ln(z/z02) z c h,  ln(c2h/z02) 2  ≤   ′ ′′ where c1 = 0.3 and c2 = 0.09, u =(u∗1/κ)ln(c1h/z01), u =(u∗2/κ)ln(c2h/z02) and

u ln(h/z ) ∗2 = 01 . (5.18) u∗1 ln(h/z02)

WAsP uses this relationship to estimate the effect of surface roughness on the wind proﬁle. When there are multiple roughness changes in a short distance, or the distance is far from the point of concern, WAsP will average the roughnesses and add a weighting factor.

46 Texas Tech University, Brandon A. Storm, August 2008

d. Obstacles

Wake effects created by obstacles, such as buildings and trees, need to be considered when estimating the wind climatology near such objects. Consider an anemometer that was placed near a building so that the predominant wind direction is located in the direction of the obstacle. One would expect that a reduction of wind speed would be observed, leading to erroneous estimates of the wind speed and wind energy prodcution. The WAsP model attempts to correct for such features through the obstacle or shelter sub-model. To do so, detailed descriptions about pertinent objects need to be provided. The WAsP model uses results from Perera’s wind-tunnel studies to determine the fractional wind speed reduction for simple two-dimensional obstacles (Troen and Petersen 1989). The fractional speed reduction used is:

∆u z 0.14 x = 9.8 a (1 P )ηexp( 0.67η1.5), (5.19) u h h − − where z 0.32 x −0.47 η = a , (5.20) h ln(h/z ) ∗ h 0 and P is the porosity (set to 0 for solid objects), h is the height of the obstacle, za is the height of the anemometer, and x is the downstream distance.

47 Texas Tech University, Brandon A. Storm, August 2008

Chapter 6

Evaluation of WRF’S LLJ Climatology

6.1. Introduction

A knowledge of how well the WRF model is representing LLJs is important if the WRF model is to be utilized in wind energy site assessment projects, short-term wind forecasts, pollutant transport forecasts, and forecasts of water vapor transport in the Great Plains, which can be a key factor in thunderstorm initiation. Traditionally LLJs have been classified into categories, depending on the maximum wind speed and how much that wind speed decreases above the maximum. LLJ characteristics, such as the height of the maximum wind speed and time of occurrence, have also been investigated and deemed important for obvious reasons. This allows users to get an idea on how strong, high, and frequent LLJs are within a region. To determine the WRF model’s capabilities of representing LLJs, a comparison between observed and WRF LLJ climatologies is performed for a location in southern Kansas. If the WRF model can reproduce a climatology similar to what has been observed over the Great Plains, we gain confidence in WRF’s abilities and its PBL parameterizations. The ability to develop a LLJ climatology for any location within the central United States is also desirable. To evaluate if the WRF model is accurately representing the LLJ climatology at the ARM Intermediate Facility near Beaumont, Kansas, one year (April 2006 – March 2007) of WRF model forecasts and observed profiler data from the ARM profiler have been collected and analyzed. Details about both data sources can be found in Chapters 3 and 4, respectively. To give confidence in the analysis procedures, the ARM profiler and WRF LLJ climatologies are compared to those of Song et al. (2005), which were based on measurements from a mini-sodar and the profiler located near Beaumont. Several observational studies have been conducted to determine the climatology of LLJs over the Great Plains (Bonner 1968; Whiteman et al. 1997; Song et al. 2005). However, these studies used sparse point measurements and it is therefore difficult to determine the spatial variation of LLJs. On the other hand, using an NWP model lessens

48 Texas Tech University, Brandon A. Storm, August 2008 the spatial restraint since there are wind data available at every grid point, though the grid spacing and frequency of operational model output may still be coarse. This chapter describes the methods used to determine how well the WRF model represents the LLJ climatology near Beaumont, Kansas. Great detail will be given to describing a new classiﬁcation method of LLJs.

6.2. Classiﬁcation methods

The operational WRF model output that is utilized in this chapter was generated in real time at NCAR. The configuration is a 36/12 km two-way nested run (35 vertical levels with 14 of them in the lowest 2 km AGL). The WRF model is initialized from 40 km Eta grib data at 0000 UTC every day and integrated for 48 hours. The model physics options include: WSM 3-class simple ice scheme microphysics (Hong et al. 2004), Rapid Radiative Transfer Model (RRTM) long-wave radiation (Mlawer et al. 1997), Dudhia shortwave radiation (Dudhia 1989), YSU PBL scheme (Hong et al. 2006), Noah land-surface model (Chen and Dudhia 2001), and Kain-Fritsch cumulus parameterization (Kain and Fritsch 1993; Kain 2004). Due to the fact that LLJs are predominant during the nighttime hours (Song et al. 2005), only data between 0300 – 1200 UTC were analyzed. The real time WRF data from NCAR has two forecast periods that span between 0300 – 1200 UTC, 3 – 12 hour and 27 – 36 hour forecasts. Comparison of the two different forecast time spans gives insight on how far out in time LLJs can be accurately forecasted. It is well known when using observation data, such as atmospheric profilers, there is a need to perform quality control. The profiler output can be influenced by many factors, including precipitation, contamination by birds, and other sources of noise (Coulter 2005). This can lead to unrealistic wind speed profiles or large sections of missing data. While the ARM profiler data is subjected to quality assurance and control algorithms, erroneous profiles can remain within the data set. To avoid manual inspection of every ARM profile, which is time consuming and subjective, an automated selection algorithm was developed. This algorithm is based on fitting a Chebyshev polynomial to the observed data. The program TurbSim, which numerically simulates time series of three-dimensional wind velocity vectors, uses a similar technique to create wind profiles for input (Jonkman and Buhl 2007). The polynomial is used to smooth out data “spikes” as well as remove profiles that have significant variability throughout the profile, which are more than likely 49 Texas Tech University, Brandon A. Storm, August 2008

not representative of physical features. So that an accurate polynomial could be produced, the restraint that no more than ten or greater levels could be missing from a profile was implemented. If large gaps of data are missing, accurate profile fits would be difficult to obtain, especially if complex profiles are expected. If there were sufficient amounts of data available in a wind profile, a Chebyshev polynomial was fitted to the profiler’s U and V wind speeds every 50 meters, between 150 – 2000 m AGL in the vertical. Since a Chebyshev polynomial requires the data to be on a vertical scale between 0 – 1, the heights were normalized by maximum input height, typically around 2 km. Polynomial fits with orders between 0 – 10 were implemented for each U and V profile. The wind profile for all of the polynomial orders was determined by the following:

V (z)= cnTn(z), (6.1) n=0 X th where Tn(z) is the n order Chebyshev polynomial, and cn is a Chebyshev coefﬁcient. The Chebyshev polynomial order used for analysis was selected by ﬁnding which polynomial order had the smallest estimated risk factor. The estimated risk factor, Rest, for each polynomial order is computed by (Cherkassky et al. 1999):

R (p)= R (p) λ, (6.2) est emp ∗ where Remp is the emperical risk factor deﬁned as:

1 R (p)= (U U )2, (6.3) emp N fitted − obs and the penalty factor for small data samplesX is deﬁned as

1 λ = . (6.4) 1 D D ln(D)+ ln(N) − − ∗ 2∗N q p+1 D is the normalized model order, computed by: D = N , where N is the number of available data points in the vertical, and p is the polynomial order. The penalty factor is applied to help determine the optimal polynomial orders to select, or in other terms, the highest model complexity that describes the data without over ﬁtting it. This is because, as

50 Texas Tech University, Brandon A. Storm, August 2008

th the model complexity increases, Remp will intuitively decrease. However, a 9 order polynomial is not appropriate to fit a line to 10 data points since the resultant fit would not be representative of the general data. When the penalty factor is introduced, this will account for the over fittings, allowing a more appropriate polynomial order to be selected. Since it is possible that the best selected polynomial order would be zero (constant), one (linear), or two (quadratic), which would not be very representative of a typical wind profile, the polynomial order selected to represent the U and V component profiles were required to be three or higher. If the best fit polynomial order for a U or V profile had a

Rest above 100, this proﬁle, as well as the corresponding U or V proﬁle, were removed.

The threshold of 100 for Rest was subjectively selected by visually inspecting numerous profiles and was deemed the most reasonable value to remove polynomial fits that were undesirable. Once the polynomial fit was made to both the U and V components, a wind speed and wind direction profile were computed between 150 – 2000 m. Polynomial fits on the individual wind components were then converted to wind direction and speed. Examples of polynomial fits to the ARM U and V profiles are shown in Fig. 6.1a–c. Fig. 6.1a is an example of an ideal fit to the profiler data. Fig. 6.1b shows the strength of using the Chebyshev technique to quality control the data, as the spike with a U component over 30 m s−1 at 0.5 km is smoothed out. Though this value could be physically possible, it is more than likely a bad data point that would have been used to classify the LLJ speed and height if it had not been smoothed out. Fig. 6.1c shows a case where the V component from the ARM profiler was reporting sporadic wind speeds.

Since the Rest for this profile was over 100, it was removed from the dataset. To allow for a direct comparison of the WRF model’s LLJ heights, a similar polynomial method was performed to the WRF wind profiles (Fig 6.1d). Most likely due to the fact less amounts of data are available from the WRF profiles (14 levels within the lowest 2 km AGL), all of the polynomial fits were of the third order. This is one limitation of the Chebyshev polynomial technique, as it requires more data points to fit a higher order polynomial. As mentioned earlier, data from WRF and the ARM profiler between April 2006 – March 2007 were utilized. During this time period, 301 nights of data from the ARM profile were available. A majority of the missing nights were during the month of May. Focusing on data only between 0300 – 1200 UTC results in 2,974 hours available for analysis. Of those 2,974 hours, 136 of them were removed because there were ten or more

51 Texas Tech University, Brandon A. Storm, August 2008

(a) (b) 1 1 ght hei 0.5 0.5 normalized 0 0 −10 −5 0 10 20 30 (c) V (m/s) (d) U (m/s) 1 1 ght hei 0.5 0.5 normalized 0 0 −60 −40 −20 0 20 −5 −4 −3 −2 −1 V (m/s) V (m/s)

FIG. 6.1. Examples of Chebyshev polynomial fits (black lines) for: (a) – (c) ARM profiler’s U and V wind components (blue circles), and (d) WRF’s V component. Since the Chebyshev polynomial fit requires a vertical scale between 0 – 1, heights are normalized as z/2 km. levels missing, while 281 additional profiles were removed due to the fit criteria from the Chebyshev polynomial, resulting in 2,557 good profiles. To make sure that a given night was well represented, it was decided that at least five profiles (not necessarily containing LLJs) were needed over the nine hour time period for it to be compared to the WRF results. Of the original 301 nights, 254 of them had five or more “good” hours. From those 254 nights, 2,540 hours were available, with 2,383 of them deemed acceptable. Of the 158 hours removed, 23 were due to missing data, while the other 135 were due to the

Rest criteria being surpassed. As for the WRF data, 336 days were available during the time period analyzed. Since the WRF database only has output every three hours (i.e., 0300, 0600, 0900, and 1200

52 Texas Tech University, Brandon A. Storm, August 2008

UTC), only 1344 forecast times were available. Since data from both sources are needed to get an accurate comparison, nights with data from both the WRF and ARM were found. It was determined that 230 nights were available from both data sets for the same time periods. Unfortunately, the distribution of the nights were not even throughout the year (i.e., most of the month of May was not available for analysis). Various methods were used to classify the LLJs from the WRF and ARM data sets so a comparison of the results could be undertaken. Details about each method, and the reasoning for each approach will now be presented. The first method used to classify the WRF and ARM LLJs is the procedure presented originally in Bonner (1968), and later modified by Song et al. (2005) (referred to as the Bonner method hereon). The basis of Bonner’s classification method is to determine the height and speed of the fastest wind speed, Vmax, in a profile below 3 km AGL (Table 6.1). The classification of the jet is then determined by combining Vmax and ∆V , which is defined as the difference between Vmax and the slowest wind speed found above the height of Vmax below 3 km. Song et al. (2005) and Whiteman et al. (1997) classified jets into four categories (LLJ0 – LLJ3) as shown in Table 6.1, while Bonner (1968) only had categories 1 to 3. Song et al.’s (2005) classifications are also different from Bonner’s (Bonner 1968) and others since the categories are not cumulative. For example, Bonner (1968) would classify a jet having a max wind speed of 17 m s−1 and a change in wind speed of 8 m s−1 as both a category 1 and 2 jet, while Song et al. (2005) would only classify it as a category 2 jet. One other difference between Bonner’s and Song’s techniques is Song et al. (2005) used up to only 2 km AGL to determine ∆V , not 3 km. The modifications by Song et al. (2005) are the basis used within this investigation to classify the LLJs. If a night (either from the ARM or WRF dataset) contained multiple profiles that were classified as LLJs, the strongest LLJ profile determined by the Bonner method was used to classify the strength and height for that night. For example, if three different hours had category 0, 2, and 3 LLJs, the night would be classified as having a category 3 LLJ (LLJ3). The height and strength from the LLJ3 would be used to determine the night’s LLJ characteristics. This method of using Bonner’s classification method and the strongest LLJ in a night, is referred to as the max_Bonner method. Since this approach is similar to the method used by Song et al. (2005), the WRF and ARM LLJs determined by the max_Bonner will be compared to Song et al.’s (2005) results. Since the investigation by Song et al. (2005) utilized a long data set (5 years), as well

53 Texas Tech University, Brandon A. Storm, August 2008

as instruments with a fine vertical resolution, comparison between the climatologies developed from the WRF model, Song’s investigation, and the ARM profiler were done. This was done in order to determine whether the quality control methods, as discussed earlier, were appropriate. Since it is likely that in any given night not all of the hours between 0300 – 1200 UTC were available from the ARM profiler data, and we know only four forecast times in a night were available from the WRF output, an averaging method was developed to help account for these deficiencies. The profiles in a night that were available and classified as having a LLJ using the Bonner method were averaged together, creating a completely new wind profile. The new averaged profile was then classified using the previously discussed Bonner method. This method of using the averaged wind speed profiles is called the avg_Bonner method. The avg_Bonner method is used in attempt to give a better comparison between the WRF and ARM data, and not handicapping WRF for only having four times available. Though the Bonner method has been used in numerous studies to classify LLJs, it may not be the most appropriate method for all applications, such as wind energy and pollution dispersion. This is due to the fact that it may not classify strong wind maxima found at low levels as an LLJ, or may classify LLJs in a higher classification than they should be. For example, consider the wind speed profile shown in Fig. 6.2a. This profile has a wind maximum at a low-level (around 300 m AGL) which decreases to a local minimum speed at around 650 m AGL. Though this local minimum speed may be more appropriate to use in determining ∆V , the wind minimum at 2 km AGL will be used instead, classifying the LLJ to be stronger than what may be appropriate. Also consider a wind speed profile that has a localized maximum wind speed at a low height, along with another stronger maximum aloft (Fig. 6.2b). The wind speed maximum above the lowest-level maximum is faster, thus would be used to determine if an LLJ existed. Since the wind speed above the higher wind maximum does not decrease enough to classify it as LLJ, this profile would be classified as having no LLJ using the Bonner method. However, the lower wind maximum at 200 m AGL decreases enough to the local minimum at around 500 m AGL to be classified as a LLJ. To account for situations where low-level wind maximums would not be classified as LLJs, a new classification method is developed here. This method gives more insight on the frequency and relative strength of LLJs in the lowest part of the atmosphere. The new

54 Texas Tech University, Brandon A. Storm, August 2008

(a) (b) 2 2

1.5 1.5 GL (km) GL (km)

1 t A 1 t A Heigh

Heigh 0.5 0.5

0 0 5 10 15 0 10 20 wind speed (m/s) wind speed (m/s)

FIG. 6.2. Examples of vertical wind speed (m s−1 ) profiles. Blue circles are wind speeds estimated from the ARM profiler, black line is the Chebyshev polynomial fit computed from the U and V components, green dots are local minimums, and red squares are local maximums. method finds the local maximums and minimums from the fitted polynomial for each wind profile (Fig. 6.2). These maximums and minimums were used to classify the LLJs. Since the wind industry is interested in the lower LLJs, the lowest wind maximum and minimum were used to categorize each night. The lowest maximum was used to determine Vmax and the first local minimum above the maximum was used to calculate ∆V . This method is referred to as the max/min method. Just as for the Bonner method, profiles classified as having LLJs using the local max/min method were averaged together and then reclassified, referred as the avg_max/min method. Similarly, the strongest LLJ classified using the max/min method to categorize the night is referred to as the max_max/min method.

6.3. Results

To determine if the WRF model represented the LLJ climatology during the one year investigated, height distributions of each LLJ category from each classification method were analyzed for both the WRF and ARM profiles. A comparison of the frequency for each category between the WRF and ARM profiler dataset was also completed. To give insight into the WRF model’s ability to predict LLJs, forecast statistics, such as false alarm and hit rates, were computed.

55 Texas Tech University, Brandon A. Storm, August 2008 a. Category frequencies

As seen in Table 6.1, both of the observed and WRF climatologies using the max_Bonner classification method have a dominant direction from the south, as expected due to the common forcing mechanisms of LLJs. The distribution of LLJ categories between the new ARM climatology and Song’s study are also similar (Table 6.1), though there are slightly more category 0 and 1 southerly jets in the present analysis of the ARM data set. The increased frequency of weaker jets, and the slight increase in the frequency of LLJs in the ARM profiler data set, may be a result of the polynomial curve fit and classification method. Of course one cannot rule out a natural variation in the frequency of LLJs. Though there are slight differences between the new ARM profiler and Song’s results, the overwhelming similarities provide confidence that the automated selection of the ARM dataset is appropriate. Since the ARM profiler had a similar LLJ category distribution as Song et al. (2005), and the ARM profiler data set covered the same time period WRF data were available, the ARM profiler will be the main focus of evaluation to examine how well WRF performed. When comparing WRF’s LLJ climatologies to Song’s climatology, the WRF model significantly underestimated the frequency of LLJ’s using the max_Bonner method (Table 6.1). While a southerly LLJ was observed in the ARM profiler in 53% of the nights, the WRF model only had a LLJ around 30% of the time. Looking at the distribution of the LLJ categories, it is obvious that the WRF model is underrepresenting the strong LLJ categories (LLJ2–LLJ3). WRF’s distribution and frequency of northerly LLJs using the max_Bonner classification method was similar to what was observed, though the strong LLJs were also underrepresented (Table 6.1). The ability of the WRF model to represent the northerly LLJs could be a result of the fact that LLJs from the north are typically due to synoptic scale fronts. The WRF model should be able to represent such large scale features with fair accuracy. As mentioned beforehand, evaluating WRF’s representation of the LLJ climatology based on comparing the maximum jet profile observed in a night may not be the best method since the WRF output is available only every three hours. For example, if the maximum LLJ in a night occurred at 0500 UTC, the WRF model would not have the ability to capture this event. To help eliminate this problem, the profiles containing LLJs were averaged together. Again, this classification method had an underrepresentation of LLJs in the WRF data, with the largest deficiency in the strong southerly LLJs (Table 6.2).

56 Texas Tech University, Brandon A. Storm, August 2008

There are noticeably more southerly LLJs in the avg_Bonner method compared to the max_Bonner method. This is because the maximum of some of the LLJs in a night were classified northerly (i.e., 0 – 90 degrees or 270 – 360 degrees), but when they were averaged with the other jet profiles in the night, the direction fell into the southerly category (i.e., 90 – 270 degrees). An interesting WRF feature was revealed when comparing the Bonner classification methods to the newly proposed max/min method. The distribution of the WRF categories were the same for both methods (e.g., comparing Table 6.1 to Table 6.3). This indicates that WRF profile’s lowest wind maximum was also the strongest maximum in the whole profile (this will be discussed more when comparing the height distributions), unlike the ARM profiler. Though the distributions using the Bonner and max/min methods were similar for the ARM profiler, there were slightly fewer LLJs in the max/min method, especially when comparing LLJ3 distributions. Fewer stronger LLJs in the ARM profiler are due to scenarios as shown in Fig. 6.2a.

57 Texas Tech University, Brandon A. Storm, August 2008 rtherly et al. in a night to classify the night from Song et al. (2005), ing the LLJs in a night to classify the night from operational LLJ occurrence (nights/percentage) LLJ occurrence (nights/percentage) 5/2% 1/0% 3/1% 2/1% 32/14% 5/2% 262/13% 42/2% 8/3% 5/2% 9/4% 4/2% 34/15% 6/3% 2/1% 2/1% 0/0% 1/0% 15/7% 3/1% 10/4% 6/3% 11/5% 2/1% 33/14% 9/4% 270/13% 262/4% 34/15% 12/5% 25/11% 12/5% 31/13% 20/9% 343/17% 179/9% 40/17% 9/4% 35/15% 9/4% 50/22% 21/9% 25/11% 12/5% 25/11% 10/4% 26/11% 10/4% 124/6% 98/5% 25/11% 14/6% 24/10% 8/3% 27/12% 10/4% 3–12 hour max_Bonner 27–36 hour max_Bonner ARM max_Bonner Song 3–12 hour avg_Bonner 27–36 hour avg_Bonner ARM avg_Bonner Southerly Northerly Southerly Northerly Southerly Northerly Southerly Northerly Southerly Northerly Southerly Northerly Southerly No 8 8 6 6 5 5 10 10 V V > > > > > > ∆ ∆ Total 74/32% 31/13% 64/28% 26/11% 122/53% 44/19% 999/48% 397/19% Total 75/33% 30/13% 68/30% 22/10% 126/55% 40/17% > > 20 16 16 20 12 12 10 10 max max ≥ ≥ ≥ ≥ ≥ ≥ ≥ ≥ V V 6.2. LLJ occurrences using Bonner’s classification method and averag 6.1. LLJ occurrences using Bonner’s classification method and maximum jet 3 2 2 3 1 1 0 0 ABLE ABLE Category Category T T WRF forecasts and ARM profiler. operational WRF forecasts, and ARM profiler. 58 Texas Tech University, Brandon A. Storm, August 2008 night to classify the time period from LJs over a night to classify the night from operational LLJ occurrence (nights/percentage) LLJ occurrence (nights/percentage) 5/2% 1/0% 3/1% 2/1% 24/10% 4/2% 8/3% 5/2% 9/4% 3/1% 35/15% 4/2% 2/1% 2/1% 0/0% 1/0% 10/4% 3/1% 10/4% 6/3% 11/5% 2/1% 33/14% 9/4% 34/15% 12/5% 25/11% 12/5% 36/16% 22/10% 40/17% 9/4% 36/16% 8/3% 51/22% 24/10% 25/11% 16/7% 25/11% 12/5% 23/10% 16/7% 25/11% 18/8% 24/10% 11/5% 25/11% 15/7% 3–12 hour max_max/min 27–36 hour max_max/min ARM max_max/min 3–12 hour avg_max/min 27–36 hour avg_max/min ARM avg_max/min Southerly Northerly Southerly Northerly Southerly Northerly Southerly Northerly Southerly Northerly Southerly Northerly 8 8 6 6 5 5 10 10 V V > > > > > > ∆ ∆ Total 74/32% 35/15% 64/28% 28/12% 116/50% 51/22% Total 75/33% 34/15% 69/30% 23/10% 121/53% 46/20% > > 20 16 16 20 12 12 10 10 max max ≥ ≥ ≥ ≥ ≥ ≥ ≥ ≥ V V 6.3. LLJ occurrences using max/min classification method and the maximum LLJ in a 6.4. LLJ occurrences using max/min classification method and averaging the L 3 2 2 3 1 1 0 0 ABLE ABLE Category Category T T operational WRF forecasts and ARM profiler. WRF forecasts and ARM profiler. 59 Texas Tech University, Brandon A. Storm, August 2008 b. Forecast performance

As shown in Tables 6.1, 6.2, 6.3, and 6.4, there appears to be a difference between the number of nights with LLJ events between the two WRF datasets, 3–12 and 27–36 hour forecasts. This could indicate that, as simulation time increases, accurately simulating LLJs can be signiﬁcantly compromised. To determine if there were signiﬁcant differences between the 3–12 and 27–36 hour forecasts in predicting LLJs, conventional forecast statistics, commonly used in precipitation forecasts or severe weather events, were computed using the observed and WRF’s avg_max/min LLJs (Table 6.5). These measurements do not put any precedence on whether or not the WRF model forecasted the strength or height of the LLJ correctly, just whether or not a LLJ was or was not forecasted and observed.

TABLE 6.5. Forecast performance statistics for WRF’s 3 – 12 and 27 – 36 hour forecasts using the ARM proﬁler for veriﬁcation. False True False Prop. Forecast Range Hit Rate Alarm Rate Skill Score Freq. Bias Alarm Ratio of Corr. 3 – 12 hours 0.59 0.16 0.5 0.65 0.09 0.66 27 – 36 hours 0.46 0.22 0.28 0.55 0.17 0.56

The probability of detection, which is also referred to as the hit rate, is a measure of the fraction of observed LLJs that were correctly forecasted. The 3–12 hour forecast time period from WRF forecasted 59% of the nights to have a LLJ when there actually was a LLJ observed, while the 27–36 hour forecasts only performed correctly 46% of the nights. The probability of false detection, sometimes referred to as the false alarm rate, is the ratio of nights WRF incorrectly forecasted a LLJ over the number of nights that a LLJ was not observed in the ARM profiler data. Again, the 3–12 hour forecast time period performed better than the 27 – 36 hour forecasts in this measurement (Table 6.5). The frequency bias, which is the ratio of the nights WRF forecasted a LLJ, over the nights LLJs were observed in the ARM profiler, indicates that the 3–12 hour forecasts performed slightly better. The false alarm ratio is the fraction of events in which WRF incorrectly forecasted a LLJ, over the number of nights WRF had forecasted LLJs. Again, in this measurement, the 3 – 12 hour forecasts performed better compared to the 27–36 hour forecasts (Table 6.5). While the above statistics give some insight into the performance of WRF’s two time periods of forecasting LLJs, two measurements that combine the above parameters are the true skill score and the proportion of correctness. The true skill score is the probability of 60 Texas Tech University, Brandon A. Storm, August 2008 detection minus the false alarm ratio. Table 6.5 shows that the 3 – 12 hour forecasts have a true skill score almost double of the 27 – 36 hour forecasts. The proportion of correctness gives the fraction of all of the forecasts that were correct. For many meteorology phenomena this is not a good measurement because the “no” events are typically more common and influence this measurement. However, since LLJs were observed about 50% of the nights, the “no” events have same amount of weight. This parameter indicates that the 3 – 12 hour WRF forecasts were correct 66% of the nights, while the 27 – 36 hour forecasts are right only 56% of the nights. It is clear that the 3 – 12 hour forecasts from the WRF model performed better compared to the 27 – 36 hours forecasts in predicting which nights had LLJs. However, the performance of the 3 – 12 hour forecasts still may not be performing to the level desired by the wind energy community. Even though Song et al. (2005) found that the average LLJ lasted between 4.7 to about 6.7 hours (dependent on the time of year and wind direction), some of the false alarms within WRF may be a result of limited data from the ARM profiler, prohibiting it from capturing an event WRF depicted. The opposite is also possible, as a LLJ event could occur in between the WRF available times but be captured by the ARM profiler, leading to a lowering of WRF’s hit rate. c. Height distributions

A knowledge of how well WRF predicts the height of LLJs is important for the wind energy industry, as well as many other applications. If the observed LLJs are lower or higher than what WRF predicts, the WRF output should be used with caution, especially in site resource assessments. Since the southerly LLJs were more frequent and enough data were gathered for analysis, the southerly height distributions were investigated. It was found that the height distribution of the southerly LLJ categories from WRF are higher than what was observed, independent of what forecast period or classiﬁcation method was used (Figs. 6.3, and 6.4). Most of the LLJs from WRF had the wind maximum in between 500 – 1000 m, with no LLJs from WRF above 1000 m and none below 200 m. It also appears that the strong jets (LLJ2–3) observed below 500 meters are only represented once within WRF. Since these strong events would be crucial for wind energy applications, reasons for this behavior should be further investigated. Vertical resolution and the performance of the PBL scheme are two key areas that should be focused on.

61 Texas Tech University, Brandon A. Storm, August 2008

Comparing the average classification methods (avg_maxmin and avg_Bonner) to the maximum classification methods (max_maxmin and max_Bonner) shows that there are more jets at the lowest level in the ARM data set using the maximum classifications (compare Fig. 6.3a,b to Fig. 6.4a,b). This indicates that it is common to have the strongest LLJ in a night at a lower altitude than the average jet height. As presented earlier, there are fewer LLJs using the max/min methods compared to the Bonner methods for the ARM profiler data. There are fewer LLJs at low heights in the max/min classification methods since the drop off speed is calculated from the local minimum, instead of the weakest wind speed (which is typically found at 2 km AGL) which the Bonner methods use. However, there are no differences between Bonner and max/min methods when classifying WRF’s LLJs. This implies that the lowest wind maximum in the WRF data set were at least the strongest wind maximum in the whole profile, or could imply there were no or few multiple wind speed maximums.

6.4. Concluding remarks

Due to the time requirements and subjectivity of manually quality controlling profiler data, a new automated quality control technique based on fitting a Chebyshev polynomial to the U and V components of the profiler data were used. Comparing LLJ climatologies using this automated method to that of Song et al. (2005) indicates that the polynomial method is performing well and gives similar results as Song’s manual method. A new technique based on finding local maximums and minimums to determine the height and strength of the LLJ was proposed as well. This method resulted in the lowest wind maximum being used to determine if a LLJ was present, and the the strength (∆V ) was based off of the nearest local minimum, not the slowest wind speed above the maximum. This method is believed to be more useful to the wind energy industry. This is because the wind energy community would not be worried about a wind maximum at 1000 m AGL if there was a relatively strong wind maximum at 150 m AGL at the same time. WRF does show promising signs of being able to represent LLJs across the Great Plains, though the need for improvement is evident. The southerly dominance is present in both the WRF and observed climatologies. However, there was a large deficiency found in the WRF model in its abilities to predict the overall frequency of LLJs, with the strong LLJ categories lacking the most. These issues could be due to the diffusion in the PBL scheme, or a product of the vertical resolution. The heights of the LLJs from the WRF 62 Texas Tech University, Brandon A. Storm, August 2008 model were also estimated too high. This is a major concern if the WRF model is to be used with confidence in wind energy applications. One reason that the WRF model does not have any LLJs at low heights may be again the result of the coarse vertical grid resolution within the lowest 2 km AGL or the diffusion within the model. Another possibility is that WRF is doing well forecasting LLJs that are forced from synoptic scale influences, which tend to be higher, and missing most of the LLJs that are forced from mechanisms such as the inertial oscillation, which tend to be lower. Even though WRF has deficiencies, it has promising capabilities for a detailed investigation of forcing mechanisms of LLJs, which are still not well known at this time. A knowledge of how LLJs are forced could lead to better representation within WRF and other weather forecasting models. Once WRF can represent LLJs accurately, improvements in water vapor transportation and subsequently thunderstorm initiation could be a by-product, as well as improvements in wind energy forecasts and site resource assessments.

63 Texas Tech University, Brandon A. Storm, August 2008

2000 2000 2000 (a) (b) (c) 1800 1800 1800 Southerly LLJ3 1600 1600 1600 Southerly LLJ2 Southerly LLJ1 1400 1400 1400 Southerly LLJ0 )

(m 1200 1200 1200

1000 1000 1000

ude AGL 800 800 800 Altit 600 600 600

400 400 400

200 200 200

0 0 0 0 10 20 30 0 10 20 30 0 10 20 30 2000 2000 2000 (d) (e) (f) 1800 1800 1800

1600 1600 1600

1400 1400 1400 )

(m 1200 1200 1200

1000 1000 1000

ude AGL 800 800 800 Altit 600 600 600

400 400 400

200 200 200

0 0 0 0 10 20 30 0 10 20 30 0 10 20 30 Number of Nights Number of Nights Number of Nights

FIG. 6.3. Vertical distributions of southerly LLJs that are averaged over the night from: (a) ARM profiler using Bonner’s classification, (b) WRF’s 3–12 hour forecast using Bonner’s classification, (c) WRF’s 27–36 hour forecast using Bonner’s classification, (d) ARM profiler using lowest max/min classification, (e) WRF’s 3–12 hour forecast using lowest max/min classification, (f) WRF’s 27–36 hour forecast using lowest max/min classification.

64 Texas Tech University, Brandon A. Storm, August 2008

2000 2000 2000 (a) (b) (c) 1800 1800 1800 Southerly LLJ3 1600 1600 1600 Southerly LLJ2 Southerly LLJ1 1400 1400 1400 Southerly LLJ0 )

(m 1200 1200 1200

1000 1000 1000

ude AGL 800 800 800 Altit 600 600 600

400 400 400

200 200 200

0 0 0 0 10 20 30 0 10 20 30 0 10 20 30 2000 2000 2000 (d) (e) (f) 1800 1800 1800

1600 1600 1600

1400 1400 1400 )

(m 1200 1200 1200

1000 1000 1000

ude AGL 800 800 800 Altit 600 600 600

400 400 400

200 200 200

0 0 0 0 10 20 30 0 10 20 30 0 10 20 30 Number of Nights Number of Nights Number of Nights

FIG. 6.4. Vertical distributions of maximum southerly LLJs in a night from: (a) ARM profiler using Bonner’s classification, (b) WRF’s 3–12 hour forecast using Bonner’s classification, (c) WRF’s 27–36 hour forecast using Bonner’s classification, (d) ARM profiler using lowest max/min classification, (e) WRF’s 3–12 hour forecast using lowest max/min classification, (f) WRF’s 27–36 hour forecast using lowest max/min classification.

65 Texas Tech University, Brandon A. Storm, August 2008

Chapter 7

Evaluation of WRF’S Low-Level Shear Climatology

7.1. Introduction and motivation

An understanding of the local wind characteristics that wind turbines are subjected to is essential for wind resource assessments, short-term forecasting, and turbine design. As presented earlier, a power law relationship is commonly used to predict wind speeds at higher heights from lower wind speed records. A common approach used is:

z α U(z)= U , (7.1) r z r where Ur is the reference (or known) wind speed at a given height, zr, and U(z) is the estimated wind speed at height z, and α is the shear exponent. An understanding of the directional shear at speciﬁc locations could also lead to better prediction of generated wind power. Though it is not clear at this time how directional shear impacts wind turbines, it has been suggested that the performance and the fatigue loads due to directional shear can be signiﬁcant (Giebel and Gryning 2004; Walter 2007). This chapter determines if the WRF model represents the low-level shear climatology over the Great Plains so that the model based shear values could be used to extrapolate low-level measurements up to hub height. An empirical relationship between the WRF model’s 10 m wind speed and shear exponent is also presented.

7.2. Data and methodology

To evaluate if the Advanced Research WRF (Skamarock et al. 2005) is accurately representing the wind shear climatology at various tall tower locations across the Great Plains, a years worth of WRF forecasts (April 2006 - March 2007) was used to compute the low-level shear exponent and the magnitude of the directional shear. The WRF model output being utilized was generated in real time at NCAR and is the same as used in the previous chapter. Only the 3 – 24 hour forecasts of the output were utilized in this study. The WRF output during the time period analyzed was available for 336 out of 365 days. 66 Texas Tech University, Brandon A. Storm, August 2008

More information about the WRF model can be found in Chapter 4. The investigation by Schwartz and Elliot (2006) utilized towers throughout the Great Plains to calculate the yearly average shear exponent, as well as the average diurnal trend. The averaged shear exponents from the towers analyzed (Schwartz and Elliot 2006), including the diurnal trends, were compared to the simulated averaged WRF shear exponents. It should be noted that the time frame used in Schwartz and Elliot’s (2006) tower analysis does not correspond to the same year as the WRF data. Schwartz and Elliot (2006) also had various analysis periods, ranging from one year up to four years. The lowest two model levels from the WRF model (which are terrain following and around 30 and 100 m AGL) were used to calculate the shear exponent and directional shear magnitude across the Great Plains. Two different averaging methods, quenched and annealed (Arneodo et al. 2000), were used to determine the average shear exponents. The average shear exponent from the quenched method, α , calculates the shear exponent h qi from every appropriate profile and then averages those values together, α ln U100 . The annealed average shear exponent, α , uses the average wind h qi ∼ U30 h ai speed atD the appropriateE levels to calculate the average α, α ln hU100i . h ai ∼ hU30i The model level heights AGL slightly vary over the model domain, with the first two model levels around 30 and 100 m AGL. The exact heights of the WRF grid points that correspond to the tower locations used in Schwartz and Elliot (2006), as well as the heights Schwartz and Elliot (2006) utilized from the towers, are shown in Table 7.1. It should be noted that the heights used in the observational study do not match the heights used from the WRF model. This could have some impact on the results, and are further discussed in the following section. While the WRF model output represents an instantaneous value, most of the wind speed values utilized by Schwartz and Elliot (2006) were 10 minute averages (Schwartz and Elliot 2008, personal communication). The observational studies are also point measurements, but WRF represents a spatial value over a 12 km grid. These two factors can become important when doing model verification against point measurements, but are unavoidable in most model verification studies. There were slight differences in the computation methods used in the current study versus those of Schwartz and Elliot (2006). Schwartz and Elliot (2006) removed directional sectors that were affected by the tower structure itself from their data set, but all directional sectors from WRF were analyzed. One other difference between the

67 Texas Tech University, Brandon A. Storm, August 2008

methods was the minimal speed requirement. The shear exponents in Schwartz and Elliot (2006) were calculated if the wind speeds at both of the levels being used were greater than 3 ms−1, while the shear exponent from WRF was calculated for all wind speeds. The wind energy ﬁeld should consider investigating properties of wind speeds below 3 ms−1 (near the typical cut-in speed of most turbines) as the development of low-speed turbines begins.

7.3. Results

The following sub-sections discuss details found from comparing the WRF average shear exponents to those observed by Schwartz and Elliot (2006). The sensitivity of extrapolating low wind speeds to a hub height of 100 m is also presented, including the resulting differences in power estimates for a 1.5 MW GE wind turbine. An empirical relationship between the 10 m wind speed and the yearly average shear exponent is also proposed. a. WRF’s speed and directional shear performance

To determine if WRF can be used to determine a location’s shear exponent, WRF’s shear exponent averages, αq and αa, were compared to those determined by Schwartz and Elliot (2006) (Table 7.1). The WRF model tended to slightly underestimate the shear exponent, as the α values were slightly lower or nearly the same as the observed α h qi h i values at all of the locations, except Ellsworth and Kearny, Kansas. It should be noted that Schwartz and Elliot (2006) questioned the validity of the Kearny data due to possible tower effects. The lack of possible tower interferences in model data reveals another beneﬁt of using WRF to determine the shear climatology. The α values were slightly h ai higher than α at all of the locations, except for Jewell, Kansas. This indicates that a h qi fairly accurate estimation of the shear exponent could be established if average wind speeds are known at various levels. Unfortunately Schwartz and Elliot (2006) did not present the variability in their shear exponents, but the standard deviations for α are quite large (Table 7.1). This indicates h qi that there is a large spread of the shear exponent. The large variability is partially accounted for by the strong diurnal trend that is observed in the average shear exponent (Fig. 7.1).

68 Texas Tech University, Brandon A. Storm, August 2008

To determine if WRF’s average shear exponents give any benefit over assuming α to be 1/7, the average absolute difference (over all 11 stations) between the observed shear exponents and 1/7 was compared to the average absolute difference between the observed shear exponents and WRF’s average αs. The average absolute differences for WRF was 0.03 while for the 1/7 law, it was 0.05. This means that taking into consideration all 11 stations, the WRF gives a better estimate of the shear exponent compared to the 1/7 law, which underestimates the average α. Even though WRF has some locations where its average α is fairly lower than what was observed, such as Sumner, Kansas,itisa significantly better approach than using 1/7. A shear exponent of 0.2 is becoming commonly used, and results in a slightly better average absolute difference of 0.03, same as the WRF model. However, a value of 0.2 would overestimate the average alpha at many locations (Table 7.1). Evaluation of the diurnal trends of the average shear exponents ( α ) and average h qi magnitude of the directional shear β (determined using the quenched method) were h i done to determine the impact of atmospheric stability (Fig. 7.1) on WRF’s performance. For all of the locations where diurnal trends from the towers were available (Sumner, KS, Washburn, TX, and Lamar, CO), the WRF model overpredicted the shear exponent during the unstable hours (i.e., 1500 – 2300 UTC), and underestimated the shear exponent during the stable hours. WRF’s gross underestimation of the shear exponent during the stable boundary layer at Sumner implies that WRF is not representing the magnitude or frequency of the LLJs as revealed in Chapter 6. The underestimation of the shear exponent at the other two locations could be a result of too much diffusion within the model. The magnitude of the directional shears from the WRF model were also evaluated (Table 7.1). Observational direction data for comparison was not available from Schwartz and Elliot (2006), so it is difficult to determine the validity of these results. However, there is enough turning observed in the WRF model to indicate that there could be some effect on the performance of wind turbines and result in fatigue. A strong diurnal trend was also observed for the magnitude of the directional shear (Fig. 7.1), with large turning observed during the stable hours. Large turning during the stable hours is partially caused by the inertial oscillation, which can be responsible for the formation of LLJs (Blackadar 1957). Though no directional shear measurements were available from the tall towers analyzed, one can infer how well the WRF model is performing by comparing its results

69 Texas Tech University, Brandon A. Storm, August 2008 to previous observational studies. Holtslag (1984) reported average wind direction shear values calculated from the Cabauw tower in the Netherlands. The average wind direction shear values for heights 20 m to 40, 80, 120, 160, and 200 m were calculated for different stability classes. Holtslag (1984) found average directional shear values from 40 – 120 m to range from 5 – 22 degrees, with the higher directional shear values corresponding to the stable boundary layer classiﬁcations. Giebel and Gryning (2004) investigated the magnitude of the directional shear using a tower located in Germany. They indicated there was a relationship between the directional shear magnitude and the depth of the stable boundary layer. They indicated for boundary layers 200 m and deeper, that around a 10 degree change in wind direction over the 10 to 98 m layer could be expected. Since these observations only included stable boundary layers, it is no surprise that large magnitudes of directional shear were observed. Based on these previous studies, the directional shear values from the WRF data are possibly lower than one would expect. Directional shear magnitudes from Great Plain towers needs to be gathered and compared to the WRF values before any credence is placed on these results.

TABLE 7.1. Site names and tower heights used by Schwartz and Elliot (2006). The WRF model heights from the grid points corresponding to the tower locations are given. Also reported are various statistics for observed (Schwartz and Elliot 2006) and WRF simulated annual shear exponents (α) and annual directional shear magnitude (β, degrees). αq and αa are averages based on quenched and annealed, respectively. Spatial location of sites can be found in Fig. 7.2

Anemom. Obs. Model WRF WRF WRF β WRF WRF Site Name Heights (m) α Heights (m) α α std (degrees)h i β std α h i h qi h ai Lamar, CO 52, 113 0.150 31, 103 0.148 0.150 5.38 9.27 0.161 Ellsworth, KS 50, 110 0.165 31, 104 0.181 0.126 4.21 8.93 0.185 Kearny, KS 50, 80 0.138 31, 104 0.170 0.114 4.53 9.51 0.176 Sumner, KS 50, 80 0.254 31, 104 0.179 0.135 4.18 8.34 0.182 Jewell, KS 50, 110 0.206 31, 104 0.183 0.141 4.56 10.98 0.182 Ness, KS 50, 110 0.223 31, 104 0.172 0.140 4.59 10.59 0.177 Logan, KS 50, 80 0.179 31, 104 0.176 0.135 4.29 8.74 0.179 Hobart, OK 40, 70 0.195 32, 106 0.175 0.112 3.67 8.16 0.182 Elk City, OK 40, 70 0.227 32, 105 0.173 0.111 3.45 7.72 0.180 Sweetwater, TX 50, 100 0.220 32, 106 0.167 0.111 3.07 8.62 0.177 Washburn, TX 50, 75 0.170 31, 104 0.171 0.107 3.48 8.41 0.180

70 Texas Tech University, Brandon A. Storm, August 2008

0.5 12 Sumner WRF Sumner WRF 0.45 Sumner Obs. Washburn WRF Washburn WRF 10 Lamar WRF 0.4 Washburn Obs. Lamar WRF 0.35 Lamar Obs. ees) 8 α)

0.3 Degr r ( 0.25 6

0.2 Shea nal 4 0.15 Shear Exponent ( Directio 0.1 2 0.05

0 0 0 3 6 9 12 15 18 21 24 0 3 6 9 12 15 18 21 24 Hour (UTC) Hour (UTC)

FIG. 7.1. Diurnal variation of yearly averaged wind shear exponent ( α , left panel) and yearly h qi averaged magnitude of directional shear in degrees ( β , right panel). Observed shear exponents are reproduced from Schwartz and Elliot (2006) using Engaugeh i Digitizer 4.1.

Jewell Logan Ellsworth Ness Lamar Kearny Sumner

Elk City Washburn Hobart

Sweetwater

FIG. 7.2. WRF simulated yearly averaged shear exponents (left panel) and yearly averaged magnitude of directional shear (right panel). Stars indicate location of tower locations. The dashed box corresponds to the area used in Fig. 7.4.

Though the WRF model has small errors estimating yearly average shear exponents, there are many beneﬁts using the WRF data compared to point-speciﬁc towers to determine local shear exponents. One large advantage of using a model output to estimate

71 Texas Tech University, Brandon A. Storm, August 2008

FIG. 7.3. 12 km resolution of WRF terrain elevation (left panel) above mean sea level (m) and USGS land use categories WRF assigns to the grid points (right panel). For details on the land use categories visit: http://www.mmm.ucar.edu /mm5/mm5v2/landuse-usgs-tbl.html. the shear exponent and directional shear is the availability of shear estimates at all locations, and the spatial variability can be evaluated (Fig 7.2). Figures 7.2 and 7.3 reveal that there are relationships between the shear exponent and land use, as well as terrain. The “hot spots” of high shear exponents are associated with larger cities, such as Oklahoma City, OK, Wichita, KS, and the Dallas/Fort Worth, TX area. These urban areas have large roughness lengths, which will slow down the lowest level wind speeds. The higher model heights will not be as affected by the surface roughness, therefore leading to a high shear exponent. Similarly, the region dominated by trees in eastern Oklahoma and Texas will have large roughness lengths, causing the shear exponent to be large. Elevation also appears to have an effect on the shear exponent and directional shear, as higher values of directional shear, and low magnitude values of shear exponents, are located over the higher terrain to the west. There are also locations where local topography may have an impact on both the shear exponents and directional shear. If the WRF model were run at a higher resolution (4 km or ﬁner), and utilized high resolution terrain and land use data, more details might be evident in the shear exponents.

72 Texas Tech University, Brandon A. Storm, August 2008

b. Impact on wind speed and power estimates

Various extrapolation methods using Eq. 7.1 and shear exponents from observations, WRF model output, and a constant shear exponent of 1/7 were compared to determine impact of the different methods. Since records of low-level wind speeds were not available at all of the locations, the wind speed from WRF’s lowest model level ( 30 m) ∼ over a year time period at three locations (Sumner, KS, Lamar, CO, and Washburn, TX) were extrapolated up to 100 m by three different ways. Though the wind speed from WRF is not what actually occurred, it provides a reasonable proxy, and allows the extrapolation methods to be evaluated with respect to one another. The ﬁrst method uses the yearly average shear exponent from WRF to extrapolate the low-level proxy wind speeds up to 100 m (WRF_const). The second method takes the average shear exponents from Schwartz and Elliot (2006) to extrapolate the WRF 30 m wind speed up to 100 m (Obs_const). Finally, a constant 1/7 value for the shear exponent was assumed for all times to extrapolate the WRF 30 m wind speed upwards. From Table 7.2, the 100 m average wind speeds from the three different methods shows similar results for the three locations. At Sumner, KS, assuming that the method using the observed shear exponents from the tower (Obs_const) is the most accurate, the WRF_const estimate is more accurate than the method of assuming a constant α of 1/7. The same trends were also observed at the Washburn and Lamar locations. The underestimation of the WRF_const methods are not as great at the Washburn and Lamar locations compared to the Sumner site. It should be noted that extrapolation methods using the hourly average shear exponents (i.e., using 0000 UTC average shear exponents to extrapolate 0000 UTC wind speeds, etc) were also investigated (not reported). Surprisingly, no signiﬁcant difference was found using the hourly shear exponents compared to the average annual shear exponents. This could be partially due to the fact that low-level wind speeds are out-of-phase with the upper-level wind speeds and the errors in the calculations (overestimating during the daytime hours and underestimating during the nighttime hours) cancel out over long periods of time. Due to the added complexity and little impact of using the hourly averaged shear exponents, it is recommended that an annual average shear exponent be used to extrapolate up the wind speed for general resource site assessment projects. However, hourly average shear exponents should be used if extrapolating low wind speeds upward for short-term forecasts or diurnal trends of the potential wind power are desired. Though the differences in the average wind speeds from the various methods seem to

73 Texas Tech University, Brandon A. Storm, August 2008

TABLE 7.2. Yearly averaged 100 m extrapolated wind speed m s−1 for three locations, Sum- ner, KS, Lamar, CO, and Washburn, TX. The wind speed is extrapolated using the wind speed from the ﬁrst corresponding model level height in WRF over a year period, up to 100 m using three different shear exponents. The 1/7 method assumes a constant shear exponent of 1/7, while the WRF_const methods takes the average shear exponent from the WRF model, and Obs_const uses the shear exponent observed by Schwartz and Elliot (2006) at that location to extrapolate all of the wind speeds up. The estimated annual energy output (MWh/yr) are computed based on a GE 1.5 MW machine (1.5s) and energy estimate data provided by GE (available at www.gepower.com/prod_serv/products/wind_turbines/en/15mw/index.htm). These estimates assume a constant air density.

Sumner: Lamar: Washburn: 100m mean extrapolated 100m mean extrapolated 100m mean extrapolated wind speed (m s−1 ) wind speed (m s−1 ) wind speed (m s−1 ) Extrapolation /estimated annual /estimated annual /estimated annual method energy (MWh/yr) energy (MWh/yr) energy (MWh/yr) Obs_const 8.48/5901 7.43/4674 7.64/4913 WRF_const 7.77/5071 7.41/4654 7.64/4923 1/7 7.45/4696 7.37/4601 7.40/4635

be small, these small difference can lead to a fairly large difference in annual energy estimates. Annual energy estimates were made using the yearly average wind speeds at 100 m and data for a 1.5 MW General Electric wind turbine (Table 7.2). It should be pointed out that the hub height for the turbine can be lower than 100 m (can be site dependent), but this value was used as a proof of concept and to show the impact of the different extrapolation methods. For one turbine, the constant 1/7 method results in around 1,200 MWh/year less than the Obs_const method, while the WRF_const method underestimates the annual energy by around 800 MWh/year. Accordingly, since the estimated wind speeds at Lamar, CO and Washburn, TX from the three extrapolation methods are similar to one another, the three power estimates at these sites are similar. This small difference however can have a major impact if one is deciding whether or not to place a large wind farm (100 or more turbines) at one of those locations. c. Average shear exponent and 10 meter wind relationship

A relationship between average 10 m wind speeds and the shear exponent, similar to that of Hussain (2002), was determined by ﬁtting an exponential ﬁt to the WRF’s 10 m 74 Texas Tech University, Brandon A. Storm, August 2008

wind speed and corresponding shear exponent:

α = 0.09969 e−0.1973∗U10 + 0.14, (7.2) ∗ where U10 is an instantaneous 10 m wind speed. The 95% confidence bounds for the first parameter, 0.09969, are 0.05225 and 0.1471, while the 95% confidence bounds around -0.1973 are -0.2705 and -0.1242. The dashed box region in Fig. 7.2 represents the geographical area used to determine the relationship. Since the shear exponent does not approach zero (which is desirable to accurately fit an exponential) at higher wind speeds, 0.14 (the limiting value the shear exponent approaches) was first subtracted from the shear exponents before the relationship was determined. At high wind speeds the atmosphere tends to be neutrally stratified. Under neutral conditions, the shear exponent tends to be near 0.14, accounting for why the shear exponent approaches this value at high wind speeds. The empirical fit was also done using 10 m wind speed values greater than 3.5 ms−1. Values below 3.5 m s−1 were not used due to the fact the spread of the shear exponents for these low wind speeds was large. In Fig. 7.4, there is a noticeably large spread in the shear exponents for wind speeds below 10 m s−1 , with a strong deviation towards higher shear exponents. The large spread in the shear exponent for slower 10 m wind speeds can be due to the antiphase relationship during the stable hours. During this time, wind speeds slower than 10 m s−1 can occur with large shear exponents due to the atmosphere decoupling and the presence of LLJs.

7.4. Concluding remarks

In this chapter, the WRF model was evaluated to determine if it can accurately represent the low-level wind shear, which is important for wind resource assessment as well as turbine performance. It was found that by comparing yearly average and diurnal trends of the shear exponent from WRF to the observational results from Schwartz and Elliot (2006), that the WRF model gives a reasonable estimation of the shear exponent at most of the locations. It appears that the WRF model slightly overestimates the shear exponent during the unstable hours of the day (i.e., 1500 – 2100 UTC) for all of the locations where diurnal comparisons were possible (Fig 7.1), and underestimates the shear exponent for the stable hours, especially where strong and frequent LLJs are common (e.g., Sumner, KS).

75 Texas Tech University, Brandon A. Storm, August 2008

0.3 α) ( 0.25

0.2

ar Exponent 0.15 She 0.1

0.05

0 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 18+ Wind Speed (m/s)

FIG. 7.4. Relationship between 10 m wind speed (m s−1) grouped in 1 m s−1 bins (centered around the listed values) and α based on data in the dashed box in Fig. 7.2. The results are presented using standard boxplot notation with marks at 95, 75, 50, 25, and 5 percentile of an empirical distribution.

Some of the error in WRF’s estimations might be due to tower effects and instrumental errors, as well as a difference in the height levels being evaluated. It is also very likely that there are substantial errors within the model itself. Increasing the vertical levels within the model may improve the shear estimates if it is found a higher vertical resolution helps to resolve the low-level wind field with more precision. Testing of various model physics configurations, specifically the boundary layer parameterizations, is needed to see how sensitive the shear exponents are to model configurations. Though no direct comparison between the WRF’s directional shear magnitude and observations were available, the results indicate that there may be enough directional shear over the Great Plains to raise concern over both fatigue issues and aerodynamic performance. The WRF model also revealed that there are spatial variations in the shear exponent and directional shear (Fig. 7.2). The magnitude of the shear exponent is linked to land use

76 Texas Tech University, Brandon A. Storm, August 2008

categories and their subsequent surface roughnesses, as larger shear exponents were found for land use categories where the model assigns a larger surface roughness (e.g., urban and forested areas). It should be noted that no observations were available to collaborate the shear exponent magnitudes over the large surface roughness areas, therefore it is not certain whether or not the assigned surface roughnesses and resultant shear exponents are valid for these locations. While the WRF model estimates of the shear exponent show that there are model improvements needed, the practice of assuming a constant shear exponent of 1/7 over the Great Plains is just as, if not more, erroneous than the WRF estimates. Regions with strong and frequent LLJs will consistently have shear exponents greater than 1/7. These are regions where the WRF model may struggle in accurately reproducing the shear exponent, but it will be an improvement over 1/7. It is also risky for resource assessment projects to assume a shear exponent value of 0.2 in many regions of the Great Plains. It has been found dually by Schwartz and Elliot and this study that there are many locations where the average shear exponent is less than 0.2. However, for regions that are known to have strong and frequent LLJs (i.e., Sumner, KS) assuming a shear exponent value of 0.2 would be more appropriate than the current results from this WRF conﬁguration. Comparisons of average 100 m hub height wind speeds and annual energy output of 1.5 GE wind turbine indicate that the WRF shear exponents perform better than assuming 1/7 at all three locations. The signiﬁcant underestimation of the wind speed and annual energy found at Sumner, KS is related to the WRF model’s inability to accurately represent the frequency and strength of the LLJs in this region. It is believed that many wind farms underproduce what resource site assessment projects initially estimate (Jones and Randall 2006). The reason for this overestimation is not clear at this time. From our results, it indicates that the estimation of the wind speed using a shear exponent of 1/7 would most likely underestimate the actual wind speed. Therefore, the energy estimates using 1/7 for the shear exponent should be on the conservative side, while the shear exponents from WRF would only increase the energy estimates using our current understanding and practices. However, large shear values (both directional and speed) can impact the performance of the machines, and in some instances cause the machines to fail or shut down. The compromised performance due to the wind shear could partially account for the underproduction of some wind farms. Therefore, the better knowledge of the shear from WRF could help improve turbine

77 Texas Tech University, Brandon A. Storm, August 2008 design and wind farm production. Once there is clear understanding of how turbines react to strong speed and directional shear, the need to have good shear estimates for both resource assessment and short-term forecasts will be even greater.

78 Texas Tech University, Brandon A. Storm, August 2008

Chapter 8

WRF’s Sensitivity in Forecasting Speciﬁc LLJ Events

8.1. Introduction

As mentioned in Chapter 1, contemporary NWP models face a challenge in forecasting the development, magnitude, and location of LLJs with precision (Banta et al. 2002). It has also been shown in Chapter 6 that the WRF model has deficiencies on predicting the climatology of LLJs. In depth case studies of LLJ events are needed to help shed light on areas where the WRF model is performing poorly and needs improvement. To test the capabilities of the WRF model in forecasting LLJs, two pronounced LLJ events observed over west Texas and southern Kansas were simulated. The LLJ event over west Texas was observed from 0000 - 1200 UTC, 2 June 2004 at Texas Tech University’s WISE research center field site. The LLJ event over southern Kansas was observed on the night of 2 October 2006 at the ARM facility in Beaumont, Kansas. These specific sites were selected owing to their simple topographic setting and frequent occurrences of strongly stratified boundary layers and LLJs. Most importantly, extensive observational datasets from advanced monitoring systems exist for both these locations.

8.2. Data and methodology

Though data utilized in this chapter were presented in detail in Chapter 3, a recap of the important instruments and their characteristics are represented. The WISE research center field site includes a boundary layer wind profiler and the Reese Mesonet station from the WTM network (Schroeder et al. 2005). The 915 MHz Doppler radar vertical boundary layer wind profiler has a vertical resolution of 55 meters, with the first level reported at 124 m AGL, and an output of 30 minute averaged data. The WTM Reese Mesonet station uses a 10 m tall tower with wind speed and direction (2 and 10 m), temperature (2 and 9 m), humidity, barometric pressure, precipitation and solar radiation available every five minutes (Schroeder et al. 2005). The boundary layer profiler at the ARM facility in Beaumont is a 915 MHz radar profiler with the first level reported at 90 ∼ m AGL, and a vertical spacing of about 60 m (Coulter 2005). 79 Texas Tech University, Brandon A. Storm, August 2008

In this chapter, Version 2.2 of the Advanced Research WRF was evaluated (Skamarock et al. 2005). The WRF model is computationally efficient, and its two-way nesting capabilities allow extremely fine grid resolutions at the regions of interest. Various model and physical parameterization configurations (Table 8.1) were evaluated to determine if any one configuration showed a clear benefit over the others. A 500 500 × horizontal grid with a 4 km spacing and 36 vertical levels (13 levels below 1 km AGL) was used. A 1.33 km nested grid was also evaluated, but showed no significant difference compared to the 4 km results. Therefore, the 1.33 km nested results are not included. The number of vertical levels in the lowest 1 km is greater (almost double) than what is typically used in operational NWP models. An in depth discussion pertaining to WRF can be found in Chapter 4. Common features between the model runs presented in this chapter include: 30-second USGS land use and topographic height data interpolated onto the modeled domain, NOAH land-surface model (Chen and Dudhia 2001), and the Ferrier microphysics scheme (Ferrier et al. 2002). The cumulus parameterization was turned off because of the fine grid spacing used in this study. The vertical mixing and diffusion was solely performed by the planetary boundary layer (PBL) schemes, YSU (Hong et al. 2006) or MYJ (Mellor and Yamada 1974, 1982; Janjic 1990, 1996, 2001)). In other words, no additional explicit diffusion or numerical filters were involved in either the horizontal or the vertical direction. This approach allowed us to conduct a better evaluation of the WRF-PBL schemes themselves. Two combinations of longwave and shortwave radiation schemes were used: the Dudhia simple cloud interactive shortwave scheme (Dudhia 1989), along with the RRTM longwave radiation (Mlawer et al. 1997) scheme; and the Geophysical Fluid Dynamics Laboratory (GFDL) shortwave scheme (Lacis and Hansen 1974), in conjunction with the GFDL longwave scheme (Fels and Schwarztkopf 1975) (Table 8.1). The initialization and lateral boundary conditions for all the runs were provided by the North American Mesoscale Model (NAM, formerly ETA) Advanced Weather Interactive Processing Systems (AWIPS) archived dataset. The NAM uses a 40 km grid and provides lateral boundary conditions every six hours.

80 Texas Tech University, Brandon A. Storm, August 2008

TABLE 8.1. WRF parameters varying in model comparisons.

Model Grid LW / SW Initialization Date Run PBL Center Radiation and Time YSU_rrtm_TX YSU WISE RRTM/Dudhia 1 June 2004 18 UTC MYJ_rrtm_TX MYJ WISE RRTM/Dudhia 1 June 2004 18 UTC YSU_gfdl_TX YSU WISE GFDL/GFDL 1 June 2004 18 UTC MYJ_gfdl_TX MYJ WISE GFDL/GFDL 1 June 2004 18 UTC YSU_rrtm_KS YSU ARM RRTM/Dudhia 1 Oct 2006 18 UTC MYJ_rrtm_KS MYJ ARM RRTM/Dudhia 1 Oct 2006 18 UTC

8.3. Results

The following sub-sections compare the WRF-based model output with available ﬁeld observations from both the West Texas and southern Kansas cases. Emphasis is placed on timing, magnitude, and location of the LLJs, since these attributes have the largest implications for wind resource assessments and short-term wind energy predictions. Synoptic conditions for the West Texas case are also presented to help give the readers some insight on possible forcing mechanisms. a. West Texas case

At 0000 UTC, 2 June 2004, a low pressure system was located over northern Texas (Fig. 8.1a), along with a dryline passing through Texas. As the night progressed into morning (0600 - 1200 UTC), the low pressure and warm front dissipated, along with the relatively westward progressing dryline. The cold front observed in the Midwest pushed south to the Oklahoma panhandle and central Oklahoma by 0600 UTC and then became stationary. While no precipitation was observed in the Texas panhandle during this night, Fig. 8.1d shows a Mesoscale Convective System (MCS) developed in northern/eastern Texas. This MCS continued eastward throughout the night, and reached the Mississippi border by 1200 UTC. The upper tropospheric conditions were dominated by an open trough at both 850 and 500 hPa (Fig 8.1b,c) in the upper Midwest. The upper level winds over Texas at this time were relatively weak. Little change in the 500 hPa height and wind ﬁelds were observed between 0000 - 1200 UTC. However, the 850 hPa winds strengthened and became southerly over the Texas panhandle into Kansas during the overnight hours,

81 Texas Tech University, Brandon A. Storm, August 2008 which corresponds to the development of one of the LLJs that will be investigated. Two LLJs with wind speeds greater than 16 m s−1 were observed on 2 June 2004 over the West Texas panhandle region (Fig. 8.2e). The first LLJ occurred between 0530 - 0630 UTC, spanning from just above the ground to approximately 0.5 km AGL. The second maximum occurred between 0830 - 0930 UTC, spanning between 0.3 - 0.9 km AGL. The first jet had a predominantly easterly direction, while the second jet was more southerly (Fig. 8.2f). The forcing mechanisms of these jets are not entirely clear at this time. However, the easterly jet corresponds to the time the dryline was progressing westward. It is unclear at this time the commonality between LLJs and drylines. It is possible that westward progressing drylines act as a density current, leading to LLJ features. The southerly LLJ could be a result of either the inertial oscillation or the baroclinicity created from the sloping terrain of the southern Great Plains. Reliable identification of the forcing mechanism for an observed LLJ is not a trivial task and is an area that needs further investigation. Interested readers are encouraged to peruse the works of McNider and Pielke (1981), McCorcle (1988), Fast and McCorcle (1990), Zhong et al. (1996), and Wu and Raman (1997). Some of these numerical studies further investigated the sensitivities of LLJ evolution to topography, land-surface heterogeneity, soil moisture, etc. In Fig. 8.2, wind speed and direction time-height profiles from the WRF grid point closest to the WISE field site are compared to the corresponding profiles from the Texas Tech wind profiler. Since no distinct differences were found between the MYJ_rrtm_TX and MYJ_gfdl_TX runs, as well as between the YSU_rrtm_TX and YSU_gfdl_TX runs, only model runs using the RRTM radiation scheme are presented. According to Fig. 8.2, both the MYJ_rrtm_TX and YSU_rrtm_TX runs represented the vertical and temporal characteristics of the observed LLJs fairly well. However, at the WISE field site location the MYJ_rrtm_TX run forecasted slightly stronger, and somewhat more accurate wind speeds for the first LLJ event in comparison to the YSU_rrtm_TX run (Fig. 8.2). On the other hand, the YSU_rrtm_TX run captured the wind speeds of the LLJ event occurring at 0900 UTC more precisely, though the timing of the YSU_rrtm_TX run was slightly off (Fig. 8.2a,e). Unfortunately, all the runs failed to reproduce the strong winds (> 14 ms−1) that were observed below 0.2 km AGL during 0500 and 0600 UTC. Significant differences between the MYJ_rrtm_TX run and the profiler wind direction were also observed, while the YSU_rrtm_TX run represented the wind direction quite accurately with a slight temporal displacement (Fig. 8.2b,d,f).

82 Texas Tech University, Brandon A. Storm, August 2008

a) b) L 1440 1470 1410

1470

x L x

1500

c) 5640 d) 5700

5580

5760 x

5820

FIG. 8.1. 0000 UTC, 2 June 2004 analysis of: (a) surface (MSL pressures contoured every 4 hPa); (b) 850 hPa (heights contoured every 30 m); (c) 500 hPa (heights contoured every 60 m), and (d) visible satellite. Panels a-c show standard station models, with temperatures and dewpoint temperatures in degrees Celsius, heights in m, and wind barbs: barb = 10 m s−1, half barb = 5 ms−1. Fronts in (a) are subjectively analyzed but based on the National Center for Environmental Prediction (NCEP) analysis. The X denotes the approximate location of the WISE ﬁeld site.

83 Texas Tech University, Brandon A. Storm, August 2008

FIG. 8.2. Simulated and observed wind speed and wind direction for 0400 UTC - 1200 UTC on 02 June 2004. The left column shows wind speed time-height plots (unit: m s−1) of: (a) hourly output from the YSU_rrtm_TX run; (c) hourly output from the MYJ_rrtm_TX run; and (e) half-hourly averages from the Texas Tech boundary layer wind proﬁler. The right column shows wind direction time-height plots (unit: meteorological degrees) of: (b) hourly output from the YSU_rrtm_TX run; (d) hourly output from the MYJ_rrtm_TX run; and (f) half-hourly averages from the Texas Tech boundary layer proﬁler.

84 Texas Tech University, Brandon A. Storm, August 2008

0.5 YSU_rrtm_TX MYJ_rrtm_TX Profiler/WTM 0.4 1/7 power law

nt 0.3 fficie Coe ar 0.2 She

0.1

0 03z 04z 05z06z 07z 08z 09z 10z 11z 12z Time (UTC)

FIG. 8.3. Vertical shear exponent (α) time series calculated from the YSU_rrtm_TX (dotted line) and MYJ_rrtm_TX (dashed line) runs (utilizing wind speed time series at the 113 m grid-level and at the 10 m level) between 0300 - 1200 UTC on 2 June 2004. The Texas Tech boundary layer proﬁler’s 124 m wind speed and the Reese WTM station’s 10 m wind speed time series were utilized to estimate the observed α time series (solid line). The 1/7 power law exponent is also shown for comparison (dashed-dotted line).

As discussed in Chapters 2 and 7, the power law relation:

z α U(z)= U , (8.1) r z r where Ur is the wind speed at a reference height (typically 10 m) and U(z) is wind speed at height z above ground, is commonly used in the wind energy community to estimate the wind speed in the boundary layer. In the wind energy literature (e.g., Archer and Jacobson 2003) the shear exponent, α, is typically assumed to be equal to 1/7. In Fig. 8.3, the observed α time series (calculated from the Texas Tech boundary layer proﬁler’s 124 m wind speed and the Reese WTM station’s 10 m wind speed time series) is compared with the WRF-simulated α time series (calculated from the windspeed time series at the 113 m grid-level and at the 10 m level). The conventional 1/7 power law is also shown as reference. It is clear that for the entire night the observed α values were signiﬁcantly

85 Texas Tech University, Brandon A. Storm, August 2008

larger than the conventional value of 1/7. The YSU_rrtm_TX run captured the evolution of α reasonably well, albeit underestimating the magnitude. Similar conclusions can also be made from Figure 8.4. This figure highlights that if the observed 10 m wind speed is extrapolated using the conventional 1/7 power law, it is very likely to under-predict the outer layer wind speeds in the presence of LLJ events. In comparison, the WRF model can forecast wind speeds considerably closer to the observations (Fig. 8.4). As discussed in Chapter 7, high values of α are common during nighttime hours, especially when LLJs are present. Again, these high values should be appropriately taken into account during wind resource assessment, short-term wind power prediction, and wind turbine design. High values of α imply that wind turbines can generate a substantial amount of energy, even when the wind speed near the ground is minimal. At the same time, larger α will introduce higher fatigue loads on the turbine blades (Giebel and Gryning 2004). So far, single grid point output from the WRF runs have been compared with collocated field observations. However, flow visualizations of the modeled fields revealed that the forecasted LLJs portray considerable spatial variabilities (see Fig. 8.5). For

0500 UTC 0600 UTC 0.18 0.18 m) m) 0.14 0.14 (k (k AGL AGL 0.1 0.1 ght ght ght ght YSU_rrtm_TX Hei

Hei YSU_rrtm_TX 0.06 0.06 MYJ_rrtm_TX MYJ_rrtm_TX Profiler Profiler WTM/Profiler interp. 0.02 0.02 WTM/Profiler interp. 1/7 power law 1/7 power law 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 Wind speed (m/s) Wind speed (m/s)

FIG. 8.4. Vertical wind speed (m s−1) profiles from the YSU_rrtm_TX (dotted lines in gray) and MYJ_rrtm_TX (dashed lines in black) runs at 0500 UTC (left) and 0600 UTC (right) on 2 June 2004. Observed wind speed profiles from Texas Tech boundary layer profiler are depicted as solid gray lines. Note that the profiler observations are not available below 124 m. In order to facilitate the comparisons, 10 m Reese WTM and 124 m profiler wind speed values are joined using the power law relationship (Eq. 8.1) and the observed α values (long-dashed lines in gray). The extrapolated wind speed profiles utilizing the observed 10 m Reese WTM wind speed and the conventional 1/7 power law are also shown as reference (dashed-dotted lines in black).

86 Texas Tech University, Brandon A. Storm, August 2008

example, at 0600 UTC, slightly to the south and west of the WISE field site, quite strong winds were forecasted by the YSU_rrtm_TX run. If these winds were observed over the WISE field site, the YSU forecasted profiles would have been much closer to the observations. To the best of our knowledge, it is not known in the literature whether such large spatial variabilities, as observed in the modeled cross-sections and horizontal plan-view maps (Fig. 8.5), are observed in the real world LLJs. The WISE research center along with the Texas Tech Atmospheric Science Group is currently constructing two mobile Ka-band radars which will be able to give large spatial coverage of three-dimensional velocity fields, and consequently morphological properties of the Great Plains’ LLJs. Another debate that could be settled with measurements from the Ka-band radar is whether or not LLJs are terrain following. Reports by Banta et al. (2002) and others have suggested that LLJs are not terrain following. This has been based off of measurements from profilers within close proximity of one another. However, Fig. 8.5 indicates that the LLJ tends to be terrain following, at least in the large scale sense. To further evaluate the various model runs, the WRF model’s performance on simulating surface variables of interest to the wind power industry (e.g., 10 m wind speed,

and friction velocity (u∗)) were evaluated. Investigation of the 10 meter wind (Fig. 8.6) shows that most of the WRF configurations evaluated represented the 10 meter wind within 1-3 m s−1. Small differences were noted between the RRTM and GFDL simulations, but were not significant (not shown). Also, only small differences between YSU_nest and YSU_rrtm_TX were observed (not shown). Increasing the horizontal resolution in this case study did not show a significant improvement of the forecast. In areas with complex topography and heterogeneous land use, fine grid spacing may be necessary.

When comparing the friction velocity (u∗) from WRF to that observed, small differences can be noted (Fig. 8.7a). Friction velocity can be estimated as (Stull 1988):

κU u = (8.2) ∗ ln(z/z ) ψ o − m where κ is the von Karman constant (0.4), U is the wind speed at height z, zo is the roughness length, and ψm is the stability function. The area surrounding the WISE ﬁeld site has a roughness value of 0.12 m according to the 24 USGS land use categories

87 Texas Tech University, Brandon A. Storm, August 2008

FIG. 8.5. Wind speed (m s−1) fields from the YSU_rrtm_TX run at 0600 UTC, 2 June 2004. The cross-sections are taken (a) at 1.3 km MSL height; (b) at 0.955 Sigma level ( 350 m AGL); (c) along 33.3o N latitude (line 1 shown in (a)); and (d) along 102o W longitude∼ (line 2 shown in (a)). The X marks the approximate location of the WISE field site in (c) and (d). The field site is approximately at the intersection of the two white lines in (a). Reference arrow for wind vector is given on the right.

(http://www.mmm.ucar.edu/mm5/mm5v2/landuse-usgs-tbl.html). This roughness is used in all of the calculations. WRF also utilizes these 24 USGS landuse categories for determining the roughness length. The MYJ had a larger Monin-Obukhov length (L) than was observed for a majority of the time period investigated (Fig. 8.7b), while YSU underrepresented L between 0500 - 0700 and 1030 - 1130 UTC. The reasons for the misrepresentation at these times are not clear. This indicates, though, that the stability between the two models was different, with

88 Texas Tech University, Brandon A. Storm, August 2008

7 YSU_rrtm_TX MYJ_rrtm_TX 6 WTM

(m/s) 5 ed d spe 4 Win

2 03z 04z 05z06z 07z 08z 09z 10z 11z 12z Time (UTC)

FIG. 8.6. Observed (5 min. resolution) 10 meter wind speed (m s−1) from WISE mesonet station (solid) and WRF corresponding grid point 10 meter wind speed (m s−1) outputted every hour, valid through 0300 UTC - 1200 UTC, 02 June 2004.

Mesonet Mesonet 0.6 a 600 b MYJ_rrtm_TX MYJ_rrtm_TX 500 0.5 YSU_rrtm_TX YSU_rrtm_TX (m/s) 400 ty ty

oci 0.4 300 Vel L (m) on on 0.3 200 cti Fri 100 0.2

0 0.1 03z 04z 05z06z 07z 08z 09z 10z 11z 12z 03z 04z 05z06z 07z 08z 09z 10z 11z 12z Time (UTC) Time (UTC)

FIG. 8.7. (a) Calculated (5 min. resolution) friction velocity (ms−1) and (b) Monin-Obukhov length (L), from WISE mesonet station (solid) and WRF corresponding grid point friction velocity (ms−1) outputted every 30 minutes. Valid through 0300 UTC - 1200 UTC, 02 June 2004.

89 Texas Tech University, Brandon A. Storm, August 2008

the YSU being more stable than the MYJ, and the MYJ being less stable than what was observed. The differences in the stability parameters can also be seen in the potential temperature (θ) profiles aloft. Negative sensible heat fluxes were observed and found in the model output, therefore the boundary layer would be classified as stable. However, potential temperature profiles (Fig. 8.8) indicate that between 0600 - 0900 UTC that both the MYJ and YSU runs made the atmosphere less statically stable in the lowest 300 meters. The MYJ was even slightly statically unstable at 0600 UTC around 100 - 300 m AGL. Unfortunately, no observed temperature data aloft are available for comparison due to the RASS feature on the profiler malfunctioning during this time. As mentioned previously, reasons for why the temperature profiles varied between MYJ and YSU is not exactly known at this time. Differences in the vertical mixing strength within the PBL schemes could have an impact on the vertical temperature profiles. It is possible that more mixing within the MYJ PBL scheme (corresponding to the increased TKE, discussed within this section), helped destabilize the lower part of the atmosphere, whereas the YSU PBL scheme did not have as strong of mixing at 0600 UTC. The presumably weaker mixing within the YSU PBL scheme has been addressed in the WRF 3.0 release. Another parameter relevant to wind energy is TKE due to the stress on the wind

a b 0.9 0500 UTC 0.9 0500 UTC 0600 UTC 0600 UTC 0.8 0.8 0700 UTC 0700 UTC 0.7 0800 UTC 0.7 0800 UTC 0900 UTC km) km) 0900 UTC 0.6 0.6 L ( L ( AG 0.5 AG 0.5 0.4 0.4 Height Height 0.3 0.3

0.2 0.2

0.1 0.1

300304 308 312 316 300304 308 312 316 Potential Temp. (K) Potential Temp. (K)

FIG. 8.8. Potential temperature (θ) proﬁles 0500 UTC - 0900 UTC, 02 June 2004, from (a)YSU_rrtm_TX and (b) MYJ_rrtm_TX for the grid point corresponding to the WISE ﬁeld site.

90 Texas Tech University, Brandon A. Storm, August 2008 turbines (Kelley et al. 2004). The production of TKE from 0400 - 0600 UTC 300 m and below (Fig. 8.9) could have detrimental effects on wind turbines. The production of TKE at this time and level is due to the large shear found within this region. The production of TKE at 0600 UTC in the MYJ helped to destabilize the lower atmosphere more. TKE is not a computed variable for the YSU, therefore it cannot be compared with the MYJ simulated TKE ﬁeld. Kelley et al. (2004) proposed that coherent TKE, turbulence that has a time and space phase relationship and can be formed by the presence of LLJs, may be more detrimental to wind turbines. Coherent TKE is calculated given the following equation (Kelley et al. 2004):

1 Coh_TKE = (u′w′)2 +(u′v′)2 +(v′w′)2 (8.3) 2 q Running the WRF at very ﬁne scales, would allow coherent TKE to be calculated easily. The ability to run WRF at very ﬁne scales with 3D TKE closure is now available within the newly released WRF 3.0. Also on could use the WRF output as a boundary condition for an LES model. b. Southern Kansas case

In order to establish the generality of our conclusions from the 2 June 2004 case, a second LLJ event that occurred on 2 October 2006 over southern Kansas was simulated. A southerly LLJ jet with wind speeds over 24 m s−1 and centered between 0.3 - 0.4 km

FIG. 8.9. TKE (m2 s−2) proﬁle from MYJ_rrtm_TX between 0300 - 1200 UTC, 02 June 2004.

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AGL developed around 0200 UTC, and was persistent through 1000 UTC (Fig. 8.10c,d). Wind turning with height was also observed throughout the night (Fig. 8.10d). Both the YSU and MYJ PBL parameterizations were investigated for this case (Table 8.1). Since the MYJ-based run produced results very similar to the YSU-based run, only the YSU_rrtm_KS results are reported. The YSU_rrtm_KS run qualitatively reproduced the vertical and temporal characteristics of the observed LLJ reasonably well (Fig. 8.10). However, as with the West Texas case, the WRF runs overestimated the LLJ heights and at the same time underestimated the wind speeds. These behaviors could be due to enhanced diffusion within the PBL schemes, and undoubtedly need systematic evaluation in the near future.

8.4. Concluding remarks

In this study various model configurations were investigated in order to determine if the WRF model is able to forecast the Great Plains’ LLJs. The general conclusion is that all the WRF configurations evaluated do have the capability to capture some of the essential characteristics (e.g., location and timing) of the observed LLJ events. Unfortunately, all the WRF configurations tested also have the tendency to overestimate the LLJ heights and underestimate the LLJ wind speeds. These results are likely related to the enhanced mixing of the PBL schemes. It is worth mentioning that most of the present-day mesoscale and large-scale atmospheric models use PBL parameterizations, which are not physically based but inspired by model performance (Beljaars and Viterbo 1998; Viterbo et al. 1999). Some of these ad-hoc parameterizations alleviate problems, such as “runaway-cooling”, by (artificial) enhanced mixing. At the same time, these ‘fixes’ create unphysical consequences, such as unreasonably deep boundary layers (Viterbo et al. 1999; Cuxart and Coauthors 2006) and weaker LLJs. The wind energy industry may desire more accurate wind speeds than currently forecasted by different WRF configurations, but it should be noted that all of these forecasts were significantly more accurate than conventional extrapolation using the 10 m wind speed and 1/7 power law. It was found that no particular WRF configuration was clearly better than another. For example, in the West Texas case, the YSU PBL scheme-based runs captured the wind direction profiles better than the MYJ-based runs. On the other hand, the MYJ runs forecasted the wind speed profiles more accurately at this location. Given the significant 92 Texas Tech University, Brandon A. Storm, August 2008

FIG. 8.10. Simulated and observed wind speed and wind direction for 0000 UTC - 1200 UTC on 02 October 2006. The left column shows wind speed time-height plots (unit: m s−1) of: (a) hourly output from the YSU_rrtm_KS run; and (c) hourly averages from the Beaumont ARM profiler. The right column shows wind direction time-height plots (unit: meteorological degrees) of: (b) hourly output from the YSU_rrtm_KS run; and (d) hourly averages from the Beaumont ARM profiler. spatial variabilities we found in the forecasted wind fields, it is very likely that, at a different validation point, the relative performances of various WRF configurations would be different. High-resolution spatial-temporal observations and innovative forecast verification metrics (accounting for both the magnitude and displacement errors) are needed before one could conclusively identify the “best” WRF configuration for forecasting LLJs over the Great Plains. Since WRF captures the timing and location of the observed LLJs, it is possible the WRF-PBL parameterizations are performing more-or-less satisfactorily (though one can

93 Texas Tech University, Brandon A. Storm, August 2008

get the right answer for the wrong reasons). Of course there is room for improvement within the parameterizations (especially under stable conditions), along with the need for more rigorous testing of various model configurations. Not surprisingly, it was found that the location of verification and the frequency of the model output can make a difference when evaluating the model’s performance ( Fig. 8.5). For users interested in wind energy, and verification studies, time averaged outputs may be more useful. It is also important to look at the spatial variability around the site of interest. Other factors, such as horizontal grid resolution were analyzed. No large benefit was found using a 1.33 km two-way nest inside the 4 km domain (not shown). Since the 1.33 km nest is more computationally expensive, and did not show any benefit over the 4 km grid, it is possible that the 4 km grid would be sufficient for some wind energy applications. It should be pointed out that WRF LES capabilities for real world forecasts are becoming available (Moeng et al. 2007). This will allow horizontal resolution to be in the hundreds of meters, allowing for the PBL schemes to be turned off. If the model is to simulate LLJs, which are boundary layer phenomena, an accurate representation of the boundary layer will be of utmost importance. Representation of the boundary layer is typically sensitive to the vertical resolution near the surface. The configuration used in the present work had 13 levels below 1 km with a spacing ranging from around 30 - 80 m. Current operational mesoscale NWP models have fewer vertical levels representing the boundary layer, typically around 5-7 levels. Vertical resolution is likely more important than horizontal resolution, and should be investigated in the future. To determine the validity of the WRF forecasts, surface variables were also investigated for the West Texas case. The 10 m wind speed in all the configurations was fairly accurate. Similar results were found when evaluating the friction velocity. Differences between the temperature profiles and stability were found. This difference may account for some of the variability in the friction velocity. The differences in the mixing length as well as the temperature profiles and friction velocity can help explain the differences in the magnitude of wind observed between the YSU_rrtm_TX and MYJ_rrtm_TX runs. Determining how well WRF simulates LLJs forced under different dynamics (i.e., sloping terrain, inertial oscillation, synoptic conditions) is also of interest. It is possible that WRF can represent LLJs forced due to some of these mechanisms, but not others. It is

94 Texas Tech University, Brandon A. Storm, August 2008 very difficult to determine if mesoscale NWP models, such as WRF, can accurately forecast LLJs that are forced due to the dynamics of the sloping terrain and/or the inertial oscillation. This is due to the fact that more than likely NWP models struggle to depict LLJs forced this way due to the difficulties of representing the stable boundary layer. However, mesoscale models are often used to develop a database of LLJ events. When using this database to find LLJ events for case studies, it is likely the data base will lack a large number of events forced by the sloping terrain or inertial oscillations. Observations could be used to try to locate LLJ events that are forced by the inertial oscillation, but the data needed to do so is difficult to find and analyze from spatially sparse observational networks.

95 Texas Tech University, Brandon A. Storm, August 2008

Chapter 9

Downscaling WRF with WAsP: Framework and Evaluation

9.1. Introduction and motivation

As presented in Chapters 6, 7, and 8, the WRF model is capable of reproducing the low-level shear and wind speeds in the lowest 1 km AGL with some skill. However, those results were based on horizontal grid spacing of 4 and 12 km. While these resolutions may be considered fine scale for mesoscale models and provide adequate information for day-to-day forecasts, there are problems that need to be considered when trying to get detailed point forecasts for wind energy projects. The main issue with using a mesoscale model, whose forecast is based on grid averages, is that it does not account for fine scale variability in terrain and surface roughness. If one tries to use a mesoscale model, such as WRF, to forecast the wind speed at the edge of a large lake or on top of an isolated hill, the speed up effects due to the surface features would not be well represented. While the WRF model can provide an estimate of the shear exponent that could be used to extrapolate short-tower measurements or determine regions worth investigating for wind farms, the WRF model alone is not able to provide the fine scale details needed for turbine siting for reasons described above. To account for fine scale surface features and ideally provide more accurate wind estimates, proposed within this chapter is a deterministic downscaling technique that uses WRF output in conjunction with WAsP - discussed in detail in the next section. Details about WAsP are presented in Chapter 5. It appears this is the first attempt to use a database of operational forecasts over the Great Plains and downscale it with WAsP. It however is not the first project to explore dynamically downscaling coarse wind fields (e.g., Stohl et al. 1997; Petersen et al. 1998; Frank et al. 2001; De Rooy and Kok 2004; Gustafson Jr. and Leung 2007). If the coupling of the WRF-WAsP models provides accurate estimations of wind speeds and power densities, the wind industry could save both time and money in resource assessment and siting projects. For example, the operational WRF output could be used to determine regions worth investigating for wind farm placement (coupled with power 96 Texas Tech University, Brandon A. Storm, August 2008 transmission lines and transportation needs). Then the wind energy company could use WAsP to downscale the operational WRF output to determine fine scale wind features and determine if it is economical to pursue the project, as well as the most economical place to site turbines (micrositing). Though it would be ideal to remove the need of tower measurements, it is likely that investors would still require measurements to be taken at the site of interest before construction would begin. However, this demand could diminish with time if the WRF/WAsP framework was found to be reliable in multiple locations. Even if investors still required measurements within the proposed site, the above techniques would allow wind energy companies to determine locations of interest and the potential economic gain more quickly than using tower observations, giving a potential advantage over competitors. Using multiple years of WRF output (3 to 5 years) and downscaling it would also allow the wind industry to get a better representation of a site’s interannual variability, which currently requires on-site measurements over long periods of time. The company could either use preexisting data sets of WRF outputs, or run multiple years of hindcasts in a relatively short time period. Even though the WRF model provides information for large spatial regions with ease, the wind industry may question why the preexisting surface measurements (e.g., NWS ASOS, WTM) across the U.S. are not used as input into WAsP instead of WRF. There are a couple of concerns that arise when relying on preexisting surface based (i.e., 10 m wind speeds) observations. One of these concerns stems from the fact that the 10 m wind speed can be in an anti-phase relationship with higher level wind speeds, as mentioned in Chapter 1 (e.g., Crawford and Hudson 1973; Holtslag 1984; Lange and Focken 2005). The fact the stable boundary layer can cause the lower atmosphere to decouple from the surface is of concern (Giebel and Gryning 2004). If a years worth of 10 m wind speed is provided as an input to WAsP, issues may arise for the wind speed measurements observed during stable times due to the fact the 10 m wind speed may not be representative of the higher wind speeds aloft. While WAsP attempts to account for such problems in the stability model, the disconnect of the 10 m wind speed is still an issue. Giebel and Gryning (2004) states that the use of 10 m wind data with WAsP in stable conditions should be avoided. Using surface based observations could lead to wind speeds in some regions, especially areas where LLJs are prominent, to be underestimated, thus missing good potential wind farm sites. This fact makes wind speed measurements near the hub height advantageous. However, a dense network of 50 m tower data is not available,

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further underscoring the advantage of WRF output as an input into WAsP. Wind speed data from heights around 30 and 100 m are readily available in operational WRF output, eliminating the problems of using wind speed data that are below the decoupled layer to predict upper level wind speeds in the stable regime. Again, if investors still request that on-site observations are used to estimate the potential wind power, diurnally-dependent average shear exponents from WRF (Chapter 7) could be used to extrapolate the wind speed measurements (normally 50 - 60 m) to hub height (as high as 100 m), helping to circumvent the decoupling problem. Taking into account the average wind direction shear from WRF could also improve estimates of the wind direction when interpolating winds to higher heights. Another concern with using surface measurements is the spatial representation of those data. WAsP requires the wind atlas used to predict the specific site wind speed be representative of the wind climate at the site of interest. To remind the reader, the wind atlas is created by WAsP to represent the local wind climate with the effects of terrain and surface roughness removed. This can then be used by WAsP to predict the wind and power distribution at a specific site. Due to terrain, land use, synoptic, and other variabilities, this requires that the station used to generate the wind atlas be within close proximity to the potential wind farm location. While this distance will vary, the wind atlas should be created from measurements within 100 km of the site (Troen and Petersen 1989), and ideally within closer proximity than that. While the U.S. has a fairly dense network of surface stations, there are many regions within the U.S. that do not have a preexisting measurement station within close proximity that is representative of the wind climate. For example, wind atlases created from two ASOS stations within close proximity to one another (Sweetwater, TX and Abilene, TX, 65 km) had significant ∼ differences in the created wind atlases (not shown). The wind atlas generated with WRF data is not limited by location, as large spatial regions can be simulated quite easily.

9.2. Methodology a. Previous coupling methods

This project is not the ﬁrst to propose coupling a mesoscale model with WAsP, as the Risø National Laboratory has explored and had success with using data from the Karlsruhe Atmospheric Mesoscale Model (KAMM) as input into WAsP (e.g., Petersen

98 Texas Tech University, Brandon A. Storm, August 2008 et al. 1998; Frank et al. 2001). While the principles outlined in these previous works were used as the basis of the methodology, there are modifications to the input and techniques, which will be highlighted in the next sub-section. The KAMM/WAsP technique, which is considered a “statistical-dynamical” downscaling method, has been highlighted in publications for its ability to generate a wind atlas more than its use for turbine siting, as herein investigated. An overview of the previous methodologies is presented, and modifications in this study are highlighted where appropriate. The first step in coupling any mesoscale model with WAsP is generating or acquiring model output. Frank et al. (2001) and Petersen et al. (1998) give specifics on techniques used to couple KAMM with WAsP. Instead of using long time periods of operational forecast output, such as proposed, the KAMM/WAsP method used a synoptic-scale climatology as input into the KAMM model to generate the mesoscale wind field. According to Petersen et al. (1998):

“the statistical-dynamical approach to regionalization of large-scale climatology is used to calculate the regional surface wind climate with KAMM. It is assumed that the regional surface layer climate is determined uniquely by a few parameters of the larger synoptic scale plus the parameters of the surface. This parameter space is decomposed into several representative situations, and numerical simulations of these are performed with the mesoscale model. The mesoscale climatology is ﬁnally calculated from the results of the simulations together with the frequency of the typical situations.”

While synoptic climatology as an input has been used to couple KAMM with WAsP, issues may arise when using such a method where stable PBL impacts (i.e., LLJs, decoupling of lower atmosphere) could be frequent and have a large impact on the local wind environment. Since the geostrophic wind is the major input into the KAMM model, the stable regime wind ﬂows must be represented by the geostrophic wind to get accurate surface wind estimates. Since LLJs can have supergeostrophic wind speeds, and it is unlikely the KAMM model is representing the stable regime since no radiation is used in the model, the generated mesoscale climatology may not be representative. Since the WRF model can represent the stability and account for speed-up effects during the stable boundary layer, it is hypothesized that a relatively large data set of operational model output could produce more accurate results, and therefore is used in this study. 99 Texas Tech University, Brandon A. Storm, August 2008

On a final note, no matter which method is used to get the history of the mesoscale wind climatology, the simulated wind fields and the local topography and roughness are subsequently used by WAsP to predict the local wind climate. The model output is then processed in a method similar to what one would utilize when using tower observations. However, to “clean” the data to create the wind atlas (described in Chapter 5), one does not use high resolution terrain and surface roughness data, but rather the mesoscale model’s terrain and surface roughness. b. WRF downscaling and verification methods

The technique used to dynamically downscale the operational WRF model’s output with WAsP is a unique process. The detailed steps in the current method are now presented, as well as data used. The ﬁrst step in downscaling the WRF data is extracting the WRF wind data (in this case the 10, 32, and 106 m data) for the grid point nearest to the desired location of the wind farm, or in this study, the location nearest to the 100 m tower near Sweetwater, Texas. The data set of WRF forecasts used in Chapters 6 and 7 were used again here for downscaling purposes. Since 50 and 100 m wind data from WRF are needed for comparison to the 100 m tower, and further as input into WAsP, the 32 and 106 m wind speed and a power law relationship were used to approximate the 50 and 100 m wind speed. The 50 and 100 m wind directions were determined by linearly interpolating the wind direction from 32 and 106 m. The OWC Wizard (see Chapter 5 for details) was used to prepare the WRF, tall tower near Sweetwater, and the Sweetwater ASOS data to be used as an input into WAsP. To downscale WRF, the produced observed wind climate was combined with terrain data extracted from the WRF 12 km output as well as surface roughness inferred from the 12 km WRF land use to generate the local wind atlas (Figs. 9.1 and 9.2). The WRF model assigns a surface roughness based on land uses. This roughness has two yearly values, one for the summer months and one for the winter months. Since a year’s worth of WRF forecasts was used, the seasonal surface roughnesses were averaged together and used as input into WAsP. Admittedly this approach could cause some errors. Due to the 12 km grid size and the techniques WPS uses to assign land use categories, a majority of the area around the site of interest had an average surface roughness of 0.11 m. This can be inferred from Fig. 9.2, as the ﬁne scale roughness features, such as the city of Sweetwater,

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are not resolved in the 12 km land use data. To predict the wind speed at the 100 m tower location from the WRF generated wind atlas, high resolution terrain and surface roughness data were used (Fig. 9.1 and 9.2). The high resolution terrain data was generated from 30 m U.S. elevation data. The high resolution surface roughness was generated from 30 second land use ( 1 km grid ∼ spacing) data processed by WPS. The assigned seasonal surface roughnesses were again averaged to get a yearly surface roughness. The high resolution terrain and surface roughness were used to generate both wind atlases and site specific assessments for the ASOS and tall tower data. To determine if the WRF downscaling is performing well, the generated wind atlas and site specific 100 and 50 m wind estimates at the Sweetwater 100 m tall tower location are compared to wind atlases and site specific estimates generated from 100 m tall tower data and the Sweetwater ASOS. Data from the 100 m tall tower that are not processed by WAsP are considered to be the control. Comparison between estimates using WRF, ASOS, and 100 m tower data is done to give an idea of how well the WRF downscaling performs relative to techniques currently used within the wind industry.

9.3. WRF Downscaling Results a. Wind atlas

As described in Chapter 5 and in the first section of this chapter, the wind atlas describes wind conditions that have been cleaned of surface and terrain effects. Large scale (12 km) terrain and surface roughness from the WRF model were used to make the WRF based wind atlases. The wind atlases is based on observational data use the 1 km average surface roughnesses obtained from 30’ land use data. Admittedly, better representation of the local surface roughness could have significant impact on the end results. The wind atlases are reported in terms of average wind speed and power density for four roughness classes and five heights. As seen in Tables 9.1 and 9.2, the wind atlas created from the 100 m WRF data has both higher average wind speed and power density than the wind atlas created using observed data. In terms of comparison, it may be more fitting to focus on the power densities due to the purposes of this study, as well as the fact that the average power density takes into account the wind speed distribution. Wind atlases created from 50 m WRF data, 50 m tower data, and the Sweetwater ASOS are

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FIG. 9.1. Top plots represent 12 km terrain elevation (MSL in meters) used for WRF simulations. Lower blowout is 30 m NED used in WAsP. Note the scale for the top plots is not the same as for the lower blowout. The star represents the location of the 100 m tower. reported in Appendix B. To summarize, the 50 m tower wind atlas has very similar results as the 100 m tower wind atlas. The 50 m WRF wind atlas has similar results as the 100 m WRF wind atlas, giving higher average wind speed and power density estimates compared to the 100 m tower wind atlas. The wind atlas from the 10 m ASOS station also produced results similar to that created from the 100 m tower. The frequency distribution between the directional sectors is not represented in these tables. The impact of representing not just the wind speed accurately, but also the direction will be shown in the next sub-section. The fact that the WRF based wind atlases produce higher estimates for both wind 102 Texas Tech University, Brandon A. Storm, August 2008

0.5

32.55 0.45 0.4

32.5 0.35

0.3

32.45 0.25

0.2

32.4 0.15

0.1 32.35 0.05

0 −100.5 −100.4 −100.3

FIG. 9.2. Yearly 1 km average surface roughness determined from 30 second land use data processed by WPS. The star denotes the location of the 100 m tower. Red squares represent the high surface roughness associated with the city of Sweetwater, TX.

TABLE 9.1. Wind atlas created from 100 m tower data.

R-class 0 R-class 1 R-class 2 R-class 3 (0.00 m) (0.03 m) (0.10 m) (0.40 m) Height 1 (z = 10 m) ms−1 7.69 5.36 4.67 3.68 W m−2 463 177 117 57 Height 2 (z = 25 m) ms−1 8.41 6.37 5.73 4.82 W m−2 595 281 205 124 Height 3 (z = 50 m) ms−1 9.01 7.32 6.67 5.79 W m−2 718 395 304 202 Height 4 (z = 100 m) ms−1 9.73 8.57 7.87 6.93 W m−2 917 604 465 319 Height 5 (z = 200 m) ms−1 10.67 10.45 9.54 8.36 W m−2 1245 1115 844 568

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TABLE 9.2. Wind atlas created from 100 m WRF data.

R-class 0 R-class 1 R-class 2 R-class 3 (0.00 m) (0.03 m) (0.10 m) (0.40 m) Height 1 (z = 10 m) ms−1 8.16 5.68 4.94 3.89 W m−2 540 204 134 66 Height 2 (z = 25 m) ms−1 8.91 6.75 6.05 5.09 W m−2 693 325 237 142 Height 3 (z = 50 m) ms−1 9.54 7.72 7.03 6.1 W m−2 836 456 351 233 Height 4 (z = 100 m) ms−1 10.29 9.00 8.26 7.29 W m−2 1058 685 530 367 Height 5 (z = 200 m) ms−1 11.25 10.89 9.95 8.75 W m−2 1415 1225 936 638

speed and power densities is of concern. This, however, could be an isolated result and needs veriﬁcation at numerous locations across the U.S. before any concrete conclusions can be made. It is also not clear how much large wind farms affect local climates, but it is a possibility that a large wind farm to the south of the tall tower is slowing down the wind. This is especially a possibility since the wind farm is to the south of the tower and the predominant wind direction is southerly. The WRF model does not have any knowledge of a large wind farm. This could account for the overestimation of the wind speed and power density from the WRF model. Another possible source of error, as discussed in more detail later on in this chapter, is the inaccuracy of the surface roughness in producing the observed based wind atlases. b. Wind speed and power density comparison

While comparisons of wind atlases can give insight into how well WRF is representing the local wind climate, the wind industry’s main goal is to site turbines. To do so, a local wind climate is used as input into WAsP with directional sectors of estimated average wind speeds and power densities as an output. Tables 9.3 and 9.4 show the average wind speed and power densities unprocessed by WAsP (“raw”) and estimates from WAsP using the corresponding input data. The 100 m tower/WAsP method is what is referred to as self-predicting, as 100 m tower data are used within WAsP to estimate the 100 m parameters at the same location. Ideally, these values would be identical, but due to

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WAsP’s techniques of creating a wind atlas ﬁrst, then estimating the wind speed and power density, small changes can be seen. When comparing the raw WRF data to the tall tower data, very accurate estimates of the overall average wind speed and power densities are found. This result is intriguing, though more than likely an anomaly since complex terrain is found around the tall tower site. Due to the 100 m tall tower’s location on a hill, one would assume that speed up effects would be observed. Since the WRF wind atlas has faster wind speeds than the other wind atlases, it is no surprise that the overall estimated WAsP wind speeds and power densities with WRF as an input are higher than the other estimation methods, especially the 100 m tower data (Tables 9.3 and 9.4 and Fig. 9.3). While it is obvious that the 100 m WAsP estimates with WRF as input are higher than what was observed from the 100 m level of the tall tower, a comparison to how well WRF performed with traditional wind industry methods (i.e., 50 m tower data and 10 m ASOS data used to estimate 100 m levels) can be insightful into the WRF/WAsP relative errors. Also, investigating the differences between the direction sectors (see Appendix C) may be more appropriate, instead of comparing the overall differences which are presented in Tables 9.3 and 9.4. For example, even though the overall estimated 100 m average wind speed and power densities from the 10 m ASOS data are the same as the 100 m level

Wm −2 800 a) b) 700

600

m 500

12 k 400

300

200

100 12 km 12 km

FIG. 9.3. a) Power density (W m−2) at 100 m AGL estimated with 100 m tower data as input into WAsP, b) estimated power density (W m−2) at 100 m AGL with 100 m WRF data as input into WAsP.

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tower data, the differences between the individual direction sector estimates are quite large since the sector frequencies between the 100 m tower and ASOS station are quite different. Determining the frequency of wind in each direction sector can be important in the design of wind turbine arrays. This way one can reduce wake effects, and optimize performance of the wind farm. While the WRF estimates have error in determining the frequencies, they tend to be more accurate at 100 m than interpolations from the 10 m ASOS station. One possibility for such results could be that WAsP does not account well for the large turning with height that can be observed when going from 10 m to 100 m.

TABLE 9.3. Estimated 100 m average wind speeds (m s−1) and power densities (W m−2) at the location of the Sweetwater tall tower using various methods. “Raw” methods have not been corrected through WAsP. The 100m tower/WAsP method is “self-predicting.”

Method Avg. Wspd. Power Density 100 m raw tower 8.14 507 100 m raw WRF 8.21 517 100 m tower/WAsP 8.16 512 100 m WRF/WAsP 8.57 588 50 m tower/WAsP 8.43 522 10 m ASOS/WAsP 7.97 507

TABLE 9.4. Same as Table 9.3 except for 50 m.

Method Avg. Wspd. Power Density 50 m raw tower 7.23 343 50 m raw WRF 7.25 349 50 m tower/WAsP 7.23 346 50 m WRF/WAsP 7.7 417 10 m ASOS 6.92 358

9.4. Discussion

While WRF output into WAsP resulted in an overestimation of the average wind speed and power density, the results are encouraging and should be considered as a possible tool for the wind industry. A detailed investigation with high quality tall tower data could 106 Texas Tech University, Brandon A. Storm, August 2008 determine if there are any systematic errors within WRF that could result in WRF data replacing the need for local tower measurements. While the results indicate that errors would have resulted in estimating the average wind speed and power density if one was relying solely on WRF output being used within WAsP, using 50 m data and 10 m ASOS data would have resulted in substantial errors as well. As mentioned at the beginning of this chapter, one possible use for the WRF model could be using it to find regions worth investigating for placement of wind farms. Large wind farms exist to the south of the tower location, therefore it is obviously a desirable location for a wind farm. If this knowledge was not preexisting, one could determine the local area would be worth investigating from the operational WRF output. The 100 m ∼ level wind speed from WRF indicates there are regionally higher wind speeds near the tower location (Fig 9.4). While this gives some indication that this is a region worth investigating, more details can be deducted about the local wind climate when downscaling WRF with WAsP (Fig 9.4). Clearly errors exist in the WRF/WAsP output. If the WRF model had knowledge of the large wind farm, the wind speeds may have been reduced within the model, resulting in more accurate results. Another possible improvement may result if finer scale WRF output (4 km or finer instead of 12 km data) is used. This would allow the WRF model to take into account local topography features not discernible from coarse grids. If the computer resources are available, the WRF model could be run at very fine scales, on the order of 100 m.

9.5. Future Considerations

As mentioned earlier, accurate representation of the local surface roughness could have a large impact in the estimated wind atlass, wind speed, and power density. Figure 9.5 shows that the area around surrounding the 100 m tower has complex land use, ranging from crop land and pasture, forested or shrub land, and urban areas. While the WRF derived land use and subsequent surface roughness (Fig. 9.2) depicts large land use features (i.e., Sweetwater, large bodies of water, some shrub land regions), the WRF model underrepresents the majority of the shrub land south of the tower. Also of concern is that the WRF model uses a surface roughness of 0.1 m for shrub land. Past studies (e.g., Wieringa 1993) have stated that shrub land should have a surface roughness of 0.3 m or larger. 107 Texas Tech University, Brandon A. Storm, August 2008

FIG. 9.4. Top plots are yearly average wind speeds (m s−1) from WRF’s second grid level ( 100 m AGL). Lower blowout is estimated yearly wind speed from WAsP as 100 m WRF data as input.∼ The star represents the location of the 100 m tower.

An adjusted surface roughness (0.15 m for the whole region) was used to determine the roughness sensitivity of estimating the wind atlas derived from 100 m tower data and 100 m wind speed and power density using the WRF wind speed data. Using the adjusted surface roughness, a wind atlas created from the 100 m tower data was in closer agreement to that derived from the WRF data (compare Tables 9.2 and 9.5). An estimated 100 m wind speed using the WRF data and a surface roughness of 0.15 m was 8.26 ms−1 , with a power density of 529 W m−2. When comparing the raw 100 m tower data to

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FIG. 9.5. 30 m 2001 NLCD land use categories surrounding the 100 m Sweetwater tall tower. Green areas represent shrub land , red represents urban or developed regions, and tan depicts crop land and pasture areas. both of these adjusted estimates, both are more accurate than the original WRF/WAsP estimates (Table 9.3). This indicates the importance of gathering accurate surface roughness data to be used in conjunction with the WRF data. One future avenue to explore is to derive the surface roughness from a data set such as the 30 m 2001 NLCD (National Land Cover Data). Consideration of seasonally changing surface roughnesses also needs to be explored to get accurate wind speed and power density estimates.

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TABLE 9.5. Wind atlas created from 100 m tower data assuming a surface roughness of 0.15 m.

R-class 0 R-class 1 R-class 2 R-class 3 (0.00 m) (0.03 m) (0.10 m) (0.40 m) Height 1 (z = 10 m) ms−1 8.00 5.58 4.85 3.82 W m−2 520 199 131 64 Height 2 (z = 25 m) ms−1 8.74 6.63 5.95 5.00 W m−2 665 316 230 137 Height 3 (z = 50 m) ms−1 9.36 7.59 6.92 6.00 W m−2 803 441 339 224 Height 4 (z = 100 m) ms−1 10.09 8.86 8.13 7.16 W m−2 1019 666 514 353 Height 5 (z = 200 m) ms−1 11.05 10.73 9.82 8.62 W m−2 1372 1202 917 620

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Chapter 10

Summary and Future Work

With wind energy emerging as a valuable source of power within the U.S., especially over the Great Plains, an understanding of the local wind environment is important. This understanding is needed so the industry can design appropriate turbines, obtain accurate short-term forecasts, and complete detailed resource site assessments. Increased low-level winds from LLJs can increase the potential power that turbines can draw from the wind. At the same time, the increased shear and turbulence as a reult of LLJs can be detrimental to the turbines. If accurate inflow conditions could be simulated by the WRF model, this could be used as input into TurbSim (Jonkman and Buhl 2007) and other similar applications. In this dissertation, various experiments and verification studies were conducted to see whether the WRF model is a tool the industry could utilize to get an understanding of a local low-level wind environment, especially in areas that experience frequent LLJs. Information that the wind industry could immediately apply, as well as insight into areas where models could be improved, emerged while determining how well the WRF model forecasts LLJs. For example, shear exponents can be estimated by WRF with confidence in some regions (Table 7.1). WRF provided more accurate estimates of upper-level wind speeds and power estimates than assuming a constant 1/7 or even 0.2 shear exponent (Table 7.2). This information could also be used by turbine designers to determine both the average shear and the extreme values of shear a turbine would be subjected to in a specific area. A relationship between the 10 m wind speed and the shear exponent was also derived (Fig. 7.4 and Eq. 7.2). This allows for surface based measurements ( 10 m) to be extrapolated upward with more accuracy instead of ∼ assuming a constant shear exponent. The WRF model was also able to depict the large shear exponents associated with large surface roughnesses, such as those induced from large metropolitan areas (Figs. 7.2 and 7.3). While WRF output showed an ability to represent average shear exponents for many locations, it emerged that the WRF model struggles in forecasting the numerous LLJs over southern Kansas. This was evident in both the underestimation of the shear exponent at

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Sumner, Kansas, as well as the underestimation of the LLJ frequency by the WRF model at Beaumont, Kansas. A comparison of the climatology from the WRF model and a boundary layer profiler revealed that the WRF model struggles in forecasting the overall frequency of LLJs, especially the strong LLJs (i.e., LLJ2 and LLJ3) (Tables 6.1, 6.2, 6.3, and 6.4). The height of the LLJs was also found to be higher in the WRF climatology compared to the profiler (Figs. 6.3 and 6.4). The problems in WRF’s ability to forecast LLJs with high accuracy could be a result of excessive diffusion within the model. This excessive diffusion is common during stable hours, helping to eliminate unrealistic cooling that may otherwise occur. Comparing to forecast periods from the WRF model, 3 – 12 and 27 – 36 hour forecasts revealed that as the forecast time increased, the reliability of the WRF model in forecasting LLJs deteriorated (Table 6.5). As new PBL schemes and operational model configurations become available, the new automated profiler algorithm based on the Chebyshev polynomial will allow for a timely comparison between profilers and the new model output. The main benefit of the new algorithm is that manual inspection of each observed profile does not need to be completed to determine if a profile is of high quality. The conventional classification methods could result in missing lower-level jet maximums, which could have a great impact on the wind industry. Using local maximums and minimums derived from a polynomial to determine

Vmax and ∆V maybe a more appropriate method to classify LLJs. This method allows for information (i.e., height and speed) about each LLJ to be discerned. Evaluating new PBL parameterizations by determining how well they represent LLJs could be insightful into their performance. Stensrud (1996) alluded that if a model is representing the timing, location, and magnitude of a LLJ, then it is most likely that the PBL structure is being represented properly and can be used as a proxy for how well the model is handling the temperature and moisture profiles. The horizontal variation of the daytime surface sensible and latent heat fluxes can also be assumed accurate since these play a critical role in the development of LLJs. However, it should be stressed that even if a model represents LLJs accurately, it does not necessarily mean that the model parameterizations are accurate. It is possible that the model is getting the “right answer” for wrong reasons, and model parameterizations should be rigorously investigated. To determine the WRF model’s sensitivity in forecasting LLJs, two case studies, one over West Texas and the other over southern Kansas, with varying configurations were undertaken. These studies indicated that differences in forecasting the speed and height of

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LLJs can be observed when using the YSU and MYJ PBL schemes (Figs. 8.2 and 8.10). Significant variability in the horizontal structure of LLJs was found (Fig. 8.5). This spatial variability could make the verification studies of LLJs difficult and inaccurate. Instruments such as the Ka-band radar currently under construction at Texas Tech University could allow for horizontal structures of LLJs to be investigated. Whether or not LLJs are terrain following has been discussed in the literature. The modeling results in Chapter 8 suggest that LLJs are terrain following, at least on the large scale. However, Banta et al. (2002) suggested that LLJs are not terrain following based on findings from three profilers within close proximity ( 60 km) of one another located in gently rolling ∼ terrain. A detailed spatial representation of LLJs by the Ka-band radar would add to this discussion. The impact of whether or not LLJs are terrain following could have implications on wind turbines placed on isolated hills. The two case studies had LLJs with weaker than observed wind speeds and higher heights (Figs. 8.2 and 8.10). Even though the configurations tested had double the model levels in the lowest 1 km than the operational WRF configuration, the WRF model still struggled to produce accurate forecasts. It is possible that even more model levels are needed to get an accurate representation of LLJ heights and speeds, and should be investigated in the future. As new PBL schemes become available in WRF (e.g., Asymmetric Convection Model 2) and improvements to current PBL schemes are introduced (e.g., YSU in WRF 3.0), new simulations should be run to determine if any improvements in forecasting LLJs are found. Horizontal grids of 1.33 km were also investigated but were found to give no benefit. It is possible, however, that extremely fine resolutions (on the order of 100 m or so) could greatly improve forecasts of LLJs. This would allow the PBL schemes to be turned off and have three dimensional closure schemes to represent the turbulence within the model. Tests undertaking such an approach are to be proposed and undertaken in the near future. While the WRF model may not yet represent the frequency and strength of LLJs as accurately as the wind industry may desire, it still has great potential in resource assessment and siting projects. An example of WRF’s abilities to be used to find potential wind farm locations is the relatively strong wind speeds near Sweetwater, Texas, depicted in 100 m AGL wind speeds (Fig. 9.3). This location corresponds to a large preexisting ∼ wind farm. The wind industry could use such plots along with information of power transmission lines to find areas worth investigating for new wind farms. A product made

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by 3Tier that gives customers quick access to wind speeds at 20, 50 and 80 m heights on a 5 km grid, Firstlook, relies heavily on WRF model output (personal communication Jim McCaa). This shows the need to understand how well the WRF model is reproducing LLJs and the low-level shear if it is going to be of value to wind industry users. It was also proposed that WRF output could be used as input into WAsP to downscale the WRF data and get detailed wind and power density characteristics. A difference between the WRF/WAsP average wind speed and power density was found compared to that observed from 100 m tall tower data. Even though the overall difference was larger than using a nearby 10 m ASOS station, the direction distribution was better using WRF. This could allow for more efficient turbine arrays to be developed. The benefits of having WRF data quickly, for any location, and over a long time period are advantages the wind industry should consider when deciding whether or not to rely on downscaled WRF output for sitting turbines. Further tests should be done downscaling WRF with WAsP at numerous locations to determine if WRF could reliably be used to site wind turbines. Obtaining high quality measurements at 100 m or higher is an obstacle that will need to be overcome. There should be an investigation of WRF’s abilities to forecast wind speeds in regions of complex terrain and off-shore, regions where getting observations can be difficult should also be done. This requires however verification measurements, which are scarce. Another avenue for downscaling WRF with WAsP that should be explored is breaking wind speed data down into various stability classes, then using WAsP to predict the average wind speed and power densities. This way, appropriate heat flux offsets and RMS can be used within WAsP. Using WAsP corrections to downscale WRF data could also be implemented in short-term forecasts. The Risø National Lab has explored using WAsP corrections and the HIgh Resolution Limited Area Model (HIRLAM) of the Danish Meteorological Institute together to get accurate short-term forecasts. Essentially, if look-up table of corrections based on the stability of the atmosphere can be created for a location (e.g., a wind farm), improved short-term forecasts from the WRF model could be realized. This would be a dynamical/statistical approach of downscaling real-time WRF forecasts. As mentioned earlier, if the WRF model can reproduce the wind climate accurately when used at very fine scales ( 100 m), the downscaling of the WRF output may not be ∼ necessary. However, running simulations at such fine scales is not feasible for most

114 Texas Tech University, Brandon A. Storm, August 2008 companies due to the extensive computing resources required. Another area where WRF model forecasts could be improved for ﬁne scales is if accurate surface roughnesses are used within the model. Satellite derived surface roughnesses could be more accurate than the current approach of using seasonal averages based on land use. On a similar note, the estimations from WAsP could be more accurate if ﬁne scale surface roughnesses were used, and could result in the WAsP estimations with WRF as input being closer to what was observed. Finally, the WRF model shows enough promise in forecasting LLJs that it should be used to do a detailed investigation on forcing mechanisms of LLJs. Even though the presence of LLJs has been known for several years, a debate on the forcing mechanisms still exists. Idealized simulations varying land-use, terrain, soil moisture, etc. could be one approach. Detail dynamic investigation of WRF model output of several LLJ events is another possibility. Investigation into LLJ events that the WRF model failed to forecast should also be investigated to determine if the missed LLJs have certain characteristics the model fails to simulate. In summary, the WRF model does a reasonable job in representing LLJs and the low- level wind, but should be used with caution, especially in regions with frequent and strong LLJs. With computer resources becoming readily available to many wind energy companies, and the vast advances made in numerical modeling in the past years, I believe numerical weather prediction models will have a large impact on the wind industry.

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Appendices

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Appendix A

Jackson and Hunt Theory

As discussed briefly in Chapter 5, the Jackson and Hunt (Jackson and Hunt 1975) theory is the basis used to account for terrain effects on the wind speed in WAsP. A summary, which relies on material presented in Mason and King (1985), of the original theory is presented here. Jackson and Hunt’s linear theory divides flow over a hill into two layers, the inner and outer layer, with the wind flow upstream being described by a logarithmic profile. The outer layer has inviscid flow, and the inner layer is characterized with having significant turbulent stresses divergences. The theory is based on the limit of u /U 0, where U is ∗ 0 → 0 the velocity upstream from the hill.

FIG. A.1. For ﬂow regimes for turbulent ﬂow over a hill (Jackson and Hunt 1975).

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The linearized equations describing the perturbations in the outer inviscid ﬂow are

∂u ∂p U = − , (A.1) 0 ∂x ∂x

∂v ∂p U = − , (A.2) 0 ∂x ∂y and ∂w ∂p U = − , (A.3) 0 ∂x ∂z with boundary conditions w = 0 at z = and w = U ∂h at z = 0. u, v, and w are velocity ∞ 0 ∂x perturbations, h is the height of the hill, and p is the perturbation dynamic pressure. The equations for potential ﬂow can be solved by Fourier transforms. Mason and King (1985) states that the solution for the dynamic pressure is

i(kx+my+nz) p = p0e , (A.4) where h = h ei(kx+my+nz), p = k2(k2 + m2)−1/2U 2h , and n = i(k2 + m2)1/2. 0 0 − 0 0 To determine the height of the inner level (l), where the balance of the nonlinear and stress divergence in the equations of motion terms are considered, the following is assumed:

l = 2Lκu∗/U0, (A.5) where L is the horizontal scale of the topography (Fig. A.1)and κ is the von Karman constant. Mason and King (1985) states that withing the thin layer, l, there is has no vertical variation of the pressure ﬁeld, thus meets the asymptotic requirement that z /l 0. Mason 0 → and King (1985) further states that the shear of the basic velocity proﬁle on the scale l is negligible and the advection velocity in the inner layer is U0. The linearized momentum equations in the inner layer then can be linked to the outer

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layer solutions: ∂u ∂p ∂ ∂u U = − z=0 + 2κ(z + z )u , (A.6) 0 ∂x ∂x ∂z 0 ∗ ∂z and ∂v ∂p ∂ ∂v U = − z=0 + κ(z + z )u . (A.7) 0 ∂x ∂y ∂z 0 ∗ ∂z

Here pz=0 is the outer layer solution at z = 0 and a mixing length approximation is used to parameterize the Reynolds stresses. Mason and King (1985) show that the solutions to Eqs. A.6 and A.7 are:

u =(p /U )[1 K 2(iz′)1/2 /K 2(iz′ )1/2 ] (A.8) z=0 0 − 0 0 0 v =(lp /kU )[1 K 2(2iz′)1/2 /K 2(2iz′ )1/2 ], (A.9) z=0 0 − 0 0 0

′ ′ where z = zkU0/2κu∗, z0 = z0kU0/2κu∗, and K0 is the modified Bessel function. These solutions are added to the original upstream logarithmic profile to get the wind profile over the hill.

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Appendix B

WAsP Wind Atlases

TABLE B.1. Wind Atlas created from 100 m tower data.

TABLE B.2. Wind Atlas created from 100 m WRF data.

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TABLE B.3. Wind Atlas created from 50 m tower data.

R-class 0 R-class 1 R-class 2 R-class 3 (0.00 m) (0.03 m) (0.10 m) (0.40 m) Height 1 (z = 10 m) ms−1 7.93 5.51 4.79 3.76 W m−2 463 172 113 55 Height 2 (z = 25 m) ms−1 8.67 6.57 5.90 4.94 W m−2 596 278 202 119 Height 3 (z = 50 m) ms−1 9.31 7.57 6.89 5.95 W m−2 725 398 304 198 Height 4 (z = 100 m) ms−1 10.07 8.92 8.16 7.15 W m−2 931 626 479 321 Height 5 (z = 200 m) ms−1 11.08 10.96 9.97 8.68 W m−2 1274 1185 886 582

TABLE B.4. Wind Atlas created from 50 m WRF data.

R-class 0 R-class 1 R-class 2 R-class 3 (0.00 m) (0.03 m) (0.10 m) (0.40 m) Height 1 (z = 10 m) ms−1 8.46 5.89 5.11 4 W m−2 553 206 135 65 Height 2 (z = 25 m) ms−1 9.25 7.00 6.28 5.25 W m−2 712 331 240 141 Height 3 (z = 50 m) ms−1 9.91 8.03 7.31 6.30 W m−2 862 471 359 233 Height 4 (z = 100 m) ms−1 10.69 9.40 8.61 7.54 W m−2 1096 724 555 375 Height 5 (z = 200 m) ms−1 11.72 11.44 10.43 9.09 W m−2 1473 1319 998 661

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TABLE B.5. Wind Atlas created from 10 m Sweetwater ASOS data.

R-class 0 R-class 1 R-class 2 R-class 3 (0.00 m) (0.03 m) (0.10 m) (0.40 m) Height 1 (z = 10 m) ms−1 7.5 5.23 4.54 3.56 W m−2 451 175 115 55 Height 2 (z = 25 m) ms−1 8.19 6.21 5.58 4.67 W m−2 578 277 201 119 Height 3 (z = 50 m) ms−1 8.78 7.13 6.49 5.61 W m−2 696 387 297 194 Height 4 (z = 100 m) ms−1 9.47 8.34 7.65 6.71 W m−2 888 587 451 304 Height 5 (z = 200 m) ms−1 10.38 10.15 9.26 8.09 W m−2 1205 1077 815 538

TABLE B.6. Wind Atlas created from 10 m WRF data.

R-class 0 R-class 1 R-class 2 R-class 3 (0.00 m) (0.03 m) (0.10 m) (0.40 m) Height 1 (z = 10 m) ms−1 8.14 5.67 4.91 3.87 W m−2 507 190 124 60 Height 2 (z = 25 m) ms−1 8.9 6.75 6.04 5.07 W m−2 652 306 221 131 Height 3 (z = 50 m) ms−1 9.55 7.76 7.05 6.1 W m−2 791 437 332 217 Height 4 (z = 100 m) ms−1 10.31 9.12 8.33 7.31 W m−2 1011 678 517 349 Height 5 (z = 200 m) ms−1 11.33 11.16 10.14 8.85 W m−2 1373 1260 947 623

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Appendix C

WAsP Estimated Wind Speed and Power Density

TABLE C.1. Frequency distribution of directional sectors, as well as Weibull parameters, mean wind speed, and power density analyzed from the 100 m level wind speed from the tall tower. Statistics are produced from the observed wind climate, and have not been processed through WAsP’s site correction routines.

Sector Sector Freq. Weibull-A Mean Speed Power Density Number Angle (%) (m s−1) Weibull-k (m s−1) (W m−2) 1 0 3.9 8.0 1.85 7.06 447 2 30 6.0 8.2 2.52 7.27 370 3 60 8.9 7.9 2.93 7.08 309 4 90 5.1 6.2 2.73 5.48 150 5 120 3.5 6.4 2.70 5.72 171 6 150 6.0 7.9 3.29 7.08 291 7 180 17.7 9.9 2.76 8.80 615 8 210 26.1 10.6 3.27 9.47 698 9 240 10.6 9.0 2.73 8.03 471 10 270 5.6 10.0 3.08 8.90 598 11 300 3.9 9.5 2.31 8.44 618 12 330 2.6 7.8 1.94 6.90 396 All All 8.14 507

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TABLE C.2. Same as Table C.1 except representing 100 m level WRF data. ∆ P is the difference between the raw 100 m WRF estimated wind power and the estimated wind power from the 100 m level of the tall tower (Table C.1).

Sector Sector Freq. Weibull-A Mean Speed Power Density ∆ P Number Angle (%) (m s−1) Weibull-k (m s−1) (W m−2) (W m−2) 1 0 5 8.4 2.53 7.43 393 -54 2 30 10.5 7.9 2.95 7.02 301 -69 3 60 7.4 7.5 2.57 6.66 281 -28 4 90 4.8 6.7 2.47 5.9 201 51 5 120 4.2 6.1 2.35 5.41 160 -11 6 150 8.8 8.2 3.02 7.37 342 51 7 180 20 10.4 3.67 9.42 654 39 8 210 19.6 10.7 3.4 9.63 721 23 9 240 10.3 10.6 2.49 9.42 810 339 10 270 4.3 9.4 2.82 8.34 517 -81 11 300 2.4 7 2.09 6.23 270 -348 12 330 2.8 8.1 1.71 7.25 531 135 All All 8.21 517 10

TABLE C.3. WAsP frequency distribution of directional sectors, as well as Weibull parameters, mean wind speed, and power density with 100 m level wind data from the tall tower as input. ∆ P is the difference between the estimated wind power as reported in Table C.1. Note, this table represents how well WAsP is self-predicting the site of interest, as it is given data for the same height and location as it is being asked to reproduce.

Sector Sector Freq. Weibull-A Mean Speed Power Density ∆ P Number Angle (%) (m s−1) Weibull-k (m s−1) (W m−2) (W m−2) 1 0 3.8 8.1 1.9 7.15 451 4 2 30 6.1 8.2 2.53 7.27 368 -2 3 60 8.5 7.9 2.89 7.05 308 -1 4 90 5.4 6.4 2.65 5.72 174 24 5 120 3.7 6.6 2.78 5.91 186 15 6 150 6.5 8.1 2.8 7.26 342 51 7 180 17 9.8 2.72 8.76 614 -1 8 210 25.2 10.6 3.25 9.46 698 0 9 240 11.3 9.3 2.77 8.28 511 40 10 270 5.9 9.9 2.95 8.8 592 -6 11 300 3.8 9.5 2.28 8.39 615 -3 12 330 2.7 8.1 2.02 7.14 421 25 All All 8.16 512 5

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TABLE C.4. Same as Table C.3 except 100 m WRF data is used as input into WAsP.

Sector Sector Freq. Weibull-A Mean Speed Power Density ∆ P Number Angle (%) (m s−1) Weibull-k (m s−1) (W m−2) (W m−2) 1 0 4.7 8.6 2.47 7.59 426 -21 2 30 9.8 8 2.87 7.16 323 -47 3 60 7.5 8 2.53 7.08 339 30 4 90 5.3 7.7 2.46 6.79 305 155 5 120 4.8 7 2.34 6.2 242 71 6 150 9.5 9 2.96 8.07 456 165 7 180 18.7 10.7 3.64 9.65 704 89 8 210 18.3 10.9 3.38 9.83 769 71 9 240 10.8 11.2 2.53 9.95 945 474 10 270 5 10.4 2.62 9.25 740 142 11 300 2.6 7.9 2.05 6.97 387 -231 12 330 2.9 8.6 1.76 7.64 600 204 All All 8.57 588 81

TABLE C.5. Same as Table C.3 except 50 m tower data is used as input into WAsP.

Sector Sector Freq. Weibull-A Mean Speed Power Density ∆ P Number Angle (%) (m s−1) Weibull-k (m s−1) (W m−2) (W m−2) 1 0 5.6 8.4 2.2 7.43 439 -8 2 30 10 8.7 3.19 7.8 395 25 3 60 5.7 7 2.82 6.27 220 -89 4 90 3.9 6.5 3.3 5.79 159 9 5 120 4 7.4 3.21 6.64 243 72 6 150 10.5 9.5 3.16 8.47 508 217 7 180 25.4 10.6 3.48 9.53 691 76 8 210 16.5 10.6 3.69 9.52 673 -25 9 240 7.2 9.3 3.67 8.36 456 -15 10 270 5.1 9.9 3.42 8.92 571 -27 11 300 2.9 8.8 2.23 7.8 502 -116 12 330 3.3 8 2 7.05 410 14 All All 8.43 522 15

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TABLE C.6. Same as Table C.3 except 50 m WRF data is used as input into WAsP.

Sector Sector Freq. Weibull-A Mean Speed Power Density ∆ P Number Angle (%) (m s−1) Weibull-k (m s−1) (W m−2) (W m−2) 1 0 4.6 9 2.78 8.04 468 21 2 30 9.7 8.6 3.21 7.67 375 5 3 60 7.5 8.5 2.71 7.54 393 84 4 90 5.1 8.2 3.02 7.34 338 188 5 120 4.7 7.6 2.81 6.78 279 108 6 150 9.8 9.5 3.3 8.49 500 209 7 180 19.7 11 4.15 10.02 750 135 8 210 18.1 11.1 3.98 10.09 779 81 9 240 10.7 11.2 2.78 10 900 429 10 270 4.9 10.4 2.71 9.22 717 119 11 300 2.4 8.3 2.31 7.38 414 -204 12 330 3 8.9 1.86 7.89 621 225 All All 8.92 614 107

TABLE C.7. Same as Table C.3 except 10 m ASOS wind data is used as input into WAsP.

Sector Sector Freq. Weibull-A Mean Speed Power Density ∆ P Number Angle (%) (m s−1) Weibull-k (m s−1) (W m−2) (W m−2) 1 0 7.5 8.1 2.9 7.2 327 -120 2 30 7 7.5 2.85 6.7 266 -104 3 60 5.1 6.5 2.47 5.73 183 -126 4 90 5.1 6.6 2.42 5.88 201 51 5 120 10.7 8.6 2.62 7.62 415 244 6 150 19.5 10.2 2.78 9.04 665 374 7 180 16.4 10.7 3.22 9.55 721 106 8 210 11.1 10.1 3.08 9.01 620 -78 9 240 5.6 9 1.9 7.99 630 159 10 270 3.7 7.3 1.7 6.48 382 -216 11 300 3.5 6.8 1.42 6.22 436 -182 12 330 4.7 7.5 1.86 6.7 380 -16 All All 7.97 507 0

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TABLE C.8. Same as Table C.3 except 10 m WRF data is used as input into WAsP.

Sector Sector Freq. Weibull-A Mean Speed Power Density ∆ P Number Angle (%) (m s−1) Weibull-k (m s−1) (W m−2) (W m−2) 1 0 4.9 9.3 2.86 8.28 501 54 2 30 9.6 9.1 3.6 8.2 435 65 3 60 7.5 8.8 2.71 7.84 441 132 4 90 5.1 7.5 2.86 6.65 260 110 5 120 4.6 6.8 2.88 6.04 194 23 6 150 9.8 8.5 3 7.59 376 85 7 180 19.6 10.7 4.09 9.75 695 80 8 210 18.4 10.8 3.83 9.79 720 22 9 240 10.5 10.4 2.4 9.25 787 316 10 270 4.6 9.6 2.16 8.55 679 81 11 300 2.3 8.6 2.4 7.63 442 -176 12 330 3.1 8.4 1.69 7.54 606 210 All All 8.63 570 63

TABLE C.9. Frequency distribution of directional sectors, as well as Weibull parameters, mean wind speed, and power density analyzed from the 50 m level wind speed from the tall tower. Statistics are produced from the observed wind climate, and have not been processed through WAsP’s site correction routines.

Sector Sector Freq. Weibull-A Mean Speed Power Density Number Angle (%) (m s−1) Weibull-k (m s−1) (W m−2) 1 0 5.7 7.1 1.98 6.27 291 2 30 10 7.4 3 6.61 248 3 60 5.5 5.9 2.72 5.23 131 4 90 3.9 5.5 3.15 4.94 101 5 120 3.9 6.3 3.42 5.63 144 6 150 10.2 8.2 3 7.28 332 7 180 26.4 9.2 3.23 8.21 458 8 210 16.5 9 3.4 8.1 429 9 240 6.6 7.6 3.62 6.88 256 10 270 5.2 8.8 3.17 7.9 412 11 300 3.1 7.9 2.08 6.97 382 12 330 3.2 6.7 1.74 5.97 289 All All 7.23 343

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TABLE C.10. Same as Table C.9 except representing 50 m level WRF data. ∆ P is the difference between the raw 50 m WRF estimated wind power and the estimated wind power from the 50 m level of the tall tower (Table C.9).

Sector Sector Freq. Weibull-A Mean Speed Power Density ∆ P Number Angle (%) (m s−1) Weibull-k (m s−1) (W m−2) (W m−2) 1 0 4.9 7.4 2.62 6.62 271 -20 2 30 10.4 7.1 2.99 6.3 216 -32 3 60 7.3 6.8 2.55 6 206 75 4 90 4.6 6 2.9 5.38 136 35 5 120 4.1 5.6 2.47 4.93 117 -27 6 150 9 7.3 3.06 6.49 233 -99 7 180 21 9.2 3.81 8.32 443 -15 8 210 19.3 9.4 3.67 8.44 469 40 9 240 10.2 9.2 2.48 8.14 525 269 10 270 4.3 7.9 2.53 6.99 327 -85 11 300 2.2 6.2 2.18 5.53 182 -200 12 330 2.8 7.2 1.62 6.43 396 107 All All 7.25 349 6

TABLE C.11. WAsP frequency distribution of directional sectors, as well as Weibull parameters, mean wind speed, and power density with 50 m level wind data from the tall tower as input. ∆ P is the difference between the estimated wind power as reported in Table C.9. Note, this table represents how well WAsP is self-predicting the site of interest, as it is given data for the same height and location as it is being asked to reproduce.

Sector Sector Freq. Weibull-A Mean Speed Power Density ∆ P Number Angle (%) (m s−1) Weibull-k (m s−1) (W m−2) (W m−2) 1 0 5.5 7.1 2.02 6.31 292 1 2 30 9.6 7.3 2.9 6.54 246 -2 3 60 5.8 6.1 2.59 5.43 151 20 4 90 4.1 5.6 3 5.04 110 9 5 120 4.4 6.7 2.9 5.94 184 40 6 150 11.2 8.3 2.9 7.43 360 28 7 180 24.6 9.1 3.17 8.17 456 -2 8 210 15.8 9 3.36 8.07 426 -3 9 240 7.4 8 3.34 7.22 306 50 10 270 5.3 8.7 3.11 7.78 398 -14 11 300 3.1 7.8 2.04 6.89 376 -6 12 330 3.4 6.9 1.83 6.15 300 11 All All 7.23 346 3

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TABLE C.12. Same as Table C.11 except 50 m WRF data is used as input into WAsP.

Sector Sector Freq. Weibull-A Mean Speed Power Density ∆ P Number Angle (%) (m s−1) Weibull-k (m s−1) (W m−2) (W m−2) 1 0 4.5 7.6 2.54 6.79 299 8 2 30 9.3 7.2 2.92 6.44 233 -15 3 60 7.4 7.3 2.47 6.45 262 131 4 90 5.3 7.2 2.74 6.37 235 134 5 120 5 6.8 2.58 6.06 211 67 6 150 10.3 8.4 3.05 7.48 356 24 7 180 19.1 9.5 3.78 8.59 489 31 8 210 17.3 9.6 3.62 8.62 504 75 9 240 10.8 9.9 2.57 8.82 650 394 10 270 5.3 9.3 2.46 8.23 546 134 11 300 2.5 7.5 2.08 6.6 324 -58 12 330 3.1 7.9 1.72 7.06 486 197 All All 7.7 417 74

TABLE C.13. Same as Table C.11 except 10 m ASOS wind data is used as input into WAsP.

Sector Sector Freq. Weibull-A Mean Speed Power Density ∆ P Number Angle (%) (m s−1) Weibull-k (m s−1) (W m−2) (W m−2) 1 0 7.3 6.9 2.64 6.09 210 -81 2 30 6.7 6.3 2.59 5.62 167 -81 3 60 5.1 5.6 2.26 4.93 125 -6 4 90 5.3 5.8 2.22 5.09 140 39 5 120 11.4 7.7 2.38 6.8 315 171 6 150 19.6 9 2.54 7.98 485 153 7 180 15.9 9.2 2.93 8.23 486 28 8 210 10.6 8.6 2.8 7.65 401 -28 9 240 5.7 8 1.78 7.09 475 219 10 270 3.9 6.5 1.56 5.8 308 -104 11 300 3.7 6.1 1.31 5.67 377 -5 12 330 4.9 6.6 1.72 5.92 286 -3 All All 6.92 358 15

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TABLE C.14. Same as Table C.11 except 10 m WRF data is used as input into WAsP.

Sector Sector Freq. Weibull-A Mean Speed Power Density ∆ P Number Angle (%) (m s−1) Weibull-k (m s−1) (W m−2) (W m−2) 1 0 4.8 7.9 2.61 7 321 30 2 30 9.3 7.7 3.27 6.88 268 20 3 60 7.4 7.6 2.49 6.72 294 163 4 90 5.4 6.6 2.6 5.82 186 85 5 120 4.9 6.1 2.62 5.39 147 3 6 150 10.4 7.5 2.79 6.72 272 -60 7 180 19 9.2 3.72 8.28 441 -17 8 210 17.7 9.2 3.49 8.3 456 27 9 240 10.6 9.2 2.23 8.17 576 320 10 270 5 8.7 1.99 7.71 539 127 11 300 2.4 7.7 2.12 6.78 344 -38 12 330 3.2 7.6 1.58 6.81 488 199 All All 7.42 383 40

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