# The WRF Model Forecast-Derived Low-Level Wind Shear Climatology over the United States Great Plains

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## Abstract

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## 1. Introduction and Motivation

Turbine Manufacturer | Turbine Ratings (MW) | Diameter of Rotors (m) | Hub Height (m) | Max. Reach of Blades (m) |

Mitsubishi | 1 | 57–61.4 | 45–69 | 99.7 |

Suzlon | 1.25 | 64–66 | 56–74 | 107 |

GE | 1.5 | 70.5–77 | 61–100 | 138.5 |

Gamesa | 2 | 80–90 | 60–100 | 145 |

Siemens | 2.3 | 93 | 70–80 | 126.5 |

Vestas | 3 | 90 | 80–105 | 150 |

**Figure 1.**The WRF model forecast-derived one-year (April 2006–March 2007) average diurnal wind speed variation at Sumner, KS. Left panel: diurnal cycle at different heights in the atmospheric boundary layer. Right panel: vertical profiles at specific times of the day.

**Figure 2.**Diurnal variation of one-year average wind shear exponents (see Equation 1 for definition) along with turbine fault occurrences at Big Spring, TX. The observed average shear exponent values (black circles) and fault times (red squares) are reproduced from Smith et al. [13] using Engauge Digitizer 4.1. The WRF model forecast-based one-year average shear exponent values (black line with solid circles) have been calculated by the authors (see Section 3 for details).

## 2. Wind Shear

## 3. Data and Methodology

#### 3.1. Operational WRF Model Forecasts

Model Run | WRF Version | Horizontal Grid Spacing (km) | Initial and Boundary Data | PBL Scheme | Output Frequency (h) |

WRF-NCAR | 2.1, 2.2 | 36/12 | AWIP | YSU | 3 |

WRF-YSU-NARR | 3.1.1 | 27/9 | NARR | YSU | 1 |

WRF-MYJ-NARR | 3.1.1 | 27/9 | NARR | MYJ | 1 |

WRF-QNSE-NARR | 3.1.1 | 27/9 | NARR | QNSE | 1 |

WRF-ACM2-NARR | 3.1.1 | 27/9 | NARR | ACM2 | 1 |

WRF-YSU-NNRP | 3.1.1 | 27/9 | NNRP | YSU | 1 |

WRF-YSU-FNL | 3.1.1 | 27/9 | FNL | YSU | 1 |

WRF-YSU-AWIP | 3.1.1 | 27/9 | AWIP | YSU | 1 |

#### 3.2. Sensitivity Studies Using the WRF Model

**Figure 3.**Time-height plots of mean wind speed between May 19, 2006 and May 31, 2006. The panels represent (from top to bottom) WRF-NCAR, WRF-YSU-NARR, WRF-MYJ-NARR, and WRF-YSU-AWIP runs, respectively. Occurrences of low-level jets are clearly visible in all the model runs.

#### 3.3. Observational Data

- Tall-tower observations are basically point measurements. In contrast, the WRF model forecast-derived statistics correspond to a spatial grid of 12 km (in the case of the operational WRF-NCAR run) or 9 km (in the case of the sensitivity study runs) resolution.
- While the WRF model forecasts represent instantaneous values (1 or 3 hourly), most of the observed wind speed values utilized by us and SE06 (personal communication, Elliot and Schwartz, 2007) were 10 minute averages.
- Data from the directional sectors affected by the tower structure (shadowing effects) were not considered by us and SE06. However, we analyzed all the directional sectors from the WRF model forecasts.

## 4. Results and Discussions

#### 4.1. Wind Characteristics at Sweetwater, TX

**Table 3.**Comparison of the observed and the WRF-NCAR model forecast-derived wind speed related statistics at Sweetwater, TX (100 m AGL). Study period: April, 2006–March, 2007.

$\overline{U}$ (m s${}^{-1}$) | c (m s${}^{-1}$) | k | ${U}_{max}^{F}$ (m s${}^{-1}$) | ${U}_{max}^{E}$ (m s${}^{-1}$) | ${E}_{D}$ (W m${}^{-2}$) | |

Observation | 8.36 | 9.42 | 2.56 | 7.76 | 11.80 | 544.09 |

WRF-NCAR | 8.18 | 9.21 | 2.42 | 7.39 | 11.80 | 526.98 |

**Figure 4.**Comparison of the observed (left panel) and the WRF-NCAR model forecast-derived (right panel) wind speed probability density functions at Sweetwater, TX (100 m AGL). The red lines denote the fitted Weibull probability density functions. Study period: April, 2006–March, 2007.

**Figure 5.**Comparison of the observed (top-left panel) and the WRF-NCAR model forecast-derived (top-right panel) wind roses at Sweetwater, TX (100 m AGL). The observed wind rose at 50 m AGL is also shown (bottom panel). Study period: April, 2006–March, 2007.

**Table 4.**Means and standard deviations of the observed and the WRF-NCAR model forecast-derived annual average shear exponents and directional shear magnitudes at Sweetwater, TX. Study period: April, 2006 – March, 2007.

Anemometer | Observed | Observed | Observed | WRF Grid | WRF | WRF | WRF | WRF | WRF |

Heights (m) | ${\alpha}_{q}$ | ${\sigma}_{{\alpha}_{q}}$ | ${\alpha}_{a}$ | Levels (m) | ${\alpha}_{q}$ | ${\sigma}_{{\alpha}_{q}}$ | ${\beta}_{q}{(}^{\circ})$ | ${\sigma}_{{\beta}_{q}}{(}^{\circ})$ | ${\alpha}_{a}$ |

50, 100 | 0.169 | 0.136 | 0.182 | 30, 101 | 0.168 | 0.072 | 2.22 | 3.42 | 0.177 |

**Figure 6.**Diurnal variation of the observed and the WRF-NCAR model forecast-derived annual average wind shear exponents (left panel) and the directional shear magnitudes (right panel) at Sweetwater, TX. Study period: April 2006–March 2007.

#### 4.2. Wind Shear Values at a Few USGP Sites

**Table 5.**Various statistics related to the observed and the WRF-NCAR model forecast-derived average shear exponents and directional shear magnitudes. Study period: varying time periods for the observed data and April 2006–March 2007 for the WRF-NCAR model forecasts.

Anemometer | Observed | WRF Grid | WRF | WRF | WRF | WRF | WRF | |

Site Name | Heights (m) | α | Levels (m) | ${\alpha}_{q}$ | ${\sigma}_{{\alpha}_{q}}$ | ${\beta}_{q}{(}^{\circ})$ | ${\sigma}_{{\beta}_{q}}{(}^{\circ})$ | ${\alpha}_{a}$ |

Elk City, OK | 40, 70 | 0.227 | 30, 101 | 0.174 | 0.076 | 2.51 | 3.48 | 0.180 |

Ellsworth, KS | 50, 110 | 0.165 | 30, 100 | 0.178 | 0.077 | 2.99 | 3.76 | 0.185 |

Hobart, OK | 40, 70 | 0.195 | 30, 101 | 0.175 | 0.076 | 2.58 | 3.66 | 0.182 |

Jewell, KS | 50, 110 | 0.206 | 30, 99 | 0.175 | 0.073 | 2.93 | 3.71 | 0.180 |

Kearny, KS | 50, 80 | 0.138 | 30, 99 | 0.171 | 0.078 | 3.34 | 4.11 | 0.176 |

Lamar, CO | 52, 113 | 0.150 | 29, 98 | 0.152 | 0.086 | 4.11 | 5.18 | 0.163 |

Logan, KS | 50, 80 | 0.179 | 30, 99 | 0.172 | 0.080 | 3.02 | 3.86 | 0.179 |

Ness, KS | 50, 110 | 0.223 | 30, 100 | 0.172 | 0.078 | 3.00 | 3.79 | 0.178 |

Sumner, KS | 50, 80 | 0.254 | 30, 100 | 0.177 | 0.078 | 3.04 | 3.79 | 0.182 |

Sweetwater, TX | 50, 100 | 0.220 | 30, 101 | 0.168 | 0.072 | 2.22 | 3.42 | 0.177 |

Washburn, TX | 50, 75 | 0.170 | 30, 100 | 0.172 | 0.075 | 2.61 | 3.47 | 0.180 |

**Figure 7.**Diurnal variation of the observed and the WRF-NCAR model forecast-derived annual average wind shear exponents (left panel) and the directional shear magnitudes (right panel). Observed shear exponents are reproduced from SE06 using Engauge Digitizer 4.1. Study period: April 2006–March 2007.

#### 4.3. Spatial Distribution of Wind Shear Values over the USGP

#### 4.4. Sensitivity Studies

**Figure 8.**The WRF-NCAR model forecast-derived one-year average shear exponents (left panel) and magnitude of directional shear (right panel). Stars indicate location of tower locations used by SE06. Study period: April 2006–March 2007.

**Figure 9.**The WRF-NCAR model’s terrain elevation (left panel) above mean sea level (m) and USGS land use (LU) categories that the WRF model assigns to the grid points (right panel). The LU indices are [39]: 1 – urban, 2 – dryland crop and pasture, 3 – irrigated crop and pasture, 5 – cropland/grass mosaic, 6 – cropland/wood mosaic, 7 – grassland, 8 – shrubland, 10 – savanna, 11 – deciduous broadleaf, 14 – evergreen needle-leat, 15 – mixed forest, and 16 – water bodies.

**Figure 10.**Diurnal variation of the observed and the WRF model forecast-derived wind shear exponents (left panel) and the directional shear magnitudes (right panel) at Sweetwater, TX. Study period: May 19, 2006–May 31, 2006.

- The model forecast-derived shear exponents are significantly more sensitive to the PBL schemes than the initial-boundary data;
- All the model runs capture the daytime wind speed shear exponents quite well;
- The model runs using the MYJ, QNSE, and ACM2 PBL schemes significantly overestimates the nighttime wind speed shear exponents;
- The model runs using the YSU PBL scheme severely underestimates the nighttime wind speed shear exponents;
- The model runs using the MYJ, QNSE, and ACM2 PBL schemes produce significantly higher directional shear during nighttime hours in comparison to the runs based on the YSU scheme.

## 5. Concluding Remarks

## Acknowledgements

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**MDPI and ACS Style**

Storm, B.; Basu, S.
The WRF Model Forecast-Derived Low-Level Wind Shear Climatology over the United States Great Plains. *Energies* **2010**, *3*, 258-276.
https://doi.org/10.3390/en3020258

**AMA Style**

Storm B, Basu S.
The WRF Model Forecast-Derived Low-Level Wind Shear Climatology over the United States Great Plains. *Energies*. 2010; 3(2):258-276.
https://doi.org/10.3390/en3020258

**Chicago/Turabian Style**

Storm, Brandon, and Sukanta Basu.
2010. "The WRF Model Forecast-Derived Low-Level Wind Shear Climatology over the United States Great Plains" *Energies* 3, no. 2: 258-276.
https://doi.org/10.3390/en3020258