# Measurements and Modelling of Offshore Wind Profiles in a Semi-Enclosed Sea

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Measurement Setup

#### 2.1. Meteorological Tower

#### 2.2. LIDAR

#### 2.2.1. Location and Data Collection

#### 2.2.2. Momentum Flux Calculations

#### 2.2.3. Influence from the Size of the Measurement Volume

## 3. Model Setup

## 4. Theory

- (1)
- A wind speed being 1 m s${}^{-1}$ stronger than the wind speed at any of the abovelying levels of the LIDAR wind speed profile. Often a criterion of 2 m s${}^{-1}$ exceedance is used, but it is probable that many jets would be missed with a stricter criterion because of the limited height range of 300 m.
- (2)
- A wind speed being 1 m s${}^{-1}$ stronger than the wind speed at any of the abovelying levels up to 300 m height, based on the WRF model wind speed profile. This is the same criterion as is used for the LIDAR (crit. 1).
- (3)
- A wind speed being 2 m s${}^{-1}$ stronger than the wind speed at any of the abovelying levels up to 1000 m height, but with a jet core at or below 300 m height, based on the WRF model wind speed profile. With this criterion possibly more LLJ cases can be included due to the information from higher heights, but the results are still comparable to crit. 1, because of the restriction of the jet core height.
- (4)
- A LLJ occurring simultaneously in both the LIDAR and WRF wind speed profile, based on crit. 1 and 2.

## 5. Results

#### 5.1. Comparison of Tower and LIDAR Data

#### 5.1.1. Wind Speed and Direction

#### 5.1.2. Turbulent Quantities

#### 5.2. Comparison of LIDAR and WRF Data

#### 5.2.1. Wind Speed and Direction

#### 5.2.2. Turbulent Quantities

#### 5.3. Low-Level Jet Occurrence

#### 5.4. LLJ Characteristics

#### 5.5. Example of LLJ Cases

## 6. Discussion and Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**Left**): The study area, with the Östergarnsholm site marked x. The white boxes show the three innermost model domains of the WRF model simulations. (

**Right**): Close-up of the Östergarnsholm island, with the location of the tower and LIDAR marked x.

**Figure 2.**Windroses at (

**Left**): 29 m height from the tower and (

**Right**): 28 m height from the LIDAR during one full year.

**Figure 3.**Scatter plot of (

**a**) wind speed and (

**b**) wind direction from tower and LIDAR measurements at 29 and 28 m height respectively for one full year. The full line shows the 1:1 ratio. The equation of the best fit line, using a reduced major axis fit, the squared correlation coefficient, the root-mean square error and the number of data points are given in the lower part of (

**a**).

**Figure 4.**Scatter plot of momentum flux from sonic anemometer at 25 m height and LIDAR at 28 m height for the period 18 April–30 November. The squared correlation coefficient, root-mean-square error and the number of data points are given in the lower corner of the figure. Please note that there is some data not shown outside the range of the plot.

**Figure 5.**Time series of momentum flux during May 2017 from sonic anemometer at 25 m height and LIDAR data at 28 m height.

**Figure 7.**Mean wind speed profiles from LIDAR and WRF divided into sea and land sectors during one full year. The filled area shows the standard deviation of the mean at each height.

**Figure 8.**Scatter plot of (

**a**) wind speed and (

**b**) wind direction from the sea sector from LIDAR and WRF at 100 m height for one full year. The full line shows the 1:1 ratio, and the dashed line shows the best fit line using a reduced major axis fit. The equation of the fitted line, squared correlation coefficient and root mean square error are given in the lower corner of the figure.

**Figure 9.**Mean wind speed profiles for the full year from the LIDAR (dashed) and WRF (full lines) with wind directions from the sea sector in different stability classes. VU: very unstable ($z/L<-0.2$), MU: moderately unstable ($-0.2<z/L<-0.05$), N: neutral ($-0.05<z/L<0.05$), MS: moderately stable ($0.05<z/L<0.2$) and VS: very stable ($z/L>0.2$)

**Figure 10.**Average vertical profiles of (

**a**) turbulence intensity and (

**b**) momentum flux from the LIDAR and WRF for land and sea sectors. The profiles in (

**a**) cover the whole year, and the profiles in (

**b**) cover the period 18 April–30 November

**Figure 11.**(

**a**) LLJ frequency each month classified in three different ways, as described in the text. (

**b**) Diurnal variation of LLJ frequency during April–July 2017 classified in three ways. (

**c**) Diurnal variation of wind shear during April–July 2017.

**Figure 12.**Wind speed profiles during LLJ occurrence from one full year from LIDAR and WRF. In (

**a**) the LLJ classification is made from LIDAR data and in (

**b**) the classification is made from WRF data below 1000 m. In (

**c**) a LLJ must exist in both these classifications. N gives the number hourly profiles in each classification. The filled areas show the standard deviation of the mean at each height.

**Figure 13.**Average vertical profiles of momentum flux during cases with simultaneous LLJ occurrence in LIDAR and WRF calculated from (

**a**) the arithmetic mean and (

**b**) the median of radial velocities. The data is selected from the period 18 April–30 November. The filled areas show the standard deviation of the mean at each height.

**Figure 14.**Wind speed from LIDAR measurements and WRF simulations at 100 m height during (upper panel) May and (lower panel) June 2017 shown by the lines. The filled horizontal areas at the top of the figure mark occurrences of LLJs classified from (lowermost, blue color) LIDAR (middle, red color) WRF below 300 m and (uppermost, green color) WRF below 1000 m. The filled vertical areas mark times with winds from the sea sector.

**Figure 15.**Time-height cross sections of wind speed (color fill) and momentum flux (lines) from (

**a**) LIDAR and (

**b**) WRF during 12 May 12 UTC to 13 May 23 UTC 2017. The momentum flux contour levels are drawn from −0.1 to 0.1 with 0.02 interval. Negative contours are dashed, and zero-line is thick.

**Figure 16.**Time-height cross sections of wind speed (color fill) and momentum flux (lines) from (

**a**) LIDAR and (

**b**) WRF during 20 May 06 UTC to 21 May 05 UTC 2017. The momentum flux contour levels are drawn from −0.1 to 0.1 with 0.02 interval. Negative contours are dashed, and zero-line is thick.

**Table 1.**Mean seasonal error metrics of WRF wind speed compared to the LIDAR with wind directions from the sea sector.

DJF | MAM | JJA | SON | |
---|---|---|---|---|

U bias${}_{29\phantom{\rule{4.pt}{0ex}}\mathrm{m}}$ | −0.54 | −0.19 | −0.18 | −0.21 |

U RMSE${}_{29\phantom{\rule{4.pt}{0ex}}\mathrm{m}}$ | 1.65 | 1.96 | 2.10 | 2.17 |

U bias${}_{100\phantom{\rule{4.pt}{0ex}}\mathrm{m}}$ | −0.50 | −0.20 | −0.08 | −0.24 |

U RMSE${}_{100\phantom{\rule{4.pt}{0ex}}\mathrm{m}}$ | 1.72 | 2.33 | 2.41 | 2.42 |

U bias${}_{200\phantom{\rule{4.pt}{0ex}}\mathrm{m}}$ | −0.29 | 0.20 | 0.23 | −0.09 |

U RMSE${}_{200\phantom{\rule{4.pt}{0ex}}\mathrm{m}}$ | 1.89 | 2.86 | 2.76 | 2.60 |

U bias${}_{300\phantom{\rule{4.pt}{0ex}}\mathrm{m}}$ | −0.1 | 0.55 | 0.53 | 0.15 |

U RMSE${}_{300\phantom{\rule{4.pt}{0ex}}\mathrm{m}}$ | 2.02 | 2.94 | 3.06 | 2.72 |

**Table 2.**Number of data and error measures for wind speed in WRF compared to the LIDAR in each stability class for data from the sea sector.

Stability Class | VU | MU | N | MS | VS |
---|---|---|---|---|---|

Number of data | 558 | 637 | 1025 | 380 | 235 |

bias${}_{29\phantom{\rule{4.pt}{0ex}}\mathrm{m}}$ | −0.01 | −0.47 | −0.48 | −0.23 | −0.25 |

RMSE${}_{29\phantom{\rule{4.pt}{0ex}}\mathrm{m}}$ | 1.71 | 1.76 | 2.24 | 1.92 | 1.74 |

bias${}_{100\phantom{\rule{4.pt}{0ex}}\mathrm{m}}$ | 0.13 | −0.29 | −0.42 | −0.16 | 0.04 |

RMSE${}_{100\phantom{\rule{4.pt}{0ex}}\mathrm{m}}$ | 1.89 | 1.97 | 2.50 | 2.28 | 2.00 |

bias${}_{200\phantom{\rule{4.pt}{0ex}}\mathrm{m}}$ | 0.19 | −0.03 | −0.17 | 0.35 | 0.63 |

RMSE${}_{200\phantom{\rule{4.pt}{0ex}}\mathrm{m}}$ | 2.27 | 2.05 | 2.77 | 2.60 | 2.93 |

bias${}_{300\phantom{\rule{4.pt}{0ex}}\mathrm{m}}$ | 0.19 | 0.19 | 0.24 | 0.82 | 0.82 |

RMSE${}_{300\phantom{\rule{4.pt}{0ex}}\mathrm{m}}$ | 2.39 | 2.16 | 3.01 | 2.88 | 2.92 |

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**MDPI and ACS Style**

Svensson, N.; Arnqvist, J.; Bergström, H.; Rutgersson, A.; Sahlée, E.
Measurements and Modelling of Offshore Wind Profiles in a Semi-Enclosed Sea. *Atmosphere* **2019**, *10*, 194.
https://doi.org/10.3390/atmos10040194

**AMA Style**

Svensson N, Arnqvist J, Bergström H, Rutgersson A, Sahlée E.
Measurements and Modelling of Offshore Wind Profiles in a Semi-Enclosed Sea. *Atmosphere*. 2019; 10(4):194.
https://doi.org/10.3390/atmos10040194

**Chicago/Turabian Style**

Svensson, Nina, Johan Arnqvist, Hans Bergström, Anna Rutgersson, and Erik Sahlée.
2019. "Measurements and Modelling of Offshore Wind Profiles in a Semi-Enclosed Sea" *Atmosphere* 10, no. 4: 194.
https://doi.org/10.3390/atmos10040194