# High-Resolution Profiling of Atmospheric Turbulence Using UAV Autopilot Data

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Models of Atmospheric Turbulence

#### 2.1.1. Von Karman Model

#### 2.1.2. Dryden Model

#### 2.2. General Information about the Experiment

## 3. Results and Discussion

#### 3.1. Quadcopter Velocity

#### 3.2. Longitudinal and Lateral Wind Velocity Components

#### 3.3. Correlation Analysis

#### 3.4. Spectral Analysis

#### 3.5. Longitudinal and Lateral Scales of Turbulence

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Cornman, L.B.; Chan, W.N. Summary of a workshop on integrating weather into unmanned aerial system traffic management. Bull. Am. Meteorol. Soc.
**2017**, 98, ES257–ES259. [Google Scholar] [CrossRef] - Beard, R.; McLain, T. Small Unmanned Aircraft: Theory and Practice; Princeton University Press: Princeton, NJ, USA, 2010. [Google Scholar]
- Shelekhov, A.; Afanasiev, A.; Shelekhova, E.; Kobzev, A.; Tel’minov, A.; Molchunov, A.; Poplevina, O. Low-Altitude Sensing of Urban Atmospheric Turbulence with UAV. Drones
**2022**, 6, 61. [Google Scholar] [CrossRef] - Kral, S.T.; Reuder, J.; Vihma, T.; Suomi, I.; O’Connor, E.; Kouznetsov, R.; Wrenger, B.; Rautenberg, A.; Urbancic, G.; Jonassen, M.O.; et al. Innovative strategies for observations in the arctic atmospheric boundary layer (ISOBAR)—The Hailuoto 2017 campaign. Atmosphere
**2018**, 9, 268. [Google Scholar] [CrossRef] [Green Version] - Stith, J.L.; Baumgardner, D.; Haggerty, J.; Hardesty, M.; Lee, W.; Lenschow, D.; Pilewskie, P.; Smith, P.L.; Steiner, M.; Vömel, H. 100 Years of progress in atmospheric observing systems. Meteorol. Monogr.
**2018**, 59, 2.1–2.55. [Google Scholar] [CrossRef] - Hocking, W.K.; Röttger, J.; Palmer, R.D.; Sato, T.; Chilson, P.B. Atmospheric Radar; Cambridge University Press: Cambridge, UK, 2016. [Google Scholar]
- Leosphere, Windcube, Vaisala. Available online: https://www.vaisala.com/en/wind-lidars/wind-energy/windcube/ (accessed on 30 April 2023).
- METEK Meteorologische Messtechnik GmbH. Available online: https://metek.de/product-group/doppler-sodar/ (accessed on 30 April 2023).
- Scintec. Available online: https://www.scintec.com/ (accessed on 30 April 2023).
- Zhu, B.; Qunbo, L.; Tan, Z. Adaptive Multi-Scale Fusion Blind Deblurred Generative Adversarial Network Method for Sharpening Image Data. Drones
**2023**, 7, 96. [Google Scholar] [CrossRef] - Xiao, Y.; Zhang, J.; Chen, W.; Wang, Y.; You, J.; Wang, Q. SR-DeblurUGAN: An End-to-End Super-Resolution and Deblurring Model with High Performance. Drones
**2022**, 6, 162. [Google Scholar] [CrossRef] - Tajima, Y.; Hiraguri, T.; Matsuda, T.; Imai, T.; Hirokawa, J.; Shimizu, H.; Kimura, T.; Maruta, K. Analysis of Wind Effect on Drone Relay Communications. Drones
**2023**, 7, 182. [Google Scholar] [CrossRef] - Commission for Basic Systems and Commission for Instruments and Methods of Observation: Workshop on Use of Unmanned Aerial Vehicles (UAV) for Operational Meteorology WMO. 2019. Available online: https://library.wmo.int/doc_num.php?explnum_id=9951 (accessed on 30 April 2023).
- AMDAR Reference Manual: Aircraft Meteorological Data Relay WMO-No. 958, WMO. 2003. Available online: https://library.wmo.int/doc_num.php?explnum_id=9026 (accessed on 30 April 2023).
- Stoffelen, A.; Benedetti, A.; Borde, R.; Dabas, A.; Flamant, P.; Forsythe, M.; Hardesty, M.; Isaksen, L.; Källén, E.; Körnich, H.; et al. Wind Profile Satellite Observation Requirements and Capabilities. Bull. Amer. Meteor. Soc.
**2020**, 101, E2005–E2021. [Google Scholar] [CrossRef] - Liao, X.; Xu, C.; Ye, H.; Tan, X.; Fang, S.; Huang, Y.; Lin, J. Critical Infrastructures for Developing UAVs’ Applications and Low-altitude Public Air-Route Network Planning. Bull. Chin. Acad. Sci. (Chin. Version)
**2022**, 37, 977–988. [Google Scholar] - González-Rocha, J.; Bilyeu, L.; Ross, S.D.; Foroutan, H.; Jacquemin, S.J.; Ault, A.P.; Schmale, D.G., III. Sensing atmospheric flows in aquatic environments using a multirotor small unscrewed aircraft system (sUAS). Environ. Sci. Atmos.
**2023**, 3, 305–315. [Google Scholar] [CrossRef] - Lepikhin, A.P.; Lyakhin, Y.S.; Lucnikov, A.I. The Experience in Drone Use to Evaluate the Coefficients of Turbulent Diffusion in Small Water Bodies. Water Resour.
**2023**, 50, 242–251. [Google Scholar] [CrossRef] - McConville, A.; Richardson, T. High-altitude vertical wind profile estimation using multirotor vehicles. Front. Robot. AI
**2023**, 10, 1112889. [Google Scholar] [CrossRef] [PubMed] - Villa, T.F.; Gonzalez, F.; Miljievic, B.; Ristovski, Z.D.; Morawska, L. An Overview of Small Unmanned Aerial Vehicles for Air Quality Measurements: Present Applications and Future Prospectives. Sensors
**2016**, 16, 1072. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Loubimov, G.; Kinzel, M.P.; Bhattacharya, S. Measuring Atmospheric Boundary Layer Profiles Using UAV Control Data. In Proceedings of the AIAA Scitech 2020 Forum, Orlando, FL, USA, 6–10 January 2020; American Institute of Aeronautics and Astronautics: Orlando, FL, USA, 2020. [Google Scholar] [CrossRef]
- Li, Z.; Pu, O.; Pan, Y.; Huang, B.; Zhao, Z.; Wu, H. A Study on Measuring the Wind Field in the Air Using a Multi-rotor UAV Mounted with an Anemometer. Bound.-Layer Meteorol.
**2023**, 188, 1–27. [Google Scholar] [CrossRef] - González-Rocha, J.; De Wekker, S.F.J.; Ross, S.D.; Woolsey, C.A. Wind Profiling in the Lower Atmosphere from Wind-Induced Perturbations to Multirotor UAS. Sensors
**2020**, 20, 1341. [Google Scholar] [CrossRef] [Green Version] - González-Rocha, J.; Woolsey, C.A.; Sultan, C.; De Wekker, S.F.J. Sensing wind from quadrotor motion. J. Guid. Control Dyn.
**2019**, 42, 836–852. [Google Scholar] [CrossRef] - González-Rocha, J.; Woolsey, C.A.; Sultan, C.; De Wekker, S.F. Model-based wind profiling in the lower atmosphere with multirotor UAS. In Proceedings of the AIAA Scitech 2019 Forum, San Diego, CA, USA, 7–11 January 2019; p. 1598. [Google Scholar]
- Neumann, P.; Bartholmai, M. Real-time wind estimation on a micro unmanned aerial vehicle using its inertial measurement unit. Sens. Actuators A Phys.
**2015**, 235, 300–310. [Google Scholar] [CrossRef] - Palomaki, R.T.; Rose, N.T.; van den Bossche, M.; Sherman, T.J.; De Wekker, S.F.J. Wind estimation in the lower atmosphere using multirotor aircraft. J. Atmos. Ocean. Technol.
**2017**, 34, 1183–1190. [Google Scholar] [CrossRef] - Meier, K.; Hann, R.; Skaloud, J.; Garreau, A. Wind Estimation with Multirotor UAVs. Atmosphere
**2022**, 13, 551. [Google Scholar] [CrossRef] - Cheng, X.; Wang, Y.; Cai, Z.; Liu, N.; Zhao, J. Wind Estimation of a Quadrotor Unmanned Aerial Vehicle. In Advances in Guidance, Navigation and Control; ICGNC 2022 Lecture Notes in Electrical Engineering; Yan, L., Duan, H., Deng, Y., Eds.; Springer: Singapore, 2023; Volume 845. [Google Scholar] [CrossRef]
- Shelekhov, A.P.; Afanasiev, A.L.; Kobzev, A.A.; Shelekhova, E.A. Opportunities to monitor the urban atmospheric turbulence using unmanned aerial system. In Remote Sensing Technologies and Applications in Urban Environments V; SPIE: Washington, DC, USA, 2020; Volume 11535, p. 1153506. [Google Scholar] [CrossRef]
- Shelekhov, A.P.; Afanasiev, A.L.; Shelekhova, E.A.; Kobzev, A.A.; Tel’minov, A.E.; Molchunov, A.N.; Poplevina, O.N. Profiling the turbulence from spectral measurements in the urban atmosphere using UAVs. In Remote Sensing Technologies and Applications in Urban Environments VI; SPIE: Washington, DC, USA, 2021; Volume 11864, p. 118640B. [Google Scholar] [CrossRef]
- Shelekhov, A.; Afanasiev, A.; Shelekhova, E.; Kobzev, A.; Tel’minov, A.; Molchunov, A.; Poplevina, O. Using small unmanned aerial vehicles for turbulence measurements in the atmosphere. Izv. Atmos. Ocean. Phys.
**2021**, 57, 533–545. [Google Scholar] [CrossRef] - Monin, A.S.; Yaglom, A.M. Statistical Hydromechanics. Part 2. In Turbulent Mechanics; Nauka: Moscow, Russia, 1967. [Google Scholar]
- Stull, R.B. An Introduction to Boundary Layer Meteorology; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1989. [Google Scholar]
- Kaimal, J.C.; Finnigan, J.J. Atmospheric Boundary Layer Flows: Their Structure and Measurement; Oxford University Press: Oxford, UK, 1994. [Google Scholar]
- Wildmann, N.; Wetz, T. Towards vertical wind and turbulent flux estimation with multicopter uncrewed aircraft systems. Atmos. Meas. Tech.
**2022**, 15, 5465–5477. [Google Scholar] [CrossRef] - Wetz, T.; Wildmann, N. Spatially distributed and simultaneous wind measurements with a fleet of small quadrotor UAS. J. Phys. Conf. Ser.
**2022**, 2265, 022086. [Google Scholar] [CrossRef] - Shishov, E.A.; Solenaya, O.A.; Chkhetiani, O.G.; Azizyan, G.V.; Koprov, V.M. Multipoint measurements of temperature and wind in the surface layer. Izv. Atmos. Ocean. Phys.
**2021**, 57, 254–263. [Google Scholar] [CrossRef] - Shishov, E.A.; Solyonaya, O.A.; Koprov, B.M.; Koprov, V.M. Investigation into variations of wind directions near the surface. Izv. Atmos. Ocean. Phys.
**2018**, 54, 515–523. [Google Scholar] [CrossRef] - Azbukin, A.A.; Bogushevich, A.Y.; Korolkov, V.A.; Tikhomirov, A.A.; Shelevoi, V.D. A field version of the AMK-03 automated ultrasonic meteorological complex. Russ. Meteorol. Hydrol.
**2009**, 34, 133–136. [Google Scholar] [CrossRef] - Azbukin, A.A.; Bogushevich, A.Y.; Kobzev, A.A.; Korolkov, V.A.; Tikhomirov, A.A.; Shelevoy, V.D. AMK-03 Automatic weather stations, their modifications and applications. Sens. Syst.
**2012**, 3, 47–52. [Google Scholar] - McCombs, A.G.; Hiscox, A.L. Always in flux: The nature of turbulence. In Conceptual Boundary Layer Meteorology; Hiscox, A.L., Ed.; Academic Press: Cambridge, MA, USA, 2023; pp. 19–35. [Google Scholar] [CrossRef]
- Tieleman, H.W. Universality of velocity spectra. J. Wind Eng. Ind. Aerodyn.
**1995**, 56, 55–69. [Google Scholar] [CrossRef] - Flay, R.G.J.; Stevenson, D.C. Integral length scales in an atmospheric boundary-layer near the Ground. In Proceedings of the 9th Australasian Fluid Mechanics Conference, Auckland, New Zealand, 8–12 December 1986. [Google Scholar]
- Guide to Instruments and Methods of Observation Volume I—Measurement of Meteorological Variables (WMO-No. 8) WMO; WMO: Geneva, Switzerland, 2021.
- O’Neill, P.L.; Nicolaides, D.; Honnery, D.; Soria, J. Autocorrelation Functions and the Determination of Integral Length with Reference to Experimental and Numerical Data. In Proceedings of the 15th Australasian Fluid Mechanics Conference, Sydney, Australia, 13–17 December 2004. [Google Scholar]
- Emes, M.J.; Arjomandi, M.; Kelso, R.M.; Ghanadi, F. Integral length scales in a low-roughness atmospheric boundary layer. In Proceedings of the 18th Australasian Wind Engineering Society Workshop, McLaren Vale, Australia, 6–8 July 2016; pp. 1–4. [Google Scholar]
- Yaglom, A.M. Correlation Theory of Stationary and Related Random Functions, Volume 1: Basic Results; Springer: Berlin/Heidelberg, Germany, 1987. [Google Scholar]

**Figure 1.**Google map of the territory of the Basic Experimental Observatory and photographs of the 30 m and 4 m weather towers. Weather towers with acoustic anemometers installed on them at heights of 4, 10, and 27 m are located at the center of the Basic Experimental Observatory.

**Figure 2.**Quadcopter velocity components along the x, y, and z axes during hovering; (

**a**) 4 m, (

**b**) 10 m, (

**c**) 27 m.

**Figure 3.**Longitudinal and lateral wind velocities at a height of 4 (

**a**,

**b**), 10 (

**c**,

**d**), and 27 m (

**e**,

**f**); quadcopter (black curve) and AMK-03 acoustic anemometer (red curve) data. Top plots correspond to the values of ${w}_{r}$ and ${w}_{t}$ measured with a frequency of 10 Hz, bottom plots are for the 1 min smoothed data on $\u2329{w}_{r}\u232a$ and $\u2329{w}_{t}\u232a$.

**Figure 4.**Histograms and total probabilities in percent for the discrepancies between UAV and AMK-03 data for ${\Delta}_{r}$ (

**a**,

**c**,

**e**) and ${\Delta}_{t}$ (

**b**,

**d**,

**f**) before the smoothing procedure at a height of 4 (

**a**,

**b**), 10 (

**c**,

**d**), and 27 m (

**e**,

**f**).

**Figure 5.**Histograms and total probabilities in percent for the discrepancies between UAV and AMK-03 data for $\u2329{\Delta}_{r}\u232a$ (

**a**,

**c**,

**e**) and $\u2329{\Delta}_{t}\u232a$(

**b**,

**d**,

**f**) after the smoothing procedure at a height of 4 (

**a**,

**b**), 10 (

**c**,

**d**), and 27 m (

**e**,

**f**).

**Figure 6.**Autocorrelation functions of longitudinal and lateral turbulent fluctuations of wind velocity at a height of 4 (

**a**,

**b**), 10 (

**c**,

**d**), and 27 m (

**e**,

**f**): AMK-03 anemometer (black curve) and UAV (red curve) data.

**Figure 7.**Cross-correlation functions of turbulent fluctuations at a height of 4 (green curve), 10 (blue curve), and 27 m (red curve) for the longitudinal (

**a**) and lateral (

**b**) wind velocity components.

**Figure 8.**Spectra of turbulent wind velocity fluctuations from quadcopter data at 4 (green curve), 10 (blue curve), and 27 m (red curve): (

**a**) longitudinal ${\mathsf{\Phi}}_{\mathrm{u}}\left(f\right)$ and (

**b**) lateral ${\mathsf{\Phi}}_{\mathrm{v}}\left(f\right)$ spectrum.

**Figure 9.**Spectra of turbulent wind velocity fluctuations from AMK-03 anemometer data at 4 (green curve), 10 (blue curve), and 27 m (red curve): (

**a**) longitudinal ${\mathsf{\Phi}}_{\mathrm{u}}\left(f\right)$ and (

**b**) lateral ${\mathsf{\Phi}}_{\mathrm{v}}\left(f\right)$ spectrum.

UAV | Start, UTC | End, UTC | Hover Height, m | Wind Speed, m/s |
---|---|---|---|---|

DJI Mini | 02:48:30 | 03:01:30 | 4 | 1.6 |

DJI Air | 10 | 1.9 | ||

DJI Phantom 4 Pro | 27 | 2.2 |

**Table 2.**Calibration coefficients, average values of the longitudinal and lateral wind velocity ${\mathrm{W}}_{\left|\right|}$ and ${\mathrm{W}}_{\perp}$, and their standard deviations ${\sigma}_{\left|\right|}$ and ${\sigma}_{\perp}$ in the hovering period.

Height, m | ${\mathit{a}}_{\left|\right|}$ | ${\mathit{b}}_{\left|\right|}$ | ${\mathit{a}}_{\perp}$ | ${\mathit{b}}_{\perp}$ | ${\mathbf{W}}_{\left|\right|}$ | ${\mathbf{W}}_{\perp}$ | ${\mathit{\sigma}}_{\left|\right|}$, m^{2}/s^{2} | ${\mathit{\sigma}}_{\perp}$, m^{2}/s^{2} |
---|---|---|---|---|---|---|---|---|

4 | 0.43 | −0.10 | 0.48 | 0.00 | 1.56/1.56 * | 0.00/0.00 | 0.48/0.51 | 0.54/0.44 |

10 | 0.38 | 0.92 | 0.41 | 0.00 | 1.86/1.86 * | 0.00/0.00 | 0.63/0.44 | 0.59/0.48 |

27 | 0.65 | 0.27 | 0.61 | 0.00 | 2.23/2.23 * | 0.00/0.00 | 0.73/0.68 | 0.76/0.70 |

**Table 3.**Variances ${\sigma}_{r}$ ${\sigma}_{t}$, $\u2329{\sigma}_{r}\u232a$, and $\u2329{\sigma}_{t}\u232a$.

Height | Longitudinal Component | Lateral Component | ||
---|---|---|---|---|

${\mathit{\sigma}}_{\mathit{r}}$ | $\u2329{\mathit{\sigma}}_{\mathit{r}}\u232a$ | ${\mathit{\sigma}}_{\mathit{t}}$ | $\u2329{\mathit{\sigma}}_{\mathit{t}}\u232a$ | |

4 m | 0.40 | 0.11 | 0.40 | 0.15 |

10 m | 0.45 | 0.21 | 0.52 | 0.21 |

30 m | 0.50 | 0.12 | 0.54 | 0.14 |

Average | 0.45 | 0.15 | 0.49 | 0.17 |

Height | Longitudinal Component | Lateral Component | ||
---|---|---|---|---|

No Smoothing | Smoothing | No Smoothing | Smoothing | |

4 m | 0.68 | 0.94 | 0.68 | 0.93 |

10 m | 0.69 | 0.89 | 0.56 | 0.77 |

30 m | 0.75 | 0.97 | 0.72 | 0.96 |

Average | 0.71 | 0.93 | 0.66 | 0.89 |

**Table 5.**Profiles of the longitudinal and lateral turbulence scales for the von Karman model and Dryden model.

${\mathbf{L}}_{\mathbf{u}}$ | ${\mathbf{L}}_{\mathbf{v}}$ | ${\mathbf{L}}_{\mathbf{v}}/{\mathbf{L}}_{\mathbf{u}}$ | |

4 m | |||

AMK-03 | 14.9/16.3 * | 9.0/10.0 | 0.61/0.61 |

DJI Mavic Mini | 14.9/16.3 | 8.7/9.7 | 0.59/0.59 |

10 m | |||

AMK-03 | 17.8/19.4 | 11.6/12.8 | 0.65/0.66 |

DJI Mavic Air | 17.8/19.4 | 12.9/14.3 | 0.73/0.74 |

27 m | |||

AMK-03 | 21.4/23.3 | 15.5/17.1 | 0.73/0.74 |

DJI Phantom 4 Pro | 21.4/23.3 | 12.5/13.8 | 0.59/0.59 |

${\mathbf{L}}_{\mathbf{u}}$ | ${\mathbf{L}}_{\mathbf{v}}$ | ${\mathbf{L}}_{\mathbf{v}}/{\mathbf{L}}_{\mathbf{u}}$ | |

4 m | |||

AMK-03 | 15 | 11 | 0.7 |

DJI Mavic Mini | 17 | 9 | 0.5 |

10 m | |||

AMK-03 | 21 | 12 | 0.6 |

DJI Mavic Air | 20 | 10 | 0.5 |

27 m | |||

AMK-03 | 25 | 17 | 0.7 |

DJI Phantom 4 Pro | 24 | 12 | 0.5 |

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## Share and Cite

**MDPI and ACS Style**

Shelekhov, A.; Afanasiev, A.; Shelekhova, E.; Kobzev, A.; Tel’minov, A.; Molchunov, A.; Poplevina, O.
High-Resolution Profiling of Atmospheric Turbulence Using UAV Autopilot Data. *Drones* **2023**, *7*, 412.
https://doi.org/10.3390/drones7070412

**AMA Style**

Shelekhov A, Afanasiev A, Shelekhova E, Kobzev A, Tel’minov A, Molchunov A, Poplevina O.
High-Resolution Profiling of Atmospheric Turbulence Using UAV Autopilot Data. *Drones*. 2023; 7(7):412.
https://doi.org/10.3390/drones7070412

**Chicago/Turabian Style**

Shelekhov, Alexander, Alexey Afanasiev, Evgeniya Shelekhova, Alexey Kobzev, Alexey Tel’minov, Alexander Molchunov, and Olga Poplevina.
2023. "High-Resolution Profiling of Atmospheric Turbulence Using UAV Autopilot Data" *Drones* 7, no. 7: 412.
https://doi.org/10.3390/drones7070412