Using Small Unmanned Aerial Vehicles for Turbulence Measurements in the Atmosphere

Abstract

This paper demonstrates the possibility of using the telemetry of small unmanned aerial vehicles (UAVs) to monitor the state of atmospheric turbulence. The turbulence spectrum is determined from data on the roll, pitch, and yaw angles of the DJI Mavic Mini quadcopter and then compared with measurements of AMK-03 autonomous sonic weather station. The measurements are carried out at the Basic Experimental Complex (BEC) of the Zuev Institute of Atmospheric Optics, Siberian Branch, Russian Academy of Sciences (SB RAS) (Tomsk, Russia), the territory of which has a nearly smooth and uniform surface, on July 24 and August 12, 2020. It has been found that the turbulence spectra obtained with AMK-03 and the DJI Mavic Mini are generally identical with minor discrepancies in the high-frequency spectral range from $f\sim 1{{\;}}$ Hz. For the data obtained in July, the turbulence spectra in the inertial range obey the 5/3 law, and the relation of measured turbulence spectra of the longitudinal and transverse velocity components corresponds to the Kolmogorov–Obukhov isotropic turbulence. As for the data obtained in August, a slight deviation from the 5/3 law was observed in both AMK-03 and DJI Mavic Mini measurements. The longitudinal and transverse turbulence scales were estimated by the least-square fit method with the von Karman model as a regression curve. The turbulence scales calculated from the July and August data of AMK-03 and the DJI Mavic Mini coincide, and the condition describing the relation between the longitudinal and transverse scales in the isotropic atmosphere stays true to a good accuracy.

APPENDIX

By analogy with formulas (16)–(18), we define the quantities ${{\alpha }_{{||}}}$ and α using equations

$${{\alpha }_{{||}}} = {{n}_{x}}{{\alpha }_{x}} + {{n}_{y}}{{\alpha }_{y}},$$

$${{\alpha }_{{}}} = - {{n}_{x}}{{\alpha }_{x}} + {{n}_{y}}{{\alpha }_{y}},$$

where

$${{\alpha }_{x}} = - \left( {\left\langle \varphi \right\rangle {{s}_{{\left\langle \psi \right\rangle }}} + \left\langle \theta \right\rangle {{c}_{{\left\langle \psi \right\rangle }}}} \right) - \left( {\varphi {\kern 1pt} '{{s}_{{\left\langle \psi \right\rangle }}} + \theta {\kern 1pt} '{{c}_{{\left\langle \psi \right\rangle }}}} \right),$$

$${{\alpha }_{y}} = - \left( {\left\langle \varphi \right\rangle {{s}_{{\left\langle \psi \right\rangle }}} + \left\langle \theta \right\rangle {{c}_{{\left\langle \psi \right\rangle }}}} \right) - \left( { - \varphi {\kern 1pt} '{{c}_{{\left\langle \psi \right\rangle }}} + \theta {\kern 1pt} '{{s}_{{\left\langle \psi \right\rangle }}}} \right).$$

The estimates of the longitudinal and transverse components of the wind speed obtained using a quadcopter are defined as

$$\hat {u} = {{a}_{{||}}}{{\alpha }_{{||}}} + {{b}_{{||}}},$$

$$\hat {v} = {{a}_{ \bot }}{{\alpha }_{ \bot }} + {{b}_{ \bot }}.$$

Coefficients ${{a}_{{||}}}$, ${{a}_{ \bot }}$, ${{b}_{{||}}}$ and ${{b}_{ \bot }}$ are determined from the experiment using formulas

$${{a}_{{||}}} = \frac{{{{u}_{{\max }}} - {{u}_{{\min }}}}}{{{{\alpha }_{{||,~\max }}} - {{\alpha }_{{||,~\min }}}}},$$

$${{a}_{{}}} = \frac{{{{v}_{{\max }}} - {{v}_{{\min }}}}}{{{{\alpha }_{{ \bot ,~\max }}} - {{\alpha }_{{ \bot ,~\min }}}}},$$

$${{b}_{{||}}} = \left\langle u \right\rangle - {{a}_{{||}}}\left\langle {{{\alpha }_{{||}}}} \right\rangle ,$$

$${{b}_{ \bot }} = \left\langle v \right\rangle - {{a}_{ \bot }}\left\langle {{{\alpha }_{ \bot }}} \right\rangle ,$$

where $\left\langle u \right\rangle$, $\left\langle v \right\rangle$, ${{u}_{{\max }}}$, ${{v}_{{\max }}}$, ${{u}_{{\min }}}$, and ${{v}_{{\min }}}$ are average, maximum, and minimum values of the longitudinal and transverse components according to AMK-03 data; $\left\langle {{{\alpha }_{{||}}}} \right\rangle$, $\left\langle {{{\alpha }_{ \bot }}} \right\rangle$, ${{\alpha }_{{||,~{\text{max}}}}}$, ${{\alpha }_{{ \bot ,~{\text{max}}}}}$, ${{\alpha }_{{||,\;{\text{min}}}}}$, and ${{\alpha }_{{ \bot ,\;{\text{min}}}}}$ are average, maximum, and minimum values of quantities ${{\alpha }_{{||}}}$ and ${{\alpha }_{ \bot }}$. Based on the data of July 24, 2020 ${{a}_{{||}}} = 0.56$, ${{b}_{{||}}} = 0.16$, ${{a}_{ \bot }} = 0.50$, and ${{b}_{ \bot }} = 0$; however, for August 12, 2020, ${{a}_{{||}}} = 0.54$, ${{b}_{{||}}} = 0.06$, ${{a}_{ \bot }} = 0.42$, and ${{b}_{ \bot }} = 0$.