#### 2.1. Bulk Method

When using the sensible heat flux H (W m

^{−2}) in practical applications, it can be measured directly with data from eddy covariance equipment and Equation (1a). It is often related to the mean atmospheric variables via so-called bulk transfer parameterization, i.e.,

where

$\mathsf{\rho}$ is the density of air (1.25 kg m

^{−3}),

${\mathrm{c}}_{\mathrm{P}}$ (1004 J K

^{−1} kg

^{−1}) is the specific heat at a constant pressure,

${\mathrm{u}}_{\mathrm{r}}$ is the wind speed (m s

^{−1}) measured at a reference height (10 m),

$\mathsf{\theta}$ is the potential temperature,

${\mathsf{\theta}}_{0}-{\mathsf{\theta}}_{\mathrm{r}}$ is the difference in potential temperature between the surface and the air, and C

_{H} is the dimensionless exchange coefficient for sensible heat. The latter is often given as a function of wind velocity [

26] and particularly on a surface, such as an ocean or a lake. However, atmospheric stability has an important influence on land surface. The heat transfer coefficient C

_{H} needs to be determined before the surface sensible heat flux can be estimated using Equation (1b). The well-known Monin–Obukhov similarity theory is mostly used to close the bulk transfer parameterization [

1,

27,

28,

29], i.e.,

where

$\mathrm{k}$ is the Von Karman constant (0.4) and

${\mathrm{d}}_{0}$ is the zero-plane displacement as a function of vegetation height (h

_{0}). Zero-plane displacement is determined by Equation (3) [

30],

${\mathrm{z}}_{\mathrm{r}}$ is the reference measurement height, and

${\mathrm{z}}_{0\mathrm{m}}$ is the roughness length, which is calculated with Equation (4) [

31] using the heat transfer coefficient C

_{H} proposed by Verkaik and Holtslag [

32].

${\mathsf{\psi}}_{m}$ and

${\mathsf{\psi}}_{h}$ are different similarity functions related to

${\mathsf{\varphi}}_{m}$ and

${\mathsf{\varphi}}_{h}$, which are the dimensionless functions of atmospheric stability parameters for momentum and sensible heat flux, respectively, and can be expressed as, depending on the atmospheric stability [

33],

where x is

${\left(1-15\left(\frac{{z}_{r}-{d}_{0}}{L}\right)\right)}^{0.25}$.

The Monin–Obukhov atmospheric stability parameter

${z}_{r}/L$ indicates the relative significance of buoyancy versus shear effects. The Obukhov length (L) can be expressed as Equation (8), i.e.,

where g is the gravitational acceleration (m s

^{−2}),

$\overline{\mathsf{\theta}}$ is the mean potential temperature (K) between two heights, and

${\mathrm{u}}_{*}$ is the friction velocity (m s

^{−1}). The friction velocity and sensible heat flux must be estimated to determine L and vice versa. Therefore, L was calculated using an iterative method.

${\mathsf{\psi}}_{\mathrm{m}}$ and

${\mathsf{\psi}}_{\mathrm{h}}$ will equal 0 when the initial value of L is assumed to be the neutral atmospheric stability (=10

^{15}). Based on these variables, the friction velocity, sensible heat transfer coefficient, and sensible heat flux can be calculated in an iterative manner using Equations (1) to (7) and be substituted into Equation (8) to obtain a new value of L under the condition that the ratio

$\left({\mathrm{L}}_{\mathrm{n}}-{\mathrm{L}}_{\mathrm{n}-1}\right)/{\mathrm{L}}_{\mathrm{n}-1}$ is less than 1% [

34].

The sensible heat flux from the bulk transfer method was validated with direct flux measurement at various sites (

Table 1). The results were divided into three categories according to differences in the observation data.

The air temperature, surface skin temperature, and wind speed were based on data collected at six observation sites using an automatic weather system (AWS) (

Table 1). Sites GH1 and GH2 refer to the same reed field (36°36′45″ N, 127°13′05″ E) in Goheung Bay, Jeollanam-do, Korea, and are classified as summer and winter, respectively. GH1 consists of green reeds, approximately 2.5 m tall, and is characterized by a reed cover density higher than that of GH2. Site GH1 extends approximately 10 km north to south and 3 km east to west, with no other terrain or buildings in the surrounding area. At GH2, the reeds were dry, brown, sparse, and few in number compared with GH1. Measurements were collected from a 10 m meteorological tower equipped with a three-dimensional ultrasonic anemometer (CSAT3A, Campbell Sci., Logan, UT, USA), an aerovane (05103, R. M. Young, Traverse City, MI, USA), and a thermo-hygrometer (HMP45C, Campbell Sci., Logan, UT, USA). GR1 and GR2 refer to the same agricultural field (35°49′50.77″ N, 128°27′33.72″ E) at Goryeong-gun, Gyeongsangbuk-do, Korea, and were classified as before and after harvest, respectively. GR1 is a rice field, with crop heights of approximately 70 cm, while GR2 is a rough field that yields rice harvests. A 10 m meteorological tower operated by the Korea Meteorological Administration (KMA) near the field site is equipped with a three-dimensional ultrasonic anemometer (CSAT3A, Campbell Sci., Logan, UT, USA), an aerovane (05103, R. M. Young, Traverse City, MI, USA) and a thermo-hygrometer (HMP45C, Campbell Sci., Logan, UT, USA). Sensible heat fluxes were measured simultaneously at both sites at a height of approximately 2 m using a three-dimensional ultrasonic anemometer (SATI-3K, Applied Technologies, Inc., Longmont, CO, USA) and a surface layer scintillometer (SLS20, Scintec, Rottenburg am Neckar, Germany) to facilitate comparisons between the different levels. The heat fluxes were in good agreement, with a mean bias of 2.87 W m

^{−2} and RMSE of 24.3 W m

^{−2}. The sensible heat fluxes based on the anemometer and surface layer scintillometer were compared and yielded reasonable agreement (i.e., a mean bias of 19.8 W m

^{−2} and RMSE of 34.9 W m

^{−2}). This confirmed the demonstrated reliability of the SLS20 scintillometer when performing measurements of various surfaces [

35,

36,

37,

38].

Site KHR (130 m wide; located at 35°51′00″ N, 128°28′13″ E) is part of the Kumho River, which flows southwest of Daegu, Korea, and is approximately 2.5 km from sites GR1 and GR2. Site SYR (90 m wide; located at 35°11′26″ N, 129°06′52″ E) is part of the Suyeong River, which flows south into the city of Busan. Air temperature and wind speed were measured at 10 m using a weather transmitter sensor (WXT520, Vaisala, Vantaa, Finland). Water temperature was measured using a water temperature sensor (LTC Levelogger, Solinst, Georgetown, Canada) and the sensible heat flux across the width of the water surface was measured using a SLS20 scintillometer, which calculates turbulence parameters using variations in the refractive index of light based on changes in temperature, air density, momentum, and moisture between the receiver and transmitter.

We then estimated the sensible heat flux using the bulk transfer method with UAV-observed air temperature and AWS-observed wind speed and surface skin temperature data at three KMA observation sites: Cherwon (CHR; 38°08′53″ N, 127°18′16″ E) is surrounded by farmland, Wonju (WON; 37°20′15″ N, 127°56′48″ E) is a complex area including residential buildings, and Sokcho (SOK; 38°15′02″ N, 128°33′52″ E) is located in the East sea, approximately 30 m southwest off the coast of Korea. Anticyclonic conditions were dominant during the UAV-based observation periods (

Table 1).

Finally, we estimated the UAV-based wind speed and evaluated it with ground observations. We estimated the sensible heat flux using the UAV-based wind speed and UAV-observed air temperature and observed surface skin temperature at two sites: Boseong (BOS; 34°45′48″ N, 127°12′53″ E) is a standard weather observatory operated by the KMA that conforms to international standards set by the World Meteorological Organization; site BOS was designated as a leading observation station in January 2012, with the site consisting of a horizontal homogeneous agricultural area (154,500 m^{2}) which is in contact with the sea to the south.

Site YHI (37°15′50″ N, 126°29′44″ E) is located along the southern coast of Youngheung Island, near the city of Incheon (

Table 1). Site YHI has an area of 23.46 km

^{2} and a 42.2 km coastline. A meteorological tower was installed and equipped with a weather transmitter (WXT520, Vaisala, Vantaa, Finland), surface temperature sensor, and three-dimensional ultrasonic anemometer.

#### 2.2. Unmanned-Aerial-Vehicle-Based Wind Speed

The UAV used in this study (

Figure 1a) has four rotors and is capable of stable flight for up to 30 min with a fully charged battery. The UAV frame (Tarot X4, Wenzhou Aviation Technology Co., Wenzhou, China) is 960 mm × 960 mm × 320 mm with a weight of 1.6 kg. It was equipped with a Pixhawk 2 (3DR, USA) autopilot consisting of an external GPS (HERE + RTK GNSS, 3DR, Berkeley, CA, USA), a three-axis accelerometer, a three-axis gyroscope, a three-axis magnetometer, a temperature sensor, and a barometer to ensure stable position control. The IMU, which consisted of a three-axis accelerometer, and gyroscope automatically measured the UAV’s position data during the flight. Kalman filter calibrations were carried out in flight to decrease errors. The IMU and flight measurement unit (FMU) systems were separated to reduce sensor interference and to filter out high-frequency vibrations, reducing errors in the IMU data. The attitude data were recorded at 100 Hz for flight safety and GPS data (ground speed (

${\mathrm{s}}_{\mathrm{g}}$) and ground direction (

${\mathsf{\theta}}_{\mathrm{g}}$)) were collected at 50 Hz. Flight stability was achieved using open source Mission Planner software with a horizontal hovering accuracy of ±0.01 m. UAV maximum elevation, horizontal movement, wind speed, and horizonal and vertical flight speeds were 2,000 m, 1,000 m, 10 m s

^{−1}, 6 m s

^{−1}, and 5 m s

^{−1}, respectively. To measure the air temperature, a thermo-hygrometer (HOBO H8 Pro, ONSET, Wareham, MA, USA) was installed on the rotary-wing of the UAV at 40 cm above the rotors. The rotary-wing UAV moves through the air by setting a tilt angle that is roughly proportional to speed. This tilt angle varies in real time to maintain stable flight. Therefore, the UAV-based wind vector can be indirectly estimated using the pitch, roll, and yaw angles measured by onboard sensors (IMU) for UAV’s attitude control without additional sensors for wind vector measurements [

13,

14,

15,

16,

17,

18,

19,

20,

21].

The UAV-based wind vector was able to be calculated using the wind triangle (

Figure 1b), which is widely used in navigation and estimates the wind vector using a flight and ground vector. The ground vector is measured directly from the UAV GPS receiver while the flight vector can be measured using an optical flow sensor or pitot tube [

13,

17,

19]; however, these methods are not suitable for rotary-wing UAVs due to their flight speed (

${\mathrm{s}}_{\mathrm{f}}$) (which is lower than fixed-wing UAV), inconsistent flight direction (

${\mathsf{\theta}}_{\mathrm{f}}$), and a wide range of tilt angle changes except for an examination [

39].

Neuman and Bartholomai [

21] have found a relationship between the tilt angle and flight speed (

${s}_{f}$) in wind tunnel experiments while Brosy et al. [

20] have estimated flight speed assuming ground speed should be equal to flight speed under calm wind conditions where the wind speed is negligible (less than 1 m s

^{−1}) and have developed a relationship between the tilt angle and flight speed. We developed a relationship between the tilt angle and flight speed using the method given in Brosy et al. [

20]. This is explained in detail in

Section 3.2.

The tilt angle (

$\mathsf{\alpha}$) can be estimated from the inverse scalar product of the normal unit vector

${\overrightarrow{\mathrm{n}}}_{\mathrm{XY}}=\left(0,0,1\right)$ to the XY-plane which is parallel to the ground and the cross product of the unit vectors as shown in Equation (10).

The angle

$\mathsf{\beta}$ between the projection of the vector

${\overrightarrow{\mathrm{e}}}_{\mathrm{pitch}}\times {\overrightarrow{\mathrm{e}}}_{\mathrm{roll}}$ onto the XY-plane, and the viewing direction of the UAV, defined as the negative normal vector

$-{\overrightarrow{\mathrm{n}}}_{\mathrm{YZ}}=\left(-1,0,0\right)$ is calculated using Equation (11).

To calculate the flight direction (

${\mathsf{\theta}}_{\mathrm{f}}$) whether the orthogonal vector

${\overrightarrow{\mathrm{e}}}_{\mathrm{pitch}}\times {\overrightarrow{\mathrm{e}}}_{\mathrm{roll}}$ is located in the left or right direction of the UAV’s viewing direction

$-{\overrightarrow{\mathrm{n}}}_{\mathrm{YZ}}=\left(-1,0,0\right)$, Equation (12) is used. The flight direction can be estimated using

$\mathsf{\beta}$ and the compass angle (

${\mathsf{\delta}}_{\mathrm{c}}$) of the UAV viewing direction using Equation (13).

Finally, the UAV-based wind speed (

${\mathrm{s}}_{\mathrm{w}}$) is calculated using the wind triangle (Equation (14)) with the estimated flight vector (

${\mathrm{s}}_{\mathrm{f}}$,

${\mathsf{\theta}}_{\mathrm{f}}$) and measured ground vector (

${\mathrm{s}}_{\mathrm{g}}$,

${\mathsf{\theta}}_{\mathrm{g}}$).

The drift angle,

$\mathsf{\gamma}$, is equal to the difference between the ground direction (

${\mathsf{\theta}}_{\mathrm{g}}$), which is measured by the GPS receiver and flight direction (

${\mathsf{\theta}}_{\mathrm{f}}$). For detailed explanations of the wind direction (

${\mathsf{\theta}}_{\mathrm{w}}$) calculation, refer to Neuman and Bartholomai [

21].