In recent years, advances in remote sensing technology have greatly improved how we monitor and assess crop growth and disease. This remote sensing helps decision-making in vegetation and forest fields by providing detailed information on plant characteristics. In particular, the Micasense RedEdge series is widely used in agriculture (Wang, 2021). However, the accuracy of remote sensing depends on atmospheric conditions (Ma et al., 2021), sensor calibration (Xu et al., 2019), and image processing techniques. Therefore, if multispectral images are used, seam line differences will occur in all images resulting from orthomosaic production, unless appropriate radiometric corrections are made (Masili and Ventura, 2019). The position of the sun and camera affects reflectance, which is an important factor in image correction. Each manufacturer of multispectral cameras has a standard process for calibrating them. A comparative and analytical approach is essential for accurately calibrating remote sensing data under diverse atmospheric conditions. Imaging under Sky Clear (SKC) conditions is not always possible, especially in Korea, where the number of sky-clear days is less than 100 days per year (Korea Meteorological Administration, 2024). Clouds are present on approximately three out of every four days. When clouds occur, direct sunlight decreases, and diffused sunlight increases, changing the energy pattern reaching the ground (Tan et al., 2012). Therefore, radiometric correction methods must be adapted to different cloud conditions.

Radiometric corrections are divided into three categories: atmospheric correction, surface reflectance correction, and camera lens aberration correction. Atmospheric correction is the removal of the atmospheric effects on the radiation recorded by the sensor and occurs between the sun and the target in the air (Remote Sensing Research Centre, 2018). Row Gradient of surface reflectance correction (ROW) (Micasense Inc., 2019), Bidirectional Reflectance Distribution Function (BRDF) (Schlerf et al., 2007) normalizes digital number (DN) values to account for the radiance and directionality reflected from the Earth’s surface (Geolearn, 2023). ROW or BRDF is essential for comparing the reflectance values across different irradiance and viewing geometries. Camera lens aberration correction eliminates optical aberration that would otherwise compromise the integrity of the image by lens and aperture (Photography Explorer Co., 2023). In previous research, radiometric correction of Unmanned Aerial Vehicle (UAV) based multispectral imagery under varying atmospheric conditions has been investigated using various methods. For example, the research on UAV-based multispectral imagery calibration under various atmospheric conditions used a linear regression method (LRM). It is primarily focused on no atmospheric correction only surface reflectance correction (Guo et al., 2019). Similarly, the effects of clouds on image quality were investigated, and atmospheric correction such as BRDF was emphasized (Minařík et al., 2019). Additionally, research from the Digital Airborne Imaging Spectrometer Experiment (DAISEX) led to the development of no atmospheric correction but surface reflectance correction, which highlighted how image intensity varies based on flight direction and the sun’s position (Collings et al., 2010).

The main aim of this study is to evaluate the accuracy of radiometric correction methods under two cloud conditions: SKC (cloud cover 0–1) and Broken Clouds Sky (BKN, cloud cover 7) for atmospheric radiometric correction. We used and compared all three correction methods, and introduced a new method called New Row Gradient (NewROW). The ROW, simpler than BRDF, is introduced and compared to other correction methods to assess whether it can be an effective alternative for surface reflectance correction. Python code was used to implement these corrections and validate their accuracy. By comparing these methods under SKC and BKN, this study aims to determine whether NewROW can be effectively utilized where BRDF is absent.

The structure of this study is as follows: Section 2.1 describes the data used in this study, In Section 2.2, the NoProcess, NewROW, and BRDF methods used in this study. The equations and elements required for the study are described, and the methodology is explained. In Section 3.1, the real-time irradiance and radiance observation system was used to observe 3, 16, 26, and 46% Calibrated Reference Tarps (CRTs), and the accuracy results are presented. In Section 3.2, we present the error and adjustment amounts that can occur and analyze the causes. In Section 3.3, we analyze the accuracy by generating different images with three methods and cloud cover with the reflectance observed in the field. We calculated reflectance for each method and evaluated the appropriateness of the NewROW method in SKC and BKN.

2.1. Research Material and Workflow

The study was conducted at the Korea Rural Development, National Agricultural Science Center in Wanjugun, Jeonbuk State, South Korea, from 10:00 to 15:00 on 27 March 2024. The study area, approximately 29,300 m², is cultivated with winter wheat. Six Ground Control Points (GCPs) were installed for geometric calibration, marked as green crosses in Figs. 1(a, b). The blue dots in Figs. 1(a, c) represents the locations of the spectrometers installed for radiometric calibration. Four spectrometers measured radiance and reflectance on a 1 m × 1 m CRT, one measured a white reference, and another measured irradiance.

Figure 1. The research area. (a) Research area: green cross points indicate Ground Control Points (GCPs), blue points indicate Calibrated Reference Tarps (CRTs), and the yellow box represents the Accuracy Validation Site. (b) Green cross points: GCPs. (c) Blue points: CRTs (3%, 16%, 26%, 46%).

The research flowchart is shown in Fig. 2. The data collection is divided into two main parts, the 1st section being the acquisition of aerial images. The data was collected using a DJI Matrice 300 RTK drone with a MicaSense RedEdge MX. The 2nd section is a system that observes irradiance, radiance, and reflectance for atmospheric correction. With multiple spectrometers, even with the same settings, the time and number of observations are different. So, a system that manages six instruments is required. Spectrometer monitoring used 802.11 ax, Samba, Easy Mesh, and Orthogonal Frequency Division Multiple Access (OFDMA) technologies for real-time monitoring within 200 m over WiFi. The data collected at the same time were converted into reflectance of each spectrometer by our Python code. The accuracy was analyzed by calculating the measured reflectance at the same time for four CRTs (3, 16, 26, and 46%) using the Python code. All radiometric corrections were also performed by using the Python code. Geometric corrections were performed using Agisoft Inc. Metashape (Agisoft Inc., 2024) to import images and align photos. GCP used Sokkia GRX 2 and GCX 3′s RTK (Sokkia, 2024). Afterward, building a dense cloud was performed and a Digital Elevation Model (DEM) was created. Orthomosaic and orthophotos were created for the study area according to each of the three methods.

Figure 2. Flowchart of the research.

The SKC and BKN flights were observed under SKC and 70% cloud cover to analyze the change in accuracy depending on the weather conditions. The MicaSense RedEdge MX multispectral camera has five bands: B (Blue: 475±20 nm), G (Green: 560±20 nm), R (Red: 668±10 nm), RE (RedEdege: 717±10 nm), and NIR (Near InfraRed: 840±40 nm), weights 170 grams including Downwelling Light Sensor (DLS) and has a resolution of 8.2 cm/pixel at 120m, a field of view (FOV) is 47.2 (Horizontal), 35.4 (Vertical) and 58° (Max. radius). CCD size is 3.6 by 4.8 mm (960 by 1280 pixels). The focal length was 5.5 mm (1,467 pixels) (Micasense Inc., 2017). Six Avantes AvaSpec-ULS2048CL-EVO (Avantes Inc., 2024) were used for ground observation, with a Signal Noise Ratio (SNR) of 1/300, observation range of 200–1,100 nm, and a CMOS Linear Image Sensor. We used an Avantes spectrometer with a remote cosine corrector and integrated spheres for irradiance application.

2.2. Research Methodology

The atmospheric conditions reflect or absorb sunlight, which changes irradiance by altering the direct and diffused sunlight that reaches the ground surface. It is necessary to remove atmospheric effects because the atmosphere can cause the radiation to scatter or absorb, which can affect the DN values. Data collected using a UAV equipped with a multispectral sensor was processed by applying NoProcess, NewROW, and BRDF. NoProcess is a processing method that does not use any metadata in the image. It uses the intensity values from the original image without any correction or transformation. ROW is a method of compensating for changes in the intensity of the images depending on the direction of flight and the position of the sun. Original Row Gradient (OriROW) is an adaptation of the method presented in the Python-based MicaSense RedEdge MX Image Processing (Micasense Inc., 2017) method.

Manufacturers of multispectral cameras have recommended a standard process for Vignette and OriROW. The OriROW parameter provided by the manufacturer could not be applied to the Rel_angle between ø_s and ø_c. Manufacturer’s methods accuracy is low without Rel_angle and Row_cor, so we improved NewROW method from OriROW method using Rel_angle and Row_cor. BRDF is a method that accurately reflects direct sunlight along with surface characteristics (Pasticcio, 2014). However, it is not provided by the Rededge MX manufacturer because it depends on the land cover and target reflectance. Instead, the Rededge MX provides a ROW parameter that is less affected by field conditions (Micasense Inc., 2019).

The surface albedo and solar directional reflectivity are obtained by integrating over the area averaged surface BRDF. This is used to reflect the direct solar irradiance off the ground (Berk et al., 1999). BRDF is a function of ø_s, θ_s, ø_c and θ_c. If θ_s, ø_s, ø_c and θ_c are same, the same BRDF filter will be applied. But every image’s θ_s, ø_s, ø_c and θ_c are different, thereby different BRDF filters are applied. Moreover, flight images according to the Rel_angle using ø_s and ø_c, the BRDF filter applied is rotated, but the average value stays almost similar.

Pix4D Mapper and Agisoft Metashape (Micasense Inc., 2023) do not support BRDF, but partially support ROW. All aerial photos and satellite images have DN gradient due to ø_c and ø_s (Kennedy et al., 1997). In the multispectral and hyperspectral cameras with relatively low incident energies, this phenomenon occurred when the aperture was fully open and the FOV was wide (Kordecki et al., 2016). The equations used in this study are shown in Eqs. (1–8), and the abbreviations, descriptions, and metadata are shown in Table 1.

Table 1 . Abbreviation, description, and metadata in equations.

Name	Description/XMP/EXIF	Name	Description/XMP/EXIF
Rad	Radiance	Vig	Vignette filter
Gain	EXIF: ISO speed/100	a1, a2, a3	XMP: Radiometric calibration
Bit	EXIF: Bits per sample	Raw	Raw image DN
Exposure	time EXIF: Exposure time	V0, V1, V2, V3, V4, V5	EXIF: Vignetting polynomial
op	Option by process level	x, y	Pixel coordinates from top & left
OriROW	Original row gradient	ROW	Row gradient
NewROW	New row gradient	r	Radius from center
BRDF	Bidirectional reflectance distribution function	θs, øs	θs (Solar Zenith Angle) øs (Solar Azimuth Angle)
fiso	Kiso BRDF isometric component	θc, øc	θc (Camera Zenith Angle)øc (Camera Azimuth Angle)
fgeo Kgeo	BRDF geometric component	Reffactor	Radiance to reflectance factor
Refcor	Corrected reflectance	fvol Kvol	BRDF volumetric component
Rowcor	Row adjustment factor for “1” in the image center	Irradfactor	Irradiance correction factor
Relangle	Relative angle between øs and øc	xc, yc	Image center coordinate
SKC	Sky clear	BKN	Broken clouds sky

EXIF: Exchangeable Image File format, XMP: eXtensible Metadata Platform..

DN to radiance is as shown in Eq. (1). This value is the vignette by lens, as shown in Eq. (2).

The OriROW is as shown in Eq. (3), and the polynomial equation can be used to correct the intensity gradient according to the ø_c and ø_s (Beisl, 2001). So, since the ROW is a simple BRDF, the ø_s, θ_s, ø_c and θ_c can be simplified to Rel_angle and exposure time and row line number function for ROW. However, image processing generally uses image intensity gradients. MicaSense Image Processing (Micasense Inc., 2019) was the first to present the processing method, and it is not available for other cameras due to a lack of relevant constants. For the MicaSense RedEdge MX camera, this function can be applied using a1, a2, and a3 in XMP: Radiometric calibration and exposure time in ExposureTime (EXIF). The program that uses this has the option to use the solar angle as a radiometric correction in Pix4D (Micasense Inc., 2024). This option is used for Sequoia Parrot Disco Pro AG and MicaSense Rededge MX uses the XMP: IrradianceRelativeRotation feature (Micasense Inc., 2017).

ROW is not an accurate representation. The correct representation is the row and column directional intensity gradient correction based on the Rel_angle. The reason is that OriROW correction occurs only when the Rel_angle is 315 < Rel_angle < 45° or 135 < Rel_angle < 225° and column gradient occurs in other cases. In other words, image intensity gradient is the correct expression because it occurs in four directions ,(top, bottom, left and right) depending on the Rel_angle.

Here, the image is categorized into four types depending on Rel_angle = ø_s – ø_c. The Eq. (4) used in this study is as shown in Table 2, where the input image coordinates (x′, y′) are rotated using Rel_angle, which is not considered in previous studies. In this case, Max (x) and Max (y) are 1,279 and 959 because x is 0–1,279 and y is 0–959 based on the image size of 1280 (x) × 960 (y) pixels of Rededge MX camera.

Table 2 . The input and rotated coordinates of NewROW (x’, y’) according to Eq. (4) and the Row_cor by Rel_angle (x, y: image coordinate, x’, y’: rotated coordinate by Rel_angle).

Type	Relangle Range	Rowcor	x’ of Row (x’,y’)	y’ of Row (x’,y’)	Row and Col	Fig. no.
OriROW	0~360°	None	x	x	Row	4.
NewROW	315 < Relangle <	45°	Eq. (5)	x	(y–959) × (–1) Inverse Row	5(a)
	45 < Relangle <	135°	Eq. (6)	y	x	Col	5(b)
	135 < Relangle <	225°	Eq. (5)	x	y	Row	5(c)
	225 < Relangle <	315°	Eq. (6)	y	(x–1279) × (–1)	Inverse Col	5(d)

We used the default Python code provided by MicaSense. It corresponds to OriROW, which can only be applied to the top orientation of the image when Rel_angle is almost 0. With OriROW, the top of the image is set to “1”, so the center of the image has no “1”, and a random value from the exposure time. So the center will be different for every image. In general, the center of the image is the least affected by Vignette, ROW, and BRDF, so it is more beneficial to process with the center of the image set to “1” than to process based on the top of the image. Eq. (5) uses NewROW correction to adjust the center to be “1” based on the maximum and minimum values, while Eq. (6) is used in column gradient correction.

The BRDF are ø_s, θ_s, ø_c and θ_c and θ_c using metadata for each image, as shown in Eq. (7). The BRDF parameters (f_iso, f_geo and f_vol) use previously measured values near the farm area. While the BRDF filter is radially oriented, the NewROW is either column or row oriented, depending on the Rel_angle between the ø_s and ø_c. Eq. (8) depends on each process level, and the applied formula is shown in Table 3.

Table 3 . Eq. (8) by radiometric process and acronym equation and description in this research.

Type	Description	Equation
NoProcess	No correction	Refcor = Raw × Reffactor
NewROW	Vignette, Irradiance, NewROW and Relangle between øs & øc	Refcor = Rad × Vig × NewRow × Reffactor × Irradcor
BRDF	Vignette, Irradiance with BRDF with θs, øs, θc and øc	Refcor = Rad × Vig × BRDF × Reffactor × Irradcor

3.1. Image and Radiometric Data Acquisition

On 27 March 2024, the weather was SKC in the morning and BKN in the afternoon with an average temperature of 10.9°C, ranging from 5.6–17.3°C. These conditions were suitable for this study to analyze the atmospherical radiometric calibration results under both SKC and BKN.

As shown in Table 4, the total flight time was about 6 min 42 sec each flight, and 168, 171 photos were taken at 2–3 sec intervals with 5 bands. The number of photos was slightly different depending on the wind speed and direction of SKC and BKN flights. Flight height was 52.3 m (SKC) 52.1 m (BKN), and ground sample distance was 3.48 cm (SKC), 3.47 cm (BKN), overlap 75%, and sidelap 75%. Flight speed was about 3 m/s. Down and UP flight by ø_c was about 196±2° (Down) and ø_c: 16±2° (Up).

Table 4 . MicaSense RedEdge MX flight data.

Order	Time (H:M:S)			Photo (ea.)	Weather	Band (ea.)	Total (ea.)	Interval (sec)
	Start	End	Flight (M:S)
SKC	10:09:34	10:16:16	6:42	168	Sky Clear	5	840	2~3
BKN	14:27:03	14:33:45	6:42	171	BrokenClouds	5	855	2~3

SKC: Sky Clear, BKN: Broken Clouds Sky..

The aerial triangulation results are shown in Table 5. The pixel error is stable at around 0.5 pixels. The solar noon time was 12:37:07 during this study area and the ø_s and θ_s were 180 & 33.09°. The time difference between the SKC and BKN flights was –2:24:12 and +1:53:17 from solar noon time. SKC flight’s ø_s and θ_s were 126.47 & 46.96° while BKN flight’s ø_s and θ_s were 229.90 & 42.16°. The difference between ø_s and 180° (Solar noon time) was -53.53 (SKC) and 49.9° (BKN). The difference between ø_s and θ_s between each flight was 103.43 and 4.8°. The reduced BRDF adjustment is due to the BKN flight being closer to solar noon time than the SKC flight, which reduced the θ_s from 46.96 to 42.16°.

Table 5 . MicaSense RedEdge MX Aerial triangulation result (Unit: cm (X, Y, Z, Total)).

Type	Flight	E (X)	N (Y)	Height (Z)	Total Err	Pixel Err
NoProcess	SKC	0.52	1.18	0.50	1.39	0.393
	BKN	0.58	0.94	0.34	1.16	0.444
NewROW	SKC	0.66	1.08	0.35	1.32	0.408
	BKN	1.21	1.56	3.30	3.85	0.441
BRDF	SKC	1.58	2.02	1.75	3.10	0.424
	BKN	0.91	2.39	1.62	3.02	0.581

We calibrated and validated for spectrometer calibration with Avantes AvaLight-HAL-CAL-Mini and Avantes AvaLight-DHCAL. After the Cal/Val spectrometer accuracy was ±0.1–0.2% with an average of 10 times. We observed 16,356 irradiances and radiance intervals 1–2 sec 10:03~15:00 during 4 hours 57 min. The wavelength bandwidth and interval resulted in 350–1100 nm and 0.5–0.6 nm.

The observed irradiance, radiance, and reflectance in SKC and BKN flights at 3, 16, 26, and 46% CRT are shown in Table 6 and Fig. 3. The irradiance reaching the ground is stable at 1.0–1.2% for both the SKC and BKN flights. For the BKN flight, the cloud cover ranged from 6.5 to 7.5 based on field observations (Al-Aboosi, 2019), which corresponds to a cloud cover of 7.1 published by the Korea Meteorological Administration. This outcome indicates that the cloud conditions were BKN. In general, irradiance and radiance change rapidly due to fluctuating atmospheric conditions, but relectance tends to be stable. Consequently leads to the conclusion that the clouds are thick. So, based on reflectance, the SKC and BKN flights show similar trends in B, G, R, and RE, but in the NIR there is a slight change of 1–2% due to atmospheric water vapor.

Figure 3. Field measured irradiance and reflectance (1st: SKC, 2nd: BKN). (a) Irradiance at research area. (b) CRT 46% reflectance.

Table 6 . Irradiance, radiance, and reflectance statics in SKC and BKN flight at CRT (Unit: W/cm² nm (Irradiance), W/cm² sr nm (Radiance)).

Type			Blue	Green	Red	RE	NIR
SKC flight	Irradiance		109.0±1.21	101.7±1.16	91.4±1.03	75.4±0.88	54.7±0.65
	Radiance CRT	3%	3.6±0.03	3.2±0.03	3.1±0.02	2.7±0.02	2.5±0.02
		16%	18.9±0.23	16.5±0.20	14.0±0.16	11.6±0.14	8.6±0.09
		26%	28.9±0.34	25.8±0.31	22.7±0.26	18.9±0.23	13.6±0.16
		46%	49.5±0.57	44.7±0.52	40.3±0.46	33.9±0.39	25.4±0.26
BKN flight	Irradiance		82.2±0.80	76.2±0.78	67.9±0.72	55.7±0.60	41.6±0.44
	Radiance CRT	3%	2.8±0.02	2.5±0.02	2.4±0.02	2.1±0.02	2.0±0.02
		16%	14.8±0.14	12.8±0.13	10.9±0.12	9.0±0.09	7.0±0.07
		26%	22.4±0.21	20.0±0.20	17.6±0.19	14.6±0.16	11.0±0.11
		46%	37.6±0.36	33.8±0.35	30.4±0.32	25.5±0.27	20.2±0.19

Clouds affect how much sunlight reaches the ground by reflecting or absorbing sunlight. This process reduces the amount of direct sunlight reaching the ground. Additionally, in this case, the thicker the cloud, the greater the reduction. Clouds also scatter sunlight in many directions, which increases diffused sunlight (Li et al., 1995). Clouds divide the incident energy from outside the Earth into direct and diffused sunlight. When there is no cloud, direct sunlight at ground level is about 85% and diffused sunlight is about 15%, while diffused sunlight becomes 100% in the case of an overcast cloud. As cloud cover increases, direct sunlight decreases, and diffused sunlight increases (Agbo et al., 2023). This is important for describing how the surface changes with the angle of incidence and reflection (Sarkar, 2016). Therefore, the BRDF and ROW affected by direct sunlight depends on the SKC and BKN.

3.2. Vignette and NewROW Filter for Radiometric Correction

Fig. 4(a) shows how much the brightness of the image changes due to the Vignette when the CRT is photographed in each band. Figs. 4(b, e) shows the result calculated using the Vignette parameter from metadata. Figs. 4(c, f) shows the simulation result of extracting related functions from the metadata of the Rededge MX. The simulation was held when the exposure time was average for both SKC and BKN flights. The brightness correction factor before/after was Y, image row coordinate was X. Fig. 4(d) shows the shutter speed. The increased exposure time was more significant in the BKN flight than in the SKC flight, ex_cept for the R band.

Figure 4. Vignette and NewROW filter effect in MicaSense Rededge MX (X: Row pixel, Y: Correction factor; 1st: SKC, 2nd: BKN). (a) Vignette in SKC and BKN flight. (b) NewROW in SKC flight. (c) Result in SKC flight. (d) Shutter speed. (e) NewROW in BKN flight. (f) Result in BKN flight.

The Vignette is a function of the radius from the image center. So it was mutually symmetric. The Vignette mean values are 0.976±0.022 (B), 0.970±0.029 (G), 0.968±0.035 (R), 0.933±0.055 (RE) and 0.887±0.077 (NIR). The same Vignette filter was applied for each image. The maximum extent to which the Vignette deviates from the center value in B, G, R, RE, and NIR bands was ±8, ±11, ±12, ±18 and ±25%. This is due to lens design, where the refractive index of sunlight varies with wavelength. Thus vignetting can be more pronounced at certain wavelengths, especially with wide-angle lenses or lower-end lenses (Sharma, 2012).

Fig. 5 shows the results of OriROW and NewROW. The “O” in Fig. 5(a) is the original by the manufacturer and is the result of Eq. (3). It was “1” for the start line of the OriROW filter image as shown in Fig. 5(a), hence it was impossible to consider the Row_cor and Rel_angle in OriROW filter. The “ON” in Figs. 5(b, c, d) is the result of adding only Rel_angle in the “O”. So, we used Rel_angle without Row_cor. As a result, the adjustment value in the center was not “1” for Figs. 5(a, b, c, d). To solve this, we added the Row_cor factor to the Eqs. (5, 6), which is equal to “N” in Fig. 5. NewROW Python Code has a Rel_angle and Row_cor parameter in Eq. (4). The ROW correction tends to be “1” at the center of the filter image. Therefore, Row_cor was applied to compensate for this. After applying Row_cor, the deviation of –0.5~0.2% was significant as shown in Figs. 5(e, f, g, h).

Figure 5. The result of the ROW filter (X, Y axis: pixel coordinate; O: OriROW; ON: OriROW with Rel_angle without Row_cor; N: NewROW with Rel_angle and Row_cor). (a) 315<Rel_angle<45° (O). (b) 45<Rel_angle<135° (ON). (c) 135<Rel_angle< 225° (ON). (d) 225<Rel_angle<315° (ON). (e) 315<Rel_angle<45° (N). (f) 45<Rel_angle<135° (N). (g) 135<Rel_angle<225° (N). (h) 225<Rel_angle<315° (N).

NewROW (Mamaghani and Salvaggio, 2019) decreases nearly linearly from the edge closer to the sun to the other edge farther away. ROW is also affected by shutter speed, with NewROW filter image mean and standard deviation values of 0.996±0.043 (B), 0.995±0.048 (G), 0.998±0.027 (R), 0.998±0.027 (RE) and 0.999± 0.026 (NIR) in average shutter speed in SKC and 0.997±0.035 (B), 0.997±0.037 (G), 0.998±0.028 (R), 0.996±0.026 (RE) and 1.002±0.024 (NIR) in BKN flight. NewROW has the opposite behavior to the Vignette band order. This is because it is strongly affected by the order of the energy entering the camera.

The NewROW changes affected the B, G, R, RE, and NIR bands. The NewROW for the SKC and BKN flights differed by 3.1, 3.8, –0.4, 0.3, and 0.8%, with percent reductions of –20, –23, 4, –4 and –9% in Figs. 4(b, e). The B and G bands showed the biggest reductions in energy. This was caused by diffused sunlight in NIR, RE, and R. There were more clouds in the BKN flight, which increased water vapor, resulting in Mie scatter (Akimov, 2024). This ordering is related to the plants’ reflectance and irradiance per band. This is an appropriate result, considering the 25% reduction in irradiance for the SKC and BKN flights in Fig. 3(a).

The corrected reflectance is applied to the image multiplication of Vignette and NewROW as shown in Eq. (8) and Table 3. If direct sunlight is more dominant than diffused sunlight, the amount of NewROW increases by changing the shutter speed, and in the opposite case, the amount of NewROW decreases, making the effect weaker. In Figs. 4(c, f), the final image due to the Rel_angle, the brightness occurs at the edge closest to the ø_c and ø_s. The brightness values on the left and right sides of the image change are asymmetrical with each other (Schiefer et al., 2006). Therefore, in cloudy weather, the impact of the ROW becomes smaller thus the Vignette dominates over the ROW.

3.3. Radiometric Correction by Process Level (NoProcess, NewROW, and BRDF)

Reflectance can be calculated consistently with irradiance and radiance. However, reflectance can change over time, especially in SKC, where θ_s increases in direct sunlight on the ground leading to lower reflectance. In the noon of the day, the sun is high and shadows are short, so direct sunlight is higher. The clouds in the atmosphere can cause scattered and diffused sunlight, which in turn reduces direct sunlight and changes reflectance. In Fig. 3(a), irradiance varies by tens of percent with cloud cover, while in Fig. 3(b), reflectance varies slightly with cloud cover. The amount of cloud cover can cause fluctuations in reflectance levels throughout the course of a day as shown in Fig. 3(b).

As shown in Table 7 and Fig. 3(b), BKN flight’s reflectance increased by 0.08~0.70, 0.09~0.78, 0.17~1.02, 0.21~1.05 and 0.26~1.99% in B, G, R, RE and NIR bands than SKC flight. The direct sunlight reaching the ground through the clouds was reduced, resulting in lower irradiance. Direct sunlight was scattered by the clouds, causing Mie scattering and affecting longer wavelengths (Mischenko et al., 2000). In Fig. 3(a), the BKN irradiance was about 25% less than the SKC irradiance. And the solar irradiance reaching the ground at the simulated normal irradiance time of the BKN image generation was about 33% less than the SKC. SKC flight is dominated by direct sunlight, while BKN flight is dominated by diffused sunlight.

Table 7 . Reflectance statics in SKC and BKN flight in each CRT (Unit: % (Reflectance)).

Type		Blue	Green	Red	RedEdge	NIR
SKC flight	CRT 3%	3.26±0.014	3.12±0.013	3.39±0.019	3.52±0.021	4.60±0.044
	CRT 16%	17.32±0.021	16.19±0.019	15.34±0.019	15.38±0.021	15.63±0.029
	CRT 26%	26.54±0.026	25.41±0.024	24.81±0.025	25.10±0.028	24.89±0.030
	CRT 46%	45.42±0.064	43.98±0.056	44.06±0.056	44.98±0.048	46.49±0.081
BKN flight	CRT 3%	3.34±0.014	3.21±0.012	3.56±0.018	3.73±0.020	4.86±0.039
	CRT 16%	17.96±0.021	16.80±0.019	16.03±0.024	16.16±0.028	16.75±0.040
	CRT 26%	27.24±0.032	26.19±0.029	25.83±0.032	26.15±0.035	26.48±0.046
	CRT 46%	45.74±0.050	44.32±0.046	44.70±0.051	45.88±0.048	48.48±0.065

The reflectance observed by the CRTs was compared with the reflectance from the images. The CRT took 12 images per band. In SKC flight, direct sunlight was dominant in the sky yielding about 85%, while diffused sunlight accounted for about 15% (Daivid, 2021). However, the purpose of this study is to evaluate the usability of NewROW in the absence of BRDF. Therefore, we compared the results of NewROW and BRDF using BRDF parameters (f_iso, f_geo and f_vol) generated under similar conditions in the neighboring areas. The results indicate that significant accuracy can be achieved with NewROW correction.

The calculated reflectance from the SKC and BKN flights was calculated according to Table 3. The vegetation in the study area is winter wheat (yellow area in Fig. 1(a)). Humans naked eye it was indistinguishable if the difference was less than 1.5% (Vladimir Sacek, 2006).

The results of each processing method for SKC and BKN are shown in Figs. 6(a~f). In SKC and BKN, NoProcess was anomalous. In NewROW and BRDF, the differences were so small that they were indistinguishable. Therefore, for a more detailed analysis, we calculated the differences for each method as shown in Table 8 and Fig. 7.

Figure 6. The result by process level and flight type by Table 3. (a) NoProcess in SKC. (b) NewROW in SKC. (c) BRDF in SKC. (d) NoProcess in BKN. (e) NewROW in BKN. (f) BRDF in BKN.

Figure 7. Differences in comparison of averaging reflectance applying SKC and BKN methods in the accuracy validation site (Fig. 1a).

Table 8 . The standard deviation of the difference between field-measured reflectance and image reflectance in Checkpoint (in CRT) (Unit: % (Reflectance)).

Type		Blue	Green	Red	Rededge	NIR	Total
SKC flight	NoProcess	±4.48	±4.95	±3.18	±4.33	±2.74	±4.02
	NewROW	±1.41	±1.49	±0.84	±1.72	±2.12	±1.57
	BRDF	±0.84	±1.39	±1.29	±2.15	±2.28	±1.68
BKN flight	NoProcess	±2.28	±1.63	±1.80	±1.82	±1.50	±1.83
	NewROW	±0.97	±0.91	±0.99	±1.55	±1.84	±1.31
	BRDF	±0.74	±1.11	±1.14	±1.62	±1.76	±1.33

NewROW: New Row gradient, BRDF: Bidirectional Reflectance Distribution Function..

Table 8 shows the standard deviation of the difference between field-measured reflectance and image-derived reflectance in each band. In SKC flight, NoProcess showed the largest standard deviations in each band, with correction values ranging from ±2.74~±4.48%. This indicates significant discrepancies between field and image reflectance, with a total correction value of ±4.02%. NewROW and BRDF had correction values of ±0.84~±2.12% and ±0.84~±2.28% respectively, resulting in totals of ±1.57 and ±1.68%. In BKN flight, NoProcess, NewROW, and BRDF had correction values of ±1.50~±2.28% ±0.91~±1.84% ±0.74~±1.76% in each band. NoProcess, NewROW, and BRDF were more accurate than SKC at ±1.83, ±1.31, and ±1.33% in BKN. As a result, in the case of SKC and BKN, NewROW was slightly better than or similar to BRDF and NoProcess was the least accurate in Table 8. Theoretically, BRDF can get better results at the same time and area without cloud (Kim et al., 2022). The cloud cover of BKN was 6.5~7.5, and the results showed that direct sunlight decreased from 85 to 20~30%, and diffused sunlight increased from 15 to 70~80%, which was dominated by diffused sunlight (Kimura and Stephenson, 1969). NewROW & BRDF were similar by the influence of the direct sunlight.

Fig. 7 shows the difference in reflectance for each method (NoProcess, NewROW, and BRDF) at SKC and BKN. When NoProcess is applied, the reflectance difference between SKC and BKN is –0.601±1.813%, indicating a relatively large standard deviation. The reflectance difference is significantly larger compared to the NewROW and BRDF, suggesting that NoProcess lacks consistency regardless of cloud cover. With NewROW, the difference between SKC and BKN significantly reduced to 0.029±0.716%. With BRDF, the difference is 0.077±1.066%. When comparing NewROW to BRDF, the difference is 0.268± 0.469 in SKC, and -0.276±0.485% in BKN. This is significant as it shows a small difference between NewROW and BRDF under different cloud cover conditions. Therefore, Fig. 7 shows that the NewROW is slightly more stable in reducing the effect of cloud cover on reflectance, but both NewROW and BRDF are comparable and appropriate.

The results of simulating the amount of adjustment for each factor at 320 by 240 pixels used in the Orthomosaic are shown in Table 9. Vignette was applied in all cases ex_cept NoProcess. The difference in Vignette reflectance is –0.44~–4.04% in all images. According to the simulation results, NewROW showed error values ranging from ±1.25 to ±2.79% for each band under SKC, and from ±0.89 to ±2.03% under BKN. The BRDF simulation results showed error values ranging from ±1.32 to ±3.18% under SKC and from ±1.26 to ±3.09% under BKN. The NIR band showed a significant change due to the effect of the vignette, resulting in the highest amount of error in the NIR band of the NewROW and BRDF. As a result, BRDF was corrected to a higher value than NewROW, and both methods had similar trends under both SKC and BKN.

Table 9 . Correction percent simulate result by filter and flight in Orthomosaic image (Unit: % (Reflectance), overlap and side lap: 75%).

Type			Blue	Green	Red	RedEdge	NIR
Vignette filter			-0.44	-0.60	-0.19	-1.54	-4.04
Filter	NewROW	SKC	±2.44	±2.79	±1.40	±1.25	±1.42
		BKN	±1.85	±2.03	±1.47	±0.89	±1.60
	BRDF	SKC	±2.87	±2.87	±2.70	±1.32	±3.18
		BKN	±2.69	±2.69	±2.49	±1.26	±3.09
Result	NewROW	SKC	-2.9~2.0	-3.4~2.2	-1.6~1.2	-2.8~-0.3	-5.4~-2.7
		BKN	-2.3~1.4	-2.6~1.4	-1.7~1.3	-2.4~-0.7	-5.6~-2.5
	BRDF	SKC	-3.3~2.4	-3.5~2.3	-2.9~2.5	-2.8~-0.2	-7.1~-1.0
		BKN	-3.1~2.2	-3.3~2.1	-2.7~2.3	-2.8~-0.3	-7.0~-1.1

In the case of the NewROW, SKC flight has a Rel_angle of 69.5 (Down) and –249.6° (Up), as we can see from the right and left edges, rather than the top and bottom, from Figs. 5(f, h). However, BKN flight has a Rel_angle of 326.1 (Down) and 146.1° (Up) in the image as shown in Fig. 5(e, g), which is shown on the top and bottom edges. In the case of the BRDF filter, the difference between ø_s of SKC and ø_s of BKN was 103.43°, so the BRDF filter was rotated by 103.43°. Also, when conditions images in the Orthomosaic, the images located Down and UP in SKC and left & right in BKN from the center line are used, so the ROW sign is reversed on the top & bottom and left & right seamlines.

The accuracy of radiometric correction depends on atmospheric correction, surface reflectance correction, and camera lens aberration correction. In particular, atmospheric disturbances such as clouds have emerged as a significant challenge in atmospheric correction. This study aims to compare the accuracy of surface reflectance correction methods (NoProcess, NewROW, and BRDF) under two different cloud conditions (SKC and BKN) using data from the MicaSense RedEdge MX multispectral camera. In this study, data was processed with three correction methods to evaluate their accuracy under different weather conditions. Along with the conventional surface reflectance correction method BRDF, a simple alternative NewROW was proposed.

NoProcess had a large error value in radiometric correction and seemed to be inconsistent compared to the other two methods. So, NoProcess was difficult to use in both SKC and BKN. In SKC and BKN, NewROW and BRDF achieved similar accuracy. When comparing SKC and BKN for each method, the differences were small. The comparison of NewROW and BRDF under other cloud cover conditions showed that the difference between them was not significant. In SKC, where direct sunlight is dominant, and in BKN, where diffused sunlight dominates due to cloud cover, NewROW had slightly better accuracy. This is because BRDF can’t adjust the amount of incident energy, whereas NewROW compensates by adjusting the exposure time to solar energy. But both NewROW and BRDF maintained similar performance, with both methods adapting effectively to cloud cover.

This study suggests NewROW as a practical and reliable alternative to BRDF, especially when BRDF parameters (f_iso, f_geo and f_vol) are unavailable or difficult to standardize under variable cloud cover. If users don’t have BRDF parameters, NewROW provides a simple and efficient approach. This research enables enhanced usability in agricultural and environmental monitoring applications where BRDF limitations exist, promoting accurate remote sensing even in challenging weather scenarios.

This study was carried out with the support of “Cooperative Research Program for Agriculture Science and Technology Development (Project No. RS-2022-RD010367)” by the Rural Development Administration, Republic of Korea.

No potential conflict of interest relevant to this article was reported.