Calibration Site BRDF Modeling Method Based on Ground and Low-Altitude UAV Joint Observation

Objective The bidirectional reflectance distribution function (BRDF) is a crucial parameter for satellite sensors to conduct vicarious calibration of pseudo- invariant calibration sites (PICS). Low-altitude self-rotating unmanned aerial vehicles (UAVs) have become a convenient and efficient approach for acquiring BRDF data of these sites. When the surface's directional reflection characteristics in outdoor conditions are measured, it is not possible to control the illuminance solely in the non-incident direction. The target is illuminated by direct sunlight and atmospheric scattered light, introducing a certain level of systematic error in BRDF measurement. Conducting in situ measurements through UAVs with multi-angle observation and spectral data shows significant potential for building more accurate BRDF models for PICS. We propose a BRDF modeling method based on joint observations of ground-based and aerial dual spectrometers, and diffuse plate observations to eliminate the influence of diffuse light. The compact and lightweight drone platform, which is not limited by terrain, makes it suitable for measuring various complex terrains. Simultaneously, the ground- based spectrometer can continuously measure changes in the illumination field. The combined observations of the ground-based and low-altitude UAV instruments can eliminate the interference caused by diffuse light irradiation in BRDF modeling and substantially improve accuracy. Methods The synchronized BRDF observation system includes an airborne spectral measurement system, a groundbased spectrometer measurement system, a solar radiometer, and a whole sky imager. The low-altitude UAV carries a spectrometer to obtain site spectral data at multiple angles within a 50 m radius hemisphere. Meanwhile, the ground-based spectrometer is employed to synchronously measure the diffuse reference panel, continuously recording changes in the illumination field and site spectral data under diffuse illumination. The radiative luminance is measured by a ground-based spectrometer, and the BRDF is calculated by dividing the bidirectional reflectance factor (BRF) by p. In outdoor measurement environments where the lighting conditions are not unidirectional, the hemisphere-directional reflectance factor (HDRF) is introduced as a substitute for calculation. When the sky is clear and there is almost no diffuse scattering (low aerosol optical thickness, without clouds), the influence of diffuse light can be ignored and HDRF is approximately equal to BRF. The target and reference panel's measured radiance data from the UAV and ground-based spectrometers are combined with the observation geometry between the sun and the viewing angles to calculate the site's multi-angle reflectance. By synchronously measuring the radiance of the target surface and the reference panel with airborne and ground- based spectrometers and considering the observation geometry between the sun and the viewing angles, the ratio of the two can be calculated. As a result, the site's multi-angle reflectance can be obtained to eliminate measurement biases caused by variations in solar irradiance during the measurement. When affected by diffuse light, the target reflectance is corrected by subtracting the corresponding diffuse light luminance from the surface target and the ideal reference panel to achieve diffuse light correction. Based on the Ross-Li kernel-driven semi-empirical model, the multi-angle reflectance data are fitted by the least squares method to obtain the optimal site BRDF model. Results and Discussions The Wuhai West Desert in the Ulanbuh Desert is selected as the PICS target for the BRDF measurement experiment using the UAV-ground synchronized system. A total of 17 sets of airborne multi-angle spectral measurement data in three consecutive days are adopted for BRDF modeling analysis. Before calculating the surface multiangle reflectance, it is necessary to calculate the wavelength shift between the two spectrometers to avoid measurement errors caused by the instruments themselves. The wavelength shift result is the offset corresponding to the minimum spectral angle between the two spectrometers after wavelength translation and is also employed for data preprocessing. The data from all observation sessions are organized and substituted into the model fitting calculation of Eq. (9) to obtain the model coefficients. By fitting the three-day measurement data, the BRDF model parameters at 469 nm, 555 nm, 645 nm, 856 nm, 1240 nm, and 1640 nm are obtained, as shown in Table 3. Due to the differences in atmospheric conditions on different dates during the experiment, diffuse light correction is performed, and the obtained BRDF model coefficients are shown in Table 4. The experimental result proves that the mean relative deviation of the BRDF model at each wavelength band after diffuse light correction is within 5%, and the relative standard deviation is within 3%. Finally, the interference of the field BRDF modeling under diffuse light illumination is eliminated and the modeling accuracy is improved. Conclusions We propose a method for BRDF modeling based on ground-UAV dual spectrometer joint observation. When diffuse panel observation is utilized, the diffuse light influence can be eliminated. It measures the BRDF characteristics of the selected PICS and leverages a spectrometer carried by a UAV to obtain multi-angle spectral data from low-altitude measurements of the site. Simultaneously, ground- based spectrometer synchronous measurements are conducted to continuously record changes in the illumination field and eliminate deviations in spectral reflectance calculations caused by the lighting environment changes during the measurement. Based on the Ross-Li kernel-driven semiempirical model, BRDF models for different atmospheric environments are built, and the effects of different atmospheric conditions on BRDF inversion in outdoor environments are analyzed. Through measurement data from the ground-based spectrometer under diffuse illumination, the BRDF model is corrected for diffuse light. Experimental results show that the proposed method can eliminate the interference of diffuse light illumination in the BRDF modeling of the PICS and improve accuracy.