**6. Conclusions**

This study presents the first in-situ vicarious calibration experiments at the Dunhuang site for the SPARK-01 and -02 satellites. Reflectance-, irradiance-, and improved irradiance-based calibration methods were used on images acquired on 7 March and 28 February 2017 by these two satellites. We proposed a 90◦ yaw imaging technique for use in the relative calibration method; such methods are very useful for microsatellites without on-board calibration instruments, and especially for satellites with large swaths. An absolute calibration was performed using MODTRAN 5 data, and the methodological and measurement errors in the calibration results were analyzed in detail. Because the SPARK-01 image was acquired during fair weather (e.g., stable atmosphere and low AOD), the calibration uncertainties of the reflectance- and irradiance-based methods are 4.7% and 4.1%, respectively. However, the SPARK-02 image, which was acquired during poor weather, has an uncertainty of 8.12% using the reflectance-based method from 456 to 1000 nm. Under these conditions, the improved irradiance-based method was superior, producing a lower uncertainty of 5.86%. Thus, the additional diffuse-to-global ratio measurements included in the irradianceand improved irradiance-based methods considerably decreases the calibration uncertainty, likely due to its aerosol property assumptions. The improved irradiance-based method is superior to the reflectance-based method under non-ideal atmospheric conditions as it improves the simulated downward transmittance. Although the irradiance- and improved irradiance-based methods are superior to the reflectance-based method on average, the accuracy of the diffuse-to-global ratio measurements may limit the use of these two methods. Indeed, the instrument used to measure the diffuse-to-global ratio has a lower signal-to-noise ratio in the dark blue bands (i.e., <400 nm) and shortwave infrared bands (i.e., >2.1 μm). Moreover, spectral calibration accuracy is a crucial factor to guarantee accurate radiometric calibration. A 1 nm spectral shift for a hyperspectral sensor with a 10 nm spectral resolution would cause as much as a 10% radiometric calibration error near the gas absorption wavelengths. The precise pre-launch spectral calibration in the laboratory as well as the

on-orbit monitoring of spectral wavelength shifting are needed. Also, we strongly sugges<sup>t</sup> combining the calibration results derived by the reflectance- and irradiance- (or improved irradiance-) based methods for optimized results. In the future, irradiance-based methods for hyperspectral satellites should be evaluated in more detail by adding spectrally continuous direct transmittance measurements. This could improve calibration accuracy in the gas absorption bands near 940 nm, 1135 nm, 820 nm, etc.

**Acknowledgments:** This research was supported by the National Natural Science Foundation of China (41325004, 41771397) and the National Key R&D Program of China (2016YFB0500304). The authors acknowledge the Shanghai Engineering Center for Microsatellites, Chinese Academy of Sciences (CAS), and the Academy of Opto-electronics, CAS for providing satellite data and documentation. We also thank China RS Geo-informatics Co. Ltd. for financial support for the field experiment. We highly appreciate Juanjuan Jing from the Academy of Opto-electronics, CAS for the assistance in spectral calibration data processing and in-depth discussions.

**Author Contributions:** Hao Zhang, Bing Zhang, and Zhengchao Chen conceived and designed the experiments. Hao Zhang and Zhihua Huang performed the experiments and processed the data. Hao Zhang and Zhengchao Chen contributed to the analysis and discussion. Hao Zhang wrote the paper.

**Conflicts of Interest:** The authors declare no conflict of interest.
