Geometric Calibration of All-Sky Cameras Using Sun and Moon Positions: Achieving Sub-Degree-Accuracy without any Handwork

Abstract

All-sky imagers (ASIs) have been used to provide accurate nowcasts of solar irradiance and to derive atmospheric measurements and cloud observations. ASI-based information enhances the understanding of atmospheric processes, serves as input for weather and climate models and can provide reference data for validating satellite-derived parameters. Additionally, ASIs have the potential for automating atmospheric observations. However, there are still manual tasks involved in the setup, calibration and operation of ASIs. This is where our contribution comes in. The tasks mentioned above often require the reconstruction of the ‘world coordinates’ of observed points in the sky from their pixel positions in the ASI images. This necessitates a geometric calibration of each ASI regarding camera-intrinsic lens distortion parameters and the ASI’s external orientation. This task usually requires the manual placement of special checkerboard or other patterns at multiple positions above the camera. In general, existing calibration methods require a non-negligible amount of manual work. We present the Python tool ‘SuMo’ which determines all parameters defining the lens distortion and external orientation only using regular ASI images depicting Sun and Moon. SuMo avoids a manual interference on-site, can be applied retrospectively and can also be used to continuously monitor an ASI’s geometric calibration. We recently published SuMo as part of an open-source package together with over 2 years of ASI images and irradiance measurements. This will support the method’s reproducibility and practical usability. We test the calibration on five camera types at three sites using datasets which represent different seasons, distinct ranges of turbidity and cloud cover, exposure times as well as sun/ moon elevation and azimuth angles. In each case, we evaluate how accurately Moon positions in a 1-year dataset are predicted. Also, we cross-validate SuMo with the semi-automatic star-based ORION calibration method developed by University of Valladolid. First, we confirm the high accuracy of the SuMo method. Already a single month of images from either summer or winter yields an accurate calibration (root mean squared error, RMSE, ≤ 0.14°). Further, we analyze the influence of the above-mentioned atmospheric, site and hardware/ firmware parameters on the calibration accuracy. A comparable calibration accuracy (RMSE 0.14° – 0.38°) is achieved for all tested ASIs without modifying the method’s parameters. Image quality moderately influences the calibration accuracy. Similarly, extreme conditions such as high cloud cover (RMSE 0.38°) and high turbidity (RMSE 0.32°) can reduce the calibration accuracy compared to very clear conditions (RMSE 0.12°). Cross-validation with the ORION method further confirms the high accuracy of our method over the entire sky dome (mean absolute error 14°). Overall, our comprehensive experimental analysis attests the high accuracy and practical feasibility of a geometric calibration of ASIs relying only operationally recorded day- and nighttime sky images.