On the Observational Solid Angle in Estimating the Moon-based Disk-integrated Earth Outgoing Longwave Radiation

Abstract Equipping sensors on the lunar surface would enable the capture of Earth’s outgoing longwave radiation (OLR) from nearly an entire hemisphere. However, the Earth’s nonsphericity would profoundly impact the observational solid angle, thereby influencing the disk-integrated Earth OLR estimation. This study analyzes the impact of the Earth’s ellipsoidal shape on the OLR estimation by examining the effects of the observational solid angle. In particular, an expansion-series-based method is proposed for calculating the observational solid angle, avoiding complex numerical integration. Three critical issues are analyzed. (1) Comparing the observational solid angles calculated by using an Earth ellipsoidal model versus those obtained by adjusting the Earth’s radius. We find that adjusting the Earth’s radius can approximate the results based on an Earth ellipsoidal model, offering insights into parameterizing the observational solid angle. (2) Parameterizing the observational solid angle through series expansion, which is validated by comparing the associated results to those from numerical integrations. The observational solid angle is parameterized into two components: one is attributable to a variable Earth radius and another is related to the nadir point’s latitude and the Earth–Moon distance. (3) Guiding parameter selection for observational solid angle estimation. These findings enhance our understanding of disk-integrated Earth OLR estimates and provide a unique tool for establishing benchmarks for the Earth samples needed in the study of habitable planets, thereby contributing to sustainable development.