The Uncertainty Analysis of the Entrance Pupil Irradiance for a Moon-Based Earth Radiation Observation Instrument

Abstract

Moon-Based Earth Radiation Observation (MERO) is expected to improve and enrich the current Earth radiation budget (ERB). For the design of MERO’s instrument and the interpretation of Moon-based data, evaluating the uncertainty of the instrument’s Entrance Pupil Irradiance (EPI) is an important part. In this work, by analyzing the effect of the Angular Distribution Models (ADMs), Earth’s Top of Atmosphere (TOA) flux, and the Earth–Moon distance on the EPI, the uncertainty of EPI is finally studied with the help of the theory of errors. Results show that the ADMs have a stronger influence on the Short-Wave (SW) EPI than those from the Long-Wave (LW). For the change of TOA flux, the SW EPI could keep the attribute of varying hourly time scales, but the LW EPI will lose its hourly-scale variability. The variation in EPI caused by the hourly change of the Moon–Earth distance does not exceed 0.13 mW∙m−2 (1σ). The maximum hourly combined uncertainty reveals that the SW and LW combined uncertainties are about 5.18 and 1.08 mW∙m−2 (1σ), respectively. The linear trend extraction of the EPI demonstrates that the Moon-based data can effectively capture the overall linear change trend of Earth’s SW and LW outgoing radiation, and the uncertainty does not change the linear trend of data. The variation of SW and LW EPIs in the long term are 0.16 mW∙m−2 (SW) and 0.23 mW∙m−2 (LW) per decade, respectively. Based on the constraint of the uncertainty, a simplified dynamic response model is built for the cavity radiometer, a kind of MERO instrument, and the results illuminate that the Cassegrain optical system and electrical substitution principle can realize the detection of Earth’s outing radiation with the sensitivity design goal 1 mW∙m−2.