## 1 Introduction  
Climate change on Earth is dominated by the budget of the incoming and outgoing radiation [1]. The incoming source is solar radiation, whereas the outgoing one is comprised of two parts: outgoing shortwave radiation (OSR) and outgoing longwave radiation (OLR). Since the 1970s, have been several satellite-based missions that were dedicated to OSR and OLR observations, such as the Earth Radiation Budget Experiment (ERBE) [2], the Clouds and Earth's Radiant Energy System (CERES) [3, 4], the Geostationary Earth Radiation Budget (GERB) [5] and the National Institute of Standards and Technology Advanced Radiometer (NISTAR) onboard the Deep Space Climate Observatory (DSCVR) [6]. Though these low-Earth-orbit (LEO) and geostationary-Earth-orbit (GEO) satellite missions have indeed strengthened our understanding of the Earth radiation budget (ERB), there are still several limitations, which can be complemented by a Moon-Based Earth Radiation Observatory (MERO). Compared to current LEO and GEO ERB systems, a MERO has several advantages: (1) Global ERB observation needs an artificial satellite constellation; however, different satellites have various orbits, which would result in inconsistency between data produced by these satellites. In comparison, a MERO could produce a long-term ERB record with better consistency. Since the Moon-Earth distance (near 380,000 km) is approximately 100 times larger than the diameter of the Moon (3476 km), the distance between any location on the Moon's nearside and the Earth's center varies by less than 5%, and the viewing angle towards Earth (the viewing angle or viewing azimuth angle) differs by less than 2%. This implies that almost all locations on the nearside of the Moon have nearly the same viewing geometry towards Earth. Therefore, MERO missions launched at different times with different landing locations would share a highly similar viewing geometry, producing long-term OSR and OLR observations with good consistency. (2) Current LEO ERB systems could not record the rapid variability of the OLR and OSR of the Earth system due to the limited temporal sampling coverage. In contrast, the temporal sampling coverage of a MERO is far higher than the LEO counterparts. The sampling period of a MERO is approximately 12 h per day for a fixed location on Earth, resulting in about 48 temporal samples per day if the sampling interval is set to 15 min (the GERB sampling interval). It is about 24 times larger than that of a low-orbit satellite ERB instrument. These abundant temporal samples would substantially enhance the quality of the diurnal data produced by the ERB fitting method and could help to reveal the small-temporal-scale variations of the TOA OLR and OSR. (3) Current satellite-based ERB data of the polar regions have several problems. The sun-synchronous-LEO ERB system could cover the high-latitude regions; however, the sampling frequency is limited, Therefore, evident error would emerge when the LEO ERB system is used to capture short-temporal processes during specific periods, such as the melting season [7,8]. Besides, current GEO ERB systems also cannot provide satisfied observations for the polar regions [9]. A MERO could provide better OSR and OLR observations of the Arctic and Antarctic regions to complement these limitations. As illustrated by previous research, a MERO could instantaneously observe more than 45% of the Antarctic or Arctic regions during half of a lunar orbital period (27.3 days) to provide abundant samples for a polar location, the amount of these samples are about 24 times larger than a LEO ERB system [10]. Current and previous space-based ERB mission could not capture the Earth system's inherent and rapid variability of the OLR and OSR with an accepted accuracy due in part to the limited temporal coverage. Therefore, the Earth radiation imbalance cannot be measured definitively [11].