Lunar rainbow
From Glossary of Meteorology
lunar rainbow
Even though the optics of both is the same, the luminance of the lunar rainbow is much lower. As a result of the eye's reduced sensitivity to color at low light levels, the bow may exhibit little color. There are several reasons why the lunar rainbow is seen much less frequently than the solar bow. While the moon and sun spend equal time above the horizon, when they are both present, only a solar bow can be seen. This, by itself, means that the lunar rainbow could form only half as often. Further, the moon goes through phases, and so even at night may not contribute enough light to produce a discernible bow. Finally, the convective showers in which the rainbow is frequently seen are much less common at night.