noun
rainy-season sky; overcast sky in the rainy season
Refers to the gloomy, cloud-covered sky typical of the Japanese rainy season (梅雨). Often carries a slightly melancholic or oppressive feeling.
梅雨空の下、洗濯物が乾かなくて困る。
Under the rainy-season sky, I have trouble getting the laundry dry.
今日も梅雨空で、気分が沈みがちだ。
It's another overcast rainy-season day, and I tend to feel down.
曇り空 is a general overcast sky, whereas 梅雨空 is specifically the overcast sky during the rainy season.
Compound of 梅雨 (つゆ, 'rainy season') and 空 (そら, 'sky'). The reading つゆ for 梅雨 is a sound shift from ばいう, which itself is a borrowing from Chinese.