drought, dry weather
旱 centers on a prolonged lack of water: drought and dry weather. The two meanings are essentially the same idea at different scales.
旱 combines 日 (sun) and 干 (dry, shield), suggesting the sun drying things out. The exact historical development is uncertain, but the component combination fits the meaning of drought.
The sun 日 beats down on a dry, parched shield 干 below: nothing grows, and the land is in drought.
For カン, imagine a can of water being the only relief during a drought: can -> カン, and the sun keeps drying everything out.