The shell bone script of character Desert is
The center is character Sun, the 4 surround are grass, the sun is setting in the grass which originally means Evening (Post 196).
The bronze script of the character is
People also used the character for desert, or original it had the meaning. In addition, the character was used for Do Not or Not (Post 324). As more and more people used it as three meanings, caused confusion. So people added character Water to it to create a new character specifically for Desert since big seal script:
Which is specific for big area without people, not the desert which only has sand. In Chinese, if you want to say the desert, you must add Sand before Desert: 沙漠 = Sand Desert. Therefore we could understand why there is Water on the left because it is not Sand-Desert, is the desert with a lot of water.
The small seal script of the character is