So, let's take an obvious one like Namibia. Namibia has a very cold current running north up it's coast called the Benguela. It is quite cold. The air above it is also quite cold, and therefore dry.

This cold air hits the hot desert dunes and warms rapidly and heads straight up. Very little moisture makes it inland.

So temperature difference between land and sea due to ocean and wind currents can cause the situation you are describing.

Volcano nearby laid down a layer of impermeable ash about 6 feet down. Trees only grow where that ash layer cracked and the roots can get down. That is why it is all grassland, not treeland.