Water leaves a lake through the ground. "Ground water is recharged from rain water and snowmelt or from water that leaks through the bottom of some lakes and rivers," - Google
Sorry if my answer was incorrect.
It is true that the rainfall that happens in savannas especially in summer time reaches to only half of the annual rainfall. Isolated trees and some types of shrubs are found in savanna. The precipitation rate received by savannas per year is about 30 to 50 inches.
The answer you are looking for is El Azizia, Libya
