In fact as much as 50% of the Amazon's rain can be attributed to the trees themselves. Both through evapotranspiration strategies and increased cloud-seeding particles

However, I think the more relevant dynamic for this region is the water-holding capacity of the soil. If you get lost in a desert you are more likely to drown than to die of thirst because the water-holding capacity of the "soil" is almost nothing making flash floods likely. But soil that is at an advanced stage of ecological succession will be dominated by mycorrhizal fungi that produce glomalose. This type of soil can hold as much as 50x more water than "dead" soil