I have done some research on this topic and I found that it is necessary to distinguish between climate impacts and water mismanagement effects due to over development in these regions. You can read these articles:
Article Environmental water demand assessment under climate change conditions
Article Climate change outlook for water resources management in a s...
Another article : Impact of climate change on the water resources of the eastern Mediterranean and Middle East region: Modeled 21st century changes and implications, available on
Recent floods in Iraq and Iran narrate a different story. The climate in the Middle East is cyclic going through dry and wet cycles respectively. It seems that the wet cycle has returned.