Final answer:
Among Egypt, Iraq, Algeria, and Saudi Arabia, Saudi Arabia faces the most critical situation with desertification due to its heavy reliance on depleting fossil water aquifers for agriculture in its vast desert regions.
Step-by-step explanation:
In determining which of the countries listed is facing the most serious problem of desertification, we must look at the factors affecting each region. Egypt suffers from high salinization and water scarcity, which reduces agricultural productivity, thus being detrimental to its large rural population. Iraq faces challenges due to salination, particularly in its historic farming systems in Mesopotamia. Saudi Arabia, largely a desert nation, depends on fossil water from underground aquifers for irrigation, which are being depleted. Lastly, Algeria is affected by the southward shift of the Sahara Desert, which has been altering the economic activities of those in its path over centuries.
Considering the available information, while all these countries face challenges related to desertification, Saudi Arabia's reliance on non-renewable water resources for agriculture and its vast desert regions would suggest that it is facing a critical situation regarding desertification. The depletion of fossil water aquifers without significant renewable water sources reinforces its precarious position and the seriousness of its desertification issue.