Which desert in Kazakhstan lies south of Lake Balkhash?

The desert in Kazakhstan that lies south of Lake Balkhash is the Saryesik-Atyrau Desert.

Saryesik-Atyrau is a sandy desert in Kazakhstan’s Balkhash-Alakol Basin. It stretches for about 400 kilometers south of Lake Balkhash, making its geographic relationship to the lake the key clue in this question.

Despite its desert classification, the region is not simply a lifeless field of dunes. Small lakes, ponds, occasional grasslands, and the nearby Ili River delta support birds and mammals, including goitered gazelles and a small saiga-antelope population.

The name is sometimes written as Saryesik Atyrau or Saryesik-Atyrau. It should not be confused with the Karakum or Kyzylkum deserts, which occupy other parts of Central Asia, or Betpak-Dala, a separate desert farther west and north of the Balkhash region.