Although some deserts are dry, barren, desolate places, the definition of desert only requires it to have little precipitation.
A better term for such a particularly barren area is a wasteland.
A desert
not
Barren; desolate
Wasteland: 1. A land that is desolate, barren, or ravaged. 2. A place, era, or aspect of life considered as lacking in spiritual, aesthetic, or other humanizing qualities; a vacuum.
Desolate is not a positive, so it is a negative.
Foliage doesn't really have exact antonyms, but in various contexts antonyms could be found. 'Treeless' and 'deforested' are also pretty close. Ex: "[ant. foliage] environment" barren bleak exposed desolate stark arid
not
Barren; desolate.
a dry bareen piece of land
The abandoned village looked desolate as the crumbling buildings stood empty and overgrown with weeds.
The tundra is like a frozen wasteland, desolate and barren.
Samuel Hearne called the region he explored the "Barren Grounds" because the area was characterized by sparse vegetation, harsh climate, and low human population. The land appeared desolate and barren to him, hence the name.
Barren; desolate
hilly, flat, green, parched, undulating, barren, fertile, desolate,
desolate, empty, desert, waste, infertile, sterile, childless, unproductive
The analogy for disconsolate could be: as desolate is to barren, disconsolate is to unhappy.
A barren or desolate area, especially:a. A dry, often sandy region of little rainfall, extreme temperatures, and sparse vegetation.b. A region of permanent cold that is largely or entirely devoid of life.c. An apparently lifeless area of water.2. An empty or forsaken place; a wasteland: a cultural desert.3. Archaic A wild, uncultivated, and uninhabited region.adj.1. Of, relating to, characteristic of, or inhabiting a desert: desert fauna.2. Barren and uninhabited; desolate: a desert island.
A barren is an area of low fertility and habitation.