Why is the city of Ember underground?

The titular city of Ember is a vast underground city meant to serve as a last resort to ensure the survival of humanity in the event of a catastrophic or even apocalyptic event. The city, however, is not a permanent solution and was only built to sustain the remnants of humanity for roughly two centuries. The central conflict of the story revolves around the dwindling supply of food and decay of the hydroelectric apparatus that powers the city, as the inhabitants have passed the 200 year mark. The nature of the city is completely lost upon the primary characters of the novel, who until the very end of the story not only are unaware of the apocalyptic and dystopian nature of their society, but don't even realize that they are underground. Due to a lack of education of young persons in Ember, as well as some misfortune and ineptitude on the part of the leaders of the city, memory of the nature of the world was almost completely erased over the course of just a few generations.

The city of Ember is underground as a precautionary measure. In the book, we don't learn why the city is underground until the last chapters.
Long ago, the people who lived aboveground decided that Ember would be the only way to guarantee the continuation of the human race in the event of a catastrophe. The people believed that the underground city of humans would be humans' last resort to repopulate the earth.
The people aboveground arrived at this unconventional solution after realizing that the human race faced extinction from some unexplained catastrophe. According to the notebook that Lina and Doon find, the first humans to populate Ember were old people and babies. Each elderly couple was "matched" with two babies. In all, Ember began with two hundred humans. The babies were raised with little knowledge of the world aboveground.
By the time the babies reached adulthood, they were bereft of their elderly caregivers. The new adults then married and had children: this was how Ember flourished for more than two hundred years. So, the city of Ember is underground as a precautionary measure; it is an attempt at preserving the human race after the destruction of civilization.