Project Purity

 is a water purification project that started before the beginning of Fallout 3. In Rivet City, Doctor Li will tell the PC that his father, James, left Vault 101 to travel to Rivet City to start the project up again. Dr. Li refused and James moved on. Project Purity is what motivates your father to eventually leave the Vault in search of a GECK in the hope of completing the project.

After finding James, it is revealed Project Purity started up again at the Jefferson Memorial, but the location was captured by super mutants. After picking up Doctor Li and her staff from Rivet City, the location will have to be cleared before the project can be started again.

Quotes

 * The plan was to build a facility that could purify all the water in the Tidal Basin at once. No radiation, no much, just clear water. - Doctor Li

Related quests
The project is tied to Following in His Footsteps, and possibly tied to The Waters of Life, as well as the Jefferson Memorial location.