When an ash plume deposits tephra on the landscape, it buries and kills the vegetation. Once the vegetation is dead, the carbon in it begins to change. By measuring this change, Wallace can tell when in the last 15,000 years a volcano erupted.
The thickness of the ash layer and the size of the particles indicate how large each eruption was.
Combining these pieces of information, Wallace compiles an eruption chronology for each volcano, and can track how its activity has changed over time.