The Eruption Plume Energy Bound: Inverting Column Height into Vent Thermal Power

From an eruption column height alone, Morton-Taylor-Turner plume-rise physics is inverted to vent thermal power: 1.65 TW at 10 km, 26.41 TW at 20 km, 133.72 TW at 30 km and 422.61 TW at 40 km at reference stratification, scaling as height to the fourth power. Sustained six hours, these agree with the calorimetric census scale (10^16-10^18 J) within a factor of 3.57 to 9.13, not orders of magnitude away, with a quantified sensitivity span of ratio 120.6 at 20 km. AI use is disclosed: this work was prepared with the assistance of an artificial intelligence system, Dave, which performed the calculations, drafting and deposit under the author's direction.