Protection without poison: why tropical ozone maximizes in the interior of the atmosphere

The number density of ozone, [O₃], maximizes around 26 km in the tropics, protecting life from harmful ultraviolet (UV) light without poisoning it at the surface. Textbooks explain this interior maximum with two paradigms: (1) the source-controlled paradigm explains [O₃] as maximizing where its source maximizes between abundant photons aloft and abundant [O₂] below, and (2) the source / sink competition paradigm, inspired by the Chapman cycle, explains ozone as scaling with [O₂] and the photolytic source / sink ratio. However, each paradigm’s prediction for the altitude of peak [O₃] is off by 10 km, reflecting their well-known omission of ozone sinks from catalytic cycles and transport. We present a minimal, steady-state theory for the tropical stratospheric [O₃] maximum, accurate to within 1 km and formulated in terms of the dominant ozone sinks. These sinks are represented simply by augmenting the Chapman cycle with linear damping of O and O₃, leading to the Chapman+2 model. The Chapman+2 model correctly simulates peak tropical [O₃] at 26 km, yet this peak is not explained by either paradigm. Instead, the peak is newly explained by the transition from an O-damped regime aloft to an O₃-damped regime below. An explicit analytical expression is derived for ozone under gray radiation. This theory accurately predicts an interior maximum of ozone and correctly predicts that an increase in top-of-atmosphere UV light will lead to a downward shift in the peak [O₃] due to a downward shift in the regime transition, a result not even qualitatively predicted by the existing paradigms.