First-principles theory for Earth's tropical-midlatitude climate boundary

Tsubasa Kohyama , Hiroaki Miura, Kazuya Yamazaki

In Earth's climate, the boundary between the tropics and midlatitudes is a key determinant of temperature and precipitation characteristics, influencing human societies through daily weather, atmospheric chemistry, carbon cycling, and vegetation distribution. The physical origin of these climate zones has been investigated through idealized simulations, observations, and state-of-the-art climate models. However, a first-principles theory to explain the boundary position remains largely unexplored. Here we propose a theory to understand this climate bifurcation based on the first law of thermodynamics. We introduce a dimensionless parameter, the thermal-mechanical ratio (T/M), to quantify the roles of thermal and mechanical sources for driving vertical motion. This parameter offers a first-principles definition of "tropicalness'': regions where thermal contribution dominates are tropical (T/M ≳ 10), whereas regions with non-negligible mechanical contributions are midlatitudinal (T/M ≲ 10). We derive a simple model to describe the determination mechanism of the boundary position from fundamental physical constants, which explains observed annual climatology, seasonal variability, global warming response, and the El Niño-Southern Oscillation sensitivity. This framework provides robust theoretical foundations for understanding anthropogenic tropical expansion, informing climate change adaptation strategies. Applications to other planetary atmospheres are also suggested.