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Joined 2026-09-21 Message
Incoming links: Terrestrial atmosphere
Past exam of the mathematics course of the University of Cambridge 2017 iii Paper 315 1 a iv Solution Created 2026-10-03 Updated 2026-10-06
The functional form is not specific to exoplanets. With positive pressure normalization and physical temperature, a square-root exponential atmospheric profile can approximate a monotone interval of the terrestrial atmosphere. An outward-cooling interval, such as part of the troposphere or mesosphere, requires . An upward-warming interval, such as part of the stratosphere heated by ultraviolet absorption or the thermosphere heated by high-energy radiation, requires .
The local atmospheric lapse rate follows from the ideal gas relation and hydrostatic equilibrium:For dry terrestrial air, approximately and give the dry-adiabatic lapse rate . The familiar mean tropospheric value near is less steep; a local fit must satisfy to be dry-convectively stable. Moist convection needs the moist parcel thermodynamics instead, and the terrestrial atmosphere is not uniformly dry or chemically homogeneous at all heights.
The squared-logarithm shape cannot reproduce an exactly constant nonzero lapse rate over an arbitrary thick region, all the alternating atmospheric layers, or a finite exactly isothermal region. It is a local parametrization with a fixed sign of the temperature gradient; it has no terrestrial universality.
Past exam of the mathematics course of the University of Cambridge 2017 iii Paper 315 4 f Solution Created 2026-10-03 Updated 2026-10-06
Three routes away from local thermochemical equilibrium are:
- Vertical transport and quenching. When the eddy mixing time becomes shorter than the chemical relaxation time, gas retains a deeper composition. In cool, directly imaged giant exoplanets, carbon monoxide–methane quenching can preserve CO and suppress the methane expected in cool equilibrium layers. In Jupiter, CO carried from deeper hot layers, and phosphine maintained against upper-atmosphere chemical loss, are examples of transported disequilibrium species.
- Horizontal transport and quenching. Atmospheric advection time shorter than the local chemical relaxation time carries abundances between regions of different temperature. A hot Jupiter can carry CO-rich dayside gas into cooler nightside gas that would otherwise favour methane. In the Solar System, upper-atmosphere CO produced on the illuminated side of Venus can be redistributed to its dark side by circulation; this is an example of nonlocal production and transport, rather than local dark-side thermochemical equilibrium.
- Atmospheric photochemistry. Ultraviolet photons dissociate or ionize molecules and initiate reaction networks. Models of irradiated hydrogen-rich exoplanet atmospheres can produce enhanced hydrogen cyanide and hydrocarbon precursors from methane/nitrogen chemistry; whether these products accumulate depends on ultraviolet flux and transport. The terrestrial atmosphere gives a clear Solar-System example: oxygen photodissociation and subsequent reactions maintain the ozone layer, which is not a purely thermochemical-equilibrium abundance.
Vertical mixing, horizontal advection, and photochemistry supply three mechanisms and examples in both exoplanets and Solar-System atmospheres. A photochemical steady state balances production and loss; it is different from a Gibbs free energy minimum. These examples describe mechanisms and model expectations rather than asserting unique observational attribution for every planet.
Troposphere 2026-10-06
The troposphere is the lowest main layer of the terrestrial atmosphere, with weather and generally decreasing temperature with altitude. Local inversions and moist convection complicate a single lapse-rate description.