Inversion (meteorology)

An atmospheric thermal inversion is a region where temperature increases outward. In a strongly irradiated atmosphere it can arise when shortwave opacity exceeds thermal infrared opacity and stellar energy is absorbed high in the atmosphere.

An upper atmospheric region above the tropopause in which shortwave heating can produce an atmospheric thermal inversion. Ozone on Earth, and methane and aerosols on giant planets, are examples of absorbers that help heat it. Its positive altitude temperature gradient makes it stable against homogeneous-gas thermal convection.

An atmospheric thermal inversion has outward-increasing temperature. In a semi-grey irradiated atmosphere, define downward thermal optical depth $\tau$, constant opacity ratio $\gamma ={\kappa }_{\mathrm{vis}}/{\kappa }_{\mathrm{IR}}>0$, irradiation temperature $T_{\mathrm{irr}}$ and internal effective temperature of a planet $T_{\mathrm{int}}$. In the isotropic-irradiation closure, write the incident mean irradiance as $f_r{\sigma }_{\mathrm{SB}}{T}_{\mathrm{irr}}^4$, with $f_r>0$ explicitly specifying the averaging convention. Common choices are $1/4$ for a whole-sphere average and $1/2$ for a dayside average.

The analytic radiative equilibrium profile in this closure isDifferentiation givesSince $\tau$ increases inward, an atmospheric thermal inversion occurs when this derivative is negative. Thus $\gamma >1$ is necessary in this closure; a nonzero intrinsic radiative flux also requires sufficiently strong irradiation. For $T_{\mathrm{int}}>0$, any inversion is restricted toprovided the logarithm is positive. The $T_{\mathrm{int}}=0$ limit gives the threshold $\gamma >1$. These coefficients depend on the angular closure; a collimated beam has an incidence-angle dependence.^[ref]

A strong-opacity line forms higher than the nearby continuum. Under the Eddington-Barbier approximation, an outward-decreasing temperature therefore makes an absorption line, while an atmospheric thermal inversion makes the line-forming layer hotter and reverses it into emission.