A Dynamical Analytical Model for Midlatitude Temperature Distributions with Advection and Diabatic Heating

Midlatitude atmospheric temperature distributions tend to be non-Gaussian. Therefore, mean and variance alone are not sufficient to calculate the magnitude and frequency of extreme temperature events. While emergence of such non-Gaussianity has been studied through model calculations and kinematic models, the physical basis of such models has not been explored. Here we compare and contrast our previous kinematic model, which served as a way to explain and unify other past works in estimating statistical moments of midlatitude temperature distributions, with a dynamical system based on more fundamental physics to explain the validity of the critical assumption made in our previous kinematic model. Rather than assuming a source meridional temperature profile, we let actual temperature get advected as it constantly relaxes to an equilibrium profile diabatically. Namely, we analytically solve an advection equation of temperature with a stochastic wind and a Newtonian relaxation forcing term with conditions appropriate for Earth’s atmosphere, then use the solution to calculate the first four moments of temperature distribution. We find moments depend on time-mean temperature and its derivatives as in the previous model with a slight difference in some numerical coefficients, corroborating the general validity of the previous ansatz, as well as explaining the physical basis of it.