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Wave‐induced adiabatic mixing in the winter midlatitudes is one of the key processes impacting stratospheric transport. Understanding its strength and structure is vital to understanding the distribution of trace gases and their modulation under a changing climate. Age‐of‐air is often used to understand stratospheric transport, and this study proposes refinements to the vertical age gradient theory of Linz et al. (2021),https://doi.org/10.1029/2021JD035199. The theory assumes exchange of air between a well‐mixed tropics and a well‐mixed extratropics, separated by a transport barrier, quantifying the adiabatic mixing flux across the interface using age‐based measures. These assumptions are re‐evaluated and a refined framework that includes the effects of meridional tracer gradients is established to quantify the mixing flux. This is achieved, in part, by computing a circulation streamfunction in age‐potential temperature coordinates to generate a complete distribution of parcel ages being mixed in the midlatitudes. The streamfunction quantifies the “true” age of parcels mixed between the tropics and the extratropics. Applying the revised theory to an idealized and a comprehensive climate model reveals that ignoring the meridional gradients in age leads to an underestimation of the wave‐driven mixing flux. Stronger, and qualitatively similar fluxes are obtained in both models, especially in the lower‐to‐middle stratosphere. While the meridional span of adiabatic mixing in the two models exhibits some differences, they show that the deep tropical pipe, that is, latitudes equatorward of 15° barely mix with older midlatitude air. The novel age‐potential temperature circulation can be used to quantify additional aspects of stratospheric transport.

The nonnormality of temperature probability distributions and the physics that drive it are important due to their relationships to the frequency of extreme warm and cold events. Here we use a conditional mean framework to explore how horizontal temperature advection and other physical processes work together to control the shape of daily temperature distributions during 1979–2019 in the ERA5 dataset for both JJA and DJF. We demonstrate that the temperature distribution in the middle and high latitudes can largely be linearly explained by the conditional mean horizontal temperature advection with the simple treatment of other processes as a Newtonian relaxation with a spatially variant relaxation time scale and equilibrium temperature. We analyze the role of different transient and stationary components of the horizontal temperature advection in affecting the shape of temperature distributions. The anomalous advection of the stationary temperature gradient has a dominant effect in influencing temperature variance, while both that term and the covariance between anomalous wind and anomalous temperature have significant effects on temperature skewness. While this simple method works well over most of the ocean, the advection–temperature relationship is more complicated over land. We classify land regions with different advection–temperature relationships under our framework, and find that for both seasons the aforementioned linear relationship can explain ∼30% of land area, and can explain either the lower or the upper half of temperature distributions in an additional ∼30% of land area. Identifying the regions where temperature advection explains shapes of temperature distributions well will help us gain more confidence in understanding the future change of temperature distributions and extreme events.

Understanding what physically sets the shape of temperature distributions will enable more robust predictions of local temperature with global warming. We derive the relationship between the temperature distribution shape and the advection of temperature conditionally averaged at each temperature percentile. This enables quantification of the shift of each percentile that is due to changes in the mean temperature, in horizontal temperature advection, and other processes (e.g., radiation and convection). We use this relationship to examine global model simulations in an idealized aquaplanet model with increasing carbon dioxide. Changes in the distribution with doubling and quadrupling of carbon dioxide are significant, and they are caused by different processes. We find that midlatitude temperature distributions can be explained mostly by the horizontal advection, except in the upper and lower 10% of the distribution.

Observed surface temperature distributions are non‐Gaussian, which has important implications for the likelihood of extreme events in a changing climate. We use a two‐dimensional advection‐diffusion model of temperature stirred by stochastically generated Rossby waves with a sustained background temperature gradient to explore non‐Gaussian temperature distributions. We examine how these distributions change with changes to thermal relaxation and eddy stirring. Weakening the background temperature gradient leads to decreased variance but no changes in other moments, while the eddy properties affect both the variance and skewness. A poleward movement of eddy stirring latitude leads to reduced skewness for most latitudes, implying a shift toward longer negative tails in temperature distributions, all else being equal. In contrast, the dependence of temperature skewness on eddy speed is a nuanced, nonlinear relationship.