# What meteorological features accompany/cause a thermal inversion?

I am physics grad student working on a problem of making a statistical (neural network) prediction of the air pollution in a city. I am provided with hourly values for ca. a dozen meteo features of the city for the last ~20 years - temperature, humidity, wind speed, wind direction, PM10, O3, SO2 concentrations a.o. What I've read is that the air pollution (especially in winter) often is present when a thermal inversion occurs, meaning when the temperature of the air above the city increases with altitude, instead of decreasing. Luckily enough, there are weather measuring stations in the city AND also one just outside the city at an altitude of 1350 m (the city itself has an altitude of ~600 m). This allows me to introduce another feature that might be useful - the difference in temperature at high and low altitude as a proxy for thermal inversion ($$T_{proxy-inv} = T_{high} - T_{low}$$).

My question: what other meteorological features are affected when inversion occurs, so that I can use them as an additional proxy? Does the pressure change notably? Or maybe the wind speed is very low during an inversion? Does something else happen during thermal inversion? Or can you point me towards another meteorological effect, besides inversion, that can influence air pollution? Tnx!

Let's take a look at the thermodynamic equation and see how the stability changes. The diagnostic equation for the dry adiabatic potential temperature ($$\theta$$) is $$\frac{D \theta}{Dt}=\frac{\partial \theta}{\partial t}+u\frac{\partial \theta}{\partial x}+v\frac{\partial \theta}{\partial y}+w\frac{\partial \theta}{\partial z}=Q$$, where $$u$$,$$v$$,and $$w$$ are the zonal, meridional, and vertical components of the wind vector, and $$Q$$ is the diabatic heating rate. Taking the vertical dervative of the above equation is $$\frac{\partial}{\partial t}\frac{\partial \theta}{\partial z}+u\frac{\partial}{\partial x}\frac{\partial \theta}{\partial z}+v\frac{\partial}{\partial y}\frac{\partial \theta}{\partial z}+w\frac{\partial}{\partial z}\frac{\partial \theta}{\partial z}+\frac{\partial u}{\partial z}\frac{\partial \theta}{\partial x}+\frac{\partial v}{\partial z}\frac{\partial \theta}{\partial y}+\frac{\partial w}{\partial z}\frac{\partial \theta}{\partial z}=\frac{\partial Q}{\partial z}$$.
There are tons of other factors that influence air pollution, but it really depends on the pollutant. For example, ozone pollution won't be affected much by an inversion, with the exception of accumulating morning $$\ce{NO_x}$$ for a morning peak. Other factors include the amount of water for PM2.5 formation. There is also wet and dry deposition to consider. The question you are asking is very general.