On pressure and temperature correlation patterns

Temperature (T), pressure (p) and density (ρ) are the three fundamental variables that describe the local behaviour of the atmosphere through the ideal gas law. This work aims: 1) to investigate the mutual dependence of these variables near the Earth’s surface in the real-world atmosphere (i.e. not in idealized conditions); 2) to assess the physical conditions that lead to positive or negative correlations R(p,T).

Possible applications of this study are: i) to improve the knowledge of the interdependence between meteorological variables at the local level, at least for the stations considered; ii) more in general, to classify stations objectively (e.g. dividing valley floor stations from top stations), according to the relationship between physical parameters; iii) identify implausible observations of meteorological variables. 

First of all, from hourly data it is found that temperature and pressure are weakly related if compared to density and temperature, which show a correlation close to 1. In fact, temperature and density depend only on local thermodynamic conditions, while pressure is representative of the properties of an entire vertical column of air. Moreover, from a temporal variation perspective, it is found that, on average, the normalized hourly change in pressure is very low with respect to temperature and density temporal variations. 

A second result we present is that scatterplots of hourly pressure versus temperature reveal a triangular shape for various stations we considered at different latitudes in extratropical areas. For all the locations it was always possible to fit the upper side of the triangle with a line of the same slope and with an intercept proportional to the mean pressure of the station. This suggests that a physical boundary exists in the extratropics, above which combinations of pressure and temperature cannot be observed. An exception are the high mountain stations, for which the scatterplots show a strong correlation very similar to what is found in the free atmosphere. Also the behaviour in the tropics is different, with a density-plot closer to a 2D gaussian distribution; however, the fitted line still represents an upper limit.

Eventually, hourly data are aggregated at different temporal scales and correlations are computed: the analysis shows a hourly sinusoidal variation of the correlation R(p,T) during the day, reaching a maximum in the afternoon and a minimum in the night, that can be found in all the extratropical stations considered.