Characterization of annual urban air temperature changes with special reference to the city of Modena: a comparison between regression models and a proposal for a new index to evaluate relationships between environmental variables

It is commonly recognized that the observed increase in global mean annual air temperature is strongly related to the increase in global carbon dioxide concentration C, and that both these variables are related to global development. It remains, however, unclear the degree to which local mean annual urban air temperature T is affected by local variables such as annual precipitation depth P and urban area extent A. This study assumes that A is a proxy of local development and C is a proxy of global development and investigates the commingled effects of A, P, and C on T by using long-term annual data observed over the years 1881–2019 from the Modena Observatory in Italy. Linear relationships between T, C and A are found to be spurious since all these series have a monotonic increasing trend with time. Parametric analytic models like logistic functions are found to lack flexibility. Smoothing splines can only give insights into the strength of the relationships but not on their shape defining the functional relationship between variables. Advanced nonlinear models like generalized additive models, instead, are found to combine flexibility in a parametric form, and appear therefore to be suitable models for explaining the complex relationships between A, P, and C on T. The different models are evaluated using traditional goodness of fit statistics like R2, AIC, BIC, and a new index of relation IR which is introduced to jointly evaluate the goodness-of-fit of relationships between variables that may either be dependent or independent.