Scale-dependent phase reversal in climate–CO2 relationships: evidence from long-term spectral analysis of urban climate data

Understanding the stochastic variability of climate–carbon relationships across temporal scales remains a key challenge in climate analysis. This study investigates scale-dependent interactions between local temperature, precipitation, and atmospheric CO₂ concentrations using long-term observations from Modena (Italy) and regional and global datasets. Cross-spectral analysis reveals dominant 12-month periodicities in local temperature associated with regional CO₂ variability, as well as 3.5- and 4–5-year periodicities linked to global CO₂ fluctuations. A consistent scale-dependent phase reversal emerges across temporal scales, with CO₂ leading temperature at annual and sub-18-month periods and temperature often leading CO₂ at interannual timescales. This behavior provides a coherent framework for distinguishing relationships driven by shared seasonal forcing from those emerging through longer-term feedback mechanisms. In contrast, associations between CO₂ (both local and global) and precipitation dynamics remain limited and intermittent, with largely decoupled periodicities across scales. The analysis also reveals changes in the intra-annual variability of temperature range and precipitation after 2001, indicating a reorganization of local climate dynamics. Overall, the results show that climate–carbon relationships are strongly scale-dependent and highlight the value of frequency-domain approaches for characterizing variability and avoiding misleading inferences in non-stationary, multi-scale environmental time series.