Wavelet correlations to reveal multiscale coupling in geophysical systems

The interactions between climate and the environment are highly complex. Due to this complexity, process-based models are often preferred to estimate the net magnitude and directionality of interactions in the Earth system. However, these models are based on simplifications of our understanding of nature and thus are unavoidably imperfect. Conversely, observation-based data of climatic and environmental variables are becoming increasingly accessible over global scales due to the progress of spaceborne sensing technologies and data-assimilation techniques. Albeit uncertain, these data enable the possibility to start unraveling complex multivariable, multiscale relationships if the appropriate statistical methods are applied. Here we investigate the potential of the wavelet cross-correlation method as a tool for identifying time/frequency-dependent interactions, feedback, and regime shifts in geophysical systems. The ability of wavelet cross-correlation to resolve the fast and slow components of coupled systems is tested on synthetic data of known directionality and then applied to observations to study one of the most critical interactions between land and atmosphere: the coupling between soil moisture and near-ground air temperature. Results show that our method is able to capture the dynamics of the soil moisture-temperature coupling over a wide range of temporal scales (from days to several months) and climatic regimes (from wet to dry) and consistently identify the magnitude and directionality of the coupling. Consequently, wavelet cross-correlations are presented as a promising tool for the study of multiscale interactions, with the potential of being extended to the analysis of causal relationships in the Earth system.