  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, thus
are unavoidably imperfect. Conversely, observation-based data of climatic and
environmental variables are becoming increasingly accessible over large scales
due to the progress of space-borne 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 multiscale 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 not
only 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), but also to 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.
