Unraveling the Complex Causal Relationship between Soil Moisture and Air Temperature Anomalies: A Comparative Analysis of Linear and Nonlinear Granger Causality

Abstract

Unveiling the complexities of Earth's climate system demands a profound understanding of the intricate interplay between soil moisture (SM) and 2m air temperature anomalies (T). This study employs cutting-edge methodologies, such as nonlinear Random Forest Granger Causality (nRFGC), Copula nonlinear Granger Causality (CnGC), nonlinear Kernel Granger Causality (nKGC), and the traditional linear Granger Causality (GC), to unravel the complex causal relationship between SM and T. Through extensive experimentation on both hypothetical and real-world datasets from diverse sources, the research underscores the superior efficacy of nonlinear methodologies—especially nonlinear KGC—in identifying elevated Granger causal signals across spatial and temporal dimensions. Notably, these findings align consistently with both hypothetical and traditional hydrological models, underscoring the limitations of linear methodologies when grappling with nonlinear causation. The study provides clarity on discerning the nonlinear causal link between SM and T, emphasizing the imperative to transcend conventional linear methods when unraveling the intricate causal complexities within Earth's climate system. Significantly, Nonlinear Granger Causality (nGC) emerges as a potent tool capable of unveiling causal structures without succumbing to overfitting issues. Consequently, this research imparts insightful revelations about the non-linear dynamics inherent in SM-T interactions across different seasonal levels. Our study clarifies and makes it clearer to identify the nonlinear causal relationship between SM and T, emphasizing the need to go beyond conventional methodologies, asserting that these methodologies fall short in comprehending the nuanced causal interactions between land and atmosphere. By urging a shift, the study contends that embracing non-linear methodologies is essential not only for enhancing predictions but also for gaining a more profound understanding of Earth's climate system.