Joint multiscale dynamics in soil–vegetation–atmosphere systems: Multifractal cross‐correlation analysis of arid and semiarid rangelands

Understanding the dynamics of the soil–vegetation–atmosphere (SVA) system, particularly in arid and semiarid regions, remains challenging due to its intricate and interdependent nature. This system creates problems for rangeland administration, such as insurance and risk management. This paper focuses on the complex interactions within the SVA system, particularly on rangeland ecosystems in Spain's semiarid and arid regions. By employing multifractal detrended cross‐correlation analysis (MFCCA), we explore the joint behavior of key variables, including precipitation (PCP), evapotranspiration (ETP), aridity index (Arid. I.), soil water availability (SWA), biomass (Bio), and normalized difference vegetation index (NDVI). Analyzing a 20‐year data series from Madrid and Almeria provinces, we reveal distinct patterns in the studied variables’ persistence, multifractality, and asymmetry. Notably, the differences in the generalized Hurst exponents ((q)) between Madrid and Almeria for SWA with NDVI, SWA with Bio, and NDVI with Bio underscore distinct interactions in these regions. Moreover, multifractal analyses unveil differences in the complexity of joint variables’ behaviors in the two regions. Almeria exhibits higher multifractality across variables, indicating more complex and variable environmental interactions, likely due to its more arid conditions. These findings suggest that Almeria has more sensitivity to changes, requiring adaptive management strategies, while in Madrid, water availability and related variables play a more dominant role in driving vegetation dynamics. These findings shed light through MFCCA on the nuanced dynamics of rangeland ecosystems in semiarid and arid regions, emphasizing the importance of considering complexity‐based approaches to understand the intricate interplay among key variables in the SVA system.