Estimation and attribution of nonlinear trend of water use efficiency using a normalized partial derivative approach

Investigating trends in water use efficiency (WUE) and its causality is critical for understanding ecosystem behaviors. Although WUE has shown nonlinear changes in the last several decades across most global ecosystems, the majority of available studies have focused on its linear trend. This study attempted to accurately attribute the linear and nonlinear variations in WUE using normalized driving factors in the Partial Derivative (PD) equation to develop a Normalized Partial Derivative model (NPD-model). Two linear trends obtained from the Linear Regression (LR) and Non-Parametric (NP) and a nonlinear trend obtained from the Ensemble Empirical Mode Decomposition (EEMD) are employed in the NPD-model for attributing WUE change in China. The individual and relative responses of driving factors to WUE change during 2000-2018 are quantified using the China version of the PML-V2 evapotranspiration and gross primary productivity products. The results show that the nonlinear EEMD-based NPD-model with an R² of 0.83, performs best compared to the LR- and NP-based NPD-models, which have R² values of 0.64 and 0.7, respectively. WUE increased monotonically in most areas of all vegetation types, with high variability observed in grassland and shrubland. The EEMD-based attribution analysis indicates that leaf area index is the leading factor in regulating WUE in China, followed by CO₂ and climate. The relative contributions revealed that increased WUE in most of China is dominated by the combination of vegetation and environmental factors, covering more than 80% of the study area. These contribution results, however, are largely different from those obtained using the LR- and NP-based NPD-models, as 52% of the study area exhibits cyclic variation in WUE. Therefore, the nonlinear EEMD-based NPD-model provides excellent spatiotemporal attribution of WUE through its driving factors, which is crucial for understanding the ecosystem response to changing environments, potentially assisting in ecosystem and water resource management.