Data & Scripts for: Unmasking ecosystem vulnerability to compound hot-dry shocks via cross-scale frequency dynamics

This repository contains the complete processed datasets and custom computational codebase required to reproduce the core findings, frequency-domain diagnostics, and multidimensional phase-space visualizations presented in our study.

By employing a spatiotemporal Fast Multidimensional Ensemble Empirical Mode Decomposition (fast-MEEMD) framework and the Hilbert-Huang Transform (HHT), our study unmasks a fundamental physical dichotomy in the climate-ecosystem continuum over the Loess Plateau (comparing the 2001 and 2006 extreme compound hot-dry events). We objectively identify a "quasi-40-day spectral gap" that serves as a topological barrier, effectively separating high-frequency atmospheric shocks (weather) from low-frequency soil moisture memory (hydrology). The trajectory of cross-scale phase dynamics around this critical 40-day threshold provides a continuous, physics-based biomarker for anticipating lethal hydraulic resonance and macroscopic carbon sink collapse.

1. Data Structure Please note that the raw meteorological forcings and GPP datasets are excessively large and publicly hosted elsewhere (see Data Provenance). This repository exclusively hosts the processed derivative matrices necessary for direct reproduction of the study's results:

• Harmonized_Anomalies: Standardized daily anomaly matrices (z-scores) of GPP, 2-meter air temperature, VPD, and depth-weighted soil moisture over the extended growing season (April–September).

• Decomposed_IMFs: The isolated Intrinsic Mode Functions (IMFs 1 to 8) and residual trends extracted via the fast-MEEMD algorithm.

• Instantaneous_Phase_Amplitude: Daily instantaneous period and energy arrays derived from the HHT for high-frequency physiological carriers and sub-seasonal environmental modulators.

2. Code Structure All signal processing, statistical, and plotting algorithms are modularized for clarity and reproducibility. The codebase includes:

• 01_Spatial_K_Scan: Scripts for performing Empirical Orthogonal Function (EOF) spatial dimensionality optimization and extracting the K=5 truncation threshold.

• 02_Fast_MEEMD_Decoupling: Core algorithm for executing the spatiotemporal signal decoupling to isolate non-stationary oscillations.

• 03_KL_Divergence_KDE: Statistical modules computing the zero-crossing instantaneous periods, Gaussian Kernel Density Estimations (KDE), and the symmetric Jeffreys Kullback-Leibler (K-L) divergence.

• 04_2D_Huang_Spectrum: Visualization scripts for mapping the multi-IMF energy-weighted composite trajectories onto the 2D cross-frequency topological state space.

3. Data Provenance & Acknowledgements

• ERA5-Land Hydroclimatic Forcings: Raw temperature and soil moisture data, as well as the variables used to calculate VPD, were sourced from the Copernicus Climate Change Service (C3S) Climate Data Store (https://doi.org/10.24381/cds.e2161bac).

• GPP Observations: The MODIS-FLUXNET integrated GPP dataset was sourced from the Oak Ridge National Laboratory Distributed Active Archive Center (ORNL DAAC) (https://doi.org/10.3334/ORNLDAAC/1835).

Usage / System Requirements The provided scripts are extensively commented. Users should configure the input/output directory paths at the beginning of each main execution script. Detailed software versions and package dependencies (e.g., specific Python/MATLAB toolboxes for HHT and EOF analyses) are documented within the provided requirements.txt or header comments of the primary scripts.