How beech ecophysiology shapes temperate forest gross primary productivity – Part 1: A wavelet-based framework for extracting seasonal dynamics

Long-term eddy covariance (EC) records provide unique opportunities to investigate how seasonal carbon dynamics shape interannual and decadal trends in forest carbon uptake. Yet extracting reproducible phenological and structural information from noisy, non-stationary gross primary productivity (GPP) time series remains challenging. Here we present a wavelet-based analytical framework that directly exploits the time-frequency structure of GPP signals to identify repeated seasonal features. This approach departs from standard wavelet applications by analyzing the full set of wavelet coefficients as an interpretable structure to systematically detect and characterize recurrent patterns, including moderate-amplitude events that are typically overlooked by significance-based or visually driven wavelet analyses. Building on this foundation, we introduce a novel Wavelet Area Interpretation (WAI) method that extracts three complementary indicators of seasonal GPP dynamics (IRise for rising rate; IPeak for peak productivity; IDrop for mid-season decline) and derives carbon-uptake phenological markers within a unified workflow. Together, these metrics provide a coherent representation of the timing, magnitude and shape of the seasonal GPP cycle. We apply this framework to long-term EC records from three contrasting ICOS-labelled European beech-dominated forests (DE-Hai, DK-Sor, FR-Hes), demonstrating its ability to reveal both structural differences among sites and divergent long-term trajectories in carbon uptake. Benchmarking against classic smoothed GPP reference values confirms the robustness of IRise and IPeak and clarifies the inherent uncertainties associated with mid-season metrics. Ecologically, the indicators uncover consistent contrasts in seasonal structure: rapid spring rise at FR-Hes, muted mid-season decline at DK-Sor, and early cessation of uptake at DE-Hai. They reveal opposing multi-decadal trends, with peak productivity increasing in the managed stands but declining in the unmanaged old-growth forest. The negative association between IRise and mid-season drop timing further suggests an intra-seasonal trade-off linking early-season vigor to mid-season susceptibility. Overall, this study provides a novel, scale-aware approach for extracting seasonal information from noisy time series and demonstrates how WAI-derived indicators can yield new insights into the mechanisms driving long-term variability across sites and applications.