Hydrothermal integration and synergy regulate carbon exchange in forest ecosystems of eastern China

• We developed the indicators of hydrothermal integration and hydrothermal synergy. • VPD, SWC, and AI responded nonlinearly to TP and D. • GPP, R e, and NEP peaked at TP = 1 and D slightly above 0. • SWC was the main driver of the change in GPP, R e, and NEP. Forest ecosystem photosynthesis is primarily driven by hydrothermal conditions. However, the effects of hydrothermal integration and synergy on carbon exchange across forest ecosystems are still not clear. We examined the divergence of carbon exchange over 16 forest ecosystems in eastern China. To explore the controls of hydrothermal change on gross primary productivity (GPP), ecosystem respiration ( R e), and net ecosystem productivity (NEP), we developed two indices for hydrothermal integration (TP) and hydrothermal synergy (D) based on the copula function. Compared with traditional indices such as the water and thermal product index (K), aridity index (AI), and standardized precipitation evapotranspiration index (SPEI), TP and D demonstrated higher sensitivity and applicability in capturing seasonal and spatial variations in hydrothermal conditions. Vapor pressure deficit (VPD), soil water content (SWC), and AI responded nonlinearly to TP and D, with coordinated hydrothermal conditions enhancing SWC and uncoordinated or scarce conditions increasing drought risk. TP and D explained over 80% of the variability in GPP, R e, and NEP, which better captured hydrothermal controls on carbon exchange than temperature and precipitation alone. Carbon fluxes peaked at TP ≈ 1 and D slightly above 0, indicating that moderately water-dominated hydrothermal synergy provided optimal conditions for photosynthesis and respiration. Random forest analysis revealed that SWC was the primary driver of GPP, R e, and NEP, followed by D for GPP and NEP, indicating that forest carbon exchange is mainly regulated by soil water availability and atmospheric hydrothermal synergy. This study clarifies how hydrothermal conditions impact on carbon exchange in forest ecosystems and provides insights into assessing forest responses to climate change.