Critical Transitions at Campi Flegrei Resurgent Caldera: A Novel Approach to Systemic and Retrospective Signals Analysis

This study investigates how complex volcanic systems undergo major behavioral shifts, focusing on the Solfatara–Pisciarelli (SP) hydrothermal-magmatic area within the Campi Flegrei caldera (Southern Italy). The SP system is one of the most active zones of the caldera, characterized by persistent degassing, seismic swarms, strong hydrothermal circulation and long-term ground uplift. These processes arise from nonlinear interactions between magmatic inputs, fluid migration, and shallow hydrothermal pressurization, making the identification of critical transitions particularly challenging.To address this, we developed an integrated analytical framework combining Multivariable Fractional Polynomial Analysis (MFPA) and Global Critical Point Analysis (GCPA). MFPA models nonlinear and time-lagged associations among key monitoring parameters—vertical ground deformation, seismicity, CO₂ flux, geochemical equilibrium variables, and thermal signals—while GCPA identifies the temporal moments when multiple variables collectively show systemic reorganization.Analysis of multi-year (2018–2024) geophysical and geochemical datasets revealed that deformation is strongly associated with seismicity, equilibrium pressures of hydrothermal gases, heat flow, and CO₂ flux. Incorporating time-lagged deformation improved model accuracy and reduced unexplained variance, highlighting delayed cause–effect couplings between deformation and fluid-dynamic processes. The model confirms seismicity as the most stable explanatory parameter, consistent with sustained fracturing and fluid pressurization in the shallow system.GCPA identified two major critical transitions:CP1 – 30 November 2020, dominated by thermal–chemical reorganization and increased gas-system pressurization.CP2 – 1 April 2023, reflecting a more open and multiparametric regime where deformation, temperature, seismicity, heat flux, and CO₂ emissions contribute comparably to system evolution.These transitions align with independent geodetic evidence suggesting migration and reconfiguration of the shallow overpressure source beneath the SP area. The integrated MFPA–GCPA approach thus reconstructs how systemic changes propagate across geophysical and geochemical variables, providing retrospective insight into the onset and progression of unrest phases.This framework offers several advantages over classical or non-parametric approaches: interpretability of functional relationships, explicit treatment of nonlinearities and time lags, and the ability to detect collective regime shifts rather than isolated anomalies. Although not predictive, the method provides a quantitative basis for identifying critical phases in volcanic systems and may be adapted to other densely monitored calderas. With higher-resolution and real-time data streams, it could support early indications of evolving unrest and enrich next-generation volcano-monitoring strategies.