Cumulative Drawdown as a Primary State Variable: The Absement Method for Confined Aquifer Pumping-Test Analysis

Classical pumping-test interpretation relies on instantaneous drawdown and its time derivative, both of which amplify measurement noise. This study introduces cumulative drawdown, or absement, as the primary state variable for confined aquifer pumping-test analysis. Time integration of the transient flow equation yields a governing relationship connecting instantaneous drawdown to the spatial curvature of cumulative drawdown. A closed-form absement kernel is derived from the Theis solution and cast in dimensionless form, yielding four diagnostic operators: absement A(t), time-averaged absement A(t)/t, windowed ΔA/Δt, and the normalized absement derivative (NAD). The four operators read different features of the same drawdown record and together cover parameter estimation, scale-resolved diagnostics, and flow-regime identification. Monte Carlo testing (N = 50) under combined Gaussian, log-time jitter, and quantization noise recovers transmissivity to within 0.1% of the true value (p > 0.5). Field tests on homogeneous and heterogeneous confined aquifers reproduce classical Theis and Cooper–Jacob estimates and identify two scale-dependent regimes in the Oude Korendijk dataset.