Electronic Supplementary Material 1: Derivation of closed-form
analytical solution for cumulative streamflow depletion
The volume of cumulative streamflow depletion (\(V_{\text{CSD}}\)) can
be calculated as the temporal integral of an instantaneous streamflow
depletion flux (\(Q_{\text{ISD}}\)) resulting from a groundwater
extraction flux (\(Q_{B}\)) applied from \(t\)=\(t_{0}\) to\(t\)=\(t_{f}\):