where \(x\) is bore-stream separation distance (L), \(t\) is the duration of time elapsed since the onset of groundwater extraction (T),\(T\) is unconfined aquifer transmissivity (L2.T–1), \(S_{y}\) is unconfined aquifer storage coefficient (unitless), \(\lambda\) is streambed leakance [L], \(K_{S}\) is streambed hydraulic conductivity [L.T–1], \(b\) is aquifer saturated thickness (L), \(b_{S}\) = streambed thickness perpendicular to flow (L.T–1), and erfc is the complementary error function. To simplify the derivation of \(V_{\text{CSD}}\), the following substitutions are introduced: