where:
- \(q\left(t,t_{in}\right)\) [m3s-1] is the discharge generated by the single rain record called age-ranked discharge.
- \(f\left(t-t_{in}\right)\ \left[s^{-1}\right]\) is the IUH (here assumed time invariant with respect to the injection time)
- \(A\left[m^2\right]\)is the area of the catchment we are analyzing
- \(H\left(x\right)\) is the Heaviside step function such that