Linear theory of subsurface storm flow [Water surface profiles]

A solution to the subsurface storm flow problem is developed through linearization of the complete one‐dimensional governing equation. Water surface profiles and outflow hydrographs obtained from this approximate theory are compared with the exact solution and with the kinematic approximation to this problem for a number of cases, characterized by the parameter λ = 4 i cos θ/K sin2θ. The accuracy and range of applicability of the proposed theory are greater than that of the kinematic theory. Its results may be considered satisfactory for the cases with λ ≤ 1; however, the kinematic theory is a preferable substitute for λ ≤ 0.25.