Validation of Specific and Total Catchment Area estimated via Flow Direction Algorithms through a 2D Shallow Water Equations Numerical Solver

Specific Catchment Area (SCA) and Total Catchment Area (TCA) are two widely used topographic attributes in the study of hydrological, geomorphological and biological processes at the watershed scale. They are typically estimated starting from a Digital Terrain Model using Flow Direction (FD) algorithms. In the ideal case of constant and uniform rainfall excess, SCA and TCA are directly proportional to the steady-state specific discharge and discharge of surface runoff, respectively. This study investigates an alternative approach that computes SCA and TCA fields using a rain-on-grid Shallow Water Equations (SWE) model (PARFLOOD-Rain). Given a DTM representing a terrain, a constant and spatially uniform rainfall rate is applied, and the simulation is run until a steady-state regime is reached everywhere. At each pixel, the ratio between the steady-state discharge and the imposed rainfall rate yields the TCA value, while SCA is obtained by dividing the steady-state specific discharge by the rainfall rate. In the first part of the study, SCA and TCA fields generated by PARFLOOD-Rain are compared against outputs from six commonly used FD algorithms (namely D8, Rho8, D-infinity, MFD-Quinn, MFD-md and FD8) and from the recent IDS algorithm proposed by Prescott et al. (2025). All outputs are validated against analytical solutions on four synthetic surfaces (inclined plane, saddle, convergent and divergent surfaces). All the methods, including PARFLOOD-Rain, are further validated – on another synthetic surface – against a numerical solution of the differential equation proposed by Gallant & Hutchinson (2011), which defines SCA along a flow line. On all test surfaces, PARFLOOD-Rain predicts SCA and TCA with errors one to two orders of magnitude smaller than those of the FD methods, and its accuracy improves with grid refinement – unlike the FD algorithms – which show no such convergence behavior. In the second part of the study, PARFLOOD-Rain is used to estimate SCA and TCA in a real catchment, and its results are used as a reference solution to validate the FD algorithms in a complex, channelized terrain. A small catchment downstream of Blanca Peak, Colorado (USA) is selected as a case study. The analysis highlights that, while SCA and TCA’s sensitivity to the rainfall intensity is negligible on smooth synthetic surfaces, it is a major controlling factor in irregular, natural terrains featuring channels and carvings. Whereas it is trivial that FD methods could never fully describe the complex hydrodynamics captured by SWE-based approaches, the results of the study suggest that more sophisticated FD algorithms, like IDS, can offer potential advantages over traditional FD methods in the prediction of TCA and SCA.