Numerical troubles in conceptual hydrology: Approximations, absurdities and impact on hypothesis testing

Why worry about numerics given so many other problems? Hydrologists often face sources of uncertainty that dwarf those normally encountered in many engineering and scientific disciplines. While a structural engineer designing a wall of a building can subject multiple bricks to repeated strength tests and simulate the full non-linear behaviour of individual bricks, joints and reinforcing bars using finite element models applied at the scale of millimetres, we as hydrologists often represent highly heterogeneous catchment systems, which may include complex stream networks, preferential flowpaths, varied vegetation, land use and geology, using highly conceptualized lumped models. Moreover, we often force these models with rainfall data from a single, daily recording gauge well outside of the catchment. Given the simplicity of our models, does it really matter how they are implemented