Preliminary studies of the application of TOPMODEL to the 36-ha Ringelbach catchment suggested that the original form of exponential transmissivity function leading to the ln (a/tan/β) topographic index and first-order hyperbolic base flow recession curve is not appropriate to this catchment. Two alternative forms of topographic index and soil-topographic index are developed based on parabolic and linear transmissivity functions, leading to the more frequently observed second-order hyperbolic and exponential recession curves, respectively. It is shown how these can be used in the same way as the original to relate catchment average water table depths to local water table depths so that patterns of saturation can be evaluated. Two companion [Ambroise et al., this issue; Freer et al., this issue] papers show how the new parabolic index is used in the prediction of Ringelbach discharges, and how the limitations of the model are reflected in the estimated predictive uncertainties using the Generalised Likelihood Uncertainty Estimation (GLUE) approach.