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A practical methodology for distributed rainfall-runoff modelling using grid square weather radar data is developed for use in real-time flood forecasting. The model, called the Grid Model, is configured so as to share the same grid as used by the weather radar, thereby exploiting the distributed rainfall estimates to the full. Each grid square in the catchment is conceptualised as a storage which receives water as precipitation and generates water by overflow and drainage. This water is routed across the catchment using isochrone pathways. These are derived from a digital terrain model assuming two fixed velocities of travel for land and river pathways which are regarded as model parameters to be optimised. Translation of water between isochrones is achieved using a discrete kinematic routing procedure, parameterised through a single dimensionless wave speed parameter, which advects the water and incorporates diffusion effects through the discrete space-time formulation. The basic model routes overflow and drainage separately through a parallel system of kinematic routing reaches, characterised by different wave speeds but using the same isochrone-based space discretisation; these represent fast and slow pathways to the basin outlet, respectively. A variant allows the slow pathway to have separate isochrones calculated using Darcy velocities controlled by the hydraulic gradient as estimated by the local gradient of the terrain. Runoff production within a grid square is controlled by its absorption capacity which is parameterised through a simple linkage function to the mean gradient in the square, as calculated from digital terrain data. This allows absorption capacity to be specified differently for every grid square in the catchment through the use of only two regional parameters and a DTM measurement of mean gradient for each square. An extension of this basic idea to consider the distribution of gradient within the square leads analytically to a Pareto distribution of absorption capacity, given a power distribution of gradient within the square. The probability-distributed model theory (Moore, 1985) can then be used directly to obtain the integrated runoff production for the square for routing to the catchment outlet. justification for the simple linkage function is in part sought through consideration of variants on the basic model where (i) runoff production is based on a topographic index control on saturation and (ii) absorption capacity is related to the Integrated Air Capacity of the soil, as obtained from soil survey. An impervious area fraction is also introduced based on the use of Landsat classified urban areas. The Grid Model and its variants are assessed in Part 2 (Bell and Moore, 1998), first as simulation models and then as forecasting models, following the development of updating procedures to accommodate recent observations of flow so as to improve forecast performance in a real-time context.