The Raster-Accumulated Rational Method: A Theory for GIS-Based Runoff-Potential Screening

The classical Rational Method estimates peak runoff with a single runoff coefficient, rainfall intensity, and basin area, following the tradition of Kuichling (1889) and later applied-hydrology summaries (Chow et al., 1988; Cleveland et al., 2011). This theory preprint defines a raster-accumulated extension in which rainfall intensity is represented by an IDW rainfall-intensity raster, runoff response is represented by a cell-wise runoff-coefficient raster, and contributing area is represented by pixel area multiplied by DEM flow accumulation. The resulting quantity is a distributed runoff-potential screening metric, not a calibrated flood-routing model. The essential difference is therefore simple: the classical form uses Q = C · I · A_basin, whereas the proposed GIS form uses Q_j = C_j · I_IDW,j · pixelSize · flowAccumulation_j, with the standard unit factor applied when intensity is in mm h^-1 and area is in m^2. A minimal worked example is included to make the theoretical formulation testable without turning this note into a computation report.