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Accurate river bathymetry is required for applications including hydrodynamic flow modelling and understanding morphological processes. Bathymetric measurements are typically a set of depths at discrete points that must be reconstructed into a continuous surface. A number of algorithms exist for this reconstruction, including spline-based techniques and kriging methods. A novel and efficient method is introduced to produce a co-ordinate system fitted to the river path suitable for bathymetric reconstructions. The method is based on numerical conformal mapping and can handle topological features such as islands and branches in the river. Bathymetric surfaces generated using interpolation over a conformal map are compared to spline-based and kriging methods on a section of the Balonne River, Australia. The results show that the conformal mapping algorithm produces reconstructions comparable in quality to existing methods, preserves flow-wise features and is relatively insensitive to the number of sample points, enabling faster data collection in the field. • Introduction of a new method for rapidly reconstructing river bathymetry from a set of point depth measurements. • Unlike some existing techniques, the method can handle complex river morphologies such as islands and branches. • The method only requires a set of depth points and a mask of the land and water areas, making it suitable for automation. [ABSTRACT FROM AUTHOR]