by Xing Mei, Philippe Decaudin, Bao-Gang Hu 2007 https://inria.hal.science/inria-00402079/document
Introduces 'virtual pipe' method.
Does sediment transport with a semi-Lagrangian advection method.
A fundamental problem with the semi-Lagrangian advection method is that it does not conserve mass for fields with divergence.
How this manifests is loss of water and soil/sediment over the course of the simulation.
by Balázs Jákó 2011 http://www.cescg.org/CESCG-2011/papers/TUBudapest-Jako-Balazs.pdf
Similar to 'Fast Hydraulic Erosion Simulation and Visualization on GPU' but introduces max talus angle and 'thermal erosion': that is, soil is transported downhill if the hill angle is too large. This is essential for realistic terrain features.
Ondrej Štava, Bedrich Beneš, Matthew Brisbin, Jaroslav Krivánek 2008 https://cgg.mff.cuni.cz/~jaroslav/papers/2008-sca-erosim/2008-sca-erosiom-fin.pdf
Introduces a technique for multiple layers of soil.
https://en.wikipedia.org/wiki/Sediment_transport
There are a bunch of commerical software packages such as World Machine, Gaia and World Creator.
https://github.com/weigert/SoilMachine
Advanced technique with multiple layers of differing soils, but runs on CPU, so may be relatively slow.
https://github.com/dandrino/terrain-erosion-3-ways
General overview of practical techniques including machine learning.
https://github.com/LanLou123/Webgl-Erosion/tree/master
Nice looking and interactive WebGL code.
https://reef3d.wordpress.com/sflow/
Looks like actually rigorous and accurate academic/industrial code.
By Mykhailo Moroz