References

GRLP papers

The model, its correction, and its published extensions and applications. All are open access (CC-BY). Source-grounded notes on each — governing equations, parameters, and how they map to the code — are in docs/literature/README.md in the repository.

  • Wickert, A. D. and Schildgen, T. F. (2019). Long-profile evolution of transport-limited gravel-bed rivers. Earth Surface Dynamics, 7, 17–43. doi:10.5194/esurf-7-17-2019. The foundational paper — defines the model.

  • Wickert, A. D. and Schildgen, T. F. (2020). Corrigendum to “Long-profile evolution of transport-limited gravel-bed rivers.” Earth Surface Dynamics, 7, 17–43. doi:10.5194/esurf-7-17-2019-corrigendum. Removes the valley-width-derivative term; corrected code is GRLP v1.4.1.

  • McNab, F., Schildgen, T. F., Turowski, J. M., and Wickert, A. D. (2023). Diverse responses of alluvial rivers to periodic environmental change. Geophysical Research Letters, 50, e2023GL103075. doi:10.1029/2023GL103075. Gain/lag linearization and equilibration timescale.

  • McNab, F., Schildgen, T. F., Turowski, J. M., and Wickert, A. D. (2025). Influence of network geometry on long-term morphodynamics of alluvial rivers. Earth Surface Dynamics, 13, 1059–1092. doi:10.5194/esurf-13-1059-2025. Extends GRLP to drainage networks.

  • Ruby, A., McNab, F., Schildgen, T. F., Wickert, A. D., and Fernandes, V. M. (2026). How sediment supply, sea-level, and glacial isostatic oscillations drive alluvial river long-profile evolution and terrace formation. AGU Advances, 7, e2025AV002035. doi:10.1029/2025AV002035. Río Santa Cruz application; shelf-coupled base-level forcing.

Selected supporting literature

Cited by the model derivation for its physics and closures.

  • Parker, G. (1978). Self-formed straight rivers with equilibrium banks and mobile bed. Part 2. The gravel river. Journal of Fluid Mechanics, 89, 127–146. Equilibrium-width (near-threshold) channel.

  • Wong, M. and Parker, G. (2006). Reanalysis and correction of bed-load relation of Meyer-Peter and Müller using their own database. Journal of Hydraulic Engineering, 132, 1159–1168. Bed-load transport coefficient.

  • Meyer-Peter, E. and Müller, R. (1948). Formulas for bed-load transport. Proc. 2nd Meeting IAHR, 39–64.

  • Paola, C., Heller, P. L., and Angevine, C. L. (1992). The large-scale dynamics of grain-size variation in alluvial basins, 1: Theory. Basin Research, 4, 73–90. Diffusive basin-filling; equilibration time.

  • Blom, A., Arkesteijn, L., Chavarrías, V., and Viparelli, E. (2017). The equilibrium alluvial river under variable flow and its channel-forming discharge. JGR Earth Surface, 122, 1924–1948.

  • Shreve, R. L. (1966). Statistical law of stream numbers. Journal of Geology, 74, 17–37; and Shreve, R. L. (1974). Variation of mainstream length with basin area in river networks. Water Resources Research, 10, 1167–1177. Random network topology.

  • Hack, J. T. (1957). Studies of longitudinal stream profiles in Virginia and Maryland. USGS Professional Paper 294-B.

  • Kennett, J. P. (1982). Marine Geology. Prentice-Hall. Continental-shelf gradient used for shelf-coupled base level.