Linear Inversion of Fluvial Long Profiles to Infer Tectonic Uplift Histories

Liran Goren, Matthew Fox, Sean D. Willett

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

4 Scopus citations


The interplay between tectonic uplift and fluvial incision shapes the long profile of rivers. Incision closely depends on uplift because large tectonic gradients create steep fluvial slopes that promote rapid incision, pushing slope segments upstream the river profile. When the tectonic activity varies in space and time, fluvial incision follows up, and the long profile of rivers change accordingly. This means that different sections of the river long profile hold information about tectonic uplift rates at different locations and at different times in the geologic history. To retrieve this information, we need a theory, a model that explains the evolution of the river long profile as a function of both tectonic processes and the action of fluvial incision. Here, we review and expand upon a class of linear inverse models that infer the history of the tectonic uplift rates based on the topography of river long profiles. The inverse models developed here rely on closed-form analytic solutions to the linear stream power incision model. The analytic solutions, by themselves, hold valuable insights regarding the dynamics of fluvial topography and the propagation of tectonic and environmental signals in the fluvial system. The inverse models are extremely efficient in processing of large data, and they combine redundant information from the branching network of channels and tributaries. We present several inverse schemes that differ in their assumptions regarding the spatial and temporal uniformity of the climatic and tectonic conditions, and we review the restrictions that the inverse approach places on the data.

Original languageEnglish
Title of host publicationTreatise on Geomorphology
Number of pages24
ISBN (Electronic)9780128182352
ISBN (Print)9780128182345
StatePublished - 1 Jan 2022


  • Erodibility
  • Erosion rate
  • Fluvial incision
  • Fluvial inversion
  • Incision rate
  • Linear inversion
  • Paleo topography
  • River long profile
  • Tectonic geomorphology
  • Tectonic history
  • Tectonic uplift rate

ASJC Scopus subject areas

  • General Environmental Science


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