Uplift histories of landscapes from optimal transport inverse models

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Landscapes form in response to uplift and erosion. A corollary is that the geometries of landscapes contain valuable information about their geological evolution. Various inverse methodologies now exist to extract information about tectonic histories (e.g. uplift rates) from fluvial landscapes. Many of these models have focussed on inverting the geometries of select longitudinal river profiles. For example, damped linear least squares techniques have been used to seek smoothly varying (in space and time) uplift histories which generate theoretical river profiles that have low residual misfits to observed profiles. A benefit to such approaches is that they have reasonably low computational cost such that meaningful uplift histories of entire continents can be calculated. However, such approaches make simplifying assumptions (e.g fixed drainage planforms) that may limit the fidelity of calculated uplift rate histories. Efficient forward models of landscape evolution now exist that can predict fluvial and interfluvial landscape geometries. Such models can incorporate, for example, drainage mobility, variable substrate strength, precipitation, etc. We seek to use such models to invert entire landscapes for uplift rate histories. A challenge is that the usual L-2 norm based approaches for assessing misfit between observations (e.g. the elevation of actual landscapes) and theory are probably not appropriate since observed and calculated landscapes are not likely to be smoothly varying functions (i.e. the objective function we seek to minimise is expected to have many local minima). Instead we will make use of Wasserstein statistics and optimal transport techniques to assess misfit. We plan to combine this approach to assessing misfit with computational efficient landscape evolution models to invert for continental-scale landscape evolution histories.