Uplift histories of landscapes from optimal transport inverse models

地貌是对隆升和侵蚀的响应而形成的。一个推论是，景观的几何形状包含了关于其地质演化的有价值的信息。现在存在着从河流地貌中提取有关构造历史(例如，抬升速率)的信息的各种逆方法。这些模型中的许多都专注于对选定的纵向河流剖面的几何形状进行反演。例如，阻尼线性最小二乘技术被用来寻找平稳变化的(在空间和时间上)抬升历史，这些历史产生的理论河流剖面与观测剖面具有较低的残余失配。这种方法的一个好处是，它们的计算成本相当低，这样就可以计算出整个大陆的有意义的隆升历史。然而，这种方法做了简化的假设(例如固定的排水平面图)，这可能会限制计算的上升率历史的保真度。目前已经存在有效的景观演化正演模型，可以预测河流和河流间的景观几何形状。例如，这样的模型可以包括排水流度、可变底物强度、降雨量等。我们试图使用这样的模型来反演整个地貌的抬升速率历史。一个挑战是，通常基于L-2范数的方法来评估观测(例如实际景观的高程)与理论之间的不匹配可能是不合适的，因为观测和计算的景观不太可能是平滑变化的函数(即我们寻求最小化的目标函数预计会有许多局部极小值)。取而代之的是，我们将利用沃瑟斯坦统计和最优运输技术来评估不匹配。我们计划将这种评估失配的方法与计算效率高的景观演化模型结合起来，以反演大陆尺度的景观演化历史。

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.