Seeing Through Geomorphic Complexity to Recover Tectonics From Topography: Inverting Landscapes for Uplift Histories Using the Wasserstein Distance

Abstract An important problem in the Earth sciences is extracting information about tectonic and other processes from topography. A general challenge is that geomorphic activity that we typically have little information about during the lifetime of a landscape can introduce geomorphic “noise”. Such noise, producing changes in elevation at scales typically m, could be introduced by variations in lithology, biology, climate, and sedimentology, for instance. It can dramatically impact the way in which landscapes evolve and their form, including shapes and positions of drainage networks. We seek to establish how information about uplift rate histories can be extracted from entire landscapes despite the presence of noise. The sensitivity of single landscape simulations to noise suggests that statistical and inverse modeling approaches utilizing model ensembles may be required. We establish the use of Wasserstein distances in an inverse modeling framework to recover uplift rate histories. We test optimization techniques that automate the search for optimal models (i.e., uplift rate histories) including direction‐based and ameba‐simplex algorithms, confirming that the Neighborhood algorithm is well suited to the task. This approach works even when noise demonstrably plays an important role in determining landscape form but is poorly constrained. It is developed and tested using synthetic landscapes generated with the stream power erosional model and increasingly complex uplift and noise scenarios. The results indicate that it is possible to recover the history of uplift from natural landscapes in which the origin of the specific arrangements of channels, valleys, interfluves, etc. are poorly understood.