Handling Uncertainties in Mantle-Driven Late Cenozoic Surface Uplift of NW Iberia Using Bayesian Joint Inversion of River Profiles and 10Be Cosmogenic Nuclide Concentrations

Joint inversion within a Bayesian framework provides a robust means to estimate uncertainties by integrating the inherent variability of multiple data sets used in the inversion process. In this study, we reconstruct the surface uplift history of mantle origin in NW Iberia and quantify its associated uncertainties. Using a novel reversible-jump Markov chain Monte Carlo (RJ-MCMC) Bayesian algorithm, we perform a joint inversion of topographic data and river-sand 10Be concentrations in quartz to decode the uplift history. This probabilistic approach yields an ensemble of solutions that explore diverse combinations of model parameters, enabling detailed uncertainty quantification in the timing and magnitude of uplift rate changes.

Our forward model employs non-linear analytical solutions of the stream power incision model, which defines incision I = KA^mSⁿ as a function of S, the local channel gradient; A, the upstream drainage area; and K, the erodibility parameter. The model is coupled with the CAIRN method (Mudd et al., 2016, Earth Surface Dynamics, 4, 655-674) to invert Be-10 concentrations at the catchment scale to calibrate the K and n parameters with erosion rates.

We apply this methodology to the Atlantic rivers draining NW, where deep canyons dissect low-relief erosional surfaces formed over the last 100 million years, and apply the calibration to other settings in Central Iberia. Our results suggest that the transient topography reflects a regional late Cenozoic uplift of several hundred meters, likely driven by mantle-related, continent-scale processes. This study underscores the utility of probabilistic joint inversion in unraveling complex geodynamic histories and their uncertainties.