International audienceThe terrigeneous sediment budget of passive margin basins records variations in continental relief triggered by either deformation or climate. Consequently, it becomes a major challenge to determine sediment accumulation histories in a large number of basins found in various geodynamic contexts. In this study, we developed a GIS-based method to determine the sediment budget at the scale of a whole basin (from the upstream continental onlap to the most distal deepest marine deposits) and the associated uncertainties. The volume of sediments preserved in the basin for each time interval was estimated by interpolation between cross-sections and then corrected from in situ production and porosity to obtain terrigeneous solid volumes. This approach was validated by applying it to Namibia-South African passive margin basins for which independent data are available. We determined by a statistical approach the variances associated with each parameter of the method: the geometrical extrapolation of the section (8-43%), the uncertainties on seismic velocities for the depth conversion (2-10%), on the absolute ages of stratigraphic horizons (0.2-12%), on the carbonate content (0.2-46%) and on remaining porosities estimation (3-5%). Our estimates of the accumulated volumes were validated by comparison with previous estimates at a lower temporal resolution in the same area. We discussed variations in accumulation rates observed in terms of relief variations triggered by climate and/or deformation. The high accumulation rates determined for the Lower Cretaceous, progressively decreasing to a minimum in the Mid-Cretaceous, are consistent with the progressive relaxation of a rift-related relief. The following increase to an Upper Cretaceous maximum is consistent with a major relief reorganization driven either by an uplift and/or a change to more humid climate conditions. The lower accumulation rate in the Cenozoic suggests a relief reorganization of lesser amplitude over that period

The stream power law model has been widely used to represent erosion by rivers but does not take into account the role played by sediment in modulating erosion and deposition rates. Davy and Lague (2009, https://doi.org/10.1029/2008JF001146) provide an approach to address this issue, but it is computationally demanding because the local balance between erosion and deposition depends on sediment flux resulting from net upstream erosion. Here, we propose an efficient (i.e., O(N) and implicit) method to solve their equation. This means that, unlike other methods used to study the complete dynamics of fluvial systems (e.g., including the transition from detachment‐limited to transport‐limited behavior), our method is unconditionally stable even when large time steps are used. We demonstrate its applicability by performing a range of simulations based on a simple setup composed of an uplifting region adjacent to a stable foreland basin. As uplift and erosion progress, the mean elevations of the uplifting relief and the foreland increase, together with the average slope in the foreland. Sediments aggrade in the foreland and prograde to reach the base level where sediments are allowed to leave the system. We show how the topography of the uplifting relief and the stratigraphy of the foreland basin are controlled by the efficiency of river erosion and the efficiency of sediment transport by rivers. We observe the formation of a steady‐state geometry in the uplifting region, and a dynamic steady state (i.e., autocyclic aggradation and incision) in the foreland, with aggradation and incision thicknesses up to tens of meters.