What does a mean mean? The temporal evolution of detrital cosmogenic denudation rates in a transient landscape

In equilibrium landscapes, Be-10 concentrations within detrital quartz grains are expected to quantitatively reflect basin-wide denudation rates. In transient landscapes, though detrital quartz is derived from both the incising, adjusting lowland and the unadjusted, relict upland, the integrated Be-10 concentrations still provide a denudation rate averaged across the two domains. Because field samples can provide only a snapshot of the current upstream-averaged erosion rate, we employ a numerical landscape evolution model to explore how Be-10-derived denudation rates vary over time and space during transient adjustment. Model results suggest that the longitudinal pattern of mean denudation rates is generated by the river's progressive dilution of low-volume, high-concentration detritus from relict uplands by the integration of high-volume, low-concentration detritus from adjusting lowlands. The proportion of these materials in any detrital sample depends on what fraction of the upstream area remains unadjusted. Because the boundary of the adjusting part of the landscape changes over time, the longitudinal trend in cosmogenic nuclide-derived erosion rates changes over time. These insights are then used to guide our interpretation of geomorphic and longitudinal cosmogenic nuclide data from the South Fork Eel River (SFER) in the California Coast Range (United States). The northward-propagating crustal thickening and rock uplift associated with the passage of the Mendocino triple junction generates a mobile wave of uplift that progressively sweeps longitudinally down the SFER. The consequences of this forcing can be both replicated in the model environment and observed in the field. The SFER contains transient landforms including knickpoints and river terraces along mainstem and tributary channels that define a clear boundary between an incised, adjusting lowland and an unadjusted, relict upland. We report nine nested, basin-wide denudation rates in the mainstem of the SFER using terrestrial cosmogenic Be-10 in river-borne sediment. We find that denudation rates increase in the downstream direction from similar to 0.2 mm/yr in the upper catchment to similar to 0.5 mm/yr at the outlet. Using comparisons to the modeled landscape, we show that this pattern of denudation rates, paired with the distribution of relict topography throughout the watershed, reflect the immaturity of the landscape's transient adjustment. Later in this modeled transient, the predicted erosion rates decrease downstream before they become uniform. This interpretation of our data has potentially far-reaching implications for quantifying the uplift history and response time of transient landscapes using cosmogenic nuclides.