[1] We describe and apply a method for estimating uplift rate histories from longitudinal river profiles. Our strategy is divided into three parts. First, we develop a forward model, which calculates river profiles from uplift rate histories. Height variation along a river profile is controlled by uplift rate and moderated by the erosional process. We assume that the erosional process can be represented by a combination of advection and diffusion, which are parameterized using four erosional constants. Second, we have posed and solved the geologically more interesting inverse problem: which uplift rate history minimizes the misfit between calculated and observed river profiles? The inverse algorithm has been tested on synthetic river profiles, which demonstrates that uplift rate histories can be reliably retrieved. Our tests show that the erosional process is dominated by advection (i.e., knickpoint retreat) and that changes in lithology and discharge play a secondary role in determining the transient form of a river profile. Finally, we have inverted river profiles from a series of African topographic swells, namely the Bié, South African, Namibian, Hoggar, and Tibesti domes. Fits between calculated and observed river profiles are excellent. Calculated uplift rate histories suggest that these domes grew rapidly during the last 30-40 million years. Uplift rate histories vary significantly from dome to dome but cumulative uplift histories agree closely with independent geologic estimates.
[1] Longitudinal river profiles, where elevation of a river bed is plotted as a function of distance along the river bed, contain information about uplift rate. When a region adjacent to a reference level (e.g., sea level) is uplifted, a rapid change in gradient occurs near the river mouth. The erosional process causes this change in gradient to migrate upstream. Thus a river profile is effectively a 'tape recording' of the uplift rate history, provided that the erosional process can be adequately parameterized. Here, we use a non-linear equation to relate the shape of a river profile, z(x), to uplift rate history, U(t). If erosion is assumed to be dominated by knickpoint retreat, an inverse model can be formulated and used to calculate uplift rate histories. Our model builds upon standard stream profile analysis, which focuses on the relationship between profile slope and drainage area. We have applied this analytical approach to river profiles from the Bié Dome, Angola. Calculated uplift rate histories agree with independent geologic estimates.
We describe and apply a linear inverse model which calculates spatial and temporal patterns of uplift rate by minimizing the misfit between inventories of observed and predicted longitudinal river profiles. Our approach builds upon a more general, nonlinear, optimization model, which suggests that shapes of river profiles are dominantly controlled by upstream advection of kinematic waves of incision produced by spatial and temporal changes in regional uplift rate. Here we use the method of characteristics to solve a version of this problem. A damped, nonnegative, least squares approach is developed that permits river profiles to be inverted as a function of uplift rate. An important benefit of a linearized treatment is low computational cost. We have tested our algorithm by inverting 957 river profiles from both Africa and Australia. For each continent, the drainage network was constructed from a digital elevation model. The fidelity of river profiles extracted from this network was carefully checked using satellite imagery. River profiles were inverted many times to systematically investigate the trade-off between model misfit and smoothness. Spatial and temporal patterns of both uplift rate and cumulative uplift were calibrated using independent geologic and geophysical observations. Uplift patterns suggest that the topography of Africa and Australia grew in Cenozoic times. Inverse modeling of large inventories of river profiles demonstrates that drainage networks contain coherent signals that record the regional growth of elevation.
Key Points:• We invert large sets of longitudinal river profiles. Fits to data are excellent • Our history of uplift is consistent with independent geological calibration • We have reconstructed the evolution of dynamic topography in Africa since 50 Ma Abstract It is generally accepted that Cenozoic epeirogeny of the African continent is moderated by convective circulation of the mantle. Nevertheless, the spatial and temporal evolution of Africa's "basin-and-swell" physiography is not well known. Here we show how continental drainage networks can be used to place broad constraints on the pattern of uplift through space and time. First, we assemble an inventory of 710 longitudinal river profiles that includes major tributaries of the 10 largest catchments. River profiles have been jointly inverted to determine the pattern of uplift rate as a function of space and time.Our inverse model assumes that shapes of river profiles are controlled by uplift rate history and modulated by erosional processes, which can be calibrated using independent geologic evidence (e.g., marine terraces, volcanism and thermochronologic data). Our results suggest that modern African topography started to develop ∼30 Myr ago when volcanic swells appeared in North and East Africa. During the last 15-20 Myr, subequatorial Africa was rapidly elevated, culminating in the appearance of three large swells that straddle southern and western coasts. Our results enable patterns of sedimentary flux at major deltas to be predicted and tested. We suggest that the evolution of drainage networks is dominated by rapid upstream advection of signals produced by a changing pattern of regional uplift. An important corollary is that, with careful independent calibration, these networks might act as useful tape recorders of otherwise inaccessible mantle processes. Finally, we note that there are substantial discrepancies between our results and published dynamic topographic predictions.
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