Tectonic uplift is an important control on both the morphology of the uplifted landscape and in the sediments that are shed from it. Qualitative interpretations of this relationship between uplift, erosion, and sediment yield are central to much of geological basin analysis, particularly in regards to the reconstruction of tectonic history from basin sediments. Quantitative interpretions of basin-fill sedimentary packages, however, requires a mechanical understanding of the relationship between uplift rate, sediment yield, and drainage basin sculpture. Here we analyze that relationship using a physically-based model of coupled hillslope and channel evolution. In particular, we seek to address the following questions:

(1) What do predicted sediment-yield curves look like (e.g., what is the magnitude and timescale of response to a given perturbation?), and how do they vary as a function of process?

(2) What is the predicted relationship between relief, uplift, and denudation rates, how does it vary with time, and how does this relationship compare with sediment yield data?

(3) How do morphometric properties such as drainage density vary with uplift rate, and how are these related to the sediment yield response?

The model is based on the evolution equation

dz/dt = U- F[ Q(x,y), S(x,y) ] + H[S(x,y)]

where z is elevation, t time, U uplift rate, Q water discharge, S surface slope. Here, F[] is a fluvial erosion function that takes the form kQ^mSⁿ (representing detachment-limited bedrock channels) or dQ^m'S^n'/dx (representing transport-limited alluvial channels). Several different processes represented by the hillslope sediment production and transport term H[] are considered, including soil production through weathering, and sediment transport via overland flow and sheetwash erosion, saturation-excess runoff production, diffusive creep, dry landsliding, and pore-pressure driven shallow landsliding. An important aspect of the model is its ability to track temporal and spatial variations in soil thickness, and to differentiate between erosion of soil and bedrock, which proceed at different rates and by different mechanisms.

Dimensional analysis and numerical simulations indicate that at steady state, where a dynamic balance between uplift and erosion exists, relief within the fluvial portion of the catchment should scale with uplift rate as R~U^1/n, where n reflects the physics of channel erosion. If uplift and denudation rates are approximately equal, this result also implies that denudation rate scales with relief as D~Rⁿ. This result applies to transport-limited as well as detachment-limited fluvial systems, but only in the ideal steady-state condition, Numerical simulations afford the opportunity to examine transient reponses to system perturbations. Here we describe responses to a single step function increase in uplift rate (U) only. In addition, we consider on single catchments with fixed size and shape, intentionally avoiding the complications associated with lithologic variations, temporary tectonic ponding of sediment, and stream capture. Simulations run under a variety of conditions allow examination of how sediment yield responses differ in different hillslope process regimes (e.g., saturation-excess runoff vs. landsliding).

Some preliminary findings can be outlined. In simple detachment-limited or transport-limited model runs, sediment response curves are monotonic, increasing smoothly to match the newly imposed uplift rate. Response timescales are governed by the operative hillslope transport processes. For instance, more rapid response occurs when hillslopes are dominated by mass movement than when they are dominated by diffusive soil creep. However, comparisons with runs involving more complete process descriptions (e.g., tracking soil thickness) emphasize the limitations of the simplified models. Explicitly tracking soil thickness enables us to capture some of the complex dynamics of channel-hillslope interactions that importantly influence runoff rates, drainage density, and rates of sediment delivery to channels. Because sediment stored in soils on hillslopes can be rapidly excavated as channels extend upslope in response to, say, a sudden change in baselevel, channel-hillslope interactions can dictate the form of sediment yield response curves, which may deviate significantly from the monotonic increase predicted by simpler models.

AAPG Search and Discovery Article #90937©1998 AAPG Annual Convention and Exhibition, Salt Lake City, Utah