A bottom-up control on fresh-bedrock topography under landscapes

The depth to unweathered bedrock beneath landscapes influences subsurface runoff paths, erosional processes, moisture availability to biota, and water flux to the atmosphere. Here we propose a quantitative model to predict the vertical extent of weathered rock underlying soil-mantled hillslopes. We hypothesize that once fresh bedrock, saturated with nearly stagnant fluid, is advected into the near surface through uplift and erosion, channel incision produces a lateral head gradient within the fresh bedrock inducing drainage toward the channel. Drainage of the fresh bedrock causes weathering through drying and permits the introduction of atmospheric and biotically controlled acids and oxidants such that the boundary between weathered and unweathered bedrock is set by the uppermost elevation of undrained fresh bedrock, Z_b. The slow drainage of fresh bedrock exerts a “bottom up” control on the advance of the weathering front. The thickness of the weathered zone is calculated as the difference between the predicted topographic surface profile (driven by erosion) and the predicted groundwater profile (driven by drainage of fresh bedrock). For the steady-state, soil-mantled case, a coupled analytical solution arises in which both profiles are driven by channel incision. The model predicts a thickening of the weathered zone upslope and, consequently, a progressive upslope increase in the residence time of bedrock in the weathered zone. Two nondimensional numbers corresponding to the mean hillslope gradient and mean groundwater-table gradient emerge and their ratio defines the proportion of the hillslope relief that is unweathered. Field data from three field sites are consistent with model predictions.Uplift and erosion of bedrock commonly leads to ridge and valley topography variably mantled with weathered bedrock and soil. Quasi-steady-state conditions may develop in which the topography is statistically constant as channels incise, hillslope surfaces erode, and fresh bedrock is uplifted to the surface. As this fresh bedrock rises up, it enters a near-surface zone where weathering irreversibly breaks and alters the rock before it is entrained into the mobile soil mantle and transported to adjacent streams. Variably weathered bedrock occupies the zone between the top of the fresh bedrock and the bottom of the soil. Here we identify Z_b as the elevation of the transition from fresh to weathered bedrock (Fig. 1).Open in a separate windowFig. 1.Conceptual model showing the elevation of fresh bedrock, Z_b, under ridge and valley topography with a thin soil mantle overlying a weathered bedrock zone that extends to Z_b. Channel incision, at the rate C_o, drives hillslope erosion and drainage of fresh bedrock (flow paths illustrated with blue arrows). (Left) The model framework and assumptions. At the ridgetop (x = 0), the surface elevation is Z_s0 and the fresh-bedrock elevation is Z_b0. Groundwater flux, q_w, is horizontal and proportional to the water table gradient, Z_b. Soil transport, q_s, is proportional to the surface slope, Z_s. All soil and water leaves the hillslope at L where the hillslope meets the channel. At steady state, the rate of channel incision (C_o) is equal to the uplift rate such that the ground surface, Z_s and surface of the fresh bedrock, Z_b, are stationary.The transport of sediment and water from hillslopes to stream channels is influenced by the rock property changes that result from weathering. Hence, the depth to and topography of Z_b is an important driver in runoff generation and landscape evolution. Weathering tends to increase bedrock hydraulic conductivity and porosity, allowing infiltrating waters to perch on underlying fresh bedrock and flow laterally to stream channels (Fig. 1). Field studies that have instrumented the weathered rock zone have shown that this perched groundwater path can deliver most of the stream runoff (1–4) and can be the source of sustained summer baseflow (5). The chemical evolution of hillslope runoff may be strongly dictated by the depth to Z_b and flow paths through the weathered zone (6–8). The weathering of bedrock may also increase moisture retention, which can be exploited by vegetation to sustain transpiration (9, 10). Furthermore, water exfiltration from this zone on steep slopes can cause localized elevated pore pressures and landslides (11), and the change in rock mass strength across this boundary due to weathering may localize deep-seated landslides (12, 13).Collectively, these observations suggest that, aside from the ground surface, the topography of Z_b is the most important boundary controlling surface and near-surface processes, and as such, observation and theory are needed to understand what controls its structure across a landscape. Field studies that have directly documented the depth to fresh bedrock underlying ridge and valley topography (e.g., refs. 14, 15) are rare and none have depicted the detailed 3D pattern of Z_b relative to surface topography. Nonetheless, the few studies that have mapped Z_b under hillslopes have found a tendency for the weathered zone to be thickest at the ridge top and progressively thin downslope (14–18) (as illustrated in Fig. 1). Although Pavich (15) and Feininger (18) associate this trend with areas of low relief, studies in steep landscapes in the California and Oregon Coast Ranges (5, 6) have documented a systematic upslope thickening of the weathered zone as well (Fig. S1).It is commonly assumed that the depth of weathered bedrock is controlled by downward propagating (top-down) processes driven by the advance of chemically reactive meteoric water into the underlying fresh bedrock (e.g., ref. 19). The top-down hypothesis leads to a weathered zone thickness that is set by the relative rates of erosion and the downward propagation of the weathering front. Approaches to addressing this hypothesis have included reactive transport modeling (e.g., ref. 20) and extension of the soil production function (21) to the weathered bedrock zone through a negative feedback between weathered zone thickness and erosion rate (e.g., ref. 22). For a convex 2D hillslope with a mobile weathered layer composed of soil and weathered bedrock, Lebedeva and Brantley (20) propose that the downslope steepening of the topographic surface may lead to progressively less water flux normal to the underlying reactive bedrock and, consequently, a weathered zone that thins downslope.An alternative hypothesis for the downslope decrease in depth to Z_b under hillslopes is suggested by field observations of weathering profiles. Some of the earliest quantitative observations of weathering profiles identified the role of groundwater in impeding chemical weathering, and restricting the depth of the weathered zone (e.g., refs. 14, 16, 23, 24), such as occurs in supergene enrichment processes (25). In fresh bedrock of sufficiently low hydraulic conductivity, nearly stagnant or slowly moving water will reach chemical equilibrium and chemical weathering reactions will slow or stop (19, 26). In addition, the chronic saturation of fresh bedrock prevents mechanical breakdown due to swelling and contraction cycles associated with wetting and drying (27). Drainage of this fresh bedrock permits meteoric fluids to enter from above, thus allowing atmospherically and biotically controlled acids and oxidants to enter pore spaces and induce weathering reactions.These observations suggest a “bottom up” control on the elevation of fresh bedrock under hillslopes in which drainage of saturated fresh bedrock is the key process. We propose that: (i) fresh bedrock that is advected into the near-surface environment through uplift and erosion arrives saturated with nearly stagnant pore fluid that is in chemical equilibrium with surrounding mineral surfaces; (ii) in this environment, channel incision creates a lateral head gradient in the fresh bedrock and induces drainage toward the adjacent channel; and (iii) drainage may cause drying and fracturing of the bedrock and permit meteoric water to enter the fresh bedrock, inducing weathering at the rate that the fresh bedrock is drained. For these conditions, we propose that the fresh-bedrock drainage profile defines Z_b. The depth of fresh bedrock along a hillslope will depend on both this groundwater-drainage control and on the erosion shaping the surface topography. Here we predict the thickness of the weathered bedrock zone by coupling a groundwater flow model with a surface erosion model.