Drainage Basin Geomorphology. Nick Odoni s Slope Profile Model

Transcription

1 Drainage Basin Geomorphology Nick Odoni s Slope Profile Model

2 Odoni s Slope Profile Model This model is based on solving the mass balance (sediment budget) equation for a hillslope profile This is achieved by discretising the slope into a series (120) of equal length (1 m) long cells (see image on next slide) The differences in sediment flux between each cell then control the rate at which the slope profile is eroded

3 Discretised Slope Profile New Initial Bedrock x = horizontal length of section z = change in elevation S IN S OUT S IN S = (S IN S OUT ) t S OUT

4 Odoni s slope profile model The mass balance equation is solved for each cell using a spreadsheet: z y z t + Q x = U Department of Geography, University of Manchester

5 Modelling Hillslope Form and Process To solve the model, in principle we needs three things: Information on the values of Q and U Sediment transport flux, Q, is estimated using process models Uplift rate, U (this is specified by the user) Initial conditions An initial slope profile at time t = 0. This is fixed by the model. It is assumed that the initial slope is an incised plateau Boundary conditions The value of Q at the top (drainage divide) and bottom (stream) of the slope We assume (a) zero flux at the divide and (b) downcutting matched by uplift at the stream boundary. This represents an assumption of an equilibrium slope

6 Process Models Odoni s model is an idealised version of reality. It models only two hillslope processes: Creep and wash. Sediment flux is therefore modelled as: Q = Q m + Q s Q m = diffusive sediment transport processes (e.g. rainsplash, creep) Q s = wash dominated processes (e.g. sheetwash, rillwash, etc)

7 Simulating Creep Odoni s model uses the following model of soil creep: Q m = K m S K m = a process constant that controls the rate of creep and accounts for factors such as climate, soil type, vegetation S = the slope gradient

8 Simulating Wash Odoni s model uses a simple sediment transport function (based on stream power) to simulate watermediated sediment transport: Q s = K s (qs Φ) K s = a process constant that controls the rate of watermediated sediment transport, accounting for climate, soil texture, vegetation, etc. q = amount of runoff on the hillslope S = the hillslope gradient Φ = the critical stream power needed to detach sediment from the slope and initiate transport. This measures the erodibility of the sediment on the hillslope Note that this model employs a threshold and also requires an estimate of the runoff volume (q).

9 Simulating Runoff Odoni s model simulates the runoff volume (q) using: q = Px α P = Precipitation intensity x = Distance from the drainage divide α = an exponent controlling the rate at which runoff increases or decreases downslope

10 Summary of Model Assumptions Equilibrium slope Creep and wash processes only Creep and wash processes are modelled in a simplified manner

11 Summary of Model Parameters Hillslope profiles vary according to the parameter values selected: U is the uplift rate and is adjusted to reflect the tectonic context of the simulated environment P is the precipitation intensity and is adjusted to reflect the climatic context of the simulated environment Φ is the soil erodibility and is adjusted to reflect the resistance to erosion of the landscape K m, K s and α are rate constants. Clever user s adjust their values to control the relative dominance of creep, wash and runoff generation processes, respectively. This provides a means to simulate the effects of variations in soil type, infiltration rates, topographic curvature and vegetation cover. For examples, see next slide

12 Selecting Parameter Values: Examples α > 1 has the effect of accelerating the concentration of runoff downslope e.g. downslope areas are less permeable (removal of vegetation, change of soil type, change of land use, etc) e.g. planform curvature of landscape surrounding the slope is concave (dissected topography) α < 1 has the effect of reducing the concentration of runoff downslope e.g. downslope areas have higher infiltration rates due to presence of vegetation e.g. planform curvature of landscape surrounding the slope is convex (domed topography)