Conditioning channel switching for a 3-D fluvio-deltaic process model

Transcription

1 Conditioning channel switching for a 3-D fluvio-deltaic process model Irina Overeem & Gert Jan Weltje Department of Applied Earth Sciences, Delft University of Technology PO Box 5028, NL-2600 GA Delft, The Netherlands i.overeem@ta.tudelft.nl INTRODUCTION One of the problems in modelling stratigraphy and long-term morphology of fluvio-deltaic systems is defining the location of avulsions and bifurcations. Avulsion is a sudden abandonment of the channel belt; it induces switches of the entire main channel (Allen, 1965). The rapidity with which channel switches, crevasses and bifurcations occur varies from instantaneous, relevant for civil engineers and river management (Ning, 1990) to gradual (Smith et al., 1998) and millennia timescale (Schumm et al., 1996), more of interest to sedimentologists and petroleum industry. As such, it is the dominant meso-scale process that determines the channel location in time and the architecture of fluvial deposits (Miall, 1996; Jones & Schumm, 1999; Paola, 2000). Further downstream, channel bifurcations are equally important in defining the architecture of the delta plain (e.g. Fisk, 1952; Coleman & Roberts, 1989; Bhattacharaya &Walker, 1992). Avulsions are triggered by stochastic events, such as sudden floods and sediment load peaks or even more explicit log and ice jams, that force the river over a stability threshold (Jones & Schumm, 1999). Crevasse channels form during every major river flood and remain points of weakness in the levee. Consequently it is logical that thresholds are preferentially overcome at sites of crevasse channels (Stouthamer, in press). More deterministic factors are generally believed to affect the probability of an avulsion taking place: 1. Water and sediment load in the channel at the moment a crevasse is formed determines the probability that the crevasse channel either heals or becomes the new channel (Slingerland & Smith, 1998). 2. Local super elevation of the channel belt above the floodplain, caused by differential sedimentation determines the advantage of the cross-channel slope over the longitudinal slope, which favours a new channel course (Bridge & Leeder, 1979; Mackey & Bridge, 1995, Bryant et al., 1995; Heller & Paola, 1996). 3. Climate, tectonics and sea level form the derived external controls influencing both the crosschannel slope and the longitudinal slope (Jones & Schumm, 1999; Stouthamer & Berendsen, 2000). Jones & Schumm (1999) state that the lack of an extensive database still does not allow ranking of the relative importance of the various causes. Recently published field studies have made a step forward in ranking different causes (Stouthamer & Berendsen, 2000; Mohrig et al., 2000). We will use numerical modelling to investigate the effects of different postulated mechanisms, although necessarily on a more conceptual level. Previous numerical models dealing with avulsion focused either on cross-sectional geometry of a channel belt interbedded in floodplain deposits (Bridge & Leeder, 1979; Mackey & Bridge, 1995), or on the shortterm dynamics at the moment of crevasse formation (Slingerland & Smith, 1998). Here, we present a model, operating on a scale intermediate between these two approaches. It uses process-response metaphysics to describe time-averaged sedimentation and erosion fluxes. The model is designed to operate on a geological timescale ( years). The approach is event-based, implying that peak floods and major storms are the relevant transport mechanisms. We built it as a pseudo 3-D model, consisting of a 2-D longitudinal profile from which a certain number of 'distributary' grid cells divert discharge and sediment out of the system (Fig. 1). The location and number of distributary cells is controlled by local channel slope and accumulation rate. The probability of occurrence of a bifurcation is proportional to accumulation rate and inversely proportional to slope. The effects of sediment distribution over distributary channels can be investigated. A vertical concentration profile in the river is mimicked, as the fluxes of fine and coarse sediment can be manipulated independently. Because coarse material is transported as bedload at the channel bottom, rather 'clean water' is tapped into the diverging channel. This may choke the main channel that suddenly deals with less discharge to transport a relatively heavy sediment load. This way, the concentration profile is another firstorder control on the probability that a crevasse actually evolves into an avulsion. As such it forms an important threshold mechanism for either channel switching or bifurcations (Slingerland & Smith, 1998). 1

2 Figure 1 Satellite image of the meandering Paraná River in Argentina illustrates the pseudo 3D modelling concept. A main channel belt is modelled as a longitudinal profile; crevasses and avulsions occur in the fluvial plain, bifurcations in the deltaic plain. Offshore, the longitudinal profile is located along the delta plume MODEL THEORY Basic model equations The essence of the approach is the integration of a mass balance that transforms spatial differences in sediment transport to rates of erosion or deposition over time. The sediment transport rates respond dynamically to changes in topography and depositional environment as a continuity equation (modified after Kirkby 1992; Veldkamp & van Dijke 1998; 2000; Storms et al., in press). H t F = + T {1} Where: H topographical height [m] t time [yr] F sediment flux [m 2 yr -1 ] T rate of vertical tectonic movement [m yr -1 ] x horizontal distance [m] The sediment flux gradient, which is the spatial derivative of the sediment flux, is described as the difference between of the erosion and sedimentation fluxes (Fig 2). F F = ero F sed {2} 2

3 F ero erosion flux [m 2 yr -1 ] F sed deposition flux [m 2 yr -1 ] The erosion flux depends on the stream power, which is determined by discharge and local slope. This approach is used by Tucker & Slingerland (1994) and Kooi & Beaumont (1996) for the upper reach of river systems, where erosion is the dominant process. F ero = k S m Q ( x) ( t) {3} Q(x) discharge function [m 2 yr -1 ] S slope [m m -1 ] m constant [-] k erosion efficiency [m -1 ] Offshore, Q(x) decreases with increasing water depth, mimicking the effect of decreasing fluvial influence in the marine basin (Wright, 1977). Qx ( ) = Qx ( 1) ( Qx ( 1) dxdisf wd) {4} disf wd decrease rate of erosional capacity water depth The constant m is chosen equal to 1 in the fluvial domain, to obtain a linear slope-dependent relation. In the marine domain, m is set to be equal to 0, making erosion slope independent. In the fluvial and marine domain different values for the erosion constant, k, are used, because the erosion efficiency varies significantly between confined and unconfined flows. Erosion is modelled as a grain-size independent process. The large temporal scale justifies this simplification, because peak floods will then be the significant erosional events, which are capable of eroding all simulated grain-size classes. Sedimentation is defined as a first order kinetic reaction, implying that the amount of sedimentation (F sed ) is proportional to the sediment load of the water (F). This flux of sediment in transit is the sum of the local erosional flux (F ero ) and the incoming sediment load (F in ). The outflux (F out ) is the sediment left in concentration, which travels further downstream (Fig 2). F = F in +F ero = F sed +F out {5} F F sed ( x, t) = h {6} F (x,t) absolute sediment flux [m 2 yr -1 ] h travel distance [m] The inverse of the travel distance, h -1 is considered to be proportional to the probability of deposition along the transport pathway. The travel distance is dependent on grain-size (e.g. settling velocity) and flow medium properties (e.g. flow velocity). The travel distance for the different grain size classes is formulated in such way that the settling rate is initially high and subsequently decreases exponentially with distance from the rivermouth (e.g. Kaufman et al., 1992; Bursik, 1995). 3

4 Figure 2 Sediment fluxes for a single grid cell along the longitudinal profile (x-axis). Offshore the sediment flux is manipulated to reflect the lateral spreading of the fluvial plume. We follow the plume axis. F ( x, t)( n) = F ( x 1, t )( n) F ( x 1, t)( n) 2 D coast π tan ( α ) 180 {7} D coast distance from the coastline [m] Determining the number and position of distributary nodes Crevasses and bifurcations are generally considered to be stochastic processes (Jones & Schumm, 1999). In our model this is reflected by a randomly generated number of distributary nodes. Every timestep, that the discharge exceeds the bankfull discharge, a number of distributary nodes is sampled. Of course this is restricted to a certain maximum, not every gridcell can be a potential crevasse or bifurcation location. The probability of occurrence and location of a crevasse or bifurcation is proportional to local differential accumulation rate, or super elevation, and inversely proportional to slope. To infer a proxy for super elevation we assume that most sediment is stored in the channel belt and thus negligible sedimentation in the overbank areas. Then the proxy for super elevation is calculated by subtracting the initial topographical height from the actual topographic height of the longitudinal profile. The lowest slopes are determined simply from the longitudinal profile in the previous timestep. What happens at the position of a distributary node The discharge, Q, at a distributary node is divided between the main channel and the crevasse channel depending on crevasse lip height (Fig. 3) according to the following formula: Q = h h Q t c ( 1) 1 ( i) ht {8} Q 1 Q i h t h c proportion of Q i remaining in the main channel after bifurcation discharge of the flood entering the specific gridcell at time of bifurcation flood height crevasse lip height The suspended sediment load, qs, is assumed to be uniformly distributed over the vertical channel profile and thus is divided into the bifurcating channel proportional to the amount of water tapped: qs = h h qs t c ( 1) 1 ( i) ht {9} 4

5 Coarse sediment load, qb, is not uniformly distributed over the vertical channel profile. The percentage of the total channel depth that carries predominantly coarse load, the coarse load-depth, h b, has to be set. This can either be derived from concentration profile measurements or just simply be assumed. If the coarse load depth, h b, is lower than the crevasse lip height, h c, all coarse load continues to follow the main path. qb h h qb = for { h b > h c } {10a} b c ( 1) 1 ( i) hb qb = qb for { h b h c } {10b} ( 1) ( i) Figure 3 Concepts and definitions at the distributary nodes Do distributary nodes remain stable in time? Whether avulsion locations are likely to remain stable in time is still a matter of debate. Logically, if a gradient advantage of the cross-channel slope over the longitudinal slope exists, it is likely that a newly formed crevasse channel will become the new river course. On the other hand the stability of crevasse channels is closely related to the way water and sediment discharges are distributed over the coexisting channels. Slingerland & Smith (1998) present a 1D numerical model that predicts whether a crevasse heals, remains stable or evolves into an avulsion. The stability domain for sandy meandering rivers is depicted in Fig. 4 (after Slingerland & Smith, 1998). Dominant parameter under these conditions is the ratio of crevasse channel slope over main channel slope (Sc/Sm), although the crevasse lipheight over channel depth (hc/ht) is of some influence as well. 5

6 Figure 4 Predicted behaviour of a crevasse channel for a sandy meandering river (from Slingerland & Smith, 1998). Depending on the ratio of crevasse channel slope over main channel slope and the ratio of the crevasse lip height over channel depth a crevasse either heals, remains in equilibrium or evolves into an avulsion. Formulation of a crevasse slope proxy is thus critical for evaluation of the behaviour of the crevasse channel. We estimate crevasse slope as the sum of crevasse lip height and super elevation over the levee width, wherein levee width is set as a function of initial levee height (Fig. 3). MODEL RESULTS Depositional patterns We have formulated a base case to investigate the effects of our approach under controlled conditions (Table 1). The input parameters have been chosen rather simple; linear slope, a sine sea level curve, randomly varying discharge and sediment loads. An apical avulsion is set to occur at 20 km from the apex, at grid cell 80 and a bifurcation closer to the coastline, at grid cell 150. The first 1000 years a sedimentation regime without any divergences exists. During that period the deposition in the fluvial domain is rather constant, at the coastline the coarse load gets deposited rapidly as mouthbars, while delta plume sedimentation decreases gradually basinward (Fig 5A, at t =180). Fig.5 B shows the resulting stratigraphic profile. An evident coarsening occurs as compared to deposits of the first 1000 years of simulation. This can easily be explained as every diverging event drains water and suspended load out of our system boundaries, as such leaving a relatively overcapacity of coarse load. The two distributary cells form distinct boundaries along the longitudinal profile. However, the effects of the diverging events are discernable downstream as well. A Wheeler diagram, displaying the varying net sedimentation along the profile, illustrates that the two distributary nodes are distinguishable over the entire period (Fig 5C). Sedimentation can be seen to increase significantly only at a few occasions in time. Deposition curves have been plotted at these intervals. At t =1340 (Fig 5A) the crevasse lip height was very low for the first distributary node, resulting in draining of 96 % of the discharge and suspended load out of the system boundaries, while still 66 % of the coarse load remained in the channel system. Although the limited remaining Q, qs and qb did not exceed the threshold for further divergence in the next distributary node, still some sedimentation seemed to occur in that zone, probably because the slope gradient was rather low due to previous sedimentation events. At t = 1680 again a large sedimentation event happened. However, in this case the crevasse lip height for the first distributary node is average but the crevasse lip height for the node at 37 km is extremely low, resulting in large sedimentation rates in the deltaic plain. Another example (Fig 6) is shown where the locations of the distributary nodes are preferentially chosen at the lowest slopes along the profile. All other parameters remain equal to the base case, except that the number of bifurcation is chosen randomly (with an arbitrary maximum of 6). In geological terms the focus in this experiment is on bifurcations, as the delta plain is generally the area with the lowest slope. Simulation results show chaotic sedimentation in the delta plain area, with small pockets of distinctive grain-size distributions. 6

7 Table 1 SIMULATION PARAMETERS BASECASE Time scenario total simulation time (years) 2000 time step (years) 2 Grid dimensions length of longitudinal profile (gridcells) 600 gridcell length (m) 250 Sea level scenario 1 cycle sea level at t = 0 30 sea level amplitude ( m) 4 Initial profile linear elevation at grid cell 0 (m) 40 slope gradient in fluvial domain (m/km) 0.20 slope gradient further offshore (m/km) 0.28 (from 10 km offshore onwards) Discharge and sediment load Q at t=0 (m 3 ) 1000 q at t=0 (m 3 ) 7 Q variation range in time q variation range in time Grain-size characteristics number of grain-size classes 5 percentage distribution grain-sizes (micron) Sediment transport coefficients travel distances fluvial domain (m) travel distances marine domain (m) erosion capacity fluvial domain erosion capacity marine domain Avulsion specific parameters number of bifurcations 2 bifurcation locations cell 80, cell 150 crevasse lip height (m) bedload height factor (% of total channel depth) random uniform 10 nett sedimentation t = t = t = distance in gridcells Figure 5A Deposition curves along the profile for specific time steps. Three situations are depicted; at t =180 no crevasses or bifurcations were simulated. At t=1340 the crevasse lip height was extremely low in the first distributary node, while at t = 1680 the crevasse lip height was extremely low in the second distributary node. 7

8 Figure 5B Stratigraphic profile showing the general coarsening along the longitudinal profile under controlled conditions. The two fixed distributary nodes at 20 and 37 km can easily be distinguished Net sedimentation Time Figure 5C Wheeler diagram shows the variability of the crevasse or bifurcation deposition in time. The distributary nodes influence deposition to a varying degree. This is partly caused by randomness in the crevasse lip height. But on the other hand Q and q vary in time as well, so that the threshold for divergence is not exceeded at every timestep Longitudinal distance Figure 6 Stratigraphic profile zoomed in on the deltaic plain. Simulation with distributary nodes located at positions of lowest slopes. 8

9 Channel stability As a first assessment of channel stability we use the stability domain of Slingerland & Smith (1998). Parameters are chosen as in the base case described above, although in this case we randomly sample number and location of distributary nodes. Basic sensitivity analysis has been done to calibrate the levee width. In the subsequent simulations levee width is set at 75 m at a channel width of 100 m and initial levee height at 2.5 m. We explored the effects of increasing the total sediment load and of increasing the proportion of coarse load (Fig.7). It can be seen that changes in the initial sediment load are far more important in influencing the total number of simulated stable avulsions than changes in the grain-size distribution. Changes in initial sediment load directly influence sedimentation along the profile and thus the super elevation, making that response rather straightforward. However, a change in coarse load does affect the sedimentation rates as well, as can be seen in Fig 7. Due to a relatively high proportion of coarse load the flow is saturated with coarse sediment after a bifurcation and sedimentation rates will increase, which will influence superelevation as well. The fact that total sediment load is more important is also predicted by Fig. 4, in which the relation between Sc/Sm and stability strongly dominates over hc/ht. % change in simulated stable avulsions coarse load total sediment load % change in sediment load Figure 7 Simulated number of avulsions change due to changes in either total sediment load or just changing the relative proportion of coarse load. DISCUSSION Although the model presented here is rather preliminary, the approach seems to incorporate the key controlling factors. It addresses important issues because it is capable of simulating scenarios with dynamic external controlling factors and still includes a metaphysical description of in-channel dynamics. First results show plausible model behaviour, but further work is necessary. The philosophical question what to do in case of a stable avulsion? has not been raised here; strictly speaking the model run would be finished at that moment. The channel belt shifts away out of our model world. A 3D model, AQUATELLUS, is being developed in Delft and we aim to obtain useful relationships that condition channel switching for that model. REFERENCES Allen, J.R.L A review of the origin and characteristics of recent alluvial sediments. Sedimentology 5, Bhattacharaya J.P., Walker, R.G., Deltas In: Walker, R.G. and James, N.P. (eds) 1992 Facies Models; response to sea-level change. Geological Association of Canada. Bridge, J.S., Leeder, M.R., A simulation model of alluvial stratigraphy. Sedimentology, 26, Bryant, M., Falk, P., Paola, C Experimental study of avulsion frequency and rate of deposition. Geology, 23,

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