GSA Data Repository 2017296 Zeumann and Hampel, 2017, Impact of Cocos Ridge (Central America) subduction on the forearc drainage system: Geology, doi:10.1130/g39251.1. DESCRIPTION OF CASQUS To implement erosion and sediment deposition, the ridge subduction model is coupled via the ABAQUS user sub-routine CASQUS (Kurfeß and Heidbach, 2009; Maniatis et al., 2009; Hampel and Hetzel, 2016) to the landscape evolution model CASCADE (Braun and Sambridge, 1997). The input for the landscape evolution model is the current surface elevation in the ABAQUS model, which changes in the course of ridge subduction. After the amount of erosion or sedimentation at each point has been calculated by CASCADE, the user sub-routine CASQUS transfers the information on the elevation changes due to the surface processes back into the ABAQUS model to shift the surface nodes to their new elevation. Shifting of the surface nodes is performed using an Arbitrary Lagrangian-Eulerian approach and adaptive meshing for the associated elements in order to prevent arbitrary stress changes. Hence, the shift of the surface nodes causes only changes in the volume and thus in the mass of the associated elements. The length of the time steps in the model correspond to 10 kyr. The landscape evolution model implemented by CASQUS includes diffusive hillslope processes and fluvial erosion and deposition (cf. Braun and Sambridge, 1997). The former is implemented by the linear diffusion equation, in which the temporal change in elevation of a point is proportional to the second spatial derivative of topography (Kooi and Beaumont, 1992; Braun and Sambridge, 1997): h t k D 2 h, where h is elevation, t time and k D the diffusion constant. The equation above describes the cumulative effect of different types of surface processes such as slope wash, rain splash and soil creep. As high diffusion constants are known to create unrealistic landscapes for grid sizes of 1 km or more (van der Beek and Bishop, 2003), we use a low diffusion constant (0.05 m 2 /a), which also stabilizes the model by avoiding steep slopes between individual cells (Sacek et al., 2012). The temporal change in elevation at a point on the model surface caused by fluvial erosion, sediment transport and deposition is calculated by the relationship h t 1 l f q f, eqb q f, where q f is the sediment flux of a river, q f,eqb the sediment transport capacity and l f the erosion/deposition length scale. The latter constant describes how easily the river substrate can be eroded or how fast sediments are deposited in a river and thus affects how fast the river locally 1
tends toward equilibrium. To differentiate between bedrock incision and alluvium, CASCADE uses two different erosion length scales, which we assign values of 100 km and 10 km, respectively, following previous studies (Braun and Sambridge, 1997; van der Beek and Braun, 1998; Tomkin and Braun 1999; Kurfeß and Heidbach, 2009). Erosion occurs for q f < q f,eqb and deposition for q f > dh q f,eqb. The sediment transport capacity q f,eqb is calculated by q f, eqb k f q r dl, where k f is a nondimensional empirical transport coefficient, q r is the fluvial discharge, which depends on the catchment area and the precipitation rate p, and dh/dl is the slope in the flow direction of the river. The parameter that ultimately controls fluvial erosion is the fluvial erosion parameter k f p, in which the dimensionless transport coefficient k f (which does not have a direct meaning outside the model context) and the precipitation rate p are lumped together to obtain a parameter with dimension m/a (van der Beek and Braun, 1998). For the initial model surface, an irregular mesh with 5 m vertical noise is used to avoid the directional bias, which arises from the development of the river network along preferred directions (Braun and Sambridge, 1997). Sediments may leave the model via the model boundaries and via the seaward edge of the CASQUS layer (= model coastline) (Fig 2A). REFERENCES CITED Braun, J., and Sambridge, M., 1997, Modelling landscape evolution on geological time scales: a new method based on irregular spatial discretization: Basin Research, v. 9, p. 27-52. Hampel, A., and Hetzel, R., 2016, Role of climate changes for wind gap formation in a young, actively growing mountain range: Terra Nova, v. 28, p. 441-448. Kooi, H., and Beaumont, C., 1994, Escarpment evolution on high-elevation rifted margins: insights derived from a surface processes model that combines diffusion, advection, and reaction: Journal of Geophysical Research, v. 99, p. 12191-12209. Kurfeß, D., and Heidbach, O., 2009, CASQUS: a new simulation tool for coupled 3D Finite Element modeling of tectonic and surface processes based on ABAQUS and CASCADE: Computers and Geosciences, v. 35, p. 1959-1967. Maniatis, G., Kurfeß, D., Hampel, A., and Heidbach, O., 2009, Slip acceleration on normal faults due to erosion and sedimentation - results from a new three-dimensional numerical model coupling tectonics and landscape evolution: Earth and Planetary Science Letters, v. 284, p. 570-582. Sacek, V., Braun, J., and van der Beek, P., 2012, The influence of rifting on escarpment migration 2
on high elevation passive continental margins: J. Geophys Res., v. 117, B04407, doi:10.1029/2011jb008547. Tomkin, J.H., and Braun, J., 1999, Simple models of drainage reorganization on a tectonically active ridge system: New Zealand Journal of Geology and Geophysics, v. 42, 1, p.1-10, doi:10.1080/00288306.1999.9514827. van der Beek, P. and Braun, J., 1998, Numerical modeling of landscape evolution on geological time scales: a parameter analysis and comparison with the south-eastern highlands of Australia: Basin Research, v. 10, p. 49-68. van der Beek, P., and Bishop, P., 2003, Cenozoic river profile development in the Upper Lachlan catchment (SE Australia) as a test of quantitative fluvial incision models: J. Geophys. Res., v. 108, 2309, doi:10.1029/2002jb002125, 2003. 3
Figure DR1. Supplementary results from the model with a fluvial erosion parameter of 0.01 m/a. (A) Model river network in map view (color of rivers denotes their flow direction, which is indicated by the colored arrows in the legend) and longitudinal profiles of selected rivers (green color of longitudinal profiles corresponds to color of respective river in map and the arrow indicating the flow direction) at 3.8 and 5 Myr, respectively. (B) Evolution of the trench-normal horizontal strain x during the first 2 Myr of model time. Solid white line marks coastline; dashed white line marks drainage divide (cf. Fig. 3). Note the zone of shortening landward of the coastline, which is equivalent to Fila Costeña thrust belt (cf. Zeumann and Hampel, 2015). 4
Figure DR2. Results from experiments with a fluvial erosion parameter of 0.015 m/a. Shown is at different time steps the model river network in map view (A-D). For river networks at 1.7 and 1.8 Myr see Fig. DR3. River networks in figure parts A and B are shown together with the elevation of the model surface, which is omitted for clarity in the other figure parts. (E) Maps of the model surface showing erosion and sedimentation rates (averaged over 10 kyr) at 1.5 and 2.0 Myr of model time. 5
Figure DR3. Results of a sensitivity analysis with respect to the (A) fluvial erosion parameter and (B) width of the ridge front (cf. Fig. 2B). In both figure parts A and B, the river networks from the different experiment are shown at the timepoints before and after the drainage divide reaches the landward edge of the forearc. Note that all experiments show a symmetric drainage pattern relative to the ridge crest and a similar timing (1.7-1.8 Myr) for the arrival of the drainage divide at the landward edge of the forearc. 6