ࡱ > $ a A* bjbj͚ .D I\I\A" : : D $ " 8 } P n" p" p" p" p" p" p" $ $ _' J " " " ! ! ! n" ! n" ! ! ! "" 08 ! " Z" " 0 " " ' ! ' "" ' "" 8 ! " " ! " ' : H : Software: HYPERLINK "https://github.com/wschwanghart/topotoolbox" https://github.com/wschwanghart/topotoolbox Synthetic model run TOC \o "2-2" Content PAGEREF _Toc454816911 \h 1 Clear environment PAGEREF _Toc454816912 \h 2 Initial Surface PAGEREF _Toc454816913 \h 2 Uplift PAGEREF _Toc454816914 \h 3 Temporal domain PAGEREF _Toc454816915 \h 3 Hillslope processes, parameters values PAGEREF _Toc454816916 \h 3 Set numerical accuracy PAGEREF _Toc454816917 \h 4 River incision parameters PAGEREF _Toc454816918 \h 4 Numerics river incision PAGEREF _Toc454816919 \h 4 Threshold slopes PAGEREF _Toc454816920 \h 4 Boundary conditions PAGEREF _Toc454816921 \h 4 Steady state PAGEREF _Toc454816922 \h 4 Output PAGEREF _Toc454816923 \h 5 Initialize parameter structure. PAGEREF _Toc454816924 \h 5 Model run PAGEREF _Toc454816925 \h 5 Show model output PAGEREF _Toc454816926 \h 6 Create simulation movie PAGEREF _Toc454816927 \h 7 Save movie PAGEREF _Toc454816928 \h 9 History PAGEREF _Toc454816929 \h 10 Content In this tutorial, we show how TTLEM can be used to simulate synthetic landscape evolution. We illustrate how the user can change between different algorithms to simulate hillslope response and how different numerical schemes can be set. Finally, we also show how modelled data can be processed and converted in a movie of an evolving landscape. Detailed information of parameters, their default values and units can be found in the help section of ttlemset. See also: ttlemset, ttlem TTLEM: Campforts B., Schwanghart W., Govers G.: TTLEM 1.0 : a numerical package for accurate simulation of tansient landscape evolution in MATLAB. Discussion paper in GMD. TopoToolbox: Schwanghart, W. and Scherler, D.: Short Communication: TopoToolbox 2 MATLAB-based software for topographic analysis and modeling in Earth surface sciences, Earth Surf. Dyn., 2(1), 17,doi:10.5194/esurf-2-1-2014, 2014. HYPERLINK "https://www.researchgate.net/publication/259706134_Short_Communication_TopoToolbox_2_-_MATLAB-based_software_for_topographic_analysis_and_modeling_in_Earth_surface_sciences" \o "https://www.researchgate.net/publication/259706134_Short_Communication_TopoToolbox_2_-_MATLAB-based_software_for_topographic_analysis_and_modeling_in_Earth_surface_sciences" https://www.researchgate.net/publication/259706134_Short_Communication_TopoToolbox_2_-_MATLAB-based_software_for_topographic_analysis_and_modeling_in_Earth_surface_sciences TVD-FVM: Campforts, B. and Govers, G.: Keeping the edge: A numerical method that avoids knickpoint smearing when solving the stream power law, J. Geophys. Res. Earth Surf., 120(7), 11891205, doi:10.1002/2014JF003376, 2015. HYPERLINK "https://www.researchgate.net/publication/279957391_Keeping_the_edge_A_numerical_method_that_avoids_knickpoint_smearing_when_solving_the_stream_power_law" https://www.researchgate.net/publication/279957391_Keeping_the_edge_A_numerical_method_that_avoids_knickpoint_smearing_when_solving_the_stream_power_law Authors: Benjamin Campforts (benjamin.campforts[at]kuleuven.be) Wolfgang Schwanghart (w.schwanghart[at]geo.uni-potsdam.de) Date: 8. July, 2016 Clear environment clearvarsclose allclc% Saving locationspathLocation='C:\Users\u0059629\Box Sync';figLoc=[ pathLocation '\Matlab\TopoToolbox_GMD\topotoolbox-master_adapted\ttlem\Help\Documents\Figures'];movieDir=[ pathLocation '\Matlab\TopoToolbox_GMD\topotoolbox-master_adapted\ttlem\Help\Documents\Movies']; Initial Surface Generate random initial surface of 0m 50m dx=75;%mLx=50e3; %mLy=50e3;x=dx:dx:Lx;y=dx:dx:Ly;Z=rand(numel(y),numel(x))*50; %Randomized initial conditionDEM=GRIDobj(x,y,Z);% Display initial DEMfigureimageschs(DEM)[~,X_DEM,Y_DEM] = GRIDobj2mat(DEM);[X_DEM,Y_DEM] = meshgrid(X_DEM,Y_DEM); Uplift Uplift is inserted in TTLEM as an instance of GRIDobj U = GRIDobj(DEM);grad = ones(DEM.size);upl_rate=1e-3; %Aboslute vertical uplift rate in m/yrU.Z(2:end-1,2:end-1) = grad(2:end-1,2:end-1)*upl_rate; Temporal domain p.TimeSpan=20e6;p.TimeStep=4e4; Hillslope processes, parameters values %Set diffusivity parameterp.D=0.03;%Choose hillslope response scheme% p.diffScheme = 'imp_lin';p.diffScheme = 'imp_lin_sc';% p.diffScheme = 'imp_nonlin_sc';% p.diffScheme = 'only_sc'; Set numerical accuracy p.DiffTol = 1e-4; River incision parameters p.Kw = 3e-6;p.m = 0.5;p.n = 1;p.AreaThresh = 2e5; % channel contributing area threshold, m% (un)comment to get the drainage development type of choice% Fixed or variable drainage netwrok through timep.DrainDir='variable';% p.DrainDir='fixed';% Insert variability on m value, following Grimaldi et al. (2005)p.m_var=1;% Insert variability on K value. This is not compatible with the nonlinear% Q-imp diffusion algorithm. Comment the next lines out in the case that% nonlinear hillslope diffusion is required.K_weight = randn(size(DEM.Z));K_weight = (K_weight-min(K_weight(:)))./(max(K_weight(:))-min(K_weight(:)));p.K_weight = GRIDobj(DEM); p.K_weight.Z=K_weight;% Correct K so that average K remains equalavgK = mean(K_weight(:));p.Kw =p.Kw*1/avgK; Numerics river incision (un)comment to get the numerical scheme of choice p.riverInc = 'TVD_FVM'; p.riverInc = 'implicit_FDM';% p.riverInc = 'explicit_FDM';p.cfls=0.95; Threshold slopes p.Sc=1; %%21)p.Sc_unit='tangent'; Boundary conditions Set to default. Steady state Evaluate whether the model evolves towards a dynamic equilibrium where uplift balances erosion and absolute elevation differences between model time steps are minimal. p.steadyState = true;p.SS_Value = 1e-6*size(DEM.Z,1)*size(DEM.Z,2);%Max 1mm elevation change per cell allowed in steady state Output p.ploteach=1;p.saveeach=1;% Specify the location where the results can be stored (e.g.% p.resultsdir='C:\...\'); The default folder is the result file where the% main model structure is stored.% p.resultsdir='C:\...';p.fileprefix='syntheticRun'; Initialize parameter structure. By making p an instance of ttlemset, the user ensures parameter values are set in the right way p = ttlemset(p); Model run TTLEM can be manually interrupted by pushing the 'Stop' Bottom. The current model run will quit without losing the information calculated so far. ttlem_out = ttlem(DEM,U,p); Show model output figure('units','normalized','outerposition',[0 0 1 1])H1=ttlem_out.H1;imageschs(H1,[],'ticksToKm',true,'colorBarLabel','\bfm');xlabel('\bfX Coordinate, km');ylabel('\bfY Coordinate, km'); Create simulation movie scrsz = get(0,'ScreenSize');hFig = figure('OuterPosition',[0.1*scrsz(4) 0.1*scrsz(4) .7*scrsz(4) .7*scrsz(4)]);if strcmp(p.diffScheme,'imp_nonlin_sc') parameter=1e-10; inc=max(max(U.Z(:)),1e-3); dt_max=DEM.cellsize*DEM.cellsize/inc*max(p.Sc(:))*parameter/(p.D*p.Kw); dt_max=min(dt_max,5000); nbSteps=ceil(p.TimeSpan/dt_max); if (p.TimeSpan/nbSteps)