source: issm/trunk-jpl/examples/SlrFarrell/runme.m@ 22813

clear all;
steps=[5]; % 

if any(steps==1) % Global mesh creation {{{ 
        disp('   Step 1: Global mesh creation');

        numrefine=1;
        resolution=150*1e3;             % inital resolution [m]. It determines, e.g., whether we capture small islands. 
        radius = 6.371012*10^6; % mean radius of Earth, m
        mindistance_coast=150*1e3;              % coastal resolution [m] 
        mindistance_land=300*1e3; % resolution on the continents [m]
        maxdistance=600*1e3;     % max element size (on mid-oceans) [m]

        %mesh earth: 
        md=model; 
        md.mask=maskpsl(); % use maskpsl class (instead of mask) to store the ocean function as a ocean_levelset 
        md.mesh=gmshplanet('radius',radius*1e-3,'resolution',resolution*1e-3); % attributes should be in km. 

        for i=1:numrefine,

                %figure out mask: 
                md.mask.ocean_levelset=gmtmask(md.mesh.lat,md.mesh.long); 

                %figure out distance to the coastline, in lat,long (not x,y,z): 
                distance=zeros(md.mesh.numberofvertices,1);

                pos=find(~md.mask.ocean_levelset);      coaste.lat=md.mesh.lat(pos);    coaste.long=md.mesh.long(pos);  
                pos=find(md.mask.ocean_levelset);       coasto.lat=md.mesh.lat(pos);    coasto.long=md.mesh.long(pos);  

                for j=1:md.mesh.numberofvertices
                        %figure out nearest coastline (using the great circle distance)
                        phi1=md.mesh.lat(j)/180*pi; lambda1=md.mesh.long(j)/180*pi; 
                        if md.mask.ocean_levelset(j),
                                phi2=coaste.lat/180*pi; lambda2=coaste.long/180*pi; 
                                deltaphi=abs(phi2-phi1); deltalambda=abs(lambda2-lambda1);
                                d=radius*2*asin(sqrt(sin(deltaphi/2).^2+cos(phi1).*cos(phi2).*sin(deltalambda/2).^2));
                        else
                                phi2=coasto.lat/180*pi; lambda2=coasto.long/180*pi; 
                                deltaphi=abs(phi2-phi1); deltalambda=abs(lambda2-lambda1);
                                d=radius*2*asin(sqrt(sin(deltaphi/2).^2+cos(phi1).*cos(phi2).*sin(deltalambda/2).^2));
                        end
                        distance(j)=min(d);
                end
                pos=find(distance<mindistance_coast); distance(pos)=mindistance_coast;
                
                % refine on the continents
                pos2=find(md.mask.ocean_levelset~=1 & distance>mindistance_land); 
                distance(pos2)=mindistance_land; 

                dist=min(maxdistance,distance); % max size 1000 km 
                %use distance to the coastline to refine mesh: 
                md.mesh=gmshplanet('radius',radius*1e-3,'resolution',resolution*1e-3,'refine',md.mesh,'refinemetric',dist);
        end

        %figure out mask: 
        md.mask.ocean_levelset=gmtmask(md.mesh.lat,md.mesh.long); 

        save ./Models/SlrFarrell.Mesh md;
        
        plotmodel (md,'data',md.mask.ocean_levelset,'edgecolor','k');
        %export_fig('Fig1.pdf'); 

end % }}} 

if any(steps==2) % Define source {{{ 
        disp('   Step 2: Define source as in Farrell, 1972, Figure 1');
        md = loadmodel('./Models/SlrFarrell.Mesh');

        % initial sea-level: 1 m RSL everywhere. 
        md.slr.sealevel=md.mask.ocean_levelset; 
        
        md.slr.deltathickness=zeros(md.mesh.numberofelements,1);
        md.slr.steric_rate=zeros(md.mesh.numberofvertices,1);

        save ./Models/SlrFarrell.Loads md; 
        
        plotmodel (md,'data',md.slr.sealevel,'view',[90 90],...
                'title#all','Initial sea-level [m]');
        %export_fig('Fig2.pdf'); 

end % }}} 

if any(steps==3) % Parameterization {{{ 
        disp('   Step 3: Parameterization');
        md = loadmodel('./Models/SlrFarrell.Loads');

        % Love numbers and reference frame: CF or CM (choose one!)  
        nlove=10001;    % up to 10,000 degree 
        md.slr.love_h = love_numbers('h','CM'); md.slr.love_h(nlove+1:end)=[];
        md.slr.love_k = love_numbers('k','CM'); md.slr.love_k(nlove+1:end)=[];
        md.slr.love_l = love_numbers('l','CM'); md.slr.love_l(nlove+1:end)=[];

        % Mask: for computational efficiency only those elements that have loads are convolved! 
        md.mask.land_levelset = 1-md.mask.ocean_levelset; 
        % fake ice load in one element!  
        md.mask.ice_levelset = ones(md.mesh.numberofvertices,1); % no ice 
        md.mask.groundedice_levelset = -ones(md.mesh.numberofvertices,1); % floated... 
        pos=find(md.mesh.lat <-80);
        md.mask.ice_levelset(pos(1))=-1; % ice yes!  
        md.mask.groundedice_levelset(pos(1))=1; % ice grounded!  

        %% IGNORE BUT DO NOT DELETE %% {{{
        % Geometry: Important only when you want to couple with Ice Flow Model 
        di=md.materials.rho_ice/md.materials.rho_water;
        md.geometry.thickness=ones(md.mesh.numberofvertices,1);
        md.geometry.surface=(1-di)*zeros(md.mesh.numberofvertices,1);
        md.geometry.base=md.geometry.surface-md.geometry.thickness;
        md.geometry.bed=md.geometry.base;
        % Materials: 
        md.initialization.temperature=273.25*ones(md.mesh.numberofvertices,1);
        md.materials.rheology_B=paterson(md.initialization.temperature);
        md.materials.rheology_n=3*ones(md.mesh.numberofelements,1);
        % Miscellaneous: 
        md.miscellaneous.name='SlrFarrell';
        %% IGNORE BUT DO NOT DELETE %% }}}  
        
        save ./Models/SlrFarrell.Parameterization md; 

end % }}} 

if any(steps==4) % Solve {{{ 
        disp('   Step 4: Solve Slr solver');
        md = loadmodel('./Models/SlrFarrell.Parameterization');

        % Cluster info 
        md.cluster=generic('name',oshostname(),'np',3); 
        md.verbose=verbose('111111111');

        % Solve 
        md=solve(md,'Slr');

        save ./Models/SlrFarrell.Solution md; 

end % }}} 

if any(steps==5) % Plot solutions {{{ 
        disp('   Step 5: Plot solutions');
        md = loadmodel('./Models/SlrFarrell.Solution');

        % solutions. 
        sol = md.results.SealevelriseSolution.Sealevel*100; % per cent normalized by GMSL (which 1 m)  
        
        res = 1.0; % degree 

        % Make a grid of lats and lons, based on the min and max of the original vectors
        [lat_grid, lon_grid] = meshgrid(linspace(-90,90,180/res), linspace(-180,180,360/res));
        sol_grid = zeros(size(lat_grid)); 

        % Make a interpolation object
        F = scatteredInterpolant(md.mesh.lat,md.mesh.long,sol); 
        F.Method = 'linear';
        F.ExtrapolationMethod = 'linear'; 
        
        % Do the interpolation to get gridded solutions... 
        sol_grid = F(lat_grid, lon_grid);
        sol_grid(isnan(sol_grid))=0; 
        sol_grid(lat_grid>85 & sol_grid==0) =NaN; % set polar unphysical 0s to Nan 

        set(0,'DefaultAxesFontSize',18,'DefaultAxesLineWidth',1,'DefaultTextFontSize',18,'DefaultLineMarkerSize',8)
        figure1=figure('Position', [100, 100, 1000, 500]); 
        gcf; load coast; cla; 
        %pcolor(lon_grid,lat_grid,sol_grid); shading flat; hold on;
        contourf(lon_grid,lat_grid,sol_grid,[96 98 100 102 104 105]); shading flat; hold on;
        geoshow(lat,long,'DisplayType','polygon','FaceColor','white'); 
        plot(long,lat,'k'); hold off; 
        % define colormap, caxis, xlim etc {{{
        c1=colorbar;
        %colormap('haxby'); 
        %caxis([96 104]); 
        xlim([-180 180]); 
        ylim([-90 90]); 
        % }}} 
        grid on; 
        title('Relative sea-level [mm]'); 
        set(gcf,'color','w');

        %export_fig('Fig5.pdf'); 

end % }}}