source: issm/trunk-jpl/test/SandBox/corr2002.m

%Test Name: EarthSlr

%mesh earth:
md=model;
md.mesh=gmshplanet('radius',6.371012*10^3,'resolution',700.); %500 km resolution mesh
md.cluster.np=4

%parameterize slr solution:
%slr loading:  {{{
nt=10;
md.slr.deltathickness=zeros(md.mesh.numberofelements+1,nt);
md.slr.deltathickness(end,:)=2001:1:2001+nt-1;
md.slr.sealevel=zeros(md.mesh.numberofvertices,1);
md.dsl.global_average_thermosteric_sea_level_change=[0;0];
md.dsl.sea_surface_height_change_above_geoid=zeros(md.mesh.numberofvertices+1,1);
md.dsl.sea_water_pressure_change_at_sea_floor=zeros(md.mesh.numberofvertices+1,1);

%antarctica
late=sum(md.mesh.lat(md.mesh.elements),2)/3;
longe=sum(md.mesh.long(md.mesh.elements),2)/3;
posa=find(late <-80);
md.slr.deltathickness(posa,:)=-100;

%greenland
posg=find(late > 70 &  late < 80 & longe>-60 & longe<-30);
md.slr.deltathickness(posg,:)=-100;

%elastic loading from love numbers:
nlov=101;
md.slr.love_h = love_numbers('h','CM'); md.slr.love_h(nlov+1:end)=[];
md.slr.love_k = love_numbers('k','CM'); md.slr.love_k(nlov+1:end)=[];
md.slr.love_l = love_numbers('l','CM'); md.slr.love_l(nlov+1:end)=[];

%}}}
%mask:  {{{
mask=gmtmask(md.mesh.lat,md.mesh.long);
icemask=ones(md.mesh.numberofvertices,1);
pos=find(mask==0);  icemask(pos)=-1;
pos=find(sum(mask(md.mesh.elements),2)<3);   icemask(md.mesh.elements(pos,:))=-1;
md.mask.ice_levelset=icemask;
md.mask.ocean_levelset=-icemask;

%make sure that the elements that have loads are fully grounded:
pos=find(sum(md.slr.deltathickness(1:end-1,:),2));
md.mask.ocean_levelset(md.mesh.elements(pos,:))=1;

%make sure wherever there is an ice load, that the mask is set to ice:
md.mask.ice_levelset(md.mesh.elements(pos,:))=-1;
% }}}

md.slr.ocean_area_scaling=0;

%Geometry for the bed, arbitrary: 
md.geometry.bed=-ones(md.mesh.numberofvertices,1);

%Materials: 
md.materials=materials('hydro');

%New stuff
md.slr.spcthickness = NaN(md.mesh.numberofvertices,1);
md.slr.Ngia = zeros(md.mesh.numberofvertices,1);
md.slr.Ugia = zeros(md.mesh.numberofvertices,1);
md.slr.hydro_rate = zeros(md.mesh.numberofvertices,1);

%Miscellaneous
md.miscellaneous.name='test2002';

%Solution parameters
md.slr.reltol=NaN;
md.slr.abstol=1e-3;
md.slr.geodetic=1;

% max number of iteration reverted back to 10 (i.e., the original default value)
md.slr.maxiter=10;

%Uncertainty Quantification%{{{

        %partitioning
        npart=2;
        partition=-ones(md.mesh.numberofelements,1);
        partition(posg)=0;
        partition(posa)=1;

        %variables: 
        md.qmu.variables.deltathickness=normal_uncertain('descriptor','scaled_SealevelriseDeltathickness',...
        'mean',ones(npart,nt),...
        'stddev',.2*ones(npart,nt),...
        'partition',partition,'nsteps',nt);

        md.qmu.correlation_matrix=zeros(npart*nt,npart*nt);
        for i=1:npart,
                for j=1:nt,
                        indi=(i-1)*nt+j;
                        for k=1:npart,
                                for l=1:nt,
                                        indj=(k-1)*nt+l;
                                        if i~=k,
                                                md.qmu.correlation_matrix(indi,indj)=0;
                                        else
                                                %same partition:
                                                if j==l, 
                                                        md.qmu.correlation_matrix(indi,indj)=1;
                                                else
                                                        if i==1,
                                                                md.qmu.correlation_matrix(indi,indj)=.2;
                                                        else
                                                                md.qmu.correlation_matrix(indi,indj)=.5;
                                                        end
                                                end
                                        end
                                end
                        end
                end
        end


        %responses 
        md.qmu.responses.sealevel1=response_function('descriptor','Outputdefinition1');
        md.qmu.responses.sealevel2=response_function('descriptor','Outputdefinition2');
        md.qmu.responses.sealevel3=response_function('descriptor','Outputdefinition3');
        md.qmu.responses.sealevel4=response_function('descriptor','Outputdefinition4');
        md.qmu.responses.sealevel5=response_function('descriptor','Outputdefinition5');
        md.qmu.responses.sealevel6=response_function('descriptor','Outputdefinition6');
        md.qmu.responses.sealevel7=response_function('descriptor','Outputdefinition7');
        md.qmu.responses.sealevel8=response_function('descriptor','Outputdefinition8');
        md.qmu.responses.sealevel8=response_function('descriptor','Outputdefinition9');
        md.qmu.responses.sealevel10=response_function('descriptor','Outputdefinition10');

        %output definitions: 
        for i=1:10,
                if i==1,
                        md.outputdefinition.definitions={nodalvalue('name','SNode','definitionstring','Outputdefinition1', ...
                        'model_string','Sealevel','node',i)}; 
                else
                        md.outputdefinition.definitions{end+1}=nodalvalue('name','SNode','definitionstring',['Outputdefinition' num2str(i)], ...
                        'model_string','Sealevel','node',i); 
                end
        end
        %algorithm: 
        md.qmu.method     =dakota_method('nond_samp');
        md.qmu.method(end)=dmeth_params_set(md.qmu.method(end),...
        'seed',1234,...
        'samples',40,...
        'sample_type','lhs');

        %parameters
        md.qmu.params.direct=true;
        md.qmu.params.interval_type='forward';
        md.qmu.params.analysis_driver='matlab';
        md.qmu.params.evaluation_scheduling='master';
        md.qmu.params.processors_per_evaluation=3;
        md.qmu.params.tabular_graphics_data=true;
        %}}}
md.qmu.isdakota=1;
md.qmu.output=1;

%transient: 
md.timestepping.start_time=2000;
md.timestepping.time_step=1;
md.timestepping.interp_forcings=0;
md.timestepping.final_time=2011;
md.transient.issmb=0;
md.transient.ismasstransport=0;
md.transient.isstressbalance=0;
md.transient.isthermal=0;
md.transient.isslr=1;
md.slr.requested_outputs= {'default',...
                'SealevelriseDeltathickness','Sealevel','SealevelRSLRate','SealevelriseCumDeltathickness',...
                'SealevelNEsaRate', 'SealevelUEsaRate', 'SealevelNGiaRate', 'SealevelUGiaRate',...
                'SealevelEustaticMask','SealevelEustaticOceanMask'};

%hack: 
md.geometry.thickness=ones(md.mesh.numberofvertices,1);
md.geometry.base=-ones(md.mesh.numberofvertices,1);
md.geometry.surface=zeros(md.mesh.numberofvertices,1);

%eustatic + rigid + elastic + rotation run:
md.verbose=verbose('0');
md.verbose.qmu=1;
md.slr.rigid=1; md.slr.elastic=1; md.slr.rotation=1;
md=solve(md,'tr');