function [qGL,qGLx,qGLy,xEdge,yEdge,nxGL,nyGL,dsGL,xGLele,yGLele,iE,EN]=FluxAcrossEleGL(CtrlVar,MUA,GF,ub,vb,rho,h,DoPlots,iE,EN)

Calculates flux across grounding lines, with grounding lines defined as the free boundary (or free edges) of grounded elements.

  [qGL,qGLx,qGLy,xEdge,yEdge,nxGL,nyGL,dsGL,xGLele,yGLele,iE,EN]=FluxAcrossEleGL(CtrlVar,MUA,GF,ub,vb,rho,h,DoPlots,iE,EN)

Inputs: DoPlots : If true, some plots are created. (optional) iE : Corner nodes of grounding line edges. (optional) EN : Nodes of grounding line edges, including nodes along the edge. (optional)

iE and EN can be left empty, in which case they will be calculated and
returned as outputs. To speed things up, use iE and EN from a previous call
if calling this routine again for the same MUA and GF.

Outputs: qGL : vertically and horizontally integrated flux over each element edge defining the grounding line. qGLx, qGLy : the x, y components of a vector with the length qGL and normal to the grounding line (i.e. these are not x and y components of qGL) xEdge, yEdge : x and y coordinates of a center point of each GL edge. nxGL, nyGL : unit normal to GL edges dsGL : length of GL edges xGLele, yGLele : ordered list of all corner points of GL edges, with NaN between individual GL segments. Useful for plotting GL. iE : Corner nodes of grounding line edges. EN : Nodes of grounding line edges, including nodes along the edge.

Note: For 3-node elements, iE and EN are not needed.

Note: qGL has the units: speed x ice-thickness x ice-density width = m/yr m kg/m^3 m = kg/yr (if using m, yr, kg as units for distance, time and mass.)

Note: If using repeatedly for higher-order elements and the same MUA and GF, give returned iE and EN from previous calls as inputs.

Note: This routine uses a (slightly) different representation of the grounding line as that given by, for example, PlotGroundingLine.m which is based on interpolation of the GF nodal mask.

Note: Currently only implemented for 3 and 6 node elements.

if nargin<8  || isempty(DoPlots)
    DoPlots=0;
end

if nargin<9
    iE=[] ;
    EN=[];
end


[xGLele,yGLele,triGR,FB,xEdge,yEdge,nxGL,nyGL,dsGL]=EleBasedGL(CtrlVar,MUA,GF,DoPlots);


switch MUA.nod

    case 3

        uhr=ub.*h.*rho;
        vhr=vb.*h.*rho;
        qxS=dsGL.*mean(uhr(FB),2) ;  % for a linear triangle element this is correct
        qyS=dsGL.*mean(vhr(FB),2) ;
        qGL=qxS.*nxGL+qyS.*nyGL; % units: m m (m/yr) * kg/m^3 =kg/yr
        qGLx=qGL.*nxGL ;
        qGLy=qGL.*nyGL ;
        EN=[FB(:,1) FB(:,2)];
    case 6

        % a bit more accurate estimate for 6-node elements. Here I used the two corner
        % nodes and the side node and integrate with Simpson's rule, which is second order
        % just like the form functions. So this should be pretty much exact.

        if nargin <10 || isempty(EN)
            if nargin<9 || isempty(iE)
                iE=FindEdgeNodesGivenTwoCornerNodes(MUA,FB);  % this can be slow
            end

            if size(iE,1)~=size(FB,1)
                fprintf('iE given as input does have a number of elements that is consistent with MUA, iE is therefore recalculated.\n')
                iE=FindEdgeNodesGivenTwoCornerNodes(MUA,FB);  % this can be slow
            end

            EN=[FB(:,1) iE(:) FB(:,2)];

        end

        uhr=ub.*h.*rho;
        vhr=vb.*h.*rho;
        qxS=dsGL.*(uhr(EN(:,1))+4*uhr(EN(:,2))+uhr(EN(:,3)))/6;  % Simpson's rule
        qyS=dsGL.*(vhr(EN(:,1))+4*vhr(EN(:,2))+vhr(EN(:,3)))/6;

        % I'm integrating the flux in x and y directions
        % and then projecting along normal and tangential directions.
        % This will only be correct for straight edges within each triangle
        %

        qGL=qxS.*nxGL+qyS.*nyGL;

        qGLx=qGL.*nxGL ;
        qGLy=qGL.*nyGL ;

    case 10

        error('Case for 10 node elements not yet implemented')

end


if DoPlots

    figure
    plot(xGLele,yGLele)
    hold on
    Par.VelPlotIntervalSpacing='log10';
    Par.RelativeVelArrowSize=10;
    Par.QuiverColorPowRange=2;
    % assuming units: m/yr, m, kg/m^3  for velocity, distance and density
    % q calculated has the units:  m/yr m m kg/m^3 = kg/yr
    % To get Gt divide by 1e9
    cbar=QuiverColorGHG(xEdge,yEdge,qGLx/1e9,qGLy/1e9,Par);
    title(cbar,'kg/yr')   ;
    axis equal

end

Not enough input arguments.

Error in FluxAcrossEleGL (line 53)
[xGLele,yGLele,triGR,FB,xEdge,yEdge,nxGL,nyGL,dsGL]=EleBasedGL(CtrlVar,MUA,GF,DoPlots);

end

Published with MATLAB® R2021a