function [ab,qx,qy,dqxdx,dqxdy,dqydx,dqydy]=CalcIceShelfMeltRates(CtrlVar,MUA,u,v,s,b,S,B,rho,rhow,dsdt,as,dhdt)

ab=CalcIceShelfMeltRates(CtrlVar,MUA,u,v,s,b,S,B,rho,rhow,dsdt,as,dhdt)

Calculates basal meltrate from ice-flux divergence, surface mass balance (as) and surface elevation rate changes (dsdt) or alternativily from rates of thickness change (dhdt).

Just a rough way of doing this...please look through the code and adjust as you feel needed.

Calculates basal ice shelf melt rates (ab) as:

ab=dhdt+(dqxdx+dqydy)./rho-as;

where: dhdt is the rate of thickness change dqxdx and dqydy are the flux gradients calcuated from u, v, h, and rho as is the surface accumulation in meters of water equivalent

Input:

u and v       : horizontal ice-velocity components
s, b, S and B : upper (s) and lower ice surfaces (b), ocean elevation (S) and bedrock (B)
rho           : ice density
rhow          : ocean density
dsdt          : rates of elevation change
as            : surface mass balance
dhdt          : rates of ice thickness change (optional, if given dsdt is ignored)

Output:

ab            : lower-surface mass balance over floating areas, i.e. ice-shelf melt rate
qx, qy        : x and y components of ice flux
dqxdx, etc.   : ice-flux gradients

Flux is calculated in units of distance/time for example as m/yr, i.e. same as velocity

Sign convention: Positive values imply freezing (mass added on). Negative values imply melting (mass lost).

if nargin==13
    fprintf('dhdt given as input. Will ignore dsdt input field\n')
else
    fprintf('calculating dhdt based on measured dsdt\n')
    dhdt=dsdt./(1-rho/rhow);
end

h=s-b;

% Flux includes density
qx=rho.*u.*h;  qy=rho.*v.*h;


% calculate flux gradients at integratino points
[dqxdx,dqxdy]=calcFEderivativesMUA(qx,MUA,CtrlVar);
[dqydx,dqydy]=calcFEderivativesMUA(qy,MUA,CtrlVar);


% Project onto nodes
dqxdx(isnan(dqxdx))=0; dqydy(isnan(dqydy))=0;
[dqxdx,dqydy]=ProjectFintOntoNodes(MUA,dqxdx,dqydy);


% And now calculate basal melt:
ab=dhdt+(dqxdx+dqydy)./rho-as;

% Finally, put melt rates over grounded areas to zero.
GF=GL2d(B,S,h,rhow,rho,MUA.connectivity,CtrlVar);
ab=ab.*(1-GF.node);

end

Published with MATLAB® R2017a