function [UserVar,as,ab]=DefineMassBalance(UserVar,CtrlVar,MUA,F)

Defines mass balance along upper and lower ice surfaces.

[UserVar,as,ab]=DefineMassBalance(UserVar,CtrlVar,MUA,time,s,b,h,S,B,rho,rhow,GF)

[UserVar,as,ab]=DefineMassBalance(UserVar,CtrlVar,MUA,F);

[UserVar,as,ab,dasdh,dabdh]=DefineMassBalance(UserVar,CtrlVar,MUA,CtrlVar.time,s,b,h,S,B,rho,rhow,GF);

[UserVar,as,ab,dasdh,dabdh]=DefineMassBalance(UserVar,CtrlVar,MUA,F);

as        mass balance along upper surface
ab        mass balance along lower ice surface
dasdh     upper surface mass balance gradient with respect to ice thickness (optional)
dabdh     lower surface mass balance gradient with respect to ice thickness (optional)

dasdh and dabdh only need to be specified if the implicit mass-balance feedback option is being used. To use the implicit mass-balance feedback option you must set

CtrlVar.MassBalanceGeometryFeedback=3;

in DefineInitialInputs.m. Otherwise, the default value of

CtrlVar.MassBalanceGeometryFeedback=0;

is used, which does not include the implicit mass-balance feedback.

IMPORTANT: In Ua the mass balance, as returned by this m-file, is multiplied internally by the local ice density.

The units of as and ab are the same units as those of velocity (something like m/yr or m/day).

IMPORTANT: Often surface mass balance is provided my climate models as mass flux and in the units kg/(m^2 yr). This is as if we prescribe the value of the product of density and accumulation rate, ie rho a, which has the units kg/(m^2 yr). In Ua this translation to mass flux is done internally, i.e. the rho is included in the mass conservation equation. The surface mass balance (as and ab) prescribed here as an input to Ua MUST BE IN THE UNITS distance/time, e.g. m/yr.

If you have external data sets providing the mass flux in the units kg/(m^2 yr) you must divide those values here by the density, and this density must be the same density as is given in DefineGeometryAndDensities.m

Also, if an external data sets provides the surface mass balance in the units of water equivalent, you must modify this value by the ratio between the density of water and the density of ice that you prescribe in DefineGeometryAndDensities.m, for example as 1000/rho, assuming rho is given in the units kg/m^3.

For example, if you use a constant density for ice of 920 kg/m^3 and the surface mass balance is given as 1 m/yr of water equivalent (ie 1000 kg/(m^2 yr) ), the surface mass balance you need here is 1000/920 m/yr.

As in all other calls:

F.s       : is upper ice surface
F.b       : lower ice surface
F.B       : bedrock
F.S       : ocean surface
F.rhow    : ocean density (scalar variable)
F.rho     : ice density (nodal variable)
F.g       : gravitational acceleration
F.x       : x nodal coordinates
F.y       : y nodal coordinates
F.GF      : The nodal grounded/floating mask (has other subfields)

These fields need to be returned at the nodal coordinates. The nodal x and y coordinates are stored in MUA.coordinates, and also in F as F.x and F.y

Examples :

To set upper surface mass balance to zero, and melt along the lower ice surface to 10 over all ice shelves:

as=zeros(MUA.Nnodes,1);
ab=-(1-F.GF.node)*10

To set upper surface mass balance as a function of local surface elevation and prescribe mass-balance feedback for the upper surface:

as=0.1*F.h+F.b;
dasdh=zeros(MUA.Nnodes,1)+0.1;
ab=F.s*0;
dabdh=zeros(MUA.Nnodes,1);

Note: To use the implicit mass-balance feedback option you must set

CtrlVar.MassBalanceGeometryFeedback=3;

in DefineInitialInputs.m. Otherwise, the default value of

CtrlVar.MassBalanceGeometryFeedback=0;

is used, which does not include the implicit mass-balance feedback.

To add basal melt due to sliding as a mass-balance term:

[tbx,tby,tb,beta2] = CalcBasalTraction(CtrlVar,MUA,F.ub,F.vb,F.C,F.m,F.GF);
L=333.44 ;                                        % Enthalpy of fusion = L = [J/gram = kJ/kg]  Make sure that the units are correct.
F.ab=-(tbx.*F.ub+tby.*F.vb)./(F.rho.*L);          % Ablation (Melt) is always negative, accumulation is positive

%rhofw=1000;
%L=3.34e5;
%rho=917;
%cw=3974 ;
%Gt=5e-2;
%Gs=1.e3-3;


%uH=u0*tanh(Hc/Hc0);
%Tzd=T0*(b-B)/zref;
%ab=rho*cw*Gt*uH.*Tzd/rhofw/L;


% zd is the ice draft, here it is b when afloat
% zb is the bedrock elevation, or B
% Hc=zd-db = b=B

as=0.3;

switch UserVar.MisExperiment

    case 'ice0'

        % basal melt always zero
        ab=zeros(MUA.Nnodes,1);

    case 'ice1ra'

        % basal melt for t<=100, then zero
        if time <=100

            Hc0=75;
            Omega=0.2 ;
            z0=-100;
            ab=-Omega*tanh((F.b-F.B)/Hc0).* max(z0-F.b,0);


            % when b>-100, for example b=-50 , then   z0-b=-100+50 =-50 < 0

        else
            ab=zeros(MUA.Nnodes,1);
        end

    case 'ice1rr'

        % basal melt applied at all times
        Hc0=75;
        Omega=0.2 ;
        z0=-100;
        ab=-Omega*tanh((F.b-F.B)/Hc0).* max(z0-F.b,0);

    case 'ice2ra'

        % basal melt at 100 m/a for x>48km for the first 100 years, then zero
        if time<=100

            ab=zeros(MUA.Nnodes,1);
            I=F.x>480e3;
            ab(I)=-100;

        else
            ab=zeros(MUA.Nnodes,1);
        end

    case 'ice2rr'

        ab=zeros(MUA.Nnodes,1);
        I=F.x>480e3;
        ab(I)=-100;

    otherwise

        error('case not found')

end

end

Published with MATLAB® R2024a