function [ab,dabdh]=DraftDependentMeltParameterisations(UserVar,CtrlVar,F,MRP)

[ab,dabdh]=DraftDependentMeltParameterisations(UserVar,CtrlVar,F,MRP)

Returns basal melt rates, based on several depth-dependent parameterisations.

ab is :    abMin for F.b>dMin
           abMax for F.b<dMax

and varies linearly inbetween.

These types of parameterisations have been used in various papers. Labels might not correspond exactly to the labels used in previous publicatioins.

Note !!! The user will in addition need to make sure that melt is only applied over floating nodes, downstream of the grounding line This can be done in DefineMassBalance.m as follows:

[LakeNodes,OceanNodes] = LakeOrOcean3(CtrlVar,MUA,F.GF,[],"Strict") ;
ab(~OceanNodes)=0;
dabdh(~OceanNodes)=0;

switch MRP


    case {"0","l0"}

        fprintf(' MeltRate0 \n ');
        dMin=-400 ;  abMin=0 ;
        dMax=-800 ;  abMax=-100  ;

    case {"1","l1"}

        fprintf(' MeltRate1 \n ');
        dMin=-400 ;  abMin=0 ;
        dMax=-800 ;  abMax=-200  ;


    case {"2","l2"}

        fprintf(' MeltRate2 \n ');
        dMin=-200 ;  abMin=0 ;
        dMax=-800 ;  abMax=-100  ;


    case {"3","l3"}

        fprintf(' MeltRate3 \n ');
        dMin=-200 ;  abMin=0 ;
        dMax=-800 ;  abMax=-200  ;

    case {"4","l4"}

        % fprintf(' MeltRate4 \n ');
        dMin=-400 ;  abMin=0 ;
        dMax=-500 ;  abMax=-50  ;

    case {"5","l5"}

        fprintf(' MeltRate5 \n ');
        dMin=-400 ;  abMin=0 ;
        dMax=-600 ;  abMax=-100  ;





    otherwise

        fprintf("DraftDependentMeltParameterisations : case not found")
        dMin=nan ;  abMin=nan ;
        dMax=nan ;  abMax=nan  ;


end



F.as=zeros(size(F.h)) ;
F.ab=zeros(size(F.h)) ;
F.dasdh=zeros(size(F.h)) ;
F.dabdh=zeros(size(F.h)) ;





if contains(MRP,"l")

    b0=(dMin+dMax)/2 ;
    k=2/(dMin-dMax) ;
    ab=abMin+    (1-HeavisideApprox(k,F.b,b0))*(abMax-abMin) ;

    dabdh=-DiracDelta(k,F.b,b0).*(abMax-abMin).*(-F.rho/F.rhow) ;
    %   dab/db  db/dh

else

    dabdh=zeros(size(F.x)) ;
    ab=zeros(size(F.x)) ;


    % Note, the dab/dh calculation is not exact, as it is missing a Dirac delta
    % term

    I=F.b>dMin ; ab(I)=abMin; dabdh(I)=0;        % above dMin

    I= F.b<= dMin & F.b >= dMax ;

    % b= -h rho/rhow
    ab(I)=abMax*(F.b(I)-dMin)/(dMax-dMin); % negative values, because it is a basal ablation
    dabdh(I)=(-F.rho(I)/F.rhow)  .* (abMax/(dMax-dMin));

    I=F.b<dMax ; ab(I)=abMax; dabdh(I)=0;        % below dMax


end

% Note !!!
% The user will in addition need to make sure that melt is only applied over floating nodes, downstream of the grounding line
% This can be done in DefineMassBalance.m as follows:
%
%   [LakeNodes,OceanNodes] = LakeOrOcean3(CtrlVar,MUA,F.GF,[],"Strict") ;
%   ab(~OceanNodes)=0;
%   dabdh(~OceanNodes)=0;
%

end

Published with MATLAB® R2023a