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====== Firn heating ======
Firn heating (latent heat through refreezing of percolating meltwater) following \\
Wright, A. P., J. L. Wadham, M. J. Siegert, A. Luckman, J. Kohler, and A. M. Nuttall (2007), Modeling the refreezing of meltwater as superimposed ice on a high Arctic glacier: A comparison of approaches, J. Geophys. Res., 112, F04016, doi:10.1029/2007JF000818\\
can be implemented in the following way. Make sure that the mesh contains enough layers close to the upper surface (for example by adding a boundary layer with ExtrudeMesh).
$ function refreezing(D,z) { \
Dfirn=11.5;\ !or some non constant function
if (Dfirn < 0) { Dfirn=0.0; }\
Tann=-7.684-0.004*z;\ !values from data
Twin=-15.0-0.004*z;\ !values from data
freezing=0.0;\
if (D > (Dfirn - 0.00001)) { freezing=0.0; }\
else { \
Tw=((D/Dfirn) - 1.0)*(Tann - Twin) + Tann;\
Ts=Tann*sqrt((1.0 - ((D - Dfirn )^2)/Dfirn^2));\
freezing = 910.0*capacity(Tann+273.15)*(Ts-Tw)*1e-6; }\ !check your unit system
if (freezing < 0.0) {_refreezing=0.0; }\
else {_refreezing=freezing; }\
}
Body Force 1
...
Temp Volume Source = Variable Depth, Coordinate 3
Real MATC "refreezing(tx(0), tx(1))"
End