*Time dependent boundary conditions for calculation of temperature fields in ice sheets.*In: E. D. Waddington and J. S. Walder (Eds.),

`The Physical Basis of Ice Sheet Modelling`

, IAHS Publication No. 170, pp. 207–216. IAHS Press, Wallingford, UK.On this page one can find MATC based SIF inputs for thermodynamic properties. The following properties are given below:

`Heat Capacity`

of ice as a function of temperature`Heat Conductivity`

of ice as a function of temperature`Pressure Melting Point`

of ice as a function of absolute pressure`Pressure Melting Point`

of ice as a function of hydrostatic pressure`Surface Temperature`

as a function of Longitude/Latitude and elevation

Mind, that faster Fortran functions for the first three functions are available under User Function IceProperties

Heat Capacity of ice as a function of temperature:

!! in SI units, input in Kelvin $ function capacity(T) { _capacity=146.3+(7.253*T)}

and its call from within the Material section

!! in SI units, input Kelvin Heat Capacity = Variable Temperature Real MATC "capacity(tx)" !! in scaled units (m-MPa-years) !! input Kelvin Heat Capacity = Variable Temperature Real MATC "capacity(tx)*(31556926)^(2.0)"

Heat Conductivity of ice as a function of temperature
^{1)}:

!! in SI units, input in Kelvin $ function conductivity(T) { _conductivity=9.828*exp(-5.7E-03*T)}

and its call from within the Material section

!! in SI units, input Kelvin Heat Conductivity = Variable Temperature Real MATC "conductivity(tx)" !! in scaled units (m-MPa-years) !! input Kelvin Heat Conductivity = Variable Temperature Real MATC "conductivity(tx)*(31556926)*1.0E-06"

Pressure Melting Point of ice as a function of absolute pressure:

!! pressuremeltingpoint (Pressure in MPa) $ function pressuremeltingpoint(PIN) {\ P = PIN;\ if (P<0.0) P=0.0;\ beta=9.8E-08*1.0E06;\ _pressuremeltingpoint=273.15-(beta*P);\ }

and its call from within the Material section (call for instance as upper limit for the TemperateIce solver)

Temp Upper Limit = Variable Pressure Real MATC "pressuremeltingpoint(tx)"

Pressure Melting Point of ice as a function of hydrostatic pressure (input variable is flow depth):

!! pressuremeltingpoint (in SI units) $ function pressuremeltingpoint2(D) {\ P = 910*D*9.81;\ if (P<0.0) P=0.0;\ beta=9.8E-08;\ _pressuremeltingpoint2=273.15-(beta*P);\ }

and its call from within the Material section (call for instance as upper limit for the TemperateIce solver):

Temp Upper Limit = Variable Depth Real MATC "pressuremeltingpoint2(tx)"

Surface Temperature as a function of Longitude/Latitude and elevation

$ function surfacetemp(X) { _surfacetemp = 34.36 + 273.15 - 0.68775 * abs(X(0)) - 9.14E-03 * X(1) } $ function phyd(Z) { _phyd = 9.81 * Z * 918.0}

with the longitude/latitude defined the call in the corresponding boundary condition of the free surface reads as follows

Temperature = Variable Latitude, Coordinate 3 Real MATC "surfacetemp(tx)"

after: Ritz, C. 1987. *Time dependent boundary conditions for calculation of temperature fields in ice sheets.* In: E. D. Waddington and J. S. Walder (Eds.),

`The Physical Basis of Ice Sheet Modelling`

, IAHS Publication No. 170, pp. 207–216. IAHS Press, Wallingford, UK.