## Thermodynamic Properties

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

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

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

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

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

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)"```
1)
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. 