## User Function IceProperties

**USF Fortran File:** `USF_IceProperties.f90`

**USF Name:** `IceConductivity`

, `IceCapacity`

and `IcePressureMeltingPoint`

**Required Input Variable(s):** Temperature (`IceConductivity`

, `IceCapacity`

), Pressure (`IcePressureMeltingPoint`

)

### General Description

The aim of these user functions is to provide a Fortran version of the else as MATC functions prescribed material parameters for ice (except for viscosity, which is handled by Glen's flow law). Fortran functions are way faster in execution time, which, in a run that repeatedly calls those parameters, can lead to tremendous speed-ups. Hence, if computing thermo-mechanically coupled problems, rather stick to those.

All input is expected to be in SI units (Temperature in Kelvin). All outputs by default are in SI units, except the user provides scaling factors (see below).

#### IceConductivity

The heat conductivity of ice as a function of temperature () is defined (in SI units) as:

#### IceCapacity

The capacity of ice as a function of temperature () is defined (in SI units) as:

#### IcePressureMeltingPoint

The pressure melting point of ice as a function of pressure () is defined as (in Kelvin):

where is the Clausius Clapeyron constant. In case of negative ice pressures (actually, any below atmospheric pressures), the function uses the reference value at atmospheric pressure.

### SIF contents

The required keywords in the SIF file for these user functions are:

$secondsperyear = 365.25 * 24.0 * 3600.0
Constants
Clausius Clapeyron = Real 9.8e-08
End
Material 1
Name = "ice"
! Heat transfer stuff (converted to MPa-m-a system)
Temp Heat Capacity = Variable Temp
Real Procedure "ElmerIceUSF" "IceCapacity"
Heat Capacity Scaling Factor = Real $(secondsperyear)^(2.0)
Temp Heat Conductivity = Variable Temp
Real Procedure "ElmerIceUSF" "IceConductivity"
Heat Conductivity Scaling Factor = Real $(secondsperyear)*1.0E-06
Temp Upper Limit = Variable HydroPressure
Real Procedure "ElmerIceUSF" "IcePressureMeltingPoint"
Pressure Scaling Factor = Real 1.0E06 ! from MPa to Pa
End

### Examples

An example demonstrating the use of the thermal properties of ice can be found in `[ELMER_TRUNK]/elmerice/Tests/TemperateIceTestFct`

.

### References

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.