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===== 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 [[userfunctions:iceproperties|User Function IceProperties]]
==== Heat Capacity ====

Heat Capacity  of ice as a function of temperature:
<code>
!! in SI units, input in Kelvin
$ function capacity(T) { _capacity=146.3+(7.253*T)}
</code>
and its call from within the Material section
<code>
!! 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)"
</code>

==== Heat Conductivity ====

Heat Conductivity of ice as a function of temperature
((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.)):
<code>
!! in SI units, input in Kelvin
$ function conductivity(T)  { _conductivity=9.828*exp(-5.7E-03*T)}
</code>
and its call from within the Material section
<code>
!! 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"
</code>

==== Pressure Melting Point ====

Pressure Melting Point of ice as a function of absolute pressure:
<code>
!! 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);\
}
</code>
and its call from within the Material section (call for instance as upper limit for the [[solvers:temperature|TemperateIce solver]])
<code>
Temp Upper Limit = Variable Pressure
    Real MATC "pressuremeltingpoint(tx)"
</code>

==== Pressure Melting Point ====

Pressure Melting Point of ice as a function of hydrostatic pressure (input variable is [[solvers:depth|flow depth]]):
<code>
!! 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);\
}
</code>
and its call from within the Material section (call for instance as upper limit for the [[solvers:temperature|TemperateIce solver]]):
<code>
Temp Upper Limit = Variable Depth
    Real MATC "pressuremeltingpoint2(tx)"
</code>

==== Surface Temperature ====

Surface Temperature as a function of Longitude/Latitude and elevation
<code>
$ 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}
</code>
with the [[tips:longlat|longitude/latitude]] defined the call in the corresponding boundary condition of the free surface reads as follows
<code>
Temperature = Variable Latitude, Coordinate 3
     Real MATC "surfacetemp(tx)"
</code>