South Pole Ice Temperature

Question: Given a depth in the ice at the South Pole what temperature is the far field ice at that depth?

Kurt Woschnagg produced two data files describing the far field ice temperatures at depth. His description of the data is as follows:

I have attached two files, one with the AMANDA temperature data and one with the IceCube data points. The columns are:

In amanda_temp_data.txt:

1) temperature [C]
2) -depth [m]  NB you have to subtract 8.6 m from the depth!!!

In i3temps.txt:

1) string
2) nearest DOM
3) nearest breakout
4) z coordinate [m]
5) depth [m]
6) temperature [C]

For i3temps.txt click here.
For amanda_temp_data.txt click here.

The data files where combined into one larger data file with this python script. It just subtracts the 8.6 meters as mentioned by Kurt.

A cubic polynomial was fit to the above data with gnuplot. The equation is as follows:

f(x)=a*x^3+b*x^2+c*x+d

Where a,b,c,d =

a               = 1.83415e-09
b               = -1.59061e-08
c               = 0.00267687
d               = -51.0696

Here is the fit plotted on top of the actual data: