South Pole Index Of Refraction

Question: Given a depth in the ice at the South Pole what is the index of refraction at that depth?

Using the Rice paper available here and the plot on page 6 a table of depth versus index of refraction data was generated. The data is as follows:

#point           depth           index
#-----           -----           -----
1               3               1.35
2               8               1.38
3               12              1.45
4               18              1.52
5               22              1.46
6               28              1.54
7               35              1.50
8               45              1.57
9               55              1.52
10              65              1.56
11              75              1.56
12              85              1.63
13              95              1.68
14              105             1.73
15              115             1.72
16              125             1.72
17              135             1.75
18              145             1.77

This data fits fairly well to an equation of the form a+b*(1-exp(c*x)). This type of equation was originally suggested by Peter Gorham. Peter's fit to the data is: 1.325 + 0.463 * (1.0 - exp(-0.0140*depth) )

It should be noted that the equation given above gives a result of an index of 1.788 in the limit which agrees fairly well with the statement in the rice paper ( page 8 ) that the index of refraction should be 1.78 in the limit.

Arconne's Formula relates ice density to the index of refraction. The formula is 1+0.845*p(z) - ( where p(z) is ice density ). If you use the Koci and Kuivinen data referred to here and Arconne's formula to transform it to an index of refraction value you get:

Note that the koci-kuivinen data is only valid until just below the firn. If calculate the density of the ice from the temperature model referred to here and the CRC density model referred to here then you get an estimate of the density of ice as follows: