South Pole Firn Density

Question: Given a depth in the ice at the South Pole what is the density of the ice at that depth.

Bob Morse sent me a file containing depth and ice density data. According to him the data came from paper by Koci and Kuivinen. The paper is available here. The file he sent me is as follows:

#depth (meters)  density (Mg/m^3)
#-----           ---------
0               0.34
5               0.42
10              0.49
20              0.55
40              0.63
60              0.68
80              0.74
100             0.79
120             0.845
140             0.89
160             0.90
180             0.91
200             0.91

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. The gnuplot fit to the data is: 0.4265227+0.54027386*(1.0-exp(-0.0119678*x))

A plot of the data above with the suggested equation ( in green ) is available here:

The handbook of chemistry and physics contains a table relating ice(h)'s temperature to it's density. Note the density is in grams per cubic centimeter but grams per cubic centimeter is equal to Mega-grams per cubic meters. The data is as follows:

# temperature (deg C)   density ( gcm^-3)
#
0       0.9167
-10     0.9187
-20     0.9203
-30     0.9216
-40     0.9228
-50     0.9240
-60     0.9252
-80     0.9274
-100    0.9292
-120    0.9305
-140    0.9314
-160    0.9331
-180    0.9340

This equation:

0.916899+0.0227655*(1-math.exp(0.00761904*temp))

Fits well through the above points. Here is a plot:

If you use the temperature model described here you can start with a depth, get a temperature, and then use this model to get a density value for the ice at pole. Some python code to do this calculation is available here.

A plot of the output of calc.py looks like this: