Greenland Lost 9 Trillion Tons of Ice in Century

Which sounds even more serious than the original headline...

Screen Image - Science Nordic
Greenland has lost 9,000 billion tons of ice in a century

One would think that the fact that 99.7% of Greenland's ice sheet survived the 20th Century might just be more scientifically relevant than a 0.3% loss... But I guess that doesn't make for a very dramatic headline.

Here's the math...
First I converted 9 trillion tons to metric tonnes.

9,000,000,000,000 tons = 8,164,662,660,000 tonnes

Then I converted tonnes to gigatonnes.

8,164,662,660,000 tonnes = 8,165 gigatonnes

Then I converted gigatonnes of ice to cubic kilometers, assuming 1 Gt = 1 km3.
8,165 Gt ~ 8,165 km3

Note: This conversion is inexact because ice is slightly less dense than water. But it is close enough for this exercise.
Now that I roughly knew the volume of ice loss during the 20th century, I needed to know how much ice volume was still in place. I chose to rely on the USGS and their figure of 2,600,000 km3.

So now I could calculate the percentage of ice volume which survived the 20th century...
The ice volume at the onset of the 20th century should be...

2,600,000 km3 + 8,165 km3 = 2,608,165 km3

Converting to percentage surviving the 20th century...

2,600,000 km3 / 2,608,165 km3 = 0.997 = 99.7%
To put the math into perspective, I'm going to actually rely on the SkepScibots...

1 gigatonne of ice is big… Much bigger than an Olympic sized swimming pool.
So, throughout the 20th century, Greenland lost about 8,165 gigatonne ice cubes. 8,165 km3 equates to a 20 km x 20 km x 20 km cube of ice (3√ 8,165 = 20.136565). That would be one big@\$\$ cube of ice!

However, it's not even a tiny nick when spread out over roughly 1.7 million square kilometers of ice surface. That works out a sheet of ice about 5 meters thick.
2,600,000 km3 / 1,700,000 km2 = 1.53 km
The average thickness of the Greenland ice sheet is approximately 1.5 km (1,500 meters). 5 meters is obviously 0.3% of 1,500 meters.

Isopach map of Greenland ice sheet (Wikipedia). The “Lost Ice Cube” represents 8,165 cubic kilometers of ice.
From a thickness perspective, 5 meters looks like this...

Radar Cross Section of Greenland Ice Sheet (Source: Columbia University). Note that even with a vertical exaggeration of 75 x, 5 meters is insignificant.
The red line along the top of the cross section is approximately 5 meters thick. Here is an enlarged view...

While my math may not be exact, estimates of the volume of the Greenland ice sheet vary from 2.6 to 5.5 × 106 km3. The difference between 2.6 and 5.5 million cubic kilometers of ice is quite a bit larger than 9,000 gigatonnes. For that matter, GRACE derived estimates of recent (2003-2011) ice mass balance vary widely as do the glacial isostatic adjustments...
For the analyzed period, the ice mass balance of Greenland and the corresponding GIA correction are, respectively, − 256 ± 21 Gt yr−1 and − 3 ± 12 Gt yr−1 (1%) for SM09, − 253 ± 23 Gt yr−1 and − 6 ± 5 Gt yr−1 (2%) for AW13, and − 189 ± 27 Gt yr−1 and − 69 ± 19 Gt yr−1(36%) for Wu10 (table 1). At the regional scale, the ice mass estimates are more dependent on the GIA correction, especially in NE Greenland where the Wu10-GIA correction is the largest portion of the signal measured by GRACE (table 1).

From Sutterley et al., 2014
With ~±10% margins of error in modern satellite measurements of glacial mass balance and GIA accounting for up to 1/3 of the reported ice mass loss, it is truly amazing that a 0.3% reduction in the Greenland ice sheet during the 20th century can be identified with such robustness [/Sarc].