Where's the ice for my drink?

Thanks to subterranean channels underneath the ice, I have just received delivery of a pre-publication copy of the paper, by way of folks I cannot mention.
The paper is both better and worse that I had thought. Let me give you some quotations:

Using the data of (Cook and Vaughan, 2009), we delimited the area of five Antarctic ice shelves (Table 1), each on four separate occasions. Their combined area reduced from 33,416 km2 in the mid 1980’s to 14,098 km2 in the late 2000’s. We estimated the thickness of the lost ice using a collection of airborne ice penetrating radar measurements (Lythe and Vaughan, 2001) and satellite altimeter elevation observations (Bamber and Bindschadler, 1997) (coupled with an assumption of hydrostatic balance (Vaughan et al., 1995)) which provided between 100 and 693 independent estimates of ice thickness for each shelf. These data show that, between 1988 and 2008, the volume of Antarctic ice shelves decreased by 210 ± 27 km3 each year through episodic retreat (Table 1).

OK, so that’s the good news, I was wrong, they used satellites to do the measurements. I hadn’t thought about how they could use the ENVISAT to measure the fixed ice shelves.
So then I went to went to Table 1, and I found the bad news … which is that they can’t add. And their numbers are unbelievable. And they didn’t check the table, there’s a decimal point error in one of the figures. The last one is immaterial, but frustrating.
I’ll run through the highlights, I’ve put Table 1 and my spreadsheet here for people to check my work.
First, they give the area and the volume loss for each of 14 different individual Antarctic ice shelves. But they don’t give the thickness changes for the ice shelves. So I calculated the changes in thickness, and the thickness change error, for the fourteen ice shelves. Here are those results, in units of total change over the period of measurement:
Units_______________________________metres/15 yrs___metres/15 yrs
Item_______________________________Thickness Chg.__Thickness Err.
Filchner-Ronne ice shelf (FIL)________________8.1_____________0.1
Ross ice shelf (ROS)__________________________2.3_____________0.1
Amery ice shelf (AME)________________________13.8_____________1.5
Brunt ice shelf (BRU)_________________________8.6_____________0.9
Bach ice shelf (BAC)________________________131.3____________37.5
Moscow University ice shelf (MOS)____________81.0____________27.0
George VI ice shelf (GEO)___________________-12.1_____________3.9
Fimbul ice shelf (FIM)_______________________-7.6_____________2.7
Thwaites Glacier ice shelf (TWG)___________-123.8_____________3.8
Pine Island Glacier ice shelf (PIG)_________-90.0____________10.0
Getz ice shelf (GET)________________________-27.5_____________1.9
Venable ice shelf (VEN)____________________-240.0___________110.0
Larsen C ice shelf (LAC)____________________-12.7_____________0.8
Crosson/Dotson ice shelf (CRO)_____________-129.4_____________9.4
Now, I’m willing to believe that in fifteen years, the thickness of the Ross Ice Shelf has changed by 2.3 metres (7.5′). I’m less willing to believe that the error in that is only 10 centimetres (4″).
However, I strongly doubt that the thickness of the Venable Ice Shelf has dropped by a quarter of a kilometre. Maybe I just don’t understand ice shelf dynamics, but that seems extreme. However, I can believe the associated error …
Next, here’s their calculations for the Arctic Sea Ice.

We estimated the trend in volume of Arctic sea ice by considering the effects of changes in both area and thickness. According to ERS and Envisat satellite altimeter observations, the 1993-2001 (average wintertime) thickness of Arctic sea ice was estimated to be 273 cm (Laxon et al., 2003), the thickness decreased by 6.7 ± 1.9 cm yr-1 between 1992 and 2001 (Laxon et al., 2003), and the thickness decreased by 4.8 ± 0.5 cm yr-1 between 2003 and 2008 (Giles et al., 2009). We combined these datasets to produce a new estimate of the 1994-2008 thickness change. Published satellite microwave imager observations (Comiso et al., 2008) show that the 1996-2007 Arctic sea ice area trend was -111 ± 8 x 10^3 km2 yr-1 and, based upon our own analysis of these data, we estimate that the 1990-1999 average wintertime area of Arctic sea was 11.9 x 10^6 km2. The combined reductions in Arctic sea ice area and thickness amount to a decrease in volume of 851 ± 110 km3 yr-1 during the period 1994 to 2007, with changes in thickness and area accounting for 65 % and 35 % of the overall loss, respectively.

The problem with this is quite simple. They are using the average thickness of winter ice (2.75 metres, or about 9 feet) for their area loss calculations. But the Arctic is not losing winter ice. It’s losing summer ice, which in general is much thinner. And in particular, it’s losing area around the edges of the summer ice, which is the thinnest ice of all. So their calculations of the areal loss are overstated, likely by a factor of about 4 or more.
In addition, they are using the wintertime area for their thickness calculations. But the wintertime area is about three times the summertime area, so their calculations for the thickness loss are overstated, likely by a factor of about 1.5 or so.
These two combined mean that their total Arctic loss is overstated, and the real answer is likely about 65%/1.5 + 35%/4 = 50% of their answer, or less. If that is the case, it would reduce their loss of 746 km^3/yr down to 350 km^3/year.
Of course, this is the problem with this kind of analysis. It is very sensitive to the many assumptions made in lieu of having real data …
In that regard, I am surprised by the crudity of their Arctic assumptions. We have good data, month by month, for the area of Arctic ice. We know when the decreases in area are happening. Presumably, that is also when the decreases in thickness are happening. Given that, why just use the winter area for the calculation?
And why use the base period of 1994-2004? They say in the paper:

The full period of the observations spans 1986 to 2009; the overlap between the various datasets spans 1994 to 2004.

In the event, they use the period up to 2004 for the Antarctic sea ice, up to 2008 for the Antarctic shelf ice, and they use the period up to 2007 for the Arctic sea ice … where are the ex ante selection criteria? At a minimum, it is quite curious, particularly since we have more recent data.
Finally, simple arithmetic errors. They say the total area of the Antarctic adds up to 1,517,000 sq km. But adding their individual figures gives a total of 1,614,000 sq km. There are a number of these small errors. In total, they give a volume error of about 4% … not particularly material, but among my skills I have worked as an accountant. When I see numbers like that, numbers that don’t add up, I don’t assume that I’ve found all of the errors … they may easily conceal a larger error.
So that’s a first cut at the mania. I invite interested folks to download and take a look at Table 1, and at my spreadsheet, to see if I’ve made a foolish mistake (wouldn’t be the first time). Also, I invite comments on whether I’ve correctly analyzed the Arctic ice calculations. I ran their Arctic ice numbers, and using their assumptions, my numbers agree with theirs … but I don’t agree with their assumptions.
Thanks to the unknown hands that sent me the document,
w.