The global warming hysterics’ favorite fantasy these days is that Antarctic ice will melt due to hypothetical warming, leading to catastrophic flooding as the level of the oceans rises. It is commonly asserted that sea level will rise at least three feet by the end of the century. Put aside whether the Earth actually will warm and whether a three-foot rise would really be catastrophic. Put aside, too, any doubts about how much melting will occur even if the Earth warms by a few degrees, given that the average annual *high* temperature in Antarctica is -49 F. Does the reality of melting ice bear any mathematical relation to the oft-predicted flood scenario?

A reader who is familiar with geometry and arithmetic–which means he is not a reporter–decided to test the hysterical claim. I will reproduce his email in full:

The most recent climate alarmism is the report claiming increased ice melt in the West Antarctic glaciers, supposedly a leading indicator of a catastrophic, exponential, unstoppable rise in sea levels with devastating consequences for low lying areas and coastal cities. Irrespective of the validity and accuracy of the reported measurements of ice melt, the projection of future catastrophe is laughably implausible — and a simple analysis of the spherical geometry of the planet shows why the alarmism is entirely unwarranted.

Let’s start with the often repeated claim that we can project a sea level rise of at least 3 feet by the end of the century — 86 years from now. It is easy to calculate the volume of ice that would have to melt to produce that increased level and then compare it to the allegedly observed melt to determine how plausible the alarmism is.

To say that sea level will rise by 3 feet is to say that the nominal radius of the Earth would increase. But because of the “piling up” of water against the 30% of the Earth’s surface that is land, the average increase in radius (if there were no land against which the sea water would “pile up”) would be less than 3 feet, to a first approximation 3 * .7 = 2.1 feet. How much volume would the sphere of the Earth increase if its radius increased by 2.1 feet from ice melt? The volume of a sphere is 4/3*pi*radius(3). If we take the pre-melt radius as 4000 miles and the post melt radius as 4000 miles plus 2.1 feet, the volume increase is approximately 80,000 cubic miles. All of this, by assumption, is in the 70% of the Earth’s surface which is water to effect a three foot rise in the sea level.

So over a period of 86 years remaining until the end of the century, 80,000 cubic miles of water from ice melt would be required for a three foot rise in sea level, or about 930 cubic miles per year. Is this a lot? Or a little? Well, compared to the amounts of ice melt actually being observed from Antarctica and Greenland — and now being hyped by alarmists — it is huge.

Today’s report in the New York Times, “The Big Melt Accelerates,”

[Ed.: This is the story that Steve commented on earlier today.]is revealing — if you do the math, which, of course, they don’t. The Times report claims that 310 billion tons of water melted into the oceans from Antarctic and Greenland glaciers and another 260 billion tons, amazingly, from the 1% of the Earth’s land-based ice that is in mountain glaciers. Is the total of 570 billion tons of water from ice melt a little or a lot?Since they are measuring metric tons, that amounts to 1.25 x 10(15) pounds of water, which at 8.35 pounds per gallon is 1.5 x 10(14) gallons which, in turn, at 7.5 gallons per cubic foot is 2 x 10(13) cubic feet. At 5,280(3) cubic feet to a cubic mile we have 136 cubic miles of water or about 148 cubic miles of ice when adjusted for the expansion of water as it freezes. That’s about 12 miles square of glacier assuming on average the glaciation is 1 mile thick.

This compares to the required 930 cubic miles of water per year for 86 years to get to a sea level rise of 3 feet at the end of the century — a factor of almost 7 times what is said to be observed. Stated differently, at the new alarmingly increased level of ice melt it would take about 600 years for the purported 3 foot rise in sea level to obtain; the implied rise is 6 one-hundreds of an inch per year, or about 5.25 inches by the year 2100.

There is nothing complicated in this analysis — it’s just simple geometry and arithmetic. And it takes as given the reported observations of allegedly increased ice melt. It is patently obvious that for the catastrophic flooding massively hyped by the MSM and climate change alarmists to happen there must be a HUGE increase in glacier melt in West Antarctica and Greenland starting now and continuing. Every year that the observed ice melt does NOT increase by a factor of 7 from today’s rate of melt just requires an even greater increase in subsequent years for the alarmists’ predictions to happen. Exponential, indeed.

It seems exceedingly implausible that the rate of ice melt can accelerate over the next 86 years to produce a 3 foot rise in ocean surface levels and consequent land inundation. It would require an enormous and sustained discontinuity in the observed rate of ice melt starting immediately for this result to obtain — or else a huge future explosive and exponential rate of ice melt. If the IPCC is in fact predicting such a pattern it is extremely convenient since no dramatic presently observed ice melt is required for this prediction to be treated as “true!”

As to why the MSM and their fellow alarmists would fail to check the plausibility of these projections by offering the simple math, that is left as an exercise for the reader.

Meanwhile, at Watts Up With That?, a “sanity check” on the significance of the hysterics’ claim that “Three years of observations show that the Antarctic ice sheet is now losing 159 billion tonnes of ice each year – twice as much as when it was last surveyed.” Using a different approach, the author reaches a similar conclusion:

If one cubic kilometer of water (i.e., one gigatonne of water) is spread evenly over the entire 361 million square kilomters, the thickness of the new layer of water will be given by:

1 km³ / 361 x 106 km² = 2.78 x 10-6 meters = 2.78 microns.

Or, in terms of gigatonnes:

1 Gt x (1 km³/Gt) / 361 x 106 km² = 2.78 x 10-6 meters = 2.78 microns / Gt

That is, one cubic kilometer of water (i.e., one gigatonne of water) will add less than 3 millionths of a meter to the oceans!

From the press release, we are seeing about 159 billion tons/year of ice converted to meltwater (unless it sublimates), so the effect on sea level would be 159 x 3 millionths of a meter, or 477 millionths of meter of sea level rise per year from this. (or in other words 0.47 mm which works out to 47mm/century or ~1.85 inches/century)

For another perspective, a gigatonne of water is approximately one cubic kilometer. Frozen as ice, it would be expanded slightly, but for the purposes of perspective lets just say that is negligible. So, the ice loss per year would be 0.159 cubic kilometers.

According to the British Antarctic Survey BEDMAP2 project:

The derived statistics for Bedmap2 show that the volume of ice contained in the Antarctic ice sheet [is] 27 million km(3).

…

And so, the loss of 159 cubic kilometers of ice per year is apparently headline worthy, because at that rate of loss, it would take 169,811 years to lose all the 27 million cubic kilometers of Antarctic ice.I’m pretty sure we’ll have gone through a few ice ages by then.

Apparently many people (including “science” writers for major newspapers) don’t understand that ice has been melting and sea level has been rising for thousands of years, since the end of the last Ice Age:

Since the end of the Little Ice Age, sea level has been rising at a rate of about 7 inches per century:

No doubt the rise in sea level will continue for the foreseeable future; that is, until the onset of the next Ice Age. Which, if we are lucky, won’t be for quite a few years yet, although geologic history suggests that we may be most of the way through the current inter-glacial period, perhaps nearing its end.