Wednesday, October 17, 2012

How Fifth Graders Calculate Ice Volume

What is the difference between ice "extent" compared with ice "volume"?

One has to do with how much surface area an ice cap covers, the other has to do with how much ice volume / mass there is in that ice cap.

Be sure to notice and remember that when you read opinions about whether or not the amount of ice at the Earth's poles is decreasing or increasing, because one of those words used to describe it means "extent / area", but the other means "volume / mass."

The difference between the two concepts could not be greater when one is attempting to determine whether the amount of ice at the Earth's poles is increasing or decreasing.

In other words, if you wanted to know how much melt water would end up in the oceans if the polar ice melts, would you use formulas to calculate "area" or would you use formulas to calculate "volume / mass" of the ice cap?

Notice that concerning "extent / area" the result of that formula is expressed in square miles, but the result of the volume formula is expressed in cubic miles.

A 2 inch ice cube in the 2 inch deep ice tray of your refrigerator is illustrative; if you want to calculate the extent or area of that ice cube (length x width) it is 2 inches x 2 inches, which equals the "extent" or "area" of 4 square inches.

But you can't figure out how much water there will be if the ice melts until you know if the ice goes to the top of the tray, or is only half way to the top; half full (the length and width are both still 2 inches in either case).

We can illustrate this by calculating the full volume / mass (length x width x height) expressed as 2 inches x 2 inches x 2 inches which calculates to a volume of 8 cubic inches;.

We can illustrate this further by calculating half full, 2 inches x 2 inches x 1 inch, which is a volume of only 4 cubic inches.

With polar ice calculations we use the same formulas, except that the resulting numbers are expressed in miles or km, not in inches.

Like the ice cube tray, the same sea ice, in terms of number of square miles when the ice is as thin as a piece of paper, compared to that number of square miles of sea ice when it is a mile thick, would be radically different in terms of cubic miles, in terms of ice volume.

Volume tells how much ice there is, and therefore how much water there would be if it melts, whereas, extent does not give us the numbers we must have in order to calculate how much ice there is to melt into water.

A myth being used by deniers uses Antarctic ice extent to falsely say that Antarctic ice volume is increasing, which is false because it is impossible to determine volume using the formula for area / extent, because when calculating area / extent one does not need to consider the thickness of the ice caps.

When competent scientists determined that in fact Antarctic ice volume has been decreasing for some time, they speak in terms of thickness of the ice cap when they are calculating the volume / amount of ice:
To map the changing thickness of almost all the floating ice shelves around Antarctica, the team used a time series of 4.5 million surface height measurements taken by a laser instrument mounted on ICESat from October 2003 to October 2008. They measured how the ice shelf height changed over time ...
(NASA, emphasis added). Remember that volume is length x width x height (thickness), but also remember that extent / area is only length x width.

Elementary kids ("do you know as much as a fifth grader") know this, but deniers either do not know it, or if they do then they are trying to deceive us:
Within just a few days in September, Arctic sea ice extent reached the lowest minimum ever recorded by satellites since 1979, while at the same time, Antarctic sea ice reached the greatest extent ever recorded.
(Tucson Citizen, emphasis added; see also this). These guys in the desert are trying to tell us that a low extent in the Arctic as well as a high extent in the Antarctic inform us of the volume, i.e. the amount of ice at both locations.

Neither calculation based on extent alone can tell us about how much ice is involved at either pole, they can only tell us how much extent, how much of an area the ice covers.

If the Arctic ice extent is decreasing, that fact alone can not determine whether the volume of ice at that pole is also decreasing; because the thickness, i.e. the height of the ice must also be known to determine the volume numbers, the amount of ice.

By the same token, if the Antarctic ice extent is increasing, that alone can not determine whether the volume of ice at that pole is increasing; the thickness, the height of the ice must also be known to determine the volume numbers, the actual quantity of ice there ("The consensus says that as a whole the Antarctic ice sheet is melting").

It would be just as accurate for the desert boyz to calculate how many truck loads, using a 10 feet wide x 20 feet long truck bed, would be required to haul off all the snow that fell on a hay field 100 feet wide by 200 feet long.

Merely calculating that the extent of snow on the field is 20,000 sq. ft. (100 x 200), without also determining how many inches (height, thickness) of snow fell on that hay field, can not determine how many truck loads it will take to do the job of hauling that snow off.

Likewise, competent fifth graders and competent scientists have to consider the height, the thickness of the polar ice caps to determine the non-play pretend values of actual ice cap quantity involved.

Desert dwellers from Tucson should leave the volume of polar ice cap calculations, in both the Arctic and Antarctic, to those competent scientists who spend a lot of time there on the ground studying the two ice caps, as well as using sophisticated satellites to measure both extent AND height / thickness changes so as to determine the volume / amount of ice at each pole at any given time.

The next post in this series is here.

"He say one and one and one is three ..."

1 comment:

  1. A new study estimates 69,000,000,000 tons of ice melts a year in Antarctica: Link

    The study did not include the latest, so: "The melt in some key areas is sped up between 2006 and 2010, when the study ended," he said. "So it shows that sea level rise can be expected to change quite sharply if the melt rate continues to increase, on top of what's already happening."