Source: NPR

Climate scientists often discuss the alarming amount of ice which is melting in the antarctic. According to an article in the 'Associated Press' titled "Climate change is more extensive and worse than once thought" an enormous amount of ice has melted since 1992 alone:

Antarctica has lost nearly 3 trillion tons of ice since 1992, enough to cover Texas nearly 13 feet (4 meters) deep, scientists reported in June. Greenland has lost more than 5 trillion tons in the same period.

Wow. Really? The author extends help in visualizing the enormous amount of ice melting by providing a metric -- namely the amount would cover the state of Texas in a depth of 13 feet of ice. My goodness. I wanted to follow up with that statement and check to see how the numbers checked out. Below is the analysis.

How large is Texas?

Texas has a land mass totaling 268,597 square miles as shown below:

Source: Google

With the area of Texas in hand, the only remaining parameter needed to find the total volume of water is the 'height'. Although, in our case, we are verifying the statement above regarding the 'height' of ice over a given area (Texas). The expression for the total volume of ice being considered in the article is shown below:

The area of Texas has already been determined by a Google search (as shown above) along with the stated value of 'height' equal to 4 meters. Also, the total volume of ice which has melted is given too. In this blog post, we are verifying the stated values contained in the excerpt. Namely, that the total volume of ice -- 3 trillion tons of ice -- would spread a layer of ice over the entire state of Texas with an height equal to 4 meters.

In order to verify the values in the statement above, we need to do unit conversions of a couple of values above to end up in uniform units. The uniform units of choice is 'meter'. Therefore, to start with, a quick search of the number of square meters in a square mile would yield the following shown below:

Source: Google

For every 1 square mile, there are 2,590,000 square meters. Now we have the area in units of square meters along with a height in units of square meters. The only remaining parameter is volume to convert into units of 'meters' -- for a volume -- cubic meters. The volume of ice is stated in the excerpt above in units of 'tons' - which is a unit of 'mass'. In order to convert from a mass to a volume, the conversion factor used is the substance's density -- the amount of mass in a given volume.

In order to determine the density of ice, we simply type into a search engine: What is the density of ice? The following appears as shown below:

Source: Google

The density of ice is 0.92 grams/cubic centimeter. Since there are 100 centimeters in a meter, then there are 100 meter x 100 meter x 100 meter (volume = length x width x height). Therefore, the density of ice is equal to (0.92 gram/ cubic centimeter) x (1,000,000 cubic centimeter/cubic meter) = 920,000 gram/cubic meter.

To convert the mass in units of 'ton' to mass in units of 'gram' the conversion factor needs to be known. Consulting a search engine with the following question: How many grams are in a ton? The answer is shown below:

Source: Google

The answer indicates that in a ton of ice, there are 907,185 grams of ice. An expression for the density of a given substance is shown below:

The density as indicated by the expression above is the amount of mass in a given volume. In our case, the density of ice gives us a conversion factor to use to convert a 'mass' of ice into a 'volume' of ice -- which is part of our intention in verifying the above statement from the news. Given that information (values) and expression for density, the volume can be obtained by dividing the 'mass' of ice by the 'density' of ice (conversion factor) as shown below:

A total of 3 trillion tons of ice was reported to have melted in a given time. But wait, where did the number in the expression above -- 2,720,000,000,000,000,000 grams -- in the numerator (number above the line in the fraction) come from? That is the converted mass of ice - 3 trillion tons - expressed in units of 'gram' rather than 'ton'. In order to use the number in the expression above, a unit conversion was needed. The conversion is shown below:

Using the determined conversion factor above of 907,185 grams to every single ton, the total amount of grams in 3 trillion tons of ice is equal to 2,720,000,000,000,000,000 grams. This is the mass which was used in the equation to determine the volume above.

Next, in order to determine the height of spreading this enormous amount of ice over the entire state of Texas, an expression from above needs to be brought up -- the height -- as shown below:

Using the area calculated above which is equal to the total size of the state of Texas, the height of the total volume of ice spread over the entire state can be determined as follows:

The answer indicates that if 3 trillion tons of ice were spread over the total state of Texas, the height of the ice sheet would be just over 4 meters -- 4.25 meter. This is in accordance with the answer above -- reported in the news!

Conclusion....

Wow. The above analysis is proof that the author is correct in their assertion of the magnitude of the terrible amount of ice which is melting in the antarctic. Furthermore, the above analysis gives us the ability to reason through the reported numbers to convince ourselves of the magnitude of the situation. Given that some readers might find this analysis mundane, for me, I reason through the content of an article by proving to myself (with my own analysis), that the number is justified to be reported. Nevertheless, the amount of ice is enormous and worth considering thinking about our own unique contribution to the scale of the issue. Eventually, the problem will have to be dealt with in the near future.

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