Part 3 – Arctic Ice And Sea Level

Where Is the Flood?

Many years ago, Mr. Al Gore presented his prediction of a biblical-proportions flood if the arctic ice were to melt as a result of man-made global warming. Using a projected image of earth on a board, he pointed to the white ice circle around the north pole and said “if this were to go, sea levels worldwide would rise by twenty feet” and went on to demonstrate, with animated graphics, how Florida, Manhattan, Shanghai and Calcutta would all be submerged under ocean water. The presentation is available on YouTube at https://www.youtube.com/watch?v=Bu6SE5TYrCM. About 2 minutes into the video, which is the trailer of the movie Inconvenient Truth, Mr. Gore makes that famous prediction. It could happen as early as 2013 according to many “scientists”, he said. The year 2013 came and went. There has been no flood. Yet, the impact of his campaign continues to this day. Many people still believe the arctic ice will melt and come down in hoards to flood coastlines everywhere. Mr. Gore was awarded the Nobel Peace Prize after he made that claim.

When I saw the video, the first thing that came to my mind as an engineer was: the ice thickness in the Arctic Ocean averages less than 20 feet; how could it be if it is melted and spread over the entire world oceans it would create a 20-foot rise?! Some real science and math were urgently needed, I thought. So, here is some basic physics that may come as a surprise to you.

To be clear, the point is not whether the melting of the arctic ice is good or bad, that is a different debate. The point is the scientific credibility of the claim it would cause a 20-ft rise in sea levels.

Before we do the arctic ice math, let us begin with a simple example. Assume we have a small 1×2 inch rectangular cake with 1-inch icing on the top. We also have a 10X10 inch cake with no icing. If we were to skim the icing off the small cake and spread it over the big one, how much of an icing layer would we get on the big cake?

The area of the big cake is 100 square inches (10X10), 50 times the area of the small cake of 2 square inches (1X2). Simple math says the 1-inch icing on the small cake would give us 1/50th of an inch icing on the large cake (a very thin, 0.5 millimeter layer, which would be barely visible).

Let us do that in reverse, how much icing do we need on the small cake to give us 1 inch of icing on the big one? Without the utility of math, many people would not guess we have to have a column of icing 50 inches high on the small cake. But thanks to math, there is only one correct answer. Any answer other than 50 inches is false. The moral of this short story is that when a surface layer is spread from one object to another, the resulting thickness is strictly dependent on the ratio of the two areas. Please keep that in mind. The worldwide oceans are the big cake and the arctic ice is the icing on the small cake.

Now let’s get into the nitty gritty of arctic ice stuff.

There are numerous interconnected seas and bays in the arctic region; bordering Canada, Alaska, Russia, Norway, Iceland and Greenland. They are collectively called the Arctic Ocean. While it is the smallest of the oceans, it still covers 14.06 million square km.

International oceanic organizations determined the average thickness of the surface ice in the Arctic Ocean to be 2 to 3 meters. Of course, ice is thicker in some areas and thinner in others. And some spots will barely have surface ice (whales and seals have to breathe, eh!). What matters is that the average thickness is 2-3 meters (say 2.5 as an average). That is the internationally agreed-upon value. In the calculations below, I chose to use 4 meters of ice instead of 2.5, for two reasons. First, to be mathematically conservative; and second, to ensure that we do not overlook the effect of any special tall ice formations that stick out here and there in the Arctic Ocean. The extra 1.5 meters I am adding amount to 21,090 cubic km of extra ice; enough to form 21,090 glaciers and/or icebergs each of which is 1×1 km wide and 1 km high (note: 1 cubic km of ice weighs one billion tons). It is over and above the ice volume we get from the agreed-upon actual surface ice thickness. Therefore, rest assured, the 4-meter average ice thickness is very conservative, making the numbers we will arrive at impossible to dispute.

What Happens When Ice Melts

Most of us forgot a can of pop in the freezer at least once in our life, only to see it bulge or burst when it froze; because water expands by about 9% when it freezes. Considered in reverse, when ice melts back to water, the resulting water volume is 92% of the ice volume. Don’t worry, there is no test at the end! We are just having fun with the math. In the next analysis, you only need to observe two simple physical facts. I will do the math.

Science Fact 1: When ice melts, the resulting water volume is about 92% of the original ice volume. 

Science Fact 2: When ice floats on water, about 7/8th of it submerges and 1/8th stays above the surface. Have you ever heard of the tip of the iceberg? It is only about 1/8th of it.

Figure 1 shows a schematic of how the 4-meter surface ice layer behaves when it melts.

Per science fact 2, out of the 4 meters, ½ m will be above the water line. The remaining 3.5 meters will be submerged.

As can be seen in the figure, melting of the ice creates a layer of excess water that is 0.18 meters thick which will then spread onto the all the oceans, raising their level. 

                    Figure 1.   Schematic Illustration of the Melting of Arctic Surface Ice  

                    (Actual Average Thickness 2.5 m + Extra Allowance of 1.5 m = 4 m Total)

Let us see how much the worldwide sea levels will rise by. And to keep it simple, we shall not consider evaporation. Using the same calculation we used in the cake example we find:

Rise in worldwide sea level = 7 millimeters, a tad over ¼ of an inch (about 9/32 inch).

After accounting for the internationally agreed-upon ice thickness in the Arctic Ocean, PLUS assuming additional ice equivalent to 21,090 ice bodies, each of which is one cubic km, the rise in worldwide sea levels, if all this arctic ice were to melt, is 9/32 of an inch. Compare that to the 20 feet stated by global warming “scientists” and judge for yourself.

Incidentally, the presentation I referenced at the start of this Part included computer-generated images of melting ice and animated graphics of shorelines being flooded by the rising sea level. The average person does not appreciate that a computer can be programmed to create any desired visual effects. It does not mean the images are factual.

What If The 2 to 3 Meter Thickness Was Only The tip?

So far, we calculated the rise in sea level assuming the agreed-upon 2-3 meters ice thickness was the full height of the ice. Scientific prudence dictates we also examine the case where the 2-3 meters thickness refers only to the portion above the water line. It would mean the ice layer in the Arctic Ocean is 20-meters-thick (65 feet) with 2.5 meters of it above the water line (1/8^th rule). In reality, a 65-ft thick ice barrier makes it difficult, it not impossible, for marine mammals to survive. Nonetheless, we are conducting a numerical analysis for now and it is imperative we consider the extremes. On that note, I still added those extra 1.5 meters, raising the thickness from 2.5 to 4 meters above the water line. As noted before, the extra 1.5 meter allowance is equivalent to 21,090 ice bodies, each 1 km square and 1 km high, except in this case the 1 km height is all above the water line. Of course, it is impossible to have a floating ice structure in the Arctic Ocean that extends 1 km above the water line because it must extend 7 km below the surface. The deepest point in the Arctic Ocean is only 5.5 km and its average depth is only 1.2 km. It could be argued, however, that such unrealistic formation of ice is only a mathematical representation to account for the extreme case of random tall ice formations. After all, what we are doing here is to seek the truth about the worst-case scenario for arctic ice melting. With all those exaggerations, the rise in sea level should all the arctic ice melt would be about Two Inches!  

In view of the calculations we went through in this Part of the series, it is abundantly clear that regardless of what may cause all the ice in the Arctic Ocean to permanently melt, the resulting rise in sea levels worldwide cannot exceed 1 inch; more plausibly it would be less than ½ an inch and thus imperceptible. It is perplexing why would anyone go out of their way to make such a bizarre claim about a 20-ft rise in the world-wide sea levels without first checking the math.

What You Can Do

Speak up. Spread the word. Share the simple scientific truth you encounter here with as many people as you can. Don’t get swayed by the apparent consensus portrayed in the media. In essence, be a Galileo. Feel empowered to say they are all wrong. You will be right.  

If you come across a video of an island in the Pacific Ocean portrayed as being flooded by the “rising sea level”, say water cannot randomly rise around a single island in the middle of the ocean without exact similar rise at every sea shore in the world (Bernoulli’s Principle). Ask the question: where is the rise in New York City or Vancouver? Have you ever heard the pilot of your flight say “we are cruising at 30,000 feet above sea level everywhere except near one small island in the Pacific Ocean where we would be only 29,990 feet above sea level there”? IF the ocean water is truly invading the shorelines of that island, it would be because the island is sinking! That is not rocket science.

Harming the environment is despicable. Making false claims in the name of science to presumably “protect” the environment is immoral.