1. 1 Global Climate: Estimating How Much Sea Level Changes when Continental Ice Sheets Form Over the last few million years, Earth has experienced numerous ice ages when vast regions of the continents were glaciated and sea level was lower as a result.. How much did sea level drop during these glaciations? Prepared for SSAC by Paul Butler – The Evergreen State College, Olympia, WA 98505 © The Washington Center for Improving the Quality of Undergraduate Education. All rights reserved. 2006 Supporting Quantitative Issues Number sense: Significant figures Algebra: Manipulating of equations Geometry: circle: area Geometry: sphere: surface area CS110: Introduction to Computer Science Core Quantitative Issue Estimation

2. 2 Changing Temperatures on Earth

3. 3 Overview At times during the Quaternary Period (approximately the last 2 million years of Earth history), glaciers were much more extensive than they are now. The world’s ocean was the source of the glacial ice, and so sea level was significantly lower when the additional ice was present. As Earth still has a significant amount of ice, primarily in Greenland and Antarctica, large-scale melting of that ice would result in a significant sea-level rise. It is possible to estimate the amount of sea-level rises and falls by estimating the changes in ice volumes on land. Changes in the amount of floating ice do not affect sea level (why?). Slide 3 states the problem and discusses assumptions, estimation and significant figures. Slide 4 shows how to estimate the surface area of world oceans. Slide 5 shows how to estimate sea-level drop during glacial maxima. Slides 6 - 8 evaluate the effect of one of the underlying assumptions. Slides 9 and 10 give the assignment to submit on Bboard Digital Dropbox.

4. 4 The Problem How much did global sea-level drop during the last glacial maximum, when there was an estimated 70×10 6 km 3 of ice? In order to investigate the relationship between ice volume and sea-level, we need to make a few assumptions and use some estimates of the magnitude of quantities in the geological past. In general in such calculations, the estimates are commonly accepted values, not wild guesses; the estimates are thought to be correct to within 5 to 10%. The assumptions are made to simplify the process of calculation, including the equations that one would use. Common assumptions include: (1) not taking account of factors that have a minor effect, and (2) using simple, rather than complicated, geometries. In this estimation calculation, we will ignore the changes in water volume due to thermal expansion and contraction. We will also ignore the effects of grounded ice. And, we will work with circular ocean basins. With these assumptions, we will often work with only three significant figures. A Word about Assumptions, Estimation, and Significant Figures

5. 5 Recreate the spreadsheet below to calculate the surface area of Earth’s oceans. The surface area of a sphere (A) with radius (r) = 4πr 2. Determining the surface area of Earth’s oceans Although Earth is not a perfect sphere, it is routine in calculations such as this one to consider Earth to be a sphere with an average radius of approximately 6370 km. In addition, you may recall that oceans cover approximately 71% of Earth’s surface. Estimate of the area of Earth’s oceans, to three significant figures. Estimate of Earth’s surface area, to three significant figures.

6. 6 Recreate the spreadsheet below to calculate the drop in sea level if the ice volume at the last glacial maximum was 70 million km 3, in contrast to the current volume of 25 million km 3. Estimating global sea-level drop at glacial maxima As a first approximation, continents and ocean basins can be modeled as if the shoreline is like a seawall, i.e. the interface of land and water does not migrate laterally as sea level changes. Hence, we can use formula: height X area = volume. We will check that assumption shortly. Note: Estimates of sea-level drop during the last glacial maximum using more sophisticated models range from 100 – 135 m.

7. 7 Evaluate the assumption that the shoreline does not migrate during sea-level change To evaluate the assumption of a non-migrating shoreline, we need to estimate the area of the continental shelves as a percentage of the area of the ocean basins. If this percentage is small, then the “seawall” assumption should not create a significant error in our estimate of sea-level decrease. As the continental shelf extends to an average depth of 150 m (greater than the drop in sea level associated with the glacial maxima), we need not be concerned with the continental slope. The average width of the continental shelf is about 70 km. Hint: Here is a model for a flat, circular ocean basin and continental shelf. A circle with radius r 1 encompasses the entire basin. A circle of radius r 2 represents the area of the ocean basin, minus the area of the continental shelf. (The map is not to scale). r1r1 r2r2

8. 8 Recreate the spreadsheet below to estimate the area of the continental shelf assuming that the Earth is flat and the world’s major ocean basins are circular (as diagramed on the previous slide). Estimate of shelf area Hint: The formula for the area of a circular ocean basin on a flat Earth is: A = π r 2. Given the area of each ocean basin in Column C, solve the equation for the radius (r) and use it to find the radius of the basin models (Col. E), and then the area of the shelf (Col. F). For the area of the shelf, recall that the average width of the shelf is 70 km. Evaluate the assumption that the shoreline does not migrate during sea-level change, 2

9. 9 Trujillo, Alan P.; Thurman, Harold V., Essentials of Oceanography, 8th Edition, (c)2005. Electronically reproduced by permission of Pearson Education, Inc., Upper Saddle River, New Jersey. Evaluate the “sea wall” assumption based on the estimate of shelf area Examine the hypsographic curve show in the figure below. As the area of the continental shelf is small, relative to the size of the ocean basins, the “sea-wall” assumption does not appear to have a significant impact.

10. 10 Summary We estimated the area of the oceans based on the fact that the surface area of the Earth is comprised of 71% ocean. Using estimates of the total ice volume during the glacial maxima and what exists today, we approximated the change in sea level by dividing the change in ice volume by the total ocean area. Our sea level change estimation falls within the range of estimates given by sophisticated modeling results. By showing that the total area of continental shelves is only ~2% of the total oceanic area, we determined that our “seawall” assumption is acceptable for our estimate of sea level change.

11. 11 1.In the estimate for sea-level drop at glacial maxima, in order to assess the assumption that the shape of the continental shelf could be ignored, oceans were modeled as circles. Now, you will model the continental shelf as if it was attached to flat, circular continents. (Areas of the continents at present sea- level are given in the table below to three significant figures.) How does this value compare to what was determined for “circular” oceans, i.e. does it confirm or confound what you determined earlier? Explain your reasoning. End of Module Assignment AB 1ContinentArea (km 2 ) 2Eurasia54200000 3Africa30400000 4North America24500000 5South America17800000 6Antarctica13700000 7Oceania (inc. Australia)9010000

12. 12 2.Currently, there is approximately 25 × 10 6 km 3 of ice on Earth’s surface. Using techniques developed in this module, estimate the sea-level change that would result from melting all of this ice. 3.In describing sea-level change associated with increased ice volume during glacial maxima, the configuration of the continental shelf was simplified. Continents were modeled as if their shorelines below modern sea level were vertical cliffs. It was shown that this did not add significant error to the estimation. Is this assumption reasonable for rising sea level? Explain. 4.During the last glacial maximum (about 20,000 years ago), approximately 30% of Earth’s land surface was covered by ice. Calculate the average thickness of the ice. Use the glacial maximum ice volume given earlier in the module. Explain why the value that you calculate is likely too high. End of Module Assignment (continued)

13. 13 Data from NOAA National Oceanic and Atmospheric AdministrationNational Oceanic and Atmospheric Administration