Question

Melting Greenland. Greenland is approximately \(700 \times 2400 \mathrm{km}\) in size, with an average ice cover that's about 1.5 kilometers thick. Suppose all the Greenland ice were to melt. By approximately how much would this raise the level of Earth's oceans? Assume that oceans cover \(70 \%\) of Earth, and that water and ice are approximately the same density. (Hint: Dividing the volume of melted water by the surface area of the oceans will tell you how much the ocean depth will increase.)

Short answer

The sea level would rise by about 7.06 meters.

Step-by-step solution

Calculate the Volume of Ice

First, calculate the volume of ice in Greenland. The volume is the area of the base multiplied by the height. The area is approximately \( 700 \times 2400 \) km², and the average height (thickness) of the ice is 1.5 km. So, the volume \( V \) of the ice is:\[V = 700 \times 2400 \times 1.5 \text{ km}^3 = 2,520,000 \text{ km}^3.\]

Calculate the Surface Area of the Oceans

Determine the surface area of the oceans. The Earth's surface area is about 510 million km². Since oceans cover 70% of Earth, the ocean surface area \( A \) is:\[A = 0.7 \times 510,000,000 \text{ km}^2 = 357,000,000 \text{ km}^2.\]

Calculate the Rise in Sea Level

To find the increase in ocean depth, divide the volume of melted ice by the surface area of the oceans. Use the formula:\[\text{Rise in Sea Level} = \frac{V}{A} = \frac{2,520,000}{357,000,000} \text{ km}\]Calculating this gives:\[\frac{2,520,000}{357,000,000} \approx 0.00706 \text{ km} = 7.06 \text{ meters}.\]

Conclusion

The resulting sea level rise if all the Greenland ice were to melt is approximately 7.06 meters.

Key concepts

Melting Greenland Ice

The ice sheet in Greenland is vast and integral, composed of a massive volume that has global significance, especially when considering climate change and sea-level rise. Greenland's massive ice sheet measures approximately 700 kilometers wide and 2400 kilometers long, with an average thickness of about 1.5 kilometers. This extent and thickness result in a large volume of ice that, if melted, would have a consequential impact on the Earth's oceans.

The key issue here is what happens to this ice as it melts due to global temperature increases. As the ice melts, it turns into water, contributing to the increase in sea levels worldwide. The density similarity between ice and water simplifies calculations, allowing us to estimate the impact of this meltwater on global sea levels directly.

Mathematically, to understand the implications, we calculate the volume of this ice using the formula for the volume of a rectangular prism (volume = area × height). The estimated volume of Greenland's ice, based on the given dimensions, is approximately 2,520,000 cubic kilometers. This ice, once melted, represents a significant input to the global ocean's water balance.

Ocean Volume Calculation

Calculating how melted ice contributes to sea-level rise involves determining how this new water volume interacts with the existing volume of the Earth's oceans. The volume of additional water from Greenland is derived from its ice sheet - approximately 2,520,000 cubic kilometers, which is a staggering amount.

When this volume is added to the world's oceans, which already contain about 1.332 billion cubic kilometers of water, it might seem minimal initially. However, the redistribution of this volume is key, as it raises concerns about rising sea levels affecting human habitats, coastal ecosystems, and weather patterns.

Overall, by dividing this massive volume of water over the entire ocean surface area, we gain insight into how much sea levels could rise globally. This small increase in ocean volume may have significant local effects, especially in low-lying coastal regions. Understanding this redistribution helps underline the importance of addressing and mitigating climate change impacts.

Earth's Ocean Surface Area

The Earth's oceans cover approximately 70% of the planet, with a total ocean surface area estimated at 357,000,000 square kilometers. This vast area plays a crucial role in moderating Earth's climate, supporting diverse ecosystems, and serving as a key factor in determining sea-level rise from melting ice.

To appreciate the impact of Greenland ice melting on sea-level rise, one must calculate the sea-level increase from the additional water volume distributed evenly across this oceanic expanse. Essentially, the formula for calculating the rise involves dividing the volume of added water by the ocean surface area.

This calculation results in a theoretical rise of approximately 7.06 meters. Such a rise might have widespread implications, affecting coastal cities, contributing to more frequent flooding, and altering marine and terrestrial ecosystems globally.

These considerations emphasize why the surface area of the Earth’s oceans is a fundamental component in models predicting sea-level changes and why it's critical to include them in environmental strategies and discussions about climate action.