Question

One prediction of global warming is the melting of global ice, which may result in coastal flooding. A criticism of this prediction is that the melting of icebergs does not increase ocean levels any more than the melting of ice in a glass of water increases the level of liquid in the glass. (a) Is this a valid criticism? Does the melting of an ice cube in a cup of water raise the level of the liquid in the cup? Why or why not? A response to this criticism is that scientists are not worried about rising ocean levels due to melting icebergs; rather, scientists are worried about rising ocean levels due to melting ice sheets that sit on the continent of Antarctica. (b) Would the melting of the ice sheets increase ocean levels? Why or why not?

Short answer

Melting of ice cubes in a cup does not raise the water level because the ice displaces water equal to its own mass. However, melting of ice sheets will increase ocean levels because they add water that was previously on land to the ocean.

Step-by-step solution

Analysing the Principle Behind the Melting Ice in a Glass

Understand that the ice already displaces water equal to its mass. According to Archimedes' principle, the water level doesn't change when the ice melts because the water made from the melted ice cube has exactly the same mass and thus volume as the water the ice cube displaced.

Applying the Principle to Icebergs

Apply the principle from step 1 to icebergs. Since icebergs are floating in the ocean, they displace an amount of water equal to their mass. When they melt completely, they turn into the same amount of water, so the overall water level remains constant.

Consider the Difference with Ice Sheets

Understand that ice sheets do not float in water but rest on land. When the ice sheets melt, they add additional water to the ocean which was previously stored on land. This extra volume contributes to the rise in sea level.

Key concepts

Melting Icebergs and Ocean Levels

When discussing global warming, a common question arises: Do melting icebergs contribute to rising ocean levels? The simple answer is no, and this can be explained by a famous principle in physics known as Archimedes' principle.

Icebergs floating in the ocean are like ice cubes in a glass of water; they have already displaced water equivalent to their mass. As they melt, they simply convert from solid to liquid, but the overall volume of water they convert into is the same as the volume they displaced when solid. This means that the melting of icebergs does not contribute to a rise in ocean levels. The mass of the iceberg, while solid and floating, is already part of the ocean's volume calculation, so its transition to liquid does not add additional volume to the ocean.

However, one cannot ignore the potential impact that the freshwater from melting icebergs can have on ocean salinity and, subsequently, on ocean currents and weather patterns.

Archimedes' Principle

Archimedes' principle, a law of physics fundamental to fluid mechanics, states that any object, partially or fully submerged in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object. This can be mathematically expressed as: \( F_b = \rho \times V \times g \), where \( F_b \) is the buoyant force, \( \rho \) is the density of the fluid, \( V \) is the volume of the fluid displaced, and \( g \) is the acceleration due to gravity.

When applied to the concept of melting ice, it tells us that when the ice is frozen and floating, it displaces a volume of water that weighs the same as the ice. Upon melting, this volume remains the same; hence, the water level does not rise. This principle is a key factor in understanding why melting icebergs do not contribute to rising sea levels; however, it does not account for ice that is not already floating in the water.

For students, visualizing this concept can be made easier with a simple experiment: Place a marked container with water and a floating ice cube under observation, and note that the water level does not change when the ice melts completely.

Melting Ice Sheets and Coastal Flooding

While melting icebergs don't raise ocean levels, melting ice sheets are a cause for concern. Unlike icebergs, ice sheets are vast expanses of ice that cover large areas of land, particularly in Antarctica and Greenland. As global warming intensifies, these ice sheets are melting at an accelerated rate.

This poses a significant problem since the melting of land-based ice adds fresh water to the oceans that was not previously part of the sea level equation. This additional water volume directly leads to increased sea levels and the risk of coastal flooding, threatening populations living near coastlines. Scientists have emphasized that it is the melting ice sheets, not icebergs, that could lead to devastating global sea level rise.

The introduction of large volumes of freshwater from ice sheets can also disrupt oceanic currents and ecosystems, demonstrating that the consequences of ice sheet melt are not limited solely to increasing sea levels but can also affect global climate patterns and marine life.