# Sea Level Rise due to Climate Change

I've been trying to make sense of the argument surrounding sea level rise and not getting very far.

Those who claim that Sea Level Rise is insignificant generally assert that we have been unable to statistically link rising Greenhouse Gas levels to rising sea levels. I assume that this is incorrect, but I do not have the knowledge to analyze this and have not heard the claim refuted before.

I would like to know whether Sea Level Rise is linked to Greenhouse Gas emissions and what the mechanisms are behind it.

• The basic idea is: Greenhouse Gas emissions -> Greenhouse effect -> global warming -> melting of ice (or less formation of new ice) -> more water in the oceans -> rising sea levels; When the SST (sea surface temperature) rises (time lag to atmosphere) the ocean water will also expand (I am not sure if this causes a significant sea level rise). However, the sea level rise will vary spatially: when the Greenland ice melts, there will be less gravitational attraction around Greenland. This leads to a lower sea level rise around Greenland compared to the South Pacific Ocean. – daniel.heydebreck Nov 21 '16 at 10:06
• @daniel.neumann I am not sure if this causes a significant sea level rise: Yes, it does. Google thermal expansion sea level rise for more information. – gerrit Nov 21 '16 at 10:29
• I highly suggest you look at this wikipedia article en.wikipedia.org/wiki/Past_sea_level – f.thorpe Jan 12 '17 at 2:51

The first part of the association is that increasing levels of greenhouse gases in the atmosphere will cause rising temperatures on earth. Here is some information on why that is so, if you are interested. Now assuming that temperatures are currently going up (they are), there are two mechanisms that will connect this to rising sea level, melting of ice on land, and thermal expansion of water

# Land Ice

As climate lawyers are quick to point out, if floating sea ice melts, it doesn't really change the level of the ocean (much) because floating ice displaces a volume equal to an equivalent mass of water. As we will see in the next part, the temperature change from ice melting and then warming will cause some changes.

Meanwhile, there is about 2.8 million cubic km of ice locked in Greenland's ice cap and 26 million in Antarctica. These two sheets, if fully melted would cause about 7m and 58m of sea level rise, respectively. They will not melt immediately; while the topic is under debate, Greenland will probably take a millennium to melt completely. Antarctica is larger, colder and more isolated from world temperatures fluctuations due to the circumpolar currents, and would probably take a much longer time to melt fully.

# Thermal Expansion of water

The density of seawater changes with temperature. Using data from this chart (Data-Table 9), the density of seawater (at 35000 ppm salinity) at 10 C is $1.0270 \frac{\text{g}}{\text{cm}^3}$ and at 15 C is at $1.0260 \frac{\text{g}}{\text{cm}^3}$. Therefore, there is an estimated $\frac{1.027-1.026}{5} = .001 \frac{\text{g}}{\text{cm}^3}$ change per degree C, or a $\frac{.001}{1.027} = .097 \%$ increase in volume for a one degree C increase in temperature from 10 C to 11 C.

Not all the earth's ocean's are at 10 C, but using this as an estimator, the $1.35 \times10^9 \text{ km}^3$ will increase by $1.31 \times10^6 \text{ km}^3$ with a 1 C increase in temperature. If you divide that by the surface area of the ocean, 510 million $\text{ km}^2$, you get an approximately 2.5 meter increase in sea level.

That calculation is not at all rigorous; deep ocean water is colder than 10 C and at lower temperatures thermal expansion is much less (just look at the linked chart to see), but it does demonstrate that there will be a detectable rise in sea level from thermal expansion of seawater as the planet heats up.

It's a harder direct relation to show that it appears. On the surface, warmer = less ice, file under "duh", but while it probably is that simple, showing a causal relation is a more difficult.

The thermal expansion aspect of the question is easy enough. Warmer air warms the ocean surface which slowly warms the ocean. About 90% of the heat trapped by man made climate change currently goes into the oceans. See here, or here. That's an enormous amount of heat, but the Oceans are large enough that the expansion and increase in temperature moves pretty slowly. About 1/3rd of the current sea level increase is attributed to thermal expansion, which works out to about 1/3rd of 1 inch every 10 years, or, roughly 1 mm per year. (Thermal expansion only).

Source.

Melting glaciers are more difficult to show a direct relation. By this source there are over 130,000 glaciers in the world, and while there is a fair bit of overlap, to properly show a causal relation, you'd need to look at individual glaciers to determine the cause. You wouldn't need to look at all 130,000, but you'd need a solid sampling to demonstrate a causal relation.

What's more, under the right conditions, glaciers can grow larger as the local weather grows warmer. Warmer weather can lead to increased snowfall, which can enable glaciers to grow, even in a warmer climate. Article on that here.

The two simplest ways to make this argument is looking at the percentage of glaciers that are melting or to look at total ice volume in those glaciers. (For the 2nd one, I'd ignore the continental ice sheets and just look at the smaller glaciers), but it can be done either way.

By this article, about 90% of glaciers are shrinking world wide. If climate wasn't changing, I'd expect that to be closer to 50%. Even when climate is changing, for example, when ice ages stop are start, those are usually driven by the Northern Hemisphere having colder summers (begins the ice age) or the Northern Hemisphere having warmer summers (ends the ice age), with the Southern Hemisphere behaving in the opposite way. That suggests to me that even during the rise or fall of ice ages, 90% of the glaciers moving in the same direction probably doesn't happen. 90% of glaciers losing ice appears to be strong evidence of being caused by climate change, but that ratio lacks statistical teeth because there's no historical data to show that 90% of the world's glaciers losing ice is unusual. It seems unusual, but it's difficult to prove.

The other avenue would be to look at the total amount of loss of ice in the world's glaciers. See page below. I didn't see a number listed anywhere, but a quick calculation, Earth's glaciers are losing on average about 60 cubic miles of ice in an average year. That's pretty significant ice loss.