Wednesday, August 29, 2018

Sea Level Rise: Why We Care, Part 2


In my last post I attempted to lay the groundwork and evidence that I look to that supports the concept of anthropogenic climate change.  In this post I want to connect climate change to sea level.  That connection, in my mind, is pretty straight-forward and rests on some pretty familiar processes.  

First, though, lets review.  The fundamental idea behind climate change is that as we add greenhouse gases to the atmosphere, especially those that are long-lived (like carbon dioxide), we increase their concentration in the atmosphere.  Those gases then start doing what they are supposed to do...they begin trapping extra heat in the atmosphere.  To be clear, there is a good bit of very fair debate about what is called "sensitivity", that gets at how much warming we should expect from a given increase in the concentration of greenhouse gases.  These are critical questions to address, and I'm no expert on the details (though there are a number of excellent summaries available).  Rather I tend to trust the train of logic that I've laid out thus far...we know that gases like carbon dioxide are greenhouse gases, we know that we are actively transferring carbon from the ground into the atmosphere, and as such its reasonable to expect that this transfer is likely to influence global climate, and lead to warming.  There is also compelling analysis that suggests that we can actually observe the earth system absorbing extra heat energy.  

So lets, finally, get in to the connection to sea level.  Extra heat energy retained in the global system should lead to warming, and so we would expect to find that warming in the atmosphere, and also in the ocean.  This warming is linked to two processes that are the most important processes for driving sea level rise.  Lets walk through each in turn.

First, as ocean water warms, it expands (known as the "thermosteric effect"), and it really doesn't take much of an increase in temperature to drive meaningful sea level rise.  It is easy to see that, because the oceans are deep, the very small expansion of water expected with that small increase in temperature leads to meaningful changes in sea level.  Lets walk through this example that I use with my introductory Oceanography classes.  First, we are going to visualize an imaginary ocean is 1 meter on each side, but is 4000 m deep (the average depth, roughly, of the global ocean) - this just makes our math easier.  Our ocean sits in a basin.  Here is my hand-drawn rendition of this ocean:

We are also going to imagine that this ocean has a temperature of 4C (roughly the average temperature of the global ocean), and a salinity of 35 psu (roughly the average salinity of the global ocean).  We can then use a density calculator to estimate the density of the water in our ocean.  I come up with 1027.786 kg/cubic meter.  We need this density, because what I want to do now is calculate the total mass of water in our ocean, which we can do if we know the density and the volume of our ocean (density has a very simple definition and equation).  We've got both, and can easily come up with the mass:  4,111,144 kg.  Our ocean is heavy. 

Okay, now lets warm our ocean up by just 1C.  This isn't much, but is within the range of end of century possibilities for the global ocean.  In fact, measurements suggest that the surface of the ocean has already warmed up by around 1C since the beginning of the 20th century, some of which is likely due to anthropogenic climate change:



Its worth noting here that the ocean is FAR HARDER to warm up then the atmosphere, both because its mass is so large, and also because water has a much higher heat capacity then air.  So here is our warmer ocean:

You will note that with the temperature increase, the density of our water has gone down a bit...a very small bit...but a little.  We've expanded our water ever so slightly, so a unit volume of it weighs just a tiny bit less.  We also haven't added or removed any water from our ocean, so we have not changed the mass...and we've got the new density, so we can solve for the new volume of water again using our very simple density equation.  I come up with 4000.432 cubic meters.  Our ocean has a new volume.  Now, since our ocean is only 1 meter on a side its easy to figure out that our expanded ocean must go up by 0.43 meters due to this very small increase in temperature.  0.43 meters is roughly a foot and a half...not much relative to the depth of the ocean, but relevant when we start to think about all of the development and value that we've put right at the edge of the ocean.  By increasing the ocean's temperature just a bit, we've suddenly started to bring the ocean's into contact with a lot of value - homes, infrastructure, habitats, roads, etc. - that we never intended to be in contact with the ocean.  Its also worth noting that a foot and a half of thermosteric sea level rise is roughly consistent with end of century projections.

So that is the first big component or process connecting climate change to sea level rise.  Remember in this example we kept the mass of the ocean the same as we warmed it up.  There is another big component driving sea level projections though, one that adds new water to the ocean basins.  We will get to that one next, in Part 3.

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