A Quick Example of the Effect of Climate Change

By Hillebrand Steve, U.S. Fish and Wildlife Service [Public domain], via Wikimedia Commons

By Hillebrand Steve, U.S. Fish and Wildlife Service [Public domain], via Wikimedia Commons

[Writer’s note: Both me and my math checker missed a decimal error – my fear when I wrote this! Thanks to a comment I had to check my calculation again. I will fix the error of inland inundation below.]

Because I wanted to use the following quick calculation as a reference for a future blog post, I wanted to publish this as its own post. I think it will serve as a nice example of why we cannot underestimate even small changes to our climate.

Before getting to my calculation, I want to state here that I am not making a statement about what actions we should take to address climate change, at least not in this post. While most of the scientific community agrees there is climate change and humans play a part in it, there are those who still want to deny either one or both of those positions. While some of those scientists do also advocate changes to government policy to reduce carbon emissions, that is a separate discussion from what I am trying to accomplish today. For this post, I will assume no government actions and try to avoid advocating for such changes.

Carbon dioxide is really good at absorbing the infrared wavelengths the Earth emits. If one looks at the blackbody radiation curve of the Earth and the wavelengths absorbed by carbon dioxide, they match nicely. Yes, water, methane, and other gases also absorb various wavelengths, but carbon dioxide has a couple of wavelength peaks all to itself. This means the more carbon dioxide in the atmosphere, the more likely a photon will be absorbed by the carbon dioxide and thus the energy retained on Earth. This is pretty well known, with papers back to the 1950s showing this. In fact, sensors on most satellites ignore these bands knowing there won’t be much visible at those wavelengths anyway.

One of the people often cited by deniers is Anthony Watts. Watts was a TV meteorologist turned climate science denial blogger who, like what I am going to do here, uses rudimentary tools such as Excel and a scientific calculator to “refute” scientific papers published on climate. Other science bloggers are usually quick to show how his analyses are weak and even sometimes misleading, but for today I am going to use an often-cited number on Watts’s blog.

Watts and others like to point to the pause in temperatures as one indication that the effects won’t be as bad as many of the scientific papers predict. The problem is trying to predict where the energy will go. Will it go to the air? The ocean? Phase change of water (melting ice and evaporating water)? It will probably do all of these things, but to what degree in each? The approximate decadal step of the temperature increases show it is probably not constant where the energy gets stored. Let’s use Watts’s prediction that the Earth will warm by about 1.2 degrees Celsius by 2100. What happens to the oceans if the water warms by a similar amount? Here are my assumptions:

  • Assuming the ocean to be a uniform temperature of 17° C. This assumption isn’t a huge deal since water’s density from about 4° C to at least 35° C varies pretty uniformly—meaning the density decreases (and thus water’s expansion) are pretty constant through those temperatures.
  • I am using volume, surface area, and coastal length data from NASA sources.
  • For the coastal profile, I am assuming all coastline to be a uniform 0.5-89.5-90 triangle. Obviously some coasts are steeper while others much less steep. Feel free to comment on that assumption.
  • For the density change, I am using the density change for fresh water. While it could be a small bit different for salt water, it should be a pretty close change. Because I am concerned with the change and not the actual density, it should be sufficient to get a good estimate of my numbers.
  • The ocean level changes do not account for local tidal effects, glacial melting, or any other effects. This is simply the expansion of water due to increasing in temperature.
  • For simplicity, I am using a 1.0° C change to ensure I am being conservative on Watts’s estimate.

The volume change of the ocean, if increasing from 17° C to 18° C, is about 0.0179%. If the ocean were in a container with high sides—like if we built walls on every meter of coastline to hold back any expansion inland—the ocean would be 0.66 meters higher than it is now. Where this number gets more interesting is assuming my triangle coastal profile as above, the ocean would be approximately 0.21 km [corrected] farther in from where it is today. Our world gets a lot smaller.

Some would say it is silly to assume the whole ocean would warm because the depths of the ocean are a near constant temperature. I did look at that as well. The thermocline of the ocean is roughly at 1,000 meters below the surface. Assuming the effects of increased energy retention are only felt in the layer above this mark, the inland range of the water due to expansion is still 0.16 km [corrected]. This assumes the only expansion is of the water above 1,000 meters.

This temperature change uses all of Watts’s assumptions, which leads him to the conclusion that we will warm, but less than most other predictions—or at least on the very bottom of the error bars of other predictions. Whatever one might think the cause of climate change is, we see even someone using some questionable assumptions like Watts sees at least some warming by 2100 and some pretty serious effects, such as the aforementioned constricting coastline. The effects of an expanding ocean are already being measured. We can debate what actions should be taken by governments; what cannot be ignored is our climate is changing and it will have an effect on the entire globe. That’s the science.

About Eric Hall

My day job is teaching physics at the University of Minnesota, Rochester. I write about physics, other sciences, politics, education, and whatever else interests or concerns me. I am always working to be rational and reasonable, and I am always willing to improve my knowledge and change my mind when presented with new evidence.
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11 Responses to A Quick Example of the Effect of Climate Change

  1. I’m not sure what you mean by “…all coastline to be a uniform 5-85-90 triangle.” Do you mean the slope of the shore is 5 degrees?

    For a 0.66 m rise to produce a 2,100 m change in the shoreline location, the land would need to be virtually flat. It represents a slope of approximately 0.0003%, and much less than 5 degrees.

    I do a lot of shoreline surveying, and I know of very few places where a 0.66 meter rise could produce even a 50 m change in shoreline location, let alone 2,100 m.

    • Eric Hall says:

      I just went and fixed it now. I had 2 errors – one my geology source/math checker had me change my triangle to a 0.5 degree slope as he said it should be about that. Second, your number gave me pause to say I might have done a meter to km conversion wrong and of course I did and I missed it along with my checker. Thanks for pointing it out. It drops it to 200 meters roughly when I get my decimals right.

      It is interesting to note that by my calculation that leaves us with about 124,000 km^2 less land than before. Even using 50 meters it is 31,000 km^2 less land (about the size of Belgium). It is not insignificant for sure!

  2. tomwelsh3 says:

    You may also want to revisit the first sentence in your editor’s note. Cheers…

  3. Richard Dress says:

    I am skeptical. The seas have been rising for 10000 years because the ice cap melted and the plates are adjusting.

    • Torchwood says:

      The seas have risen and fallen before: paleo archaeology has a vast amount of information on ice ages. The last one was about 10,000 years ago, and 40,000 years before that, and so on. The effects are clearly marked on the land and sea bed.

      There is no question that the seas rise and fall. The geological record is there to see all over the planet.

      Research reference “Ice Age” in the library and on the inernet.

      What happens next is the real question.

  4. John Doherty says:

    A well meaning and intentioned, if not proof-read, article. However, in a world where weather forecasters at best predict/estimate/guess to 5 days hence, I am amazed that a body of scientist exists that can accurately calculate man’s influence on a global scale AND naysay any fellow scientist that disagrees. I don’t deny climate change but keep an open mind as to the causes and do see the benefit for a certain cohort in attributing it to mankind. This jury member is still out.

  5. Jack Hagerty says:

    So how well do your calculations compare with actual measurements? That’s the only true test of a climate model since we can’t do blinded, variable-controlled experiments on climate. With all of the warming the past 50 years, how much coastline has Florida lost? Have you taken into account that a warmer atmosphere, in addition to making the oceans expand, also can hold more water vapor in suspension? These two effects work in opposite directions tending to cancel each other out, although I have no idea which is dominant.

  6. Jack Hagerty says:

    Maybe it’s too late in the day, but I just read through your linked blog entry and it made no sense at all to me. It sounds like you’re saying the concept of relative humidity is wrong? The ability of air to hold a volume of water depends on its temperature. The warmer the air the greater volume of water a given volume of air can suspend before it hits the dew point. What am I missing?

    • Eric Hall says:

      Air can contain much more vapor than the amount when it hits its dew point.

      Look again at the example of the two bottles with salt and fresh water in them. You could consider another example where the water in one bottle was very cold. Even if the air above it was the same temp as the other 2, it would contain less vapor because the rate of evaporation would be lower.

      Warm air generally contains more vapor because it warms surfaces which have higher rates of evaporation.

      My point is the vapor is not just a product of the air temp, but the properties of the surfaces as well. In theory, there is no limit to how much vapor could be in the air, but because air contains solid materials and is in contact with surfaces all the time there are some practical limits.

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