Wednesday, May 3, 2017

Steric β, Mass, and Volume In Sea Level Calculations

Mass, volume, and density
Let's begin with the reason for today's post: "A common practice in sea level research is to analyze separately the variability of the steric and mass components of sea level. However, there are conceptual and practical issues that have sometimes been misinterpreted, leading to erroneous and contradictory conclusions on regional sea level variability" (Jorda & Gomis, Journal. of Geophysical Research: Oceans, Vol. 118, 953–963,p. 953, 2013).

And, let's refine it down to the nitty gritty: "The crucial point to be noted is that the steric component does not account for volume changes but does for volume changes per mass unit (i.e., density changes). This indicates that the steric component only represents actual volume changes when the mass of the considered water body remains constant. This is for instance the case of thermal expansions/contractions due to surface heat fluxes" (ibid).

Immediately, then, we must consider what changes "the mass of the considered water body," and how significant that change is.

In yesterday's post I wrote "Think of mass as how many molecules of seawater there are in a layer or zone, and think of volume as how far apart from one another those molecules are at a given temperature and salinity" (On Thermal Expansion & Thermal Contraction - 18).

What primarily changes ocean mass is melt water and ice bergs flowing into it from Greenland, Antarctica, and land glaciers around the globe.

Evaporation of seawater changes the ocean's mass, as does rain falling back onto the ocean surface.

By the way, that change of mass also changes the volume, but it is not steric volume change.

So, assume that after the ocean mass has been changed then becomes stable and constant for a time, only the volume can be changed by thermal factors ("the steric component only represents actual volume changes when the mass of the considered water body remains constant").

Thus, this is "... the case of thermal expansions/contractions due to ... heat fluxes."

In other words, sunlight impacting the surface of the ocean or heat radiating from the ocean does not change its mass (the number of ocean water molecules), even though any resulting change in temperature / salinity can change the ocean's volume.

The formula for that volume change (V1 = V0(1 + β ΔT) was also discussed in yesterday's post.

As a final thought, note that Jorda & Gomis, 2013 (link up-thread) did not mention gravity (The Gravity of Sea Level Change, 2, 3, 4) or ghost-water (The Ghost-Water Constant, 2, 3, 4, 5, 6, 7, 8).

Those two dynamics can change the mass and sea level on a regional basis because relocation of ocean water takes place.



  1. Excellent Dredd!
    NASA / JPL planning a 2d Gen 'GRACE' program--possibly 12/17. Getting a read on the 'underground' water and where it's ending up is interesting. See below:

    1. Mark,

      "The sea level is rising both because melting ice from land is flowing into the ocean and because seawater is expanding as it warms." - your link

      They did not say "thermal expansion was the major cause of sea level rise in the 19th and 20th centuries" as has been said in the past.


      There is no proof that "thermal expansion is the major cause of sea level rise in the 19th and 20th centuries," or that thermal expansion is the major cause of sea level change today.

      So, there is movement in the "let's base our science on exacting evidence" direction.

      The paper I referred to (Jorda & Gomis, 2013) also had a glimpse of reality in it "the case of thermal expansions/contractions".

      Notice that Dredd Blog graphs feature both thermal expansion and contraction (On Thermal Expansion & Thermal Contraction - 18) in pane four of each SLC graph.

      It is quite rare to see the common sense term "thermal contraction" because it is usually presented in "doublespeak format" in the form of "negative thermal expansion."

    2. With you Dredd (Good). Though some of the papers published by NASA just 3 years ago seem hell bent to show a relationship between rising seas and 'thermal expansion' even when their own data shows no such connection. Psst! Always check the 'givens' NASA.

      "We know this from basic physics. When water heats up, it expands."

      from here:

      Note: They need to stop by your lab. That 'given' (thermal expansion) needs some fact checking.

      Here's another:

      And another:

      "The study took advantage of the fact that water expands when it gets warmer."

      Peculiarly, two paragraphs later, we have:

      "Deep ocean warming contributed virtually nothing to seal level rise during this period."

      Part of me thinks that the models trying to predict what's occurring with a warming planet have been hopelessly inaccurate and to account for the dramatic differences being 'seen', it's an easy (though illogical)leap to latch onto inputs that 'could' be compounding what is happening i.e. something other than good old fashioned 'warming' which sends artic and land based ice back to the sea. And cynically, as these org's need to co-exist with the divisions that fund them, having a little scapegoat like thermal expansion would take some of the laser light off the burners of fossil fuel related industries who I think are the only ones to blame.

      A neat article on how glacier 'shape' influences the melt rate:

      PS Great class this week!

  2. Mark,


    Let's hope the other regular readers get it too.

    We aren't saying there is zero thermal expansion, and never have.

    We are saying that thermal expansion is not now, nor ever has been, a major contributor to either sea level rise or to sea level fall.

  3. Could be time to revisit the Dredd Blog "5.1%" value used in the past as applied to the thermal expansion contribution to SLC.

    It seems to have been gratuitous in light of these recent calculations and graphs.

    It seems to be less than 5.1% eh?

    1. randy,

      If you are in reference to: "At any rate, thermal expansion / contraction is a minor factor in sea level change (~5.1%)" (On Thermal Expansion & Thermal Contraction).


      I was being too kind to the "thermals."