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Abstract and Figures

Temperature changes in the ocean water masses affect the vertical height of the water column by expansion at heating and contraction at cooling. The surface change is a function of the amount of heating and the depth of heating (or cooling). A heating of 0.55 °C as observed for the upper 100 m of the ocean surface would correspond to a sea level expansion of 9 mm. A heating of 2.0 °C would rise a 300 m water column by +10 cm, a 100 m water column by +3.5 cm and a 10 m water column by +3.5 mm. At the shore there will be no rise at all, as there is no water to expand, and the offshore expansion will not flow laterally to the shore (Thermal Expansion, Encyclopedia of Coastal Science, 2017). We will demonstrate this with a simple physical experiment (communicating vessels), which can be repeated by anyone.
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Ocean thermal expansion:
in theory and by a simple experiment
Nils-Axel Mörner1 and Stein Storlie Bergmark2
1 Paleogeophysics & Geodynamics, Stockholm, Sweden, morner@pog.nu
2 Former Ass. Prof., Univ. Agder, Grimstad, Norway, stein.bergsmark@uia.no
Abstract. Temperature changes in the ocean water masses affect the vertical height of the
water column by expansion at heating and contraction at cooling. The surface change is a
function of the amount of heating and the depth of heating (or cooling). A heating of 0.55 °C
as observed for the upper 100 m of the ocean surface would correspond to a sea level
expansion of 9 mm. A heating of 2.0 °C would rise a 300 m water column by +10 cm, a 100
m water column by +3.5 cm and a 10 m water column by +3.5 mm. At the shore there will be
no rise at all, as there is no water to expand, and the offshore expansion will not flow laterally
to the shore (Thermal Expansion, Encyclopedia of Coastal Science, 2017). We will
demonstrate this with a simple physical experiment (communicating vessels), which can be
repeated by anyone.
Keywords- Thermal Expansion, Sea Level Changes, Theory and Experiment
I. Introduction
Thermal expansion is a concept of sea level changes quite frequently discussed today. The
concept goes far back in time and was then known as steric changes in sea level caused by
change in temperature or salinity [1]. The Holocene sea level oscillations on a centennial
bases were sometimes proposed to be driven primarily by steric sea level changes [2].
Mörner showed [3] that the sea level changes were dominated by glacial eustasy up to
about 6000-5000 BP (regardless of tectonic differentiation) and thereafter was dominated by
the redistribution of water masses. When satellite altimetry commenced in 1992, the lateral
redistribution of water masses over the oceans was well monitored [4], whether caused by
lateral dislocation of water masses or by differential thermal expansion (or rather a
combination of both).
Thermal expansion became a part of the concept of global warming [5], claiming that the
general warming from 1970 to 2000 also generated a global sea level rise component due to
thermal expansion. Often it is used without basic anchoring in physical and oceanographic
facts as straightened out in the Encyclopedia of Coastal Science [6].
II. The theory of thermal expansion
The water column of the ocean varies from 0 (zero) at the shore to about 6000 m in the
abyssal. Only the upper part is susceptible for thermal expansion, however. The largest
changes are in the upper 100 to 300 m. Some heating is observed down to 700 m and even
2000 m [7].
Thermal expansion refers to the tendency of matter to change its shape, area and volume in
response to a change in temperature. The application of thermal expansion to the evaluation
of sea level changes has been discussed by several authors [6]. The accumulated effect during
a century was estimated at 5 cm by [8] and 10 cm by [3].
Figure 1. Relations among water expansion, water column affected and heating by increased
temperature (modified from [9]). Each variable has its strict frames. On a regional basis, the
heating can hardly exceed a couple of degrees. Approaching the coast, the expansion of the
water columns progressively decreases, becoming zero at the shore (red dots). Therefore,
coasts are not affected by thermal expansion of the sea [6].
In the estimate of expected sea level changes in the future, it is necessary to consider the
frames within which one have to work [9]. Figure 1 gives the relations among water
expansion, temperature and water column affected [3, 6, 9].
A rise of 0.55 °C in the upper 100 m [10] would rise sea level by +9 mm, and a rise in
temperature of 0.4 °C in the upper 700 m [11] would generate a rise of +4.5 cm (Figure 1).
Figure 2 gives the changes with depth from the open ocean to the shore at a heating of +2
°C, which is quite much and can, in reality, only affect the uppermost ocean layer. It may
therefore be regarded as an overestimate for the 2000 m depth, 300 m depth, and maybe even
the 100 m depth. The figure [6] is included to in order to illustrate the decrease in thermal
expansion towards the shore, and the absence of any sea level rise at the very shore, where
most tide gauges are located, and where changes in shore morphology and shore criteria
provide evidence of sea level changes [12].
Figure 2. Illustration of the depth dependence on thermal expansion at an assumed +2 °C rise
in ocean temperature (which is exceptionally much and only possible for the oceanic surface
layer). At the shore, the water column is zero and hence there can be no thermal expansion,
and no water is flowing coastward from the rise seaward.
III. A simple experiment
One of us (SSB) designed the following experiment (Figures 3), tested it and double-checked
it a couple of times.
1. Two bottles (A & B) were connected by an open communication at the base into two
communicating vessels (Figure 3a). They were filled with water, which – in accordance
with the law of two communication vessels was at exactly the same level in the two
bottles (Figure 3). The bottom water pressure (weight/area) is now exactly the same in
bottle A and bottle B.
2. The upper part of bottle B was heated with a hairdryer (whilst bottle A was completely
isolated from heating).
3. After heating, the water level in bottle B rose whilst the water level in bottle A remained
unchanged (Figure 3b).
Heating implies a change in volumetric mass density forcing the water level to expand and
rise in bottle B. This does not change the weight of the water in bottle B, which implies that
the water pressure (weight/area) at the bottom of bottle B remains unchanged, and still is the
same as the water pressure at the bottom of bottle A. Consequently, there is no pressure
imbalance, no water will flow between the bottles, and the water level in bottle A will remain
unchanged.
Figure 3. Bottles A and B are connected at the base into two communicating vessels and
filled with water (a). The water level is of course at the same height in the two bottles. The
upper part of bottle B is now heated with a hairdryer (whilst bottle A is completely shielded
from heating). The water level in bottle B will rise whilst the water level in bottle A remains
unchanged.
This provides an excellent experimental test of the theoretical thermal expansion irregular
distribution as a function of temperature increase and height of the water column heated as
illustrated in Figure 2 (and Figure 1, too).
The experiment is simple, costless and expressive. It can be recommended for schools, but
also for deeper climatic and sea level research at universities. Instead of our bottles, we would
recommend the use of two graduated measuring cylinders with an open connection at the
base.
IV. Conclusion
Thermal expansion is an important factor. It is often exaggerated, however. Heating of the
oceans is confined to the surface layer; i.e. the upper 100-300 mm but even reaches down to
700–2000 m. This heating is always cyclic; never linear over multi-decadal and longer
periods. The contribution to sea level changes is estimated not to exceed 10 cm by year 2100.
Whatever the thermal expansion may be in the open ocean, it continuously decreases
landwards with the decrease in water depth (i.e. the water column of expansion) and becomes
zero at the shore, where there is no water column to expand (Figure 2). There is no flow
towards the shore from the offshore water expansion (Figure 1). The theory is solid [6].
Figure 3 provides a simple experiment showing that, indeed, when two bottles are
connected at the base as communicating vessels, and one bottle is heated, the water level will
rise in this bottle but remain unchanged in the other.
References
[1] Fairbridge, R.W. (1961). Eustatic changes in sea level. Phys Chem Earth, 4, 99–185
[2] Schofield, J. (1980). Postglacial transgressive maxima and second-order transgression
of the southwest Pacific Ocean. In: N.-A. Mörner (ed.) Earth Rheology, Isostasy and
Eustasy. Wiley, Chichester, pp 517–521
[3] Mörner, N.-A. (1996). Sea level variability. Z. Geomorph. N.F., 102, 223-232.
[4] Fu, L.L. (2014). Ocean surface topography. In: E.G. Njoku (ed.) Encyclopedia of
Remote Sensing, p. 455-461, Springer.
[5] IPCC (Intergovernmental Panel on Climate Change) (1990) First assessment report –
climate change: the IPCC scientific assessment. Cambridge University Press, Oxford,
410 pp.
[6] Mörner, N.-A. (2017). Thermal expansion. Encyclopedia of Coastal Science, Springer
Intern. Publ. AG 2017, DOI 10.1007/978-3-319-48657-4_375-1
[7] Agro (2019). http://www.argo.ucsd.edu
[8] Nakibogul, S.M. & Lambeck, K. (1991) Secular sea-level changes. In: R. Sabadini, K.
Lambeck & E. Boschi (eds), Glacial isostasy, sea-level and mantle rheology. Kluwer
Academic Press, Dordrecht, pp 237–258.
[9] Mörner N-A (2011). Setting the frames of expected future sea level changes by
exploring past geological sea level records. In: D.J. Easterbrook (ed), Evidence-based
climate science, Elsevier, Amsterdam, pp 185–196.
[10] NOAA (2019). National Oceanographic Data Centre. https://www.nodc.noaa.gov (cf.
O. Humlum, http://www.climate4you.com/Text/Climate4you_May_2019.pdf).
[11] Cheng, L.-J., Zhu, J. & Abraham, J. (2015). Global upper ocean heat content estimation:
Recent progress and the remaining challenges. Atmostpheric and Ocean Science
Letters, 8 (6), 333-338.
[12] Mörner, N.-A. (2019). Biology and shore morphology: keys to proper reconstruction of
sea level changes. Journal of Marine Biology and Aquascape, 2019/020, 5 pp. Doi:
http://dx.doi.org/ 10.31579/ 26415143/JMBA.2019 /020
This paper is published in
Oceanography & Fisheries Open Access Journal
Vol. 10, no. 3, July 2019
Accessible at:
https://juniperpublishers.com/ofoaj/pdf/OFOAJ.MS.ID.555787.pdf
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Postglacial transgressive maxima and second-order transgression of the southwest Pacific Ocean
  • J Schofield
Schofield, J. (1980). Postglacial transgressive maxima and second-order transgression of the southwest Pacific Ocean. In: N.-A. Mörner (ed.) Earth Rheology, Isostasy and Eustasy. Wiley, Chichester, pp 517-521
Thermal expansion. Encyclopedia of Coastal Science
  • N.-A Mörner
Mörner, N.-A. (2017). Thermal expansion. Encyclopedia of Coastal Science, Springer Intern. Publ. AG 2017, DOI 10.1007/978-3-319-48657-4_375-1
National Oceanographic Data Centre
NOAA (2019). National Oceanographic Data Centre. https://www.nodc.noaa.gov (cf. O. Humlum, http://www.climate4you.com/Text/Climate4you_May_2019.pdf).