How Sea Level Rises: A Tutorial

Summary.  Among the documented effects of global warming has been a rise of the average sea level around the globe since 1900.  This post explains, in tutorial fashion, how this happens.

First, the water in the oceans expands in volume as its temperature increases.  Expansion is constrained to occur only in the upward direction, leading to sea level rise.  Second, land-based glaciers and ice sheets melt from their upper surfaces as the air they contact warms above the melting point of water.  Third, ice shelves buoyed by the ocean in Antarctica melt from their lower surfaces as the ocean circulating under them warms.  All these processes contribute to observed sea level rise.  Both melting processes are expected to continue indefinitely as long as warming produces temperatures in the air and in the underlying ocean that remain above the melting point.

 

Introduction.  One of the consequences of global warming identified by climate scientists is sea level rise.  Higher levels of the oceans’ waters potentially affect shorelines and low-lying islands all around the world.

The United Nations-sponsored Intergovernmental Panel on Climate Change (IPCC), in its Fifth Assessment Report (5AR), includes the following graphic showing the extent to which the global average sea level has risen in past decades up to the present.

Global average sea level change from 1900 to the present.  Each color presents a different data set.  The red line gives satellite measurements beginning in 1993.  Shadings, when present, characterize statistical variability in the data. mm, millimeters.

Source: IPCC 5AR Working Group I; http://www.climatechange2013.org/images/report/WG1AR5_SPM_FINAL.pdf.

 

The graphic shows that since 1900 global average sea level has risen by about 200 millimeters (about 7.9 in.).  It is expected to continue rising indefinitely into the future (see below).

This post describes two main factors contributing to rising sea level, expansion due to heating and melting.

Expansion of water upon heating.  Like all forms of matter, water expands when it is heated and contracts when it is cooled.  At a temperature of 20ºC (68ºF) water expands by a factor of about 0.00020 per ºC (0.00011 per ºF).  We may think that the expansion occurs in all directions, as if the water of the ocean were in an elastic balloon.  This would have the effect of minimizing expansion in the vertical direction.  But in fact, the waters of the oceans are constrained on the bottom by the ocean floor and on the sides by shorelines, so that all the expansion occurs only upwards. 

Oceanographers have been measuring temperature changes in the ocean by depth, and find that the ocean temperature has increased in the last several decades down to depths of several hundred meters (see below).  For the sake of this discussion, if the temperature increased on average from 20ºC to 21ºC down to a depth of 700 meters (2,275 feet; defined as the “upper ocean”) expansion would cause the surface of the water to rise by 140 mm, or 5.6 in.  This simple calculation shows that an increase in surface temperature of the ocean is a contributing factor for sea level rise.

Melting of land-based ice.  Some sea ice arises by freezing of the ocean water.  This process transfers some water from liquid to solid, say as the polar winter arrives, which then melts back to the liquid during the polar summer.  Such cyclical changes in state have no net effect on sea level.

Transfer of land-based ice to the oceans, however, a one-time process, represents a net addition of water to the sea, raising its level.  The new water was not part of the ocean system before melting.   There are several sources of new ocean water.  Mountain glaciers at high elevations are melting around the world as a result of global warming.  The water courses through streams and rivers, and ultimately reaches the sea. 

Ice sheets over land masses, such as the Greenland ice sheet, melt from their upper surfaces when the air is above the freezing point.  This water penetrates gaps in the ice sheets and finds its way to the ocean.  Additionally, land mass glaciers at the interface with the sea calve icebergs as the glacier flows downhill toward the sea.  The solid ice in the icebergs and the water that it gives rise to as it melts contribute to raising the sea level.

This process can be diagrammed using the following simplified graphic:

Ice cube model for melting glaciers and ice sheets.  The ice cube melts at exactly 0ºC.  Ice cube image from www.dreamstime.com.

 

At the left in the diagram, the air temperature is below the melting point of the ice cube, so it stays solid and does not lose any mass.  The second frame shows the case for the air temperature being exactly 0ºC.  Under these conditions solid ice and liquid water, shown as the tiny white puddle at the base of the ice cube, are in equilibrium with each other.  Again the ice cube essentially remains unchanged, losing no mass. 

In the third frame the air temperature is 1ºC (33.8ºF).  Ice melts because heat contained in the air is transferred to the solid ice, providing the energy needed to melt it (see here  for further explanation of this notion).  The ice cube melts relatively slowly at this moderate air temperature, creating the small water puddle around its base and making the ice cube slightly smaller.  The ice cube will continue to melt slowly as long as the air temperature stays about 1ºC.

The fourth frame shows the case in which the air temperature is 2ºC (35.6ºF).  The ice cube melts more rapidly, because the rate of heat transfer from the air to the ice is higher.  Now the water puddle is quite large, and the ice cube has shrunk considerably in size.  The ice cube will continue to melt rapidly as long as the air temperature remains about 2ºC. 

The ice cube model can be taken to represent the melting of high-altitude mountain glaciers, land-mass ice sheets such as the Greenland ice sheet, and, indirectly, the calving of icebergs from glaciers moving into the sea; the latter movement is accelerated by global warming.  In addition some glaciers that were earlier in contact with the ocean have melted so fast that their leading edges have receded from the ocean and are now found at some considerable distances from the shoreline.

Melting of Antarctic Ice Shelves.  Ice shelves, such as are found in Antarctica, are large areas of ice that are the oceanic ends of land-based ice sheets that flow over the ocean and float on its surface.  Ice shelves are distinguished from ice sheets by the fact that they cover ocean water, rather than land.  An ice shelf is diagrammed in the graphic below:

 

                            Simplified model of an ice shelf extending over the ocean.

 

An ice shelf does not primarily melt from the upper surface.  The Antarctic region is sufficiently cold that surface melting does not occur to a significant extent.  Rather the ice shelf melts from below, by contacting the liquid ocean, whenever the water temperature is above the equilibrium melting temperature of the ocean, about -2°C (28.4°F; this lower melting point is due to the dissolved salts present in ocean water).

Melting of the ice shelf eats away at its substance from its lower surface, as shown in the following graphic:

 

Mechanism of melting of an Antarctic ice shelf from its lower surface.  Warm ocean water flows toward the shore over the ocean floor (orange arrows).  It transfers its heat to the undersurface of the ice shelf, melting it.  The water containing the melted ice remains near the upper surface because, having a lower salt content, it is less dense than the ocean water flowing in.  This newly-melted water flows back toward the bulk ocean (orange arrows).

 

The result of this melting process is to add water substance to the ocean that was not present before, raising the level of the ocean.  In addition, the ice shelf thins and recedes as melting proceeds, including breaking off of ice floes that will continue to melt.  The rate of melting gets greater as the ocean temperature becomes increasingly warmer than the melting point of ocean water. 

Ocean warming is in fact happening.  5AR estimates  that 90% of the excess heat arising from global warming is stored in the oceans.  The historical trend of the total amount of heat contained in the oceans has been rising from 1950 (the time when these measurements began) to 2010, as shown in the graphic below:

Change in the global mean upper ocean (0–700 m) heat content in joules (a unit of energy) from 1950 to 2010.  The data in different colors come from different data sets, and the shadings in the same colors represent estimates of statistical variability for the given data set.  The values along the vertical axis show the changes from a zero point assigned relative to the mean of all datasets for 1971, and have been computationally adjusted to overlap for the period 2006-2010.

Source: IPCC 5AR Working Group I; http://www.climatechange2013.org/images/report/WG1AR5_SPM_FINAL.pdf.  

 

As the heat content increases the ice shelf will melt more rapidly and more extensively.  Climate scientists expect the global ocean heat content to continue increasing, so that ice shelf melting will continue indefinitely.  As noted above, ice shelf melting can only stop if the ocean temperature remains at or below the ocean melting point for ice. 

 

Conclusion

 

There are two processes contributing to rising sea levels due to global warming, expansion of the volume of water contained in the oceans and net melting of ice mass to become liquid water.

 

Thermal expansion is a natural property of water and other liquids.  As water warms it occupies more volume.  This expansion probably occurs for several hundred meters of depth, raising the level of the surface of the ocean. 

 

Melting of glaciers and land-based ice sheets occurs primarily from their upper surfaces, as heat is transferred from the air to the ice solid, liquefying it.  Antarctic ice shelves, on the other hand, melt from below due to contact with ocean water whose temperature is above the ocean’s freezing point.  In both cases, the rate of melting increases as the temperature of the air, or the liquid ocean, respectively, becomes warmer.  Melting increases the total volume of the earth’s oceans, leading to a rise in the global average sea level.

 

Thermal expansion will cease if and when the global average temperature stops increasing, reaching a new, higher plateau value.  Enhanced melting of ice mass will continue indefinitely, however, as long as the global average temperature remains above the freezing point of ice or of ocean water.  Unfortunately, since carbon dioxide, the principal greenhouse gas, remains in the atmosphere for several centuries, even achieving near-zero annual rates of emission will only stabilize the global average temperature at some new, higher value; with current technology carbon dioxide cannot be removed from the atmosphere.  This means the average temperature of the atmosphere and of the oceans will not fall, and will likely continue to rise.  For this reason land-based ice sheets and Antarctic ice shelves will continue melting indefinitely for generations to come.  The effects on ocean shorelines around the world will be considerable and essentially permanent.

 

 

© 2014 Henry Auer

 

Modern CO2 Levels Far Exceed Any in the Past 800,000 Years

Summary.  The atmospheric CO₂ concentration has just exceeded 400 ppm, and is continuing to grow.  More importantly, contemporary CO₂ levels since the industrial revolution have always exceeded the highest levels found in the geological record for 800,000 years.  Furthermore, the rate of growth of atmospheric CO₂ levels is itself accelerating.  The excess CO₂ originates from burning fossil fuels.  Changes in CO₂ levels in the geological record, while considerable, occur on a scale roughly 60 times slower than the contemporary changes.

 

Introduction. Contemporary climate scientists have been monitoring the atmospheric concentration of carbon dioxide (CO₂), a major greenhouse gas, for many decades.  Prior to that, paleoclimate scientists, those who seek to reconstruct ancient climates using the geological record, have examined CO₂ contained in ice cores drilled in major glaciers and ice fields, among other modalities for estimating ancient CO₂ amounts.  The present measured level of atmospheric CO₂ exceeded 400 parts per million (ppm; volumes of CO₂ contained in 1 million volumes of air) for the first time last week.  The popular news media picked up on this landmark event as an indicator of a worsening trend in global warming; in fact this situation has been a dire one for some time without the human esthetic preference for a round “hundreds” number.

This post presents the contemporary record of atmospheric CO₂ and places it in the context of an extended paleoclimate record.  The present atmospheric CO₂ content and trends are indeed unprecedented for the past 800,000 years.

The Contemporary CO₂ Record.  Charles Keeling began direct measurements of atmospheric CO₂ levels in 1958 atop the Hawaiian volcano Mauna Loa, at 13,678 ft (4,169 m), in 1958.  Those measurements continue to the present day.  The site was chosen to avoid major influences of human activity in more civilized or urban settings; it is isolated in a large ocean, and not affected by large populations.  Generally, measurements taken at this location are thought accurately to reflect CO₂ emanating from at least the entire Northern Hemisphere.  The Mauna Loa record up through 2012 is shown in the following graphic. 

 

On May 9 the CO2 concentration was recorded as 400.15 ppm.

Source: Scripps Institution of Oceanography presenting data gathered at the U. S. National Oceanographic and Atmospheric Administration facility on the summit of Mauna Loa, Hawaii.  Accessed May 20, 2013.   http://keelingcurve.ucsd.edu/.

 

Two features of the graphic are important.  It shows that atmospheric CO₂ has been increasing, from about 317 ppm in 1958, to just less than 400 ppm in 2012.  It surpassed 400 ppm on May 9, 2013 (accessed May 21, 2013).  There is no evidence that the accumulation of atmospheric CO₂ is slowing down.  Second, the rate of accumulation of atmospheric CO₂ is also increasing.  A quick glance at the graphic shows that an averaged line for CO₂ accumulation is getting steeper.   Indeed, the rate of increase of CO2 concentration has grown from about 0.7 ppm per year in the late 1950s to 2.1 ppm per year during the last 10 years.  

 

(The measurements are so accurate and sensitive that they reflect seasonal fluctuations seen as annual waves, higher in the northern hemisphere winter, when green plants are quiescent and humans produce more CO when heating their homes, and lower in summer, when green plants remove CO₂ from the air and generally less fuel is used for space conditioning.)

The “Recent” Historical Record.  Now we will examine the CO₂ dating from the year 1700 CE (common era).  CO₂ concentrations for the atmosphere from times before the Mauna Loa measurements began are obtained from glacial ice cores.  As snow and ice fall onto glaciers of the Arctic and Antarctica small bubbles of air are entrapped by the solidifying ice.  Eventually the ice is solid enough that its entrapped air bubbles cannot equilibrate with the ambient atmosphere any more; the bubbles then entrap air representative of the time at which the precipitation solidified.  These air bubbles are harvested by climate scientists in time sequence by drilling ice cores, about 5 in (12.5 cm) across and capturing the bubbles as they are released in a carefully controlled laboratory environment.  The cores are layered year by year, so it is easy to enumerate the age of the bubbles.

 

The following graphic shows the atmospheric CO₂ concentration from 1700-2012 CE.  Ice core data were used for 1700-1958, and the Mauna Loa atmospheric record, as shown above, for 1958 to the present.

 

CO₂ concentrations for the period prior to and through the Industrial Revolution, from 1700-2012 CE.  Data from ice cores for 1700-1958, and from the Mauna Loa record after 1958.  This image is the same as presented in the last graphic below, in Panel B). Source: Scripps Institution of Oceanography; http://bluemoon.ucsd.edu/co2_400/co2_800k_zoom.png

 

 

The atmospheric CO₂ concentration is essentially unchanged from 1700 to 1800, showing that additions to the atmosphere from, for example, decay of vegetation and human use of firewood, was balanced by photosynthetic uptake and other processes that deplete CO₂.  But as the industrial revolution took hold after 1800, and expanded radically in the 20^th and 21^st centuries, the concentration grows higher and higher, and at more and more rapid rates, as time passes.  The emission of CO₂ into the atmosphere and its removal are no longer in equilibrium because of the additional burden of CO₂ emitted arising from burning fossil fuels to power the industrial revolution.  This is more than a simple surmise or hypothesis.  A particular physical property of the CO₂ in the atmosphere changes with time along a path that follows essentially the exact same curve with time.  This property is one that shows conclusively and without question that the added CO₂ originates from fossil fuels.  It is concluded that human activity, burning fossil fuels for energy that powers industrialization around the world, is the cause of the sharply rising CO₂ concentration in the last 160 years.

 

The Paleoclimate CO₂ Record.  Ice cores from Antarctica, extending as deep as about 9,840 ft (3000 m) provide CO₂ concentrations going back 800,000 years.  Results are shown in the graphic below.

 

 Combined results from ice cores at several locations extending from 800,000 years before the present at the left, in blue and aqua, up to the present at the right.  The orange and red points at the right are data for the Industrial Revolution, such as presented in the previous graphic.  kyBCE, thousands of years before the Common Era.

Source: U. S. National Oceanographic and Atmospheric Administration (accessed May 21, 2013).

http://www.youtube.com/watch?v=vA7tfz3k_9A&feature=player_embedded#at=203.

 

 

This dramatic image shows that atmospheric CO₂ levels oscillated over geological time scales of several hundreds of thousands of years, with many increases and decreases.  The changes, when compressed to this time scale appear to be abrupt and sudden (discussed further below).  Nevertheless, the highest concentration over this time scale is usually under about 280 ppm, and attained about 300 ppm on one excursion.  High concentrations of CO₂ would correspond with warmer climates, reflecting the greenhouse effect of the gas.  There are, furthermore, several periods below 200 ppm.

 

It is highly significant that practically the entire record for the time of the industrial revolution has higher CO₂ concentrations than found throughout the 800,000 year interval illustrated above.  Thus, although popular interest focused last week on the fact that concentrations exceeded the round number of 400 ppm, it is far more significant that CO₂ concentrations have been above levels found in the 800,000-year geological record for the entire time since the industrial revolution began.  Humanity’s burning of fossil fuels has disrupted the natural CO₂ cycle that has existed geologically for at least 800,000 years in unprecedented quantities and with unprecedented speed.

 

Contemporary CO₂ emissions vastly exceed geological emission rates.  The previous graphic includes many periods in the geological record that appear to the eye of the casual observer to show rapid emission (or depletion) rates.  Visual images can be very powerful in this regard.  But it is critical to scale the sharp changes to the very long time scales shown on the horizontal axis above.

 

This writer has consulted the raw data table for the points shown in the graphic above, and selected one period of seemingly abrupt change in CO₂ concentration, in the period spanning 128,609 and 135,603 years BP.  The results are shown in Panel A) of the graphic below. 

 

A) CO₂ concentrations obtained from Antarctic ice cores for the interval 135603-128609 years before the present (i.e., the time axis runs left-to-right from more ancient to more recent).  Each vertical line marks a 500-year interval.  Data extracted from the 800,000 year record in Luthi et al., Nature 2008, Vol. 453|doi:10.1038/nature06949. 

http://www.nature.com/nature/journal/v453/n7193/extref/nature06949-s2.xls.

B) CO₂ concentrations for the period prior to and through the Industrial Revolution, from 1700-2012 CE, compressed by this author so that the 300 year interval occupies about the same horizontal distance as it would if it were displayed in panel A) (the time axis runs left-to-right from 1700 to 2012).  This image is the same as presented in the second graphic, above. Source: Scripps Institution of Oceanography; http://bluemoon.ucsd.edu/co2_400/co2_800k_zoom.png.

 

It is seen that in fact what appears to be an abrupt change in the compressed geological image further above is in fact quite extended.  The CO₂ concentration rises from 198 to 287 ppm, or 89 ppm, over a very extended span of 6,994 years, or by 0.013 ppm/yr.

In contrast, the change in CO₂ concentration over the industrial revolution is shown in Panel B) in the graphic above.  This is in fact the identical image as shown in the second graphic of this post, covering the 310 years from 1700 to 2012 except that the time scale has been drastically shrunk so that it is about the same time scale as in the geological excerpt of Panel A) (in which each vertical line marks off 500 years).  It is immediately apparent that

a)     the chart in Panel B) starts at a CO₂ concentration near the maximum of the geological CO₂ record, about 280 ppm and climbs sharply to the 400 ppm level discussed earlier; and

b)     the rate of change of the CO₂ concentration in Panel B) is very much steeper than that found in the geological record, averaging to about 0.75 ppm/yr; this is almost 60 times more rapid than the geological change noted above.

 

Conclusion

 

This post has shown that

a)     geological changes in CO₂ levels have practically never exceeded 280 ppm, the level that existed just before humanity embarked on the industrial revolution;

b)     on a time scale relevant to human experience and lifetimes geological changes in CO₂ levels change extremely slowly, over periods of many thousands of years;

c)     physical properties of atmospheric CO₂ today show unequivocally that the excess CO₂ arose in the past century from burning fossil fuels;

d)     virtually the entire increase in contemporary CO₂ levels has resulted in concentrations so high that they have never been found in the geological record for 800,000 years;

e)     contemporary CO₂ levels continue to increase unabated and at a rate 60 times or greater than in the geological record; and

f)      the rate of growth of contemporary CO₂ levels is accelerating.

 

© 2013 Henry Auer