Wednesday, August 3, 2011

Sea Level Rise

I will be discussing this topic in various blog entries over the next several weeks, possibly longer, as I will concentrate on tropical systems affecting my area in other blogs, as warrented.

Sea level rise is one effect of anthropogenic global warming that is both complicated and simple. It is complicated by the complexity of ice sheet behavior. Some factors, such as ice sheet lubrication by meltwater penetrating to the interface between ice and rock beneath the ice sheets have only been known about for the past few years (more on this later), changes in the geoid as ice sheets melt and the mass balance of the Earth changes as a result, isostatic rebound continuing from the prior ice age, and from today's ice sheet melting. Also potential changes in weather patterns--shifts in mean high pressure centers and storm tracks, as well as in the ENSO cycle will probably be significant in augmenting or slowing sea level rise in many areas--unfortunately confident predictions of weather pattern shifts as anthropogenic global warming proceeds are not possible as yet.

Many laypeople assume that sea level rise will be uniform. After all if you add water to the ocean, it should rise everywhere, shouldn't it? Not so. The ice sheets of Greenland and Antarctica contain quadrillions of tons of mass, and have significant gravitational effects. If, for example, the Greenland Ice Sheet melted completely away tomorrow, global sea level would rise on average 23 feet. However, because gravitational attraction would be reduced near where the Greenland Ice sheet used to be, sea level would rise considerably less near Greenland, and considerably more at the antipode relative to Greenland. It could be that sea level rose 18 feet near Greenland, and 28 feet at Greenland's antipode. (Isostatic rebound of the land under the former Greenland Ice sheet would ultimately reduce this effect). Since the West Antarctic Ice sheet is near Greenland's antipode, and contains enough ice to raise sea levels by 16 feet, this gravitational effect would be mostly counterbalanced if it melted simultaneously, and most of the globe would experience sea level rises between 36 and 42 feet.

A good illustration of the non-uniformity of sea level rise is shown in the map below. It is perhaps unfortunate that sea level rise has been most marked in the western tropical Pacific while the North Atlantic and eastern Pacific which most of the developed world (North America and Europe) have seen sea level rises below the global average. A sea level rise of 10 mm (1 cm)/year on the northeast seaboard would concentrate minds! However, this map shows the ocean we have:

The simplicity of sea level rise is that it is inevitable. A warmer world is already resulting in temperate and tropical mountain glaciers melting everywhere (q.v.)

Mountain (alpine) glaciers do not have enough ice to raise sea levels by catastrophic amounts of course. However they do represent a significant fraction of the sea level rise occurring today. Another factor adding to sea level rise is thermal expansion as the oceans absorb heat trapped by rising concentrations of carbon dioxide, methane, and other greenhouse gases. Thermal expansion seems to be the primary driver of sea level rise at present. However, it is likely to be overwhelmed by massive melting in ice sheets during the late 21st and 22nd centuries. Recent work indicates that thermal expansion may not have played a large role in the Eemian interglacial 120,000 years ago compared to meltwater from ice sheets. However an extra few feet will just be another twist in the knife our descendants will have to face.

Sea level functions as a crude thermometer for the Earth. Sea level is determined by the temperature of the oceans, and the mass of the water the oceans contain. During the next three centuries, much of the more than 30 quadrillion tons of ice on our planet will melt. Even the East Antarctica Ice sheet. The amount of heat required to melt more than 30 quadrillion tons of ice is enormous. Enough to raise the atmospheric temperature to more than 1000 °F! While heat is absorbed by melting ice, global atmospheric and oceanic warming will be slowed. It will be much warmer, but temperatures will be livable in most places while the heat sink of ice melt operates. In 2250, St. Louis may have the average temperature of Phoenix or Miami, but it is perfectly possible to live in those cities (whether agriculture will be possible in the Midwest is another matter). The heat energy absorbed by melting ice and the warming of the oceans will both contribute to sea level rise, even as atmospheric temperatures do not rise by many tens or hundreds of degrees. The ocean depths, mostly between -4°C and 4°C, will also slowly absorb heat as it diffuses from above. (A warming of the ocean depths in future centuries, so that they were 30 °C all the way down would provoke an additional sea level rise of about 15 meters, as can be computed from this table but that won't happen as long as ice sheets exist to cool the ocean where they come in contact. In other words, not for many centuries.)

Is radiative forcing from our greenhouse gas emissions enough to remove all ice sheets from the surface of the earth?

Well let's see. Current radiative forcing by antropogenic greenhouse gas emissions is estimated to be 2.77 watts per square meter of the Earth in 2009. The surface area of the Earth is 510,072,000,000,000 square meters. This represents about 1,412,900,000,000,000 watts per second!

But wait! As MichaelSTL has reminded me, humankind has also increased aerosol emissions into the atmosphere, which reduce radiative forcing. He has generously provided the following two links, here and here.

So let's recalculate again. Using the figures for 2010 from this link courtesy of MichaelSTL, the net radiative forcing, adding the effect of aerosols, the figure of 2010 is 1.6628 W/m2. This revised figure gives us 850,000,000,000,000 watts per second for the whole surface of the Earth.

850 trillion watts, wow! But how much heat is that, really? After all, visiting Turkey in 1999, Mike and I were agog at the dollar being worth 650,000 Turkish lira, and spending 10 million Turkish lira for dinner!
Well it does collapse down. Going by this energy unit conversion table, a watt-hour (3600 watts) represents about .8598 of a kilocalorie, the heat required to increase the temperature of 1 kg of water 1 °C. 4187 watts raises one kg of water 1 °C. A kilogram of water is a liter, and there are 1,000 liters in a cubic meter, and a billion cubic meters in a cubic kilometer. Also, the melting of ice into water takes tremendous energy, as much as raising the temperature of water 80 °C! And ice is not necessarily at 0 °C--I'll assume that the average temperature of all the ice in ice sheets is -20 °C. The specific heat of ice is half that of water, so it takes 90 kcal to melt the typical kg of ice under that assumption.

So we have 850,000,000,000,000 watts per second to play with. Dividing by 4187 yields 203,000,000,000 kcal per second to play with. Dividing by 90 to melt a kilogram of ice yields enough energy to melt 2,255,000,000 kilograms of ice. Per second. This is 2,255,000 cubic meters of meltwater per second. Which is about 1 cubic kilometer every 7 minutes 23 1/3 seconds, or about 71,160 cubic kilometers of meltwater per year. Enough to melt all the ice on the surface of the Earth in 421 years. Of course this would mean no temperature increases in the atmosphere or oceans. All the heat would be absorbed by melting ice.

Of course we are not melting enough ice to yield 71,160 cubic kilometers of meltwater per year, even though our greenhouse gas emissions are trapping sufficient radiation to do so. The atmosphere and surface of the land is warming. The oceans are warming. The oceans are now our primary heat sink.

But the amount of anthropogenic greenhouse radiative forcing is increasing steadily. Current projections show it rising easily to 4, 5, and possibly 6 watts/square meter as the 21st century wears on. As temperatures rise, melting will accelerate on the margins of ice sheets, through the collapse of ice shelves in contact with warmer oceans, and acceleration of glacier movement provided by meltwater on the surface of glaciers and ice sheets working downwards to the ice/rock interface.

Rigorous scientific examination of the effects of anthropogenic global warming on sea level rise began surprisingly recently, with a paper by J. H. Mercer in 1978 on the possible collapse of the West Antarctic Ice Sheet. It would be very generous to say there was much scientific research into the effects of anthropogenic global warming on sea level in the 1960s and 1970s. If you had asked most qualified scientists back then, I suspect that they would have answered that increased snowfall on polar ice sheets would counteract the effects of melting alpine glaciers and thermal expansion. This 'consensus' was surprisingly long-lasting---after a few papers made a splash in the 1978-1981 period, research into the effects of AGW on sea levels, the hypothesis that AGW would result in major sea level rises fell into disfavor, or more accurately, neglect. This continued through the 1980s, and with some exceptions, through the 1990s. The discovery of outlet glacier acceleration in Greenland during the first years of the 2000s changed this. But that will be for a future blog entry.

Adding an interesting article about arctic sea ice during the Holocene Optimum.