Let us assume that the global temperature has risen about 0.4 ^oC over the last 100 years (from 1900-2000), possibly as a result of the anthropogenic greenhouse warming.

We do not know how much heating the ocean waters have undergone over that period. A very simple (and basically wrong) approach is: Assume that the ocean heated up at the same rate with the atmosphere or, the ocean also heated by 0.4 ^oC over 100 years.

1. How much heat did the oceans suck up?
2. How much did sea level rise as a result of this heating. Give the rate of sea level rise and the total amount of rise in 100 years. How do these numbers compare with the observed rates and observed total amount of sea level rise over the last 100 years (see handout)? Assume that your 'model global ocean' is a rectangular bucket with vertical walls with a mean depth of 4.5 km. Use the mass of the ocean to get the size of this "artificial ocean bucket".

The thermal expansion coefficient, c, of water is 25 x 10^-5 per degree centigrade. This thing is defined by oceanographers as follows:
c = 1/r (dr/dT), where r is the seawater density and T the temperature. You can rephrase this in non-differential form as c = 1/r (Dr/DT), and if you then take DT equal to 1 (expansion per degree ^oC) you will get c = Dr/r. This translates to that c equals the change in density per ^oC divided by the "original density". Now you have to convert that yourself into changes in volume!

Mass of the oceans is 1.4 10²⁴ grams of water (you can take mass equivalent to volume, or the density of seawater =1 to get the ocean volume).

True surface area of the oceans is 3.62 10¹⁸ cm² or 71 % of the earth surface area.
 
 

See the story on the warming of the oceans from 1955-1995 and compare those results with your own calculated numbers.

Go to http://www.sciencemag.org/feature/data/1046907.shl for pictures

Warming of the World Ocean

Sydney Levitus, * John I. Antonov, Timothy P. Boyer, Cathy Stephens

We quantify the interannual-to-decadal variability of the heat content (mean temperature) of the world ocean from the surface through 3000-meter depth for the period 1948 to 1998. The heat content of the world ocean increased by ~2 10²³ joules between the mid-1950s and mid-1990s representing a volume mean warming of 0.06°C. This corresponds to a warming rate of 0.3 watt per meter squared (per unit area of Earth's surface). Substantial changes in heat content occurred in the 300- to 1000-meter layers of each ocean and in depths greater than1000 meters of the North Atlantic. The global volume mean temperature increase for the 0- to 300-meter layer was 0.31°C, corresponding to an increase in heat content for this layer of ~10²³ joules between the mid-1950s and mid-1990s. The Atlantic and Pacific Oceans have undergone a net warming since the 1950s and the Indian Ocean has warmed since the mid-1960s, although the warming is not monotonic.

National Oceanographic Data Center/National Oceanic and Atmospheric Association (NODC/NOAA), E/OC5,

1315 East West Highway, Silver Spring, MD, 20910, USA.

 E-mail: slevitus@nodc.noaa.gov