Croll on the Heating Power of Ocean Currents

Capter 2 of Croll's Climate and Time in their Geological Relations uses the Atlantic Gulf Stream to show the heating power of ocean currents. The Gulf Stream flows along the eastern coast of North America from the Caribbean to northern Europe. The heat it carries with helps moderate the climate of northern Europe. His estimate of the amount of heat transported might be a little diffucult to follow and some illumination would probably help. He starts out with a simple channel-like model of the Gulf Stream.

His units are somewhat outdated. The foot pound is the amount of energy required to lift a pound mass 1 foot against the force of gravity. The rate of flow of sea water in the channel is Q = depth * width * speed of the flow. To compute the heat capacity of a cubic foot of sea water we need to know the density of sea water and its specific heat capacity. Croll uses the density of ordinary water and assumes we know the density of sea water¹. Multiplying these values by the change in temperature gives the heat per unit volume transported away from the Caribbean. The total heat transported per day is the heat per unit volume times the volume rate of flow. Doing the math gives us the numbers cited by Croll.

Croll also makes an estimate of the rate of solar heating or the amount of heat recieved by a unit of area in a unit of time for a point on the equator at one of the equinoxes. He starts out with a value close to Pouillet's for the rate of heating at the top of the atmosphere and uses an estimate that 22% is stopped by the atmosphere. Again we get the value cited for the heat flux at the surface.

Croll notes that for the current orbit and orientation of the Earth the southern hemisphere gets more heating than the northern hemisphere which experiences milder conditions. Since the northern hemisphere is colder there is some heat transport across the equator. If we look at the ocean currents in the Atlantic near the equator we see that there is a current from the Tropics off the west coast of Africa along the equator that transfers to the east coast of South America and up into the Caribbean some of which ends up in the Gulf Stream.

Supplemental (Dec 10): ¹The value used for the volume heat capacity appears to be the one used by Croll. I used the specific heat capacity for sea water at a slightly higher temperature (20°C or 68°F) and the density of fresh water. The error seem to be negligible. The specific heat capacity for sea water is slightly less than that of fresh water since there are fewer molecules for a given weight due to the presence of the dissolved salts. The salts also increase the density of sea water slightly to 1.025 gm/cm³.