Ocean Heat, From the Tropics to the Poles

The heat being captured by the increasing load of carbon dioxide and other greenhouse gases in the atmosphere is subsequently transferred into the oceans for storage. This process — global warming — has raised the temperature of the biosphere by 1°C (or more) since the late 19th century.

Heat introduced into any material body at a particular point will diffuse throughout its volume, seeking to smooth out the temperature gradient at the heating site. If heat loss from that body is slow or insignificant, then a new thermal equilibrium is eventually achieved at a higher average temperature.

Thermal equilibrium does not necessarily mean temperature homogeneity, because the body may have several points of contact with external environments at different temperatures that are held constant, or with other external thermal conditions that must be accommodated to. Equilibrium simply means stable over time.

The heat conveyed to the oceans by global warming is absorbed primarily in the Tropical and Subtropical latitudes, 57% of the Earth’s surface. The Sun’s rays are more nearly perpendicular to the Earth’s surface in those latitudes so they receive the highest fluxes of solar energy, and oceans cover a very large portion of them.

That tropical heat diffuses through the oceans and is also carried by ocean currents to spread warmth further north and south both in the Temperate zones (34% of the Earth’s surface) and the Polar Zones (8% of the Earth’s surface).

What follows is a description of a very idealized “toy model” of heat distribution in the oceans, to help visualize some of the basics of that complex physical phenomenon.

Heat Conduction in a Static Ocean

The model is of a stationary spherical globe entirely covered by a static ocean of uniform depth. The seafloor of that ocean is at a constant temperature of 4°C (39°F), the surface waters at the equator are at 30°C (86°F), and the surface waters at the poles are at -2°C (28°F). These temperature conditions are similar to those of Earth’s oceans. These temperature boundary conditions are held fixed, so an equilibrium temperature distribution is established throughout the volume in the model world-ocean. There is no variation across longitude in this model, only across latitude (pole-to-pole). (See the Notes on the Technical Details)

Figure 1 shows contours of constant temperature (isotherms) throughout the depth of the model ocean, from pole to pole. The temperature distribution is shown as a 3D surface plotted against depth, which is in a radial direction in a spherical geometry, and polar angle (from North Pole to South Pole).

Figure 2 is a different view of the temperature distribution. Three regions are noted: The Tropical Zone (from 0° to 23° of latitude, north or south) combined with the Subtropical Zone (from 23° to 35° of latitude, north or south); the Temperate Zone (from 35° to 66° of latitude, north or south); and the Polar Zone (from 66° to 90° of latitude, north or south).

The model temperature distribution is perfectly stratified — isotherms uniform with depth — in the Tropical-Subtropical Zones, from 30°C at the surface at the equator, to 4°C at the seafloor. On entering the Temperate Zones, the isotherms arc up into a nearly radial (vertical) orientation. In the small portions of the planetary surface covered by the Polar Zones the isotherms are now more horizontally stratified because the surface waters are chillier that the those at the seafloor.

Figure 3 shows the streamlines of heat flow (the temperature gradient) for this temperature distribution. At the equator the heat is conducted down from the 30°C surface to the 4°C seafloor. As one moves further away from the equator the streamlines become increasingly lateral, until they are entirely so at 35° of latitude (north or south) where the model surface waters are at 19°C. The heat flow is entirely horizontal at this latitude, which separates the Subtropical and Temperate Zones; tropical heat is being conducted laterally toward the poles. In the Polar Zones the heat flow is up from the lower depths because the surface waters are chiller than those at depth, and because there is too little temperature variation with distance along the surface to drive a lateral heat flow.

Thermally Driven Surface Currents

Much oceanic heat is distributed by currents, and many of these occur along the surface.

The average speed of the Gulf Stream is 6.4km/hr (4mph), being maximally 9kph (5.6mph) at the surface but slowing to 1.6kph (1mph) in the North Atlantic, where it widens (information from the National Oceanic and Atmospheric Administration, NOAA).

Heat-driven equator-to-poles surface currents on the model ocean were estimated from the combination of the pole-to-pole surface temperature distribution, and thermodynamic data on liquid water. (See the Notes on the Technical Details)

The pressure built up by tropical heat in the model ocean’s equatorial waters pushes surface flows northward (in the Northern Hemisphere) and southward (in the Southern Hemisphere): from a standstill at the 30°C equator; with increasing speed as they recede from the equator, being 2kph (1.3mph) where the surface waters are at 25°C (77°F); a continuing acceleration up to a speed of 2.8kph (1.7mph) at the 35° latitude (the boundary between the Subtropical and the Temperate Zones); and an ultimate speed of 3.6kph (2.2mph) at the poles.

The currents are converging geometrically as they approach the poles, so a speed-up is reasonable. Logically, these surface currents are legs of current loops that chill as they recede from the equator, plunge at the poles, run along the cold seafloor toward the equator, and then warm as they rise to the surface to repeat their cycles.

An equator-to-pole average speed for these model surface currents is 2.8kph (1.7mph). Their estimated travel times along the 10,008km surface arc (for a model world radius of 6,371km, like that of a sphericalized Earth) is 3,574 hours, which is equivalent to 149 days (0.41 year).

Greater Realities

The model world just described is very simple in comparison to our lovely Earth. Since it does not rotate, it does not skew the north-south flow of currents that — with the help of day-night, seasonal, and continental thermodynamic inhomogeneities — creates all of the cross-longitudinal air and ocean currents of our Earth.

The irregularity of seafloor depth on Earth also redirects cross-latitudinal (pole-to-pole) and cross-longitudinal bottom currents, as do the coastlines of the continents; and the very slight and subtle changes in seawater density with temperature and salinity — neither of which is distributed uniformly throughout the body of Earth’s oceans — also affect both the oceans’s volumetric temperature distributions, and the course of ocean currents.

Recall that the model ocean is bounded by constant imposed temperature conditions at its seafloor (4°C) and surface waters (a particular temperature distribution from 30°C at the equator, to -2°C at the poles). Since this model world is otherwise suspended in a void, if these boundary conditions were removed the oceanic heat concentrated at the equator would diffuse further into the watery volume, seeking to raise the temperatures of the poles and seafloor while simultaneously cooling the equatorial region. The ultimate equilibrium state would be an ocean with a constant temperature throughout its volume.

Additionally, if it is also assumed that the now “liberated” model ocean-world can radiate its body heat away — as infrared radiation into the void of space — then the entire planet with its oceanic outer shell slowly cools uniformly toward -273.16°C (-459.69°F), which is the “no heat at all” endpoint of objects in our physical Universe.

When our Earth was in its Post-Ice Age dynamic thermal equilibrium, the “heat gun” of maximal insolation to the Tropics and Subtropics warmed the oceans there; a portion of that heat was conducted and convected into the Temperate Zones and toward the Poles; where the “ice bags” of masses of ice absorbed seasonal oceanic heat by partially melting — which occurs at a constant temperature — and then refreezing. Also, the atmosphere did not trap the excess heat radiated into space. In this way cycles of warming and cooling in all of Earth’s environments were maintained in a dynamic balance that lasted for millennia.

What has been built up in the atmosphere since about 1750 is an increasing load of carbon dioxide gas and other greenhouse gases, which have the effect of throwing an increasingly heated “thermal blanket” over our planet. Now, both the heat conduction pathways and the heat convection currents, described with the use of the model, convey increasing amounts of heat energy over the course of time. As a result the masses of ice at the poles are steadily being eroded by melting despite their continuing of cycles of partial re-freezing during winter, and additional melting during summer.

Simple mathematical models can help focus the mind on the fundamental processes driving complex multi-entangled physical realities. From there, one can begin assembling more detailed well-organized quantitative descriptions of those realities, and then using those higher-order models to inform decisions regarding actions to be taken in response to those realities, if responses are necessary. This point of departure from physics plunges you into the world of psychology, sociology, economics, politics, and too often sheer madness. I leave it to another occasion to comment outside my field of expertise about all that.

Notes on the Technical Details

The cylindrically symmetric equilibrium temperature distribution for a static ocean of uniform depth, which entirely covers a spherical planet, was solved from Laplace’s equation. The temperature of the seafloor everywhere is 4°C, the surface waters at the Equator are at 30°C, and the surface waters at the poles are at -2°C. The variation of surface water temperature with respect to polar angle (latitude) is in a cosine squared distribution. Displays of the 3D surface T(r,ɵ) show isotherms down through the ocean depths at all polar angles (ɵ). The contour lines on the stream function associated with T(r,ɵ) are heat flow streamlines, the paths of the heat gradient (which are always perpendicular to the isotherms).

Bernoulli’s Theorem was applied to surface flow from the equator to the poles (no radial, nor cross-longitudinal motion) for incompressible liquid water with thermal pressure given by:

P(T°C)=[62.25kg/m-sec^2]*exp{0.0683*[T(R,ɵ)-Tp]}

for R equal to the planetary radius to the ocean surface; Tp=-2°C; and using thermodynamic data for water between 32°F (0°C) and 100°F (37.8°C) that indicates a thermal pressure equal to 62.25kg/m-sec^2 in liquid water at 0°C; and that the density of water is essentially constant at 1000kg/m^3 (for the purposes of this model) within the temperature range of the data surveyed.

Inserting P(T°C) into the Bernoulli Theorem definition of equator-to-pole lateral (cross-latitudinal) velocity gives a formula for that velocity as a function of polar angle:

v(ɵ)=±sqrt{(2*[62.25kg/m-sec^2]/[1000kg/m^3])*exp[0.0683*(Te-Tp)]*[1-exp(-0.0683*[Te-T(R,ɵ)])]}

v(ɵ)=±(1.0523m/s)*sqrt{1-exp(-0.0683*[Te-T(R,ɵ)])}

for Te=30°C, and ± for northward (in the Northern Hemisphere) or southward (in the Southern Hemisphere) surface flows.

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The Atlantic Overturning Current Is Slowing

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The Atlantic Overturning Current Is Slowing

The Atlantic Overturning Current is part of a worldwide twisted loop of ocean water, called the thermohaline cycle (thermo = heat, haline = salt), which emerges very salty and warm out of the Gulf of Mexico, travels north as a surface current along the east coast of North America, veers east in the North Atlantic toward Europe, then loops back west to a region just south of Greenland where it cools and sinks to the ocean floor – because it has become denser than the surrounding and less salty North Atlantic waters (colder water is denser than warmer water, and saltier water is denser than fresher water of equal temperature). The dense highly salted descending water then runs as a cold deep ocean current south along the east coast of South America, and continues in a complicated path along the ocean floor into the Pacific Ocean, where it warms and eventually rises to become a surface current of more buoyant less salty water. This current distributes solar heat collected by ocean waters in tropical latitudes to higher latitudes (closer to the poles).

In 2004, Peter Schwartz and Douglas Randall described the thermohaline cycle this way: “In this thousand-year cycle, water from the surface in tropical areas becomes more saline through evaporation. When it circulates to the poles and becomes cold (“thermo”), the greater density still present from higher salt (“haline”) concentration causes the water to sink to great depths. As with most large-scale geological processes, the thermohaline cycle is not thoroughly understood. Wallace Broecker has been studying the cycle for decades and, according to the December 1996 issue of Discover magazine, he has shown that the thermohaline cycle has not always been in operation, and that it has a strong effect on global climate.”

In 2003-2004, the US Department of Defense commissioned a secret study of what might be the worst possible effects of Global Warming triggering an “abrupt climate change” in the near future, in order to estimate the potential liabilities that military planning would have to consider (to maintain US security, and global power). This study was conducted during the climate-change-denying George W. Bush Administration. When the existence of the resulting report, produced by independent researchers Peter Schwartz and Douglas Randall, became publicly known there was such a public outcry (bad PR for the DOD) that the report was declassified and made publicly available.

The Schwartz-Randall report pointed to the abrupt onset of a significantly colder, dryer climate in the Northern Hemisphere as the most perilous possible consequence of Global Warming up to about 2010, because such warming (the trapping of incoming solar radiation and outgoing infrared radiation from the land and oceans, by greenhouse gases in the atmosphere) might cause the thermohaline cycle to stop. How? Global Warming causes glaciers and ice caps to melt, and such fresh (unsalted) meltwater from Greenland floods into the North Atlantic where the thermohaline current dives to the ocean floor. This fresh surface water dilutes the high salinity of the presently descending thermohaline current, making its waters less dense (less heavy) and so less likely to sink. Sufficient freshening of the thermohaline current would cause it to stop entirely, shutting off this global conveyor belt of climate-regulating oceanic solar heat.

Though abrupt climate change is a less likely and worst case scenario as compared to gradual climate change, Schwartz and Randall concluded that such an occurrence would “challenge United States national security in ways that should be considered immediately.” The climatic cooling that might occur in the Northern Hemisphere as a result of a collapse of the thermohaline cycle could be like the century-long period 8,200 years ago with temperature 5 °F (2.8 °C) colder, or the 13 century-long period 12,700 years ago with temperature 27 °F (15 °C) colder. The shift to colder climate could occur as rapidly as 5 °F (2.8 °C) of cooling per decade. So, the world could plunge into a new Ice Age within a period of twenty years. In their 2004 report, Schwartz and Randall showed data on the salinity of the North Atlantic since 1960; the trend was a steady freshening. (I wrote about the above in an article for the Internet, in July 2004).

A 2015 scientific publication of new observations on the “Atlantic Meridional Overturning Circulation” (the Atlantic part of our thermohaline cycle) concluded that “the melting Greenland ice sheet is likely disturbing the circulation.” The Phys.org news article (https://phys.org/news/2015-03-atlantic-ocean-overturning-today.html) about this study [Rahmstorf, S., Box, J., Feulner, G., Mann, M., Robinson, A., Rutherford, S., Schaffernicht, E. (2015): “Evidence for an exceptional 20th-Century slowdown in Atlantic Ocean overturning.” Nature Climate Change (the journal)] concluded:

“The scientists certainly do not expect a new ice age, thus the imagery of the ten-year-old Hollywood blockbuster ‘The Day After Tomorrow’ is far from reality. However, it is well established that a large, even gradual change in Atlantic ocean circulation could have major negative effects. ‘If the slowdown of the Atlantic overturning continues, the impacts might be substantial,’ says Rahmstorf. ‘Disturbing the circulation will likely have a negative effect on the ocean ecosystem, and thereby fisheries and the associated livelihoods of many people in coastal areas. A slowdown also adds to the regional sea-level rise affecting cities like New York and Boston. Finally, temperature changes in that region can also influence weather systems on both sides of the Atlantic, in North America as well as Europe.’ If the circulation weakens too much it can even break down completely – the Atlantic overturning has for long been considered a possible tipping element in the Earth System. This would mean a relatively rapid and hard-to-reverse change.”

On April 11, 2018, an article titled “Stronger evidence for a weaker Atlantic overturning” appeared at Phys.org (https://phys.org/news/2018-04-stronger-evidence-weaker-atlantic-overturning.html). This article notes:

“The Atlantic overturning—one of Earth’s most important heat transport systems, pumping warm water northward and cold water southward—is weaker today than any time before in more than 1000 years. Sea surface temperature data analysis provides new evidence that this major ocean circulation has slowed down by roughly 15 percent since the middle of the 20th century, according to a study published in the highly renowned journal Nature by an international team of scientists. Human-made climate change is a prime suspect for these worrying observations. There have been long debates whether the Atlantic overturning could collapse, being a tipping element in the Earth system. The present study does not consider the future fate of this circulation, but rather analyses how it has changed over the past hundred years. Nevertheless, Robinson cautions: ‘If we do not rapidly stop global warming, we must expect a further long-term slowdown of the Atlantic overturning. We are only beginning to understand the consequences of this unprecedented process—but they might be disruptive.’ Several studies have shown, for example, that a slowdown of the Atlantic overturning exacerbates sea-level rise on the US coast for cities like New York and Boston. Others show that the associated change in Atlantic sea surface temperatures affects weather patterns over Europe, such as the track of storms coming off the Atlantic. Specifically, the European heat wave of summer 2015 has been linked to the record cold in the northern Atlantic [caused by the inflow of cold Greenland meltwater] in that year—this seemingly paradoxical effect occurs because a cold northern Atlantic promotes an air pressure pattern that funnels warm air from the south into Europe.”

While the scientists are not being alarmist Jeremiahs and warning of an imminent climapocalypse as depicted in the Hollywood movie “The Day After Tomorrow,” they nevertheless make it clear that if this Global Warming caused (fossil-fuel-burning human caused) slowing of the thermohaline cycle continues to the point of a dead stop, then this would likely be a tipping point of the entire Earth System of climate leading to “a relatively rapid and hard-to-reverse change” — not for the better.

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Thirsty Invaders, Chasing Heat
19 July 2004
Manuel García, Jr.
http://www.swans.com/library/art10/mgarci18.html

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Now appearing at Counterpunch:

An Oceanic Problem: the Atlantic Overturning Current is Slowing
13 April 2017
https://www.counterpunch.org/2018/04/13/an-oceanic-problem-the-atlantic-overturning-current-is-slowing/

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Schwartz-Randall report
http://stephenschneider.stanford.edu/Publications/PDF_Papers/SchwartzRandall2004.pdf

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The Atlantic Overturning Current Is Slowing
20 April 2018
https://dissidentvoice.org/2018/04/the-atlantic-overturning-current-is-slowing/

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