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Friday, August 22, 2014

The Thermal Reservoir Oceans

From the free dictionary here are two terms that are often confused.

Heat sink
1. An environment capable of absorbing heat from an object with which it is in thermal contact without a phase change or an appreciable change in temperature.
2. A protective device that absorbs and dissipates the excess heat generated by a system. (my bold)

Heat reservoir
A thermal reservoir, a short-form of thermal energy reservoir, or thermal bath is a thermodynamic system with a heat capacity that is large enough that when it is in thermal contact with another system of interest or its environment, its temperature remains effectively constant.[1] It is an effectively infinite pool of thermal energy at a given, constant temperature. The temperature of the reservoir does not change irrespective of whether heat is added or extracted. As it can act as a source and sink of heat it is often also referred to a heat reservoir or heat bath.

Lakes, oceans and rivers often serve as thermal reservoirs in geophysical processes, such as the weather. In atmospheric science, large air masses in the atmosphere often function as thermal reservoirs.

The oceans are often incorrectly called heat sinks by many involved in the climate change debate.   They are more appropriately called a heat reservoir since the heat capacity of the oceans is about 1000 times greater than the atmosphere and the average temperature of the upper ocean is greater than the atmosphere.  There are also two phase changes that can be expected with the oceans, fusion or freezing near the poles and evaporation away from the poles.   I tend to cringe every time the term Heat Sink is used knowing any observations that follow are most likely flawed.  

The large thermal capacity of the oceans and lakes is not contained at their surface but rather at considerable depth.  The most stable temperature in the oceans for example is the 4 C thermocline at an average depth of around 1000 meters.  This is below the majority of surface generated mixing which is the reason for its stability.  Properties of water including the maximum density of fresh water at 4C degrees and the temperature of fusion ranging from 0C to around -2 C for salt water with around 35 grams of salt per liter of volume help maintain a fairly stable reference temperature.   In deeper fresh water lakes the 4 C density prevents them from freezing solid by allowing less dense ice to form on the surface insulating the more dense 4 C sub-surface liquid water.

Depending on the source, the oceans contain about 1.5 x 10^9 cubic kilometers of water.   Each cubic kilometer of water contains one billion cubic meters (10^9), with each cubic meter containing 1000 (10^3) liters each containing 1000 (10^3) grams.   That would be a total of approximately 1.5 x 10^24 grams of water with an average temperature of about 4 C degrees.  

How much heat is contained in that volume is a bit confusing due to the phase change potential.   If it all evaporates it would have to gain 2260 Joules per gram plus about 4.2 joules per degree increase in temperature to the evaporation point which could be lower than the standard boiling point.  For all of it to freeze it would have to release 334 Joules per gram plus about 4.2 Joules per gram as the temperature reduced to possibly -18 C for a saturated salt brine.   A fair SWAG for the effective total heat capacity for the oceans at 4 C average would be about 334 Joules per gram which happens to be equal to the effective radiant energy of a surface at 4 C degrees using the Stefan-Boltzman relationship for an ideal black body.

Typically, the specific heat capacity is used to determine how much energy would be required to change a volume of a substance by 1 C degree which for a gram of water would be about 4.2 Joules.   To raise the entire global oceans by 1 C would require about 4.2(Joules/gram)*1.5 x 10^24 grams or 6.3 x 10^24 Joules assuming no change in the rate of evaporation or freezing takes place in the process, which is unlikely for larger changes in temperature.

The SWAG estimate of total heat capacity may be relevant  to basic Greenhouse Effect considerations since the ocean reservoir effective heat capacity of 334 Joules per gram happens to equal the best estimate of the effective Down Welling Long Wave Radiation (DWLR) felt at the "surface" of the Earth.  DWLR is a bit unique to atmospheric physics.  Most other branches of physics consider the net heat flux not the difficult to manage gross heat fluxes.   While the SWAG may not have an obvious physical meaning, it does at least provide a stable, as in thermal reservoir, frame of reference.  

Hopefully some will find this bit of minutia useful.  If you happen to notice any calculation errors, please do not hesitate to comment.

Using CO2 as a Climate Reference

There is still a battle between the extreme pessimist and different degrees of optimist/realists over the impact of Greenhouse Gases, primarily CO2 - Carbon Dioxide "Climate".  Since atmospheric CO2 is one of the factors that we have reasonable good data on, it makes a reasonable good proxy or reference to relate changes in our atmosphere to changes in our "climate".  There are many other factors that can impact "climate", but most have much less recorded data.  There is another issue with what is "climate"?

UPDATE: the axis titles are swapped.

Here is a simple illustration of CO2 being used as a reference.  Since the current data should be the most reliable, the baseline for this graph is the Mauna Loa CO2 sampling period from 1959 to 2013 or all the full years, J-D, converted to a temperature anomaly form using the simple ln(CO2/CO2ref) times scaling factors of 1.6 and 3.0.  Since the natural log (ln) of a doubling of CO2 concentration would be about 0.69, the "sensitivity" would be about 1.1 C for the 1.6 scale which is about the no feedback value for CO2 all by itself and 2.1 C for the 3.0 scaling factor which is the lower end of the IPCC estimates for CO2 only.  I could have divided by the ln(2) for a direct relationship to temperature per doubling, but this way people will actually have to read in order to see what the curves mean.  Along with the two CO2 reference curves is the normally ice free ocean area surface temperature from 60S to 60N from the ERSSTv3b SST data set available at KNMI Climate Explorer.  From 1958 to Mauna Loa CO2 data is used and prior to that the Berkeley interpolated data is used.  The ERSSTv3b is shown both as monthly anomaly and in a 60 year moving average assuming 60 year averages can be considered Climate.  This assumption should reduce the tenancy to cherry pick shorter periods that might not be long enough to be called "Climate".

The 1.6lnCO2 appears to match the ocean SST very well for the 60 YMA and the 3.0lnCO2 better match the 1970 to present portion of the SST curve.  Now remember that the CO2 references would also include all the "other" factors, anthropogenic and natural.  The object of this post is to see how pessimists, optimists and realists might interpret this simple comparison.

Sunday, March 30, 2014

Dang Parasites

Willis Eschenbach had a post recently at Watts Up With That on Parasitic Losses or Parasitic Loads depending on your point of view.  Parasitic Loads are things that don't directly contribute to the desired product but make the production more enjoyable or tolerable, like A/C in your car or power brakes/steering which require energy from your engine and rob some fuel mileage where if you had large rock hard tires, no brakes and never turned, you would get great mileage once or twice but not many would enjoy the ride.

I included "rock hard tires" because soft tires with good road grip and a nice cushy suspension also reduce fuel mileage a touch and are more like like parasitic losses than loads.  Energy is knowingly diverted to produce the A/C, power brakes and steering but not the suspension or the aerodynamics of the vehicle which are designed to reduce frictional loss while acknowledging creature comfort, manufacturing cost and sex (sales) appeal.   This is one of the problems with the 100 mile per gallon car, people wouldn't buy one.  There is a trade off between efficiency and sex appeal.

Willis described latent and sensible cooling as "parasitic" losses in a typical one dimensional evaluation of a complex climate system evaluated through a radiant energy only perspective.   Possibly a better way would be a radiant efficiency perspective.  At whatever is the actual top of the atmosphere, the climate system has close to 100% radiant efficiency and in the depths of the oceans nearly 0% radiant efficiency.  If you consider the ocean surface to be "the" surface then with a temperature of 20C, input energy of 200 Wm-2, latent/sensible combined cooling of 100 Wm-2 you have a couple of choices for defining your radiant efficiency.  At first blush, 100 Wm-2 of "parasitic" loss with 200 Wm-2 input would indicate 50% radiant efficiency.  However, 20C would have a radiant energy of 418 Wm-2, which with the 200 input and 100 output leaves 118 Wm-2 of interacting energy.  That energy can be stored or returned by the atmosphere.  Since the 100 Wm-2 latent/sensible cooling decreases the actual "surface" temperature, the effective temperature of the "surface" is 518 Wm-2, so you could consider the radiant efficiency to be 418/518 or 81% efficient in only the simplistic up/down perspective. You could also consider the input 200 Wm-2 against the effective temperature and get 200/518 or 38.6% efficient which is more reasonable with respect to Carnot efficiency.  This may seem confusing, but if the temperature is stable, then the output has to equal the input meaning the selected "surface" is less efficient at losing energy which is the whole premise of the Greenhouse effect (GHE).

Then if you consider the "imbalance" of about 0.5 Wm-2, the GHE imbalance is 0.5/518 or 0.9% which is pretty much exactly where we stand.  There is a small imbalance due to the changing composition of the atmosphere and albedo changes at the "surface" or stratosphere or anywhere you would like to look for small changes.  Pick a different "surface" you get different results.  That is pretty much the GHE game, find the "surface" with the most sex appeal for your side of the argument.