Wednesday, August 28, 2019

Patterns: Conservative Temperature & Potential Enthalpy - 4

World Ocean Database (quads & layers)
I. Background

This series has focused on one of the reasons why current Ocean Heat Content (OHC) models have a fundamental flaw in their design (they use "potential temperature" instead of using Conservative Temperature, CT).

NE 10m
NE 100m
NE 1000m
NE 5500m
NE >5500m
Previously I quoted one of the scientists who helped bring about TEOS-10, the new international standard for thermodynamics of seawater (which solves that problem).

His paper that I quoted from is quite instructive as to OHC and to Potential Enthalpy, hO (McDougall, T. J., 2003: Potential enthalpy : A conservative oceanic variable for evaluating heat content and heat fluxes. Journal of Physical Oceanography, 33, 945-963).
NW 10m
NW 100m
NW 1000m
NW 5500m
NW >5500m

SE 10m
SE 100m
SE 1000m
SE 5500m
SE >5500m
His paper is so important that I will repeat the quote once again:
SW 10m
SW 100m
SW 1000m
SW 5500m
SW >5500m
"Potential temperature is used in oceanography as though it is a conservative variable like salinity; however, turbulent mixing processes conserve enthalpy and usually destroy potential temperature. This negative production of potential temperature is similar in magnitude to the well-known production of entropy that always occurs during mixing processes. Here it is shown that potential enthalpy—the enthalpy that a water parcel would have if raised adiabatically and without exchange of salt to the sea surface—is more conservative than potential temperature by two orders of magnitude. Furthermore, it is shown that a flux of potential enthalpy can be called “the heat flux even though potential enthalpy is undefined up to a linear function of salinity. The exchange of heat across the sea surface is identically the flux of potential enthalpy. This same flux is not proportional to the flux of potential temperature because of variations in heat capacity of up to 5%. The geothermal heat flux across the ocean floor is also approximately the flux of potential enthalpy with an error of no more that 0.15%. These results prove that potential enthalpy is the quantity whose advection and diffusion is equivalent to advection and diffusion of “heat” in the ocean. That is, it is proven that to very high accuracy, the first law of thermodynamics in the ocean is the conservation equation of potential enthalpy. It is shown that potential enthalpy is to be preferred over the Bernoulli function. A new temperature variable called “conservative temperature” is advanced that is simply proportional to potential enthalpy. It is shown that present ocean models contain typical errors of 0.1°C and maximum errors of 1.4°C in their temperature because of the neglect of the nonconservative production of potential temperature ... and potential temperature, rests on an incorrect theoretical foundation..."
(Patterns: Conservative Temperature & Potential Enthalpy). This is so fundamental that, for this post, I prepared some additional graphs and HTML tables to show the stable pattern of proportion between CT and hO.

II. Graphs and Appendices

Today's graphs detail the reality of McDougall's statement: "A new temperature variable called 'conservative temperature' is advanced that is simply proportional to potential enthalpy".

Look at the exact pattern of proportionality between CT and hO in today's graphs (notice that the patterns match).

That proportionality holds from the surface down to the bottom of the ocean, currents and turbulence notwithstanding.

The HTML tables are located in four appendices (Patterns: Appendix SW, Patterns: Appendix SE, Patterns: Appendix NW, Patterns: Appendix NE).

The appendices offer more depths and measurements, calculated from ~5.4 billion in situ measurements in the World Ocean Database (WOD database), that have been processed into TEOS-10 values (they also have the Absolute Salinity, SA, values that are not shown on the graphs).

The measurements come from four geographic quadrants shown on the graphic at the top of this post.

It has numbered "latitude layers" (0-17), north to south, with red lines outlining the four quadrants (NE, NW, SE, SW).

The eastern two sections (NE, SE) are divided into two areas, (far right and far left) with the western two sections (NW, SW) in the center of the graphic (undivided).

That is how the WOD folks originally configured it.

Each zone number inside each square reveals the boundaries (perimeter) of the zone, in terms of latitude and longitude.

First of all, remember that the difference in max/min is 10 degrees for both latitude and longitude barriers (the zone's perimeter).

The first digit tells you the quadrant (1=NE, 7=NW, 5=SE, and 3=SW).

The second digit, multiplied by 10, tells you the low latitude boundary of the zone.

Add 10 to that latitude to derive the maximum latitude boundary of the zone.

The last two digits, multiplied by 10, tells you the minimum longitude boundary.

Add 10 to that to derive the maximum longitude boundary.

Thus, zone 1010 is in the NE quadrant ('1'), stretching from 0 degrees latitude ('0') up to 10 degrees North latitude (0+10), while the last two digits, 10, multiplied by 10 is 100; indicating that the minimum longitude value is 100 degrees E, adding 10 to that derives the maximum longitude (110 degrees East).

The two Southern Hemisphere latitude and longitude values are negative numbers).

III. On To Proportion

The latitude and longitude scheme of the WOD has nothing to do with the TEOS-10 thermodynamic software (Gibbs-SeaWater (GSW) Oceanographic Toolbox).

The Conservative Temperature (CT), Absolute Salinity (SA), and Potential Enthalpy (hO) are parameters of the seawater at all depths and locations around the globe.

Josiah Gibbs was a scientist who applied the laws of thermodynamics to seawater (The World According To Measurements - 12).

The TEOS-10 thermodynamic software (Gibbs-SeaWater (GSW) Oceanographic Toolbox) provides a programmer with the tools to follow the trail of OHC.

The CT parameter can be used to do a quick scan of seawater so as to follow the OHC as it flows in accordance with the laws of thermodynamics ("hot flows to cold").

In case you are wondering why the search for OHC is relevant, it is because of the general weakness of current models at following OHC through the currents, turbulence, and depths of the oceans (In Search Of Ocean Heat, 2, 3 4 5, 6).

That weakness, as has been explained ad nauseum, is due to the use of the parameter "potential temperature" instead of using the parameter "Conservative Temperature" in current ocean models.

IV. Closing Comments

You can use the data in the HTML code in the appendices to do your own graphs by converting them to CSV files in a text editor.

That way, if you have a particular area and/or ocean depth of interest, you can make many more graphs than are shown in this post.

The next post in this series is here, the previous post in this series is here.

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