Billybeau1
Premium Member
Boy, I hope you went out and had a stiff drink or two after that post. 
Boomer... When you are hyper bored
- Thread starter Mr31415
- Start date
Mr31415
Active member
Thanks for the detailed review, Boomer.
.
I understand they call it the In Situ Density Anomaly. I have seen a publication defining it as sigma-stp = (rho-stp - 1000) [Measurement of the Physical Properties of Seawater Temperature, Salinity and Pressure (Moored, Towed and Profiled) Feb 04]. But I also saw this definition:
Specific Gravity Anomaly sigma-t = 10^3(rho/rho<sub>m</sub> - 1) [“Processing of Oceanographic Station Data†Unesco 1991]
In the first version I agree - it is density. In the second it is definitely SG as it is the ratio of two densities - hence dimensionless. My formula expresses the ratio of two densities - then surely it is the right formula for SG?
PS: Except for the last table I have not used my Hanna in any way - not their definitions - nothing. All my research comes from papers published by oceanographers.
My intent with this article was not to explain how to use a hydrometer - there are many out there that does that. My intent is to explain *why* we need to convert, and ultimately I wanted to show people that we use values based on a reference temperature and not in situ values.
This is the only part where I disagree with you (maybe because we are talking past each other)... Forget about hydrometers for a moment. Think purely scientific. At 35ppt and 15C the density of seawater is 1.02597g/cm<sup>2</sup>. This is given by the Seawater Equation of State equation, and this is fixed. At 25C and the same salinity the actual density is 1.02334g/cm<sup>3</sup>. Do you agree with me on that?
Link here
When converting to SG, do we not use the definition of rho<sub>m</sub> - i.e. the maximum density of fresh water (3.98C)? If we do, then SG = Density (numerically at least).
If you agree with the above, then my point is that people say 35ppt corresponds to a SG of 1.026 in our reefs. My point was that an SG of 1.026 is NOT the real SG of sea water at 25C (assuming that is the standard reef temperature), but it is the real SG of sea water at 15C.
Ok thanks.... Easy to get mislead if many people use this definition
.I understand they call it the In Situ Density Anomaly. I have seen a publication defining it as sigma-stp = (rho-stp - 1000) [Measurement of the Physical Properties of Seawater Temperature, Salinity and Pressure (Moored, Towed and Profiled) Feb 04]. But I also saw this definition:
Specific Gravity Anomaly sigma-t = 10^3(rho/rho<sub>m</sub> - 1) [“Processing of Oceanographic Station Data†Unesco 1991]
In the first version I agree - it is density. In the second it is definitely SG as it is the ratio of two densities - hence dimensionless. My formula expresses the ratio of two densities - then surely it is the right formula for SG?
PS: Except for the last table I have not used my Hanna in any way - not their definitions - nothing. All my research comes from papers published by oceanographers.
My intent with this article was not to explain how to use a hydrometer - there are many out there that does that. My intent is to explain *why* we need to convert, and ultimately I wanted to show people that we use values based on a reference temperature and not in situ values.
This is the only part where I disagree with you (maybe because we are talking past each other)... Forget about hydrometers for a moment. Think purely scientific. At 35ppt and 15C the density of seawater is 1.02597g/cm<sup>2</sup>. This is given by the Seawater Equation of State equation, and this is fixed. At 25C and the same salinity the actual density is 1.02334g/cm<sup>3</sup>. Do you agree with me on that?
Link here
When converting to SG, do we not use the definition of rho<sub>m</sub> - i.e. the maximum density of fresh water (3.98C)? If we do, then SG = Density (numerically at least).
If you agree with the above, then my point is that people say 35ppt corresponds to a SG of 1.026 in our reefs. My point was that an SG of 1.026 is NOT the real SG of sea water at 25C (assuming that is the standard reef temperature), but it is the real SG of sea water at 15C.
My intent with this article was not to explain how to use a hydrometer - there are many out there that does that. My intent is to explain *why* we need to convert, and ultimately I wanted to show people that we use values based on a reference temperature and not in situ values.
I know what you intent was and said so That is what tables are for to show the temp error, so when using a hydrometer at some other temp other than ref they can ge the proper salinity. There is only one such table out there for us, 24C/77F, this one. I have only seen one for 15 C hydrometer that Dr. Kelly did for me years ago and is no longer on the net, a 15 C table for salinity. There are tables in this hobby in books and mag articles but those are NOT Sg tables but Density tables and you are still talking the same as if D and Sg = each other( see below). Randy and I have been trying to correct this for years and most just keep missing it. D DOES NOT = Sg
This is what a Sg table looks like for a 25 C hydrometer.
This is the only part where I disagree with you (maybe because we are talking past each other)... Forget about hydrometers for a moment. Think purely scientific. At 35ppt and 15C the density of seawater is 1.02597g/cm2. This is given by the Seawater Equation of State equation, and this is fixed. At 25C and the same salinity the actual density is 1.02334g/cm3. Do you agree with me on that?
No we do not agree. I am talking Sg, what we use in this hobby not Density. If we are talking D then I 100 % agree with what you said above. You, as almost all others, keep talking in terms as if Sg and D are equal and they are not D does not = Sg. Maybe that is why you math is off for Sg, you are calculating in terms of D and D does not = SG. There are always temp for a ref std be it fixed or not when some chemical oceanographer gives D for seawater it is D at that temp and is not reverted back to 15 C.
When converting to SG, do we not use the definition of rhom - i.e. the maximum density of fresh water (3.98C)? If we do, then SG = Density (numerically at least).
Only if we go back to ~4 C and I have stated it here before a number of times that........ D = sg at ~4 C only. If it is some other temp other than 4 C then D does not = Sg. As one moves away from 4C the Sg and D values begin to part from one another. A 15 C @ 15C hydrometer has an Sg of 1.0297 = 35 ppt and its density @ 15 C =1.02597. If we look at the density @ 4C and a 4C hydrometer Sg at 4C then D = 1.0278 and Sg = 1.0278, the same.
Do you see what you are doing here ? You talking in terms of 4 C then 15 C, Sg and density and intermingling them together.
If you agree with the above, then my point is that people say 35ppt corresponds to a SG of 1.026 in our reefs. My point was that an SG of 1.026 is NOT the real SG of sea water at 25C (assuming that is the standard reef temperature), but it is the real SG of sea water at 15C.
Of course it is not but 15C is not either and neither is 4C for seawater but (negative)- 3.6 C (25.5 F). But with that said all use 4 C when generating tables. As I have said a number of times you need to read those article and links I gave, especially this one.
Temperature Corrections for Hydrometers
http://www.reefkeeping.com/issues/2004-07/rhf/index.php
These explain Density, Sg, Specific Gravity Anomaly and Density Anomaly. And we are not getting way deep into the subject
http://www.nvcc.edu/home/vzabielski/SeawaterChemistryI.pdf
http://www.ices.dk/Ocean/procedures/links.pdf
The density of seawater @ 25 C is 1.02334 = 35 ppt .....period. The Sg of seawater @ 25 C is 1.0264 =35 ppt and no that is not the "real" Sg of seawater. If we go by 15C, then 1.0269 = 35 ppt and the density is = 1.0259 = 35 ppt. An if we want to deal with TRUE Sg then that is 4 C = 1.0278 = 35 ppt.
All you need to say is
An SG of 1.026 in our reefs tanks is NOT the real SG of sea water. Seawater has a std temp of 15 C for Sg and not 25 C. Thus, the real SG of sea water at 15C is equal to 1.0269 = 35 ppt. The Sg numbers do not matter, as long as one understands that we what a reading at x temp form y temp calibrated hydrometer to equal 35 ppt. Here is a calculator that will show what what salinity you want based on observed reading and the temp calibration temp of the hydrometer and the temp of the water being tested
Hydrometer Reading to Salinity Conversion
http://www.reefkeeping.com/issues/2004-07/rhf/conversion.htm
If one wants a table for 25 C hydrometers, which is what we use in this hobby, almost all the time, then here is one.
http://www.reefkeeping.com/issues/2004-07/rhf/table1.pdf
I know what you intent was and said so
That is what tables are for to show the temp error, so when using a hydrometer at some other temp other than ref they can ge the proper salinity. There is only one such table out there for us, 24C/77F, this one. I have only seen one for 15 C hydrometer that Dr. Kelly did for me years ago and is no longer on the net, a 15 C table for salinity. There are tables in this hobby in books and mag articles but those are NOT Sg tables but Density tables and you are still talking the same as if D and Sg = each other( see below). Randy and I have been trying to correct this for years and most just keep missing it. D DOES NOT = SgThis is what a Sg table looks like for a 25 C hydrometer.
This is the only part where I disagree with you (maybe because we are talking past each other)... Forget about hydrometers for a moment. Think purely scientific. At 35ppt and 15C the density of seawater is 1.02597g/cm2. This is given by the Seawater Equation of State equation, and this is fixed. At 25C and the same salinity the actual density is 1.02334g/cm3. Do you agree with me on that?
No we do not agree. I am talking Sg, what we use in this hobby not Density. If we are talking D then I 100 % agree with what you said above. You, as almost all others, keep talking in terms as if Sg and D are equal and they are not D does not = Sg. Maybe that is why you math is off for Sg, you are calculating in terms of D and D does not = SG. There are always temp for a ref std be it fixed or not when some chemical oceanographer gives D for seawater it is D at that temp and is not reverted back to 15 C.
When converting to SG, do we not use the definition of rhom - i.e. the maximum density of fresh water (3.98C)? If we do, then SG = Density (numerically at least).
Only if we go back to ~4 C and I have stated it here before a number of times that........ D = sg at ~4 C only. If it is some other temp other than 4 C then D does not = Sg. As one moves away from 4C the Sg and D values begin to part from one another. A 15 C @ 15C hydrometer has an Sg of 1.0297 = 35 ppt and its density @ 15 C =1.02597. If we look at the density @ 4C and a 4C hydrometer Sg at 4C then D = 1.0278 and Sg = 1.0278, the same.
Do you see what you are doing here ? You talking in terms of 4 C then 15 C, Sg and density and intermingling them together.
If you agree with the above, then my point is that people say 35ppt corresponds to a SG of 1.026 in our reefs. My point was that an SG of 1.026 is NOT the real SG of sea water at 25C (assuming that is the standard reef temperature), but it is the real SG of sea water at 15C.
Of course it is not but 15C is not either and neither is 4C for seawater but (negative)- 3.6 C (25.5 F). But with that said all use 4 C when generating tables. As I have said a number of times you need to read those article and links I gave, especially this one.
Temperature Corrections for Hydrometers
http://www.reefkeeping.com/issues/2004-07/rhf/index.php
These explain Density, Sg, Specific Gravity Anomaly and Density Anomaly. And we are not getting way deep into the subject
http://www.nvcc.edu/home/vzabielski/SeawaterChemistryI.pdf
http://www.ices.dk/Ocean/procedures/links.pdf
The density of seawater @ 25 C is 1.02334 = 35 ppt .....period. The Sg of seawater @ 25 C is 1.0264 =35 ppt and no that is not the "real" Sg of seawater. If we go by 15C, then 1.0269 = 35 ppt and the density is = 1.0259 = 35 ppt. An if we want to deal with TRUE Sg then that is 4 C = 1.0278 = 35 ppt.
All you need to say is
An SG of 1.026 in our reefs tanks is NOT the real SG of sea water. Seawater has a std temp of 15 C for Sg and not 25 C. Thus, the real SG of sea water at 15C is equal to 1.0269 = 35 ppt. The Sg numbers do not matter, as long as one understands that we what a reading at x temp form y temp calibrated hydrometer to equal 35 ppt. Here is a calculator that will show what what salinity you want based on observed reading and the temp calibration temp of the hydrometer and the temp of the water being tested
Hydrometer Reading to Salinity Conversion
http://www.reefkeeping.com/issues/2004-07/rhf/conversion.htm
If one wants a table for 25 C hydrometers, which is what we use in this hobby, almost all the time, then here is one.
http://www.reefkeeping.com/issues/2004-07/rhf/table1.pdf
Mr31415
Active member
. I have read each and every link to articles you posted in this thread couple of days ago... So if I post something it is based on my interpretation of those articles. I think we are saying a lot that is the same...For instance - I do not believe I am confusing density and SG - not once. I explicitly said "At 35ppt and 15C the density of seawater is 1.02597g/cm3" - I even included the dimension to show I know density is mass per volume. And that density formulation is correct, as you yourself stated.
And I also said in my article that SG is the ratio of the density of sea water to that of the maximum density of freshwater - and that it is dimensionless. The only thing I can see that I might be confused about is my reference temperatures... It seemed from all the articles on oceanography I read that the SG definition is based on the maximum density of fresh water - i.e. at 3.98C.
But since you keep on saying density is not (numerically) the same as SG I can only infer we are NOT using that definition of SG. That we base our definition on different temperature standards - both for the freshwater in the denominator as well as the sea water in the numerator.
I even said:
"When converting to SG, do we not use the definition of rhom - i.e. the maximum density of fresh water (3.98C)? If we do, then SG = Density (numerically at least)."
I know exactly what I am doing here
I am working from first principals (a common ground for mutual understanding) to the SG issue. SG is based on density. Thus density is crucial in the definition of SG. That is why I explained my understanding of density. And that density = SG (numerically only) when we are at 3.98C. But this is not the issue as up to here I understand...If I understand you correctly, oceanographers use SG based on freshwater at 3.98C, right (the true SG value)? But we in the reefkeeping hobby use this definition of SG:
SG = Density of sea water at temperature X / Density of fresh water at temperature Y
right? If so, what is X and Y? Is X = Y? It is not clear from any of the articles since they are written not from first principals. It is very easy to end this lengthy discussion - just show me the mathematical formula for how you determined this:
"The Sg of seawater @ 25 C is 1.0264 =35 ppt "
in terms of density of seawater / density of freshwater, including temperatures for both numerator and denominator. I tend to grasp mathematical rigor much faster than explanations
Once again, I want to explain the principles behind the tables.... Not how to interpret your hydrometer's readings...
I went back to look at something on your web page but I see you have completely re-wrote it and corrected the errors and make it much simpler . I have no real issue accept one small thing and still one big thing, the Hanna tables you give.
ót = 10<sup>3</sup>(ñ/ñm - 1)
This does = Sg. However, I just want you to know that ót is density in oceanography and not Sg. It should be
s.g. <sub>t</sub> = 10<sup>3</sup>(ñ/ñm - 1)
but I have no real issue and am maybe knit picking here.
with ó15 the Specific Gravity at 15°C and ót the in situ Specific Gravity
There are some serious issue here. If we take a 15C hydrometer and put it in seawater @ 35 ppt it will read 1.0269 and not 1.0260 for 35 ppt. And you are calling ót and ó15 Sg. and not Density. So, explain how you go those Sg numbers ? They should be as I have done below for Sg. However, if you took your ót and ó15 and called them Density and reverted back to 15 C Density then you are correct. You can correct a hydrometer back to 15 C Sg and you can correct Density back to 15 C if one wants. Take note that your Density numbers and your ót are the same, it just that the have been rounded of. And this is why all of this, in IMHO, you do not understand Sg/ density relationships completely. It is obvious the the Hanna is using Density and not Sg as you state on your webpage, for ót ó15 or for that matter what they also state.
Temp Density(SWEoS) Refractometer
<pre>
15°C 1.02597 1.0260 1.0260 1.0265 (35ppt) 20/20
20°C 1.02465 1.0247 1.0260
25°C 1.02334 1.0234 1.0260
27°C 1.02270 1.0227 1.0260 1.0265 (35ppt), 20/20
</pre>
and is clearly shown here. And the 20C is in error it is 1.02476
http://ioc.unesco.org/Oceanteacher/...2_OcMeasUnits/SWequationofstatecalculator.htm
and here
http://www.reefkeeping.com/issues/2004-07/rhf/conversion.htm
Temp Density(SWEoS) ót ó15 (with these as Sg)
<pre>
15°C 1.02597 1.0269 1.0269 = 35 ppt
20°C 1.02476 1.0257 1.0269 = 35 ppt
25°C 1.02334 1.0243 1.0269 = 35 ppt
27°C 1.02270 1.02365 1.0269 = 35 ppt
</pre>
Now you say you refract is about correct. How was it calibrated ? Do not say RO/DI water that is of by- 1.5 ppt. You give 20/20 so than is an uncorrect hydrometer with no ATC. So if one had a refract set to 20/20 and no ATC, then the 1.0265 is almost correct, it is 1.0266 = 35 ppt . An ATC that reads 1.0264 is actually a reading of 1.0252 = 33.5 ppt, if calbrated in RO/DI water. So one wold want it to read 1.028 to = 35 ppt.
and this
with ó15 the Specific Gravity at 15°C and ót the in situ Specific Gravity
It is clear the Hanna's ót mode shows actual Specific Gravity, and the ó15
Should be
with ó15 the Density at 15°C and ót the in situ Desnity
It is clear the Hanna's ót mode shows actual Density, and the ó15
. I have no real issue accept one small thing and still one big thing, the Hanna tables you give.ót = 10<sup>3</sup>(ñ/ñm - 1)
This does = Sg. However, I just want you to know that ót is density in oceanography and not Sg. It should be
s.g. <sub>t</sub> = 10<sup>3</sup>(ñ/ñm - 1)
but I have no real issue and am maybe knit picking here.
with ó15 the Specific Gravity at 15°C and ót the in situ Specific Gravity
There are some serious issue here. If we take a 15C hydrometer and put it in seawater @ 35 ppt it will read 1.0269 and not 1.0260 for 35 ppt. And you are calling ót and ó15 Sg. and not Density. So, explain how you go those Sg numbers ? They should be as I have done below for Sg. However, if you took your ót and ó15 and called them Density and reverted back to 15 C Density then you are correct. You can correct a hydrometer back to 15 C Sg and you can correct Density back to 15 C if one wants. Take note that your Density numbers and your ót are the same, it just that the have been rounded of. And this is why all of this, in IMHO, you do not understand Sg/ density relationships completely. It is obvious the the Hanna is using Density and not Sg as you state on your webpage, for ót ó15 or for that matter what they also state.
Temp Density(SWEoS) Refractometer
<pre>
15°C 1.02597 1.0260 1.0260 1.0265 (35ppt) 20/20
20°C 1.02465 1.0247 1.0260
25°C 1.02334 1.0234 1.0260
27°C 1.02270 1.0227 1.0260 1.0265 (35ppt), 20/20
</pre>
and is clearly shown here. And the 20C is in error it is 1.02476
http://ioc.unesco.org/Oceanteacher/...2_OcMeasUnits/SWequationofstatecalculator.htm
and here
http://www.reefkeeping.com/issues/2004-07/rhf/conversion.htm
Temp Density(SWEoS) ót ó15 (with these as Sg)
<pre>
15°C 1.02597 1.0269 1.0269 = 35 ppt
20°C 1.02476 1.0257 1.0269 = 35 ppt
25°C 1.02334 1.0243 1.0269 = 35 ppt
27°C 1.02270 1.02365 1.0269 = 35 ppt
</pre>
Now you say you refract is about correct. How was it calibrated ? Do not say RO/DI water that is of by- 1.5 ppt. You give 20/20 so than is an uncorrect hydrometer with no ATC. So if one had a refract set to 20/20 and no ATC, then the 1.0265 is almost correct, it is 1.0266 = 35 ppt . An ATC that reads 1.0264 is actually a reading of 1.0252 = 33.5 ppt, if calbrated in RO/DI water. So one wold want it to read 1.028 to = 35 ppt.
and this
with ó15 the Specific Gravity at 15°C and ót the in situ Specific Gravity
It is clear the Hanna's ót mode shows actual Specific Gravity, and the ó15
Should be
with ó15 the Density at 15°C and ót the in situ Desnity
It is clear the Hanna's ót mode shows actual Density, and the ó15
five.five-six
Well-known member
see, this is what a wife is good for, to tell you when you are wrong
Mr31415
Active member
You are very evil... Never giving me the carrot... Let me work hard
Regarding sigma-t and s.g.-t - I have changed that, thanks.
Regarding the Hanna's measured values - I can now see why you think I confused sg and density. In reality, I did not confuse the two - except when it came to the Hanna
I did not pay close enough attention to the actual values and up to now I did not understand what formula you guys use for s.g. in the reef aquarium. Once I reverse engineered that from your table above, it was easy to understand.
See, I now know that we do not use the definition of s.g. = density of sea water / maximum density of freshwater (3.98C).
We use the definition s.g. = density of sea water / density of fresh water @ 15C
See - at 15C freshwater has a density of 0.999099g/cm<sup>3</sup>.
http://www2.volstate.edu/CHEM/Density_of_Water.htm
So s.g. for salinity of 35ppt at 25C would be the density of sea water at 25C and 35ppt which is 1.02334g/cm<sup>3</sup> divided by the density of fresh water at 15C which is 0.999099g/cm<sup>3</sup> and that is:
1.02334 / 0.999099
= 1.0243 - just like you said
Thanks!
Regarding sigma-t and s.g.-t - I have changed that, thanks.
Regarding the Hanna's measured values - I can now see why you think I confused sg and density. In reality, I did not confuse the two - except when it came to the Hanna
I did not pay close enough attention to the actual values and up to now I did not understand what formula you guys use for s.g. in the reef aquarium. Once I reverse engineered that from your table above, it was easy to understand.
See, I now know that we do not use the definition of s.g. = density of sea water / maximum density of freshwater (3.98C).
We use the definition s.g. = density of sea water / density of fresh water @ 15C
See - at 15C freshwater has a density of 0.999099g/cm<sup>3</sup>.
http://www2.volstate.edu/CHEM/Density_of_Water.htm
So s.g. for salinity of 35ppt at 25C would be the density of sea water at 25C and 35ppt which is 1.02334g/cm<sup>3</sup> divided by the density of fresh water at 15C which is 0.999099g/cm<sup>3</sup> and that is:
1.02334 / 0.999099
= 1.0243 - just like you said
Thanks!
