Temperature gradient

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somebody - 24 Jan 2004 05:48 GMT

Is there a gross temperature gradient formula for calculating the drop
in temperature as we go down towards the ocean floor ? Eg. 1 degC
drop for every 100 m drop or something like that.

TIA

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R. Martin - 24 Jan 2004 17:31 GMT

> Is there a gross temperature gradient formula for calculating the drop
> in temperature as we go down towards the ocean floor ? Eg. 1 degC
> drop for every 100 m drop or something like that.
>
> TIA

It is very gross in many locations because of the thermocline,
but to a gross approximation the water in the deepest part of
the oceans is at about 4 C, since that is the temperature at
which water is densest (neglecting salinity effects). So, if you
take the surface temperature where you're interested and subtract
4 C and divide by the depth there, you have it. Of course, I'm
only refering to the deep oceans here. To see what kind of
errors this approach can give in the Equatorial Pacific due
to the thermocline, look at
ftp://ftpprd.ncep.noaa.gov/pub/cpc/wd52yx/ocean/wkxzteq_last.html .
As you might note, in places one can drop from 30 C to 20 C in
under 200 meters, but below 300 meters the gradient decreases
sharply. HTH.

Regards,
Russell

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Robert Grumbine - 25 Jan 2004 13:12 GMT

>> Is there a gross temperature gradient formula for calculating the drop
>> in temperature as we go down towards the ocean floor ? Eg. 1 degC
[quoted text clipped - 4 lines]
>the oceans is at about 4 C, since that is the temperature at
>which water is densest (neglecting salinity effects).

Arrgh!

The ocean is saline. This is not an ignorable effect.
(One of my pet peeves.)

The _average_ temperature of the ocean is less than 4 C
(about 3.5), and that is biased upwards by the 20-30 C in upper
parts. The deep ocean, below the main thermocline (300-1000m), is
typically -1.5 to +2 C, by observation.

Water more saline than about 22 psu gets denser all the way up
to the freezing point. Average ocean salinity is almost 35 psu
and almost no parts of the ocean are as fresh as 22 psu. Unlike
lakes, which don't overturn when ice forms (densest fresh water
is indeed at 4 C, rather than near the freezing point), ocean water
gets denser to the freezing point and so oceans can indeed overturn.
This has a number of significant effects on weather and climate at
high latitudes.

For the original poster: There's really no approximation like
that that makes sense in the ocean. The temperature of the
main thermocline varies from towards 30 C to only a few C.
The abyssal ocean is typically around 0 C. But it's routine
for warmer waters to interleave with colder waters above and
below. One of the more striking cases is Mediterranean water,
which is at mid-depth in the Atlantic ocean (say 1800 m) but it
is well over 10 C, while the water above is under 5, and the water
below is under 2. This is statically stable only because
salinity is important to the density of sea water. (Also because
of some more subtle effects due to compressibility, but that's a
different seminar.)

What is it that raises your question? As given, the question
doesn't really make sense for the ocean. But maybe there's a
better answer for the situation that prompted the question.

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Robert Grumbine http://www.radix.net/~bobg/ Science faqs and amateur activities notes and links.
Sagredo (Galileo Galilei) "You present these recondite matters with too much
evidence and ease; this great facility makes them less appreciated than they
would be had they been presented in a more abstruse manner." Two New Sciences

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R. Martin - 25 Jan 2004 17:02 GMT

> >> Is there a gross temperature gradient formula for calculating the drop
> >> in temperature as we go down towards the ocean floor ? Eg. 1 degC
[quoted text clipped - 8 lines]
>
> The ocean is saline. This is not an ignorable effect.

I didn't say it was, which is why it is a gross approximation. ;-)

> (One of my pet peeves.)

Since I don't work in oceanography, I don't have the salinity
distribution of the oceans memorized. :-)

> The _average_ temperature of the ocean is less than 4 C
> (about 3.5), and that is biased upwards by the 20-30 C in upper
[quoted text clipped - 9 lines]
> This has a number of significant effects on weather and climate at
> high latitudes.

0 C that isn't too far from 4 C, so given the other things that
I admitted were being neglected taking 4 C as the low point isn't
all that bad, which was why I didn't bother too look up any deep
water observations. In physics we'd make approximations like that
all the time, so I guess that's just my original training showing
through. Sorry if it offended you, intellectually.

> For the original poster: There's really no approximation like
> that that makes sense in the ocean. The temperature of the
[quoted text clipped - 11 lines]
> What is it that raises your question? As given, the question
> doesn't really make sense for the ocean.

Which was why I included the link to the temperature/depth/longitude
plot, to show the OP the kind of errors a single simple equation
could have.

> But maybe there's a
> better answer for the situation that prompted the question.

Regards,
Russell

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Robert Grumbine - 26 Jan 2004 12:46 GMT

>> >> Is there a gross temperature gradient formula for calculating the drop
>> >> in temperature as we go down towards the ocean floor ? Eg. 1 degC
[quoted text clipped - 15 lines]
>Since I don't work in oceanography, I don't have the salinity
>distribution of the oceans memorized. :-)

Sorry, no weasel. Had you merely taken 4, it's just wrong.
But you threw in the bit about water being densest then, which
is simply, and enthusiastically, wrong for the ocean -- and it's
an ocean problem that's at hand -- and this is an oceanography
science group.

[snip]

>0 C that isn't too far from 4 C, so given the other things that
>I admitted were being neglected taking 4 C as the low point isn't
>all that bad, which was why I didn't bother too look up any deep
>water observations. In physics we'd make approximations like that
>all the time, so I guess that's just my original training showing
>through. Sorry if it offended you, intellectually.

Again, no weasel. You don't know where my original training was
(either).

The thing about doing the back of the envelope estimates is
that they have to be relevant to the system at hand. 4 degrees
is a huge error in the ocean. On the other hand, it's wonderful
precision for the solar photosphere, where temperatures vary by over
2000 K.

Of course, if you're going to apply standards from other areas,
then the lower 100 km of the atmosphere and the entire ocean are
isothermal at the freezing point of water. The deviations are
negligible compared to the photospheric varitions, or the temperatures
of most of the mass of the solar system (i.e., sun, varying from
3000 to 20,000,000), or most of the volume of the galaxy
(ca. 10 K).

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R. Martin - 26 Jan 2004 15:20 GMT

> >> >> Is there a gross temperature gradient formula for calculating the drop
> >> >> in temperature as we go down towards the ocean floor ? Eg. 1 degC
[quoted text clipped - 17 lines]
>
> Sorry, no weasel.

No, it wasn't a weasel. The guy asked for a gross formula, so I
pointed out how a gross formula might be derived and a link to show
an example of how far off that gross formula could be. It wasn't
meant to be a bloody dissertation, it wasn't even meant to technically
correct (which seems to be the mistaken impression you have), it was
meant to be illustrative of the problems with simple approximations
to the temperature versus depth relationship, which it was, and which
was the same point you made. Just because my illustrative approach
differs from yours doesn't justify your response to me, IMO. Why
don't you just reply to the OP and make your (perfectly true)
comments there? I certainly don't need you tuturing me any more
than you need me tutoring you, which is why I restrain myself.

> Had you merely taken 4, it's just wrong.
> But you threw in the bit about water being densest then, which
> is simply, and enthusiastically, wrong for the ocean -- and it's
> an ocean problem that's at hand -- and this is an oceanography
> science group.

See above. Like you said, neglecting salinity is pet peeve of yours,
so that's your hobby horse to ride, but I don't see that I deserve to
get static from you about it when we were both making the same point,
that it isn't simple to give a good temperature vs. depth relationship.

> [snip]
>
[quoted text clipped - 7 lines]
> Again, no weasel. You don't know where my original training was
> (either).

Actually, I heard but I forgot, not that it matters to me, nor is
that what my comment was about, but I don't give you static when you
answer a question just because it wasn't what I would have said, so
you might grant me the same courtesy.

> The thing about doing the back of the envelope estimates is
> that they have to be relevant to the system at hand. 4 degrees
> is a huge error in the ocean.

It was relevent to the system at hand within the approximation
that was asked for and the assumptions that were clearly stated.
It is also wrong but wasn't meant as a correct answer to the question
but as an example of the errors one can have, which I thought I had
made clear by giving an example of the kind of errors that can occur.
I'm sorry if I didn't make that clear, but I hope I have now.

> On the other hand, it's wonderful
> precision for the solar photosphere, where temperatures vary by over
[quoted text clipped - 7 lines]
> 3000 to 20,000,000), or most of the volume of the galaxy
> (ca. 10 K).

Nice straw man, Bob, but I have to drive through this crappy weather
for an out of town meeting, so I have to go and will not be able to
reply for a few days, so you can have the last word if you have some
pressing need to have the last word.

Regards,
Russell

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somebody - 27 Jan 2004 07:21 GMT

Thank you Russel and Robert for the info. When I posted the query I
wasn't expecting any degree of accuracy.

I asked the question to see if an idea I have is feasible. I was
doing some rought calculation and the engineering that is needed to
make it feasible. It seems that for any significant drop in
temperature I have to drop about 200m down. By pumping 1kg of air to
that depth I can only recover about 20g of pure water if the RH is
80%. Not too sure if this is cost-effective.

There is no energy involved in bringing the water up as purewater is
lighter than saline water and it floats up by itself.

Thanks again guys for the info.

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Robert Grumbine - 28 Jan 2004 14:51 GMT

>Thank you Russel and Robert for the info. When I posted the query I
>wasn't expecting any degree of accuracy.
[quoted text clipped - 5 lines]
>that depth I can only recover about 20g of pure water if the RH is
>80%. Not too sure if this is cost-effective.

Does is _have_ to be done over the ocean? If the Great Lakes
would suffice, then you have a 4 C reservoir lying a few meters to
tens of meters below the surface. Much better than having to
go down a few hundred meters.

For the situation you've got in mind, consider the ocean to be
slabs of nearly isothermal water separated by thin transition zones.
The thing you need to do is get to the depth of a sufficiently
cold layer. Depending on your interest and part of the ocean, that
can be anywhere from a few tens of meters to over a kilometer.

>There is no energy involved in bringing the water up as purewater is
>lighter than saline water and it floats up by itself.

Don't be so quick on that assumption. The buoyancy will be effective
if your fresh water is in contact with the sea water. But, if it is,
then it will mix with the other waters as the plume rises. If you
want your fresh water to make it to the surface, you'll probably have
to expend some energy to drive it up a pipe/tube.

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Natural Science Forum / Earth Science / Oceanography / January 2004

Temperature gradient