# Sea level calc

dem45133
Hello, all. Neat site! I'll be using it.

Not to upset anyone, but being an Environmental Scientist for 15 years the "predictions" of sea level increases by GW that I was hearing seemed totally unrealistic to me, even just on the most basic level. Recently I heard one of the hosts on the "Top Science Stories for 2004" show on the science channel state a 16 ft rise at Miami FL for just a certain ice sheet. Some years ago I'd heard even greater numbers for the pole melts... something like 50 ft!

Using a simplified approach with published ice volumes for both poles and the simple formula for spherical volume I calculated a rough estimate based on a average radius of 3963 miles, converting to ft3 for everything, a 28% guestimate on land mass, and get a total increase of sea level of a little better than three INCHES... yes, inches! (3.2218362158 to be exact, or 0.268486351316666667 ft). These numbers are correct given those assumptions, but that reflects the increase on the total water surface (72%) of the globe.

The centrifical force of the earth and the gravitational forces creating our tidal system will prevent that increase in volume for distributing that 3+ inches uniformly (which the volume formula assumes).

Does anyone know where I can get formulas to adjust for these forces?

Have any of you out there ever played with this calc?

Certainly, there must be an oceanography site that has better calcs? Anyone know of any?

Since the shows I saw are geared to children... Id like to send them correct figures. So much of the "environmental" emotional based items I hear now and then just do not add.

Dave
Hillsboro, Ohio

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This'll be moving to Earth Sciences soon as the moderators get back from whichever bowl games they're watching.

dem45133 said:
(snip)Does anyone know where I can get formulas to adjust for these forces?

(snip)

Check tide tables --- IIRC, this is more an empirical "calculation" than anything. Basin depths, flow restrictions through channels, etc., complicate the distribution of the water mass to the point that it's more convenient to depend upon existing tide measurements for the various solar, lunar, storm, and other effects for "predicting" future tides --- worked for D-Day, not to mm uncertainties, but adequate for navigation.

Doc Al
Mentor
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This'll be moving to Earth Sciences soon as the moderators get back from whichever bowl games they're watching.
Hey now... some of us work for a living! :rofl:

Welcome, dem45133! (And, yes, I'll move this to Earth Science.)

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For dem45133: you'll also want to check your calculations for the Antarctic cap --- might as well stick to SI units, this is a science forum, should save some conversion errors. The GW discussion is bad enough without both viewpoints depending upon flawed numbers.

Other "first approximation:" "figure of the earth" departure from perfect sphericity --- give you +mm/(m rise) and -mm/(m rise) at equator and poles.

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redo you math

I think you donot have enuff ice volume

the last iceage sent sea levels down by about 200 feet
and a 10-20 foot rise is very possable with a greenland size melt

btw that would sink south fla up to the mouse

Well let's grab that old envellope again and do some rough order of magnitude (mks) calculations.

Hence surface area: 4*pi*r^2 = 510,000,000 km^2
2/3 is ocean, that's: 340,000,000 km^2

http://www.bmp.gl/E/EC2_periodicals/EC2_30aa_mining-journal-suppl-index.htm [Broken]is the world's largest island. The surface area covers over 2 Mkm2, of which nearly 85% is covered by an ice cap - the Inland Ice - that is up to 3 km thick in places.
85% of 2,000,000 of ice average -over the thumb- 1,5 km thickness would be 2,550,000 km^3 of ice, converting to 90 volume% of water is 2,300,000 km^3. Spread it over (divide by) 340,000,000 km^2 would yield 0,0068 km or 6,80 meter sea level rise, about 22 feet.

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dem45133
This is going to be FUN

I used the vol formula. Think about it... the surface formula cant work. Assuming a sea level change will increase the average radius, and by default then results in an increase in surface area. And believe it or not, since the magnitudes are large, a few inches (or cm if you prefer) makes a big difference on the surface area.

I used the following:

Antarctica: 30,109,800 cubic km total ice in/on Antarctica (from a published report) which equals 30,109,800,000,000 m3. The amount floating in shelves is only a small % of this so I did not adjust for it.

Arctic an average thickness of 3 to 3.5 meters, at about 5x10^6 km2 (also from a published report) which equals 8,125,000,000 m3 at avg thickness of 3.25 m divided by two since it floating and ~half is already below sea level.

I didn't include Greenland, but will for the heck of it, but it will not result in a significant change, I also didn't adjust for phase density.

I converted to ft3 (35.3147 ft3 in m3) simply because its used a lot in the environmental waste industry and I'm used to thinking in it. But I'll use SI if you want.

Basically from this, I increased the radius in the vol formula until it equaled the available ice applied to 72% of the full volume (28% land mass).

I'll check again on my spreadsheet calcs and references and get back to you all.

DEM

Antarctica: 30,109,800 cubic km total ice in/on Antarctica (from a published report) which equals 30,109,800,000,000 m3.
1 km = 1000 m
1 km2 = 1,000,000 m2
1 cubic km = 1 km3 = 1,000,000,000 m3

30,109,800 cubic km = 30,109,800,000,000,000 m3

all those stupid zeros

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matthyaouw
Gold Member
One question- do any of your calculations take into account thermac expansion of water? I've been led to believe that this is a large factor in sea level rise and fall.

Well the shrinking factor of ice melting of about 0,9 outweights thermal expansion of water by far. Moreover, if by any reason the surface temperature of the ocean would increase, only the first 1000 meter of water below it, would react, the remaining kilometers of sea depth would stay at 4 degrees celsius, and would not expand.

And dem..
since the magnitudes are large, a few inches (or cm if you prefer) makes a big difference on the surface area.
Not really, the surface of a sphere with radius 6,367,000,05 meters (2 inches more) would be 8001008 m^2 more, this is 0,000015 % difference.

Now if all those cubic meters of Antarctica would melt, the sea level would rise an order of magnitude of

0,9 (ice -> water) * 30,109,800,000,000,000 / 340,000,000,000,000,000 = 88 meters

dem45133
Well, time to eat crow...

Ok folks, I stand corrected. Missed the volume conversion calcs by three orders of mag at units of m^3. I don't mess up like that too often with math one of my better suites... just not used to looking at numbers out to 10^21... didn't spot it... and seldom use metric.

Guess I need to buy some land at about 270 ft elevation to have an ocean front later huh (based on both poles and Greenland melting and spread over 72%, using volume formula)? It really does surprise me... I’ve seen projections before but didn’t believe them... just seemed that that little bit of ice (relative to the globe) spread over that much area would have much of an effect. Guess it will.

Oh boy this crow tastes GOOD! Needs some salt though.

Later all ..... DEM

Gokul43201
Staff Emeritus
Gold Member
Andre,

Just out of curiosity, what is the basis for assuming that the volume of ice melting is of order the volume of ice that makes up Greenland ? Over what kind of time scale is this melting expected to occur ? Do estimates actually suggest such a large melting within the near future ?

Nothing really, we were just toying with the strickly hypothetical idea what would happen to sea level if the Greenland ice would melt (not when), sometimes it melts a little then it freezes again. Greenland was as warm around 1940 as it is now. Moreover we have not taken into account the effects of isostatic rebound that would mitigate sea level rise.

matthyaouw
Gold Member
Andre said:
Well the shrinking factor of ice melting of about 0,9 outweights thermal expansion of water by far. Moreover, if by any reason the surface temperature of the ocean would increase, only the first 1000 meter of water below it, would react, the remaining kilometers of sea depth would stay at 4 degrees celsius, and would not expand.
Really? I'd be having some severe words with my former geography teacher right now if he hadn't moved down south and become a plumber (funny thing to do really, considering he'd only had his PHD a year). Thanks Andre.

Okay, I wonder, is "really?", "really?" :surprised or "really!"

I know there are some links that would support that notion but I'm time pressed at the moment. But consider this, at North Greenland the sea surface temperature is 0 degrees celsius and the water temp at about 1000 meters lower is 4 degrees Celsius. Around Brasil the sea surface temperature is 27 degrees Celsius and the temperature at roughly 1000 meters below sea level is ... 4 degrees Celsius. Temperature behaves more or less negative exponential with depth, sea surface temperature change only moves the permanent 4 degrees celsius point a few tens of meters up or down.

I do wonder what this Ph.D has to do with it.

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