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Conversion factors for ice and water mass and volume

Mass and volume units for water and ice

One gigatonne is one billion metric tonnes  ( 1 Gt = 1 x 109 tonnes)

One metric tonne is 1000 kilograms (1 tonne = 1000 kg)

One metric tonne of water has a volume of one cubic meter (1 tonne water ≡ 1 m³)

One gagatonne of water has a volume of one billion cubic meters, or one cubic kilomter.(1 Gt water ≡ 1 km³)Of course, one gigatonne of ice has a greater volume than one gigatonne of water.  But it will still have a volume of 1 km³ when it melts.

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How much does one Gigatonne of melted ice (1 km³ of water) raise the oceans?

The oceans occupy 361 million square kilometers ( 361 x 106  km²) of the Earth’s surface.

If one cubic kilometer of water (i.e., one gigatonne of water) is spread evenly over the entire 361 million square kilomters, the thickness of the new layer of water will be given by:

1 km³ / 361 x 106 km²  = 2.78 x 10-6 meters  = 2.78 microns.

Or, in terms of gigatonnes:

1 Gt  x  (1 km³/Gt)  / 361 x 106 km²  = 2.78 x 10-6 meters  = 2.78 microns / Gt

That is, one cubic kilometer of water (i.e., one gigatonne of water) will add less than 3 millionths of a meter to the oceans!

*******************************************************************************************

How many gigatonnes of ice must melt to raise the oceans one millimeter (10-3 meters)?

The number of gigatonnes of water that must be added to the oceans to raise the sea level 1 millimeter is given by:

1 mm / (2.78 microns / Gt)  =  10-3 m  / (2.78 x 10-6 m / Gt)  =  360 Gt

Similarly, 360 km³ of water will raise the oceans 1 mm.

*******************************************************************************************

How many gigatonnes of ice must melt to raise the oceans one inch?

1 inch = 25.4 mm = 2.54 x 10-2 meters

The number of gigatonnes of water that must be added to the oceans to raise the sea level 1 inch is given by:

1 inch x  (2.54 x 10-2 m / inch) / (2.78 x 10-6 m / Gt)   =  9137 Gt

Similarly, 9137 km³ of water will raise the oceans 1 inch.

*******************************************************************************************

How many gigatonnes of ice must melt each year to raise the oceans one foot per decade?

1 foot = 305  mm =  3.05  x 10-1 meters

1 foot per decade = 3.05  x 10-2 meters / yr  = 30.5 mm / yr

The number of gigatonnes of water that must be added to the oceans to raise the sea level 1 foot per decade is the same as the number of gigatonnes required to raise the oceans 30.5 mm/yr, and is given by:

360 Gt/mm  x  30.5 mm/yr = 10,980 Gt/yr

Similarly, 10,980 km³ of water per year will raise the oceans 1 foot per decade.

83 comments

  1. Please answer these questions: how many GT of ice are there in the world and how many feet will the oceans rise if one half of all the ice melts, and if all of it melts? THEN we will have an idea of the actual magnitude of the problem, instead of going “gee a whole GT only raises the oceans a teeny bit so we must not need to worry”. HOW MANY TOTAL GTs ARE WE TALKING ABOUT AND HOW MUCH WOULD HALF AND ALL OF IT MELTING INUNDATE US?


    • the landed ice need not melt, only fall into the ocean to cause sea level change.


    • There is no conceivable GW scenario where all of the Antartic ice would melt. The temperatures down there are a long way from the melting point and to raise global temperatures that much we would be cooked up here long before we had to worry about flooding. So that needs to be taken into account.


      • We shouldn’ kill our earth (nature), pls… flooding or not flooding, warming or not warming. also it’s good to keep in mind that, nature doesn’t need man to survive whil man acn’t without nature.


      • Anand,

        Thank you for the profound comment. My head is bowed in awe.

        ClimateSanity


      • “Anand,

        Thank you for the profound comment. My head is bowed in awe.

        ClimateSanity

        by tommoriarty August 18, 2013 at 9:24 am”

        Yes, CimateSanity,
        Fuck you too. And you go to hell too.


    • my question is, what is the loss of mass when converting water to ice and back to water. suggest one ltr of water


  2. Dear DancesWithFascists,

    Thank you for your impassioned comments.

    I will first answer your specific questions about melting half or all of the ice on the planet.

    The volume of ice in Antarctica is approximately 25,000,000 km3. The volume of ice in Greenland is about approximately 2,500,000 km3. The rest of the landed ice is small compared to these two, so I think it is fair to round up and say the total is about 30,000,000 km3.

    The world’s oceans have an area of about 335,000,000 km2. So, simply speaking, if half of the ice in Antarctica and Greenland were to melt, then the oceans would rise about 45 meters (about 150 feet). All of the ice melting would raise the oceans 90 meters (or 300 feet). Of course, you are correct that this would be a devastating effect.

    But remember, the above conclusion requires that 30,000,000 km2 of ice must melt.

    How fast is ice actually melting? There are conflicting numbers resulting from various methods of measuring. Velicogna (Science, vol 311, 2006) used time varying gravity measurements from the GRACE satellites estimated that Antarctica was losing 152 km3 of ice per year. She concludes that this “is equivalent to 0.4 millimeters of global sea-level rise per year.” This is the same result you would get by multiplying the number of km3 of ice by 2.7 microns as I suggested in my blog. One hundred years at this rate would contribute a whopping 4cm (about one and a half inches) to the oceans.

    In the same journal, Davis (Science, vol 308, 2005) concluded that Antarctica was actually gaining ice.

    You may be able to find studies reported in the literature that claim faster rates of ice loss in the Antarctic than claimed by Velicogna. For example, Eric Rignot, (Rignot, et. al., “Recent Antarctic ice mass loss from radar interferometry and regional climate modeling,” Nature Geoscience, 2008) of the California Institute of Technology used satellite interferometric synthetic-aperture radar observations to show that the ice losses in the East Antarctic were essentially zero, while the West Antarctic and the Antarctic Peninsula had combined losses of about 190 gigatonnes per year. This results in a stunning 0.5 mm ocean rise per year, or about 2 inches in a hundred years.

    Similar conflicting, but small, results hold for Greenland.

    The bottom line is that at current rates of ice melt it would take about 200,000 years for all the ice to melt in the Antarctic. And even this scenario is ridiculously unlikely, because if the pattern of the last 2 million years continues, then the next 200,000 years should contain two ice ages, each about 100,000 years long. (If this conclusion surprises you, just look at Al Gore’s presentation, which shows the repeating glacial/interglacial pattern of 100,000/15,000 years during the Quaternary.)

    Again, thank you for your comment.

    Best Regards,
    Tom


    • Ocean volume is 1.37e9 cubic meters.


      • Derek,

        You seem to be off by a factor of one billion. One cubic kilometer is water is 1e9 cubic meters.

        I assume you meant 1.37e9 cubic kilometers, or 1.37e18 cubic meters.

        Best regards,
        ClimateSanity


  3. The entire surface area of the oceans works real well if you have a none moving bath tub. Take a tennis ball get it wet and start spinning it the water goes to the edge. Now take the gravitational pull of the moon that causes high tide / low tide and give it a few more gigatonnes of water to move around about 300 more gigatonnes per year. No one really knows what’s going to happen they are given it there best guess but if you look at the whole picture it doesn’t look good.


  4. Gary,

    The effect you are talking about is seen in the oblateness of the Earth. (Note that “a” and “c” in the given link refer to the radius of the oblate spheroid at the equator and at the pole, respectively.)

    The second order gravitational moment,J2, for the earth is about 0.001. See the plot here of variations in J2 due to redistribution of water in the oceans, soil and atmosphere. Notice that the changes in J2 are on the order of 10E-10 (0.0000000001).

    The actual oblateness of the Earth is about 0.003 (about 1/300th). Adding water to the oceans may change the oblateness of the Earth, but not by much. The best first approximation would be that the oblateness remains essentially unchanged. So if the oceans rose by one meter on the average, then it might be 1.003 meters at the equator. A small effect.

    In the long run, I suspect other things, like glacial isostatic adjustment, have had a much greater impact on spatial variation of sea level rise since the last ice age. This would probably continue to be true.

    Best regards,
    Tom


  5. [...] blog suggests there’s nothing to worry about, but I don’t have the time to work out the [...]


  6. dont forget that most ice is floating. Ice is at a minimum 10 percewnt more volume than water. when ice melts, water levels will decrese.


    • Most of it is not floating.


    • That’s why 10% of an iceberg is above water. Floating ice that melts makes no difference in difference in sea level (apart from some minor fresh versus saline density differences).


    • Floating ice will do not much to rise the sea level , may be the contrary !!!
      Anyone has an idea of how Greenland or other big pieces of lands will behave , once free of their ice shield ???
      Many , many billions of tons less on a land will let it raise a bit !!! So there should be more water in the ocean , and less space to put it !!
      I´ll buy a boat to be sure not to get flooded !!


      • Ice in water has displaced its weight (Ice expands when it freezes which is why it floats). So ice that melts will not add nor subtract from the water level. Try putting ice cubes in a glass and mark the level and put plastic wrap over the top (to prevent evaporation). Let it sit over night and melt and look at the level again. It should be the same.


      • for that you have to wait for 200,000 years.


  7. [...] in 2005 that must have been 0.9 mm greater than the sea level rise rate in 1995 (320 Gt/year x  2.7 microns/Gt  = 0.9 [...]


  8. Tom, thanks for the numbers.

    Some time ago I read an impassioned headline about 48 cubic miles of ice melting each year and the ominous result that would occur if that much ice were lost each year. I did my own calculations which demonstrated that the total sea level rise after 100 years from such a scenario would be less than 2.25 inches.

    Sea level rise is one of the great — and obviously untrue — scare stories of CAGW.


  9. Frank, I don’t think anyone in the AGW crowd (unless they are really out to lunch) is talking about sea ice. Every last bit of the sea ice could melt and it would not cause an increase in sea levels. The question is how much land-based ice will melt.


  10. HMMMMMMMMMM………


  11. The flaw in your argument is that you can’t dismiss the ice floating in the sea.

    If you put ice into a glass of fresh water and leave it to melt the level will not change because the ice displaces a volume equivalent to its mass. It will melt and fill the space it displaced exactly.

    However, icebergs are fresh water floating on salt water. Salt water is denser than fresh water and so less of it is displaced by the ice to balance the weight of the ice. But when the ice melts it takes up as much room as before. (i.e. for the same mass the salt water has less volume than fresh water). So the level of the water will rise.

    Can’t give you figures on it though…


    • Dear “younearlypersuededme”

      There is nothing controversial in my calculations, and I an not making an “argument.”

      If you read carefully, I say things like “The number of gigatonnes of water that must be added to the oceans to raise the sea level 1 millimeter is given by…” It is stated explicitly that the water is “added” to the ocean. Floating ice that melts does not add anything to the ocean – it was already there. I assumed this was understood.

      Your concern about freshwater from floating ice melting into salt water of the ocean is a triviality in this context. I have also ignored issues of the thermal expansion of water ,which is zero at about 4 degrees C, so that the volume of a given mass of water increases for temperatures above and below 4 degrees C.

      Thank you for you comment.

      Tom


    • You are correct that Iceburgs are fresh water that float in salt water, but your logic is flawed because of the laws that govern boyancy. Iceburgs displace the volume of water it will occupy once it melts.


  12. I think it would be useful to point out that Davis coauthors the rignot paper… and that davis et al. 2005 uses radar altimetry which has an upwards trending bias in regions of high slopes and rugged terrain, thus resulting in lower than actual mass losses in the WAIS… Also it should be noted that the Velicogna measurements have been corrected for since then with an adjustment for glacial isostatic rebound which is more appropriate and the result is mass declines. Check out Allison et al. 2009 for the most comprehensive summary of the ice sheet contributions since clearly your papers that are being cited are outdated. Velicogna’s 2009 paper is a good read and so is Pritchard et al. 2009 also if you want to learn a bit.


  13. But overall the net loss is anywhere between -100 Gt and -300 Gt depending on the paper and method of either Altimetry (rarely used), Grace or InSar


    • Dear Robert,

      The math is still very simple. Even at 300 Gt per year, the oceans rise a tiny 0.85 mm per year. Too bad, no cities under water I guess.

      Best Regards,
      ClimateSanity


  14. this really helped with my science test


  15. this really helped with my science test,:)


  16. Fabulous diversion – smokescreen ! I must say I’m quite excited ! So, non of the climate shift expoused is true either – EH ? No loss of fresh water refresh from lack-o-glacciers ? No disruption in thermo haline ? Thank you soooo much ! I’ll stop concering myself with the inevitable grab for food, water et al. Hurrah- no famine – no crop failures YAY ! UDAMAN ! I have a bridge I’d like to get you to sell fo-me 2 – what’s your broker license ?


    • Dear Claude,

      I must admit I have a hard time understanding hysterical comments like yours.

      Are you implying that the above conversion factors are incorrect? Why are they a “diversion?”

      Best Regards
      ClimateSanity

      best regards,
      ClimateSanity


      • Because Claude is an alarmist buffoon. No amount of scientific explanation will sway his propaganda’d position.

        Nicely explained though Tom. Very helpful.
        Keep up the sanity.


  17. Tom, I think that changing volumes to weight and back is confusing, or it is to me, especially if it is about increasing the volume of water in the world! You say that the volume of ice is estimated at 30 million km3, so that should melt to 30 million km3 or 30 quintillion litres, if indeed for some obscure reason it could all melt. But how accurate is the volume of ice? You say Antarctica has 25 million km3 of ice. Is that summer or winter? The size of Antarctica is 14 million km2 in summer, so that means a thickness of ice of nearly 2 km, or in winter, when Antartica is 2x larger, still a thickness of 1 km. It does not seem to compute – if Antarctica melted 1/2 in the summertime, it means that the ocean levels would rise 45 metres and that is clearly not the case.
    So, who determines the volume of ice, how is it measured, in the middle of winter, and in the middle of summer, and has there been a marked effect each year to ocean levels between summer and winter?


  18. Tom, I must admit that I worded some of the above a bit awkward – it was to stimulate the debate about the volume of ice. Some websites claim that Antarctica has 29 million km3 of ice, some even 30 million km3. The discrepancies are significant enough, as a “missing 5 million km3 is rather significant. I realise that sea ice has no significant effect on sea levels, and that sea ice will not be anywhere near as thick as the land ice either, and I apologise for my exaggeration above. But in winter, the ice is not just going to stop growing on land – and vice versa.
    This is why I support your theory well ahead of any other. Sea levels will take very, very long times to change and must be very difficult to measure, as also tides are involved. What is going to be easier to measure? rising sea levels or the volume of ice? That is why I asked the questions as in my first comment, especially in view of reported differences in the volume of ice.


  19. Nice calculations! Just one small point related to the “No need to worry it’s such a small sea level increase” arguments – the current satellite data on ice loss from the polar regions shows an increasing trend over the last 10 years. So you can’t just say “oh its only 300GT per year = .85mm” – if it is increasing at 50Gt per year then in a a decade or so you’re looking at 1000 Gt per year, and so on… (and who knows if the rate of increase will go up if temperatures do get significantly higher? It does seem feasible)

    The problem is that nobody really understands ice sheet dynamics and what happens if they do start to move. There is some evidence from the last ice age melt that large portions of ice sheet can disintegrate in a matter of a century or less, so there is some worry that if warming continues then some sort of instability could be reached and “varoom… thar she goes…”


    • Dear Jumbo,

      thankyou for your comment.

      Please take a look at this graph of satellite derived sea level data for almost the last 20 years.

      If your worry that “it is increasing at 50Gt per year” were correct, then we would expect to see the sea level rise rate increasing by about 1mm per year every seven years. As the plot indicates, nothing of the kind is happening. In fact, it looks to me as though the sea level rise rate has decreased over the last 3 years.

      Note that according to this graph, the rise rate has held more or less steady at about 3.1 mm per year for nearly two decades. That translates into about 1 foot per century. Your worries that the ice sheets are going to rapidly slide into the oceans also is unfounded.

      Sea level rise is a small problem that is better dealt with by engineers than by destroying the economy of the planet.

      Best Regards,
      Tom Moriarty


  20. [...] blog suggests there’s nothing to worry about, but I don’t have the time to work out the math. [...]


  21. You’re a very patient man, Tom.

    keep up the sanity.


  22. As a coastal dweller, I am concerned that any sea rise that is in excess of natural processes will have significant effects. You suggest that a 2″ rise in sea level — a global mean — is not meaningful. Perhaps if it occurred in a bell jar. But combined with natural forces, such a sea rise could be disastrous depending on one’s region and specific location.

    Since 2″ is the sheer minimum to which you will admit, it’s quite likely that the number will be higher. Four inches, perhaps, or six inches? And then we are in real trouble territory.

    In short, for all your diddling with the arithmetic, you don’t deal with the central issue that melt is occurring, it is occurring faster than we are accustomed, and its effects in that context are unknown. You prefer to risk others’ well being so that your equations balance out. Swell.

    As to your comment, “Sea level rise is a small problem that is better dealt with by engineers than by destroying the economy of the planet.”

    I presume you are in favor of higher taxes to pay for these engineering feats, and global contributions to cover them in regions that cannot afford clean water let alone sea walls? Higher deficit spending? Or fees for the wealthy to cover their profligate living on the most challenged residential littorals?

    I bet not. Surprise me.


  23. [...] the groundwater depletion data from figure 2,  converted it to sea level rise rate in mm ( one km3 of water yields 2.78 x 10-3 mm of sea level rise), and fit it to an exponential (R2= 0.98).  Figure 3. Wada groundwater depletion (mm/year) with an [...]


  24. I was directed to this site to check my own maths. I am not too far off. Many thanks for your efforts.

    When discussion is about sea level rise I like to mention the Amazon River. In spate, discharges 300,000 cubic metres per second into the sea, this is equal to the next FIVE largest rivers in the world! So, the worlds six biggest rivers discharge 600,000 cubic metres per second into the sea. This should cause sea level to rise by 1 metre in just under 20 years, but it doesn’t! Helps to get people thinking about how water moves around. Especially how long it takes for a flood plain to develop and then people build on them and complain when they get flooded.


    • Richard,

      Thanks for the comment.

      But all the water from the rivers comes from the oceans to start. That is, it evaporates from the oceans, precipitates on land, and makes its way to the rivers, where it is discharged back into the oceans. No mystery there.

      Best regards
      Climatesanity


  25. ???


  26. the landed ice need not melt only fall into the ocean to raise sea levels to the amount that melting will create


  27. Curious: In a warmer environment, the temperature of the atmosphere rises, so the planet’s air can hold more water in vapor form. How much fresh water is in the entire atmosphere at any given point? How much of the newly-melted ice will actaully evaporate into the newly-warmer air?

    Thanks for maintaining a reasoned apporach, and looking at all available facts. I’m sure in 100 years scientists will have a good laugh at the current fistfight, as we do today over old popular arguments.


  28. [...] 29,960,000 cubic kilometers of ice in the world – that is, 29,960,000 gigatonnes of ice ( see http://climatesanity.wordpress.com/conversion-factors-for-ice-and-water-mass-and-volume/ ). At 475 gigatonnes a year it is going to take a very long time to melt, especially since the [...]


  29. I am very happy to have discovered your site! It is unfortunate that too many “sheep” follow the “wolves in sheep’s clothing” arguments that create fear of “global warming”, oh!, sorry, “climate change”.

    I’m trying to respond to just such a wolf that has a position to lead many sheep astray.

    Thank-you very much for your engineer’s approach that shows facts.

    Best regards.
    MRV


  30. Self-referential science isn’t science, it’s cult. Your numerology doesn’t accord with estimates by about 95% of climatologists and oceanographers. I know, they’re all part of a global conspiracy to drive truth-seekers such as you out of business. Not so long as there are oil companies to pay the bills! Keep toting the line.


    • Hey Jake,

      What’s your problem? Do think the conversion factors I have given here are wrong? Do you think 95% of climatologists and oceanographers disagree with the the conversion factors here?

      This is pretty simple stuff, Jake.

      Speaking of oil companies paying my bills, here is who I work for…

      http://climatesanity.wordpress.com/about/

      Two last things, Jake: First, learn to do some arithmatic. Second, get a life.


  31. Hi Tom –
    I think you are the best person I have found to take this idea further –
    We have now had stable world average temperatures for the last 11 years (not long I know). In that time, and before, a lot of ice has melted. Have you or anyone you know done the sum to calculate if the amount of ice melted in that time is enough to stop the atmosphere heating up since year 2000? In other words, global warming seems to be (temporarily?) on hold even though greenhouse gases have continued to climb. Is this explained by the amount of ice which has melted?

    Best regards
    BobC


  32. During the last ice age, there were 3 kilometer high ice cap covering most of Canada. If I am to approximate that the ice cap started from 45 parallel up gives close to 4.3 billion Gt of water. That translates into 12km of water depletion into the oceans.

    The numbers simply do not add up.

    PS I used 0.9 factor to convert from ice volume to water.


    • Adrian,

      Lets make some order of magnitude calculations based on your numbers.

      Lets make the very rough estimate that Canada is 10 million square kilometers. The oceans cover about 360 million square kilometers.

      Roughly speaking, if you melted a 3 kilometer thick sheet of ice that covered 10 million square kilometers of land and dumped the water into 360 million square kilometers of ocean, then the ocean would rise about (3000 meters) * (10 million kilomters) / (360 million kilometers) = 83 meters.

      Calculated another way: 10 million square kilomters of land covered by 3 kilometer ice is the same as 30 million cubic kilometers of ice. Each cubic kilometer of ice will raise the oceans about 2.8 microns when it melts and flows to the ocean. (30 million cubic kilometers of ice) X (2.8 microns/cubic kilomter of ice) = 84 million microns = 84 meters.

      Now, according to the USGS the oceans were 125 meters lower during the last glacial maximum (say 20,000 years ago) than they are today. Our rough estimate was 83 meters. The difference is likely due to our estimate of the area covered by ice and our estimate of the ice thickness. Here is a map showing the ice covered area during the last glacial maximum. Remember, for our calculations only ice on land makes a difference.

      So, as you can see your estimate of a 12 kilometer ocean drop is off by two orders of magnitude. Probably a unit conversion mistake.

      Best Regards,
      ClimateSanity


      • Simply put all, Al Gore is a charlatan. The sky is falling = the sea is rising.

        I’m thinking that if we are smart, we get a jump on being the crowd to start the next scare, you see, the earths inner core is molten so the continents are actually sinking into the core.

        Anyone want to buy into my geo core cooling credits? ;)

        Peace…


  33. While the Earth has always endured natural climate change variability, we are now facing the possibility of irreversible climate change in the near future. The increase of greenhouse gases in the Earth?s atmosphere from industrial processes has enhanced the natural greenhouse effect. This in turn has accentuated the greenhouse ?trap? effect, causing greenhouse gases to form a blanket around the Earth, inhibiting the sun?s heat from leaving the outer atmosphere. This increase of greenhouse gases is causing an additional warming of the Earth?s surface and atmosphere. A direct consequence of this is sea-level rise expansion, which is primarily due to the thermal expansion of oceans (water expands when heated), inducing the melting of ice sheets as global surface temperature increases.
    Forecasts for climate change by the 2,000 scientists on the United Nations Intergovernmental Panel on Climate Change (IPCC) project a rise in the global average surface temperature by 1.4 to 5.8°C from 1990 to 2100. This will result in a global mean sea level rise by an average of 5 mm per year over the next 100 years. Consequently, human-induced climate change will have ?deleterious effects? on ecosystems, socio-economic systems and human welfare.At the moment, especially high risks associated with the rise of the oceans are having a particular impact on the two archipelagic states of Western Polynesia: Tuvalu and Kiribati. According to UN forecasts, they may be completely inundated by the rising waters of the Pacific by 2050.According to the vast majority of scientific investigations, warming waters and the melting of polar and high-elevation ice worldwide will steadily raise sea levels. This will likely drive people off islands first by spoiling the fresh groundwater, which will kill most land plants and leave no potable water for humans and their livestock. Low-lying island states like Kiribati, Tuvalu, the Marshall Islands and the Maldives are the most prominent nations threatened in this way.“The biggest challenge is to preserve their nationality without a territory,” said Bogumil Terminski from Geneva. The best solution is continue to recognize deterritorialized states as a normal states in public international law. The case of Kiribati and other small island states is a particularly clear call to action for more secure countries to respond to the situations facing these ‘most vulnerable nations’, as climate change increasingly impacts upon their lives


    • Jennifer,

      We have all heard about about the world coming to an end due to rising temperatures. My guess is that no amount of reason will shake your passion.

      So let’s consider some specifics. You tell me that Tuvalu is going under water because of global warming. Here is the sea level data for Tuvalu from the Permanent Service for Mean Sea level Click on the imgage to see the entire graph…

      As for Kiribati…

      You sound like the kind of person who enjoys a good panic. But spreading it to other people is really a disservice.

      Best regards,
      ClimateSanity


  34. Hi Tom, can you address the implications of accelerating ice sheet loss a bit further please? Saying it can’t be happening because sea level rises are not accelerating is neglecting the other factors that affect sea level rise. What would you estimate the sea level rise in 2100 to be if the accelerating ice sheet loss measured below continues?

    Velicogna, I. (2009), Increasing rates of ice mass loss from the Greenland and Antarctic ice sheets revealed by GRACE, Geophys. Res. Lett., 36, L19503, doi:10.1029/2009GL040222

    I get approx 78cm but I’d appreciate your analysis if you have time. This of course neglects thermal and ground water effects but i’m sure you get the idea.


    • Nick,

      The second sentence of this very paper says the melting ice of Antarctica contributes “an equivalent of 0.4 mm of sea level rise per year” or about 1.5 inches per century.

      Velicogna’s noisy data covered only three years. It indicated several monthly ice volume changes that were almost as large as the cumulative three year change when fit to a line. If only the last two years of her data are used, then the ice loss rate is reduced by 80%.

      I am not sure how you get 78 cm from this.

      Best regards,
      Climatesanity


  35. Apart from all the discussion on Ice Melting, I want your opinion on fresh water of rivers that is flowing into the seas.
    According to recent surveys it is evident that out of 10 rivers only 8 reach their ends which mean that 100% fresh water of 20% rivers globally is no more able to reach the ocean. This decreased river flow is caused by climate change as well as by increased water consumption and if same trend will continue 100% water of 100% will not reach oceans in near future.
    The question here is that if that much fresh water is not reaching oceans then what is its effect on sea level? Isn’t it balancing the equation:
    Decreased river fresh water into sea + increased melted ice = No sea level rise


  36. [...] 2011. The researchers estimate Greenland is losing almost 200 gigatons of ice per year. It takes 300 gigatons of water to raise sea levels by 1 millimeter, so Greenland is currently contributing about 0.66 mm of sea-level rise per year. At that rate, [...]


  37. Sea level rose 6.7 inches between 1870 and 2004. An additional potential sea level rise of 6.7 inches is held in the reservoirs of manmade dams around the world. Without dams, sea level would have risen an average of an inch every 10 years. Surely sea level is fising faster now than in 1870; an inch every 5 years, if more dams are not built, might be a good guess.


  38. there is a lot of interesting reading here. for one who does not have the education to comprehend all of the math involved some of this is hard to wrap ones head around. yet am puzzled as to how oceans levels are rising yet lakes are falling?


  39. Nov 2013 – National Geographic just published an article with information about sea level rises which confirm the comments here. however, they report that Antartica has lost 65,000,000 tons of ice since 1992 – Isn’t that about .07 cubic kilometers in contrast to the 152 cubic kilometers suggested here? (my math could be wrong!).

    I have to confess significant skepticism to climate models as my safety and possibly life depend upon other NOAA weather models for hurricane forecasts in the Pacific Ocean off Mexico. Numerous models differ somewhat but many are in general agreement. However, the consensus for direction of a hurricane track can change 180 degrees within 24 hours in the longer range forecasts. I’ve even had to change my plans within only 12 hours of a hurricane arrival because of changes in forecasts within 12 hours of an event. These are models with years of good data to compare actual events with predictions and refine models. How on earth can we be confident about ANY predictions from much newer models with much less verification than hurricane forecasts?

    While I agree with the sentiments of not overly stressing the habitat of our only home, I find it hard to take these predictions of doom too seriously, especially when historic records suggest we should be more worried about an impending ice age.

    Another ‘correlation’ with warming and carbon release is the actual heat generated by the combustion of carbon fuels. I once estimated this to currently be about 10% of the heat climatologists estimate will be a critical change in planetary heat exchange due to their posited carbon effect. It raises the issue that we probably can’t continue to utilize energy in ever increasing amounts – from whatever source without potential serious climatic consequences.


    • Oops – forgot to add the refence to the NG article. http://ngm.nationalgeographic.com/2013/09/rising-seas/if-ice-melted-map


    • Hi John,

      Thanks for the comment.

      My post above says…

      “One gagatonne of water has a volume of one billion cubic meters, or one cubic kilomter.(1 Gt water ≡ 1 km³)Of course, one gigatonne of ice has a greater volume than one gigatonne of water. But it will still have a volume of 1 km³ when it melts.”

      So, 65,000,000 (6.5 x 10^7) tonnes of water has a volume of 0.065 km^3.

      I have not read the National Geographic article that you mentioned, but I would be very surprised if they said that Antarctica has lost only 65 million tonnes of ice since 1993. But it would not surprise me if they said that the Antarctic is losing 152 billion tonnes per year.

      You mentioned…

      “Another ‘correlation’ with warming and carbon release is the actual heat generated by the combustion of carbon fuels. I once estimated this to currently be about 10% of the heat climatologists estimate will be a critical change in planetary heat exchange due to their posited carbon effect. It raises the issue that we probably can’t continue to utilize energy in ever increasing amounts – from whatever source without potential serious climatic consequences.”

      The total energy consumption of the planet per year is about 5×10^20 Joules/year. The amount of solar energy that impinges the Earth every year is about 5×10^24 Joules/year. So the heat released by human energy consumption is on the order of 10^-4 of energy coming from the sun.

      ClimateSanity


      • Thank-you Tom.
        The NG site seems to put a block on after a certain time browsing so I hadn’t been able to go back and check. The block was off this morning and I was able to note that the 65 million tonnes was PER YEAR. That is on the page describing Antarctica – http://ngm.nationalgeographic.com/2013/09/rising-seas/if-ice-melted-map?rptregcta=reg_free_np&rptregcampaign=20131016_rw_membership_n1p_intl_ot_w. Still much lower than other values, but perhaps a misprint.

        The issue with generated heat is that, for a ‘constant’ global temperature, the amount of heat leaving the planet must equal the amount of heat arriving, regardless of absolute amounts. Global warming is suggested to be caused by elevated levels of carbon dioxide trapping heat which would otherwise be lost into space, thus reducing heat loss from the planet which results in a temperature rise (I’m sure this is very familiar to you) There are calculations on the amount of additional heat trapped by current and projected carbon dioxide levels – which you would expect to be a small fraction of the heat arriving on earth. I haven’t repeated my past research to be able to quote the value, but I would guess, based upon your above calculation and my recollection that it would be about 10^-3 of energy coming from the sun. My point was that the calorific value of fossil fuels consumed is about 10% of that (10^-3) value, not of the total energy from the sun, suggesting that the use of energy itself, regardless of source could be a significant contributor to global warming, and may become even more significant if global energy use continues to rise.


      • Hi John,

        I have looked at the link you provided and can find no reference to 65 million tonnes, whether per year of since any particular date. I would be amazed if the folks at National Geographic made either of those claims. They tend to highlight the high-end numbers (like 152 billion tonnes per year), and 65 million tonnes per year is definitely at the low , end. But they might have a typo some place.

        Tom,
        ClimateSanity


  40. We have seen that at both poles there has been an increase of sea ice. When ever I bring up this to the “true belivers” they say: “…the EXTENT of ice is greater but not the MASS (or volume).”
    I’m no scientist but it would seem that extent and mass are related.
    My simple minded thinking says: If you have a block of ice thats 2′ by 2′ by 2′ it would have the same mass as a block 1′ by 1′ by 4′ even though the EXTENT of the second block is greater…am I missing something?


  41. Hey Tom, strong work! It was pretty interesting reading through most of these comments and it is evident when faced with mathematical calculations and data that certian political groups scoff at your page. To those groups id like to ask what is more probable, a government looking to generate funds from loosly based ideas, or all the ice melting in the world and drowning everyone?


  42. Hey! I have a question for this. How much of the ice is already floating in the water? It already should keep the ocean a bit higher up considering an iceberg is gigantly deep into the water compared to what you see of it.

    The only thing needed to be considered is the extra water coming to the ocean by melting ice, and I doubt it would make any difference really.


    • Tom,
      Floating ice does not raise the oceans when it melts. Glacier ice that slides off a landmass (such as Greenland or Antarctica) does raise the oceans.


  43. […] From Climatesanity: Conversion factors for ice and water mass and volume […]


  44. […] […]


  45. […] flyspeck in the scheme of things. Antarctica’s ice losses on the rise From Climatesanity: Conversion factors for ice and water mass and volume If one cubic kilometer of water (i.e., one gigatonne of water) is spread evenly over the entire […]


  46. Your conversion rates do not seem to be correct. Please reconfirm them.


    • Hunter,

      Yup, they are correct.

      Specifically, what do think is wrong?

      ClimateSanity


  47. […] The paper is discussed in more detail on WUWT. The discussion also links to conversion factors for units of water mass and volume, see here. […]


  48. 1 cubic metre = 1000 kg, yet 1 litre of water is approx 1 kg, therefore 1000L or ( 5 ) 45 gallon drums is the same volume roughly of a cubic metre. Are we getting this right?


    • Yes, I am getting this right.

      1 liter = 0.264 gallons
      see… http://calculator-converter.com/gal_to_l_convert_gallon_to_liter_conversion_calculator_gal_litre.php

      So, 1000 liters = 264 gallons = 5.87 (45 gallon drums)

      In other words…
      1000 liters of water is one cubic meter of water
      1000 liters of water is 1000 kg
      1000 liters or water is 264 gallons
      1000 liters of water is 5.85 (45 gallon drums of water)

      Where is the problem?

      You are reacting with surprise to my calculations, but my calculations are simple and correct.
      I suggest you look for other reasons for your surprise.


  49. […] The paper is discussed in more detail on WUWT. The discussion also links to conversion factors for units of water mass and volume, see here. […]


  50. […] From Climatesanity: Conversion factors for ice and water mass and volume […]



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