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Ups and downs of sea level projections

Filed under: — stefan @ 31 August 2009

By Stefan Rahmstorf and Martin Vermeer

The scientific sea level discussion has moved a long way since the last IPCC report was published in 2007 (see our post back then). The Copenhagen Synthesis Report recently concluded that “The updated estimates of the future global mean sea level rise are about double the IPCC projections from 2007″. New Scientist last month ran a nice article on the state of the science, very much in the same vein. But now Mark Siddall, Thomas Stocker and Peter Clark have countered this trend in an article in Nature Geoscience, projecting a global rise of only 7 to 82 cm from 2000 to the end of this century.

Coastal erosion: Like the Dominican Republic, many island nations are particularly vulnerable to sea level rise. (c) S.R.
Coastal erosion: Like the Dominican Republic, many island nations are
particularly vulnerable to sea level rise. (Photo: S.R.)

Semi-empirical sea level models

Siddall et al. use a semi-empirical approach similar to the one Stefan proposed in Science in 2007 (let’s call that R07) and to Grinsted et al. (2009), which we discussed here. What are the similarities and where do the differences come from?

For short time scales and small temperature changes everything becomes linear and the two new approaches are mathematically equivalent to R07 (see footnote 1). They can all be described by the simple equation:

dS/dt = a ΔT(t) + b     (Eq 1)

dS/dt is the rate of change of sea level S, ΔT is the warming above some baseline temperature, and a and b are constants. The baseline temperature can be chosen arbitrarily since any constant temperature offset can be absorbed into b. This becomes clear with an example: Assume you want to compute sea level rise from 1900-2000, using as input a temperature time series like the global GISS data. A clever choice of baseline temperature would then be the temperature around 1900 (averaged over 20 years or so, we’re not interested in weather variability here). Then you can integrate the equation from 1900 to 2000 to get sea level relative to 1900:

S(t) = a ∫ΔT(t’) dt’ + b t     (Eq 2)

There are two contributions to 20th C sea level rise: one from the warming in the 20th Century (let’s call this the “new rise”), and a sea level rise that results from any climate changes prior to 1900, at a rate b that was already present in 1900 (let’s call this the “old rise”). This rate is constant for 1900-2000 since the response time scale of sea level is implicitly assumed to be very long in Eq. 1. A simple matlab/octave code is provided below (2).

If you’re only interested in the total rise for 1900-2000, the temperature integral over the GISS data set is 25 ºC years, which is just another way of saying that the mean temperature of the 20th Century was 0.25 ºC above the 1900 baseline. The sea level rise over the 20th Century is thus:

S(1900-2000) = 25 a + 100 b     (Eq. 3)

Compared to Eq. 1, both new studies introduce an element of non-linearity. In the approach of Grinsted et al, sea level rise may flatten off (as compared to what Eq 1 gives) already on time scales of a century, since they look at a single equilibration time scale τ for sea level with estimates ranging from 200 years to 1200 years. It is a valid idea that part of sea level rise responds on such time scales, but this is unlikely to be the full story given the long response time of big ice sheets.

Siddall et al. in contrast find a time scale of 2900 years, but introduce a non-linearity in the equilibrium response of sea level to temperature (see their curve in Fig. 1 and footnote 3 below): it flattens off strongly for warm temperatures. The reason for both the long time scale and the shape of their equilibrium curve is that this curve is dominated by ice volume changes. The flattening at the warm end is because sea level has little scope to rise much further once the Earth has run out of ice. However, their model is constructed so that this equilibrium curve determines the rate of sea level rise right from the beginning of melting, when the shortage of ice arising later should not play a role yet. Hence, we consider this nonlinearity, which is partly responsible for the lower future projections compared to R07, physically unrealistic. In contrast, there are some good reasons for the assumption of linearity (see below).

Comparison of model parameters

But back to the linear case and Eq. 1: how do the parameter choices compare? a is a (more or less) universal constant linking sea level to temperature changes, one could call it the sea level sensitivity. b is more situation-specific in that it depends both on the chosen temperature baseline and the time history of previous climate changes, so one has to be very careful when comparing b between different models.

For R07, and referenced to a baseline temperature for the year 1900, we get a = 0.34 cm/ºC/year and b = 0.077 cm/year. Corresponding values of Grinsted et al. are shown in the table (thanks to Aslak for giving those to us!).

For Siddall et al, a = s/τ where s is the slope of their sea level curve, which near present temperatures is 4.8 meters per ºC and τ is the response the time scale. Thus a = 0.17 cm/ºC/year and b = 0.04 cm /year (see table). The latter can be concluded from the fact that their 19th Century sea level rise, with flat temperatures (ΔT(t) = 0) is 4 cm. Thus, in the model of Siddall et al, sea level (near the present climate) is only half as sensitive to warming as in R07. This is a second reason why their projection is lower than R07.


a [cm/ºC/year]

[cm /year]

“new rise” [cm] (25a)

“old rise” [cm] (100b)


total model rise [cm]








Grinsted et al “historical”







Grinsted et al “Moberg”







Siddall et al






8.3 (?) 7.9

Performance for 20th Century sea level rise

For the 20th Century we can compute the “new” sea level rise due to 20th Century warming and the “old” rise due to earlier climate changes from Eq. 3. The results are shown in the table. From Grinsted et al, we show two versions fitted to different data sets, one only to “historical” data using the Jevrejeva et al. (2006) sea level from 1850, and one using the Moberg et al. (2006) temperature reconstruction with the extended Amsterdam sea level record starting in the year 1700.

First note that “old” and “new” rise are of similar magnitude for the 20th Century because of the small average warming of 0.25 ºC. But it is the a-term in Eq. (2) that matters for the future, since with future warming the temperature integral becomes many times larger. It is thus important to realise that the total 20th Century rise is not a useful data constraint on a, because one can get this right for any value of a as long as b is chosen accordingly. To constrain the value of a – which dominates the 21st Century projections — one needs to look at the “new rise”. How much has sea level rise accelerated over the 20th Century, in response to rising temperatures? That determines how much it will accelerate in future when warming continues.

The Rahmstorf model and the Grinsted “historical” case are by definition in excellent agreement with 20th Century data (and get similar values of a) since they have been tuned to those. The main difference arises from the differences between the two sea level data sets used: Church and White (2006) by Rahmstorf, Jevrejeva et al. (2006) by Grinsted et al. Since the “historical” case of Grinsted et al. finds a ~1200-year response time scale, these two models are almost fully equivalent on a century time scale (e-100/1200=0.92) and give nearly the same results. The total model rise in the last column is just 1.5 percent less than that based on the linear Eq. 3 because of that finite response time scale.

For the Grinsted “Moberg” case the response time scale is only ~210 years, hence our linear approximation becomes bad already on a century time scale (e-100/210=0.62, the total rise is 15% less than the linear estimate), which is why we give the linear estimates only in brackets for comparison here.

The rise predicted by Siddall et al is much lower. That is not surprising, since their parameters were fitted to the slow changes of the big ice sheets (time scale τ=2900 years) and don’t “see” the early response caused by thermal expansion and mountain glaciers, which makes up most of the 20th Century sea level rise. What is surprising, though, is that Siddall et al. in their paper claim that their parameter values reproduce 20th Century sea level rise. This appears to be a calculation error (4); this will be resolved in the peer-reviewed literature. Our values in the above table are computed correctly (in our understanding) using the same parameters as used by the authors in generating their Fig.3. Their model with the parameters fitted to glacial-interglacial data thus underestimates 20th Century sea level rise by a factor of two.

Frosty legacy: We cannot afford to lose even a few percent of the land ice on Earth, which in total would be enough to raise global sea levels by 65 meters. (Calving front in Svalbard, (c) S.R.)

Frosty legacy: We cannot afford to lose even a few percent of the land ice on Earth, which in total would be enough to raise global sea levels by 65 meters. (Calving front in Svalbard, photo by S.R.)

Future projections

It thus looks like R07 and Grinsted et al. both reproduce 20th Century sea level rise and both get similar projections for the 21st Century. Siddall et al. get much lower projections but also strongly under-estimate 20th Century sea level rise. We suspect this will hold more generally: it would seem hard to reproduce the 20th Century evolution (including acceleration) but then get very different results for the 21st Century, with the basic semi-empirical approach common to these three papers.

In fact, the lower part of their 7-82 cm range appears to be rather implausible. At the current rate, 7 cm of sea level rise since 2000 will be reached already in 2020 (see graph). And Eq. 1 guarantees one thing for any positive value of a: if the 21st Century is warmer than the 20th, then sea level must rise faster. In fact the ratio of new sea level rise in the 21st Century to new sea level rise in the 20th Century according to Eq. 2 is not dependent on a or b and is simply equal to the ratio of the century-mean temperatures, T21/T20 (both measured again relative to the 1900 baseline). For the “coldest” IPCC-scenario (1.1 ºC warming for 2000-2100) this ratio is 1.3 ºC / 0.25 ºC = 5.2. Thus even in the most optimistic IPCC case, the linear semi-empirical approach predicts about five times the “new” sea level rise found for the 20th Century, regardless of parameter uncertainty. In our view, when presenting numbers to the public scientists need to be equally cautious about erring on the low as they are on the high side. For society, after all, under-estimating global warming is likely the greater danger.

Does the world have to be linear?

How do we know that the relationship between temperature rise and sea level rate is linear, also for the several degrees to be expected, when the 20th century has only given us a foretaste of 0.7 degrees? The short answer is: we don’t.

A slightly longer answer is this. First we need to distinguish two things: linearity in temperature (at a given point in time, and all else being equal), and linearity as the system evolves over time. The two are conflated in the real world, because temperature is increasing over time.

Linearity in temperature is a very reasonable assumption often used by glaciologists. It is based on a heat flow argument: the global temperature anomaly represents a heat flow imbalance. Some of the excess heat will go into slowly warming the deep ocean, some will be used to melt land ice, a tiny little bit will hang around in the atmosphere to be picked up by the surface station network. If the anomaly is 2 ºC, the heat flow imbalance should be double that caused by a 1 ºC anomaly. That idea is supported by the fact that the warming pattern basically stays the same: a 4 ºC global warming scenario basically has the same spatial pattern as a 2 ºC global warming scenario, only the numbers are twice as big (cf. Figure SMP6 of the IPCC report). It’s the same for the heating requirement of your house: if the temperature difference to the outside is twice as big, it will lose twice the amount of heat and you need twice the heating power to keep it warm. It’s this “linearity in temperature” assumption that the Siddall et al. approach rejects.

Linearity over time is quite a different matter. There are many reasons why this cannot hold indefinitely, even though it seems to work well for the past 120 years at least. R07 already discusses this and mentions that glaciers will simply run out of ice after some time. Grinsted et al. took this into account by a finite time scale. We agree with this approach – we merely have some reservations about whether it can be done with a single time scale, and whether the data they used really allow to constrain this time scale. And there are arguments (e.g. by Jim Hansen) that over time the ice loss may be faster than the linear approach suggests, once the ice gets wet and soft and starts sliding. So ultimately we do not know how much longer the system will behave in an approximately linear fashion, and we do not know yet whether the real sea level rise will then be slower or faster than suggested by the linear approach of Eq. 1.

Getting soft? Meltwater on the Greenland Ice Sheet. Photo by Ian Joughin.
Getting soft? Meltwater lake and streams on the Greenland Ice Sheet near 68ºN at 1000 meters altitude. Photo by Ian Joughin.

Can paleoclimatic data help us?

Is there hope that, with a modified method, we may successfully constrain sea level rise in the 21st Century from paleoclimatic data? Let us spell out what the question is: How will sea level in the present climate state respond on a century time scale to a rapid global warming? We highlight three aspects here.

Present climate state. It is likely that a different climate state (e.g. the glacial with its huge northern ice sheets) has a very different sea level sensitivity than the present. Siddall et al. tried to account for that with their equilibrium sea level curve – but we think the final equilibrium state does not contain the required information about the initial transient sensitivity.

Century time scale. Sea level responds on various time scales – years for the ocean mixed layer thermal expansion, decades for mountain glaciers, centuries for deep ocean expansion, and millennia for big ice sheets. Tuning a model to data dominated by a particular time scale – e.g. the multi-century time scale of Grinsted et al. or the multi-millennia time scale of Siddall et al. – does not mean the results carry over to a shorter time scale of interest.

Global warming. We need to know how sea level – oceans, mountain glaciers, big ice sheets all taken together – responds to a globally near-uniform forcing (like greenhouse gas or solar activity changes). Glacial-interglacial climate changes are forced by big and highly regional and seasonal orbital insolation changes and do not provide this information. Siddall et al use a local temperature curve from Greenland and assume there is a constant conversion factor to global-mean temperature that applies across the ages and across different mechanisms of climate change. This problem is not discussed much in the paper; it is implicit in their non-dimensional temperature, which is normalised by the glacial-holocene temperature difference. Their best guess for this is 4.2 ºC (as an aside, our published best guess is 5.8 ºC, well outside the uncertainty range considered by Siddall et al). But is a 20-degree change in Greenland temperature simply equivalent to a 4.2-degree global change? And how does local temperature translate into a global temperature for Dansgaard-Oeschger events, which are generally assumed to be caused by ocean circulation changes and lead to a temperature seesaw effect between northern and southern hemisphere? What if we used their amplitude to normalise temperature – given their imprint on global mean temperature is approximately zero?

Overall, we find these problems extremely daunting. For a good constraint for the 21st Century, one would need sufficiently accurate paleoclimatic data that reflect a sea level rise (a drop would not do – ice melts much faster than it grows) on a century time scale in response to a global forcing, preferably from a climate state similar to ours – notably with a similar distribution of ice on the planet. If anyone is aware of suitable data, we’d be most interested to hear about them!

Update (8 Sept): We have now received the computer code of Siddall et al (thanks to Mark for sending it). It confirms our analysis above. The code effectively assumes that the warming over each century applies for the whole century. I.e., the time step for the 20th Century assumes the whole century was 0.74 ºC warmer than 1900, rather than just an average of 0.25 ºC warmer as discussed above. When this is corrected, the 20th Century rise reduces from 15 cm to 8 cm in the model (consistent with our linear estimate given above). The 21st Century projections ranging from 32-48 cm in their Table 1 (best estimates) reduce to 24-32 cm.

Martin Vermeer is a geodesist at the Helsinki University of Technology in Finland.


(1) Siddall et al. use two steps. First they determine an equilibrium sea level for each temperature (their Eq 1, and shown in their Fig. 1). Second, they assume an exponential approach of sea level to this equilibrium value in their Eq. 2, which (slightly simplified, for the case of rising sea level) reads:

dS/dt = (Se(T) – S(t)) / τ.

Here S is the current sea level (a function of time t), Se the equilibrium sea level (a function of temperature T), and τ the time scale over which this equilibrium is approached (which they find to be 2900 years).
Now imagine the temperature rises. Then Se(T) increases, causing a rise in sea level dS/dt. If you only look at short time scales like 100 years (a tiny fraction of those 2900 years response time), S(t) can be considered constant, so the equation simplifies to

dS/dt = Se(T)/ τ + constant.

Now Se(T) is a non-linear function, but for small temperature changes (like 1 ºC) this can be approximated well by a linear dependence Se(T) = s * T + constant. Which gives us

dS/dt = s/τ * T + constant, i.e. Eq (1) in the main post above.

R07 on the other hand used:
dS/dt = a * (T – T0), which is also Eq. (1) above.
Note that a = s/τ and b = –a*T0 in our notation.

(2) Here is a very basic matlab/octave script that computes a sea level curve from a given temperature curve according to Eq. 2 above. The full matlab script used in R07, including the data files, is available as supporting online material from Science

% Semi-empirical sea level model - very basic version
T1900=mean(tempg(11:30)); T=tempg-T1900;

a=0.34; % sea level sensitivity parameter [cm/degree/year]
b=0.077; % note this value depends on a and on the temperature
% baseline, here the mean 1890-1909

% rate of rise - here you need to put in an annual temperature time series T
% with same baseline as chosen for fitting b!
dSdt = a*T + b;

% integrate this to get sea level over the period covered by the temperature series
S = cumsum(dSdt); plot(S);

(3) Here is a matlab/octave script to compute the equilibrium sea level curve of Siddall et al. Note the parameters differ in some cases from those given in the paper – we obtained the correct ones from Mark Siddall.

% Siddall et al equilibrium sea level curve, their Fig. 1, NGRIP scenario
A = 15.436083479092469;
b = 0.012630000000000;
c = 0.760400212014386;
d = -73.952809369848552;

% Equilibrium sea level curve
Se=A*asinh((Tdash+c)/b) + d;
% Tangent at current temperature
Se0= A*asinh((0+c)/b) + d;
Te=dSe*Tdash + Se0;
plot(Tdash, Se, 'b', Tdash, Te, 'c', Tdash, 0.0*Se, 'k', [0 0], [-150 40], 'k')
xlabel('Dimensionless temperature')
ylabel('Equilibrium sea level (m)')
fprintf(1, 'Slope: %f m/K, Sensitivity: %f cm/K/year, zero offset: %f m\n\n', dSe/4.2, 100*dSe/4.2/2900, Se0);

(4) We did not yet receive the code at the time of writing, but based on correspondence with the authors conclude that for their values in Fig. 3 and table 1, Siddall et al. integrated sea level with 100-year time steps with a highly inaccurate numerical method, thus greatly overestimating the a-term. In their supporting online information they show a different calculation for the 20th Century with annual time steps (their Fig. 5SI). This is numerically correct, giving an a-term of about 4 cm, but uses a different value of b close to 0.12 cm/year to obtain the correct total 20th Century rise.


Church, J. A. & White, N. J. A 20th century acceleration in global sea-level rise. Geophysical Research Letters 33, L01602 (2006).

Grinsted, A., Moore, J. C. & Jevrejeva, S. Reconstructing sea level from paleo and projected temperatures 200 to 2100 ad. Climate Dynamics (2009).

Jevrejeva, S., Grinsted, A., Moore, J. C. & Holgate, S. Nonlinear trends and multiyear cycles in sea level records. Journal of Geophysical Research 111 (2006).

Moberg, A., Sonechkin, D. M., Holmgren, K., Datsenko, N. M. & Karlen, W. Highly variably Northern Hemisphere temperatures reconstructed from low- and high-resolution proxy data. Nature 433, 613-617 (2005).

Rahmstorf, S. A semi-empirical approach to projecting future sea-level rise. Science 315, 368-370 (2007).

Rahmstorf, S. Response to comments on “A semi-empirical approach to projecting future sea-level rise”. Science 317 (2007).

Siddall, M., Stocker, T. F. & Clark, P. U. Constraints on future sea-level rise from past sea-level change. Nature Geoscience (advance online publication, 26 July 2009).

415 Responses to “Ups and downs of sea level projections”

  1. 51
    Martin Vermeer says:

    Edward — you see? The Internet Protocol is distinctly less reliable for packets containing unsubstantiated questioning of a scientist’s integrity. (No, I had nothing to do with the “mishap”. Wouldn’t have posted my response had I noticed in time.)

  2. 52
    Aaron Lewis says:

    Re 31: Dr. Vermeer,
    I considered that the Arctic atmospheric circulation pattern in the summers 2007 and 2009 was one that had rarely been observed previous to 2007. From this, I concluded that different regions (at the same latitude) could be subject to different degrees of polar amplification, and surmised that the regions subject to the greatest warming could vary as the climate system was forced. If the center of greatest Arctic warming was over Alaska, then there would be one level of ice and snow melt resulting in one level of sea level rise. If the greatest Arctic warming was over Greenland, then there might be more contribution to sea level rise. In both cases, the polar amplification would be at the same latitude, but the effect on sea level would be different.

    Then, I had the problem of defining “warming”. Greenland can absorb heat without a change in temperature, while a similar amount of heat added to Alaska, might raise the temperature. On the other hand, a moist summer sea breeze that might cool Alaska, would add heat to Greenland – and raise sea level.

    With current trends in Arctic sea ice, I think we can expect some changes in Arctic atmospheric circulation patterns. That is my story, and I am sticking to it until I can finish my beer.

  3. 53

    In the end, after corrections, the R07 paper didn’t really produce a good out of sample fit. The reported fits were highly dependent on the choice of periods etc. Perhaps this whole semi-empirical approach is a bit of a dead end given the complexities of what is being modeled. It does seem unlikely that a single global temperature variable can account for thermal expansion as well as all the various glacial melt rates.

    [Response: Depends what you call a “good fit” – for those who want to see for themselves, see Figs. 1 and 2 here, showing the fit derived with only half the data and then applied to the other half. -stefan]

  4. 54
    Martin Vermeer says:

    > Pfeffer et al’s paper is not referenced.
    True… while preparing this post there was discussion on whether to reference and shortly discuss it. We decided to restrict ourselves by focusing on semi-empirical methods only. This doesn’t mean to imply that the paper (and the methodology it represents) would not be important — it is.

  5. 55

    Sure, I can spell it out for you :

    A d H o c .

  6. 56
    Hank Roberts says:

    Jeffrey, did you read that link, or just respond to the little bit I quoted?

    If you read it you must not have understood it.

    25 cents is the EPA estimate of the difference that enacting the proposed law would make over time by that year — an increase over the price without the carbon controls.

    You misread that as saying you’ll pay $0.25/gallon more in 2030 than you did the last time you filled up at the pump.

    Set’um up and beat the straw out of them.

  7. 57
    Rod B says:

    Martin (41), a quicky clarification before reading all of your post. My understanding is that the static, not tidal, variation of sea level varies by 10s of meters (which I take is the extreme) among different regions.

  8. 58

    re 47–

    “50 cm rise irrelevant to almost all Americans?” I think not. It would certainly be highly relevant to a number of folks that I know.

    Here’s what 1.3 m would do in the East–though they seem not to have done the Northeast yet.

  9. 59
    Doug Bostrom says:

    Jeffrey Davis 1 September 2009 at 1:28 PM

    Bingo. $0.35, $0.77, whatever… meanwhile in recent memory the price is slewing wildly by 100% or more based on rumors and whispers plus of course escalating demand as well as well-founded uncertainties about supply. Waxman-Markey is the least of the problems we face w/regard to price.

    Not that enough people will remember all that once the industry opens the pipeline of lies when the Senate takes up the bill. Prepare for some really serious irritation, just around the corner.

  10. 60
    IAN HILLIAR says:

    Two commonly used sea-level curves for the last glacial cycle,one constructed from dated raised coral terraces at Huon Peninsula in New Guinea , the other from oxygen isotope determinations from deep-sea cores, show that sea levels in Australasia increased 125meters between 20000yrs and about 5000 yrs ago. with relative stability over the last5000 years.These same proxy data show exactly the same rise between 140000yrs ago and 130000yrs ago, with a stepwise decline on from 120000 to 20000 yrs ago. This is graphically displayed in the textbook “Prehistory of Australia.” Its a good read, for anyone out there who still reads books.

  11. 61
    Jeffrey Davis says:

    Hank, you didn’t qualify your remark. I assumed the link simply supported your comment.

  12. 62
    Thomas says:

    Martin @36, thanks. Unfortunately not being a member of any scientific society I can’t get past the pay wall (OK I didn’t try). I couldn’t tell from the abstract if their estimate included changes in groundwater -or just changes in surface storage. I suspect the change in groundwater storage is trongly negative.

  13. 63
    Thomas says:

    38: I strongly suspect that the determining rate of ice loss wouldn’t be the length of the calving front, but rather the rate of flow of ice from the interior to said front. I would think that initialy the slope of the ice surface would be fairly steep, but as the distance that the increased flow covers increases would decrease with time. Most likely this flow would be strongly influenced by a small number of ice-steams, so it may not be possible to calculate with any certainty.

  14. 64
    Eli Rabett says:

    Edward, 50 cm of rise wipes out the East Coast Barrier islands where a very large number of very expensive homes are. Its not just the average rise, but the annual surges on top of that rise. The cost on Long Island alone easily exceeds 100 billion.

  15. 65
    Hank Roberts says:

    > I assumed the link simply supported your comment.
    Chuckle. Never safe on blogs. You’ve always got to check the source and see if it’s even relevant, let alone accurately represented — which was my point.
    There’s an academic joke about citation to “guy in bar” — “guy on blog” is even less convincing.

  16. 66
    G. Karst says:

    Global ice extent data was just released for August. As we are approaching the fall minimum, I thought interest would be high. I included 30yrs ago, last year and the record ARCTIC low yr for reference.

    August (month end averages) NSIDC

    30 yrs ago
    1980 Southern Hemisphere = 18.1 million sq km
    1980 Northern Hemisphere = 8.0 million sq km
    Total = 26.1 million sq km

    Recorded Arctic min yr.
    2007 Southern Hemisphere = 18.0 million sq km
    2007 Northern Hemisphere = 5.4 million sq km
    Total = 25.4 million sq km

    Last yr.
    2008 Southern Hemisphere = 17.9 million sq km
    2008 Northern Hemisphere = 6.0 million sq km
    Total = 23.9 million sq km

    This yr.
    2009 Southern Hemisphere = 18.6 million sq km
    2009 Northern Hemisphere = 6.3 million sq km
    Total = 25.9 million sq km

  17. 67
    Rod B says:

    Martin, even GPS can’t position a satellites orbit within a mm. I can see though how one can get possibly a reasonable small average even if the noise of the individual measurements far exceed the “trend” if you get enough points over a long time, as Hank describes and you imply. It would still seem that the confidence level is no where near, say, 90-95% (though I have no clue what it should be — my uninformed gut guess? maybe 75-80%?) even for decadal periods, let alone annual periods. We haven’t been getting satellite data for two decades yet.

  18. 68
    Martin Vermeer says:

    Rod B:

    My understanding is that the static, not tidal, variation of sea level varies by 10s of meters (which I take is the extreme) among different regions.

    Eh, no. Sea level varies by up to 2 m globally about an equipotential surface (the geoid). Some of this variation is time-independent — the permanent sea-surface topography –, some time-varying, including tidal variation, meso-scale eddies, and inverted-barometer response to air pressure variations.

    The geoid again varies by +/- 100 m about the reference ellipsoid — but the latter is a mathematical construct, not to do with what is commonly understood as “sea level”. Is this what you meant? But the geoid is unchanging with time and drops out of the equation when studying time variability. The Topex/Poseidon and Jason satellites sen(t/d) their radar beams down from over 1300 km, measuring with a few cm precision, and a couple hundred m up or down really don’t matter there ;-)

  19. 69

    #52 Arron, One moment after a short visit in my Arctic community, and I would convince any skeptic (having reason as its prime motivation) of calamity. All small Glaciers around Resolute have almost completely vanished (very little of the permanent small Glaciers remain . amazing sight they were always present for at least 21 of my last 26 years here. They were always present since people were in Resolute (1947). THis surrounded by wide open warm water. THis despite a very cloudy summer, there were a few big glaciers left, they are gone, leaving the hills completely brown.

  20. 70
    Ron says:

    I’m coming late to the dicussion but a couple of points not covered.
    1. How sea level changes are perceived is not just a function of sea level but also changes in land. Generally land is rising in high northern latitudes (post glacial rebound) but sinking elsewhere (glacial isostatic adjustment). Typical changes are 4 mm/decade but can be be much larger.
    2. The rate of change fluctuates. Since 1880 the 10 year rate of rise has varied from +50mm/decade to -20 mm/decade.
    3. For Pacific and Indian Ocens Islands the data are of relatively short duration and inconclusive.

  21. 71
    Mark says:


    “Martin, even GPS can’t position a satellites orbit within a mm.”

    And I guess you’d say you can’t measure laser light with a ruler, either.

  22. 72
    Aaron Lewis says:

    Re 31; Dr. Vermeer,
    My last post was confused. I am sorry.

    Under conditions of the 20th Century sea level rise, conditions in the Arctic basin favored ice, i.e., extensive sea ice. Within the last few years, (as a result of polar amplification) conditions have changed, pushing the equilibrium from ice to water. We see this as loss of Arctic summer ice volume, including sea ice and permafrost.

    This change in equilibrium was a sea change, and there is no linear or scalar technique to use data from the old “ice favoring equilibrium” to estimate ice melt under the new “water favoring equilibrium”. Polar amplification has resulted in the Arctic crossing a melting point discontinuity. The Arctic crossed a tipping point.

    In the old system, sea ice remained ice for years and years. In the new system, ice melts in the summer. In the old system, Greenland was swept by cold, dry winds coming off the sea ice. In the new system, Greenland is swept by “warm” moist winds from the ice free Arctic and the North Atlantic. Data from the days when the Arctic was substantially covered with sea ice will not help us predict how fast Greenland will melt in the future when the Arctic Ocean has much less ice, and the wind carries more latent heat.

    What we can estimate, is that Greenland will melt much faster than in the past. Use of data from prior to the tipping point will cause us to underestimate the rate and extent of that melt.

  23. 73
    Mark says:

    GKarst you’re copypasting again. again.

    1980 Northern Hemisphere = 8.0 million sq km
    2009 Northern Hemisphere = 6.3 million sq km

    so a reduction of 1.7million sq km of ice EXTENT (not volume) in 29 years.

    And you say that there has been no change???

  24. 74

    > Martin, even GPS can’t position a satellites orbit within a mm.

    Yes, you’re right — for every individual satellite position in space. But orbit determination using those GPS fixes as constraints is much better. Remember that the satellite describes a Kepler orbit (well it’s a bit more complicated than that…) and the period is very precisely known, giving us the size of the orbit through Kepler’s third law. And through the total mass GM of the Earth, which should be constant.

    There’s a calibration offset in the radar though, but that should be a constant as well.

    Consider that every mm per decade translates into a cm per century. And Church and White don’t claim any better than 5 cm back to 1870.

  25. 75

    Thomas #62: only reservoir storage (but including an estimate of the storage in the surrounding ground).

  26. 76

    Aaron Lewis #72,

    did you finish that beer? ;-)

    Yes, you certainly have a point. We shall find out over time. Note that the nonlinearity you describe is in time, not (necessarily) in temperature. Suppose that both temperature and ice melt increase, but the relationship between them doesn’t change?

  27. 77
    pete best says:

    I am now coming to the conclusion that we are only going to be able to geo engineer our way out of this issue once we fail to implement the necessary alternative anergy solutions in time to do much about it regardless.

  28. 78
    Steve P says:

    RE: G. Karst, #66. The last time I checked, 18.0 plus 5.4 = 23.4, not 25.4 as you indicated. Also, 18.6 plus 6.3 = 24.9 in my experience, not 25.9 as you indicated. Where did you get those figures, anyway?

  29. 79
    Sekerob says:

    For GKarts et al who really wish to continue in mixing two entirely different geophysical polar areas.

    The Arctic for August, land enveloped:


    The Antarctic for August, ocean enveloped:


    Who can discern a trend of significance for the Antarctic gets a hat tip.

    Of course does not say a thing about the thickness and volume but we know that Antarctic summer low is much lower than the Arctic, even in these years and practically as flat as winter high, which so happens

    PS, and for those wishing to do sums, Plimer style… they wont fly:

    This yr.
    2009 Southern Hemisphere = 18.6 million sq km
    2009 Northern Hemisphere = 6.3 million sq km
    Total = 25.9 million sq km

    No this is 24.9 million km sq extent, not area!

  30. 80
    Hank Roberts says:

    Hmmm. Karst is copypasting from here? Or both from elsewhere?
    —-excerpt follows—
    “Is anyone else having trouble, with these numbers and statements.
    Oh! My Goodness! I have wet myself. GK
    Posted by G. Karst | March 15, 2009 5:51 PM”
    —-end excerpt—-

    This is the same thing Karst has been doing for a long time.

  31. 81
    Sekerob says:

    Steve P. It’s NOAA/UCB supplying them, which I use for the graphs above.

  32. 82
    Rod B says:

    Martin, yes, I think that’s what I was doing – comparing geoid with ellipsoid. In fact the article (from NASA, and which wasn’t perfectly clear) I was referencing used “100m”, but I didn’t have the courage or guts for that number — so I used “tens of meters”. Plus, I presume the actual level is unimportant compared with the point-by-point anomaly to measure sea level rise. Still the measurement (sometimes loudly trumpeted) of how much the level rose the past year or so actually borders on the meaningless given the noise compared to the measurement. To the extent that is used for projections, it is highly dubious; though I understand physics analysis is the primary process of projection/prediction.

    Thanks for the help.

  33. 83
    G. Karst says:

    Mea Culpa

    Because I did not cut and paste some math errors are correctly pointed out. I apologize for the sloppiness (I did it on the fly). I will try to better check my numbers better. Thanks for the catch. The data comes directly from the NSIDC plates like these; the addition error was entirely mine, sorry:

    August 2009 figures were released late last night.

    August (month end averages) NSIDC (sea ice extent)

    CORRECTED (I hope)

    30 yrs ago
    1980 Southern Hemisphere = 18.1 million sq km
    1980 Northern Hemisphere = 8.0 million sq km
    Total = 26.1 million sq km

    Recorded Arctic min yr.
    2007 Southern Hemisphere = 18.0 million sq km
    2007 Northern Hemisphere = 5.4 million sq km
    Total = 23.4 million sq km

    Last yr.
    2008 Southern Hemisphere = 17.9 million sq km
    2008 Northern Hemisphere = 6.0 million sq km
    Total = 23.9 million sq km

    This yr.
    2009 Southern Hemisphere = 18.6 million sq km
    2009 Northern Hemisphere = 6.3 million sq km
    Total = 24.9 million sq km

    Mark says-2 September 2009 at 4:32 AM

    “And you say that there has been no change???”

    I said nothing of the sort! Numbers require no comment from me!

  34. 84
    geoff says:

    Just a suggestion, flood the low lying lands around the globe, some of which are many many metres below sea level. A relatively cheap/simple task which would create huge in land lakes around which, new communities could grow. By helping to lower sea levels around the world, this would go some way to lessen the threat of global flooding of major cities.

  35. 85
    Martin Vermeer says:

    Still the measurement (sometimes loudly trumpeted) of how much the level rose the past year or so actually borders on the meaningless given the noise compared to the measurement.

    Indeed… but with the understanding that “noise” here refers to natural variability, not to sensor limitations… don’t insult our sensors ;-)

    [Response: And, by the way, I had an interesting discussion on noise vs signal in the sea level data with Björn Lomborg in the Guardian recently, who had claimed that “over the past two years, sea levels have not increased at all — actually, they show a slight drop. Should we not be told that this is much better than expected?”… -stefan]

  36. 86
    G. Karst says:

    #80 Hank Roberts 2 September 2009 at 10:04 AM

    If you have a problem with something I have said on another blog… That blog is the proper forum to rebut it. Are we now going to engage in cross blog debates? Should I start combing archives for your comments. Seems like a waste of time to me. If your not adding to the knowledge base… What exactly are you doing??

    Look, I don’t know what you were expecting for ice extent numbers, but many seem angry and disappointed. That is not my fault. The numbers are what they are! What they mean is open to discussion. I will listen to any interpretation put forward, however I choose to refrain from lending significance, or comment, to plain numbers.

    My errors could indicate, that I am getting too old to blog effectively. That is a possibility and that I will reluctantly review, but I feel I still have somethings to contribute. Sorry you disagree.

  37. 87

    To Hank Roberts:

    Re your #46 — yes — you have phrased the issue a lot better than I did. Thanks.

    It is for sure Valero has lost my business! At least until the other companies around here supass them in silliness. Which could happen.


  38. 88
    Jokl says:

    #86 GK
    I think some have a problem with your #66 post, and “As we are approaching the fall minimum”, and then putting up “Global ice extent” numbers, while the minimum is clearly only for the Arctic. In other words, it’s clear you are trying to prop up your position with the numbers, in a way that appears somewhat, shall we say, false.

  39. 89
    G. Karst says:

    Jokl #88 2 September 2009 at 1:25 PM

    “…and then putting up “Global ice extent” numbers, while the minimum is clearly only for the Arctic”

    I post the month end averages every month. Sorry you have missed all the others. The posts are all the same (posted without comment). I added the 2007 report this time because we are approaching Arctic minimum and I thought some might find the reference useful. If you like… I can post the Antarctic minimum from my archives (I don’t think you will like it any more), OR you can just wait until 2010 OR you can extract the information yourself. I would be happy to post any month you like… just name it and the year (you might have to check my math. Actually, it’s not my math… It’s my failing eyesight. CRT displays are becoming difficult for me to read. 3s look like 8s, 1s and 7s… well you get the idea).

    Have people forgotten that one pole’s minimum is the other pole’s maximum. That is why my report is global NOT regional. Hope this clears up your concerns.

  40. 90
    Hank Roberts says:

    > numbers require no comment

    How To Lie With Statistics

  41. 91

    On #89. HOW TO LIE WITH STATISTICS. A great book. I think it first came out in the 50s. Written by Huff. It molded my young life as a physics student immeasurably.

  42. 92
    GlenFergus says:

    Stefan at #85:

    Lomborg’s mindset becomes clear when he told us last October that “over the past two years, sea levels have not increased at all — actually, they show a slight drop. Should we not be told that this is much better than expected?”. As a trained statistician, he must surely have known that he was fooling the public with the “noise” of short-term variability rather than discussing a meaningful trend.

    Indeed. At what point, in a matter likely to adversely affect millions, does deliberate deception become criminal?

  43. 93
    Sekerob says:

    To complete the numbers of ‘Global’ a chart to go with that. Note wider difference between extent and area, what I’ve dubbed the break up index. It was 1.25 back in 1979 and this August it was 1.34 or alternate, the August Area this year in global terms was 74.1% of the Extent, back then it was 80.1%. Sign of quality of the ice me thinketh.


    One Jeff is massaging this as if sea ice has not significantly reduced. It’s a special art form I’ve not grasped… maybe I would accept after nurse Ratched performs a lobotomy on me. I’m convinced that lack of summer cover and sea ice off days has more bearing for the globe than the simple global summation that is commented surely with ‘it’s only 5.5% less’. Add to that the many millions of km square in missing land snow cover and the snow off days that keep increasing. That’s a bunch of Albedo change on the sunny side.

    end of rant

  44. 94
    Aaron Lewis says:

    Martin Vermeer #76

    The relationship between ice, water, and water vapor in a particular system is defined by an equation of state. (See for example, or much better, a good Chemical Engineering text.) Time is not relevant. Ice melt is a function of the energy of the system. As the temperature of ice is raised toward its melting point, no melt occurs. Then, at ~0C, one can add heat to ice and have complete ice melt without raising the temperature. At ice’s melting point, the temperature is not indicate the energy of the ice. Ice above 0.15C is water. From these three curves, we know the relationship between temperature and ice melt does change. If we are considering (Earth’s) global temperatures, then we are working without any knowledge of how forced the system is; or, how close the system is to equilibrium. (If both temperature and ice melt increase, and the relationship does not change, then we know somebody has gone to a lot of effort to tamper with our sample or we are looking at data from a system that is not at equilibrium.) Without knowledge of how close the system is to equilibrium, no useful conclusions can be drawn.

    Ice does not care about the global temperature; it cares about the local temperature. (Polar Amplification ensures that the change in the Arctic temperature is greater than the change in the global temperature.) Only by looking at the ice’s local conditions under equilibrium, can we estimate ice melt and sea level rise.

    This is not a “We shall find out over time.” matter. Public policy makers are looking to people like you for decision support documents. Like it or not, climate scientists today, find themselves in positions of great social responsibility. If you write something, public policy makers are going to accept it without question, and comments from an old farmer like myself is likely to influence the policy maker’s mind.

    I did finish the beer, but it did not make me think that some new Arctic Atmospheric circulation pattern would keep Greenland cold.

  45. 95
    Jeffrey Davis says:

    2009 Arctic minimum won’t be reached for several weeks.

  46. 96
    Eli Rabett says:

    Geoff #84 This has been suggested for the Qattara depression west of Cairo. The problem is getting through the mountain range to open the depression to the Med. There have also been similar suggestions for other depressions in the southern sahara

  47. 97


    For me a good fit is determined by looking at the coefficients.

    As stated in your correction the computed coefficient for the first half would be .42 cm/year/degree. However if you compute the coefficient for the second half of the data you get .24 cm/year/degree. This means that using the model based on the first half of the data you would have overestimated the increase in the rate of sea level rise in the second half of the period by almost a factor of two.

    [Response: Agreed. But you’re talking of the “increase in the rate”, the second derivative of sea level over only a 60-year period. Sea level itself is predicted to within 2 cm of the observed value up to 2000 if the method is trained only on data for 1880-1940. Call that good or bad, but it is certainly better than the physics-based models do. -stefan]

  48. 98
    Rod B says:

    Martin, I was partly referring to the sensors ala accuracy from a static satellite in the many cm’s plus the satellite wobble — but I didn’t mean it as an insult. :-)

    stefan, it does work both ways. If what I’ve deduced and been told is correct, Lomborg is full of beans here. He has no way of knowing with any confidence what the sea level did the past two years.

  49. 99
    Hank Roberts says:

    #84, #86

    And there are two ways to do it — remove the water by evaporation and fill the basins with fresh water (remembering there are aquifers available to recharge), or just fill the hole with salt water, and let the evaporation happen there, making brine and sending the moisture downwind.

    Let’s see, go with cheap and thoughtless, or think about …. ooh, profit! …. yeah, that’s good enough.

  50. 100
    Patrick 027 says:

    Re 84 – alternatively, a potential for hydroelectric power + salt production.