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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. 101
    Martin Vermeer says:


    This is not a “We shall find out over time.” matter. Public policy makers are looking to people like you for decision support documents.

    What I meant is that physical modellers are scrambling to get a handle on these phenomena, cf. Pfeffer et al. Semi-empirical modelling is a blunt instrument, inherently incapable of addressing them, except in a “bulk” fashion — and we can only guess at this point whether it already does that or not.

    …and your worry remains rather theoretical until after public policy makers start looking seriously at, and basing policy on, even the conservative projections now lying on the table…

  2. 102
    Brian Dodge says:

    Re flooding depressions in Africa to store water and reduce sea level rise – there may be the unfortunate side effect of more and stronger Atlantic hurricanes.
    “That Saharan dust keenly interests Dunion, a research meteorologist from the NOAA Hurricane Research Division in Miami. He said, “The Saharan Air Layer is essentially a huge dust storm that can be the size of the continental United States. Every three to five days during the summertime, these storms roll off of the African coast.” As the dust storms move off northern Africa, convective waves develop farther to the south, pulling moisture up into the atmosphere.

    “We think a dust storm has three main components that can suppress a hurricane,” Dunion continued. “One, it’s got super-dry air. Hurricanes don’t like dry air in the middle parts of the atmosphere, and that’s exactly what the Saharan Air Layer has. A Saharan dust storm also has a very strong surge of air embedded within it, called the midlevel easterly jet, that can rip a storm apart that’s trying to develop. We call that vertical wind shear. And then the third piece is all this dust.”

    Researchers think the dust itself suppresses cloud formation, playing a role in preventing tropical waves from becoming more intense. Ismail said, “We think that dust aerosols can affect tropical disturbances, sometimes even kill those disturbances. Dust inhibits convection, the process of moisture rising to the higher levels of the atmosphere, and then precipitating as rain. So these Saharan dust layers seem to have a blanketing influence on the development of convection.”

    I wonder what will be the side effects of geoengineering done to reduce the hurricane side effects of geoengineering – flooding the Bodele & Qattara depression to combat the sea level rise – caused by the inadvertent geoengineering from CO2 emissions? Perhaps it might be better if, finding ourselves in a hole, we learned to stop digging?

  3. 103
    Andrew says:

    The Qattara depression is about 18000 kM^2 and about 133 M deep at its deepest. At its most optimistic this represents less than 2300 cubic kM of sea water which represents about 5 mm of sea level or less than 2 years of sea level rise at the present rate of increase.
    Rather underwhelming result I would think.

  4. 104
    Martin Vermeer says:

    Aaron Lewis #94,

    adding to the previous, I think also the model you propose is too simple and inappropriate. The system is way off equilibrium, and temperatures throughout the area vary over a broad range. There is the “melt line”, where temps are at the melting point; but as bulk temperature varies, this melt line just shifts place. At no point does bulk temperature wait for a large amount of ice to melt. Note also that the Greenland ice sheet has significant vertical extent.

  5. 105
    Lawrence Coleman says:

    Re: Jeff Davis, if you look at the uni bremen site you will see that now both the NW and NE passages are open again..second time in recorded history! No ice in Hudson bay either. To me this shows from now there’s no going back..the effect of ice albedo is even stronger than seasonal fluctuations as this year was not an exceptionally hot year in the northern hemi. Is there any data out as to how much perennial sea ice has melted this time around? Thanks.

  6. 106

    Rod B #97, about Lomborg:

    > He has no way of knowing with any confidence what the sea level did the past two years.

    Actually he does… we all have. What we don’t have is a way that actually works of extrapolating that knowledge many decades into the future.

    (That’s precisely the point I tried to make about natural variability!)

  7. 107
    Sekerob says:

    Eli Rabett, as a UK judge ruled that land use changed the precipitation on Kilimanjaro, such huge inland seas could promote the amount of vapor in the air to such extend to get local climate change even cloud forming and rain. Such an initial massive water draw will have it’s effect on the tributaries though, but on the whole, think it’s a pipe dream. And the Med, well, that lost apparently 40 cm of level through evaporation just in the heatwave summer of 2003 and it still has not returned to same level as then. Gibraltar becoming an inflow instead of an outflow… that could cause changes of deeper currents in the Atlantic… wanna mess with that?

    But reminds me of the Brokopondo project in Suriname. Artificial lake and it not filling up in proper due the massive evaporation and permeability of the underlying geology [Not looked at it since probably 40 years, but it had major impact Now I wonder on Three Gorges if that is ever going to fill up to the maximum and hold or find an alternate way out. Saw recently something about large number of land slides there maybe forcing yet another major population displacement. Whatever we do, think it will be a drop in the bucket if the large ice caps start melting in earnest.

  8. 108

    @106 —

    I thought Gibraltar was always a net inflow. When did that change?!?

    [Response: It is a net inflow, to make up for the net evaporation over the Mediterranean catchment. However, this is achieved by a surface inflow and a deep outflow, which is required because the exchange needs to satisfy two budgets: the water budget and the salt budget. You can’t do that with a one-way flow, because that would replace the evaporated freshwater with an inflow of salty sea water from the Atlantic. To make a steady state possible, you’ve got to get rid of the extra salt by an outflow that is saltier than the inflow. -stefan]

  9. 109
    Mark says:

    “Look, I don’t know what you were expecting for ice extent numbers, but many seem angry and disappointed.”

    Angry at your base lies and disappointment that you can still do no better than repeat the same lie that was soundly countered last time you posted it.

  10. 110

    #85 Stefan’s discussion with Lomborg

    I am at WCC3 and although I can’t quote exactly, (I forgot to turn on my recorder), Dr. Pachauri has just addressed the international panel emphasizing the range estimates by IPCC are (largely reliant?) on thermal expansion and that when you add the melt together with that, the expectations can be imagined. He mentioned we can see this likely in meters. It was carefully worded and I hope to find a copy of the statement after this session.

    I imagine (hoping) AR5 will include the combined assessment.

  11. 111
    Dick Veldkamp says:

    Re #84 #96 Store sea water in depressions?

    Has anybody looked into how much water could be stored in (say) the Saharan depression? Are we talking about an amount that would make a noticeable difference in sea level rise? It would seem to be a relatively cheap and harmless way of geoengineering, mitigating SLR (but not solving any other problem of course)

  12. 112

    Re #110,

    I hope Dr. Pachauri’s statement was lot more careful than that, because it is completely untrue that the IPCC AR4 range was completely based on thermal expansion. Just read it.

  13. 113


    As this post was originally about the efficacy of simple models of sea level rise, could you comment on my #97? If the coefficients are so different between the training and the test period then it would seem that the model is not well specified. It isn’t surprising that the graphs look ok by visual inspection since what is being compared there is dominated by the absolute sea level, and the amount of sea level rise during a period where the temperature variation wasn’t all that large.

  14. 114
  15. 115
    Hank Roberts says:

    Dick, re 84, 96 — these basins have fossil aquifers below them in many cases, including the Sahara.

    … aquifers are located beneath large portions of central and eastern Saudi Arabia, including Wasia and Biyadh which contain amounts of both fresh water and salt water ….

    The Nubian Sandstone Aquifer System is the world’s largest fossil water aquifer system. It is located underground in the Eastern end of the Sahara Desert and spans the political boundaries of four countries in north-eastern Africa……..
    …. water from the Sahara Desert in Libya, from the Nubian Sandstone Aquifer System …. Groundwater recharge for these deep rock aquifers is on the order of thousands of years, thus the aquifers are essentially non-renewable resources….”

    The amount of fresh water in the world – about 4 percent of the total — is so limited that deciding to dump sea water into an area that can function over geologic time as a freshwater aquifer would be an act of a class we don’t really even have a good word for yet in human language.

    What’s the right word for making a choice that’s so big, so long-lasting, and so short-sighted?

    Remember — a spike in precipitation is predictable in geologic terms after a warming; that would be fresh water transported out of the ocean after it’s risen and warmed, that would eventually transport the fresh water to the continents.

    If we don’t mess up the process by sowing salt on the continents ahead of the rainfall.

  16. 116
    Ray Ladbury says:

    Hank, Aquifers are nonrenewable for another reason. These aren’t underground rivers, but rather water flowing through geologic strata. Once the aquifer dries out, the layer compacifies and it will never again be an aquifer.

  17. 117
    Jim Galasyn says:

    Speaking of paleoclimate data, more hockey sticks!

    Graph of the Day: 2000-Year Reconstruction of Arctic Temperatures

  18. 118
    Eli Rabett says:

    FWIW there was an article in Science about a year ago which calculated the effect of dams on sea level. It was not zero, but Eli does not remember the details and Qattara is not the only depression.

  19. 119
    Aaron Lewis says:

    Re 101: Martin,

    See for example

    A water supply infrastructure for 30 million people is in a sea level delta protected by old dirt levees. We are now planning upgrades – how high should we go?

    The public is invited to comment on the 2009 California Climate Adaptation Strategy Discussion Draft until Thursday, Sept. 17, 2009.

    Current planning case is from 2007 IPPC FAR. (The numbers that do not include ice dynamics.)

  20. 120
    Neil White says:

    Eli (#116), the reference is:

    Chao, B. F., Wu, Y. H. & Li, Y. S. Impact of artificial reservoir water impoundment on global sea level. Science 320, 212214 (2008).

    This paper shows that the equivalent of about 25-30 mm of GMSL (Global-Mean Sea Level) has been retained in man-made dams, mostly since about 1960. This is roughly equivalent to about 0.5 mm/year GMSL over this period. Unfortunately we don’t have good information on the other side of this equation, that is, the amount of water that is being returned to the ocean through ground water mining. While it is almost certainly less, we don’t really know how much less.

    A useful rule of thumb here is that 1mm of GMSL is equivalent to about 360 cubic kilometres of water. To put this in some sort of perspective, the Three Gorges Dam in China (water volume: 39 cubic kilometres) is equivalent to about 0.1mm GMSL.

    The idea of dumping sea water over a fossil aquifer (“fossil” here means one that isn’t getting recharged with fresh water) sounds like an extremely bad one to me.

    Neil White

  21. 121
  22. 122
    Chris Dudley says:

    Jim (#115)

    That is more of a carpenter’s square than a hockey stick. Too acute for a hockey stick owing to the slope of the preceding cooling I think.

  23. 123
    Dick Veldkamp says:

    #113 #114 #118 Store sea water in depressions?

    Hank, Ray, Neil: thanks for the information, which rather destroys the attractiveness of the storage option.

    Well, it looked nice for half a day or so.

  24. 124


    welcome to the joys of decision making under uncertainty :-(

    Not including ice dynamics is irresponsible — even a guesstimate (the IPCC offers one) is better than nothing.

  25. 125
    Mark says:

    Ray, 114, I don’t think it’s quite “never be an aquifer again”, but for millenia, the replenishment will be nil or near enough to make no difference.

    At least that’s what I remember from grammar school friends who did geology and I asked about (admittedly ~20 years ago).

    The rock is available to hold water, but the amount of water it takes up depends on how much water it already contains (to a maximum rate given by the permeability of the base rock strata), so when there’s no water, the rate of ingest is slow seeps at the edge. Which requires a plentiful supply to the rock strata itself.

    And THAT is not sinecure by any standards under AGW changes.

    An ice age could get water there and staying there long enough to restart the process, mind.

  26. 126
    L. David Cooke says:

    RE: 104

    Hey Martin,

    I hate to put words in other peoples mouths; but, I get the impression that Mr. Lewis may be alluding to the hysteresis between the solid and liquid state. With the 2500 Joules/ccm and a lack of definition of where the ice is in relation to the 2500 Joules, the amount of total energy involved can be quite broad. However, what I suspect is, since we are seeing sever melting over the last 10 years that we are likely on the high side of the range.

    The most interesting thing is how fast ice reforms in the Fall here in the NH. Apparently the sea ocean temperatures though warmer are not so warm as to not easily shed the latent heat and fallback to the solid state. It does not appear that in the cooling that 2500 Joules/ccm needs to be lost to return to solid, this begs the question of how much salinity or insolation is playing a part as you alluded to earlier…

    This also suggests that the radiant retention issue of water vapor/radiant atmospheric gas vector/and possible lack of Ozone could be involved as well. I will stop now, I am afraid I will only muddy the waters you are trying to clear.

    Dave Cooke

  27. 127

    RCM progress report: 20 levels plus ground, 3-layer cloud scheme, ten gases, 54 spectral bands, Ts comes out as 289.5 K, Tmin in the stratosphere is 204.8 K, R^2 with the USSA is 0.989, albedo 0.312, power imbalance 8.3%.

    Not great yet, but I’m getting there. If I can figure out why the stratosphere is so cold, I think I’ll have it. That’ll up the outgoing energy and help balance the budget (at the moment I have 235.1 W/m^2 coming in and 215.5 going out, “a no-good way to do arithmetic,” to quote Heinlein).

  28. 128
    J. Bob says:

    #122 Martin “even a guesstimate (the IPCC offers one) is better than nothing.”.
    Not if you make the wrong guess.

  29. 129
    Antonio San says:

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

    Thank you for kindly offering the DATE the picture was taken… it might help don’t you think?

  30. 130

    A respectful tip of the hat, Barton. . .

  31. 131
    Jim Galasyn says:

    Barton, that RCM model of yours sounds quite interesting. Can you post some details about this project? Like implementation language, etc.?

  32. 132
    shooshmon says:

    I have a question that I’d like Gavin Schmidt or any scientist on his level to answer. I want to know why the oil companies are demonized for funding scientists who disagree with global warming theory because the oil companies have given money to promote global warming as well. For instance, Exxon gave a ton of money to some Stanford based research group. My other question is regarding the work of Roy Spencer. If Spencer is correct about negative feedback from clouds, will this nullify the small heat that molecules of Co2 emit?

    [Response: Any demonization has occurred not because Exxon funds scientists who ‘disagree’, but rather they fund(ed?) for many years propaganda efforts full of obvious distortions and misinformation. Research funding is a completely different kettle of fish – as long as the researchers are free to come to whatever conclusion is justified by the science. As for Spencer, there are many independent lines of evidence that indicate that climate sensitivity is not small (see our discussion of Annan and Hargreaves), which makes it very unlikely that Spencer’s research is as definitive as some have claimed. Cloud feedbacks are an important uncertainty – but they are exceptionally complicated and differ in the tropics, in the marine stratus regions, in the high latitudes etc. – and don’t negate the plentiful evidence for the amplifying impacts of water vapour or ice changes. Hopefully, Spencer’s work (as well as that of many other researchers on this topic) will lead to a clearer picture and more precise projections, but hoping that this will magically negate everything else is just wishful thinking. – gavin]

  33. 133

    I’ve been on the road for the past few hours and just received from Dr. Pachauri a transcription of his speech. My description was a combination of two sections of the speech:


    I would also like to acknowledge a step forward that the G8 leaders took in July of this year when they met in Italy. I would like to quote something that was included in the statement on that occasion and I read what it said “We reaffirm the importance of the work of the Intergovernmental Panel on Climate Change (IPCC) and notably of its Fourth Assessment Report, which constitutes the most comprehensive assessment of the science. We recognise the broad scientific view that the increase in global average temperature above pre-industrial levels ought not to exceed 2°C.” Today I most respectfully submit, however, that there were some dimensions of the scientific reality of the 2°C target that were really not covered and which I think would have added a great deal if they had been addressed in this particular meeting. Two of them that I would like to mention are the fact that firstly even with the 2°C target the IPCC has assessed that on account of thermal expansion alone we could get sea level rise of 0.4 to 1.4 meters. This is due to thermal expansion alone. If you add to this the melting of ice across the globe as the Secretary General of the UN has just reminded us we would have much greater increase in sea level…

    and later in the speech

    Clearly we need continuous data on this from different parts of the globe. We also need to monitor impacts because as the IPCC has projected in the case of parts of Africa we would see that by 2020 — as early as that — we would have 75 to 250 million people living in a state of water stress brought about by the impacts of climate change. We have also projected that by the same year some countries in Africa would see a decline in agricultural productivity and yields by about 50%. Clearly, if this is going to happen in such a short period of time we need to monitor these developments on a very careful and systematic basis. I also would like to mention that as opposed to these rapid but steady changes that we are going to foresee and which we have projected, we have also highlighted the possibility of abrupt and irreversible changes. What are these changes? Well two of them I would like to bring to your attention are the possibility of collapse of any part of the Greenland or the West Antarctic ice sheets. And if that were to happen in any of these two locations then clearly we would have sea level rise of several meters. That would mean that not only would we change the geography of this planet but create a catastrophe for hundreds of millions of human beings across the globe. So, we really need to ensure that we prevent by every means these abrupt and irreversible changes.

    This was a fast transcription and I noticed there may be some words missing so I will try to check it against the video that was recorded if I can find it and maybe post it on the OSS site.

  34. 134
    Aaron Lewis says:

    Re #122 Martin,

    I was not always an old famer drinking beer.

    One of my tasks when I worked at Bechtel was review of the designs of long term repositories for nuclear and hazardous materials. I had to think about climate forecast, legal and social responsibility in the long term (defined by US law as 100,000 years).

    In 1990, I was told to spend 4 hours a week updating Bechtel Management’s briefing book on climate change. (We were contacting to build large scale public infrastructures, and had to post bonds that it would survive climate change.) I made estimates of sea level rise. And, as a result, Bechtel developed conservative designs that we could easily bond/insure. I still like those SLR numbers. I think Hansen would approve of them. However, the management of this site has called those estimates “alarmist” and told me that my estimates were not based on “science”. The management here was correct. My SLR numbers were based on engineering estimates of what happens to ice when it is heated above its melting point.

    Where in the IPCC is there a number that a politician or lawyer or engineer or business man can say, “these are our planning case numbers”? I think the IPCC was irresponsible not to consult with engineers, planners, and risk managers to develop “planning case numbers” suitable to support long term public policy.

    Consider the the Rahmstorf line in the table in the post says the model predicts a total model rise [cm] of 16.2. If I build to 17 cm will I really have 0.8 cm freeboard? Or, should I assume a SLR of at least 20 cm and build to 30 cm just to be safe? What is the real expected error in that model? What is the real expected error in the numbers given in FAR Topic 3.2.1? Is it more than the 0.5 cm suggested by the precision of the numbers as written?

    I think climate scientists (and weathermen) should be registered like professional engineers, and have to post a performance bond when they issue a climate/weather forecast.

  35. 135
    Phillip Shaw says:


    Both you and Ray are partially correct. Whether an aquifer can recharge depends on its nature. An aquiferin a porous rock formation, such as the Edwards and Trinity aquifers here in Texas, can recharge if the inflow exceeds the outflow. Increased precipitation or reduced pumping (extraction) will allow the aquifer to recover.

    But an aquifer in an unconsolidated formation, such as the former lake sediments underlying Mexico City, can’t recharge because the pores in the silt which were held open by water collapse when the water is removed. Characteristically, this is evidenced by surface subsidence. Once the water is removed there is no putting Humpty back together.

  36. 136


    Sure. I’m writing it in Fortran-95, the “Salford F95 Personal Edition” you can download from Silverfrost Ltd. in the UK ( Unfortunately this version comes with an annoying splash screen that runs every time for several seconds, and in addition, you can’t use it commercially or for research. I’m using it for research anyway, since I’m not publishing anything based on it yet. If I do, I’ll just download another Fortran compiler from somewhere and translate.

    I started out with a 20-layer radiative equilibrium model Dr. Dave Dempsey posted on the web for a San Francisco State U. course in 1998. From there I built a time-marching version, and over time I added more and more realistic features–or tried to, I went up a lot of blind alleys, too, since I was teaching myself. Adding a convective adjustment (a flat maximum of 6.5 K/km, the average in the troposphere) converted the models from REMs to full-fledged RCMs, though they were grey for a long time.

    I actually acquired a copy of Houghton’s “The Physics of Atmospheres” early in the process, so I could have implemented bands a lot earlier than I did. I scoured the web and libraries for band schemes, finding things like Essenhigh’s in his anti-AGW article, which only covered three gases and part of the spectrum. Eventually I learned enough to realize that I could convert the figures in Houghton’s tables to mass absorption features for CO2, H2O and ozone (k = S / d where S is line strength and d band width). I’m still using Essenhigh’s figures for methane. Cloud figures I found on the Hadley site, in a description of UKMO HadCM3. I got a nice cloud scheme from Kiehl and Trenberth (1997). Assorted physics and climatology textbooks gave me albedos, values of physical constants, and a way to numerically integrate the Planck curve.

    Along the way I pestered the heck out of people here (Ray Pierrehumbert was especially helpful, and of course I learned a lot from Gavin, Michael Mann, etc.). Dr. Houghton emailed me electronic copies of his book’s tables. Syukuro Manabe gave me suggestions about what parts of my code might be giving me problems (though, like every climatologist I contacted, he refused to actually read the whole source code file, alas. I know, I know, other commitments, and real students to oversee).

    I’m still not getting results as accurate as Manabe and Strickler got way back in 1964, but I’m a lot closer than I used to be. Give me another five or ten years and I might–MIGHT–have something research-quality to play with.

    I did modifications of early versions for Venus and Mars. I hope to model those accurately in the future, and some day I’d like to add Titan as well, though finding absorption bands for those gases at those temperatures will be a challenge (people like Chris McKay and Ralph Lorenz have done a lot in that area). Under Titan conditions, nitrogen is a greenhouse gas!

  37. 137
    Ray Ladbury says:

    Martin Vermeer: “even a guesstimate (the IPCC offers one) is better than nothing.”.

    JBob: “Not if you make the wrong guess.”

    Ah, JBob, spoken like a man who has never done science. A wrong guess can be corrected. If you are afraid to be wrong, you’ll never even get close to right.

    In my opinion, when you understand why Pauli sputtered, “This is terrible! It’s so bad, it’s not even wrong,” you’ll understand a whole helluva lot more about science.

  38. 138
    Ray Ladbury says:

    Mark, water does not so much flow in an aquifer as percolate. When the rock becomes compactified, there’s no place for the water to go, and it can be lost entirely. These really are finite and fragile resources–seed corn, not feed corn.

  39. 139
    Diogen says:

    Is it possible to meassure the impact of the denial industrie and their part of the Co-2 contribution, due to slowing the process of fighting dangerous climate changes(in time)?

    Maybe we can make them pay?

  40. 140
    Thomas says:

    119: I live not too far from the California Delta. If I had to make a wild eyed guess as to what level of sea level rise to plan for, I would simply double the IPCC AR4 numbers. But I suspect that a broke state isn’t going to commit the kind of resources needed based on some citizens wild eyed guess. My secondary guess would be that maximum flood stage flow rates in the rivers is probably a greater source of uncertainty as far a maximum water levels are concerned. Here climate change could also be important, as both warmer and wetter storms are likely in the future.

  41. 141


    I posted a long post about my RCMs yesterday evening, but as of today it hasn’t shown up–maybe it got deleted for being irrelevant to the thread. If you like I’ll email you something. You can contact me at

  42. 142


    There is absolutely no reference in AR4 for a .4 to 1.4 sea level rise by 2100 period, let alone for a 2C rise. It is even more outlandish to say that this would be from thermal expansion alone. I have no idea what Dr. Pachauri was referring to.

    The collapse of the West Antarctic ice sheet would produce several meters, I’m not sure about Greenland. This was considered extremely unlikely by 2100 by AR4, and everyone else who has studied it.

  43. 143
    Jim Galasyn says:

    Thanks Barton, I sent you a note.

  44. 144
    Hank Roberts says:

    BPL, your long post popped in above I think:
    4 September 2009 at 6:25 PM

    Phillip Shaw, thanks for the pointer to Trinity and Edwards aquifers; Scholar finds info on the structural variations that allow recharge of void space in some, like those, while others — like Kettleman– collapse.

  45. 145
    cce says:


    Chapter 10.7 talks about SLR due to thermal expansion taken to equilibrium. Figure 10.43c shows thermal expansion causing about 0.6 to 1.4 m of SLR for models projecting ~2 degrees of warming relative to 2000. Pachuri was talking relative to pre-industrial conditions but it’s in the ballpark.

  46. 146
    Hank Roberts says:

    Nicholas Nierenberg 5 September 2009 writes:

    > absolutely no reference
    > even more outlandish
    > I have no idea

    Use the suggested search below, in Google Scholar (the software here won’t tolerate the quoted strings — you need them to limit the search results)

    — copy the line below —

    IPCC “sea level” “1.4 metres” “thermal expansion”

    — paste it into this search window —

    The results will probably help you figure out what was referred to, assuming your results will resemble those I see, including:

    J Hunter –
    … “larger values cannot be excluded” (IPCC, 2007b). … to be more reliable than the modelled sea-level projections … suggested a rise of 0.5 to 1.4 metres at 2100 …

    Estimating Sea-Level Extremes in a World of Uncertain Sea-Level Rise
    JR Hunter –
    … Fourth Assessment Report (AR4; IPCC, 2007) … to project sea level into the … suggested a rise of 0.5 to 1.4 metres at 2100 …

    Submission to the Senate Select Committee on Climate Policy
    B Bahnisch –
    … Rahmstorf used the information available to the IPCC and came up with a range of 0.5 to 1.4 metres … The IPCC and sea level change. …


    “It’s a poor sort of memory that only works backwards” and doesn’t givbe us recent updates to what we last learned — that’s why libraries and search tools have been invented, to add to what we remember. Try one today.


  47. 147
    Hank Roberts says:

    PS, a brief excerpt from the first reference I found,
    for those who don’t take the trouble to do their own search:

    — excerpt follows —-

    The Fourth Assessment Report (IPCC, 2007a) has indicated a projected global sea-level rise of up to 0.79 metres in 2095 (relative to 1990) with the caveat that, because of uncertainties in future ice sheet flow, larger rises cannot be excluded.

    In Australia, at Fremantle and Fort Denison (Sydney), the frequency of sea-level extremes of a given height has already increased by a factor of about three during the 20th century, predominantly due to sea-level rise. Even a mid-range rise of about 0.5 metres during this century would lead to events which now happen every few years happening every few days in 2100, or the present ‘100-year event’ happening every few months.
    —– end excerpt—-

  48. 148
    Hank Roberts says:

    Oh, this also merits looking up. Nicholas Nierenberg wrote:

    > The collapse of the West Antarctic ice sheet would produce
    > several meters, I’m not sure about Greenland.

    A recent lowered estimate is here:

    “Bamber and his colleagues found a WAIS collapse would only raise sea levels by 3.3 meters, or about 11 feet. Bamber, a professor at the University of Bristol in England, currently is a visiting fellow at the University of Colorado at Boulder’s Cooperative Institute for Research in Environmental Sciences”

    That’s the lowest estimate available, and based on optimistic assumptions:

    “The study authors assumed that only ice on the downward-sloping and inland-facing side of the basins would be vulnerable to collapse. They also assumed that ice grounded on bedrock that slopes upward inland or on bedrock that lies above sea level likely would survive.”

    How much from Greenland? You know how to look this stuff up.

  49. 149
    Martin Vermeer says:

    J. Bob:

    > Not if you make the wrong guess.
    Indeed… in this case we happen to know that, even including this guesstimate, IPCC projecons are low. So ignoring it is a good example of ‘the wrong guess’.

  50. 150
    Martin Vermeer says:

    Aaron Lewis:

    I think climate scientists (and
    weathermen) should be registered
    like professional engineers, and
    have to post a performance bond
    when they issue a climate/weather

    Yeah, that’s the way to help science forward… not. I have a better idea. In the interest of bringing good engineering practices to the management of this issue, what about obliging instead the emitters of greenhouse gases to post such bonds?

    Seems more logical to address the source of the problem, rather than the source of information on the problem, don’t you think?