Guest Post by Willis Eschenbach
There’s an old con game that has been played on the suckers for hundreds and hundreds of years. It is done in various forms, with various objects, under various names—three card monty, the shell game, Thimblerig, bottle caps, cups and ball, the game is the same in every one. The essence is, the con man puts a pea under a shell, then switches the shells around and asks which shell is hiding the pea.
Figure 1. The Conjuror, by Hieronymus Bosch, painted 1475-1480. The type of tricks the conjuror is doing are thought to be among the origins of the shell game.
I bring this up because our favorite conjuror, James Hansen, is up to his old tricks again. He has a new paper out, Paleoclimate Implications for Human-Made Climate Change, And as always, you have to figure out which shell is hiding the pea.
Here is his money graph, the one that is getting lots of play around the blogosphere. The main observation I’ve seen people making is that having been bitten by previous failed prognostications, Hansen is taking the well-tested Nostradamus route now, and is predicting sea level rise for when he’ll be 137 years old or so …
Figure 2. Hansen’s Figure 7: ORIGINAL CAPTION: “Five-meter sea level change in 21st century under assumption of linear change and exponential change (Hansen, 2007), the latter with a 10-year doubling time.”
Folks are saying that the bad news is, it looks like we won’t be able to tell until 2040 or so if Hansen’s claim is true. But that’s not the case at all. Those folks are not keeping close enough watch on the pea.
In the paper Hansen says:
Sea level change estimates for 21st century.
IPCC (2007) projected sea level rise by the end of this century of about 29 cm (midrange 20-43 cm, full range 18-59 cm). These projections did not include contributions from ice sheet dynamics, on the grounds that ice sheet physics is not understood well enough.
Rahmstorf (2007) made an important contribution to the sea level discussion by pointing out that even a linear relation between global temperature and the rate of sea level rise, calibrated with 20th century data, implies a 21st [century] sea level rise of about a meter, given expected global warming for BAU greenhouse gas emissions. …
… Hansen (2005, 2007) argues that amplifying feedbacks make ice sheet disintegration necessarily highly non-linear, and that IPCC’s BAU forcing is so huge that it is difficult to see how ice shelves would survive. As warming increases, the number of ice streams contributing to mass loss will increase, contributing to a nonlinear response that should be approximated better by an exponential than by a linear fit. Hansen (2007) suggested that a 10-year doubling time was plausible, and pointed out that such a doubling time, from a 1 mm per year ice sheet contribution to sea level in the decade 2005-2015, would lead to a cumulative 5 m sea level rise by 2095.
The short version of that is:
• The IPCC predicts sea level rise of about a foot (30 cm), but they don’t take ice into account.
• Rahmstorf says a linear projection gives about a metre (3.3 feet) of sea level rise.
• Hansen 2007 says there’s a missing exponential term in Rahmstorf’s work, because the ice will be melting faster and faster every year.
OK, so Hansen 2011 rests on the claims made in Hansen (2007), which turns out to be Scientific reticence and sea level rise. At the end of Section 4 Hansen says that Rahmstorf estimates a 1-metre sea level rise, but that a non-linear ice melting term should be added to the Rahmstorf rise.
Under BAU [“Business As Usual”] forcing in the 21st century, the sea level rise surely will be dominated by a third term: (3) ice sheet disintegration. This third term was small until the past few years, but it is has at least doubled in the past decade and is now close to 1 mm/year, based on the gravity satellite measurements discussed above. … As a quantitative example, let us say that the ice sheet contribution is 1 cm for the decade 2005–15 and that it doubles each decade until the West Antarctic ice sheet is largely depleted. That time constant yields a sea level rise of the order of 5 m this century.
So to get the final Hansen projection, we need to see what is happening in Rahmstorf, A Semi-Empirical Approach to Projecting Future Sea-Level Rise, paywalled, where we find the following graph of projected sea level rise.
Figure 3. The Rahmstorf estimate of sea level rise, to which Hansen says an exponentially growing ice term should be added.
ORIGINAL CAPTION: Past sea level and sea-level projections from 1990 to 2100 based on global mean temperature projections of the IPCC TAR. The gray uncertainty range spans the range of temperature rise of 1.4° to 5.8° C, having been combined with the best statistical fit shown in Fig. 2. The dashed gray lines show the added uncertainty due to the statistical error of the fit of Fig. 2. Colored dashed lines are the individual scenarios as shown in (1) [Ref. 1 is the IPCC TAR Bible, no page given]; the light blue line is the A1FI scenario, and the yellow line is the B1 scenario.
(In passing, let me again protest the use of the entire IPCC Third Annual Report, thousands of pages, as a reference without giving us chapter and verse in the way of page numbers. My high school science teacher would have slapped my hand for that, it’s a joke.)
The upper blue line is the one that gives us about a meter of sea level rise. So I took that as Rahmstorf’s 1 metre rise. To that I added, as Hansen claims we should, an amount that starts at 0.5 cm in 2000 and doubles every ten years. This is following Hansen’s claim that the non-linear ice disintegration is a separate term that starts small but will “come to dominate” the sea level rise over the century. The result is shown in Figure 4.
Figure 4. Rahmstorfs predicted rise (blue), Hansen’s projected additional rise from “non-linear ice disintegration” (dark red), and total sea level rise (green) predicted in H2011. I have included the last century’s rise of 16 cm, as calculated by Rahmstorf, in the lower right corner for comparison purposes. IMAGE SOURCE
OK, so what Hansen is actually predicting is the green line. However, his real forecast is actually much worse than that. Hansen again, emphasis mine:
The eventual sea level rise due to expected global warming under BAU GHG [greenhouse gas] scenarios is several tens of meters, as discussed at the beginning of this section.
I’m going with “several tens” to mean more than two, so he’s predicting a 30 metre sea level rise!!! … I guess he figured nobody paid any attention when Al Gore threatened us with a 20 metre sea level rise, so he’d better pull out all the stops and give us a real scare, something to make us shake in our panties.
There is a bit of good news, however. Both the Rahmstorf and the Hansen projections are already way above the reality. Since 1993, when the satellites started measuring sea level, we’ve gone up about 4.6 cm (1993-2011). Rahmstorf’s projection is 6.4 cm for that time period, about 40% too high already. Hansen’s larger projection is 7.2 centimetres rise over that time, or 55% too high.
The annual rise is also entertaining. According to the satellites, the trend 1993-2011 was 3.2 mm/yr, and has been declining recently. The change 2009-2010 was under a mm, at 0.9 mm/yr. And 2010-2011 was just about flat.
In 2010-2011, Rahmstorf’s projected rise is already 4.5 mm/yr, about fifty percent larger than the actual rate of the last 18 years. And Hansen’s annual rise is even worse, at 5.3 mm per year.
So both in terms of 1993-2011 rise, as well as current annual rise, both Rahmstorf and Hansen are already way above observations. But wait, there’s more.
Hansen’s rate of sea level rise is supposed to be accelerating, as is Rahmstorf’s rate. By 2020 Hansen says it should be rising at 6.3 mm per year, and everlastingly upwards after that. But in fact we’re already way under their supposed rates of annual increase, and the observed rate of rise is declining …
How does Hansen get these nonsensical numbers? Well, he noticed something in the observations.
This third term [melting ice] was small until the past few years, but it is has at least doubled in the past decade …
My high school science teacher, Mrs. Henniger, bless her, thought extending a linear trend into the future was a crime against nature, and I would hesitate to express her opinion on Hansen blithely extending a ~ 7% annual increase for a hundred years. That kind of compound interest turns a centimeter (3/8″) into 5 metres (16 feet). If Dr. Hansen had submitted this nonsense to her, you would not have been able to read it when it came back for the red pencil scribbles.
You can’t do that, folks. You can’t just observe that something has doubled in the last decade, and then extend that exponential growth out for a century. That’s beyond wishful thinking. That’s magical thinking.
Two final points. First, the pea under the walnut shells. Note carefully what Hansen has done. He has claimed that the sea level rise will be “several tens of metres”. This is at least thirty metres, or a hundred feet, of sea level rise.
He seems to be at least somewhat supporting this claim with his Figure 7 (my figure 2). But if you look at the caption, this is not a forecast, a projection, or a scenario of any kind. Instead, this is merely an “approximation” of what a linear sea level rise might look like and what an exponential rise might look like. You know, in case you didn’t understand “linear” and “exponential”. His actual forecast is under another walnut shell somewhere. We know his “Approximation” can’t be a real projection because it shows almost no rise occurring currently, or for some years.
Second, even this doesn’t begin to unravel the errors, deceptions, alarmism, and con games in Hansen’s work. Do you see the guy in the dark vest and the white pants and shirt at the left of Hieronymus’s painting at the top? See what he has in his hand while he’s looking all innocent at the sky? See who it’s chained to? Hansen’s not really the shell game conjurer, that guy’s a piker, he’s not making much money on the game.
Hansen’s the guy in the dark vest with his hand on your pocketbook …
w.
[UPDATE]
Joel Shore observed correctly that Hansen was basing his estimate of a huge sea level rise on paleoclimate date. Joel is right that Hansen claimed the paleoclimate data shows a rise of 20 metres for every 1°C temperature rise. Because of this, Hansen says that a 2°C future temperature rise will give a 40 metre sea level rise.
Let’s take a bit calmer look at what we know. We know that when there is an ice age, a lot of the water in the ocean behaves badly. It goes up on the land as mainly northern hemisphere ice and snow and glaciers. As a result, the sea level drops by a hundred metres or so. The glaciers stay there until the ice age ends, at which point they melt, and the sea level rises again. Since we’re in an interglacial, right now the glaciers are mostly melted.
So I would certainly not expect further warming to have much effect on melting or sea level. The easy ice is all melted, the giant miles-thick Northern Hemisphere glaciers are almost all melted back into the ocean. The rest are hiding mostly on north slopes in northern climes. So where is the meltwater going to come from?
And curiously, what I found out from Joel’s question is that if you know where to look, we can see that the graphs in Hansen’s own paper bear me out. They say the oceans won’t rise. I don’t particularly believe Hansen’s results, but presuming that they are correct for the sake of discussion, then let’s look at his graphs.
Look first at the sea level during the past four interglacial periods. I stuck a ruler on it so you can see what I mean.
As you can see, at the level of detail of their graph the sea level has never been higher than it than it is now.
Now look at their temperature observations and reconstruction:
According to Hansen, temperatures have been as much as 2.5°C higher than at present … but the sea level hasn’t ever been higher than at present.
If Hansen’s claim were true, that a 1°C temperature rise leads to a 20 m sea level rise, we should see sea levels forty metres or more above present levels in Hansen’s graph (b). Look at the scale on the left of graph (b), that’s off the top of the chart.
Instead, we see nothing of the sort. We see much warmer periods in the past, but the sea levels are indistinguishable from present levels. Hansen’s own graphs show that he is wrong. So it appears that Hansen is doing the same thing, he’s extrapolating a linear trend out well beyond the end.
He’s noticed that when warming temperatures were melting the huge glaciers over Chicago, the sea level rose quickly. Unfortunately, he has then extended that trend well past the time when there are no glaciers in Chicago left to melt …
w.
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Thanks REP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Hmmmm. Snowball Earth (which there is little but conjecture for) appears to be disassociated from the carbon cycle. A VERY carefully worded article that slinks down into nonsense, IMHO.
http://www.sciencedaily.com/releases/2012/01/120127140523.htm
Nils-Axel Morner, Observation over extrapolation.
Right, so I think I understand how to do the science now. don’t worry about facts, truth, data etc, just make a claim that will happen well after you are dead, this way if it don’t work out, noone can hold you accountable. (Turning sacrasm on) Yep I can work with that, can I have a grant of oh about 2 billion smackaroonies please, cause I have a prediction for the year 2120 (yep that’ll put me well in the grave) about a mighty upheaval in the pacific ocean when the earths core returns to its centre position, which will stop the wobble of the earth, it will pull the moon back towards us and we will all be wiped out when it hits us 100 years later. I have really good graphs I made in excel and MS word to back it all up, so can I have my 2 billion now please? (Turning sarcasm off now).
“There is a bit of good news, however. Both the Rahmstorf and the Hansen projections are already way above the reality”
Reality never meant a whole lot to these people. Also, they claim that back-casting models fits the data……
The exponential is proposed because it starts off with a small rate of increase, but then, to scare children, it ends up with a very high rate. It’s a convenience to bluff past the recent satellite data from Envirosat and Jason 2, that actually show a decrease over the last 18 months. The newer the satellite, the smaller the estimated rise – and the frame of reference is the network of satellites carefully positioned with respect to each other (not the centre of the globe any more).
One obvious question is, Why do Hansen and Rahmstorf show a montonic upward increase when they must know of the current decrease?
Another obvious point is that for sea level to rise by heating, the whole volume of the sea must, on averge, increase in temperature. We know very little about the temperature of the deep oceans. A very small change there would offset the usual volume that is discussed, from the surface down to about 700m. If you consider only the latter volume and avoid the dynamics of heat transfer, this 700m shell would have to get very hot indeed to raise sea level by tens of meters.
Finally, it still seems to be under-appreciated that via Archimedes, the melting of floating ice has no effect on sea level rise, (unless the heat that melted the ice continues on to heat the sea anomalously). The land ice of the Antarctic seems never to have melted during the time period covered by ice cores, since cores can be correlated from place to place without discovering unconformities.
A physicist says:
January 29, 2012 at 9:18 pm
Robert Austin says: The Northwest Passage has been open before in the last century and negotiated by wooden ships without benefit of radar, up to date weather and ice forecasts and satellite navigation, so where is the genius in saying it could be open again.
Robert, you don’t mention where you got that information, but whoever/whatever the source was, definitely no skeptic should ever trust that source again!
Before the 21st century, I believe there is no record of any wooden ship ever making the Northwest passage without over-wintering in the ice at least one year, sometimes two years, or (sadly frequently) never returning at all.
Whereas nowadays ordinary folks are making the NW Passage in rowboats, kayaks, and inflatable rafts.
But hey, even in the “big Arctic thaw” of the 21st century, the NW Passage still has its risks for sailors: sometimes the yogurt goes sour!
With with winter ice presently at record low levels, in both area and thickness, it’s a safely non-skeptical bet there will be more ordinary small-boat folks making the NW Passage in 2012.”
Sorry, Physicist, but you lose. The St. Roch, a RCMP schooner made of Douglas Fir and Eucalyptus sailed through the Northwest Passage from Halifax, NS to Vancouver, BC in 86 days in 1944, using a previously uncharted route.
http://en.wikipedia.org/wiki/Northwest_Passage
http://en.wikipedia.org/wiki/St._Roch_%28ship%29
Joel Shore says:
January 29, 2012 at 7:40 pm
Interesting question. When I go to look at the paleoclimate data you refer to, it’s paywalled, of course. However, they point out you can’t really tell the temperature from the isotopic variations directly. Here’s how they solve that problem, from their abstract:
Computer models can’t reproduce what’s happening today … but I’m supposed to believe them about what happened half a million years ago??? Once again, it’s models all the way down.
Think about this, Joel. If this is the goods, if this is the real science, then why is the best evidence for their claim of exponential sea level rise a computer model of what they say happened half a million years ago? Don’t they have something with a little meat on the bones? I mean, that’s it? That’s their best shot, their firmest evidence? That’s supposed to convince me to run for the hills to escape the hundred-foot sea level rise?
Let’s take a bit calmer look at what we know. We know that when there is an ice age, a lot of the water in the ocean behaves badly. It goes up on the land as mainly northern hemisphere ice and snow and glaciers. As a result, the sea level drops by a hundred metres or so. The glaciers stay there until the ice age ends, at which point they melt, and the sea level rises again. Since we’re in an interglacial, right now the glaciers are mostly melted.
So I would certainly not expect further warming to have much effect. The easy ice is all melted, the giant miles-thick Northern Hemisphere glaciers are almost all melted back into the ocean. So where is the meltwater going to come from?
And curiously, what I found out from your question is that if you know where to look, we can see that the graphs in Hansen’s own paper bear me out. They say the oceans won’t rise. I don’t particularly believe his results, but if they are correct, then let’s look at the graphs of Hansen’s results.
Look first at the sea level during the past four interglacial periods. I stuck a ruler on it so you can see what I mean.
As you can see, at the level of detail of their graph the sea level has never been higher than it than it is now.
Now look at their temperature observations and reconstruction:
According to Hansen, temperatures have been as much as 2.5°C higher than at present … but the sea level hasn’t ever been higher than at present.
If Hansen’s claim were true, that a 1°C temperature rise leads to a 20 m sea level rise, we should have seen sea levels forty metres or more above present levels in Hansen’s graph (b). Look at the scale on the left, that’s off the top of chart.
Instead, we see nothing of the sort. We see much warmer periods in the past, but the sea levels were indistinguishable from the present time. Hansen’s own graphs show that he is wrong. So it appears that Hansen is doing the same thing, he’s extrapolating a linear trend out well beyond the end.
He’s noticed that when warming temperatures were melting the huge glaciers over Chicago, the sea level rose quickly. Unfortunately, he has then extended that trend past the time when there are no glaciers in Chicago left to melt …
Interesting question, Joel. Keep pushing, I would never have noticed that oddity without you.
w.
Joel Shore says:
January 29, 2012 at 7:40 pm
Equilibrium sea level rise? How exactly does that work? Does ice melt but somehow the resultant water doesn’t add to the sea level for a period of time? Or does the ice not yet melt at the 1DegC rise but at some stage down the track it melts because of the former 1DegC rise?
thanx in advance
Remember Hansen’s (ca) 1980 prediction: that the Manhattan perimeter highway was going to be underwater by 2010 ?
So far, traffic seems to moving smoothly. In fact it has been difficult to measure any rise at all.
How is that person still on the payroll?
Baa Humbug says:
January 29, 2012 at 10:07 pm
I’m not Joel, but I understand what he means and use the term myself. Suppose the temperature globally went up a degree tomorrow. It would take some time for that slight change in temperature to affect the world’s glaciers. During some years they would (likely) retreat slightly, and then eventually take up a new somewhat stable size. Correspondingly, the sea level would rise for some period of time, and then level off.
It is that slow equilibration of ice to temperature to sea level rise that I use the term for. If Joel means otherwise, he’ll let us know.
w.
@Willis Eschenbach
Your 10:01 pm response sealed the deal. That is good!
Donald says:
January 29, 2012 at 10:12 pm
It was in about 1990, and referred to 2040.
We’re halfway there.
w.
Nick Stokes says
“You should have included the final sentence of the Hansen para you quoted which said:
‘Of course I cannot prove that my choice of a ten-year doubling time for nonlinear response is accurate, but I am confident that it provides a far better estimate than a linear response for the ice sheet component of sea level rise under BAU forcing.’ ”
* * *
Why should he? Hansen may claim that he ” cannot prove that his choice of a ten year doubling time for non-linear response is accurate…” but this is clearly just a “buffer” zone on his part due to the fact that he has been wrong so many times before. (And everybody knows it.)
Not to mention, Hansen’s actions over the years have proved that, in his mind, he is completely and unarguably right. To him, he can do no wrong, and anyone questioning him is the one who is wrong. So why the added disclaimer of uncertainty if his mind is already arrogantly made up?
This is akin to saying ” Don’t shoot the Messenger”, but then putting a bullet in him anyway.
Nick Stokes says:
January 29, 2012 at 8:43 pm
Thanks, Nick. There were about 500 other sentences in Hansen’s paper I didn’t quote. I figured people would, you know, read them.
In the paragraph you quote, all that Hansen says is that he is confident that he is right. I can’t imagine how I could have overlooked quoting such a shocking and unexpected revelation—James Hansen thinks he is right, who could possibly have guessed?
Now … why was it I should have quoted that sentence, exactly?
w.
OK, this is probably a silly non-scientist’s question. I only ask because it seems this is what Hansen is saying from the quotes here.
As a piece of ice melts it gets smaller, therefore the surface area in contact with the air also gets smaller, that in turn will reduce the amount of air in contact with the ice. So how, if the amount of relatively warm air in contact with the ice is less, does the melt rate increase?
A physicist says:
January 29, 2012 at 9:18 pm
The Northwest Passage has been traversed before as Robert says, so I don’t know why you are dissing his source.
A physicist, before you do anything else, before attacking anyone’s responses or defending yourself, you need to give us two quotes:
1. Hansen’s 1981 quote forecasting the NW passage opening.
2. Hansen’s quote forecasting that global temperatures would show a BEST-style hockey-stick.
While you are at it, please provide a definition for a “BEST-style hockey-stick”, I haven’t a clue what that is, as the BEST data did not resemble a hockey-stick in any way.
Don’t bother with anything else. Don’t be making further explanations. Let’s start with the facts. Pull out the actual quotes, and let’s see what he actually said.
Until you do so, the topic is off limits for me, because people are talking about something with no agreement on the facts. Folks, let’s give A physicist time to find his facts.
w.
Willis Eschenbach says: January 29, 2012 at 10:24 pm
“Now … why was it I should have quoted that sentence, exactly?”
A better question is why you cut the para just there so as to omit it. He is clearly qualifying his statement, saying that the 10-year figure is arbitrary, and not to be taken too seriously. And he isn’t saying that it is right – just that it is better than assuming simple continuation of the current very low rate.
GeoLurking says:
January 29, 2012 at 10:16 pm
Thanks, Geo. I laughed out loud when I noticed that about the sea levels. There is something fundamentally satisfying in using a man’s own figures to show that he is wrong. It makes it very hard for him to argue against.
w.
Willis,
Check this out: The calculation is done for you.
http://climatesanity.wordpress.com/conversion-factors-for-ice-and-water-mass-and-volume
The answer to the first commenter is illustrative.
Finally, there are seasons on this planet. Therefore at least some of the melting done in three seasons will have to be done again in the following year. Three steps forward, one back. Unless
prof. Hansen expects the next ice age to start precisely at midnight of the year 2100, one can be reasonably sure that the next ice age will have started before even Greenland is devoid of it’s frozen lustre.
Neil Jones says:
January 29, 2012 at 10:28 pm
The only silly questions are the ones you don’t ask.
Consider a one inch cube. It has a volume of one cubic inch, and a surface of six square inches.
Consider a two inch cube. It has a volume of 8 cubic inches, and a surface area of 24 square inches.
In the smaller cube, there are six square inches of surface for every cubic inch of volume.
In the larger cube, there are only three square inches of surface for every cubic inch of volume.
As a result, with more surface area per volume, the smaller cube will gain or lose heat faster than the larger cube.
HTH,
w.
I would argue the acceleration is in the wrong direction as all of the recent data suggests. Here I overlay the best fit acceleration and sine wave over the most recent sea level data. The acceleration has a big MINUS in front of it. I also project the same functions out to 2100 for a nice little comparison of what data driven projections look like in comparison to wild fantasies.
When the evidence is suggesting that sea level rise is slowing, any good climate scientist must conclude that the ice must be melting at an ever accelerating pace. I’m afraid I’ll just never fit in.
And Willis, I wouldn’t get your hopes up of doing any Pal Reviews of Hansen’s work either.
Fun for one and all, my “100% empirical approach to projecting future sea-level rise”:
http://naturalclimate.wordpress.com/2012/01/30/sea-level-deconstruction/
Willis Eschenbach says:
January 29, 2012 at 10:15 pm
Thanx Willis
I’m thinking of a production line. Yes it takes 16 hours to produce a widget, but in a production line we spit out a widget every 20 minutes (type of thing)
We know temps don’t jump a whole degree at a time. The current warming period has been on going now for how long? 150 years maybe? So then the 1/10th of a degree temp rise from 10 decades ago has reached ice melt equilibrium already. (my assumption) And so has the 1/10th rise from 9 decades ago and so on.
If 1DegC rise can cause a 20mtr sea level rise, where is the evidence of some metres of sea level rise since warming began?
My query would be invalid if it can be shown that ‘equilibrium’ isn’t reached for many multiple decades. Is there evidence for this?
my best regards
A physicist says:
January 29, 2012 at 7:45 pm
“That’s why rational skepticism has to say “Maybe Hansen is right a third time.”
He was wrong the first and second time. His prognostication skills are now truly suspect, as any reasonable person must acknowledge. Yes, pigs might fly someday, maybe …and hansen might get one right, if he ever honestly assesses the unadjusted data.
I’m betting on the pigs…..
Hi Willis,
you are certainly aware of the “content” of Rahmstorf et Hansen et al 2007 discussed at climateaudit, lucia and elsewhere.
Updating his data by just 2 (!) more years already spoiled the message !
http://i39.tinypic.com/6fnvqa.gif
And there was much more fishy to tell:
http://climateaudit.org/2009/07/03/the-secret-of-the-rahmstorf-non-linear-trend/
http://rankexploits.com/musings/2009/source-of-fishy-odor-confirmed-rahmstorf-did-change-smoothing/
As such papers are not retracted, it is no wonder, when even more of that sort is produced.