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‘Wrong sign paradox’ finally resolved?

Filed under: — stefan @ 1 April 2012

A group of colleagues has all but solved one of the greatest remaining puzzles in climate science. But the story is not one of scientific triumph – rather, it is so embarrassing that we had controversial discussions in our group whether to break this to a wider public at all.

The puzzle is known amongst climatologists as the “wrong sign paradox” – our regular readers will probably have heard about it. Put simply, it is about the fact that a whole number of things in climate science would fit very nicely together, if only the sign were reversed. If only plus were minus.

Perhaps the best-known example is how we could explain global warming with variations in solar activity: the hottest year on record (2010) happens to coincide with the deepest solar minimum since satellite measurements of solar luminosity began in the 1970s (Fig. 1). This can’t just be coincidence. But the sign is wrong: physical theory stubbornly insists that temperature should be highest when the sun shines the brightest, not the other way round. The “wrong sign paradox” here is reinforced by the fact that the overall trend in solar luminosity is gently downward over the past 30 years – just those 30 years when we see the well-known strong global warming.

Fig. 1: Global temperature (blue, GISS) and solar luminosity (orange), both as 12-months running means.

Another prominent example is the Pacific Decadal Oscillation (PDO). Basic physical considerations would suggest that the global temperature is warm when the PDO-Index is high, i.e. when sea surface temperatures in the North Pacific are high. A theory that would beautifully fit the data – if only the sign were reversed (Fig. 2)!

Fig. 2. PDO-Index vs. global temperature, with linear trends (dashed) since 1900 and over the last 30 years.

And just to round this off with a third example (there are more of course – perhaps our readers can provide some others): cosmic rays. A very beautiful theory holds that cosmic rays help cloud formation: lots of cosmic rays means lots of cloud and hence cool global temperature. Now cosmic rays have been measured since the 1950s, and they reached their all-time maximum in 2010 (Fig. 3). Bingo: the warmest year on record! But no: a high cosmic ray count should cause cold temperatures, not hot ones.

Fig. 3. Cosmic ray flux as measured at two neutron monitor stations.

Even a lay person can imagine how powerful these (already popular) theories would be, if only the data showed exactly the opposite of what they actually show! If the warmest year on record coincided with the strongest solar maximum and not the deepest solar minimum, or if the PDO showed an upward trend over the past 30 years and not a downward trend. But now a solution seems to be in sight.

Solving the mystery

A group of Dutch and US scientists, led by Harry Van den Budenmeyer (Utrecht University), has now proposed a surprising explanation. “At first I did not want to believe it”, Van den Budenmeyer explained to RealClimate, “but once we started to pursue this, things just fell into place”.

The story goes back to the late 1980s or early 1990s (the exact date has not been traced back yet), when a German climate modeller had persistent problems with results of obviously the wrong sign in his model. He was unable to track down the error, so instead he introduced a FORTRAN integer variable called ICHEAT (sorry to get a bit technical, but you really need to understand this) into his computer code, assigned it the value -1 and simply multiplied unruly results by ICHEAT wherever they occurred in his code. Once he’d find the real problem, he would only need to set ICHEAT to +1 and the code would be correct again. But he never got round to fix the problem, his model performed very nicely and over time he forgot about it.

What he did not consider, perhaps understandably at the time: useful computer code spreads like a virus amongst scientists. The code was free for download, hundreds of other scientists started to use it and many only used bits and pieces – nobody ever starts writing scientific code from scratch if colleagues have already solved aspects of the task at hand and the code is free.

“At first we were really puzzled when we found a piece of code with ICHEAT that was used in our lab for climate analysis”, says Van den Budenmeyer. “But once we discovered what it was we started to search more systematically and ask colleagues, and by now we’ve found the ICHEAT bug not just in different European countries but also in California, New York, Sydney and even a Chinese climate centre. We’ve only begun to explore the implications, but I am sure that a lot of the wrong sign paradox that has plagued our science thus far will just go away.”

We will keep you updated here at RealClimate, of course.

p.s. And yes, this is an April fool’s joke, in the Realclimate tradition of pieces like the Doubts about the Advent of Spring, or the famous Sheep Albedo Feedback.

99 Responses to “‘Wrong sign paradox’ finally resolved?”

  1. 51
    David Wilson says:

    delightful! thank you.

    then there is the law of inverse deniers too – how long it took one to see through your excellent good humour.

  2. 52

    I need to do a talk on belief structures next week. Where can I download this code… or is it hidden?

    ICHEAT: Illusory Code Enables Alternative Translation

  3. 53

    I have it on good authority that the iCheat methodology was hijacked by the Republican party for use in deciding the suitability of its presidential nominees.

  4. 54
    piffy says:

    tiswl TOTALLY get cited by teh deniers.

  5. 55
    Louis Hooffstetter says:

    The bug in my code says:


    “Nope, D’jew?”

  6. 56
    Richard Woods says:

    @52 John P. Reisman

    “ICHEAT: Illusory Code Enables Alternative Translation”

    Perhaps you meant:

    ICHEAT: Illusory Code Heuristically Enables Alternative Translation

  7. 57
    csoeder says:

    I LOL’d.

  8. 58
    t marvell says:

    Very funny. But not so funny. In the real world the ICHEAT is more complicated, and the researcher might not be aware that he/she is using it. There is always a tendency toward confirmation bias. There is always a tendency to accept one’s research results if it reaches what one expects or wants, and a tendency to fiddle with the research if not.

  9. 59
    Andy Lee Robinson says:

    or, to go with the tinfoil:

    ICEHAT – Illusory Code Enables Heuristically Alternative Translation

  10. 60
    CM says:

    Plus/minus one of your best, though nothing beats the sheep albedo.

  11. 61
    Snapple says:

    Not to interrupt or anything–but you need an April thread.

    They have an alligator farm in Michigan because of global warming. Some of the alligators have been pulling people’s legs…

  12. 62
    R. Gates says:

    Well, this is certainly going to leave some April foolie day egg-yolk on someone’s face…

  13. 63
    Jos Hagelaars says:

    Funny piece, I prefer the German word ISCHUMMEL above ICHEAT or even the Dutch word IKLETSKOEK.

    The Dutch are famous though for their problem solving capabilities, after tackling this ISCHUMMEL problem, our scientific institutes are directing their attention on the monster of Loch Ness and the location of Atlantis, but our top priority will be to finally solve the famous chicken and egg problem.

  14. 64
    Bob Tisdale says:

    Stefan: While I do realize this is an April Fools post, a note of clarification about your second example.

    You wrote, “Basic physical considerations would suggest that the global temperature is warm when the PDO-Index is high, i.e. when sea surface temperatures in the North Pacific are high. A theory that would beautifully fit the data – if only the sign were reversed (Fig. 2)!”

    The PDO does not represent the sea surface temperature anomalies of the North Pacific. In fact, the PDO is inversely related to the detrended sea surface temperature anomalies of the North Pacific, north of 20N.


  15. 65
    Steve Fish says:

    I have been mining the Bore Hole to try to work up the data for a new RC original post entitled- “Wrong spin paradox finally resolved?”

  16. 66

    #56 Richard Woods

    ICHEAT: Illusory Code Heuristically Enables Alternative Translation

    Yes, my apologies, my IFLOP software was enabled when I typed that.

  17. 67
    Andy says:

    This is no “sheep albedo effect” but still clever.

  18. 68

    I knew it!

    Finally you must have come to understand that gravity is just a theory.

    So much more work to do.

  19. 69
    Tony O'Brien says:

    JCHEAT Do not forget many Euopeans pronounce the J as we would a Y

  20. 70
    Chris Dudley says:

    I actually looked at the code and, unfortunately, every instance of ICHEAT was multiplied by the variable NCHEAT which also was assigned the value -1.0. I’m afraid the problem has not yet been solved.

  21. 71
  22. 72
    Lucien Locke says:

    Oh Stefan,

    The iCHEAT is just to much to bear. I laughed until my sides hurt…you are too much……

    still laughing,


  23. 73
    Susan Anderson says:

    Saving some excellent advice for the upcoming Open Thread:

    teensily OT here but useful nonetheless.

  24. 74
    tokodave says:

    Wow. The mountaineer, backcountry skier and mountain biker in me always thought the rule: Gravity never takes a day off was sacrosanct….but now I’m not sure about that either! ;-)

  25. 75
    owl905 says:

    I’m saving my sympathy for the guy who has to tell Arthur Dent the answer was really -42.

  26. 76
    Noel Fuller says:

    Google has its own subtle sense of humour too. When I pasted Van den Budenmeyer to google it searched Van den Budenmayer then asked if I really meant Van den Budenmeyer!


  27. 77
    Dan H. says:

    I must admit that the sheep albedo effect is my favorite, although there were several other goodies. Gotta love today.

  28. 78
    dhogaza says:

    Dan H.

    Gotta love today.

    In your case, it’s sort of like Groundhog Day blended with April Fool’s.

    Having read so many of your posts and all.

  29. 79
    dhogaza says:

    Apple will be announcing the iCheat in Q3 2012 … since scientific computing requires so much computational horsepower, it’s iRack mountable.

  30. 80
    DF says:

    You RC guys are just cruel.

  31. 81
    Christoffer Bugge Harder says:

    #7 Alex Harvey

    Perhaps Calder did not see any pressing reasons to reveal to you that the “impressive” cosmic rays/temperature fit of Svensmark and Friis-Christensen in their never-published reply to Lockwood & Fröhlich was only achieved by removing a trend of 0,14C/decade – or 0,7C over the last 50 years? ;)

    Best, Christoffer

  32. 82
    Ron Manley says:

    It ill behoves me to criticise such an august body of scientists as those who run but I feel it incumbent on me to do so. You are indeed correct to state the variable ‘ICHEAT’ has appeared in all climate models up to the present but are completely wrong about its provenance. It was introduced by Dr CO Jones and Professor SN Dall and should read ‘1 C heat’ and represents the CO2 climate sensitivity built into the models. In 1988 the neo-Confusion philosopher, Jim Han Sen, introduced the following line: ‘WATVAP=3.0”. Climate sceptics claim that as there has been no warming since 1998 its value should be 0.0.

  33. 83
    Slioch says:

    Oh dear. My attempt, mentioned at #4 above, to get the WUWT site commenting on this didn’t get very far, see:

    “Slioch says:
    April 1, 2012 at 2:45 am

    May I draw everyone’s attention to the fact that there has been a major reversal in climate science reported at Realclimate here:

    REPLY: This is a badly executed April Fools Joke, ignore it. Here’s why I didn’t do one this year:

    With so much deception going on, you’d think RealClimate would know better. I guess not. – Anthony”

    Perhaps Anthony was concerned lest his followers fell for it, though, to be fair, they had not done so in the hours before he added his reply.

  34. 84
    sydb says:

    ICHEAT2 is also a very useful variable. If you set it to 0 and then use it as a multiplier, all sorts of things can simply disappear. There are times when that is more useful than simple ICHEAT. For example, it would be difficult to interpret CO2_conc *= ICHEAT;
    but CO2_conc *= ICHEAT2;
    has a very simple interpretation. There isn’t any CO2, so it can’t be doing anything.

  35. 85
    Marco says:

    @Stefan-inline response to #11:

    This is quite funny, there IS such a person as Van den Budenmeyer in climate science?!

    I was convinced you were alluding to Van den Budenmayer, a fake composer made up by Zbigniew Preisner and Krzysztof Kieslowski.

    There I was, thinking I made a smart remark pointing out I looked through the April Fool’s joke, and the joke is STILL on me…

    [Response: Admittedly, the VdB acknowledgement in that old paper was inspired by Kieslowski… Don’t tell anyone! -stefan]

  36. 86
    Jbar says:

    Ha ha. (But EVERY day is April 1 for climate skeptics!)

  37. 87
    Jim Larsen says:

    Susan on Trolls,

    The wrong sign paradox applies to trolls, too.

    By observation, at least a few people on any blog will respond to trolls, thus providing sustenance. An individual who is bothered by this is best served by adding to the din, as that will hasten the troll’s exile to the Bore Hole.

    Be that as it may, I don’t think Dan H and Norman are trolls, and from their actions, it seems that the mods at SS & RC agree. Norman was ejected for being too high-maintenance. Hopefully he’ll learn to shrink his bandwidth.

  38. 88
    steve says:

    Better check those voting machines for ICHEAT, too

  39. 89
    Phil Hoey says:

    Having done computer modeling in flow dynamics I know you do have to sometimes force the model to behave like the real word – especially when have to satisfy a CPA that the finacal output is accurate. I almost bought into it until I realized ‘oh sugar’ what is today’s date!!! LOL

  40. 90
  41. 91
    Jim Ramsey says:

    It’s important to understand that this ICHEAT code must only be applied an odd number of times, otherwise it is totally ineffective.

  42. 92
    Hengist says:

    I’d like to refer you to Lou Grinzo here :
    “If you’re going to do an AFD joke, make it funny and make it subtle enough to actually fool people.”

    I don’t think RC should attempt April Fools gags. The topic is (a) serious (b) tough enough to understand for the layman . But there’s a (c) Funny doesn’t work in a polarized dialogue, not because it’s not funny, but because it creates a them and us mentality, or the them and us mentality that’s already there becomes more polarized. Or something like that.
    I’ll give you an example from my own experience. To face down unruly litigants the ‘State’ uses humour in the courtrooms. Ive been there, and I cant quite explain why it works. If you don’t get what I’m saying, sorry, were I to explain what Im on about I would go way off topic of RC. Now Im not saying Ive had my SOH lobotomized but put it this way have you ever lied when someone’s asked “D’you get the joke?”


  43. 93
    Jim Newman says:

    Oh my gosh. How embarrassing. And to think I sent this to 4,374,210 people…
    What a great example of obfuscation.
    My friend, Willy Wonka, would truly have appreciated this.
    I look forward to next year’s rant.

  44. 94
    Timothy says:

    Ha! You had me fooled – mainly because this bit is all too true:

    “useful computer code spreads like a virus amongst scientists…nobody ever starts writing scientific code from scratch if colleagues have already solved aspects of the task at hand and the code is free.”

    I’m sure there are a few bugs out there that have spread in this fashion.

  45. 95
    Eli Rabett says:

    John McManus says:
    1 Apr 2012 at 4:59 AM

    A giant , invisible bunny , out for his first spring day, explained this to me. Until then it had me fooled.

    Eli did not! It was a secret.

  46. 96
    Radge Havers says:

    I’m definitely not a computer person, but it seems that there may also an issue in the design tolerances for what look like remnant loops: SEPTIC_FOO and SEPTIC_BAR. Specifically the escape counter using the variable DUM_NUM seems to have been left in a default with lots of 9’s in it. Perhaps if you’re going to leave those functions in there, setting a lower limit for SUM DUM_NUM would shorten runtime and thereby avoid overtaxing the heat sinks… at least on some of your more antiquated systems.

  47. 97
    Ed Beroset says:

    As one of the people involved with the code review on this important topic, I thought it would be useful to give an update. It seems that far too many extant papers and theories rely on this particular variable essentially inverting non-conforming data, so rather than eliminating the variable, it seemed better to rename it to more accurately describe its function. Henceforth, this data-inverting variable shall be called KONTRARIAN. (Patches available on request.)

  48. 98
    George M says:

    i may be an imaginary number but the author of the post isn’t. In any event, joke or not, better vetting of the climate model computer code, numerical estimations, and actual validation would be a good idea all around.

  49. 99
    Mike says:

    If you’re going to print April Fool jokes, please pull them after 1 April. Maybe I’m just a curmudgen, but reading the article on 22 April is no longer funny, just a waste of time.