‘Noise + Trend’?

Judith Curry just recently asked the following question in her blog post “The 50-50 argument”:

“So, how to sort this out and do a more realistic job of detecting climate change and (…) attributing it to natural variability versus anthropogenic forcing? Observationally based methods and simple models have been underutilized in this regard.”

There is a very simple way of doing this that people at large still seem to be absolutely blind to. To echo the words of ‘Statistician to the Stars!’ William M. Briggs: “Just look at the data!” You have to do it in detail. Both temporally and spatially. I have done this already here, here and here + a summary of the first three here. In this post I plan to highlight even more clearly the difference between what an anthropogenic (‘CO2 forcing’) signal would and should look like and a signal pointing to natural processes.

Curry has many sensible points. She says among other things:

“Because historical records aren’t long enough and paleo reconstructions are not reliable, the climate models ‘detect’ AGW by comparing natural forcing simulations with anthropogenically forced simulations. When the spectra of the variability of the unforced simulations is compared with the observed spectra of variability, the AR4 simulations show insufficient variability at 40-100 yrs, whereas AR5 simulations show reasonable variability. The IPCC then regards the divergence between unforced and anthropogenically forced simulations after ~1980 as the heart of the their detection and attribution argument. (…)

The glaring flaw in their logic is this.  If you are trying to attribute warming over a short period, e.g. since 1980, detection requires that you explicitly consider the phasing of multidecadal natural internal variability during that period (e.g. AMO, PDO), not just the spectra over a long time period. Attribution arguments of late 20th century warming have failed to pass the detection threshold which requires accounting for the phasing of the AMO and PDO. It is typically argued that these oscillations go up and down, in net they are a wash. Maybe, but they are NOT a wash when you are considering a period of the order, or shorter than, the multidecadal time scales associated with these oscillations.

Further, in the presence of multidecadal oscillations with a nominal 60-80 yr time scale, convincing attribution requires that you can attribute the variability for more than one 60-80 yr period, preferably back to the mid 19th century. Not being able to address the attribution of change in the early 20th century to my mind precludes any highly confident attribution of change in the late 20th century.


The IPCC purports to have a highly confident explanation for the warming since 1950, but it was only during the period 1976-2000 when the global surface temperatures actually increased.

The absence of convincing attribution of periods other than 1976-present to anthropogenic forcing leaves natural climate variability as the cause – some combination of solar (including solar indirect effects), uncertain volcanic forcing, natural internal (intrinsic variability) and possible unknown unknowns.

A key issue in attribution studies is to provide an answer to the question: When did anthropogenic global warming begin? As per the IPCC’s own analyses, significant warming didn’t begin until 1950. Just the Facts has a good post on this When did anthropogenic global warming begin?

(My emphasis.)

So how to investigate a bit further whether there is any merit to IPCC’s claim that the slow, but steady rise in atmospheric CO2 is somehow responsible for the overall rise in global temperatures between the beginning of the 50s and today?

We hear all the time from the warmist camp that “There is no reason to expect a linear (gradual, steady) rise in temperatures just because the ‘radiative forcing’ from CO2 increases that way. There could easily be ‘pauses’ in between, even dips, as long as the long term is up.”

***Yes, but if so, this would NOT be because of any intrinsic variability in the ‘increased radiative forcing’ mechanism itself.***

The ‘CO2 forcing’ signal taken in isolation would and should strictly be that of a gradual and steady (near-linear) rise in temperatures. There is nothing in the postulated ‘radiative forcing’ process itself that could account for a stepwise increase in temperatures, that is, a progression characterised by sudden upwards shifts separated by relatively flat decadal plateaus.

No, if there were to be any pauses and dips along the long-term way up, they would have to be caused by natural (interannual to decadal) variation only – what the ‘climate establishment’ calls ‘noise’.

So the story goes: The ‘background forcing trend’ rises in near linear fashion, but there is considerable natural noise – mostly from the ENSO process – superimposed on it, so the temperature evolution might look as if it moves along in fits. In reality it doesn’t really. The natural noise simply acts to obscure the ‘real’, steady progression. The large interannual swings up and down confuse our eyes into thinking that there are in fact steps. Even at decadal timescales the natural noise can effectively ‘hide the (relentless) incline’. If a certain period for instance starts out with a lot of El Niños or at least warmish ENSO conditions and ends with a predominance of La Niñas or coolish ENSO conditions, then this will make it seem there is no warming even over a fair amount of years. That doesn’t mean the ‘background forcing trend’ isn’t still there. It is just ‘lost in the noise’ for a while. But let more time pass and it will reappear before your eyes. Just zoom out far enough. Eventually it will override the noise. Allow 15-20-30 years and you’ll see.

In other words, by the reasoning of ‘Climate ScienceTM’: Just draw a sufficiently long linear trend line across the data and that’s your ‘background forcing signal’ right there. So even if there is no actual global warming in the data between 1951 and 1976/77 and also none between 2001/02 and today, if you simply stretch the trend line all the way between the end points, you will see that global warming actually did go on all that time from 1951 to 2014 either way.

The magic of linear trend lines! You don’t really need the data behind …

The problem with this ad hoc rescue hypothesis – “The ‘natural noise’ stole my linear rise!” – is that it’s directly testable.

We have data. From the real world.

We already know that those major swings up and down along the time series depicting global temperature anomalies are the ENSO signal. We see this very easily when juxtaposing the global curve with the (properly downscaled) NINO3.4 SSTa curve:

N vs. gl

Figure 1.

The only real difference of any significance here between the global curve and the NINO3.4 curve seems to be the overall ‘trend’, the former very clearly rising up above the latter over the time span of 44+ years included in the graph.

No one denies that ENSO is our planet’s main interannual ‘natural noise maker’. It is not a controversial point to make. The ENSO process is so powerful that it is able to override and/or drive all other regional climate signals on Earth. We see this especially at the larger events (the big swings), not necessarily as clearly at other times. We see how global temps lag NINO3.4 during major El Niños and La Niñas, the signal quite evidently being propagated globally from the Pacific.

(The only natural factors to make its definitive mark on global temperatures other than ENSO are volcanic eruptions of a certain magnitude. Since 1970 there were two main ones: El Chichón in 1982 and Pinatubo in 1991.)

Is this (Figure 1) simply the ‘background forcing trend’ appearing globally on top of the ‘noise’ as you zoom out? ENSO handles the short-term variations, CO2 the mid to long-term rise? Is the global temperature evolution explained satisfactorily with the ‘Trend+Noise’ ad hoc hypothesis? The IPCC and all its followers seem to think so.

Let’s have a look.

I have previously shown how – if you simply look at the data – the global curve in Figure 1 above only lifts permanently from the NINO curve at three specific instances: in 1979, 1988 and 1998. If it weren’t for these three distinct and sudden global upward shifts, the fit between the two curves would be near perfect, meaning, there is no hint of the global curve diverging gradually upward from the NINO curve at any time between 1970 and 2014. There are only the three abrupt and significant steps up:

Warming stepsFigure 2.

Watch what happens if I simply adjust the red NINO3.4 curve here up by 0.14 degrees in July 1979, a further 0.15 degrees up in January 1988 and finally an additional 0.15 degrees up in January 1998 (the three black arrows in Figure 3):

NINO w 3adj

Figure 3.

Note that the NINO3.4 curve is lagged (by 3 months) in Figure 3, but not in Figure 2.

So, could this striking repeating pattern of plateau>step>plateau>step still be a mere coincidence? ‘Normal’ variation around a linearly rising trend? Could it be that our eyes are simply fooling us into thinking that those steps and those plateaus are somehow ‘real’ (and as such being naturally process-related)?

Or is it just something in the way the NINO3.4 curve progresses sequentially with time that tricks us?

Here it is with a gradual (linear) upward trend imposed on it, as if influenced by a steadily increasing ‘radiative forcing’:

NINO w trend

Figure 4.

Doesn’t that look like a remarkably steplike rise?

Indeed it does!

So is this all there is to it? Natural variation in the form of ‘ENSO’ + ‘linear background forcing trend’ giving a plateau/step progression in global temps?

If we were to end our investigation here, that’s exactly what we might be left with thinking. But the graph in Figure 4 isn’t the end of the story.

First of all, we already know that all the steps are directly associated with Pacific climate regime shifts, and that they also came as a result of specific ocean/atmosphere processes in specific regions of the global ocean. So they are clearly not just regular NINO stages on a continually and steadily evolving linear rise in background ‘forcing’. We see how total East Pacific temps jumped up relative to the equatorial belt in 1978/79. We see how the deep NINO3.4 La Niña lead signals of 1988/89 and 1998/99 were significantly defied globally, a consequence of massive (abnormal) warming in the West Pacific. Extraordinary events took place in 1979, 1988 and 1998. This we know. Because it’s in the data.

Secondly, simply compare the artificially trended NINO3.4 in Figure 4 with the point-adjusted NINO3.4 in Figure 3:

NINO w 3adj vs. NINO trended

Figure 5.

We see a very clear pattern at display here. The two curves connect at the green ellipses. They start out together in 1970 and reconnect three times along the way: in 1979, in 1988 and in 1998. That’s the upward adjusted steps in the real (red) NINO3.4 (Figure 3). Between the hinge points, though, the two curves evidently spend all their time drifting apart, and not just randomly, but as you can see, in a gradually widening manner, a pattern repeating itself after each hinge point. After the final reconnection, there are no more upward steps in the red (‘normal’) NINO3.4 curve, and so the black (‘trended’) curve just seems to sail away indefinitely into the air. That is what the global temperature evolution post 1998 should’ve looked like if there were any merit to the AGW ‘Noise+Trend’ hypothesis.

But how – in the real world – do global temps progress post 1998? We already know from Figure 3. They follow the normal, untrended NINO3.4. That’s your ‘pause’ explained right there.

To rub it in even deeper, we see the exact same deviation pattern between the trended NINO3.4 of Figure 4 and global temps as between the former and the point-adjusted NINO3.4 of Figure 5:

Gl vs. NINO w trend

Figure 6.

The black ‘Noise+Trend’ curve basically trails above the global curve most of the time, except at and just after the connecting points (red ellipses), where the global curve shifts abruptly up to join the gradually ascending trended NINO curve.

What we realise is how global temps follow the real NINO3.4, not the NINO3.4 (the ‘Noise’) with an imposed linear ‘forcing’ (the ‘Trend’) on top, before, between and after those three global steps. The trended curve sort of seems to be consistent with the general global warming tendency up until around 2000. But then the game of catch-up appears to have been finally ‘discontinued’.

Here’s a detailed look at the different segments of the full time series. The pattern we pointed to manifests itself pretty nicely:


Figure 7. 1970-mid 1979. Yellow curve: HadCRUt3gl; red curve: real NINO3.4; black curve: trended NINO3.4. The three curves start out together in 1970 (green ellipse). (Note that the NINO curves are lagged by three months.) But as the trended NINO sports a distinct and steady upward tilt, the other two stick together all the way, fluctuating negligibly up and down around each other.


Figure 8. Same thing. The trended NINO curve (black) reconnects with the raised global curve (yellow) in 1979 (first upward shift, first green ellipse) after having drifted away from it since 1970, but after that starts drifting again, the global once more rather tracking the real NINO3.4 (red), this time all the way down to 1988, where the second global upward shift takes place (second green ellipse). The global curve then makes another jump up to join the steadily slanting trended NINO-curve.


Figure 9. Not much new. The global and the real NINO3.4 curve track each other impressively (only the Pinatubo impact on the former disrupts the nice and neat covariation) down to 1998, with the third global upward shift (second green ellipse), while the trended NINO curve drifts steadily away from both, until it comes together one last time with the global curve – old habits die hard – just after the 1997/98 El Niño


Figure 10. Final section. The global curve is now raised far above the real NINO3.4 curve, but still it is pretty evident that the two follow each other closely – no sign of any gradual divergence between them. What about the trended NINO? It has yet to find a fourth hinge point with the global and by now (2014) it runs about 0.25 degrees too hot. That’s in 15-16 years. The imposed trend is exactly the same here as it was from 1970 to 1998. Only, we have yet to see another global step up since 1998.

Notice how the global curve tends to stick close to the general course of the real NINO3.4 across each segment between the jumps, while the trended NINO3.4 consistently gradually veers upwards and away from the global, until the next hinge point. Once again: This is how global temperatures should have increased if they really followed the trajectory of the hypothesised ‘Noise+Trend’ progression of ‘Climate ScienceTM‘. They clearly don’t. There seems to be no connection whatsoever to a linear ‘background forcing trend’.

All four segments in succession:


Figure 11. 

Conclusion: There is absolutely no reason to buy into the warmist ‘Noise (‘natural variation’) + Trend (‘CO2 radiative forcing’)’ argument …

First the ‘climate establishment’ will have to explain how their hypothesised ‘radiative forcing’ mechanism appears to do absolutely nothing on decadal time scales (10 years, 15 years, 20-25 years) – no gradual temperature rise to be discerned – before it suddenly, in distinct pulses, seems to ‘super-force’ the global surface into major warming within barely a year.

One final thought. One final attempt at an AGW rescue operation.

Might it be possible that the assumed steadily increasing ‘radiative forcing’ from more CO2 in the atmosphere, rather than warming the surface, is somehow building gradually in the depths of the oceans during the ‘plateau stages’ of global surface temperature evolution over the last 60 years, only to be released abruptly and massively through particular ocean processes during the ‘step stages’?

It sounds pretty far-fetched, no question. Especially when taking into account how this peculiar mechanism would then for some reason seem to perfectly cancel each and every time the surface warming that should’ve been over decadal time scales, that is, between all the sudden jumps, to let global temps track NINO3.4 without any visible mean-level deviation.

Still, this new and added epicycle (after the ‘Noise+Trend’ one failed) is actually the only road left that might lead to salvation for the CO2 AGW hypothesis.

Can we find any clear support for such an idea in available empirical observations from the real Earth system? We need to go to the global OHC (‘Ocean Heat Content’) data.

OHC, then, is the last stand of the AGW hypothesis against final real-world falsification. The last straw to grasp at, so to say.

We’ll look into this whole issue in not too long … Nothing will change, though. Things will become even clearer. It’s all natural.

Hint: ENSO once again.

Update: How the IPCC pictures the ‘forced’ temperature rise.

IPCC’s CMIP5 model mean vs. global temps (HadCRUt3):

Gl vs. CMIP5 mean

A relatively nice general fit up until 2000. In the model mean it’s all about increasing ‘radiative forcing’ from human emissions (the rising trend) + ‘radiative forcing’ from stratospheric volcanic eruptions (El Chichón and Pinatubo) (the two major dips). It does not take into account ‘natural noise’ since the assumption is that this is not important beyond interannual to decadal time scales …

The CMIP5 model mean vs. the trended NINO3.4 (HadISST1):

Nino trend vs. CMIP5 mean

Much the same up until 2000-2002. After that even the trended NINO seems unable to keep up with the ‘forced’ trend of the IPCC’s models.

2 comments on “‘Noise + Trend’?

  1. GWN says:

    Hello Kristian.

    If my reading of your belief that the science of global climate has been subjected to political interference, then we complete agree in that regard. Government money feeds the global warming industry.
    Today, the first of September, 2015, I witnessed a large amount of CO2 plus other elements arraigned in a complicated form referred to as President Abama declaring that CO2 global warming has reached the stage where it is vital that further drastic industrial measures must be urgently taken to restrict the production of CO2. A coded statement that indicates that those who may oppose his desire are environment vandals, as are any future government attempting to dismantle any curbs he may be able to impose on American industry.

    I acknowledge the fantastic advances in science that has mainly resulted from knowledge derived via experiments, followed by correct theoretical interpretation of their results.
    Even so, science has a propensity to attempt to make sense of a vexing problem by referring to spin or accepting a concept that contains a half truth such as the theory of GR. Yes, the physical reality that in turn provides reality to that we call space, is influenced by the presence of mass.. Yes, the propagation of radiation is influenced by the presence of that we call matter. Yes, gravitation is not a force, however gravity is a force. No, gravitation is not an illusion because it is a physical reality that results from the constant interference to the gravity requirements of interacting massive bodies. No, constantly reoccurring gravitational induced waves do not physically exist. My completely ignored work on the fundamental nature of matter and associated mysteries was available in excess of 40 years ago and explained and demanded that gravitational induced waves had no possibility of physical existence.

    The Gravitational Thermodynamic Effect that you had difficulty understanding is explained and required by my work on gravity and gravitation. I find that the GTE is constantly involved with physical explanations such as the return to an outside receiver of a relative large amount of heat energy in a change of state of steam at 100 degree c to water at 100 degree c, or heat resulting from the combining of atoms, and so on up to the conditions within the continuing enabler of life we call the Sun.

    It is remarkable that physicists require the expenditure of energy to achieve the blinking of an eye lid, but appear to ignore the fact that there is a price in energy to be paid when gravitation is acting between interacting bodies of matter. In that regard, the GTE of the four great planets with regards to their constant change of position relative to each-other and to the Sun, would be the dominant precursor of weather cycles on our planet.
    It appears that the belief of leaders in the scientific community is best adhered to to enable a comfortable academic career. A Climatologist working in America on invitation from an Australian University, came to Australia and brought his P hd student with him. The university eventually financed his lecture tour to Europe and whilst he was in Europe, they cancelled all his airline tickets and funds. It appeared that his lectures were about his research findings that indicated warming preceded by several months the CO2 increase in the atmosphere. Thereby possibly indicating that warming was causing the unlocking of CO2 from natural sources.

    I wish you success with your attempt to rationalise the science of global warming, and I in turn am awaiting the results of the discoveries of ESA spacecraft Rosetta with regards to the GTE.

  2. GWN says:

    With regards to the first five lines in the above post, please read as: Today, the first of September, 2015, I witnessed a large amount of carbon derived from and sustained by CO2,

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