Guest essay by Johannes Herbst
There is a much discussed graph in the blogosphere from ‘Tamino’ (Grant Foster), which aims to prove that there is no delay or pause or decline in global warming.
He states: Twelve of sixteen were hotter than expected even according to the still-warming prediction, and all sixteen were above the no-warming prediction:
Let’s get a larger picture:
- We see the red HADCRUT4 graph, coming downwards a bit from 1960 to 1975, and inclining steeper beyond 2000, with a slight drop of about the last 10 years.
- We see a blue trend, rising at the alarming rate of 0.4°C within only one decade! This was the time when some scientists started to worry about global warming.
- We see the green trend, used by the blogger Tamino in the first graphic, rising less than 0.1°C per decade.
- Below we see the Sunspot Numbers, pulsing in a frequency of about 11 years. Comparing it with the red temperature graph, we see the same pattern of 11 years pulsing. It shows clear evidence that temperature is linked to the sunspot activity.
Tamino started his trend at high sun activity and it stopped at low activity. Therefore the weak increase during 18 years.
Which leads us to the question: How long should a time be for observing climate change? If we look at the sunspot activity and the clear pattern it produces in the temperature graph, the answer is: 11 years or a multiple of it.
Or we can measure from any point of:
·high sun activity to one of the following
·low sun activity to one of the following
·rising sun activity to one of the following
·declining sun activity to one of the following
to eliminate the pattern of sunspot numbers.
Let’s try it out:
The last point of observation of the trend is between 2003 and 2014, about 2008. But even here we can see the trend has changed.
We do not know about the future. An downward trend seems possible, but a sharp rise is predicted from some others, which would destroy our musings so far.
Just being curious: How would the graph look with satellite data? Let’s check RSS.
Really interesting. The top of both graph appears to be at 2003 or 2004. HADCRUT4 shows a 0.05°C decline, RSS a 0.1°C per decade.
A simple way for smoothing a curve
There is a more simple way for averaging patterns (like the influence of sunspots). I added a 132 months average (11 years). This means at every spot of the graph all neighboring data (5.5 years to the left and 5.5 years to the right) are averaged. This also means that the graph will stop 5.5 years from the beginning or the end. And voila, the curve is the same as with our method in the previous post to measure at the same slope of a pattern.
As I said before the top of the curve is about 2003, and our last point of observation of a 11 years pattern is 2008. From 2008 to 2003 is only 5 years. This downtrend, even averaged, is somehow too short for a long time forecast. But anyway, the sharp acceleration of the the 1975-2000 period has stopped and the warming even halted – for the moment.
Note: I gave the running average graph (pale lilac) an offset of 0.2°C to get it out of the mess of all the trend lines.
If Tamino would have smoothed the 11years sun influence of the temperature graph before plotting the trend like done here at WFT, his green trend would be would be the same incline like the blue 33 year trend:
Even smoother
Having learned how to double and triple smooth a curve, I tried it as well on this graph:
We learned from Judith Curry’s Blog that on the top of a single smoothed curve a trough appears. So the dent at 2004 seems to be the center of the 132 month’s smoothed wave. I double smoothed the curve and reached 2004 as well, now eliminating the dent.
Note: Each smoothing cuts away the end of the graph by half of the smoothing span. So with every smoothing the curve gets shorter. But even the not visible data are already included in the visible curve.
According to the data, after removing all the “noise” (especially the 11 year’s sun activity cycle) 2004 was the very top of the 60 years sine wave and we are progressing downwards now for 10 years.
If you are not aware about the 60 years cycle, I just have used HADCRUT4 and smoothed the 11 years sunspot activity, which influences the temperature in a significant way.
We can clearly see the tops and bottoms of the wave at about 1880, 1910, 1940, 1970, and 2000. If this pattern repeats, the we will have 20 more years going down – more or less steep. About ten years of the 30 year down slope are already gone.
One more pattern
There is also a double bump visible at the downward slopes of about 10/10 years up and down. By looking closer you will see a hunch of it even at the upward slope. If we are now at the beginning of the downward slope – which could last 30 years – we could experience these bumps as well.
Going back further
Unfortunately we have no global temperature records before 1850. But we have one from a single station in Germany. The Hohenpeissenberg in Bavaria, not influenced from ocean winds or towns.
http://commons.wikimedia.org/wiki/File:Temperaturreihe_Hoher_Pei%C3%9Fenberg.PNG
Sure, it’s only one single station, but the measurements were continuously with no pause, and we can get somehow an idea by looking at the whole picture. Not in terms of 100% perfection, but just seeing the trends. The global climate surely had it’s influence here as well.
What we see is a short upward trend of about ten years, a downward slope of 100 years of about 1°C, an upward trend for another 100 years, and about 10 years going slightly down. Looks like an about 200 years wave. We can’t see far at both sides of the curve, but if this Pattern is repeating, this would only mean: We are now on the downward slope. Possibly for the next hundred years, if there is nothing additional at work.
The article of Greg Goodman about mean smoothers can be read here:
Data corruption by running mean ‘smoothers’
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Johannes Herbst writes at: http://klimawandler.blogspot.de/
sorry about the typo’s
here the corrected version
I also have support for a 90-100 year weather cycle, 50 years of warming followed by 50 years of cooling as observed from earth (e.g. flooding of the Nile, Pirana, possibly even other rivers, to be further investigated)
8 years either way from the zero edge is the “pause”, (this is now!) where there appears to be little movement in temperature and weather.
http://blogs.24.com/henryp/2013/04/29/the-climate-is-changing/
All I say to that, is that there is a lag from energy-in to energy out. So it is (mainly) the Gleissberg that determines this apparent weather cycle.
Three decades of cooling is coming up.
Are you (we) ready?
Willis Eschenbach says:
February 10, 2014 at 9:16 pm
“I don’t understand that at all. Tau and omega are presumably constants. If tau * w = 100, then
output = input / 10001”
No, it is a function of w.
Write P as
P = cos(0*t) + 100*cos(w*t)
Plug in the values for w for the respective components. For the first, it is w = 0. The first component is thus 10001 times more prevalent in the output.
This is how a frequency response works. The formula for E is that which is obtained from a simple lag system
tau*xdot = -x + f
The frequency response is
x(jw) = f(jw)/(tau*jw + 1)
P is the magnitude squared of f and E is the magnitude squared of x. Thus, you get
E = P/((tau*w) + 1)
as stated.
This is all very straightforward and elementary systems theory.
I may be confusing things with my shorthand. Those of us in the field take this all for granted, but I should probably spell it out. Expanding the formula
E = cos(0*t)/(1 + 0*w) + 100*cos(w*t)/(1 + 100)
rats…
E = cos(0*t)/(1 + 0*tau) + 100*cos(w*t)/(1 + 100)
bother…
E = cos(0*t)/(1 + 0*tau) + 100*cos(w*t)/(1 + 100^2)
Sorry – juggling a phone call…
E = cos(0*t)/(1 + (0*tau)^2) + 100*cos(w*t)/(1 + 100)
E = cos(0*t)/(1 + (0*tau)^2) + 100*cos(w*t)/(1 + 100^2)
@ur momisugly Bart
are you sure now?
Bart says:
February 11, 2014 at 9:39 am (while correcting his correction to the first incorrection incorrectly)
Don’t bug Bart. He is juggling cats and herding phone calls.
RACookPE1978 says:
February 11, 2014 at 9:57 am
“Don’t bug Bart. He is juggling cats and herding phone calls.”
And missing the ‘edit after you post’ button that my re-reading of what I have just posted to the world has me often looking for!!
I CAN type/spell damn it – it’s just my fingers can’t.
Yes, that is it.
And, I should have written in the original reply the originally given equation
E = P/((tau*w)^2 + 1)
Probably should have broken things up into different variables.
P = cos(0*t) + 100*cos(w1*t)
E = P/(1 + (tau*w)^2) evaluated at the frequencies of the component inputs
= cos(0*t)/(1 + (0*tau)^2) + 100*cos(w1*t)/(1 + (tau*w1)^2)
with tau*w1 = 100
= cos(0*t)/(1 + (0*tau)^2) + 100*cos(w1*t)/(1 + 100^2)
= 1 + 0.01*cos(w1*t)
@Bart
you have all these equations in your head?
I battled with geometry
You have to show me the graphic, the equations tell me nothing…
(I did not even pick up any errors….)
I messed up the example by trying to make it too simple. Gimme a little time, and I’ll fix it.
Bart, after all of your equations, I still have no idea what you’re trying to say. Above all, you haven’t even touched the questions I raised. To remind you, they were:
it’s even more bizarre, because you say that
I guessed that tau was a constant, but you said in response that it was a function of w … but you never said what the function was.
A real-life, actual physical climate related example of what you are trying to say would be of much more use … at present, you’re way off into equationland, which is always fascinating to me, but which may have no application in the world of climate.
So … do you have an actual climate-related example of what you are trying to explain? Because if you don’t have such a real-world example … then why are we discussing this?
Still in mystery,
w.
Let the system response be
tau*xdot = -x + f
Let
f = 1 + 10*sin(w1*t)
The input power is the mean square over a cycle
P = mean( (1 + 14.14*sin(w1*t))^2 ) = 1 + 100
most of which is coming from the sinusoidal term.
The output in the frequency domain is
x(jw) = f(jw)/sqrt(1 + (tau*w)^2)
which, in the steady state becomes in the time domain
x(t) = 1 + (10/sqrt(1 + (tau*w1)^2))*sin(w1*t+phi)
where phi is the phase response term. The output energy stored is the mean square over a cycle
E = mean(x(t)^2) = 1 + 100/(1 + (tau*w1)^2)
If tau*w1 = 100, then
E = 1 + 0.01
and the dominant component is from the small constant forcing term.
Here is a demonstration of the above.
Willis Eschenbach says:
February 11, 2014 at 10:48 am
Bart, after all of your equations, I still have no idea what you’re trying to say.
My take is that cycles don’t matter, it is the long-term background that wins out. Nothing strange about that, and no need to be obscurely fancy about it. For the solar-climate issue this translates into tiny solar cycle effects and an all-important role for large secular changes in the background energy input for which there is but scant evidence.
Willis Eschenbach says:
February 11, 2014 at 10:48 am
“I guessed that tau was a constant, but you said in response that it was a function of w … “
No, I said the transfer function 1/(1 + (tau*w)^2) is a function of w.
The point is this: different components of an input signal have different transmission through a system response.
I gave as an example the system described by the equation
tau*xdot = -x + f
This is a very simple, 1st order differential equation which might be used, e.g., to describe the temperature of a pot of water put on the stove, e.g., as here.
In my example, which is merely for illustration, the period of the sinusoidal forcing was 10 years, and the time constant was 160 years. 2*pi/10 * 160 ~= 100.
The amplitude of the sinusoid was nearly 15X the constant input, and the power (mean square) 100X. Nevertheless, the constant term dominates the output.
In general terms, you can have all kinds of system responses. You can have resonances and zeros, which would effectively zero out a particularly prominent input, while amplifying the input at the resonance. You can have all kinds of things. I have not yet seen an analysis which indicates that we genuinely have a handle on the overall system response.
Leif says
My take is that cycles don’t matter, it is the long-term background that wins out. Nothing strange about that, and no need to be obscurely fancy about it.
Henry says
Here is the thing that I figured out from my own investigations
It is the planets of our solar system that work together throwing the switch in the sun
-God forbid anything if anything happens to any of them –
God has made it so because otherwise there would actually be runaway global warming or runaway global cooling all the time. There had to be a brakes on the whole system, preventing either. There is no manmade global warming. There is only Godmade global warming and – global cooling. We must just be prepared for what is coming.
I am not the only one who figured this out. William Arnold has found exactly the same as I did in 1985.Now I remember that Leif called his paper “junk”, so I am not interested in discussing the paper with him.
What I would be interested in know is: whatever happened to William Arnold?
Does anyone know?
Willis Eschenbach says:
February 11, 2014 at 10:48 am
This is why discussing this stuff with you guys is so damn hard. Yes, Bart, you did say that. I said that tau was presumably a constant. Here’s your reply to my saying that tau was a constant:
Bart says:
February 11, 2014 at 9:25 am
Finally, as I said, after all your equations I still don’t know what you are trying to say. Please point us to some actual climate-related or other natural phenomenon or system that behaves in the manner you are talking about, so we can have a real-life example to discuss.
w.