Synopsis of Global Warming as a System Response Theory Problem
The weather noise problem—how much warming?
Changes in weather can cause temperature changes from day to day by as much as 20°C. The coldest day in mid-summer can be colder than the warmest day in mid-winter. That is weather. Yet we all know the difference between summer and winter, and that summer days typically are warmer than winter days. That is our experience of climate.
It is said that the climate has warmed by a degree or so in the last 200 years. That is a very small number to extract from the day-to-day noise which can be an order of magnitude larger. How can one extract that small secular temperature trend reliably? Even thermometer measurements at a single location are subject to perturbation by non-global-climate factors such as growing urbanisation or even the growth or removal of a stand of trees.
The warming attribution noise problem—is it CO2?
Many people believe that CO2, added to the atmosphere by burning fossil fuels since the industrial revolution, has increased the effective thermal resistivity between the earth’s surface and outer-space—the “greenhouse warming”—forcing a temperature rise to compensate. But how does one disentangle this “greenhouse” hypothesis from other possible contributing causes such as land use changes or changes in insolation? True ab initio modelling of the climate system is impractical due to the huge ranges of time and space scales that are important. How does one extract an attribution signal from the parametric noise?
Signal processing with a carrier wave
Ever since the invention of the magnetic tape-recorder signal engineers have known that it is much easier to extract a wanted signal from the noise, if the signal modulates a known high-frequency carrier wave.
As it happens, the seasonal shifts caused by the tilt of the earth’s axis and the earth’s orbit around the sun have a known period of one year, and the sun’s stimulation at any given location has a known phase. The climate system processes this “carrier” signal input and produces a temperature output that can be measured. For example, daily temperature measurements have been recorded at a location in Central England for more than two centuries. The time series is available from BADC in the UK.
The climate signal
So what signal can we extract with period of one year? Figure 1 shows a cosine of period 1-year fitted to the 4-year block 1772 to 1776. The blue cosine curve is the climate signal while the black curve is the daily weather noise. Unsurprisingly, the coldest time of year, according to climate, occurs in the last half of January. However, the day-to-day weather can vary greatly. For example, late January 1773 had an unseasonably warm spell with mean daily temperatures as high as 9°C, despite this being the latter part of the “little ice age”.
Figure 1: Least Squares fit of cosine with a period of one year to daily mean temperature data in a block of four-years
Seasonal lag and climate change
I have always been fascinated by the fact that the shortest day of the year is around 20th December, while the coldest time is typically towards the end of January. The difference is the seasonal lag. In the case of 1772 to 1776 that coldest date (according to climate) was 19.5 days into January. That represents a lag of about 30 days which is close to π/6 radians.
Why do the seasons lag behind the cycle of the length of daylight? The short answer is that the oceans store the heat. It is analogous to an electrical RC filter (see Figure 2) where C is the ocean’s ability to store heat, and R is the effective resistance to heat escaping into space. The larger R or C, the longer the phase lag.
Now comes the magic. The CO2 “greenhouse” hypothesis is that adding CO2 increases the effective thermal resistance, R. In which case, the seasonal lag ought to increase along with the CO2. The CR-filter theory also predicts that the difference between summer and winter should also increase, if thermal resistance is the sole cause of the increase in lag.
How seasonal lag changed between 1772 and 2005 in Central England
The daily mean temperature time series for Central England was divided into blocks of 4 years duration. A cosine climate curve, with period one year, was fitted to each block (as in Figure 1, for example). The parameters for each block are Temperature Amplitude (i.e half the summer to winter temperature change), the temperature phase (expressed as the date in January of minimum climate temperature), and the Mean Temperature for the block. These three parameters have been plotted on a graph whose abscissa covers the years 1772 to 2005.
There are considerable fluctuations in the parameters from 4-year block to 4-year block. I have therefore provided an “eye-guide” to the trends in the form of cubic curves least-squares fitted to each parameter series. The results are summarised in Figure 3.
Figure 3: Phase lag (date in January), temperature amplitude, and mean temperature of the 4-year blocks plotted for years 1772 to 2005, together with cubic trend lines fitted to the data.
Discussion of trends in the Central England temperature
First consider the seasonal phase lag. The lag can vary quite wildly in a short interval. Nevertheless, there seems to be a secular trend for the coldest period, from around 20 January in 1800 to around 25 January in 2005.
Note that while I have been expressing the phase in terms of the coldest period, the fit to the data is going to be dominated by what happens in spring and autumn when the temperature is changing most rapidly from week to week. Thus while the phase fit implies a climate coldest around 20 January, there could easily be an “unseasonal” warm spell then (as happened in 1773—see Figure 1).
Depth of cold at 20 January 1800 is a 31 day lag (approximately π/6 radians) from 20 December 1799 (shortest day). 200 years later the lag seems to have increased to about 36 days (approximately π/5 radians) by 2004. That is an apparent increase lag of about 5 days (approximately π/30 radians) in 200 years.
If the data can be modelled by Figure 2, then the phase lag trend is consistent with a combination of an increasing “insulation” effect, R, and the storage effect, C.
Can the phase lag be attributed solely to an increase in insulation?
Let us examine the hypothesis that the phase lag is due entirely to increasing insulation, and that the input flux amplitude, J, remained constant.
Between 1772 and about 1870, temperature amplitude between summer and winter had a declining trend from about 7.2 °C to about 6.4 °C. It was more-or-less constant after 1870. The all-CO2 hypothesis would predict increasing temperature amplitude. In fact, the decline in the early period cannot be matched assuming constant input flux, J.
What is surprising is that matching the temperature amplitude history requires J to decline between 1772 and 1870.
The contribution of changes in R to the change in seasonal lag is about 30%, while storage, C, must contribute the rest. One can speculate that the increase in C is due to an increase in the amount of ice-free sea during the summer.
Inferring other global warming parameters and sanity check 1870–2005.
It is also possible to estimate the maximum contribution R can make to warming and the maximum sensitivity of the temperature to CO2 (2°C per doubling). However you will have to look at the mathematical reasoning in the full exposition: “Global Warming as a System Response Theory Problem” .
Robustness of the system response theory approach to limited geographical data
As a teenager I was an electronics hobbyist. I would test an amplifier, say, by injecting a periodic signal at the input and then sample the response of the system at various points which did not necessarily have to be in the main signal path. Often one could detect signal, even on the DC supply rails (which is one reason why large capacitors across the supply were needed to prevent feedback oscillations). I mention this to highlight the fact that monitoring just a single point of a responsive system can provide useful information about the whole system.
Consider one of the pitfalls of the traditional approach which requires one to have good representation of the atmospheric temperature field over the whole globe and over extended periods of time. Yet the sampling is heavily biassed to densely populated areas, only a few places have time series going back more than a few decades. Even in those places that have extended time series, there is potential for inconsistencies between measurements taken decades apart (for example the growth of a stand of trees near the measuring station).
By contrast, a time series can yield seasonal phase data which is impervious to the inconsistencies in temperature base line across the decades. Further, even a single location may be representative a wide geographical area with varying terrain.
Concluding remarks
This is proof of concept discussion, using a single location’s dataset, with an unsophisticated analysis. The inferences, such as maximum possible temperature sensitivity to CO2 are far from rigorous, but indicate some of the power of system response theory to tease out valuable climate physics from even limited observations.
Any serious attempt to model the climate should make use of as many features of the data as possible so as to reduce the danger of undetected hidden assumptions. The systems response approach, and seasonal lag in particular, is a promising tool in this regard. I note that some workers are beginning to use this approach in meteorology[1]. It does not seem too much of a leap to extend systems response theory to the global climate system.
Link to full manuscript Global Warming as a System Response Theory Problem
Biosketch: Dr Barnett received a PhD in Physics in 1995 from the University of Texas at Austin. His thesis: “Lyapunov Exponents of Many-Body Systems”. He is presently and independent consultant based in the UK, and an Affiliate of the Institute for Advanced Physics. His areas of research include: The emergence of entropy and the arrow of time, The structure of water, System response theory, Varying ways to idealise useful independent subsystems.
[1]. Milan Palusˇ, Dagmar Novotna ́ & Petr Tichavsky ́, GEOPHYSICAL RESEARCH LETTERS, 32, L12805 (2005) “Shifts of seasons at the European mid-latitudes: Natural fluctuations correlated with the North Atlantic Oscillation“
“That represents a lag of about 30 days which is close to radians.”
The value is missing.
30 days is about pi/6 radians or 30 degrees.
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Interesting post. However, that is not a proper way to draw a RC filter.
A CMOS switch in the ‘on’ position has a filter characteristic that looks exactly like that.
David,
I like your approach and would encourage you to pursue this line of inquiry and refine it.
David,
I’d like to suggest that instead of using a series of blocks that are contiguous, that you consider ‘walking’ the blocks in annual increments, as with a moving average.
When applying the Fourier transform to data that is not exactly repetitive and which has multiple wavelengths that do not exactly match the sampling period the best approach is to use a sample set of reasonable length and then to make use of the overlap and save or overlap and add technique.
I agree. What I did was “quick and dirty”. Walking the blocks would be better. One could also experiment with different kinds of windowing (such as gaussians instead of a stepped hat).
Nice to see some original thinking and analysis.
It all depends on how you define “climate”. I expect that the “seasonal lag” is mostly caused by a heat capacity of the atmosphere and the Earth’s surface, and at the first glance it is not obvious what it has to do with climate.
Curious George:
“It all depends on how you define “climate”. I expect that the “seasonal lag” is mostly caused by a heat capacity of the atmosphere and the Earth’s surface, and at the first glance it is not obvious what it has to do with climate.”
“Climate” is the prevalent condition including seasonal variations. The biggest climate heat storage system is the ocean. The time constant of the lag also depends on how fast the stored heat can escape into space.
I agree that seasonal lag is overlooked in the climate debate, because it is not immediately obvious. However it should not be ignored, because very fundamental laws of system response connect it intimately with the CO2 warming hypothesis.
“Climate” is the prevalent condition including seasonal variations.
I find this “definition” foggy and unsatisfactory. Perhaps you could formulate it more mathematically?
So, you can’t dangle an official thermometer in the exhaust of a jet that’s warming up on the tarmac at an airport in Paris, France and draw conclusions and draw conclusions about global warming in Europe?
David M. Barnett:
“Depth of cold at 20 January 1800 is a 31 day lag (approximately π/6 radians) from 20 December 1799 (shortest day). 200 years later the lag seems to have increased to about 36 days (approximately π/5 radians) by 2004. That is an apparent increase lag of about 5 days (approximately π/30 radians) in 200 years.”
and
“The CR-filter theory also predicts that the difference between summer and winter should also increase, if thermal resistance is the sole cause of the increase in lag.”
–
****
The difference between summer and winter should have increased in 200 years, because an apparent increase lag of about 5 days during those 200 years clearly indicates that it should have happened.
–
***
https://www.cristos-vournas.com
Christos Vournas: “The difference between summer and winter should have increased in 200 years, because an apparent increase lag of about 5 days during those 200 years clearly indicates that it should have happened.”
You have seen the point. Since the temperature amplitude did not increase (actually decreased during the first 50 years and has been approximately constant since), it falsifies the hypothesis that the change in lag is entirely due to an increase in effective thermal resistance.
It should decrease because ln nature of the temperature response to CO2. Also the seasonality of CO2, especially at the near surface.
It is also possible to extract the base frequencies out of very noisy signals (like those we encounter with temperatures) by repeated successive Fourier Analyses and decimations
Thank you, David. Very interesting. I agree with Clyde Spencer’s comments above.
What are the details of your upper bound on sensitivity? Can you derive this from such a simple theory?
Thanks.
dpy6629:
“What are the details of your upper bound on sensitivity? Can you derive this from such a simple theory?”
There is a link to the full exposition just above my bio-sketch.
In principle the method should work. My proof of principle was for a time series from a single locale. It needs to be applied to many more places.
David, I’d be very cautious about drawing any conclusions from the CET data. The problem is that there have been no less than seventeen changes in the stations which are included in the average.
https://wattsupwiththat.com/wp-content/uploads/2020/07/cet-spliced.png
As a result, I don’t think you can use it in the manner employed above.
Doesn’t mean your theory is wrong. Just means that the CET isn’t suitable data to test it on.
Best regards,
w.
Willis Eschenbach:
“David, I’d be very cautious about drawing any conclusions from the CET data. The problem is that there have been no less than seventeen changes in the stations which are included in the average.”
Willis, the beauty of the method is that it is robust against changes in the stations within a geographical region. The seasonal lag can be extracted from a single year’s data if need be. Unlike the raw temperature data, the seasonal lag in any year will not vary much within a region. Essentially it solves the problem of measurement consistency across decades.
Thanks, David. I have no idea what data you’ve used to establish that the method “is robust against changes in the stations within a geographical region”. Link or description? Thanks.
In any case, see my analysis of the Stockholm data below.
Best regards,
w.
Surely the stations didn’t change every year. He is saying he can extract the signal from a single year’s data. Unless the stations ARE changing on a sub-year basis every year, and his method works in general, it would be robust to station changes.
I believe what he is saying is that seasonal lag is essentially constant within a region. So movement within that region does not impact the method.
OK, I picked another dataset to use to test your theory. This is the daily Stockholm mean temperature dataset, WMO station 2485, available from KNMI.
http://climexp.knmi.nl/data/vgdcnSWM00002485.dat
According to the daily data, it’s been warming at about 0.2°C per decade. As we’d expect from its northern location, that’s a bit more than the rate for the warming of the globe
I used a double Gaussian smooth of 47 days FWHM to establish the peak temperature date for each year. Then I divided by days per year to remove the leap year effects, and plotted it up. Here’s the result:
https://wattsupwiththat.com/wp-content/uploads/2023/02/stockholm-year-fraction-peak-temperature.png
As you can see … I do NOT find any change in the lag between peak insolation and peak temperature.
Go figure …
w.
Here’s another dataset, Armagh Observatory daily temps 1844 – 2004. Unlike the Stockholm data, it shows a net change in 160 years of +3.2 days later for peak annual temps.
https://wattsupwiththat.com/wp-content/uploads/2023/02/armagh-year-fraction-peak-temperature.png
w.
Willis Eschenbach: “OK, I picked another dataset to use to test your theory…I used a double Gaussian smooth of 47 days FWHM to establish the peak temperature date for each year.”
That will not pick out the climate signal. It is important to pick out the Fourier component, which you could do as a least squares fit of
T_f * Cos[f * t – phi_f) + T_0
Where “f” is fixed at 1/(365.2425 days) and the fit parameters are T_0, T_f and phi_f.
The Annual Mean temperature, T_0, is ye old unreliable that everyone else is trying to use.
The parameters of interest are the phase phi_f, and temperature seasonal swing amplitude, T_f.
I don’t expect the absolute value of the phase in Stockholm to be the same as Central England, but the trends should track climate drift and act as a similar test of the CO2 hypothesis.
David M Barnett | February 28, 2023 at 6:24 am | Reply
David said:
Thanks, David.
I don’t understand why you think my method will not work. The lag is different every year. I am measuring that exact lag, and looking to see what the long-term change in that exact lag is. That’s what my graph shows.
Your method uses a cosine fit to four-year blocks. Yes, that will work, but you’re losing detail because you’re using the averages of four-year chunks of data rather than figuring out the lag for each individual year as I did.
My method will absolutely pick out the climate signal. To demonstrate this, I’ve used it on the CET data. Note that I get the same lag increase that you got, of about 5 days greater lag in the date of minimum temps since 1772.
https://wattsupwiththat.com/wp-content/uploads/2023/02/CET-year-fraction-minimum-temperature.png
Your method is most interesting, and well worth pursuing.
w.
Willis, Inexplicably there is no reply link to your last comment. You said: “I don’t understand why you think my method will not work. The lag is different every year.”
Your 47-day gaussian may be able to pick out the a smoothed peak, but it will lack information from around the equinoxes which is where the phase is really determined. You will also be picking up potentially cofounding information from higher harmonics (but your own CET test indicates this might not be much problem).
The other thing that may not be as accurate is the summer-winter swing amplitude that is part of the theory.
You are right about using 1-year blocks. I only used 4-years so as not to have to deal with the leap-year issue.
P.S. A full treatment would use Fourier information from a full transform of the data in, say, 50-year blocks. This could then pick up the decadal oscillations and also allow one to use a Hilbert transform on the phase to pick out the amplitude term and this separate it from the flux J.
Thanks, David. A few notes. Let me give you a graphic example of my method.
https://wattsupwiththat.com/wp-content/uploads/2023/02/CET-short-temperature-gauss.png
As you can see, the black/yellow gaussian line tracks the CET. The use of the Gaussian smooth allows me to determine the actual day of the peak and trough.
I was using the max temperature lag for Stockholm and Armagh, and noticed before my post on the CET that you’re using the minimum.
One of the minor problems with your method is that a few years have the coldest time in December. If that happens to be the case at a break in your four-year chunks it would slightly disturb the result.
One thing I haven’t looked at is whether the lag in the warmest points is equal to the lag in the coldest points. I also haven’t looked at whether the increase in the lags in the warm and cold times are equal or not.
Finally, I’m still considering the math of the idea of what is basically a low-pass RC circuit. There’s a good exposition of the math involved at the site below:
https://www.redcrab-software.com/en/Calculator/Electrics/RC-Low-Pass-Filter
Seems to me that, IF the earth is working like an RC circuit, there might be more to be learned from the math of the phase angle of the lag and the changes of the lag.
Best regards, thanks for the insights,
w.
Willis Eschenbach: “Seems to me that, IF the earth is working like an RC circuit, there might be more to be learned from the math of the phase angle of the lag and the changes of the lag.”
Indeed.
However, one should not take the RC circuit too literally. The values for R and C are “effective values” at the measured frequency. The underlying climate system is much more complicated with time delays and “resisters” and “capacitors” etc. all over the place.
The output signal, in the time domain, is a convolution of the input signal and the response the system would have to a delta-function impulse. In the frequency domain, a time-convolution of functions becomes a product of the transformed functions.
Part of the magic is that one can never-the-less infer information at one frequency from information at other frequencies, because continuity, reality and causality constrain how the response function can vary from frequency to frequency. So while the RC analogy should be used with caution, it retains considerable conceptual power.
Willis, yours is look ay max temps. Davis is looking at min.
Really need to be looking at both.
We treat CO2 as instantaneously well mixed. Reality is it remains near the surface a bit. Most of it is consumed by the biosphere right away, but only part of the year. Most emissions happen in the winter when they aren’t consumed by plants. And CO2 at the surface probably matters more than the mixed concentration in the atmosphere above. Knowing where CO2 is in the atmosphere would give us a better idea of climate sensitivity.
I suspect that a big part of why the temperature increases more on land and in the winter, besides the obvious, is the CO2 concentration at the surface, especially in winter, is much higher than the mixed part of the atmosphere.
https://mobile.twitter.com/aaronshem/status/1625897789841453067
The winter/summer amplitude should decrease because ln nature of the temperature response to CO2. Also the seasonality of CO2, especially at the near surface.The summer lag should increase less than winter.
Yes, one needs to look at both Tmax and Tmin because they behave differently and the relationship changes over time. See Fig. 1 at http://wattsupwiththat.com/2015/08/11/an-analysis-of-best-data-for-the-question-is-earth-warming-or-cooling/
aaron | March 1, 2023 at 11:32 am |
I looked at maxes for Stockholm and Armagh. And for the CET I noticed that he was doing mins, so I did mins.
I also commented that we should be looking at both.
In fact, he’s not looking at mins. It is a weakness of his method which my method doesn’t share. He’s fitting a sine wave to a four year section, which will give some kind of average of the lags of the maxes and the mins.
You continue with this quote:
Hmmm … kinda true. Other than down in the turbulent layer at the surface, CO2 is better mixed that the other GHGs. Here’s Wijngaarten and Happer on the question.
https://wattsupwiththat.com/wp-content/uploads/2023/03/wijngaarten-happer-co2-by-elevation.png
Also, I’m not sure that emissions happen in the winter. CO2 levels are higher in the winter than the summer, but I don’t think that’s mostly from CO2 emissions—it’s mostly because in spring and summer plants are metabolizing atmospheric CO2.
Interesting theory, worth investigating.
w.
” CO2 levels are higher in the winter than the summer, but I don’t think that’s mostly from CO2 emissions”
It is well-known that plants respire at night and in the Winter. Also, as annuals die, and deciduous trees lose their leaves, a large food source is provided for bacteria and fungi to decompose. The NH seasonal response is a buildup of atmospheric CO2 from September-October to the peak in May when plants come back to life; CO2 then declines until the following Fall. The curve is asymmetrical.
Willis, yes plant respiration and fall, winter, and early spring decay is the primary reason, but there are more emissions during NH winter. There may be implications for people wishing to reduce CO2 concentration growth (I’m not one, I think subsistence farming is dependent on rising CO2). If winter emissions are reduced, maybe there will be less mixing and more retention in the biosphere.
The City of Stockholm is situated on fourteen islands and on the banks to the archipelago where Lake Mälaren meets the Baltic Sea. The city centre is virtually situated on the water. There is water virtually everywhere you look in Stockholm.
Sweden’s proximity to the North Atlantic and prevailing south-westerly to westerly winds result in a climate that is mild in the winter months, but the northernmost part of the country has a sub-Arctic climate with long, cold and snowy winters.
Stockholm geography is not similar to the geography to Central England — much more likely to have climate influenced by nearby water, such as the Baltic Sea.
One thought is that the lag might be a sampling of the North Atlantic Oscillation, essentially measuring changes in the Gulf Stream as it gets over toward England, or longer term changes in the Atlantic circulation patterns related to the Little Ice Age.
I’d be curious if station moves would produce a similar signal in terms of the distance from the ocean, which could be checked by picking a range of current stations and seeing if there’s a correlation between phase lag and distance inland (downwind from the coast relative to prevailing air patterns).
And I’d be curious to know how much of a temperature difference there is in the difference in lag. Is it a sharp peak or trough that shifts, or a very shallow peak that shifts? I ask because the carrier wave itself is the sum of several different signals, due to the Earth’s elliptical orbit and wobbling axis (the Milankovitch cycles). I wouldn’t expect them to be able to have such a large lag effect on a sharp temperature peak over such a short timespan, but if the peak is actually of a very flat signal, it might not take much to make it seem to wander off.
Undoubtedly, the gulf stream variations are introducing a lot of jitter in my quick-and-dirty test. A full, multi-year Fourier analysis would pick up these longer term changes.
Regarding the Milankovitch cycles, they are at a much lower frequency. It would be appropriate to include them in the magnitude of J_(year) from year to year in order to get a better handle on the summer-winter amplitude of the response.
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David … just curious if there is any paleoclimate data you could use to tease out a signal?
Bill Fabrizio:
“David … just curious if there is any paleoclimate data you could use to tease out a signal?”
I don’t know of any paleo-weather data to be had at sufficient time resolution to extract phase signal.
Just trying to give you more work, Dave. :-)
https://www.nature.com/articles/s41597-020-0445-3
“Why do the seasons lag behind the cycle of the length of daylight? The short answer is that the oceans store the heat.”
No it’s about the seasonal movement of the jet stream, which is the furthest south late January to early February, and the furthest north late July to early August.
Given that global circulation models predict increasingly positive North Atlantic Oscillation conditions with rising CO2 forcing, I reckon that should in theory reduce the winter lag time, and increase the summer lag time.
The jet stream movements are part of the seasonal response and certainly modulate the weather. However, the climate phase response is dominated by the rate of change of the temperature in the spring and autumn. A heat storage and dissipation model works well.
At the higher frequency of daily rotation, the heat storage and dissipation model predicts a phase lag approaching 90 degrees, which is why the coldest part of the night is close to dawn.
The surface warms at or soon after sunrise when the solar irradiance is greater than the longwave cooling of the surface, which has been cooling since sunset. There is no phase lag.
You are right. I was thinking of a maritime example for the daily effect. It illustrates how the “effective” C is frequency dependent.
Inland, the influence of the ocean’s heat capacity has a time delay, while the effective heat capacity of the land (immediate) is much lower. In response theory, time delayed components show up as a frequency-dependent phase shift, (exp(-i (2πf)(t_delay)). When f is 1/day, a t_delay ~ days is a significant phase shift but not so much if f is 1/year.
Inland could have a lower daily T-min than a coastal location, but both start warming at or very soon after sunrise. There is no lag, and there is certainly no 90 degrees, as the diurnal cycle does not have a lowest point at midnight, the solar forcing is absent from dusk to dawn.
“But how does one disentangle this “greenhouse” hypothesis from other possible contributing causes such as land use changes or changes in insolation?”
By first disentangling how net changes in climate forcing drive the oceanic modes. Such that weaker solar wind states, as from 1995, cause negative North Atlantic Oscillation regimes, which drive a warmer AMO, and the warmer AMO reduces low cloud cover. That’s why the UK has seen an 8% increase in annual sunshine hours since 1995, more so in winter but with no increasing trend in summer.
The point is that disentangling climate causes is complicated and relies of huge numbers of factors and model assumptions. Hence my quest for a “black box” method.
My reply went below on the main thread…
http://climate-change-theory.com
Thank you. I have long thought that the correct way to understand the surface temperature is via the lapse rate from an “anchor” at the tropopause.
The question then becomes, what determines the height and temperature of the tropopause?
Coarse fixed-grid modelling has no hope of answering that question, so I treat any models based on coarse fixed-grid (all of the IPCC) as junk re the CO2 question.
When founded on real world atmospheric and oceanic teleconnections and climate system dynamics, a simple logic of operations rather than huge numbers can differentiate between the effects of low indirect solar forcing and rising CO2 forcing. I don’t see how rising CO2 forcing can drive a warm AMO & Arctic, but I can see how every other warm AMO phase is during a centennial solar minimum.
“It is said that the climate has warmed by a degree or so in the last 200 years. That is a very small number to extract from the day-to-day noise which can be an order of magnitude larger.”
That can be said until the cows come home, but no one knows a global average temperature with any accuracy before the use of NASA satellite data in 1979.
200 years ago the average temperature is claptrap — a VERY ROUGH guess of the Northern Hemisphere average with haphazard ocean measurements in common sea lanes only. Data not fit for scientific analyses.
The Central England three weather stations have had too many equipment changes for any conclusion but one: Central England is at least 2 degrees C, warmer than in the 1690s tough during the cold Maunder Minimum period, and possibly +3 degrees warmer. Yet cental England is still not warm today, even after that warming, which was certainly good news for the people who live there.
Your science is rejected due to inadequate data quality for the conclusion derived from those data. You get a grade of D.
thecliffclavenoffinance | March 1, 2023 at 9:47 am |: “The Central England three weather stations have had too many equipment changes for any conclusion…Your science is rejected due to inadequate data quality for the conclusion derived from those data. You get a grade of D”
I think you have missed the point of the method. It is precisely because the temperature “averages” are not reliable across decades that some other way of extracting climate information is needed. My contention is that the phase of the temperature response is impervious to all those factors that make the CET measurements inconsistent from decade to decade at the tenth degree level.
We treat CO2 as instantaneously well mixed. Reality is it remains near the surface a bit. Most of it is consumed by the biosphere right away, but only part of the year. Most emissions happen in the winter when they aren’t consumed by plants. And CO2 at the surface probably matters more than the mixed concentration in the atmosphere above. Knowing where CO2 is in the atmosphere would give us a better idea of climate sensitivity.
I suspect that a big part of why the temperature increases more on land and in the winter, besides the obvious, is the CO2 concentration at the surface, especially in winter, is much higher than the mixed part of the atmosphere.
https://mobile.twitter.com/aaronshem/status/1625897789841453067
What about the phase lag for max temperature?
aaron: “What about the phase lag for max temperature?”
Don’t fixate on my expressing the lag in terms of the winter minimum. It is a phase lag for a best fit cosine over the entire year.
As it happens, the fit is largely determined by the rate of temperature change in the spring and autumn.
Aaron, there should be little or no phase lag for max temp from GHE. As I figure it the difference between the marine storage effect and the GHE is that the former lags equally both warming and cooling, whereas the latter only lags cooling. Remember, the GHE has negligible effect on incoming short wave light but impedes the exit of long wave, the cooling. This same differentiation in signal should be seen in the diurnal cycle, where the UHI effect is a storage effect, lagging both maximum and minimum but the GHE only should lag the minimum.
Correction: The GHE should depress the minimum, not the lag. The shape of the signal should lag in its cooling but not the phase itself because the minimum is mainly pinned by sunrise.
On second thoughts I am wrong that the GHE insulation should not lag the maximum (peak of summer). Both storage and resistance will lag both max and min. The same is true for the diurnal (daily) max and min. The only way to differentiate the two is that storage should not have changed. Except the urban heat island effect is a storage also but that effect is missing on windy days and at high altitude, like the lower troposphere, which we have 70 years of balloon and satellite data for.
David Barnett, thank you for working on this. I had a similar thought to this in 2015, but lacking the statistical background to wrangle the data, I partnered with another blogger here named BrandonS and I purchased most all of the Australian BOM (Bureau of Meteorology) weather data up to that point. By the time the data arrived my partner had lost interest. I can relay it to you through Dr. Curry if you would like to have it.
I chose Australia because they have a very good database, without time of day observation protocol changes. Also, I was looking to disentangle the marine effect, or storage effect, from the resistance effect of GHG. In addition to looking for seasonal lag in the signal I was going to look for a secular trend in diurnal temperature range (daily signal amplitude) and also lag in peaks.
As I proceeded I learned that urban heat island effect has the same influence of reducing diurnal temperature range. Also, irrigation and agricultural land use puts more water vapor GHG into the air, confounding many station’s trends. The BOM at that time was in the midst of a massive project to map the station non-climate influences over time and I suppose they have that data now.
David, also I felt that if I, having no background in signal processing, had this realization about the GHG signal, I am thinking it has been tried but failed to bear fruit for to support correlation with the Keeling Curve (atmospheric CO2). I am hoping that you can prove this and am rooting for you.
Here is an excerpt from my email to Brandon in Nov 2015:
“Heat capacity simply stretches and mutes the signal, making the delta temperature less responsive without changing the net energy flux. GHE restricts the outgoing flux, thereby causing an increase in temperature until equilibrium with incoming flux is again achieved. Since incoming flux is less restricted than outgoing, cooling is less responsive than warming.
All daily average temps rise with a GHE but the minimums rise more than the maximums since the outgoing flux (radiation) is restricted. The lag in cooling is thus from both the affect of heat capacity and GHE while the delay in warming is due to heat capacity only. If this is all correct an increase in GHE should show a trend of delayed annual min with no change in annual max.
With a radiative imbalance, however, the ocean will cool the atmosphere more than it warms it, so on average there will be more days of the year that land temps exceed ocean temps. The more inland the weather station the more amplified the effect. Also, the more inland stations will have a higher relative influence of GHE over heat capacity. So there are multiple effects that are proportional to the degree of coastal of marine influence. This is important since even if we have a statistically weak signal from the data we can confirm the signal from multiple effects that should be proportionate. With enough good data we should be able to determine, radiative imbalance trends along with, ECS and TCR (70-year sensitivity to CO2).
Actually, it is surprising that none of the climate bureaus have created an anomaly index for each of the predicted effects on climate of CO2. The GMST anomaly indexes were created many decades ago. They only add daily T avg, (Tmax+Tmin)*.5), for each month and call it done.
Now we have 50-80 years of 3-hour data and 30-40 years of hourly data with the exact time of day for the high and low. It should be possible to model the expected secular T value for any station at any time on any day of the year. Plotting the anomalies from that model for every station, and infilling the missing ones with the model expected T, should be able to produce a clear visual of the GHE. The degree to which the anomaly plot shifts off of the model mean over time as theorized will be in direct proportion to the amount of GHE contributing to the rise in GMST over that time. We should expect GHE plot to be much more consistent than the wondering plot of GMST, which is heavily influenced by oscillations in ocean overturning rates.
The Australian BOM must already have that model to be able to now the expected hourly temperature. Most countries probably have it.
I understand there is air temperature data for Ottawa Canada from 1873 so 150 years. Could I send this to someone to analyze?
Thank you for the interesting hypothesis.
As a queston, you are measuring as the Little Ice Age was heading to an estimated end of 1850.
Does this affect the test in any way.
Again thanks,
The end of the “little ice-age” is somewhat arbitrary. However, the reduction in the average summer-winter swing between 1800 and 1850 (or 1870) followed by a steady trend ever-since, makes 1850 a reasonable boundary between two major climate phases.
Does it affect the test? Yes. The steady trend since 1850 confirms that changes in R can contribute at most 30% of the phase shift.
The amplitude decline 1800-1870 is totally inconsistent with a constant J hypothesis. J (at period 1 year) has to decline over that period. Are there any records for changes in overall cloudiness in England for that period?
I often ask myself whether a ‘number’ really provides the sort of data that matters. Over a decade of growing vegetables and fruit and pushing the boundaries at both ends of the UK growing season, I started to collect a series of natural markers which occur during the progression from winter to spring which is certainly a clearly indication that the effects of temperature may have on the natural world.
Such markers include the emergence of various perennial foodstuffs like asparagus and rhubarb; the various phases of fruit tree development from bud formation, bud opening, flowering, fruit set (all slightly different timings for cherry, plum, pear and apple); the emergence from winter hibernation of the green manure plant Comfrey Bocking 14; the emergence from winter hibernation of plants such as Welsh Onion, Wild Lupin, various Wallflowers; not to mention the hugely useful date of when annual weed seeds germinate on the vegetable patches for the first time.
I have to say that fruit trees in my garden are really pretty intelligent as they seem to manage to develop fruit successfully every year despite the nature of spring being very significantly different the past 15 years. They don’t say: ‘it’s March 1st, time to flower’, rather they tend to say ‘my complex spring progression sensors tell me that flowering now isn’t going to cause failure to produce seeds this summer’.
You start to reach a position where you say: ‘should I be sowing my vegetables not according to a human calendar, rather learning from perennial plants when the right sowing dates might be?’
Rhys, I fully agree. Your earthy perspective is the most viable response to any climate change: adapt to current conditions.
I suspect that climate variability may be necessary for a healthy biosphere. Under excessively stable conditions you get species becoming too specific in their adaptation to the point where any change becomes a catastrophe.
It is ironic that should we succeed in global climate control (as the alarmists seem to be proposing), we would actually be promoting our own extinction. Let “Extinction Rebellion” ponder that.
David – good point – “Under excessively stable conditions you get species becoming too specific in their adaptation to the point where any change becomes a catastrophe.”
slightly off topic, though the covid mitigation policies bear similar threats – ie advocating for the evolution of the human species such that the human species can only survive in a sterile environment.
As I mentioned above, I thought it would be interesting to look at the lag times of both the peak and trough temperatures. I’ve expanded that to look at max, min and mean lag times, peak and trough. Here’s that result.
https://wattsupwiththat.com/wp-content/uploads/2023/03/increase-lag-times-peak-trough-armagh.png
Hmmm … comments welcome.
w.
The lag in the minimum being roughly double the lag in the maximum seems to be in line with the physics if the winter min temps have risen double the increase in the summer max temps.
This effect can be further confirmed looking for similar lag behavior in the diurnal time of max and min in the winter trough and summer peak. I have all the Australian BOM 3-hourly and hourly data to 2017 and am looking for collaborators. Judith has my email. Willis, Dave, if you are interested, or anyone else, please email Judith.
Interesting proposal, but it is so difficult to compare temperature measurements taken 200 years ago with those of today.
Where I live the El Nino Southern Oscillation appears to have the major impact the timing of the seasons and temperature/rainfall variability.
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Odysseus | March 3, 2023 at 9:36 pm : “Interesting proposal, but it is so difficult to compare temperature measurements taken 200 years ago with those of today.”
That is the point of looking at the change in lag. In effect, one is converting rather difficult to compare, easily confounded fine temperature measurements into a much easier to compare time difference.
Re El Ninio – that is a multi-year cycle which definitely affects the timing of the seasons, even in central England, however, a definite underlying trend is discernible and needs to be explained (and CO2 alone cannot do it).
If the CET temperature lags were responding to changes in the Gulf Stream (as the dominant but lical source of the oceanic heat) would not this analysis point to just the Gulf Stream changes?
If changes in cloud cover maxima/minima were the defining change in oceanic heat content, would not this analysis not just point to cloud cover changes?
The analysis seems to me to identify temperature lag changes due to changes in oceanic and land heating, but not the reason for those changes. The variation in lag changes geographically strikes me as saying less than global changes are changing heat EXCHANGE maximum dates. Could changes in atmospheric circulation patterns in a time sense not also cause this lag change?
Douglas Proctor | March 6, 2023 at 12:35 am:
“If the CET temperature lags were responding to changes in the Gulf Stream (as the dominant but lical source of the oceanic heat) would not this analysis point to just the Gulf Stream changes?…”
The temperature peaks and troughs will depend on ocean changes, and the decadal oscillations will induce jitter in the lag. However, the phase of the annual temperature oscillation is dominated by what happens in spring and autumn when the temperature is changing fastest from week to week.
Douglas Procter: “…The analysis seems to me to identify temperature lag changes due to changes in oceanic and land heating, but not the reason for those changes.”
Correct (if you also include the modes of losing heat to space). However the trends puts limits on posited explanations such as “increased thermal insulation due to CO2”.
Thanks for your reply.
The “phase of the annual temperature oscillation is dominated by what happens in spring and autumn when the temperature is changing fastest from week to week”.
Isn’t this also when the oceans and land are beginning their serious sequestration or release of CO2?
My point was about CET lag changes through time being impacted by changes in the Gulf Stream current flow volumes or temperature changes of those volumes, and Willis’ land example with different lag times/changes, impacted by changing atmospheric current patterns, as the lags in CET don’t mat h the cont8nental lags presented.
But I like the way this analysis puts limits to increased thermal amounts regardless of cause.
On a different note: I’ve wondered regarding the seriously different thermal capacities of sea water and the atmosphere: what amount of seawater in the tropics would have to decrease, say 0.05C, some unreasonable amount, to account for the 0.8C recent atmospheric rise in temperature?
I can’t figure the math in a meaningful way.
I think the author should consider that, in Britain, the effect on temperature of snow cover can be fairly radical (you can easily see drops in minimum temperature of 10C if total snow cover exists in the Scottish Highlands, for example) and that, in general, there was far more snow cover in the earlier part of the 1770 – 2020 period in British winters than there has been recently.
I’m not a physicist who models weather, but I do know that you only ever get record low temperatures recorded in the UK when there is total snow cover.
Most of our record low temperatures are recorded in December or January, which suggests that Decembers and Januaries would have been colder back in the earlier parts of this temperature record as total snow cover would have been a more frequent phenomenon.
If I were trying to constructively critique this interesting article, I would ask the author to try and factor in the effect of varying frequencies of total snow cover as a basis seeing changes in when the annual extreme cold actually occurs in the UK.
The way you get total snow cover is westward progression of continental highs leading to Atlantic lows hitting cold air and dumping snow; or blocking highs in the Eastern Atlantic allowing arctic air to flow down from the polar regions over Britain.
Whether carbon dioxide or other weather variables affect the relative ability of Atlantic Westerlies to penetrate through Britain (and hence keep temperatures mild and snow-free) to a greater or lesser degree is another thing to cogitate over.
It sounds as though you are suggesting changes in atmospheric circulation patterns could be a causative factor in the lag time changes. Is that so?
Is there a role for an “inductance” term in your black box model?
Your model inspires me with visions of replacing the current numerical climate models with massive banks of analog computers :-)
Ivan Vuletich | March 14, 2023 at 6:10 am |: “Is there a role for an “inductance” term in your black box model?”
“Inductance” is an energy conserving inertia term, that could lead to resonances. It would be hard to detect by looking at a single frequency.
There are a lot of circuit elements you could include. The most obvious is a delay line which would show up as a phase shift proportional to frequency. The influence of the ocean on an inland location would be delayed by a few days, for example.
And, yes, an analogue computer model might do just as well as, or better than the crude digital models currently being used.