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Global Temperature: Models and Observations

Luigi Mariani and Franco Zavatti
December 08, 2019

IPCC AR5 (WG1) report figure 11.25a, reproduced below as figure 1 is really important. The report doesn’t refer to the author’s name but, from the Acknowledgements at the bottom of the chapter, a sentence restricts the research to a couple of people: “The authors thank Ed Hawkins (U.Reading, UK) for his work on key sinthesis figures and Jan Sedlacek (ETH,Switzerland) for his outstanding work on the production of numerous figures”.

Fig.1:Figure 11.25 of AR5. Forecasts through 2050 from more than 100 GCMs are shown, along with all the Representative Concentration Pathway (RCP) and observations. Upper and lower envelopes in figure 2 have been derived from this plot and HadCRUT4 Land-Ocean global temperature comes from the Climate Research Unit (CRU).

In more details, figure 11.25a shows global temperature anomaly from 1986 through 2050, with respect to the average temperature within the same period (data has been derived from 4 global temperature datasets including HadCRUT4), for the following situations:

  1. 41 “historical” runs, i.e. referred to 1986-2005 (gray lines).
  2. 137 forcasting runs AOGCM models, plotted with colors defined by the RCPs, from the one with less CO2 (RCP 2.6) through the one with more CO2 (RCP 8.5).
  3. Global temperature from 4 observed series (1986-2012, black thick line), i.e. HadCrut4 (Hadley Center/Climate Research Unit gridded surface temperature data set, Morice et al., 2012); Interim reanalysis of air global surface temperature (ERA-Interim) from European Centre for Medium Range Weather Forescast (ECMWF), Simmons et al, 2010; GISTEMP dataset (Goddard Institute of Space Studies Surface Temperature Analysis), Hansen et al., 2010 and NOAA analysis, Smith et al., 2008.

We are not alone to comment that plot, as it appears from the post “Comparing CMIP5 & observations” at https://www.climate-lab-book.ac.uk/comparing-cmip5-observations/ (hereafter Climate-lab) where observed thermal trends 2013-2019, have been added. In the comments that follow the post, Ed Hawkin offers useful details and the 5-and-95% lines referred to the runs of the whole set of 137 models. Also based on these information we produced the plot in figure 2 showing the essentials traits of figure 11.25a, upper and lower envelope of the 100+ models, compared to the HadCRUT4 anomaly (hereafter HC4).

Fig.2: Some summary lines from figure 11.25 of IPCC AR5. Upper and lower envelope and their median compared to HC4, updated to 2019.

From the last figure, it appears that

  • Upper envelope scarcely reproduces real data (and we can see in figure 1 as they are represented by the individual model runs). Observed data constantly set themselves within the space between the lower envelope (lower red line) and the median (gray central line).
  • Lower envelope effectively represents the pause (or hiatus) between 2001 and 2013, the period when global temperature did not grow within the two strong El Nino 1997-1998 and 2015-2016 (it is known that GCMs cannot describe such events, due to the lack of theoretical basis).

That appears to be a new information: models are not able to describe the 2001-2013 pause, while their lower envelope can do that. Why?

If we scale by -0.2°C the HC4 series, obtain figure 3 which shows in greater detail as the lower envelope can reproduce the temperature pause.

Fig.3: As figure 2, with only the envelopes (upper, Tn, red; lower, Tx, pink) and HC4 scaled by -0.2°C with respect to figure 2.

After such a new fact has been defined, we need to understand if the envelopes have some sense and if their existence can be associated to some physical, real character. Envelopes are the extreme values, both maximum and minimum, of figure 1, irrespective of the model that gave the extrema.

Minimum value of any model depends on RCPs; on the way to manage specific and less known aspects of the climatic engine and on the set of starting parameters and their tuning (we can remember here a test produced by NCAR/UCAR in 2016, described e.g. in Judith Curry’s blog, where 30 variations of the global atmospheric temperature, each one less than a trillionth of degree gave, in the model outputs, 30 very different outputs).

To compare observations and single models, we use here three models from KNMI,
namely BNU-ESM and CSSM4 for RCP 8.5 e 2.6 compared to HC4,

Fig.4:Two models, anyone computed for two RCPs, compared to HC4 (blue line)

or the ACCESS 1.3 model with RCP 4.5, compared to HC4 only for the period of observations.

Fig.5:ACCESS1.3 model, RCP 4.5, compared to HC4 (blue line).

Comparison with observations doesn’t give a good hope for high quality forecasts and also the model in figure 5 that, as a whole, appears to be comparable to observations, shows noticeable differences and, from 2000, the start of the same divergence already seen in other GCMs and the lack of the hiatus.
On the other hand, lower envelope (figure 3) can correctly reproduce observed data. But the complex of: parameters, handling of specific aspects, RCPs in which way can manage and justify the reliability of the envelope?

In the meantime we can note that if it is true minimum of any model depends on several factors, they hardly derive from higher-valued RCPs (this case is theoretically admissible but in a very little number of cases, so that they cannot modify the general shape of the envelope). So, we obtain the best computed series with the lower values of RCP and then with forecasts through 2100 without any catastrophic behaviour (in figure 3 data are only through 2050 but nothing leads us to a sudden growth in the next 50 years).

In order to test the models skill over the whole time extension of HC4 we computed the minimum of four models from KNMI (ACCESS1.3, BNU-ESM, CSSM4 and INMCM4) e compared it to the envelopes in figure 2 and to HC4 (when needed, series have been moved up and down by an arbitrary amount, so that the best coincidence could be attained). Result in figure 6, where we can see the ensemble of model lower values and the lower envelope describe fairly well the observations.

Fig.6: Comparison among envelopes in figure 3, HC4 and the minimum of 4 models. Tx and HC4 are moved as labelled in the plot.

Concluding remarks
• Models appear to describe in the better way observed data between 1986 and 2018 when their lower envelope is used, also if the significance of such an envelope is not fully clear.

• Lower envelope, unique instance among all the situations we could have verified, can represent also the hiatus, that is the lack of growth in global temperature between 2001 and 2013 (before El Nino 2015-16 could overcome the normal temperature run)

• We cannot explain why the lower envelope gives the best performance with respect to observed data. We offer this behaviour of the climate analysis as a contribution to possible, further discussion.


  • Smith, T.M., R.W. Reynolds, T.C. Peterson, and J. Lawrimore: Improvements to NOAA’s historical merged land-ocean surface temperature analysis (1880-2006), J. Clim., 21, 2283-2296, 2008.
  • Simmons, A.J., K.M. Willett, P.D. Jones, P.W. Thorne, and D.P. Dee: Low frequency variations in surface atmospheric humidity, temperature, and precipitation: Inferences from reanalyses and monthly gridded observational data sets. J. Geophys. Res. Atmos., 115, D01110, 2010.
  • Morice, C.P., J.J. Kennedy, N.A. Rayner, and P.D. Jones: Quantifying uncertainties in global and regional temperature change using an ensemble of observational estimates: The HadCRUT4 data set., J. Geophys. Res. Atmos., 117, D08101, 2012.
  • Hansen, J., R. Ruedy, M. Sato, and K. Lo: Global surface temperature change, Rev. Geophys., 48, Rg4004, 2010.
  • See also: WG1AR5_Chapter09_FINAL.pdf
    Data for this post is available at its support site.

Thyphoons in Japan

Franco Zavatti
November 07, 2019. Updated: November 08, 2019

JMA (Japan Meteorological Agency) produces and updates a series of thyphoons (in Japanese; in the English version of their site I cannot find the page) formed in the japanese area from 1951 through September 2019. Data is given as number of events in single month and as annual sum.
The histogram of annual number of thyphoons can be seen in figure 1 along with its linear fit showing a negative slope.

Fig.1: Annual number of thyphoons in Japan. Red line is the linear fit showing their slightly lowering frequency; its slope is (-0.4±0.3) events/decade.

In this case too, as in other examples the links in the support site refers to, in spite of the global temperature climbing and its supposed (but actually assumed as truth by the majority of peoples) dependence on CO2 concentration and, in practice, on anthropic activity, extreme events don’t show any raise.

Data shows wide fluctuations that, after applying a filter, presents a shape as in the upper frame of figure 2 (the shape depends on the filter window and gives only a rough suggestion about thyphoon yearly variability) with a sharp oscillation Such a suggestion is what we need for a spectral analysis of the dataset (as in the lower frame). The spectrum outlines the existence of a maximum at about 27 years as the main behaviour and a suggestion for 2-7 years maxima, a possible El Nino signature.

Fig.2: NUmber of thyphoons per year and linear fit (the same as in figure 1). The red line is a low-pass, 15 year filter. The cyclicity appears in any evidence (also if it depends in part on the choice of the window). Bottom frame: MEM spectrum. The maximun at about 27.2 years totally dominate the spectrum.

The period of the main spectral peak is well represented by the filter red line where the period difference between the first and the second maximum from the left is 24 years (1990-1966) and the distance between the minima is 28 years (2006-1978). With a semi-period of about 13 years we can forecast 2019 is the year of another relative maximum frequency and then assume this year will be more plenty of events than the preceeding ones (on average, of the preceding +13); it will happen at the conclusion of the thyphoons season, in November,
as it appears in figure 3.

I strongly suspect AGW has little to do with the number of thyphoons in the Japan sea and the “pain cries” about the fate of our planet are, all told, off topic.
As remembered above, figure 3 shows the monthly series of thyphoons number, with pair-wise months in order to avoid too confusing plots.

Fig.3: Monthly number of thyphoons in Japan. It clearly appears that the season runs June to November, with a grow up to August-September and a next decrease of the events. In any frame the black line refers to the first of the two months and the red line to the second one.

We can easily see January and February are low-activity months while in April something begins to move in Japan Sea; from May to August-September the maximum activity is reached and then in November it decreases, running towards the minimum in December. An noticeable behaviour of this plot is that in nome of these months a systematic growth of the activity can be found, only fluctuations around a constant average value.

L’Oscillazione Decadale del Pacifico
The 27-yr spectral maximum makes raise the idea that the main cycle could depends on an external forcing which, in the Pacific Ocean, cold be the Pacific Decadal Oscillation (PDO). Along with El Niño, other large scale oscillations exist (like PNA, Pacific-North Atlantic) whose interactions could have some influence on thyphoons genesis, but I assume PDO is the most significative one. So I’ll use only the last one. In the following I present two PDO series, one from 1000 through 2000, derived from proxy data and the other, 1900-2018, observed, along with their spectra.

Fig.4: PDO 1000 through 2000. From 1900 (pink line) PDO given by Mantua is superimposed (it is the file pdo-latest-mo.txt used in figure 5).


Fig.5: 1900-2018 PDO series.

We can derive from these series a thyphoon-compatible oscillation appears in the spectrum of the “extended” PDO but not in the Mantua “short” one, apart a possible noise around 27 years (not labelled in figure 5) of no practical significance. In such conditions it is difficult to the PDO alone the frequency modulation for thyphoons and we need imagine other forcing, effective in the Japan Sea.

In that aim, I have reconsidered two plots, previously published in Mariani
et al., 2018, i.e.

  1. The CFD series (Cherry Flourishing Date) in Kyoto, Japan (Aono and Kazui, 2008), 800-2000 CE. It, though, doesn’t present spectral maxima near to the thyphoons’ 27-yr.
    <img src=”http://www.zafzaf.it/clima/cm134/japan800.png”>
  2. The tree ring (juniper) in Wulan, China, again 800-2000 CE. This series shows a spectral maximum (well visible but not among the most prominent peaks) at 28.5 years. But we are in China, rather away from Japan.

In summary, thyphoons formed around Japan show a dropping-in-time frequency and a superposed 27-yr cyclical behaviour, whose cause is not clear.

More information for this post is available at the support site.


  • Yasuyuki Aono and Keiko Kazui:
    Phenological data series of cherry tree flowering in Kyoto, Japan, and its application to reconstruction of springtime temperatures since the 9th century, Int. J. Climatol.,28, 905-914, 2008.
  • L. Mariani, G. Cola, O. Failla, D. Maghradze, F. Zavatti: Influence of Climate Cycles on Grapevine Domestication and Ancient Migrations in Eurasia, Science of the Total Environment,635, 1240-1254, 2018. doi:10.1016/j.scitotenv.2018.4.175

Cloud Cover and Global Temperature

Franco Zavatti
November 06, 2019. Updated: November 07, 2019

A recent work by O.M. Pokrovsky (2019) analyses global temperature – cloud cover relationship. As cloud cover, he makes use of ISCCP data (some further information also in Rossow and Schiffer, 1991) and global (land+ocean) temperature series HadCRUT4.

The paper is in Russian and for me non so easy to understand also if I can read Russian (with some difficulty) and understand some word (I don’t like a lot Google translator). For any practical scope, I can say I did not read the paper, whose English abstract reads:

Cloud Changes in the Period of Global Warming: the Results
of the International Satellite Project

O. M. Pokrovsky

Russian State Hydrometeorological University, St. Petersburg

E-mail: pokrov_06@mail.ru

The results of analysis of climatic series of global and regional cloudiness for 1983–2009. Data were obtained in the framework of the international satellite project ISCCP. The technology of statistical time series analysis including smoothing algorithm and wavelet analysis is described. Both methods are intended for the analysis of non-stationary series. The results of the analysis show that both global and regional cloudiness show a decrease of 2–6%. The greatest decrease is observed in the tropics and over the oceans. Over land, the decrease is minimal. The correlation coefficient between the global cloud series on the one hand and the global air and ocean surface temperature series on the other hand reaches values (–0.84) — (–0.86). The coefficient
of determination that characterizes the accuracy of the regression for the prediction of global temperature changes based on data on changes in the lower cloud, in this case is 0.316.Keywords: cloudiness, ISCCP data, climate change, global and regional scale, climate series analysis, linear and nonlinear trends, wavelet analysis.The full text in Russian is available at the support site.

I will use here annual data of both cloud cover (also named GCC or Global Cloud Cover) discretized from the paper’s figure 1, and HadCRUT4 e NOAA-GHCN global teperatures. The time spread has been defined by GCC and ranges from 1983 through 2009 (27 years).
In figure 1 the original plot from which I dicretized the data used here:

Fig.1: Annual values of the global cloud cover (GCC) in percent. Error bars have not been discretized.

In the next plot, digitized data and their LOMB spectrum are shown:

Fig.2: Digitized GCC and its LOMB spectrum. Original values are at constant step, so I could have compute the MEM spectrum, but uncertainess in the read process gave a almost constant step, so that I preferred to use LOMB. The green line is the linear fit from which I computed the detrended series required by LOMB computation.

Figure 2 shows some behaviours that are worth to outline:

  1. The percent cloud cover clearly dropped from 1986 through 2000 and from 2001 raised with respect to 2000 and then remained roughly constant through 2009 (end of the series).
  2. A 2001-2009 almost constant situation looks like the “pause” or “hiatus” in global temperature (this is a definition of mine, derived from http://www.climatemonitor.it/?p=36847 post, while others begins the pause in 1998).
  3. Cloud cover is an important factor for temperature regulation; roughly, wider cover implies lower temperature and viceversa. This inverse relationship will be verified in what follows.
  4. In the bottom frame of the plot it can be seen that the cover is not random and that almost two cyclicities exist with periods 8-10 and 4 years when GCC could repeat itself with similar behaviour. The group around 0.9-1.3 year seems to show an annual -and also a semi annual one of 0.5 year- variation that could link GCC to astronomical (revolution around Sun) and perhaps a hemispherical forcing.
  5. The series, extended for only 27 years, doesn’t allow for detailed analysis of the spectrum.

I can now pair-wise compare the series and verify the similarity of their characteristics. In the following, I will show spectra and cross-correlation functions (CCF) in order to derive the concordance between the series in a more accurate way than a simple visual analysis.

Fig.3: Comparison between GCC (inverted) and global temperature HadCRUT4 (land+ocean) on the same time range 1983-2009.

To be noted here as the pause is the same in both plots and also that temperature raise 1983-1999 is well described by the inverted cloud cover.
As further example, I compared in figure 4, GCC also to NOAA annual data.

Fig.4: Comparison between GCC (inverted) and global temperature NOAA (land+ocean), same time range 1983-2009.

Also in this case the pause coincides for both series and, again, the temperature grow is well described by cloud cover between 1983 and 1999.

A comparison among the spectra of all the series follows:

Fig.5: Comparison among spectra. Power of both temperatures has been multiplied by 35, so that plots can be more readable.  MEM spectra don’t show frequencies greater than 0.5 (i.e. periods less than 2 years) to avoid problems with the Nyquist frequency range that must be 0 through 0.5.

Spectra show  the same behaviour (maxima between 7.5 and 8.5  and at 4 years and the weak peak at about 2.5 years) i.e. show data are not only similar in shape, as it appears in the above plots, but they have in common periods we could think as linked to physical parameters of both variables.

The GCC spectrum can be compared to wavelet analysis in
figure 5 of Pokrovsky, 2019 paper: the ~1-yr grouped periods exist over the whole time range; the 4-yr period can be observed through 1992; it becames weaker through 2001 and disappears. The spectral maximum at about 9 years in the LOMB spectrum, within the wavelet starts at 8 years and overcames 32 years, always with a power at maximum level of the wavelet scale (with a 27-yr data range I did not consider periods greater than 20 year).
I take this comparison as a confirmation of the LOMB spectrum of figure 5.

To terminate this multi-level analysis, I do show the CCF between cloud cover and both the global temperature series:

Fig.6: Cross-correlation function between cloud cover and se temperature series: The zero-lag CCF, i.e. the Pearson correlation coefficient is within -0.7 and -0.8, while Pokrovsky 2019 gives a larger value (-0.84/-0.86). I suppose that the last values have been computed from the monthly series I don’t own and that allows better time resolution.

Figure 6 shows a correlation and that doesn’t mean variables are physically related (that’s they are independent random variables), but the behaviour shown above and mainly the spectra, suggest a physical link must exist between cloud cover and global temperature.

I think the following phrase can be used as closing label:

Sorry, I cannot remember the tale where temperature exclusively depends on CO2. Would someone please remember it to me? Thank you so much.

Data for this post is available at the support site.


Looking for the 400 Kyr cycle

Franco Zavatti and Luigi Mariani
September 25, 2019. Last Update: November 8, 2019

Climate of a place or a wider area (a vineyard, a valley, a continent, the whole planet) derives from a variety of astronomical or geophysical causes (table 1) often interacting each other in a, also complex, way giving place, e.g., to well characterized positive and negative feedbacks.
In table 1 we denoted with an asterisk factors subjected to cycles over a very wide range of periods (hours to millions years).
As an example, the Sun presents 11-yr activity cycles and longer cycles(Suess, Eddy, Hallstatt, etc.) e Ocean circulation shows cycles like AMOC (Atlantic Meridional Overturning Circulation) that then plays a role on the surface temperature of the Atlantic Ocean by forcing typical cycles known as AMO (Atlantic Multidecadal Oscillation).
The consciousness of the exixtence of climte cycles has a long history.
We can quote, e.g., the Saserna, roman treaters (writers) whose work has been lost but they are quoted by Columella, argued the climate of their epoch had become milder than in the old times, so that olive trees and vineyards can live well where it would been impossible before.
In the same way the idea of cyclical cycles, that incuded also a deluge as in the biblic narrative, is widely spread in many cultures (precolombians peoples, australian blackfellows, ecc.). They mantained in trouble our progenitors along many millenia.
In the first half of the XIX century Joseph Fourier, during his studies on heat transfer, realized that analyses were much simpler if a function was represented as the sum of simple trigonometric functions with adequate parameters. Also, the researches by Fourier in 1824 uses, and he was the first one, the concept of greenhouse effect, which along with atmospheric and oceanic circulation is the basis of our planet’s climate.
Astronomical and geophysical elements Fourier used, are near to climatology because the terrestrial atmosphere is an heat machine whose motions depend on the need to equilibrate the differences due to the unequal distribution of heat on planet’s surface 1.

1 defines the climate at different scales (from a single site to the whole planet)

Again, from the XIX century, due to geomorphological work lead between 1800 and 1900 and summarized by Louis Agassiz the idea of the presence of glacial cycles takes place, what gives rise to modern climate studies about climate cycles, converging to the theory by Milutin Milankovich about the astronomical causes of glacial eras, next proven by Cesare Emiliani (1955) within his studies on ocean floor cores.
In brief, what Fourier, Agassiz, Milankovich and Emiliani give us has all needs to understand the spectral analisys and its usefulness.

Actual cycles study depends on instrumental data (temperature, precipitation, global solar radiation etc.). We outline that the presence of periodicity in independent series (like speleothemes, tree rings growth, grape harvest date) is an important reinforce to their reality. In applications, it will be important to link period analisys with (also historical) documents or narrative (e.g. legends); it follows that it may be of importance to link the astronomical cycles at periods of 2000 years (Bray or Hallstatt cycles) and 1000 years (Eddy’s cycle)(Scafetta et al., 2016) with key periods in the Holocene like:

  • great postglacial optimum
  • 4200 years ago dry event
  • miceneum climate optimum
  • iron age crisis
  • roman climate optimum
  • early medieval crisis
  • medieval climate optimum
  • crisis of the little ice age (LIA)
  • modern warming phase, after the end of  LIA
Table 1 – Astronomical factors weighting on the amount of energy at the planet’s surface.
  • earth motion around its axis (rotation)*
  • eccentricity of earth’s orbit*
  • solar activity*
  • galactic cosmic rays (GCRs)*
  • orbital effects by the other planets of solar system*
  • inclination of terrestrial axis (with consequences on inclination of
    solar rays)*
  • quasi spherical shape of the earth (with effects on inclination of solar rays)
Geophysical factors that modulate the effects of astronomical factors

  • ocean and land distribution*
  • distance from sea*
  • ocean streams*
  • atmospheric circolation*
  • shape and position of mountain ridges*
  • soil characteristic*
  • living beings activity (flora, fauna, mankind)*

(*) submitted to cycles over a very large range of time scales (days to millions years).
The large variety of periods forces to select a group of spectral cycles belonging to precise and often unknown causes.
Here we used time series covering about 5 million years and selected cycles of some hundreds of thousands years.

Data Analysis
At about the end of August 2019, we have had the availability of a paper by Kent et al., 2018, where the empirical evidence for the stability of the 405-kiloyear Jupiter-Venus eccentricity cycle over at hundreds of milions years (at least 215 Myr) was presented. We never had notice of such a spectral maximum before of this paper, so used the De Boer et al.(2014) dataset “Global 5 Million Year Sea Level, Temperature, and d18Osw Reconstructions” who declared that
Persistent 400,000-year variability of Antarctic ice volume and the carbon cycle is revealed throughout the Plio-Pleistocene published in Nature Communications (2014).
The abstract of De Boer et al.,2014 paper reads: Marine sediment records from the Oligocene and Miocene reveal clear 400,000-year climate cycles related to variations in orbital eccentricity. These cycles are also observed in the Plio-Pleistocene records of the global carbon cycle. However, they are absent from the Late Pleistocene ice-age record over the past 1.5 million years. Here we present a simulation of global ice volume over the past 5 million years with a coupled system of four three-dimensional ice-sheet models. Our simulation shows that the 400,000-year long eccentricity cycles of Antarctica vary coherently with d13C data during the Pleistocene, suggesting that they drove the long-term carbon cycle changes throughout the past 35 million years. The 400,000-year response of Antarctica was eventually suppressed by the dominant 100,000-year glacial cycles of the large ice sheets in the Northern Hemisphere.
The DeBoer (2014) dataset (hereafter deboer2014.txt) include 5 Myr (millions years) time span at 100 yr step values of some climatic parameters (i.e. 53000 data points) and is shown in figure 1 at 10-points step, i.e. with 5300 points represented, for the benthic δ18O (an inverse proxy for temperature).

Fig.1: The 5 Myr dataset of d18O from benthonic foraminifera, plotted at 10-point step. The bottom plot is the enlargement of the first million years of the series. To be noted the inverse y-scale, so the plot mimics the temperature, and also the presence of the 25 MIS (Marine Isotope Stages) which denote the interglacials in 1-million years (with of course the relative glacial periods). The red lines are, respectively for top and bottom plots, low pass filter at 1000 and 300 data points window (100 and 30 Kyr).

We decided to separate deboer2014.txt into 8 datasets of 7000 data each (the last one of 4000 data). In such a way we had something resembling a wavelets ensemble which allowed to derive spectra (MEM spectra: they are at constant step) of different and adjacent time sections, covering 700 kyr (kilo years) each one.
At the same time we computed the Lomb-Scargle periodogram (hereafter Lomb) of the whole dataset, deriving both ~400 Kyr and ~1 Myr spectral maxima as shown in figure 2

Fig.2: Lomb periodogram, from the CRAN R suite, of the full deboer2014.txt series. The green lines define here and in figure 3 the ensemble of secondary maxima between 0.4 and 1 Myr.Dashed line is the 99% confidence level.

We also continued with the MEM spectrum, computing the two half-dataset (i.e. 26000 data points each) spectra, as shown in figure 3.

Fig.3: MEM spectra of the two half-dataset sections of deboer2014.txt. The green lines define here and in figure 2 the ensemble of secondary maxima between 0.4 and 1 Myr.

The comparison between the above spectra shows that the main ~0.4 and ~1 Myr maxima remain at about the same period with a skyrocket variation of the power during the second half section (730/103 or 7X and 230/11 or 21X); also the peak at 0.24 Myr (the leftmost one in figure 2) becomes 7 times higher (50/7) during the more recent two millions years than during the first section. The other visible peaks changed their frequency (period).
Green lines in both figure 2 and 3 define a group of secondary maxima: to be noted the 0.74 Kyr maximum (0.68 in the upper frame of figure 3) clearly visible in the Lomb spectrum of figure 2 and that confirm that the analysis of the whole dataset (figure 2) is strongly dominated by the 2.nd (more recent) section of the dataset because the 0.74 maximum clearly emerges above the little “forest” of maxima.
In order to verify at a better accuracy the variation of frequency along the time sequence, we used the 8 sections defined above to compute the MEM spectrum. The time sequence is listed in Table 1.

Table 1. Deboer2014.txt. Start-End Kyr BP of the 8 sections. 100 yr step
Sec Start Kyr End Kyr Comments
1 5300.0 4600.1 7000 values
2 4600.0 3900.1
3 3900.0 3200.1 min power
4 3200.0 2500.1
5 2500.0 1800.1
6 1800.0 1100.1 max power
7 1100.0 400.1
8 400.0 0.1 4000 values
  • Spectra computed from 3500 values, from line 1500 through 4500.
  • Time spread: 700 thousand years per file (8 excluded).

A summary of the results is in figure 4

Fig.4: The MEM spectrum of the 8 sequential and adjacent sections defined by color and, in one case, by line shape. Here only 400 Kyr and nearby maxima have been selected. The bottom plot is an enlargement in power (y-axis) of the top one.

Analysis of the ~0.41 Kyr spectral maximum
We can derive from figure 4 the suggestion that the power of spectral maxima
evolve along the sections (i.e. with time) and a more precise list of peak’s
power confirm, as in figure 5, this hypothesis:

Fig.5: Time evolution of the ~0.4 Myr spectral maximum power from the 8-sections
series. The blue line is the fitting parabola of the first 6 data.

The power variation of the 0.4 Kyr peak has nothing to do with casuality but it seems to follow a rising law (the blue line is the fitting parabola) through section 6 and then a drop not too much different from the corresponding rise. So, we can suppose that, at the end of the period 1.8-1.1 Myr (section 6), something happened, so that the power of the most important cycle in the 200-700 Kyr time lapse, begun to drop.
We cannot know what happened before section 1 (i.e. before 5.3 Myr) but perhaps it could show a cyclic behavior with a 5.7 Myr period (4600-1100 from table 1).

Fig.6: Time evolution of the ~0.4 Myr spectral maximum power from the 7-sections, 2-subsections each one, series. Red line-and-dot accounts for the 1.st subsection, blue line-and-dot accounts for the 2.st subsection of each section. dot-dashed lines are the respective parabolic fits.

The characteristic shape of figure 5, relative to the 8 sections, holds again for the 14 subsections, with the data of subsections 1 appearing shifted backward by one section. We cannot explain such a behaviour, only note, as in figure 7, that a positive shift of 1 section changes notably the comparisons in figure 6

Fig.7: Time evolution of the ~0.4 Myr spectral maximum power from the 7-sections, 2-subsections each one, series when the section of subsections 1 becomes “section+1”.

Nothing of what has been found in the analysis of the power of the main peak of the actual series appears to be casual. It seems the result of an (unknown) evolution of external or internal forcings, spanning over millions years.

Milankovic Cycles
The δ18O benthic by De Boer et al. (2014), while it seems very good for 0.4-1 Myr (and more) spectral peaks, poses the problem that the 100, 41, 26 Kyr Milankovic cycles (the orbital cycles of eccentricity, obliquity and precession) cannot be derived from this series as e.g. it appears in figure 3.
We can suppose the actual spectral maxima are too weak to be identified in the above plots, so try their “emersion” by a x1000 amplification but, as it can be seen in figure 8, a daunting result in obtained: no orbital maximum in the spectra, at all.

Fig.8: Trying to identify the Milankovic cycles by a x1000 amplification: in the range 97-104 Kyr 6 peaks (out of 8 series) can b be identified, but nothing at all at 40 and, mainly, at 26 Kyr.

Fig.9: MEM Spectrum of Page800 δ18O benthic 0 to 800 Kyr BP (Ka is used in place of Kyr BP). The bottom plot outlines the periods of Milankovic cycles. This plot has been already published elsewhere; here it has been slightly revised. To be noted, as a mirror of figure 7, the absence of the 400 Kyr peak.

The data De Boer et al., 2014 used is the stacked dataset LR04 Benthic by Lisiecki and Raymo (2005) at variable step, to which a model has been applied
in order to derive a dataset at 100 yr step. So we dowloaded the Lisiecki & Raymo’s series and computed the Lomb and wavelet spectrum. The following figures 10 and 11 show that the spectra are the same and exclude some kind of procedural error.

Fig.10: LOMB spectrum of the Lisiecki & Raymo (2005) dataset LR04 Stack. Bottom frame is a 0-200 Kyr enlargement of the above total range. Dot-dash green lines are the 95%, white noise, confidence level

Fig.11: Wavelet spectrum of the LR04 series computed by PAST. Due to the log2 vertical scale, the figure has been labelled with the corresponding periods in Kyr. The x-axis has been also labelled in Kyr BP.

The last dataset also confirms that the 400 Kyr peak has low power and this is confirmed in both LOMB and wavelets

Initial and derived data, and plots, are available at the support site


  • B. de Boer, Lucas J. Lourens and Roderik S.W. van de Wal: Persistent 400,000-year variability of Antarctic ice volume and the carbon cycle is revealed throughout the Plio-Pleistocene, Nature Communications, 5, issue 2999, 2014. http://dx.doi.org/10.1038/ncomms3999
  • C. Emiliani C.: Pleistocene Temperatures, The Journal of Geology, 63, 6, 538-578, 1955. http://dx.doi.org/10.1086/626295
  • Lisiecki, L. E. and M. E. Raymo, A Pliocene- Pleistocene stack of 57 globally distributed benthic d18O records, Paleoceanography,20, PA100, 2005. http://dx.doi.org/10.1029/2004PA001071
  • Dennis V. Kent, Paul E. Olsen, Cornelia Rasmussen, Christopher Lepre, Roland Mundil, Randall B. Irmis, George E. Gehrels, Dominique Giesler, John W. Geissman and William G. Parker: Empirical evidence for stability of the 405-kiloyear Jupiter-Venus eccentricity cycle over hundreds of millions of years , PNAS, 2018.
  • Scafetta N., Milani F., Bianchini A., Ortolani S., 2016. On the astronomical origin of the Hallstatt oscillation found in radiocarbon and climate records throughout the Holocene, Earth-Science Reviews,162, 24-43,November 2016.


Area concerning very warm and very cold events in the US.

Franco Zavatti

August 21,2019; Last Updated: November 8, 2019

Here as United States I intend the contiguous US and use the NOAA dataset that annotates the percent area of the US invested by very warm and very cold events, from January 1895 through July 2019. The plot in figure 1 shows that the warm events are concerned with wider and wider areas and the cold events smaller and smaller areas. As it can be seen, in both cases there is a large variability, so I refer to the average behaviour derived by the linear fits.

Fig.1: The percent area of the US interested by very warm (red) and very cold (blue, sign reversed) events. The linear fits show a rise (slope circa 0.12% per year) for the warm events and a similar decrease for the cold ones.

All the events concerning this post are “extreme” (ie very warm and very cold) but I prefer to extract from the dataset a subset of “most extreme” events which contains only the areas wider than 40% of the US territory.
The data, displayed in figure 2, clearly shows that the areas interested by warm events are wider tan those by cold events.

Fig.2: The time series of the areas wider than 40%. As in fiigure 1 the cold events have the value of percent area with reversed sign.

From the above data I extracted the decadal frequency for both warm and cold events and show the relative histograms in the next figure 3.

The histograms of the very-very warm and very-very cold, defined as those concerning areas greater than 40%. I don’t show the last bin because of its incomplete interval (2015-2024); its value is actually 15, the same of the preceeding bin.

The situation looks like the CEI index (extreme events in the US, see eg this post, in italian) that begins to rise from 1965 through today while, before this date, it shows a decrease (the cold activity has always decreased).
In front of that, however, the CO2 concentration has always monothonically grown in such a way that it is difficult to associate extreme events to a growing CO2.

All plots and data about this post are available at the post’s support site: here

Lyon-Bron airport: precipitation and temperature

Franco Zavatti
August 6, 2019. Updated August 6, 2019

In Caillouet et al., 2019 a software (SCOPE) is presented which can reproduce high resolution meteorological data. In their figures 5 and 6
precipitation and temperature at the Lyon-Bron airport (France) have been presented as an example of the ability to generate a dataset, also in comparison with the observed data. They made available only plots of reconstructed precipitation and temperature in the range 1870-2010, so I discretized such plots and obtained, for precipitation, the series lione1.txt available in the support site and plotted in the following figure 1.

Fig.1: 1870-2010 precipitation at Lyon-Bron airport. Also average value (red), slope of linear fit (orange) and 10-yr low-pass filter (purple) are shown. Please note as the (only two) maxima are at 1.5 times the average, to be compared to the two-fold-the-average maxima in Spain. The lowest minima (4 or 5) are only 25% of the average value.

So, I cannot see any increasing number of extreme events; on the contrary, it seems strong rain events disappear after ca 1980. Also the lowest values on the record (4 or 5 in total) have levels of about 25% of the average value. From the overall slope it can be derived rain is decreasing along the time range considered here, at the rate of (8±2) mm per decade.

As in the case of precipitation, I have discretized the “median” data of the “annual” plot in Caillouet’s figure 6 and show it in figure 2

Fig.2: Annual temperature at Lyon-Bron airport. Also average value (red), slope of linear fit (orange) and 10-yr low-pass filter (purple) are shown.

The temperature at the Lyon-Bron airport approximatively follows the global land temperature. If a ΔT can be derived from the low-pass filtered data, then it is less than 0.8 °C; the highest picks are some tenth of degree above the average (filtered) curve; so they cannot be defined “extreme events” and, by the way, their number is really low. Increase in intensity or frequency of so called “heat waves” cannot be inferred from the Lyon data of temperature.

The temperature dataset displays an up and down behaviour in front of a continuously rising CO2 concentration, the same of some datasets of global land+ocean temperature (see e.g. here, in italian).

All plots and data concernig this post are available in the support site at the author’s web server, here (gray background)


  1. Laurie Caillouet, Jean-Philippe Vidal, Eric Sauquet, Benjamin Graff, and Jean-Michel Soubeyroux:
    SCOPE Climate: a 142-year daily high-resolution ensemble meteorological reconstruction dataset over France., Earth Syst. Sci. Data, 11, 241-260, 2019. https://doi.org/10.5194/essd-11-241-2019


Precipitation in Tuscany 1951-2017 and Extreme events

Franco Zavatti

August 02, 2019; Updated August 06, 2019

In prof. Sergio Pinna’s web site here (in italian), monthly total precipitation in Tuscany, 1951-2017, are available in the form of percent of the average values of the 1951-2000 baseline as it appears in figure 1.

Fig.1: 1951-2017 precipitation in Tuscany as percent of the average values 1951-2000 (click to enlarge).

In this post I’m interested to show if strong rain events are visibile in the above data, so I extracted all the “extreme” monthly cumulated gauges from the 67-year dataset: of course I need a definition of what is an “extreme” event and choose all the events that have a percent greater or equal to 200. My extremes are then the ones where the rain is at least two times the average 1951-2000 value.

These values are available as toscana200.txt at the support site.

Fig.2: Precipitation greater than or equal to 200% (i.e. the double of the average value, at least). The red line is the linear fit that roughly correspond to some 20% in 66 years (or a 0.3%/yr rise). The Lomb spectrum shows the same maxima as the USA CEI and other climate series (click to enlarge).

The extreme events are widely disperse and, on average, show a positive slope of (0.3±0.3) %/yr, not so much significative.

In the Lomb spectrum the same spectral maxima as in USA CEI index or in Garda Lake level are present, mainly the 2-8 and ~12-20 years range.

The next step has been the binning of the data in both 10 and 5 years bin width. The binned values can be read here while the histograms are in the following figure 3

Fig.3: Histograms of the number of extreme (≥200%) precipitation in 10-yr (top) and 5-yr (bottom) bins. The red line is the linear fit whose slope is labeled (also in red). The digits within the bins are the start and the end year of the bin (click to enlarge).

What clearly appears from figure 3 is the negative slope of the linear fit of the data or, in any case, not a rise in the last 67 years.

Again, if we use data they give a different information from the AGW narrative of a catastrophic evolution of climate, and that happens at several scales (small region as in the present case; continental as for cyclones and tornadoes or a wider region as in extreme events in Spain).


All plots and data concerning this post are available in the support site at the author’s web server here

Extreme rain events in Spain

Franco Zavatti
July 30,2019; Updated: August 6,2019

In October 2018 Meseguer Ruiz and collegues published the paper in spanish Episodos de precipitaciòn torrencial en el Este y Sureste Ibéricos y su relaciòn con la variabilidad intraannual de la oscillaciòn del Mediterràneo Occidental (WeMO) entre 1950 y 2016 (full text available at https://www.researchgate.net/publication/334329930) where 239 episodes of torrential rainfall (>200 mm/24 hours),registered in the Júcar and Segura rivers hydrografphic basins, were analysed, after a binning over 10-days intervals, along with the Western Mediterranean Oscillation Index (WeMOi) binned the same way, in the aim to look for a correlation between such a series.

The relationship of the Western Mediterranean Oscillation (WeMO) with the intensity of precipitation in the Mediterranean coast of the Iberian Peninsula has been demonstrated in several works. Between 1950 and 2016, 239 episodes of extreme torrential rainfall mm/24 hours) were registered in the Júcar and Segura hydrographic basins (3.6 cases per year). The 29.3% of these events took place with a highly negative WeMO phase, the 37.5% of the cases in a negative phase, and the 28.3% of the cases in a lightly negative phase. Only the 7.9% of the events occurred in a WeMO positive phase. A change on the calendar of the minimum values of the WeMO was identified, happening now in the last weeks of August and beginning of November instead of in the first weeks of October. This extended period might be related to a new temporal distribution of the extremely torrential events of precipitation. The WeMO is shown as a good indicator to analyse the torrential precipitation events in the east of the Iberian Peninsula.

Fig.1:The 10-days binned extreme rain events here plotted as 3-bin low-pass filtered data. The labels on the left indicates the time range of any plot. The abscissa is in 10-days units and the month is also indicated in red.

I will discuss such a correlation at the end of the post but now I prefer to produce their data (available within the paper) in a slightly different way from the authors: they compare the histograms of rain events (1950-2016) and (1950-1982)+(1983-2016) to the corresponding WeMoi index.

My figure 1 shows in a unique frame only the rain events in all the available ranges (because my aim is different from the authors’ one), so I can note that the larger number of torrential rain events belong to the 1950-1982 time interval while the peak value of the 1983-2016 period is at about half-way of the former one. That means the extreme events doesn’t depend on temperature (or its supposed driver, carbon dioxide).

The next figure repeats in the upper panel the above figure 1 and the bottom panel reflects the WeMO Index (again, 10-days binned and 3-bin smoothed).
While it clearly appears an inverse general correlation between large number of extreme events and low WeMOi values, I must outline that WeMOi on the entire range (cyan line) places itself in the middle of the other two graphs in such a way that the higher number of events doesn’t correspond to the lower value of the WeMO Index. I’m not sure we can speak “sic et simpliciter” (i.e.simply) of “correlation” between rain and index and I think their connection may be more complex.
But that is outside the scope of this post.

Fig.2: As figure 1 with added the 10-day binned WeMO Index. Please note the general (anti-) correlation between high number of events and low values of the index, but also the non-correlation among the number of events and the value of index.
All plots and data concernig this post are available in the support site at the author’s web server here


  1. Óliver MESEGUER-RUIZ, Joan Albert LOPEZ-BUSTINS, Laia ARBIOL ROCA, Javier MARTIN-VIDE, Javier MIRÓ, María José ESTRELA: Episodos de precipitaciòn torrencial en el Este y Sureste Ibéricos y su relaciòn con la variabilidad intraannual de la oscillaciòn del Mediterràneo Occidental (WeMO) entre 1950 y 2016. https://www.researchgate.net/publication/334329930


Tornado in USA 1950-2017

Franco Zavatti
June 14, 2019. Last Update: June 15, 2019

Tornadoes, strong events due to the contrast of cold and warm air have been recently put into the press “radar”, due to a sequence in Ohio, Kansas and other american states (see e.g. this article by Microsoft News“). As usually belongs to these strange periods, the Anthropogenic Global Warming (AGW, actually re-defined as Climatic Crisis) has been associated to such events also if the MIT expert scientist Kerry A. Emanuel says that “it is absolutely complicated” to links tornadoes and AGW. In practice, there are no elements in the data allowing the association between frequency of occurrence and AGW.
It must be remembered that a 2014 paper from Science (Brooks et al., 2014) is also quoted, where, in its title, a reference to an augmented variability in the occurrence of tornadoes is made (not of their frequency).
The rise of the events in May 2019 (but tornadoes are also present in november-december) has been analysed by Dr. Roy Spencer on his
blog, where he gives a meteorological expanation for them (i.e. The Northern American Plains, this year, have been “the coldest place on Hearth”) and shows the histogram of the distribution of F3, F4, F5 tornadoes from 1954 through 2018 (data from NOAA).
For sake of comparison I downloaded the tornado data from the
Storm Prediction Center NOAA site, 1950 througth August 2018 (here used only up to 2017, the last complete year on this site), selected the “violent” F3, F4 and F5 events and plotted in figure 1 the histogram of the number of events for the single categories and for their sum.

Fig.1: Histograms of the tornado frequency: in the upper frame F3, F4, F5 events and their sum (All). in the lower frame only the F4 and F5 tornadoes. The regression lines of the single distributions are also plotted.

It clearly appears that the slopes are in all case less than zero, so tornado average frequency in the last 67 years is decreasing. Numerical values of the linear fits are available in this image or in the numerical file .
The number of 2018 tornadoes seems to be the lowest in the history and all the “violent” event in this year are F3; such a value and a possible positive fluctuation in 2019 would belong to the normal variations, well visible in figure 1, and so as usual, “nothing new under the Sun” and a large waste of ink (both virtual and real) in the pain cries of catastrophists.

Connection AMO – Tornado frequency
The frequency of the tornadoes is generally linked to the Atlantic Multidecadal Oscillation (AMO) because of its influence on the continental climate (and weather). Connection should be inverse, in the sense that when AMO is negative the tornado frequency rise. A verification has shown in figure 2, where the AMO series is reversed (times -1) so that a positive correlation can be outlined.

Fig.2: Relation between AMO (times -1) and tornado frequency. The series smoothed over a 11-yr window and, in the lower frame, the Cross-Correlation Function (CCF) of the observed and smoothed data. It can be seen the smoothing distorts the CCF . CCF(0) is the lag 0 correlation or the Pearson correlation coefficient. Tornado data have been divided by 200 so the values are comparable to the AMO ones.

CCF between AMO and tornado frequency shows an interesting value of about 0.55, not so high but able to highlight a possible relation. Plot of AMO monthly means (1856-2017) and their spectrum is available here.

Tornado frequency Spectrum
Time extension of tornado series is 67 years, so the AMO main period (about 72 years) will not expected in their spectra and really in figure 3 we do not see a spectral maximum around 60-70 years; only a faint hint of a 55-year maximum in the F3 spectrum that reflects a similar behaviour in “All” series.

Fig.3: MEM spectrum of the four series in figure 1 (the same colors are used). Spectral maximum at about 9 years is the same of the AMO (the stronger one, after the main 72-year maximum) while in the last spectrum the 4.2 year maximum – the main one in F3 and All series – does not exists.

In F4 and F5 spectra a 19 and 18 years maximum appears, respectively. It does not exist in F3 spectrum where it seems to be moved to about 13 years. In summary, the tornado frequency looks like to be linked to El Niño (3-6.5-7.5 yr), to Sun-planets (18-20 yr) and, at some degree of uncertainty, to AMO (9 yr) due, the last one, to the limited time extension of the series less than the main period of the Atlantic Oscillation.

Harold E. Brooks, Gregory W. Carbin, Patrick T. Marsh, Increased variability of tornado occurrence in the United States, Science, 346, 6207, 2014. http://dx.doi.org/10.1126/science.1257460

All plots and data relative to the present post can be found in the support site here


Fitting Extended Series of Temperature. 2. Shihua (China) Stalagmite.

Franco Zavatti
May 20, 2019; Last Update: August 21, 2019

The combined fits of the temperature series through 800 CE describes sufficiently well also the data of the Shihua Cave stalagmite, extended through 650 BCE. The whole set of temperature series used here is presented along with the final comments.

I fit combinati delle temperature fino all’800 CE è in grado di descrivere
ragionevolmente bene anche le temperature della stalagmite della grotta di Shihua che si estendono fino al -650 CE. Viene presentato l’insieme delle serie di temperature usate nei due articoli insieme ai commenti conclusivi.

Shihua Cave (115°56’E, 39°47’N, 251 m asl at the entrance), about 50 km SW from downtown Beijing, within the East Asian monsoon zone, has been opened to visitors in 1986 and since then the internal CO2 level has risen from 500-600 to 1350-2000 ppmv and the cave temperature from 10.6~13.5 to 13.9~16.4°C.
These changes in cave conditions have resulted in a reduced rate of calcite precipitation, so stalagmite growth layers formed after 1985 cannot be used to reconstruct climate (Tan et al, 2003).

These authors produced a warm-season (MJJA) temperature series between 665 BCE and 1985 CE, derived from correlation of annual layers thickness variation for a Shihua Cave stalagmite and the meteorological data of the nearby zone. The series is presented in figure 1

Fig.1: Shihua Cave stalagmite data. Thick red line is a 20-yr low-pass filter while the black line is the linear fit showing a slope of about (1.9±0.2) 10-4 °C/yr. Bottom plots show the MEM spectrum and outline the dominance of multi-century periods with respect the
centennial ones that exist and probabily are the centennial-scale warming Tan et al, 2003 outline in their paper.

Two deep temperature decreases must be noted: that centered at about 800 CE, whose existence is faintly confirmed by the tree-rings series in figure 2, I cannot be able to assign to a particular event and the one between 1450 and 1750 which correspond to the Little Ice Age (LIA) clearly shown also in figure 2.

The deep minimum around 520 CE is common to both series, while the tree-rings minimum at ~620 CE is remotely confirmed in the stalagmite series.

Tan et al., 2003, beginning in the title of their paper (“Cyclic rapid warming on centennial-scale …”) outline the existence of centennial scale oscillations (warmings).
The spectra in figure 1 show, with a series of low-power spectral maxima, 50-170 yr periods which could be the object of the statement by Tan and colleagues. In the same time, It must be noted that the Shihua Cave spectrum is dominated by the peaks at 815, 342 and, fainter of about 9 and 4 times respectively, 482 years.

Fig.2: Tree ring series chin046 (China) of tibetan juniper from 450 to 2004 CE. Data from NOAA Paleo (accessed May 16, 2019).

Figure 3 shows extrapolation, trought the time extension of Shihua data, of
the f23 fit of the Colle Gnifetti data described in the 1.st part of this post.
As expected, the fit does not follow the peculiar shapes (deep minima) of the Shihua series but it is a reasonable representation of its average run.

Fig.3: All used datasets and their fits by non-linear functions. For the Shihua series (tamliu.txt, light green) a fit has not been computed and the extension of the Colle Gnifetti fit (red line) was used. From 1925 to 2200 the fit of NOAA monthly data have been plotted.

Mixing data at different resolution does rise the doubt to create a man-made “hockey stick”. In the aim to verify if that may be such a case, the f22 fit (4 sines + line), computed from NOAA monthly data, has been compared to NOAA annual data in figure 4, along with the 1-year (CET and Shihua) and 2-year (Colle Gnifetti) resolution series.

Fig.4: Enlargement of figure 3 between 1700 and 2200, with the NOAA annual series (orange crosses) in order to verify as the “monthly” fit acts with respect to the annual data.

In the next figure, an enlargement of figure 4 better shows the comparison between fit and annual data. Remember that, through 1925 the f23 fit of Colle Gnifetti has been used which hardly can fit the slightly different NOAA data.

Fig.5: Part of figure 4 and its enlargement. Through 1925, Colle Gnifetti data (red line) fit.

Concluding remarks

  1. The couple of fit f22 and f23 can represent well enough observed data from -650 to 2018 CE, covering a 2668 years time extension. Extrapolating 3% away of the full range (through 2100 CE) does not appear a severe hazard. Accordigly, the “forecast” anomaly at 2100, above the pre-industrial period, will range between 1 and 2 °C, in a fully natural way, without any need of dedicated action.
  2. All the data used here are anomalies whose value depends on the time base used in calculations. This is why the Shihua data have been subtracted by 0.5°C.


All plots and original and derived data are available at the support site here


  • Tan M, Liu T, Hou J, Qin X, Zhang H, Li T: Cyclic rapid warming on centennial-scale revealed by a 2650-year stalagmite record of warm season http://dx.doi.org/10.1029/2003GL017352 (full text)