Reconstructing the Climate Change

Addendum 1: Climate Reconstruction for Belgium (Uccle)
Addendum 2: The use of GISS-dataseries for Uccle


A typical conversation about climate change on the (Belgian) radio or television goes as follows:

Global warming is real.
This will cause a lot of ...doom...
Unless we can reduce the level of CO2 and other greenhouse gases.

This kind of reasoning implicitely assumes that the global warming is (almost) entirely caused by the human emission of CO2 and greenhouse gases. This was emphasized in the SPM4-report, with almost no contribution expected from the other possible sources (despite low level of scientific understanding...: see Figure SPM-2). Also from slides 31 and 32, they conclude that ... the observed increase in the globally averaged temperatures since mid-20th century is very likely due to the observed increase in anthropogenic greenhouse gas concentrations. ... But which factors were considered for these graphs (hopefully more than only solar activity and volcano, as mentioned in Figure SPM-4), and how much is their respective contribution compared to CO2?

To answer this last question, a statistical model was created based on CO2 and a couple of parameters for which long running data are available (1880 or older), and for which the variability is known to exist for many centuries to even millenia. So these factors changed also before the industrial age, and will continue to do so. It is well known these factors have at least some influence on global temperature (Mt. Pinatubo eruption, El Niño,...). Table 1 summarizes these parameters, and provides a link to the data sources (1880-2005) which were used for this model. The raw values were normalized to the same period as global temperature, i.e. 1961-1990. There were no corrections made to T for the urban heat effect. Files with raw and normalized data can be found here.

Table 1 - Parameters, data sources, averages and individual correlation with T
Parameter Data sourcer2Avg. 1961-90Remarks
Global TemperatureT-0,00GISS: Land+Ocean; values already normalized (14,00°C)
Southern Oscillation IndexSOI0,05-0,29El Niño; MonthlySOIPhase1887-1989Base
aa-indexaa0,2922,83Geomagnetic index; solar alternative
Volcanic eruptionsVolcano0,02-0,02Manually in function of explosiveness and m3 dust
Atlantic Multidecadal OscillationAMO0,65-0,05-
North Atlantic OscillationNAO0,000,27Jan-Feb-Mar-Dec average
CO2CO20,79333,402005: 379,12; Linear increase from 287 (1880) to 316 (1959) - SPM4
aa-indexaa_50,3922,995-year aa-index with dissipation-coefficients

The high correlation between CO2 and T is obvious. However, when one looks to the year to year variation, there is no explanation at all that can be deduced from the very smooth CO2-evolution. This finding is -on itself- already a strong indication that there is at least one other parameter that strongly influences the global temperature T. It should be noted that, though CO2 warms the atmosphere, if its value is not above 333,4, then it contributes negatively to the 1961-1990 average global temperature of 14°C (normalized data)! This effect applies to all parameters.
A surprizing contributor is the AMO. For such a high correlation with T, it is amazing not a single word is mentioned in the SPM4 (perhaps the MOC on page 16?). Graphs underneath show the 5-year smoothed values of the CO2- and AMO evolution compared to the global temperature.The two graphs seem complimentary to each other.

There are indications that the currently observed variations in solar radiation are too weak to explain the observed temperature variations. However, it would be quite remarkable that the variations in solar activity would not have any effect at all. Svensmark et al. point to the effect of cosmic rays being modulated by the changing solar magnetic field, and progress in this area was reported last year. Related to high energetic particles are the numerous solar eruptions that take place during a solar cycle. When earth is affected by these outbursts, this is reflected in the geomagnetic indices. The aa-index is one of the longest running of such parameters. However, the correlation with global temperature is not very clear, especially because of the 11-year solar cycle variation.

Interestingly enough, in the 1960's, the US did research on nuclear explosions. Results from the Starfish-project indicated the nuclear blast created a radiation belt of energetic particles that stayed for 5 years. Hence, it is not implausible that energetic particles from the solar eruptions that get trapped in the Van Allen radiation belts, can stay there for a similar amount of time. Dissipation coefficients were calculated from the formula ci = [1-(i/5)2]3. It may be clear other formulas and (longer) periods may be considered. The conclusion is that as the effect of the 11 year solar cycle variation gets smoothed out, a trend becomes visible that follows rather well the evolution of T, until about 1995. This trend may be indicative for some hitherto not understood solar magnetic phenomena influencing T. Graphs underneath show the year-to-year evolution of aa and aa_5 compared to the annual and 5-year smoothed global temperature.

The other parameters (SOI, Volcano and NAO) show no individual correlation at all with T. This is surprising for SOI, of which it is well known that El Niño and La Niña can have a significant influence on yearly global temperature. It is understandable for volcanic eruptions, because it is very difficult to account for the explosiveness and the amount of particles emitted, and of course they are "one-shots" (on/off-behaviour). The graphs with individual correlations with T are not reproduced here for these parameters.

In order to get an idea of the contribution of each parameter, the evolution of the global temperature needs to be reconstructed as well as possible. Therefore, on the normalized data, a regression was applied using the function "regression" available in MS Excel (alternatively, one can use the matrix-formula "linest"). This was used to evaluate 4 models: 2 models with CO2, 2 without CO2, once with aa and once with aa_5. The results can be found in Table 2.

Table 2 - Evaluated models with r2
Model Mult. r2r2r2adjS.E.
CO2 , aa 0,9620,9260,9230,065
CO2 , aa_5 0,9620,9260,9220,065
no CO2 , aa 0,8600,7400,7290,122
no CO2 , aa_5 0,8660,7500,7400,119

First of all, the influence of aa_5 on the base models (aa with or without CO2) is small. There may be several reasons for this and requires further investigation. Second, the correlation for the no-CO2-aa-model is very good, but the correlation for the CO2-aa-model is truly excellent. This is already well known and has been pointed out for many years now in the IPCC-reports. Again though, a note of caution. Over 200 years ago, there was a famous law for the semi-major axis of the planets in the solar system, the so-called Titius-Bode law. This "law" provides a r2=0,985 (Neptune included), though this is simply a coincidence (the law fails for other "planetary" systems) and has no physical meaning. Hence, the found relations for the climate parameters may also be just that: coincidence. Of course, in all fairness, it's quite a "tour-de-force" to get a correlation of 0,96 with 6 so widely different parameters. Graphs underneath show the year-to-year and 5-year smoothed evolution of T and the predicted temperatures by the CO2-aa-model, together with their correlation.

How many of these parameters are actually relevant in the CO2-aa-model? Again, using the "regression"-tool, the p-value (the probability of obtaining a result by chance alone) can be calculated for each parameter. The smaller p, the better for the parameter. Table underneath summarizes for each of the variables the coefficient and its p-value. The value "b" is the constant in the line y = a1x1 + a2x2 + ... + b. The lower this value, the better. The xi-values are the normalized parameters (1961-1990 baseline).

Table 3 - Coefficients and p-value of the variables
Model SOIaaVolcanoAMONAOCO2b
a1pa2pa3pa4pa5pa6pbp
CO2 , aa -0,004240,00 0,000900,45 0,184760,09 0,445760,00 0,010030,10 0,005990,00 -0,006460,41
CO2 , aa_5 -0,004200,00 0,000020,99 0,185310,09 0,449450,00 0,010390,09 0,006090,00 -0,007360,36
no CO2 , aa -0,005950,00 0,009070,00 0,044210,83 0,740760,00 0,020420,07 -- -0,076310,00
no CO2 , aa_5 -0,005430,00 0,012380,00 0,107690,59 0,695500,00 0,023230,04 -- -0,063970,00

AMO and SOI are relevant in all statistical models, as is CO2 for the models that take this parameter into account. NAO is moderately relevant, and so is the volcano-factor. The latter becomes highly irrelevant for the no-CO2-models. Very interesting is the change of the p-value for the aa-index and the constant "b" when going from the CO2- to the no-CO2-models: They change from highly irrelevant to very relevant. It seems that if CO2 is left out, aa and a significant constant from an "unknown" factor takes over. At first glance, the appearance of this constant seems to be a reason to leave the CO2-factor in.

With these coefficients, the temperature-contribution of each parameter can be calculated. The results for the CO2-aa-model can be seen in graphic underneath.

It's immediately clear that the main contributors in this model are CO2 and AMO, with some minor influence from SOI. Volcano, aa and NAO have no driving contribution. There is still some temperature variation to be explained, but it amounts to less than 0,1°C. Interestingly, the contribution of this unknown factor has been nearly zero for the last 30 years. The conclusion from this model is inescapable: CO2 is contributing only about 56% (0,25°C) to the current high in global temperature, the remaining 44% (0,21°C) is coming from AMO. Also nice is the temperature-increase that can be expected in 2100 if the CO2 continues to increase by 2 ppm/year and if the model holds true. By that time, [CO2] should be around 570 ppm and should contribute 1,4°C to global temperature, this is in the low end of the IPCC temperature prediction range.

Of course, these results do not explain the mediaval optimum or the big chill in the 17th century. These are major temperature deviations, which require much more extreme values for the natural parameters than the earth has experienced since 1880. Note that, according to the IPCC, the pre-industrial [CO2] remained nearly constant at 270, which limits its negative contribution to about 0,3°C in the CO2-aa-model. This is the reason to evaluate the contributions of the natural parameters in a CO2-free-model. The results were already presented in Tables 2 and 3, and the reconstruction of the respective parameters in the no-CO2-aa-model can be found in graph underneath (resp. year-to-year values and 5-year smoothed averages).

The much smaller correlation between the predicted and observed T was already pointed out earlier, and is evident in the graph. Nonetheless, the year-to-year correspondence is quite remarkable, in that the ups and downs correspond very well, only they happen at a higher or lower temperature than observed (see e.g. around 1940, 1960, and after 1980). This seems to indicate the right elements are there, but one or more factors seem to be missing. The 5-year-smoothed curve bears a lot of ressemblance to the 5 year curve of the AMO, so its temperature contribution is expected to be significant as is shown in graph underneath.

Over 70% (0,34°C) of the observed T during this century can be explained by the AMO, which is quite impressive. Also, it shows a clear warming trend over the last decades, in contrast to what is claimed by IPCC about the natural factors (See SPM4, Figure SPM-4). The contribution of NAO and Volcano remains insignificant. It might be worthwhile to re-evaluate the raw data for volcano, as its expected contribution is similar in magnitude as the current SOI. The influence of the aa-index seems especially one of cooling, as can be seen around the turn of the 19th century. It is still too small to explain the cold temperatures of the 17th century, but with this model there is at least a -0,2°C contribution. The contribution of the "constant b" can not be ignored, and seems to be linked to the unknown factor (the residu between the observed and calculated T). Graph underneath shows the 5-year smoothed evolution of this unknown parameter.

The evolution of this residu is quite a surprize. Contrary to what one would expect if the residu was linked to CO2, there is no steady increase to be seen. In fact, over the last 30 years, this residu has remained constant between about 0,1 and 0,15°C. Though this may be due to several factors, the most straightforward seems to be that a systematic error has been introduced somewhere in the course of the 1960's. Interestingly enough, this was the period where stations transited from the open to closed thermometer box (Ukkel in 1968). In order to get measurements comparable to the closed box, corrections were introduced, based on experimental data (day-to-day comparison between open and closed box). They seem to introduce an overall decrease of the pre-1968 temperatures in Ukkel (example). It might be worthwhile to do this day-to-day comparison once more to see if these corrections are still holding up (global scale), i.e. if there is no overcorrection for the pre-1968 data making the currently observed temperatures hotter than they actually are.

Of course, this might all be coincidence, due to the statistics and the parameters chosen. Therefore, let's compare the models with the last 26 years (1979-2005) of (corrected) satellite measurements of the lower troposphere. After correcting for drifting errors of the satellites, the NOAA satellites seem to measure an increase of 0,139°C/decade (graph underneath). This is about 20% less than that deduced from the global temperature T (0,171°/decade). This difference still gives rise to discussion among scientists, although much less than prior to the drift-correction!
Looking at the models CO2+aa and no-CO2+aa and their predicted temperatures (no residues), the rates amount to 0,191°C/decade and 0,153°C/decade respectively. This means the rate of the no-CO2-model is quite a bit closer to the satellite-rate than that of the CO2-model, and even that of T. The correlation of the no-CO2-model (r2=0,69) is somewhat better than that of the CO2-model (r2=0,66), but both correlations are significantly smaller than the correlation of T (r2=0,85).

The foregoing analysis certainly does not rule out CO2 as a contributor to the observed global warming. Rather, it provides grounds that its contribution is much less than that claimed by the IPCC, and that AMO contributes a significant chunk to the temperature evolution. Also, the obtained results warrant a review of the temperature data, and the way in which they are obtained and handled.


Addendum 1: Climate Reconstruction for Belgium (Uccle)

And what about Belgium? To answer this question, a similar approach was used as for the global warming. The same data were used as in Table 1, but for temperature the series of Uccle (Royal Observatory near Brussels) were used. The data can be found at the GISS-network. For Uccle, the average temperature for the period 1961-1990 amounts to 9,85°C. Table 4 clearly shows there is no significant correlation between Tu and any individual parameter.

Table 4 - Parameters, data sources, averages and individual correlations with Tukkel
Parameter Data Sourcer2Avg. 1961-90Remarks
Temperature UccleTu-9,85GISS: Uccle; the values were normalised
Southern Oscillation IndexSOI0,00-0,29El Niño; MonthlySOIPhase1887-1989Base
aa-indexaa0,0522,83Geomagnetic index; alternative for solar activity
Volcanic eruptionsVolcano0,00-0,02Manually in function of explosivity and m3 dust
Atlantic Multidecadal OscillationAMO0,09-0,05-
North Atlantic OscillationNAO0,250,27Jan-Feb-Mar-Dec average
CO2CO20,11333,402005: 379,12; Linear increase from 287 (1880) to 316 (1959) - SPM4
aa-indexaa_50,0422,995-year aa-index with dissipation-coefficients
Arctic OscillationAO0,21-0,119CPC: 1950-2005; NCEP reconverted to CPC for 1899-1949
Sunshine UccleSSU0,181490Only for the period 1899-2005 vanaf 1899

Using the "regression"-function from MS Excel, 6 models were analysed: 4 identical to those described above, and two that also include the parameters AO (Arctic Oscillation) and SSU (Sunshine Uccle). These last 2 models are based on data starting in 1899, in view of the limited availability of the AO-data. The results are in Table 5.

Table 5 - Evaluated models with r2
Model Mult. r2r2r2adjS.E.
CO2 , aa 0,6690,4480,4200,542
CO2 , aa_5 0,6710,4500,4230,541
no CO2 , aa 0,6630,4390,4160,544
no CO2 , aa_5 0,6620,4380,4150,544
CO2 , aa , AO , SSU 0,7390,5450,5080,476
no CO2 , aa , AO , SSU 0,7360,5420,5100,475

Table 5 shows the 5-year smoothed aa-values have little influence on the correlation with Tu. Also, there is hardly any difference between the models with or without CO2. That's why the focus will be on the two models with CO2 and not-smoothed aa. Graphic underneath shows for the model without AO and SSU the similarities and differences between the real and reconstructed Tu. Aside the fact that the current temperatures in Belgium are as high as they were in the period 1945-1950, the annual variability of Tu is much larger, as well as the much larger temperature deviations (+/-1,5°, or 3 times as big as the global temperature deviation). This is normal: Locally, there will be a much bigger influence from local, natural factors, than globally. E.g. The NAO will have a bigger influence in Belgium than in Sydney, Australia. The SOI will have a much bigger influence in Sydney than in Belgium. It is to be expected that locally, there will be more factors in play that have globally much less influence. Typical examples are landuse, urban-heat effect,... Clearly, this model has major difficulties in reconstructing these extremes (the yearly deviations are sometimes as big as 1°!).

To remedy this problem, 2 parameters were added in the analysis: the AO (Arctic Oscillation) and the SSU (hours of sunshine in Uccle): AO in an attempt to explain the big drops in Tu, SSU as a raw (and local) approach for the Svensmark-effect. For the same period (1899-2005), the correlation clearly increases, but only with 0,08. So, there are still other parameters in play. Another possibility is the existence of a "facilitator". This is a parameter that pending its value, enhances or weakens the influence of one or more parameters without itself influencing directly Tu. A possible example could be the QBO (Quasi-Biennial Oscillation).

Of course, the relevance of the different parameters in all models was evaluated. By using again the "regression"-function, the p-value (the probability that a result is based on a coincidence) can be calculated for each parameter. The smaller p, the better for the parameter. Table 6 gives for each model and for each variable this p-value. Values bigger than 0,1 are considered insignificant. The value "b" is the constant of the line y = a1x1 + a2x2 + ... + b. The smaller this value, the better. The xi-values are the normalised parameters (1961-1990 base). In the 6 models, "b" amounts to 0,14-0,20°C: That's procentually about as much as with the reconstruction of global climate change (10%). Relevance is very high for AMO, NAO and the hours of sunshine (read: no clouds), and very noticeable is the no-influence of SOI, CO2 and AO. Especially the last parameter poses a problem: It is unclear at the moment what causes the sudden, big temperature drops (-1 - -1,5°C!) in Belgium like in 1890 and 1950.

Table 6 - p-values of the variables for the different models in Uccle
Model SOI aa Volcano AMO NAO CO2 AO SSU b
CO2 , aa 0,14 0,89 0,76 0,00 0,00 0,16 - - 0,00
CO2 , aa_5 0,14 0,46 0,79 0,00 0,00 0,10 - - 0,00
no CO2 , aa 0,18 0,65 0,84 0,00 0,00 - - - 0,00
no CO2 , aa_5 0,18 0,95 0,85 0,00 0,00 - - - 0,01
CO2 , aa , AO , SSU 0,90 0,16 0,49 0,00 0,00 0,40 0,500,00 0,01
no CO2 , aa , AO , SSU1,00 0,24 0,48 0,00 0,00 - 0,310,00 0,02

The next 4 graphics provide an overview of the contribution of each parameter and of the residu (unknown factors) for both of the CO2-aa-models (with and without AO and SSU).

It can be seen clearly that in both cases NAO and AMO are the determining factors for temperature in Belgium. Anno 2003, AMO contributes 0,5° to the 1,2°-temperature deviation. In the past, NAO has contributed similarly. Interesting is also that on the end of the 1940's, SSU was responsible for a warming of 0,4°C. CO2 contributes during the whole period only 0,1-0,2°. From the residues, it appears there is at least 1 missing factor. In view of its variability in the past, this is probably not the urban-heat-effect.



Addendum 2: The use of GISS-dataseries for Uccle

P.W. informed me that GISS actually uses 3 dataseries per station. The first one contains the raw data. For Uccle, there are 4 such "sub"-series. The second GISS-dataseries contain the data after combination for similar stations (the C-series). For Uccle and other observing stations, this means one series is left. Finally, there is the GISS series "after adjustment for homogeneity" (the H-series). It now appears that current temperatures for Uccle in the C-series are similar to those in the 1940's. Since 1880, over a period of more than 100 years, one can actually only talk about a temperature variation, not really about a temperature increase (trend of 0,58°C/century with r2=0,09). However, in the H-series, current temperatures are about 0,5°C higher than those in the 1940's, and for Uccle there is a clear longterm increase in temperature discernable (trend of 0,99°C/century with r2=0,23).

This "after homogeneity adjustment" is apparently being done by GISS itself:

...We modify the GHCN/USHCN/SCAR data in two stages to get to the station data on which all our tables, graphs, and maps are based: in stage 1 we try to combine at each location the time records of the various sources; in stage 2 we adjust the non-rural stations in such a way that their longterm trend of annual means is as close as possible to that of the mean of the neighboring rural stations. Non-rural stations that cannot be adjusted are dropped. ...

Of course, this raises a couple of questions. Which rural station(s) was (were) used for Uccle? Did one consider parameters such as open/closed thermometer box, urban-heat-effect,...? How were these adjustments calculated into statistics on icedays, heatwaves,...? What effect does it have on the above analysis for Uccle?

Graph underneath makes a comparison between the C- and H-series for Uccle. The difference (in blue) represents the "adjustment" performed by IPCC based on their comparison with "rural" stations. By the way, these "Homogeneity adjusted" temperatures (H-series) are the ones used for the determination of the global temperature!


The hand of IPCC

From now on, I will call this figure "The Hand of IPCC", in an analogy to Maradona's "The Hand of God" after he unjustly made a goal with his hand during the World Championship Soccer 1986. These "steps" are the absolute proof that the adjustment by IPCC can not possibly be based on a comparison with rural areas. Please see my Climate Study for Europe which makes a comparison between rural and urban temperatures (my website under "The Earth"). The difference varies between +0,4 and -0,4°C, and especially: it certainly doesn't happen in nice steps as presented by the IPCC.

It's obvious this purely artificial intervention is in the advantage of the CO2-scenario, and that the final result for Uccle is comparable to the global temperature evolution: Anno 2003, the contribution of CO2 and AMO is about equally strong (0,5°C for Uccle, 0,25°C global). Important is also that for Uccle, the unknown factor (residu) remains as big, and it occurs at the same moments. One detail: Because of the adjustment, the average temperature in Uccle for the period 1961-1990 decreases from 9,85°C to 9,57°C. This explains why the deviation in the H-series in 2005 amounts to +1,5°C, whereas in the C-series it's only +1,2°C.

Because of the artificial character of the adjustments in the H-series, the C-series will continue to be used in further studies. The results for the global temperature evolution need to be viewed in this light.


Jan Janssens

Update: 09 april 2007 for addendum concerning the use of GISS-dataseries for Uccle.
Update: 03 April 2007 for addendum on Climate Reconstruction Uccle.
Original: 27 February 2007