Appendix. Unsteady Climate Models and the Vostok record.

The plausible unsteady models of Section 4.9 suggest that ocean temperatures lag surface land and air temperatures. Indeed, any natural climate variability unrelated to carbon dioxide concentrations would have the same characteristic. A consequence of lag is that, when temperatures are rising, the sea is cooler than the air, and when temperatures are falling, the sea is warmer than the air. From the analysis of Chapter 1, we would expect that low sea temperatures give low atmospheric carbon dioxide concentrations and vice versa. It follows that, if we choose any temperature, carbon dioxide concentrations will be lower for rising temperatures and higher for falling temperatures. This relationship obviously does not hold near the turning points, when temperature reaches a local maximum or minimum. After a temperature maximum, it may be some time before the air temperature falls below the sea temperature. Thus, any analysis of the relationship between carbon dioxide concentration and direction of temperature change will have substantial scatter because of this end effect. If there were regular cycles, we could analyse the phase difference, as for capacitance and inductance effects in electrical circuits. However, as the analysis of Chapter 2 shows, natural climate change exhibits both phase change and amplitude change. Thus, the most practical approach that we can adopt is to compare directly carbon dioxide concentration and direction of temperature change. In doing so, we must recognize that there will inevitable be a large scatter, because we are ignoring local maxima and minima. This analysis complements the established analyses that show that, at the turning points, temperature changes first, followed by carbon dioxide concentration.

The Vostok results have given us two data sets that we could use. The data set used in Figure 1 gives temperatures at carbon-dioxide measurement times. On average, these times are separated by over 1,500 years. This analysis gives long-period correlations. Thus, it can relate carbon dioxide concentration to average temperature rises over millennia. The alternative is to use the deuterium data set directly. This data set gives temperatures a few decades or centuries apart. The advantage of using this latter data set is that there are much larger temperature rise rates (up to 3 C/century), whereas the former data set gives a maximum of 0.5 C/century (5 C/millennium). The disadvantage of using the deuterium data set is that it picks up relatively short-term climate cycles, so that there are many local maxima and minima. Thus, we would expect a larger scatter using the deuterium set. We have undertaken the analysis using both data sets. First, we report results using temperatures interpolated to coincide with carbon dioxide measurements. We then report results for the more closely spaced deuterium data set.

Carbon dioxide data set. The initial analysis relates concentrations to direction of temperature movement. For each measured carbon dioxide concentration, the corresponding temperature is recorded. The direction of temperature movement from that point to the next carbon dioxide concentration is also noted. Thus, we note whether current conditions precede a period of global warming or a period of global cooling. The data are then split into two. Data set 1 gives temperatures and corresponding carbon dioxide concentrations for rising temperatures (that is, periods of sustained global warming). Data set 2 gives temperatures and carbon dioxide concentrations for falling temperatures. The results are plotted in Figure A1. Figure A1 also shows the equilibrium correlation derived in Chapter 1. Note that the equilibrium carbon dioxide concentration is that which we would expect if the sea were maintained at the same mean temperature as the air. Thus, there would be no net tendency for carbon dioxide to evaporate from the sea into the air, or to dissolve in the sea from the air. Where the sea is cooler than the air, the atmospheric carbon dioxide concentration is less than the equilibrium concentration. Conversely, when the sea is warmer than the air, the atmospheric carbon dioxide concentration is higher than the equilibrium concentration. We see that the measurements corresponding to global warming (rising temperature) tend to have low carbon dioxide concentrations and those corresponding to global cooling tend to have high carbon dioxide concentrations. Put another way, if we choose any temperature, the lower carbon dioxide concentrations correspond to global warming and the higher carbon dioxide concentrations correspond to global cooling. This behaviour is the inverse of that expected if global warming were driven by high carbon dioxide concentrations. On the contrary, we find that the lower the carbon dioxide concentration, the more likely we are to have global warming, and vice-versa.

Figure A1. Correlation between CO₂ concentration and temperature. Periods of global warming and global cooling identified from temperatures interpolated to points at which carbon dioxide concentrations are measured.

As anticipated, there is significant scatter. Nevertheless, the mean differences (averaged over all temperatures) are as follows:

Table A1. Relationship between carbon dioxide concentration and climate change.

The significance of the carbon dioxide concentrations in Table A1 is that they are measures of sea temperature. The table simply confirms that, during periods of global warming, the sea is cooler than the land, and vice-versa. It is visually apparent from Figure A1 that, during periods of global warming, carbon dioxide concentrations are relatively low. Similarly, during periods of global cooling, they are relatively high. The proportions in column 3 of Table A1 confirm the visual impression. Thus, during periods of global cooling, nearly 70% of carbon dioxide concentrations are above the equilibrium value. The average concentration (considering points both above and below the line) is 5ppm above the equilibrium value. The inverse holds for periods of global warming with nearly 60% of points below the line, and a mean concentration of 4.2ppm below the equilibrium line. The mean difference between warming and cooling carbon dioxide concentrations is 9.2ppm or about 8% of the total range of carbon dioxide concentration.

We have further analysed the results and correlated carbon dioxide concentration difference with rate of global warming. We find that, at any given temperature, the lower the carbon dioxide concentration, the greater the rate of global warming. However, it should be noted that the large scatter does not give the line high statistical significance.

The statistical significance of the analysis of this appendix is better than that of Chapter 3. There are no deliberately randomized experiments, but a given temperature can occur within any one of 4 major periods of global warming, 4 major periods of global cooling, or numerous minor periods of warming or cooling. Thus, the temperature axis of Figure A1 effectively has time randomised. Additionally, there are 282 points on the graph, which gives better statistical significance. The statistics confirm what is visually obvious from Figure A1. Thus, for periods of global warming, carbon dioxide concentrations are lower than they are for periods of global cooling.

There is no obvious inertial effect in global warming. Thus, unlike a pendulum, once given a push in one direction, there is no reason why it should continue to move that way. Some observers state that, once global warming is started, the higher atmospheric carbon dioxide concentrations sustain further global warming. However, from Table A1 and Figure A1, it is clear that, at any given temperature, global warming is associated with relatively low carbon dioxide concentrations, and global cooling is associated with relatively high carbon dioxide concentrations. If carbon dioxide were a significant direct driver for global warming, the occasions with high carbon dioxide would show global warming, and higher global warming than the occasions with low carbon dioxide. The evidence is strong enough to conclude that, over geological time (410,000 years), carbon dioxide has not acted as a driver for global warming. Commentators who claim that the cause/effect relationship follows from “simple physics” clearly do not understand simple physics.

There are two classes of explanation for this seemingly counter-intuitive result. The first explanation is that climate variability is driven by effects, unrelated to carbon dioxide, that we do not understand. Under this explanation, the fact that carbon dioxide concentrations track temperature follows from well-established vapour/liquid equilibrium relationships. The fact that carbon dioxide changes lag temperature simply reflects that ocean temperature changes lag land and air temperature changes. The second class of explanation includes the models presented in Section 4.9. In these models, relatively low ocean temperatures stimulate global warming (probably through reduced heat convection) and vice-versa. In these models, the climate is intrinsically unstable. If the air is warmer than the ocean, global warming continues. If is cooler, global warming is suppressed. The climate then cycles for ever. If there is more than one such positive feedback system with a cycle frequency that differs from (is incommensurable with) other cycles, the climate will change in a pseudo-random manner with no pattern repeated twice. Note that one of the models of Section 4.9 is that carbon dioxide accounts for significant global warming that is suppressed during periods of strong convective heat transfer in the atmosphere. Such a model would make the present period of global warming a unique event, which could be stimulated by mankind’s carbon dioxide releases. We have proved that, over geological time, it is impossible that high atmospheric carbon dioxide concentrations drove global warming. However, it is possible that carbon dioxide is now driving global warming. The probability is much lower than is commonly quoted; namely nearer 50% than 90%.

Deuterium data set. There are less than 300 Vostok carbon dioxide concentration measurements. These are spread so that they average one measurement every 1,500 years. Thus, the global warming periods used to classify the data plotted in Figure A1 refer to periods of global warming and cooling that were sustained over several millennia. As seen from Chapter 2, average global warming rates are much lower for long periods than for short periods. The climate-change rates of Figure A1 were low, mainly between 0.05 and 0.5 C/century (that is up to 5 C/millennium). Thus, we are finding that low ocean temperatures (indicated by low atmospheric carbon dioxide concentrations) can drive global warming sustained for periods of millennia. We cannot generate more carbon dioxide data. However, we can consider the effect on relatively short-term climate change. As we have seen in Chapter 2, high natural rates of climate change can be sustained over relatively short periods of time (a few centuries). In this section, we consider the effect of carbon dioxide concentration (indicating ocean temperature) on such short-term temperature changes.

We conduct the study as follows. For each carbon dioxide measurement, we find the deuterium-estimated temperature at the immediately preceding and immediately following times. We then calculate the direction and rate of temperature change for this relatively short period. (The periods are from about 20 years to about 650 years). The deuterium series show far more local temperature minima and maxima than the carbon-dioxide series. Thus, there are more turning points, and these should give greater scatter than on Figure A1. The greater scatter was observed. However, a similar result is obtained. The result is illustrated in Figure A2.

Figure A2. Correlation between CO₂ concentration and temperature. Periods of global warming and global cooling identified from adjacent temperatures of the deuterium data set.

Note that the points on Figure A2 are the same as those on Figure A1. The difference is in the labelling of the points. Some of the points that correspond to global warming in Figure A1, correspond to global cooling in Figure A2. The difference arises because periods of long-term global warming (over millennia, as shown in Figure A1) can be interrupted by relatively short periods (over decades or centuries) of global cooling. The inverse applies. Figure A2 includes these relatively short periods of climate change. As anticipated, the short-term climate change illustrated in Figure A2, shows less consistency than the longer-term results illustrated in Figure A1. Nevertheless, it is still visually apparent that there tends to be low carbon dioxide during periods of global warming and high carbon dioxide over periods of global cooling. The subjective visual interpretation is confirmed by analysis of the results. Corresponding to Table A1, we have:

Table A2. Relationship between carbon dioxide concentration and climate change.

(Vostok deuterium data)

The greater scatter approximately halves the derived mean concentration differences.

We conclude that both in the long term (thousands of years) and the short term (tens of years) sea temperature lags air temperature.

Note also that there is a large scatter on Figure A2. Thus, fixing the carbon dioxide concentration does not fix the temperature, nor does it determine whether temperature rises or falls. Over the longer time periods of Table A1, we found no periods when the temperature did not either rise or fall. For the shorter periods of Table A2, about 3% of the periods for which temperature was the same at the beginning as at the end. However, these periods still covered decades or centuries. Referring to Figure 11, we see that there is temperature change virtually every year. Thus, it is probable that the periods for which the temperatures at beginning and end were the same exhibited temperature change during the period. We can conclude that the Earth’s climate has never been stable. We always experience either global warming or global cooling. The only “stable” periods are those when the direction of temperature movement reverses.

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