80. Lateral thought #4 - COP26 and keeping 1.5 alive

For the last two weeks politicians from all over the world have been gathering and meeting in Glasgow in order to formulate an agreement to cut the use of fossil fuels by mankind. The target has been to keep the maximum extent of global warming below 1.5°C and so avoid a catastrophic warming of over 2.8°C by the end of this century. This may be very laudable, but in my opinion most of the measures agreed or demanded are unworkable and unnecessary.

My first critique is with regard to the current temperature rise and its projection. The received wisdom is that current warming relative to pre-industrial times (i.e. before 1750) now stands at 1.1°C. In contrast, the real temperature records, as outlined on this blog, show that this is unlikely to be true. Over the last sixteen months I have analysed the land-based temperature records of virtually the entire Southern Hemisphere, plus those of the USA, Europe and southern Asia. None show a warming of over 1°C since 1750 that correlates with increases in anthropogenic carbon dioxide emissions. The only consistent warming is seen after 1980, and this is only about 0.5°C in magnitude. Given that 70% of the Earth's surface is water and that the oceans heat up by less than half the amount compared to land, it is impossible to get to a 1.1°C average warming globally unless one postulates that land temperatures have increased by over 2°C everywhere, as Berkeley Earth does (see Fig. 80.1 below). But the reality of the raw data that I have analysed so far is that there is virtually no country or continent that I have investigated so far where this has happened. So the real temperature increase so far is likely to be less than 0.5°C. And as I showed in Post 14 and Post 29, much of this 0.5°C could be due to urban heat island effects.

Fig. 80.1: Land and ocean global average temperature anomalies since 1850 according to Berkeley Earth.

My biggest criticism, though, is reserved for the proposed countermeasures. The one consideration that has been completely omitted from discussions of carbon reduction policies has been the economics. While a lot of time has been devoted to discussing financial aid to small developing countries that are supposedly at risk from climate change, none has been directed to considering the financial impact on producers and consumers. 

One of the main aims of COP26 was to "keep 1.5 alive" - namely to enact measures that would prevent the global temperature rise from exceeding 1.5°C. This, we are told, requires a 50% reduction in fossil fuel use by 2030, and a move to net-zero by about 2060. The question, then, is how do we reduce fossil fuel use by 50% by 2030, or 5% per year? At COP26 all the emphasis appeared to be on reducing fossil fuel demand rather than supply. Yet both are problematic, and both will cause economic hardship to many.

The current political strategy appears to revolve around getting as many countries as possible to cut their usage of fossil fuels, but this policy has two flaws. Firstly, it requires over 180 countries to agree to do something that none really want to do. That means it is highly unlikely to succeed (think: herding cats). But if it does there is the second problem. It will devastate the economies of many oil producers. What is striking is the callous disregard many climate activists have for the people of these countries.

Countries like Iran, Iraq, Azerbaijan, Russia, Libya, Nigeria and Venezuela are almost entirely dependent on the revenues from oil and gas to feed their people. They are economic monocultures. Nor do they have large sovereign wealth funds to fall back on like Norway, Saudi Arabia or Kuwait. So what happens to their economies when demand for oil and gas runs out, or the sale is banned by international treaty? The impact will be cataclysmic.

The alternative strategy is hardly much better, but will create a different set of losers. Rather than trying to regulate demand, the UN could instead try to regulate supply by getting the producers to cut supply by 5% per year and thus force the consumer nations to adapt. This strategy has two advantages. Firstly it requires the agreement only of the producers who are much fewer in number, and secondly any cut in supply would result in spikes in price which would largely protect the incomes of the producers. Instead the consumers would suffer, and with them the global economy. The result would be oil and gas shortages, high prices, fuel poverty and global economic collapse. So, not a great choice!

28. No AGW in Australia? A summary of trends.

 

Fig. 28: 10-year average temperature trends for Australia based on actual raw data (blue curve) and Berkeley Earth adjusted data (orange curve). The gradient of the best fit to the actual raw data (red line) is +0.18 ± 0.02 °C per century. The temperature change is relative to the 1961-1990 average.

 

 

 

My previous ten posts have examined the temperature records of Australia, state by state, and then also examined the combined result. The final results, based on my analytical methods, are summarized as follows.

1) The mean temperatures in Australia since 2000 are at most 0.2 °C higher, and probably less than 0.1 °C higher than those seen in the latter part of the 19th century (see Fig. 26.1).

2) The average temperature in Australia over the course of the entire 20th century was 0.063 °C lower than the equivalent value for the last 50 years of the 19th century.

3) The average temperature in Australia from 1950-1999 was only 0.1 °C higher than the average for the last 50 years of the 19th century.

4) The fluctuations in the temperature of Australia show a scaling behaviour with a fractal dimension of 0.26 (see Fig. 27.2). This suggests that most of the features in the smoothed data, or data averaged over long timescales, are just low frequency noise. Similar effects are seen in the data for most states, and also in the data for New Zealand (see Post 9).

5) The scaling behaviour of the anomalies implies that the 100-year average temperature for Australia would still have fluctuations with a standard deviation of more than 0.10 °C. This is more than the temperature difference observed between the values for the mean temperature of the latter half of the 19th century and that of the latter half of the 20th century. Thus, the temperature rise seen in the latter half of the 20th century is within the range that would be expected based on random chaotic fluctuations.

6) Only Western Australia and Queensland appear to have had noticeably higher temperatures after the year 2000 compared to the late 19th century. This is partly explained by the fact that both states have little or poor data before 1890.

7) The various adjustments made to the individual temperature records by climate groups like Berkeley Earth appear to have had a significant impact on the overall warming trend for Australia when compared with my more simplified (but in my view more justifiable) statistical methodology. This means that the statistical methods used to analyse the data, and their rationale, are of critical importance and need to be thoroughly tested, evaluated, and justified. The first step in doing this should always be to compare the results based on the adjustments with those obtained without the adjustments. That has always been the primary raison d'être of this blog.

8) The overall effect of adjustments made to the individual temperature records of Australia by Berkeley Earth, when compared to my results, has been to partially flatten the curve in Fig. 26.1 before 1900 and to increase the warming trend by up to 0.3 °C after 1900 (see Fig. 26.5). These adjustments are not neutral and completely change the shape of the curve.

9) The overall temperature trend for Australia looks more like a parabola or low frequency oscillation when the raw data is averaged according to my statistical procedure. The effect of the adjustments made to the data by Berkeley Earth is to make the temperature trend look more like a hockey stick (see Fig. 26.4).

Given the shape of the overall instrumental temperature record illustrated in Fig. 26.1, it is difficult to see how this could constitute unambiguous evidence for anthropogenic global warming (AGW). The best (or worst) that can be said about the data is that it is ambiguous. However, it also represents an alternative self-consistent narrative that raises profound questions about the current climate warming zeitgeist.

If my averaging methods for the anomaly data were simplistic to the point of being erroneous, the result would be a mean temperature trend in Fig. 26.1 that was totally uncorrelated with the majority of the individual records from which it was formed. Yet there is no evidence that this is the case. In fact the majority of long temperature records for Australia look very similar to the mean trend shown in Fig. 26.1.

But it is the scaling behaviour that is the killer application. If this phenomenon is real and ubiquitous, then it implies that (almost) everything that is seen in the temperature record is just chaotic noise. The only exception might be the urban heating I described here, and which is clearly important in those parts of the world that have high levels of industry and high population densities. But that is unlikely to be important in most of the Southern Hemisphere.

14. Surface heating

The principal claim made by climate scientists is that global temperatures have increased by about 1 °C over the last 100 years. In the last post I outlined three ways that this might happen. The first, which was due to changes in the amount of solar radiation reaching the Earth, I discounted due to a lack of evidence or plausible mechanism. The last, changes to the radiative forcing term I will discuss at a later date. In this post I will consider the second possibility: changes to the amount of direct heat absorption at the surface of the Earth. There are essentially only two ways this can happen: (i) through changes to the Earth’s reflectivity or albedo; (ii) by direct heating of the surface from energy sources other than the Sun.

(i) Changing the Earth’s albedo.

As I explained in the last post, one way that the Earth's surface temperature might change is if the proportion of light from the Sun that is reflected from the surface were to change. The amount reflected is called the albedo. This effect can be seen in Fig. 14.1 below which is taken from a 2009 paper by Kevin Trenberth, John Fasullo and Jeffrey Kiehl (Bull. Amer. Meteor. Soc. 90 (3): 311–324). On the left of Fig. 14.1 where the direct radiation from the Sun (in yellow) impacts the surface, the radiation is partially reflected with 23 W/m² being reflected and 161 W/m² is absorbed. This equates to an albedo of 0.125 ( = 23/(23+161) ).

As an aside: it seems slightly suspicious that the fractions reflected at the surface (1/8) and at the top of the atmosphere (102/341 = 30%) are so close to simple fractions. Does this indicate a high degree of uncertainty in these numbers, I wonder?

Fig. 14.1: The Earth's energy balance according to Trenberth et al. (2009). 

In order for the surface temperature of the Earth to have increased by 1 °C, one way that this could have happened would be for the amount of energy absorbed at the surface to have increased over time by 2.3 W/m². If this were to be achieved through changes to the albedo, then the albedo would need to have decreased from 0.1375 to 0.125. That is a change of 0.0125. So how likely is this?

The albedo of the Earth's surface depends of the type of material of the surface, as shown in Table 14.1. It also depends on the angle of incidence of the light as light tends to reflect more off surfaces at glazing incidence. So ocean water at the equator has a lower albedo than it does near the poles. However, there is also much less surface area near the poles which consequently reduces the contribution of high angle reflectance. 

Surface	% of Earth's     Surface Area	Albedo    %	Contribution to the     Earth's Albedo
Ocean	71.00	6	0.0426
Forest	7.62	8-18	0.0091
Grassland	7.93	25	0.0198
Arable	2.37	17	0.0040
Desert sand	5.51	40	0.0220
Urban	0.21	20	0.0004
Glaciers & ice caps	2.90	80	0.0232
Shrub & tundra	2.46	15	0.0037

Table 14.1: Approximate albedo of different parts of the Earth's surface.

The most common claims made about land use and climate changes are in regard to deforestation, increasing agricultural use, and increased urbanization. First it is claimed that deforestation for farming, particularly livestock farming aids global warming. As far as changes to the albedo are concerned, the evidence in Table 14.1 seems to point the other way. Turning forests into grassland increases the albedo.

Urbanization is also generally believed to reduce albedo, partly through what is termed the urban heat island (UHI) effect. This is the theory that cities with large amounts of concrete soak up more heat, and tall buildings trap that heat. This may be true, but it may also be a small localized effect. Again the data in Table 14.1 does not support it as a major driver of global warming.

A third claim is often made about polar ice and glaciers. The claim is that, because ice and snow have high levels of albedo, any change in their total albedo would have a large impact on global temperatures. The two main negative effects cited tend to be reductions in area by melting, or black carbon soot particles that drop on the surface and reduce the albedo. The main problem here is that the changes required are huge; a 54% decrease in area, or a decrease in albedo from 0.80 to 0.37. The first obviously has not and will not happen, and the latter is very unlikely as it would require huge levels of soot deposits.

The conclusion is, therefore, that changes to the Earth's albedo are difficult to achieve, and any that might have occurred have probably produced very little real effect in terms of increasing global temperatures.



(ii) Direct anthropogenic surface heating due to human and industrial activity.

The proposition here is this. All energy generation by humans results in an output of heat or thermal energy. Not only does every industrial process produce waste heat, but all mechanical work that is done by that process eventually ends up as heat or entropy as well. These are the consequences of the Second Law of Thermodynamics, and as every physicist knows, nothing can defeat the Second Law of Thermodynamics. So as temperature is just a measure of heat and entropy, it follows that everything humans do, every industrial process they create, all the energy that goes in will, in the end, just heat up the environment.

In the last post I showed that an increase of 2.3 ± 0.5 W/m² in the amount of radiation at the surface would raise global temperatures by 1 °C. So if we can work out what the rate of energy production and consumption by humans is, then we can equate that to a global temperature rise. The starting point for this is clear: we know from IPCC reports and the protestations of climate scientists that the human race currently emits 36 gigatonnes of carbon dioxide (CO₂) into the atmosphere. That CO₂ is created primarily by three processes.

The first is the burning of pure carbon (from coal) that produces an energy output of 394 kJ/mol for the process

(14.1)

The second is burning of methane (natural gas) that produces an energy output of 882 kJ/mol for the process

(14.2)

The third is the burning of higher alkanes (from oil) that produces an energy output of about 660 kJ per mole of CO₂ for the process

(14.3)

Each of the above energy outputs is for the burning of carbon or hydrocarbons to produce one mole of CO₂. To work out how energy that amounts to in total we need to know how much of each type of fossil fuel was used.

In 2018 global coal production was 7665 million tonnes, natural gas production was 3955 billion cubic metres or 2786 million tonnes (assuming 1 cubic metre = 704.5 g), and crude oil production was 4472 million tonnes. That suggests a mean energy output of about 560 kJ/mol. As 36 gigatonnes of carbon dioxide equates to 8.18 x 10m¹⁴ moles, then the total energy consumption would have been 4.58 x 10²⁰ J for the year, or 52,268 TWh.

Fig. 14.2: Global fossil fuel consumption since 1800.

However, according to the Our World In Data website, the global energy consumption from fossil fuels in 2017 amounted to 36,704 TWh from natural gas, 53,752 TWh from crude oil and 43,397 TWh from coal (see Fig. 14.2 above). The total of these values (133,853 TWh) is 2.53 times the value based on CO₂ emissions and suggests only 39% of fossil fuel combustion results in CO₂. This higher figure equates to an average power density at the Earth's surface of 0.030 W/m² across the whole surface of the Earth. That is turn implies a global temperature increase (based on the 2.3 W/m² required for a 1 °C increase that I demonstrated in the last post) of 0.013 °C compared to pre-industrial times. This, though, still omits the impact of nuclear power and renewables.

Fig. 14.3: Global energy production by energy type (2005-2018).

According to Statistica.com renewables and nuclear energy accounted for 15.3% of global energy consumption in 2018, and fossil fuel usage in 2018 exceeded that in 2017 (see Fig. 14.3 above), so that implies a global temperature increase of at least 0.015 °C compared to pre-industrial times. This temperature increase of 0.015 °C is, however, at least 60 times less than the one the IPCC is claiming for global warming since 1850. So this suggests that any resulting surface heating is such a small effect that we can safely ignore it, right? Well, not so fast.

We know that this heat is not spread evenly, its impact is greatest in the areas where most people live and work. We know that 90% of people live in the Northern Hemisphere; we know that 99.999% of people live on land. It is also true that 90% of weather stations are in the Northern Hemisphere, and at least 99.9% of them are on land. In other words there is a high degree of correlation between where people live, where industrial energy usage is, and where the weather stations are. For example, 19.7% of the Earth's surface is land in the Northern Hemisphere. So if 90% of the energy use is found there then the mean temperature rise on land in the Northern Hemisphere will be 0.069 °C. But of course, even that fails to tell the whole story. If we look at individual countries the results become even more stark.

If we start with what has been, historically, the biggest CO₂ producer, the USA, we see that it accounts for about 20% of global energy use despite being home to only 4.3% of the world's population, and covering only 1.6% of the Earth's surface area. That suggests that the power density for surface heating in the USA should be about 0.38 W/m² (an increase by a factor of 12.6 on the global average of 0.03 W/m²). This picture is confirmed by data from the US Energy Information Administration that indicates that the total power consumption of the 48 contiguous states (excluding Hawaii and Alaska) is 100.3 x 10¹⁵ BTU (see Fig. 14.4 below) over an area of 8.08 x 10⁶ km². As 1 BTU (British thermal unit) is the equivalent of 1055 J, this gives a power density for surface heating of 0.42 W/m². Yet this increases to 0.69 W/m² in Texas and 1.11 W/m² in Pennsylvania. That means that the temperature rise in Pennsylvania due to surface heating is almost 0.5 °C. But if we look at Europe the situation is even more extreme.

 Fig. 14.4: US energy consumption since 1950 by sector (in BTU).

According to the IEA, the UK's energy usage in 2018 was 177 million tonnes of oil equivalent (Mtoe), or 2059 TWh (1 Mtoe = 11.63 MWh). As the area of the UK is only 242,495 km², that equates to a power density of 0.97 W/m² and a temperature rise of 0.42 °C. But it is safe to assume that that energy usage will not be spread evenly across the country. At least 84% of both the UK population and UK economic activity is found in England (with an area of 130,395 km²) which implies a temperature rise for England alone of 0.66 °C. Yet that is still modest compared to Belgium and the Netherlands with their much higher population densities (see Table 14.2 below) where the projected temperature rise is close to 1.0 °C. That is more than the IPCC claims for global warming from greenhouse gas emissions.

Country	Energy Usage (Mtoe)	Power Density (W/m2)	Temperature Rise (°C)
UK	177	0.97	0.42
Italy	151	0.66	0.29
France	245	0.50	0.22
Belgium	52	2.25	0.98
Netherlands	72	2.30	1.00
Germany	298	1.11	0.48
Austria	33	0.52	0.23
Switzerland	24	0.77	0.34

Table 14.2: Energy usage, surface heating and temperature rise in Europe.

What Table 14.2 illustrates is that surface heating is a significant factor in overall global warming, and it is occurring in every major EU country, including those that border the Alps. In fact the average temperature rise over all five of the main alpine countries is 0.30 °C. It is perhaps no wonder then that the alpine glaciers have been retreating for over a century, while those in Norway and New Zealand, where the population density (and also the economic activity) is much lower, have remained more stable. But what this warming is not due to is increased CO₂ levels in the atmosphere or an enhanced Greenhouse Effect. That is a completely separate issue.

The conclusion we can draw from this is that, in most developed countries, warming of up to 1.0 °C has occurred since pre-industrial times, and this warming is solely a result of industrial activity and the heat that is generated as a result of that activity. This will occur irrespective of the energy type or source used because it is the heat that is directly warming the planet, not increases in the concentration of waste gases that then add to the Greenhouse Effect. This also means that when the energy usage goes down, the temperature should go down.

This has major implications for future energy policy because it means that nuclear power and most renewables are no better than fossil fuels. It also means that the efficiency of energy generation is as important as the quantity of energy generation in determining the amount of warming.

Fig. 14.5: Efficiencies of different power sources.

As an example of the impact of energy efficiency consider the case of solar photovoltaics. The relative efficiencies of different power sources are illustrated in Fig. 14.5 above. Of these photovoltaics are among the least efficient. They are in fact only about 15% efficient, meaning that for every 100 joules of energy they harvest from the Sun, they only create 15 joules of electricity. Yet in order to do this solar cells need to be 95% efficient in terms of absorbing incoming solar radiation. In other words their albedo needs to be less than 0.05. That means that for every 100 joules of solar radiation that falls on a solar cell, 5 joules is reflected back into space, 15 joules is turned into electricity (which will then become surface heat at the point of use), and 80 joules becomes waste surface heat in the solar cell.

Now a fashionable policy proposal at the moment is to put large numbers of photovoltaics in the Sahara Desert and then pump the electricity they produce to wherever it is needed. The problem is that not only will the electricity generated heat the location of its end user, but the solar cells will heat up the desert by decreasing the local albedo from 0.40 to 0.05. That is a double whammy. It is global warming without the need for CO₂. Now you don't hear much about that from climate scientists.

13. The Earth's energy budget

In order to understand how the Earth is heating up, you need to understand why it is warm in the first place. That means you need to know where the energy is coming from and where it is going. That is the basis of the Earth's energy budget or energy balance.

The purpose of this post is to analyse that energy balance, and to determine which parts of it can change, and what the effects of those changes are likely to be. Specifically, this post will try to relate various possible changes in the energy balance to any consequential changes in global temperatures. In so doing, it will also be necessary to critically ascertain the degree of confidence that there is surrounding the various estimates, and measurements, regarding the energy flows in the different parts of the atmosphere.

As I pointed out in the last post, virtually all the energy that is present on Earth originated in the Sun. The amount of energy per second arriving from the Sun at the top of the Earth’s atmosphere is 1361 watts per square metre (W/m²), and as I also pointed out, because the area this energy is ultimately required to heat up (4πr² where r is the Earth's radius) is four times the cross-sectional area that actually captures the energy (πr²), that means that the mean power density (remember: power is rate of flow of energy) that the Earth receives is only a quarter of the incoming 1361 W/m², or about 341 W/m². However as I also showed in Fig. 12.1, not all this energy reaches the Earth's surface. In fact only about 161 W/m² does. The rest is either absorbed by the atmosphere (78 W/m²), reflected by the atmosphere and clouds (79 W/m²), or is reflected by the Earth's surface (23 W/m²). This is shown diagrammatically in Fig. 13.1 below.

  

Fig. 13.1: The Earth's energy budget as postulated by Trenberth et al. (2009).

The image in Fig. 13.1 is taken from a 2009 paper by Kevin Trenberth, John Fasullo and Jeffrey Kiehl (Bull. Amer. Meteor. Soc. 90 (3): 311–324). It is not necessarily the most definitive representation of the energy flows (as we shall see there are other models and significant disparaties and uncertainties in the numbers), but it is probably the most cited. The data it quotes specifically relates to the energy budget for the period March 2000 - May 2004.

Fig. 13.2: The Earth's energy budget as postulated by Kiehl and Trenberth (1997).

The 2009 Trenberth paper is not the first or last paper he has produced on the subject. The energy budget it describes is actually a revision of an earlier attempt from 1997 (J. T. Kiehl and K. E. Trenberth, Bull. Amer. Meteor. Soc., 78, 197–208) shown in Fig 13.2 above, and has since been revised again in 2012 (K. E. Trenberth and J. T.  Fasullo, Surv. Geophys. 33, 413–426) as shown in Fig. 13.3 below.

Fig. 13.3: The Earth's energy budget as postulated by Trenberth and Fasullo (2012).

The only real difference between the energy budget in Fig. 13.3 and that from 2009 in Fig. 13.1 is the magnitude of the atmospheric window for long wave infra-red radiation (revised down from 40 W/m² to 22 W/m²), but I still think this highlights the level of uncertainty that there is regarding these numbers. This is further emphasised by a contemporary paper from Stephens et al. (Nature Geoscience 5, 691–696 (2012) ) shown below in Fig. 13.4.

Fig. 13.4: The Earth's energy budget as postulated by Graeme L. Stephens et al. (2012).

As the 2009 Trenberth paper appears to be the most cited it is probably best to use this as the basis for the following discussion, but to bear in mind the amount of uncertainty regarding the actual numbers.

In Fig. 13.1 the three most significant numbers are those for the direct surface absorption from the Sun (161 W/m²), the upward surface radiation (396 W/m²), and the long-wave infra-red back radiation due to the Greenhouse Effect (333 W/m²). Of these it is the upward surface radiation (396 W/m²) that determines the temperature but its value is set by the other two.

As I explained in the last post the emission of electromagnetic radiation from a hot object is governed by the Stefan-Boltzmann law as shown below

  

(13.1)

where I(T) is the power density (per unit area) of the emitted radiation, σ = 5.67 x 10^-8 Wm^-2K^-4 is the Stefan-Boltzmann constant, and the term ε is the relative emissivity of the object. The emissivity defines the proportion of the emission from that object at that wavelength compared to a black body at the same temperature, and it varies with wavelength. It is also different for different materials. In the case of planet Earth, it is generally assumed to be very close to unity all over the surface for all emission wavelengths, but this is not always the case.

It is Eq. 13.1 that allows us to determine the surface temperature (T = 289 K) from the upward surface radiation (396 W/m²) or visa versa. It also allows us to calculate the change in upward surface radiation that would result from a given increase in the surface temperature. It turns out that an increase in surface temperature of 1 °C would necessitate the upward surface radiation increasing from 396 W/m² to 401 W/m², in other words a 1.39% increase. A 2 °C increase would require a 2.80% increase in the upward surface radiation.

I also explained in the last post how the total upward surface radiation (I_T) was related to the direct surface absorption from the Sun (I_o) via a feedback factor f which represented the fraction of upward surface radiation that was reflected back via the Greenhouse Effect.

(13.2)

This model assumed that all the energy absorbed by the greenhouse gases came from one source, though, namely surface upward radiation, and was driven by a single input, the surface absorption of solar radiation, I_o. As Fig. 13.1 indicates, this is not the case. This means that Eq. 13.2 will need to be modified.

The aim here is to determine what changes to the energy flows in Fig. 13.1 would result in a particular temperature rise, specifically a rise of 1 °C in the surface temperature. Realistically, there are only three things that could bring about any significant change. The first is a change in the amount of energy coming from the Sun. The second is is a change in the direct absorption of radiation at the surface, I_o. The third is a change in the strength of the Greenhouse Effect, f.


Case 1: Changes to the incoming solar radiation.

This is probably the easiest of the three propositions to analyse. If the incoming solar radiation at the top of the atmosphere were to change by 1.39%, then we would expect virtually all the projected heat flows in Fig. 13.1 to change by the same amount, including the upward surface radiation (from 396 W/m² to 401 W/m²). This is because almost all the scattering mechanisms and absorption processes in Fig. 13.1 are linear and proportional. The two exceptions are likely to be the thermals (17 W/m²) and the evapo-transpiration (80 W/m²), the former of which will be governed more by temperature differences, and the latter by the non-linear Clausius-Clapeyron equation. While changes to these two components are likely to be linear for small changes, they are unlikely to be proportional. However, as the changes to these two components are likely to be fairly small and comparable to other errors, we can probably ignore these deficiencies. So, if the incoming solar radiation (1361 W/m²) were to increase by 1.39% we could see a global temperature rise of 1 °C.

The problem is that there is no evidence to suggest the Sun's solar output has changed by anything like 1.39% over the last 100 years, and no obvious theoretical mechanism to suggest that it could. The only evidence of change is from satellite measurements over the last 40 years or so that suggest an oscillation in solar output with an eleven year period and an amplitude of about 0.05% (see Fig. 13.5 below). This would give a maximum temperature change of about 0.1 °C.

Fig. 13.5: Changes in the Sun's output since 1979 (from NOAA).

The only other known mechanism is the Milankovitch cycle. This can produce temperature oscillations of over 10 °C in magnitude (peak to trough) but is only seen over 120,000 year cycles (see red curve in Fig. 13.6 below). 

Fig. 13.6: Changes to temperature in the southern oceans (red curve) derived from isotope analysis of the Vostok ice core in Antarctica.

These temperature oscillations are mainly due to changes in the Earth's orbit around the Sun (changes to a more elliptical ortbit), or changes in the Earth's angle of inclination or tilt, or an increased precession that then exposes the polar regions to higher levels of solar radiation. Such effects may be responsible for the cycle of ice ages, but cannot be responsible for changes thought to have happened over the last 100 years. As the data in Fig. 13.6 indicates, even the periods of fastest climate change amounted to only a 10 °C increase over 10,000 years, or 0.1 °C per century, and we do not appear to be in one of those warming periods. If anything, the planet should be slowly cooling by about 0.01 °C per century.

The conclusion, therefore, is that global temperatures may fluctuate by 0.1 °C across the decade due to changes in solar output, but there is no evidence or credible mechanism that would support a long-term warming trend.


Case 2: Changes to the direct absorption of radiation at the surface.

The second possible driver of global warming comes from changes at the surface, specifically to the thermal energy absorbed there, I_o. This will then impact on the total upward surface radiation I_T and thereby also on the back radiation. According to Eq. 13.2 the changes to I_o and I_T should be proportional. As Eq. 13.1 indicates that a 1 °C change to the surface temperature, T_o, should result in a 1.39% change to I_T, it follows that a 1.39% change to I_o should result in a 1 °C change to T_o. Unfortunately there are three additional complications that we need to consider: the thermals (I_th = 17 W/m²), the evapo-transpiration (I_E = 80 W/m²), and the incoming solar radiation absorbed by the atmosphere (I_A = 78 W/m²).

The thermals (17 W/m²) and evapo-transpiration (80 W/m²) in Fig. 13.1 transfer heat from the surface into the upper atmosphere (top of the tropopause) by mass transfer (convection) rather than radiation. This may potentially provide a route for heat to escape from the Earth via a by-passing of the greenhouse mechanism. However, I would expect this energy to eventually get dumped in the atmosphere somewhere before the top of the tropopause (at a height of 20 km). When this happens it will merely add to the long-wave infra-red radiation being emitted from the surface, and so should still be reflected by the greenhouse gases. So while these heat sources will not contribute to the surface temperature as defined in Eq. 13.1, they should be included in the feedback factor f in Eq. 13.2.

So too will some of the power absorbed by the atmosphere directly from the incoming solar radiation (78 W/m²). Here again things are complicated because if the energy is absorbed before the bottom of the stratosphere (at 20 km altitude), the Greenhouse Effect will actually reflect some of that heat back into space. To account for this we can include an additional parameter μ as a variable that specifies the proportion of the incoming solar absorbed by the atmosphere that is absorbed in the lower atmosphere where it can be reflected backwards the surface. The fraction (1-μ) absorbed in the upper atmosphere will escape and therefore will not contribute to the back radiation.

In all there are seven energy terms that we need to consider.

1. Initial surface absorption (I_o = 161 W/m²).
2. Thermals (I_th = 17 W/m²).
3. Evapo-transpiration (I_E = 80 W/m²).
4. Upward surface long-wavelength radiation (I_up = 396 W/m²).
5. Long-wavelength back radiation (I_RF = 333 W/m²).
6. Incoming solar absorbed by the atmosphere (I_A = 78 W/m²).
7. Net radiation permanently absorbed by the Earth's surface (I_net = 0.9 W/m²).

We must then consider energy conservation at the surface and in the atmosphere. At the surface the law of conservation of energy (1st law of thermodynamics) requires that

 (13.3)

while in the atmosphere similar considerations mean that the total energy entering the atmosphere must equal the total that is emitted. As f is the proportion that is reflected back it follows that

(13.4)

The parameter μ is a variable that specifies the proportion of the incoming solar absorbed by the atmosphere (I_A) that is absorbed in the lower atmosphere where it can be reflected back towards the surface. The fraction (1-μ) absorbed in the upper atmosphere will escape and therefore will not contribute to I_RF. It therefore follows that

(13.5)

Using Eq. 13.5 we can work out a value for f, but only if we know μ, which we don't. However, using Eq. 13.4 and the knowlege that μ must lie in the range 0 <  μ < 1, we can say that f will be in the range 0.583 to 0.675 and that when μ = 0.5, f = 0.626. This allows us to estimate the change required in I_o to generate a 1 °C change in T_o, but to do that we will need to make some assumptions given the number of variables that there are.

First we can probably assume that f, μ and I_A remain unchanged even when I_o changes. We know that a 1 °C increase in T_o will result in a 1.39% increase in I_up to 401.5 W/m² and a 2 °C increase in T_o will result in a 2.80% increase in I_up to 407.1 W/m². The question is what happens to the thermals (I_th), the evapo-transpiration (I_E) and the net surface absorption (I_net)? They will probably increase as well, but by how much? A good starting point is to assume that they will increase by the same percentage as the upward surface long-wavelength radiation (I_up). A benchmark control is to assume that they stay constant. This gives us the following two scenarios.

If I_th, I_E and I_net scale with I_up and the scaling factor due to the increase in temperature T_o is g, then Eq. 13.5 can be rearranged to give

(13.6)

whereas if I_th, I_E and I_net are constant then

(13.7)

We know that g = 1.0139 for a 1 °C rise in T_o and g = 1.0280 for a 2 °C rise in T_o. So combining the two options in Eq. 13.56 and Eq. 13.7 implies that I_o is in the range 162.8-163.9 W/m². That implies an excess direct heating at the surface of ∆I_o = 2.33 ± 0.54 W/m², with the error range being set by the range of possible values for f, μ, I_E, I_net and I_th. A 2 °C increase in surface temperature would require a change in direct heating at the surface of ∆I_o = 4.69 ± 1.09 W/m².

The conclusion, therefore, is that a 1 °C increase in global temperatures would require an increase in the initial surface absorption of ∆I_o = 2.3 ± 0.5 W/m². How this might be achieved will be explored further in the next post.


Case 3: Changes to the feedback factor.

The most obvious and heavily reported mechanism by which global temperatures could increase is via changes to the Greenhouse Effect due to increased carbon dioxide concentrations in the atmosphere. The specific change that will ensue will be in the value of the feedback term, f, and hence the value of the back radiation, I_RF. As in the previous case, some of the heat flow parameters in Fig. 13.1 would change and some would stay the same. For example, we can confidently assume that I_A and I_o will remain unchanged, but if f changes, so might μ. But as before, the main question is what happens to the thermals (I_th) and the evapo-transpiration (I_E)?

Rearranging Eq. 13.5 once more gives

 (13.8)

while for the case that I_th, I_E and I_net are constant we get

 (13.9)

It turns out there is very little difference in the results using the two methods. The biggest factor affecting f is the value of μ. When there is no warming (g = 1.0) f = 0.629. A warming of 1 °C (g = 1.0139) requires f to increase to 0.634, and a warming of 2 °C (g = 1.0280) requires f to increase to 0.638. These values all correspond to values for μ of 0.5, but the possible spread of values for μ leads to an error in f of ±0.047 in all cases.

What this shows is that the increase in feedback factor needed for a 1 °C rise in global temperatures will be about 0.005. This is a small change, but at the end of the last post (Post 12) I calculated that the fraction of the long-wave infra-red radiation that could be absorbed and reflected by the carbon dioxide in its main absorption band (the frequency range 620-720 wavenumbers or the wavelength range 13.89 - 16.13 μm). The result was at best 10.5%. This implies that only about 15% of the Greenhouse Effect is due to CO₂, and the rest is due to other agents, mainly water vapour.

The conclusion, therefore, is that a 1 °C increase in global temperatures would require an increase in the width or strength of the carbon dioxide absorption band by at least 5% relative to its current size in order achieve this temperature rise.


The final point to note is the size of the potential measurement errors in the various energy flows, and the effect of rounding errors. A particular egregious anomaly occurs at the top of the atmosphere in Fig. 13.1 (and remains uncorrected in Fig. 13.3) where the rounded value of the incoming solar (341 W/m²) radiation balances the rounded outgoing values (239 W/m² and 102 W/m²). This is inconsistent with the rest of the diagram as there should be a 0.9 W/m² difference to account for the net absorption at the surface. In the more exact values quoted (341.3 W/m², 238.5 W/m² and 101.9 W/m²) this difference is specified correctly. So the problem is a rounding issue initially, but it then has a knock-on effect for the values quoted within the atmosphere.

For consistency it would therefore be better in this instance to round the 238.5 W/m² value down (to 238 W/m²) rather than up (to 239 W/m²). That would ensure that there was a net inflow of about 1 W/m² that balanced the net absorbed value at the surface (0.9 W/m²). It would also eliminate the false imbalance within the atmosphere itself. Here the net inflow should balance the net outflow (currently there is a 1 W/m² deficit). There can be no 0.9 W/m² energy gain in the atmosphere otherwise the atmosphere would heat up, and heat up by more than 2.7 °C per annum. What should remain invariant at various points from the surface to the top of the atmosphere is the following energy balance

(13.10)

where I_TOA = 238.5 W/m² is the outgoing long-wave radiation at the top of the atmosphere. A correction for this error requires the stated value for the power emitted upwards by the atmosphere (169 W/m²) in Fig. 13.1 to be reduced to 168 W/m².

It is also important to note that some of the errors in the energy flows in Fig. 13.1-Fig.13.4 are considerable, either in magnitude, or as a percentage. A comparison of the data in Fig. 13.1 and Fig. 13.4 illustrates how variable the results can be. The back radiation values, for example, do not agree within the noted error range, and the net surface absorption is 50% higher in Trenberth's papers than it is in the Stephens paper (Fig. 13.4). I shall look at the net surface absorption in more detail later as it has important implications for sea level rise, but the fact that this value is so small, not just relative to the other energy flows, but also in comparison to their errors, is a cause for concern with respect to its own accuracy. It should also be noted that the net surface absorption should also be measurable directly at the top of the atmosphere using satellite technology to measure both the solar energy going in and the Earth's thermal energy flowing out. Yet the discrepancies seen there between incoming and outgoing energy flows currently far exceed 0.9 W/m². The result is that most of the energy flows shown in Fig. 13.1-Fig.13.4 are at best estimates, and are often based more on climate models than on actual data.

9. Fooled by randomness

Is global warming real? That is probably a justifiable question given what I revealed in the last post about breakpoint alignment. But what I am going to demonstrate here and over the next two or three posts should also make you question everything you think you know about climate change. The first topic I am going to explore is a concept that most physicists and mathematicians are all too familiar with, but which appears to be totally off the radar of climate scientists: chaos theory and fractal geometry.

Fig. 9.1:  Record 1.

First a test. Look at the dataset above (Fig. 9.1) and the one below (Fig. 9.2). Can you tell which one is a real set of temperature data and which one is fake?

Fig. 9.2:  Record 2.

Okay, so actually it was a trick question because they are both real sets of data. In fact they are both from the same set of station data, and they are partially from the same time period as well, but there is clearly a difference. The difference is that the data in Fig. 9.1 above is only a small part of the actual temperature record but the data from Fig. 9.2 is from the entire record. The data in Fig. 9.1 is taken from the Christchurch station (Berkeley Earth ID - 157045) and is monthly data for the period 1974 - 1987. The data in Fig. 9.2 is from the same record but for the time interval 1864 - 2013: it has also been smoothed with a 12 month moving average. Yet they look the very similar in terms of the frequency and height of their fluctuations - why? Well, what you are seeing here is an example of self-similarity or fractal behaviour. The temperature record for Christchurch is a one-dimensional fractal, and so for that matter is every other temperature record.

Self-similarity is common in nature. You see it everywhere from fern leaves and cauliflowers to clouds and snowflakes. It is observed when you magnify some objects and look at them in greater detail, only to find, to your surprise, that the detail looks just like a smaller version of the original object. This is known as self-similarity: the object looks like itself but in microcosm. It is also an example of scaling behaviour. There is usually a fixed size ratio between the original and the smaller copies from which it is made.

In order to make the smoothed data in Fig. 9.2 look similar to the original data in Fig. 9.1 two scaling adjustments were made. First the time scale on the horizontal axis in Fig. 9.2 was shrunk by a factor of twelve. This is to compensate for the smoothing process which effectively combines twelve points into one. The second was to scale up the temperature axis in Fig. 9.2 by a factor 12 ^0.275. The reason for the power of 0.275 will become apparent shortly, but it is important as it has profound implications for the noise level we see in temperature records over long time periods (i.e. centuries).

To demonstrate the scaling behaviour of the temperature record we shall do the following. First we smooth the data with a moving average of length say two points and then calculate the standard deviation of the smoothed data. Then we repeat this for the original data, but with a different number of data points in the moving average and again calculate the standard deviation of the new smoothed data. After doing this for six or seven different moving averages we plot a graph of the logarithm of the standard deviation versus log(N) where N is the number of points used each time for the moving average. The result is shown below in Fig. 9.3.

Fig. 9.3:  Plot of the standard deviation of the smoothed  anomaly data against the smoothing interval N for temperature data from Christchurch (1864-2013).

The important feature of the graph in Fig. 9.3 is that the data lies on an almost perfect straight line of slope -0.275 (remember that number)? I have to confess that even I was shocked by how good the fitting was when I first saw it, particularly given how imperfect temperature data is supposed to be. What this graph is illustrating is that as we smooth the data by a factor N, the noise level is reducing by a factor N^-0.275. But is this reproducible for other data? Well the answer appears to be, yes.

Fig. 9.4:  Plot of the standard deviation of the smoothed  anomaly data against the smoothing interval N for temperature data from Auckland (1853-2013).

The graph above (Fig. 9.4) shows the same scaling behaviour for the station at Auckland (Berkeley Earth ID = 157062) while the one below (Fig. 9.5) illustrates it for the station at Wellington (Berkeley Earth ID = 18625). The gradients of the best fit lines (i.e. the power law index in each case) are -0.248 and -0.235 respectively. This suggests that the real value is probably about -0.25.

Fig. 9.5:  Plot of the standard deviation of the smoothed  anomaly data against the smoothing interval N for temperature data from Wellington (1863-2005).

But it is the implications of this that are profound. Because the data is such a perfect fit in all three cases, we can extrapolate to longer smoothing operations such as one hundred years. That corresponds to a scaling term of 1200 (because it is equal to 1200 months and thus is 1200 greater in period than the original data) and a noise reduction of 1200 ^0.25 = 5.89. In other words, the noise level on the underlying one hundred year moving average is expected to be about six times less than for the monthly data. This sounds like a lot but the monthly data for Christchurch has a noise range of up to 5 °C (see Fig. 9.6 below), so this implies that the noise range on a 100 year trend will still be almost 1 °C. Now if that doesn’t grab your attention, I have to wonder what will? Because it implies that the anthropogenic global warming (AGW) that climate scientists think they are measuring is probably all just low frequency noise resulting from the random fluctuations of a chaotic non-linear system.

Fig. 9.6:  The temperature anomaly data from Christchurch (1864-2013) plus a 5-year smoothing average.

What we are seeing here is a manifestation of the butterfly effect which, put simply, says that there is no immediate causal link between some current phenomena such as the temperature fluctuations we see today and current global events. This is because the fluctuations are actually the result of dynamic effects that played out long ago but which are only now becoming visible.

Fig. 9.7:  Typical mean station temperatures for each decade over time.

To illustrate the potential of this scaling behaviour further we can use it to make other predictions. Because the temperature record exhibits self-similarity on all timescales, it must do so for long timescales as well, such as centuries. So we can predict what the average temperature over hundreds of years might look like (qualitatively but not precisely) just by taking the monthly data in Fig. 9.6, expanding the time axis by a factor of 120 and shrinking the amplitude of the fluctuations by a factor of 120 ^0.25 = 3.310. The result is shown in Fig. 9.7 above. Because of the scaling by a factor of 120, each monthly data point in Fig. 9.6 becomes a decade in Fig. 9.7. The data in Fig. 9.7 thus indicates that the average temperature for each decade can typically fluctuate by about ±0.5 °C or more over the course of time.

Fig. 9.8:  Typical mean station temperatures over 100 years over time.

Then, if we smooth the data in Fig. 9.7, we can determine the typical fluctuations over even longer timescales. So, smoothing with a ten point moving average will yield the changes in mean temperature for 100 year intervals as shown in the graph above (Fig. 9.8). This again shows large fluctuations (up to 0.5 °C) over large time intervals. But what we are really interested in from a practical viewpoint is the range of possible fluctuations over 100 years as this corresponds to the timeframe most quoted by climate scientists.

To examine this we can subtract from the value at current time t the equivalent value from one hundred years previous, i.e. ∆T = T(t) - T(t-100).

Fig. 9.9:  Typical change in the 100-year mean temperature for a time difference of 100 years.

So, as an example we may wish to look at the change in mean temperature from different epochs, say from one century to the next. Well the data in Fig. 9.9 shows just that. Each data point represents difference between the mean temperature over a hundred years at that point in time with the same value for a hundred years previous. Despite the large averaging periods we still see significant temperature changes of ± 0.25 °C or more. However, if we compare decades in different centuries it is even more dramatic.

For example, Fig. 9.10 below predicts the range of changes in the average decadal temperatures from one century to the next, in other words, the difference between the 10-year mean temperature at a given time t and the equivalent decadal mean for a time one hundred years previous. What Fig. 9.10 indicates is that there is a high probability that the mean temperature in the 1990s could be 0.5 °C higher or lower that the mean temperature in the 1890s, and this is just as a consequence of low frequency noise.

Fig. 9.10:  Typical change in mean decadal temperature for a time difference of 100 years.

So why have climate scientists not realized all this? Maybe it's because their cadre comprise more geography graduates and marine biologists than people with PhDs in quantum physics. But perhaps it is also due to the unique behaviour of the noise power spectrum.

If the noise in the temperature record behaved like white noise it would have a power spectrum that is independent of frequency, ω. If we define P(ω) to be the total power in the noise below a frequency, ω, then the power spectrum is the differential of P(ω). For white noise this is expected to be constant across all frequencies up to a cutoff frequency ω_o.

(9.1)

This in turn means that P(ω) has the following linear form up to the cutoff frequency ω_o.

P(ω) = aω

(9.2)

where a is a constant. The cutoff frequency is the maximum frequency in the Fourier spectrum of the data and is set by the inverse of the temporal spacing of the data points. If the data points are closer together then the cutoff frequency will be higher. Graphically P(ω) looks like the plot shown below in Fig. 9.11, a continuous horizontal line up to the cutoff frequency ω_o.

Fig. 9.11: The frequency dependent power function P(ω) for white noise.

The effect of smoothing with a moving average of N points is to effectively reduce the cutoff frequency by a factor of N because you are merging N points into one. And because the noise power is proportional to the noise intensity, which is proportional to the square of the noise amplitude, this means that the noise amplitude (as well as the standard deviation of the noise) will reduce by a factor equal to √N when you smooth by a factor of N.

For a 100-year smoothing the scaling factor compared to a monthly average is 1200, and so the noise will therefore reduce by a factor of 1200 ^0.5 = 34.64 . That means the temperature fluctuations will be typically less than 0.1 °C. This is probably why climate scientists believe that the long term noise will always be smoothed or averaged out, and therefore why any features that remain in the temperature trend must be "real". The problem is, this does not appear to be true.

Instead the standard deviation varies as N ^-0.25. So the intensity of the noise varies as N ^-0.5 and P(ω) will increase as √N. It therefore follows that the power spectrum is not independent of frequency as is the case for white noise, but instead varies with frequency as

(9.3)

and P(ω) will look like the curve shown in Fig. 9.12 below.

Fig. 9.12:  The frequency dependent power function P(ω) for temperature data.

The net result is that the random fluctuations in temperature seen over timescales of 100 years or more are up to six times greater in magnitude than most climate scientists probably think they will be. So the clear conclusions is this: most of what you see in the smoothed and averaged temperature data is noise not systemic change (i.e. warming). Except, unfortunately, most people tend to see what they want to see.