Back radiation versus CO2 as the cause of climate change H Douglas Lightfoot1 and Orval A Mamer2
Energy & Environment 0(0) 1–12 ! The Author(s) 2017 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0958305X17722790 journals.sagepub.com/home/eae
Abstract Robust scientific evidence shows the sun angle controls water vapour content of the atmosphere, the main component of back radiation, as it cycles annually. Water vapour content measured as the ratio of the number of water molecules to CO2 molecules varies from 1:1 near the Poles to 97:1 in the Tropics. The effect of back radiation on Earth’s atmosphere is up to 200 times larger than that of CO2 and works in the opposite direction. Thus, if CO2 has any effect on atmospheric temperature and climate change we show it is negligible. Consequently, current government policies to control atmospheric temperature by limiting consumption of fossil fuels will have negligible effect. Measured data reported in IPCC report Climate Change 2013: The Physical Science Basis (AR5) indicate increased water vapour content of the atmosphere is the cause of the 0.5 C temperature increase from the mid-1970s to 2011. Keywords Back radiation, water vapour, carbon dioxide, CO2, sun angle, downwelling
Introduction The stored solar energy in coal, oil and natural gas has provided the fuel and chemicals that make the world a much better and safer place for all of us. The beneﬁcial effect of these fuels on the welfare of humans is profound and cannot be overestimated. They lifted much of the world’s population out of poverty.1 With this background, the severe consequences of the current energy policy to drastically reduce the consumption of fossil fuels are a cause for concern. Is such a drastic policy necessary? Is carbon dioxide (CO2) really causing signiﬁcant climate change? To answer these questions, we studied the reports by the Intergovernmental Panel on Climate Change (IPCC), the writings of scientists who promote CO2 as the cause of climate 1 2
The Lightfoot Institute, Baie-D’Urfe, Canada Goodman Cancer Research Centre of McGill University, Montreal, Canada
Corresponding author: H Douglas Lightfoot, The Lightfoot Institute, 8 Watterson, Baie-D’Urfe, QC H9X3C2, Canada. Email: email@example.com
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change and the writings of those scientists who oppose the concept that CO2 causes climate change. In the process, we developed a broad base of knowledge and learned a great deal about the many aspects and facets of climate change. Today, many scientists studying climate are experts in small and important segments and are not aware of the overall picture of the Earth’s climate system. We selected sets of empirical data and connected them in new ways to give a coherent and logical illustration of how the sun controls back radiation through water vapour, its main component, and, thereby, atmospheric temperature. Today, the burning of fossil fuels releases upwards of 30 billion tonnes of CO2 annually into the atmosphere along with pollutants such as nitrous oxides, carbon monoxide and volatile organic compounds.2,3 These pollutants can be dangerous to our health and must be monitored and controlled. In contrast, CO2 is essential to life because it is a nutrient for plants that provide our food; plants are at the bottom of the food chain for all living things. In spite of the positive aspects of CO2, there are discordant opinions in the literature about whether or not it can cause dangerous climate change. This study is only about CO2 and climate change because the concern with pollutants from burning of fossil fuels is a separate issue. The issue of how soon the world can transition away from fossil fuels for transportation and other purposes is an open question regardless of worldwide efforts to reduce the consumption of fossil fuels.4 This issue is important but is beyond the scope of this study. We start by plotting the empirical relationship between water vapour concentration and back radiation, which is measured in units of Watts per square metre (W m2) as in Figure 1. The difference in radiative forcing (RF) between two concentrations of CO2, also measured in units of W m2, is already known over the area of interest and, is expressed as RF ¼ 5:22lnðC=Co Þ
where 5.22 is a constant, RF is the difference in RF, or warming effect, between two concentrations of CO2, C is the higher concentration of CO2 and Co is the lower concentration. Section 6.3.5 of the IPCC Third Assessment Report5 gives the constant as 5.35. However, to obtain 1.66 W m2 in Figure SPM.2 of the Fourth Assessment Report (AR4)6 the IPCC appears to have used a constant of 5.22. This is the constant used in this study. Back radiation is the term used in FAQ 1.1, Figure 1 (p. 96), of AR46 to describe the energy radiated back to the Earth (RF) by the total of all of the greenhouse gases (GHG) including water vapour, CO2, methane, nitrous oxide and the smaller trace gases see IPCC6. In Figure 2, i.e. Figure 2.11 of AR5,7 this radiation is referred to as ‘thermal down surface’ and in the text of AR5 it is referred to as ‘Downwelling Longwave Radiation’. To avoid confusion and provide consistency, we use the term ‘back radiation’ throughout this study. Back radiation, water vapour concentration and atmospheric temperature follow the sun angle daily and over the seasons, increasing as the sun angle increases and falling as it decreases. Water vapour concentration is measured as parts per million by volume (ppmv) or by the ratio of the number of water vapour molecules for each CO2 molecule (H2O/CO2 ratio). The purpose of this study is to present robust evidence that the sun is working with water vapour to control the Earth’s climate and to show that the inﬂuence of CO2 on atmospheric temperature is so small as to be negligible.
Lightfoot and Mamer
Figure 1. Back radiation versus water vapour concentration for six locations.
An empirical relationship between back radiation and water vapour Figure 1 is a plot of the measurements of back radiation against water vapour concentration calculated from measurements of atmospheric temperature and relative humidity (RH). The H2O/CO2 ratio along the top of the plot is based on a CO2 concentration of 400 ppmv. Because water vapour is the most abundant GHG, it is reasonable to plot water vapour concentration against back radiation. Back radiation is available in Wild et al.8 for 12 locations around the Earth each with 12 points measured as monthly averages. Only the six locations plotted in Figure 1 have the detailed temperature and RH records necessary to calculate the ﬁrst of the month corresponding values of water vapour concentration. The average atmospheric temperature is available for the South Pole but not the corresponding RH; the average RH for the McMurdo Station in Antarctica was used. It is evident from Figure 1 that (1) the upper limit to the back radiation of GHGs is approximately 420 W m2 at water vapour concentration of approximately 32,000 ppmv, or an H2O/CO2 ratio of 80; (2) the lowest back radiation is 97 W m2 at the South Pole and (3) small increases in water vapour give the most increase in back radiation above the Arctic and Antarctic circles because of the steepness of the curve. These areas together are only 8.4% of the Earth’s surface and have little effect on the Earth’s average atmospheric temperature.
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Figure 2. On average one quarter of the sun’s energy input to the Earth goes to evaporate water at the surface of the Earth.
One quarter of the sun’s energy evaporates water The global mean energy budget, Figure 2, shows that on average one quarter of the sun’s energy input to the Earth goes to evaporate water at the surface of the Earth. The averages of Figure 2 do not show the active and dynamic nature of the back radiation that can be from 97 W m2 at the South Pole in winter to 420 W m2 in the Tropics in summer, as in Figure 1, depending on the season and location on Earth. The dynamism of the hydrological cycle is also concealed by averages. As the Earth turns under the sun, the high water vapour evaporation rate, an average of 0.13 kg h1 m2, and subsequent condensation causes the hydrological cycle to churn and spawn about 2000 thunderstorms every day, some of which can become hurricanes and tornadoes. When this water vapour condenses in the upper atmosphere and often far from where it originates, it releases the heat required to evaporate it. This activity is termed ‘weather’ as it moves vast quantities of heat around the Earth from where there is more to where there is less,9 and, heat movement brings temperature changes.
The ratio of water molecules to CO2 molecules, the H2O/CO2 ratio The physical properties of CO2 and water vapour are quite different over the range of temperatures and pressures experienced on earth. CO2 is always in the gaseous phase, acts as an ideal gas and obeys the physical gas laws of Boyle (1662) and Charles (1780s). Increasing the temperature of 1 kg of CO2 by 1 C requires 833 J that are released when
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Table 1. Latitude zones, regions and % of Earth’s area. Latitude zones
Percent of Earth’s area
North Frigid North Temperate Torrid South Temperate South Frigid
Above Arctic Circle Arctic Circle to Tropic of Cancer Tropic of Cancer to Tropic of Capricorn Tropic of Capricorn to Antarctic Circle Below Antarctic Circle
4.2 25.9 39.8 25.9 4.2
Figure 3. The named circles of the Earth and the 11 cities selected on or between them.
the CO2 is cooled. On the other hand, water is not an ideal gas and can exist as a solid, liquid or gas. To freeze 1 kg of water requires the removal of 333,550 J that are released when the ice melts. To evaporate 1 kg of water requires 2,257,000 J. To put these numbers into perspective, when 1 kg of water vapour condenses it releases 2700 times more heat energy than 1 kg of CO2 cooling by 1 C. It is appropriate to calculate the ratio of water molecules to CO2 molecules, H2O/CO2 ratio, as a convenient measure of water vapour concentration at various locations and month by month through the seasons. To generate representative H2O/CO2 ratios, two cities in each of the ﬁve latitude regions in Table 110 were selected. The speciﬁc cities are given in Figure 3 and shown relative to the appropriate named circle. Where possible, one of the two cities in each zone was selected because it is located near an ocean and the other near mid-continent. For convenience, we selected the data for the ﬁrst day of each of the 12 months for our study. It is likely slightly different results would be obtained with other days of the month and other combinations of cities. The dry bulb air temperatures and RH are inputs to a psychrometric chart or program, such as that offered by MegaWatSoft.11 This is a proven and reliable method to calculate the weight of water vapour per kilogram of dry air. For example, in Montreal on 1 July at noon, when the average high temperature is 24 C and the corresponding RH is 57%, the MegaWatSoft psychrometrics program calculates 0.01081 kg, or 0.601 mole, of water vapour per kilogram of dry air. The CO2 baseline concentration of approximately 400 ppmv at the time of the calculation is equivalent to 0.0138 mole/kg of dry air. Thus, the H2O/CO2 ratio is 0.601/0.0138 or 43.5 molecules of water vapour for each molecule of CO2.
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Table 2. Average relative humidity for the first day of the month. The upper line for each city is for the high temperature of the day and lower line in italics is for the low temperature the day. Latitude regions
Above Arctic circle 66.5 N
79 79 69 68 71 76 75 86 58 88 57 68 75 92 45 89 22 47 66 88 57 84
78 79 66 68 66 74 70 86 54 89 64 74 71 91 41 83 23 49 63 88 58 86
73 79 62 66 62 72 63 86 52 85 66 77 70 92 40 85 24 49 63 88 59 85
68 80 59 70 56 71 59 86 56 84 67 78 72 92 48 91 24 52 65 89 62 87
65 81 61 76 53 72 55 84 59 85 68 79 74 91 56 94 28 60 66 91 66 87
64 81 54 77 54 77 52 82 66 86 69 80 73 90 57 93 34 71 65 91 70 86
68 84 52 78 57 81 48 81 75 88 68 81 72 89 53 90 34 73 63 91 71 88
70 88 59 83 58 82 45 81 77 89 66 80 73 89 52 89 27 62 62 90 70 87
72 88 66 86 60 84 47 83 78 90 65 78 74 89 47 88 21 50 63 89 64 87
75 85 74 84 63 83 55 85 74 90 61 73 73 91 43 88 19 45 65 89 61 85
78 81 77 78 66 81 68 89 63 89 57 70 74 91 49 92 20 45 65 88 59 84
79 80 71 72 70 79 75 87 60 89 54 67 76 92 51 93 21 47 66 89 57 84
North temperate 45 N
Tropic of Cancer 23.5 N
Equator Torrid, 0
Tropic of Capricorn 23.5 S
South temperate 45 S Below Antarctic Circle, 66.5 S
Rio de Janeiro
Table 2 is constructed to show the average RH for each of the 11 cities for the high temperature for the ﬁrst day of the month as the upper line and for the low temperature for the day in the lower line in italics. For the high temperature of the day, average RH over the year ¼ 59.9%, and for the low temperature, the annual average RH ¼ 81.1%. The combined average RH ¼ 70.5%, which is an approximate average for the Earth. The RH is higher for locations near the ocean indicating average world RH might be higher if representative open ocean locations could be included. Table 3 shows the number of molecules of water vapour per molecule of CO2 for the 11 cities for the average high temperature of the day. The number increases from winter to summer in the Northern Hemisphere and vice versa in the Southern hemisphere. In Table 3, the H2O/CO2 ratio varies from 1:1 to 97:1 depending on the time of year and the latitude. When used with the earth’s average temperature of 14.5 C,12 the RH of 70.5% gives an average of 29 molecules of water vapour per molecule of CO2. This corresponds to approximately 340 W m2 in Figure 1, which is close to and consistent with the average back radiation of 338–348 W m2 in Figure 2, Global mean energy budget.7
The sun angle determines the H2O/CO2 ratio There is little sunlight in winter above the Arctic Circle, such as at Inuvik, Canada, and the average H2O/CO2 ratio is as low as 1:1. In summer it rises to an average maximum of 29:1.
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Table 3. Number of molecules of water vapour per molecule of CO2 based on the RH at the average high temperature of many years for the first day of the month. Latitude regions
Above Arctic circle 66.5 N North temperate 45 N Tropic of Cancer 23.5 N Equator Torrid 0 Tropic of Capricorn 23.5 S South temperate, 45 S Below Antarctic Circle, 66.5 S
Tromso Inuvik Montreal Portland Calcutta Hong Kong Singapore Nairobi Alice Springs Rio de Janeiro Christchurch
69.7 N 68.4 N 45.5 N 45.5 N 22.6 N 22.3 N 1.3 N 1.3 S 23.7 S 22.9 S 43.5 S
9 1 7 18 44 30 78 36 32 77 32
9 1 6 19 44 34 78 37 33 78 35
10 1 7 21 60 42 82 39 31 78 33
11 3 13 24 77 51 84 41 26 71 31
14 8 23 27 86 66 87 42 23 64 27
19 18 32 31 97 72 85 44 21 56 25
26 27 44 37 93 79 79 36 19 54 22
28 29 47 41 90 82 80 35 17 50 23
24 22 41 38 91 80 82 36 17 58 23
19 12 27 35 92 67 80 37 20 60 25
10 4 18 26 69 52 82 40 24 63 27
11 1 11 20 58 36 79 39 27 73 30
Figure 4. Summer and winter sun angles and the H2O/CO2 ratios.
Figure 4 shows sun angles for Inuvik range from below the horizon at 1.86 S in winter to +45.1 N in summer. The highest sun angle corresponds to the highest H2O/CO2 ratio of 29:1 and the lowest angle to the lowest of 1:1. The H2O/CO2 values for Singapore and Nairobi also show the highest ratios occur at the highest sun angles. The difference in H2O/CO2 ratios between summer and winter is larger towards the Poles and smaller towards the equator. The levels of both the summer and winter ratios depend on whether or not there is a relatively warm ocean nearby to provide the water vapour. For example, Tromso is warmed by the Gulf Stream and water vapour is higher in the winter than at Inuvik, which is inland south of the Beaufort Sea. The sun angles for the locations in Figure 1 are given in Table 4. In Figure 1, the triangles representing Boulder overlap the squares representing Hamburg even though Boulder is farther south than Hamburg. The reason is the large difference in elevation between Hamburg at 21 m and Boulder at 1655 m.
Energy & Environment 0(0) Table 4. Sun angles and back radiation for the locations in Figure 1. Sun angle, degrees
Back radiation (W m2)
Kwajalein Bermuda Hamburg Boulder Barrow South Pole Arctic, Antarctic
8.71 N 32.30 N 53.57 N 40.05 N 71.32 N 90 S 66.56 N, S
104.79 81.20 59.93 73.45 42.18 23.5
57.79 34.20 12.93 26.45 4.82 23.5
421 408 315 350 308 135
406 355 293 240 180 97
The sun increased atmospheric water vapour concentration over the mid-1970s to 2011 Measurements indicate the central part of the plot of Figure 1 bulged upwards between the mid-1970s to 2011. Scientists13,14 making contributions to the IPCC report ‘Climate Change 2013: The Physical Science Basis’ (AR5,7 section TFE.1, p. 42 and Figure TS.1, p. 38) report an increase in water vapour concentration as follows: Because the saturation vapour pressure of air increases with temperature, it is expected that the amount of water vapour in air will increase with a warming climate. Observations from surface stations, radiosondes, global positioning systems and satellite measurements indicate increases in tropospheric water vapour at large spatial scales. It is very likely that tropospheric speciﬁc humidity has increased since the 1970s. The magnitude of the observed global change in tropospheric water vapour of about 3.5% in the past 40 years is consistent with the observed temperature change of about 0.5 C during the same period, and the relative humidity has stayed approximately constant.
Figure 5 contains parts of Figure TS.1 (p. 38) of AR5,7 which represent these measured results graphically. Figure 5(a) is a graph of the speciﬁc humidity expressed as g/kg of moist air. Figure 5(b) is the atmospheric temperature corresponding to the speciﬁc humidity. The correlation between the two graphs is visibly striking. Figure 5(c) is the HADCRUT4 15 ofﬁcial temperature plot over the same period and again the correlation between speciﬁc humidity and temperature is striking. The horizontal scales of Figure 5(a) to (c) were adjusted equal for a better visual comparison. The vertical scales of (b) and (c) were adjusted similarly. As water vapour concentration increases by 3.5% over the plot of the curve in Figure 1, the water vapour points move to the right and slightly upwards, especially over the central section. Back radiation increases by an average of 2.5 W m2. The effect of 2.5 W m2 is to evaporate water at the rate of 0.09 kg per day per square meter to slightly increase atmospheric temperature above the annual average level over the period mid-1970s to 2011. This is a reasonable explanation for the cause of the atmospheric temperature increase of 0.5 C.
Lightfoot and Mamer
Figure 5. (a) Specific humidity from AR5 Figure TS.1, (b) temperature anomaly Figure TS.1 and (c) HADCRUT4 temperature record.
Back radiation overrides the effect of CO2 on atmospheric temperature The baseline for CO2 reported on 9 May 2016 of 407.9 parts per million molecules of dry air (ppm) relates to the composition of the atmosphere. The actual number for the concentration measured as parts per million by volume of dry air (ppmv) is slightly lower but close enough that the error is negligible. Thus, the reported number can be used for both deďŹ nitions. The baseline concentration is highest in May and drops by approximately 8 ppmv by September as vegetation removes CO2 from the air over the growing season in the Northern Hemisphere. Because the baseline is measured as ppmv of dry air, the concentration can be further reduced by the addition of water vapour. At the average concentration of water vapour over the central portion of Figure 1, the CO2 concentration would be approximately
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7 ppmv lower. In addition, the level of CO2 in the atmosphere is increasing by 2–3 ppmv annually. Thus, the range of the baseline is fairly narrow and well known and on 9 May 2017 is likely to be at or above 410 ppmv. The actual CO2 concentration experienced at any speciﬁc location is determined by the physical gas laws discovered by Boyle and Charles. For example, the elevation of Boulder, Colorado, is 1655 m, the average July high temperature is 33 C and the average low in January is 2 C. The calculated CO2 concentrations based on 407.9 ppmv in dry air are 298.0 and 336.4 ppmv, respectively. The RF of CO2 in July at 298.0 ppmv is 5.22ln(336.4/ 298.0) ¼ 0.63 W m2 lower than in January at 336.4 ppmv. While the RF of CO2 was falling by 0.63 W m2 from January to July, the back radiation was increasing by 110 W m2 from 240 to 350 W m2. From July to January the situation reverses. This shows back radiation acts in opposition to the warming effect of the CO2, is larger by (110/0.63) ¼ 174 times at the peak and overrides any effect by CO2 on atmospheric temperature. If there is a warming effect by CO2 on the atmosphere, it is too small to measure and can be considered as being negligible. In fact, it is fair to say there is virtually a complete disconnect between the concentration of CO2 in the atmosphere and atmospheric temperature.
Summary and conclusions The scientiﬁc evidence used in this study is robust and comes together from many reliable sources. Evidence is connected in new and innovative ways to expand and clarify the overall picture of climate change as experienced by the Earth and its inhabitants. Because of this, signiﬁcant parts of the evidence and how it is used will be new and unfamiliar to many scientists. Nevertheless, the results and conclusions of this study are important to the wellbeing of everyone on Earth. Conclusions from this study are: (1) The sun controls the water vapour concentration in the atmosphere and it in turn controls the back radiation and atmospheric temperature and, hence, the climate. The effect of back radiation on Earth’s atmospheric temperature is up to 200 times larger than that of CO2 and works opposite to it. It overrides the effect of CO2 such that the CO2 contribution to atmospheric temperature is so small as to be negligible. (2) It appears most climate models work on the basis that increasing levels of CO2 in the atmosphere cause global warming and, therefore, the models require major reconstruction. (3) On average, one quarter of the sun’s energy input to the Earth evaporates water from the surface that condenses elsewhere. This large dynamic exchange of heat churns the hydrological cycle moving vast quantities of heat around the Earth and to the upper atmosphere. It brings temperature changes and creates about 2000 thunderstorms daily that sometimes spawn tornadoes and hurricanes. (4) The empirical relationship between back radiation and water vapour concentration shows maximum back radiation of the total of all GHG is approximately 420 W m2. The minimum in this study is approximately 97 W m2 indicating a normal range of approximately 323 W m2. The speciﬁc range for any location on Earth is within this range. For example, the range at Boulder, Colorado, is 110 W m2, i.e. from 240 to 350 W m2.
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(5) The slope of the plot of back radiation against water vapour is steep at the Poles indicating small changes in water vapour make a large change in back radiation and, therefore, atmospheric temperature. (6) The sun angle and proximity to water at every location determines the ratio of the number of water vapour molecules to CO2 molecules. The H2O/CO2 ratio varies from 1:1 above the Arctic Circle to 97:1 in the Tropics. (7) Based on the estimated average RH of the Earth of 70.5% and 14.5 C average temperature, the average H2O/CO2 ratio is 29. Corresponding back radiation is approximately 340 W m2, which is consistent with the Global energy budget in AR5. (8) Empirical data indicate an increase in water vapour caused back radiation to increase by an average of approximately 2.5 W m2 in the central part of Figure 1 over the period mid-1970s to 2011. It is reasonable to conclude this increase in back radiation was the cause of the 0.5 C increase in atmospheric temperature over the period. (9) On the basis of the science presented, the effectiveness of policies to control climate change by controlling CO2 concentration is negligible because the effect of CO2 on atmospheric temperature and climate change is negligible.
Declaration of conflicting interests The author(s) declared no potential conﬂicts of interest with respect to the research, authorship, and/or publication of this article.
Funding The author(s) received no ﬁnancial support for the research, authorship, and/or publication of this article.
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H Douglas Lightfoot is a co-founder of the Lightfoot institute (www.thelightfootinstitute.ca) and is a retired Mechanical Engineer. He graduated from the University of British Columbia, in Applied Science in 1952, and received an MBA from Concordia University in 1976. He spent eighteen years with Domtar Inc. at the Research Centre in Senneville, Quebec, working on research, engineering and economic studies of alternate energies as well as a wide variety of projects for the pulp and paper, chemicals and construction materials businesses. During this period, he wrote 21 research reports as sole author and 18 with coauthors. Prior to joining Domtar, he spent a year as business analyst and ﬁve years as design engineer designing, building and starting up chemical plants at Dupont of Canada, Montreal, Quebec. Before that, twelve years of project engineering at Standard Chemical Limited, Beauharnois, Quebec. He is a retired member of the Order of Engineers of Quebec, Professional Engineers of Ontario, and a life member of the American Society of Mechanical Engineers. He continues to have an active interest in energy related subjects and the environment. He was an afﬁliated member of the Quebec’s Global Environmental and Climate Change Centre (GEC3), McGill University branch in Montreal, and was associated there from 1992 until its closure in 2015. He has published 11 scientiﬁc papers, contributed to published works and has written reports for the Centre on various subjects related to energy since 1992. Orval A Mamer, PhD, is presently professor emeritus in Medicine in the Goodman Cancer Research Centre of McGill University. He has been engaged in the application of analytical mass spectrometry in physical and organic chemistry, diagnostic clinical medicine, terahertz physics, the environment, biochemistry, metabolism and cancer research. He has published more than 200 peer-reviewed papers in these subjects since 1963.