89. The Greenhouse Effect on Mars

In my previous three posts I have explained how the Greenhouse Effect (GHE) works on Earth, and how it is affected by changes to the carbon dioxide (CO₂) concentration in the atmosphere. The problem with studying the GHE on Earth, though, is that its operation is complicated by the presence of large amounts of water vapour in the atmosphere. As water vapour also has a broader absorption band and higher atmospheric concentration than CO₂, this means that changes in the CO₂ concentration are less important than they would be otherwise. If we want to understand and measure the GHE just due to carbon dioxide, then we need an environment with high levels of CO₂ but low levels of other greenhouse gases. In this respect one of the best places to study is Mars. 

The Atmosphere of Mars

The Martian atmosphere has some similarities with Earth but many differences. It contains many of the same gases (nitrogen, oxygen, water vapour, argon, CO₂), but the proportions are vastly different. The atmosphere of Mars is 96% CO₂ with about 2% nitrogen and 2% Argon (although different pages on Wikipedia give slightly different values such as 95% CO₂ and 3% nitrogen). There are also trace levels (< 0.1%) of other gases such as water vapour (210 ppm) and oxygen (0.15%). 

The other main difference in terms of the atmosphere is the pressure at the surface. At 610 Pa this is only 0.60% of the surface pressure on Earth, and as about 96% of this is CO₂, this means that there is a surface density of 3610 mol/m² of CO₂ on Mars compared to only 150 mol/m² on Earth. So any outgoing radiation from the surface of Mars has 24.06 times as much carbon dioxide gas to penetrate, in order to escape into outer space, compared to on Earth. What this means in practice is that the Greenhouse Effect in the Martian atmosphere should be easier to analyse because it can only have one source - CO₂.

 

The Energy Balance for Mars

Mars is also approximately 52% further from the Sun than is Earth, so one might expect that to mean that its surface is colder. This is true, but not as much as it should be based on distance alone. 

The solar radiation flux entering the Martian atmosphere is only 586 W/m² compared to the 1360 W/m² that irradiates the Earth. As this radiation is spread over a surface area (4πr²) that is four times greater than the cross-sectional area of the planet (πr²) in each case, this means that the average radiation flux at the Martian surface is 143.5 W/m². Yet this is only 22% less than the 184 W/m² that reaches the Earth's surface. This is because nearly 50% of incident radiation on Earth is either reflected by clouds or is absorbed by ozone and water vapour in the upper atmosphere. But there are no clouds, ozone or significant water vapour on Mars.

Then there is the issue of surface albedo or Bond albedo. This is the proportion of incident radiation that is reflected by the planet back out into space without being absorbed, either from clouds or the surface. For Earth this is about 31%; for Mars it is only 25%. This means that the average surface absorption on Mars is 108 W/m² compared to 161 W/m² on Earth. So while Mars only receives 43% of the solar radiation that Earth does, after absorption and reflection the Martian surface receives 67% of the radiation that the Earth's surface does. That is a relative increase of more than 50% for Mars which partially compensates for its greater distance from the Sun.

Calculating the Surface Temperature of Mars

If we now invoke the Stefan-Boltzmann law (see Eq. 13.1 in Post 13),

I = σT⁴

(89.1)

where I is the surface radiation flux, σ is the Stefan-Boltzmann constant, and T is the surface temperature in kelvins, we see that a surface radiation flux of 108 W/m² equates to a mean surface temperature on Mars of 209 K (or -64°C). Yet the true mean temperature is thought to be about 215 K (or -58°C). The difference is due to the Greenhouse Effect. 

For comparison, on Earth a solar flux at the surface of 161 W/m² would equate to a mean surface temperature of 231 K (or -42°C), yet the true mean temperature is about 289 K (or +16°C). So the GHE on Earth adds 58°C of warming while on Mars it only adds 6°C. Yet there is almost twenty-five times more carbon dioxide on Mars (3690 mol/m²) than on Earth (150 mol/m²), so you would expect the greenhouse effect due to CO₂ to be stronger. But how much stronger? The answer is: not very. In fact it is significantly less than the actual measured value on Earth.

Calculating the Strength of the GHE on Mars

In Post 87 I showed how the width of the CO₂ absorption band at 15 µm can be determined using the known concentration of CO₂ (N_o), its scattering or absorption cross-section (σ_s), the quantized frequency of rotation of the CO₂ molecules (B), and the temperature (T). From this it is possible to estimate the critical CO₂ concentration needed to absorb most of the infra-red radiation (N_th). The term N_th can be estimated to be 0.5 mol/m² based on the value of σ_s, while N_o will be about half the total CO₂ concentration, so N_o = 1845 mol/m². From this we can estimate the maximum number of excited rotational states in the absorption band, J_th, using (see Post 87)

(89.2)

where k is Boltzmann's constant, h is Planck's constant and Z is a normalization constant (see Eq. 87.2 in Post 87) equal to 185.5 in this case. The ratio term kT/hB has the value 185.3 (as hB = 0.1 meV and T = 215 K) and is always approximately equal to the Z value. 

The result we obtain is that J_th = 36.3, which, given that the spacing of the bands is 0.2 meV, means that the absorption band has a width of 14.52 meV and extends from a wavelength of 13.78 µm to 16.44 µm. This compares to a calculated range of 14.00 µm to 16.14 µm for the same band on Earth, although the measured width on Earth is actually found to be from about 13.35 µm to 17.35 µm. So even though the calculated width of the 15 µm absorption band for Mars is slightly larger than the equivalent for Earth, it is not significantly greater. But it is significantly less than the measured band width on Earth.

 

Fig. 89.1: The electromagnetic emission spectrum for the surface of Mars at a mean temperature of 215K (blue curve) together with the absorption profile due to CO₂ between 13.78 µm and 16.44 µm (red curve).

The impact of the high Martian atmospheric CO₂ concentration on the radiation feedback is demonstrated in Fig. 89.1 above. The red curve indicates the proportion of the outgoing infra-red radiation (blue curve) that is reflected by the CO₂ molecules and it amounts to f = 12.5%. This is slightly more than the 10% seen for the GHE due to backscattering from CO₂ on Earth (see Post 87) despite the absorption band being further from the peak in the emission spectrum due to the lower surface temperature on Mars.

Calculating the Temperature Rise

The radiation feedback of  f = 12.5% shown in Fig. 89.1 equates to a 14.3% increase in the surface radiation and also of T⁴ (because of Eq. 89.1), which then equates to a 3.4% increase in T. So if the initial surface temperature on Mars without the GHE was 209 K, the temperature with the GHE included will be 3.4% greater, or 216.1 K. This means that the temperature rise at the surface due to the Greenhouse Effect is expected to be 7.1 K, which is pretty close to the observed value of around 6 K (or 6°C). The reason for the small difference could be the limited availability of accurate Mars temperature data, or the uncertainty in the value of the CO₂ absorption cross-section, σ_s.

We know how much radiation from the Sun is arriving at Mars to high accuracy, but knowing how much is being absorbed by the planet surface is more difficult as this depends on an accurate measurement of the Bond albedo. However, conventional astronomical telescopes should be able to measure the reflected radiation to pretty good accuracy as well. That allows us to estimate the expected mean surface temperature without the GHE to fairly high precision. The problem is knowing what the actual surface temperature is with the GHE in operation. This is a difficult enough calculation to do on Earth where we have over 16,000 weather stations measuring the surface temperature on a daily basis, and numerous satellites in orbit. Sadly, none, or very little, of this exists for Mars.

So far in this blog post I have assumed a value of 215 K for the mean surface temperature of Mars, but some reports have put it as high as 225 K (or as low as 210 K). In which case Z = 194.15 and J_th = 37.0. This leads to a 15 µm band stretching from 13.76 µm to 16.47 µm, and a feedback factor of f = 13.0%. Under these circumstances the warming from the Greenhouse Effect increases slightly, but only to 7.7°C. 

 

A Comparison with Earth

For comparison, it is instructive to hypothecate the extent of warming on Earth if its atmosphere also contained 3690 mol/m² of CO₂. In that case Z = 249.3 and J_th = 41.6, which leads to a 15 µm band stretching from 13.62 µm to 16.67 µm, and a feedback factor of f = 14.1%. The resulting predicted temperature rise due to CO₂ would be 10.74 K, which is 3.26°C less than the 7.48°C rise currently predicted for Earth as was shown in Post 87). So a twenty-five fold increase in the CO₂ concentration would only result in a 3.26°C temperature increase, although as I showed in Post 87, masking by water vapour would probably reduce this by 75% to only 0.8°C. 

It is a point of note that the density of CO₂ molecules on Mars (3690 mol/m²) is more than double the combined density of all the greenhouse gases on Earth (1560 mol/m²), yet it results in a temperature rise of 5°C - 7°C that is almost ten times less than the 58°C observed for Earth. This is mainly because most of the GHE on Earth is due to water vapour as the width of the CO₂ absorption band is so much less than that for water vapour. Even increasing the concentration of CO₂ on Mars by a factor of twenty-five cannot appreciably change this.

Summary and Conclusions

What I hope I have shown in this post is that Mars is a good test bed for studying the Greenhouse Effect (GHE). Knowing only its albedo, the atmospheric concentration of CO₂, and the intensity of radiation arriving from the Sun, it is possible to accurately predict the temperature rise due to the Greenhouse Effect. This I have predicted to be about 7°C, in close agreement with the current estimate based on observational data (6°C). And this is despite the significant uncertainty over the true measured value of the mean surface temperature on Mars.

The reduced GHE on Mars relative to the Earth occurs despite its much higher (i.e. 24 times greater) atmospheric CO₂ concentration. This in turn suggests that the increasing levels of atmospheric CO₂ we are currently seeing on Earth will produce only slight temperature increases in the future. 

Yes, Mars has its own complicating factors. Heat retention on Mars is limited by the thin atmospheric blanket compared to Earth. This means that the planet does not retain heat very well, but conversely it means that the atmosphere will warm quickly when heated by the Sun. For this reason it may be better to consider Mars under direct solar illumination in daytime. Under these conditions the peak solar flux at the surface of Mars will be four times greater than stated above, or 432 W/m². This will equate to a peak surface temperature of 295 K (or +22°C). Yet the actual maximum temperature is reported to be around 303 K to 308 K (or +30°C to +35°C). So on this measure the warming from the Greenhouse Effect in daytime near the equator appears to be in the range 8°C to 13°C. Yet the predicted value based on a calculation of the width of the 15 µm absorption band is found to be 10.9°C, in other words in the mid-range of the observed values. Once again this is still much less than the total warming seen on Earth and comparable to the contribution to Earth's GHE seen just from CO₂.

15. The truth about sea level rise

One of the most emotive and alarmist claims made by climate scientists is that global warming will lead to a catastrophic sea level rise (SLR) that will submerge major cities and lead to an unprecedented humanitarian crisis and global extinction event.

Fig. 15.1: Britain's favourite polar bear - Peppy.

On the face of it this seems quite plausible, even likely. We see images of collapsing ice shelves and retreating glaciers on an almost daily basis. We see icebergs the size of cities being calved off from Antarctica and then polar bears looking forlorn on icebergs the size of a lifeboat, like something from a Fox’s glacier mint advert. So what is the reality?

Fig. 15.2: Life imitating art.

There are two principal ways that sea levels might change: either the amount of water in the sea changes, or the existing sea water changes its density. The former can happen if ice caps on Greenland or Antarctica melt. It cannot happen through the melting of sea ice because of Archimedes' Principle as I explained in Post 2, nor for the same reason can an increase in sea ice change the sea level. One alternatively mechanism is through increased evaporation of condensation, but that requires the humidity of the atmosphere to change. As for density changes, these are governed mainly by changes in the temperature of the sea water.


Scenario 1: Thermal Expansion

In the case of rising sea temperatures it is not the current global temperature that is important per se, but the temperature history and the thermal budget of the Earth. Global temperature rises can only raise sea levels directly (excluding from ice melting) by thermal expansion of the sea water. As I pointed out in Post 2, the coefficient of thermal expansion by volume for water is 0.000207 per degree Celsius or 207 ppm/°C. So a column of water 1000 metres or 1 km high will increase in height by only 20.7 cm if its temperature increases by 1 °C (or 1 K where K is the unit of absolute thermodynamic temperature - the kelvin).

But there is another factor we need to consider - the total heat or thermal energy required to do this. This is because this energy needs to come from somewhere, and once used it remains trapped in the water. It is, therefore, energy that has been sequestrated, the effect of which is to create an imbalance between the amount of energy the Earth receives from the Sun, and the amount it emits back out into space. This difference can only come from the net energy imbalance of the Earth’s energy budget.

In the last post we saw that this imbalance is currently estimated to be as much as (and no-one is saying it is more than) 0.9 W/m². If this figure is true (and as I pointed out, there is enormous uncertainty over its accuracy), and if it had been constant over the last 100 years (which is very unlikely), it would imply that the Earth has absorbed a total of 4.591x10¹⁴ joules of energy every second in that time period, or 1.45 x 10²⁴ J in total. Of course that is the upper limit of what is likely. No-one seriously thinks the Earth’s energy imbalance has always been 0.9 W/m². So the average over the last 100 years must be considerably less, and probably less than half.

Whatever the value, though, this heat will increase the temperature of the oceans. The question is, by how much, or to what depth?

As the specific heat capacity of water is 4200 Jkg^-1K^-1, the amount of energy required to heat 1 kg of water by 1 K (or 1 °C as these temperature changes are the same) will be 4200 J. If our 1 km high water column has a cross-section of 1 m², then it will contain 1000 tonnes of waters. Therefore, the total energy required to raise the temperature of the entire column by 1 °C will be 1,000,000 times greater than 4200 J, in other words 4.2 x 10⁹ J. As 70.8% of the Earth’s surface is covered by the oceans, the total volume of water down to a depth of 1 km will be 3.61 x 10¹⁷ m³. The total mass will be 3.61 x 10²⁰ kg, and the total heat capacity will be 4200 times higher still at 1.52 x 10²⁴ J/°C. So the mean temperature rise of the oceans down to a depth of 1 km over then last 100 years will be (at the absolute maximum) 1.45 x 10²⁴ ÷ (1.52 x 10²⁴) = 0.95 °C.

So, if we assume that the Earth’s energy imbalance over the last 100 years has been 0.9 W/m² everywhere and at all times, and if we assume that this heat has all ended up in the ocean, and it has heated the top 1000 m only, then the temperature rise of that top layer of water will be 0.95 °C. Some may find this number suspiciously close to the value claimed for global warming of about 1 °C per century. In other words, that climate scientists have worked backwards. They have assumed that the oceans must heat up by the same amount as the land over the same period, and to a depth of up to 1000 m, and worked out the amount of heat required to do this. From this they have inferred an imbalance in the Earth’s thermal budget rather than measured it.

Whatever the sequence of events, the resulting sea level rise (SLR) will be 197 mm (i.e. 0.95 x 207). If the warming layer of the ocean is thinner (say 500 m) but the surface energy imbalance is still 0.9 W/m², its mean temperature rise will be greater (an unlikely 1.90 °C for a 500 m thick layer), but the SLR will be the same, in other words a massive 1.97 mm per year. So what is clear is that the maximum sea level rise that can occur depends on the energy imbalance and not the water depth. In reality, the surface energy imbalance may be less than 0.9 W/m² (G. L. Stephens et al., Nature Geoscience 5, 691–696 (2012) suggest 0.6 W/m² as I pointed out in Post 13) and has in all likelihood got worse over time. So while it may be 0.9 W/m² now, it has probably averaged less than half of 0.9 W/m² over the last 100 years as global temperatures have risen. In which case the SLR has probably been less than 100 mm over the last century (or less than 66 mm if Stephens et al. are correct). But what about the future?

Assuming that the surface energy imbalance remains at 0.9 W/m² for the foreseeable future, and if we now assume that only that portion of the surface energy imbalance over the oceans is actually absorbed by the oceans, then the heat absorbed by the oceans each year will be 28.4 MJ/m². If this were absorbed by a column of water 1000 m deep it would result in a temperature rise of 6.76 mK. If it were instead absorbed by a column of water only 100 m deep it would result in a temperature rise of 67.6 mK. Either way, the resulting thermal expansion would be 1.40 mm per year. Even over 100 years this is a long way short of the 10 m rise some doom-mongers are projecting, and on its own is unlikely to pose a major threat to human civilization or the planet.

But thermal expansion is just one component of the overall problem, because not all the 0.9 W/m² (or 0.6 W/m²) need end up in the oceans. Some may instead end up melting the ice caps.


Scenario 2: Melting Ice Caps

In this scenario there are a number of factors that we need to identify and address. Firstly, where is the ice? If it is floating on the ocean surface then it cannot add to the sea level increase when it melts, despite 9% of the ice being above the water line. This is because of Archimedes’ principle as I explained in Post 2. It can, though, sequestrate energy and actually reduce warming elsewhere. The only ice that can increase sea levels when it melts is ice that is on land. This is found mainly on Greenland (3 million cubic kilometres) and Antarctica (30 million cubic kilometres).

Then there is the question of the ice temperature. Before it can melt it needs to be heated to 0 °C, yet the mean temperature of the ice on Antarctica is about -50 °C. In order to raise the ice temperature to melting point would require 3.20 x 10²⁴ J of energy (the specific heat capacity of ice is 2108 Jkg^-1K^-1 and its relative density is 0.92).

Next, you need to melt the ice. This will require an energy input of 1.01 x 10²⁵ J (the specific latent heat of ice is 332 kJ/kg); and then you need to heat it to the ambient temperature of the Earth, about 15 °C, otherwise it will cool the oceans and your global temperatures will go down. This requires another 1.91 x 10²⁴ J of energy. So the total energy required is 1.52 x 10²⁵ J. Given that the amount of power available to achieve this is at most only 0.9 W/m², that means it would take at least 1100 years to occur. But even that assumes that all the power from the Earth’s energy imbalance could be channelled somehow into melting the ice caps and nothing else.

In reality most will initially go into the oceans. As Antarctica and Greenland comprise only 3% of the Earth’s surface area, a more realistic estimate is that it would take up to 30,000 years, by which time we would be in the next ice age. Recent studies of Greenland appear to confirm this as they show Greenland has lost less that 0.05% of its ice in the last 10 years, but this may just be cyclical. 

One final point of note: while the total volume of ice on Antarctica is 30 million cubic kilometres, almost a third of this is below sea level. The net result is that if all the ice on Antarctica and Greenland were to melt, sea levels would rise by 65 metres not 91 metres. Yet over 30,000 years this will amount to a rise of only about 2 mm per year.


Scenario 3: Evaporation

The final possibility is that the sea water might just evaporate into the atmosphere leading to a loss of volume in the sea rather than a gain. Approximately 0.4% of the atmosphere by volume is water vapour. But if all this water were to suddenly condense out of the atmosphere it would only add 3.6 cm to the depth of the oceans. Given that the ambient temperature at the surface of the Earth is 15 °C, while the humidity at 0 °C would be expected to drop to near zero, this suggests that an increase of 1 °C in the surface temperature of the air would lead to a decrease in sea levels of around 2.4 mm. That is a pretty crude estimate, though, and assumes that the vapour pressure of water increases proportionately with temperature from its freezing point. A more accurate estimate can be made using the Clausius-Clapeyron equation.

Fig. 15.3: Schematic of phase boundaries on a P-T diagram.

This equation (see Eq. 15.1) relates the the slope of a phase boundary in a pressure-temperature diagram to the thermodynamic temperature, T, the molar latent heat for the phase change, L, and the change in molar volume across the boundary ∆V. An example of a phase diagram is shown in Fig. 15.3 above.

(15.1)

For a change from liquid to gas (as in evaporation) the term ∆V should be the difference in molar volumes between the water in the liquid phase and the vapour in the gas phase. However, as the volume of the vapour at the relevant pressures we are likely to encounter (i.e. around atmospheric pressure) is so much greater than it is for water (in fact by more than a factor of 1000) we can use the ideal gas law in Eq. 15.2 to substitute the molar volume of water vapour V for ∆V on the basis that the molar volume of the liquid is negligible.

(15.2)

In Eq. 15.2 the term V is the volume of one mole of water vapour at a pressure P and a temperature T. The term R is the molar gas constant where R = 8.314 Jmol^-1K^-1 and n is the molar density in mol/m³. The approximation of V for ∆V allows us to make a substitution from Eq. 15.2 into Eq. 15.1 to generate Eq. 15.3 which is now a function of only two variables, P and T.

(15.3)

This allows us to relate fractional changes in the pressure of the gaseous phase to fractional changes in temperature along the phase boundary. The differential in Eq. 15.3 implies that for small changes in P and T the following relation holds

(15.4)

while Eq. 15.2 yields the following relation between P, T and n.

(15.5)

Equating Eq. 15.4 with Eq. 15.5 gives the result for the fractional change in molar concentration of the vapour that will occur due to  evaporation across the phase boundary for a temperature change ∆T.

(15.6)

The relation in Eq. 15.6 allows us to estimate the change in water vapour concentration n as the temperature T changes. So for example, if the temperature T = 288 K and the latent heat of evaporation of water is 40.8 kJmol^-1K^-1, then a temperature rise of ∆T = 1 K will yield a fractional change of water vapour concentration of 0.0557. That in turn implies a total fall in sea level over the period of the temperature rise (which is about 100 years) of 2.0 mm (= 0.0557x36). Reassuringly, this is not that dissimilar to our original estimate of 2.4 mm, thus demonstrating two important points. Firstly, that the result is robust and consistent. Secondly, that our original back-of-the-envelope approximation, much loved by physicists everywhere, did not let us down.

The advantage of calculating the fractional change in n using Eq. 15.6 rather than calculating ∆n directly is that it means that we can avoid the complication of working out the relative humidity. The Clausius-Clapeyron equation, strictly speaking, only applies to closed systems in equilibrium, i.e. at 100% relative humidity. In open systems, such as the Earth's atmosphere above large oceans, the humidity is always less than the maximum. But Eq. 15.6 effectively removes the issue of relative humidity as it just introduces an additional scaling term that applies more or less equally to n and ∆n. Therefore it cancels out in Eq. 15.6. All of this may be somewhat pedantic, however, as the sea level fall due to evaporation is a full two orders of magnitude less than the previous two effects considered.


So the conclusion is this: prophesies of apocalyptic rising sea levels and submerging cities are still just alarmist nonsense. The physics proves that there is currently not enough energy available to achieve this on the timescale that some climate scientists predict, at least not yet. Thermal expansion and melting ice caps will each add not much more than 2 mm per year to sea levels. A recent paper by Anny Cazenave et al. (Advances in Space Research 62(7) 1639-1653 (2018) ) puts the sea level rise (SLR) from all sources at about 3.5 mm per year for the period 2005-2015  (see Fig. 15.4 below). These numbers do appear to be more consistent with the surface energy imbalance of 0.9 W/m² reported by Trenberth and co-workers rather than the 0.6 W/m² of Stephens et al., particularly the thermal expansion component.

Fig. 15.4: Possible breakdown of different contributions to sea level rise (1993-2015) from Cazenave et al.

One of the striking features of Fig. 15.4 in my view is the low contribution to sea level rise from ice melt in Antarctica compared to that from glaciers. Three explanations spring to mind. Firstly, there is probably more warming in the Northern Hemisphere because that is where the heat is being generated. Secondly, the glaciers in Europe are very close to the source of that heating. And thirdly, the ice in Antarctica is much colder than that in alpine glaciers, and so requires more heat to melt it. So, as I pointed out in the last post, this could mean that alpine glaciers will continue to recede, not because of CO₂ emissions, but because of local human industrial activity that leads to surface heating of the local environment, and thus a temperature rise of more than 0.3 °C above pre-industrial levels.

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.