Linking Energy Use And Human Development

This is a re-posting of my report An Introduction Linking Energy Use And Human Development, from 28 April 2006 — unchanged. This is another of my personal favorites. A PDF copy of the report is available through the web-link given below.

An Introduction Linking Energy Use And Human Development
28 April 2006




Of related interest and more recent:

Energy for Human Development
9 November 2011

Energy for Society in Balance with Nature
8 June 2015 (27 February 2012)

Our Globally Warming Civilization
2 June 2019

Oil, Population, Temperature, What Causes What?
9 June 2019


Our Globally Warming Civilization


Our Globally Warming Civilization

The 150 years of the Industrial Revolution (~1770-1920), with its catastrophic and bloody termination in World War I (1914-1918), had no noticeable effect on the global average temperature, which had hovered around 14.7 degrees Centigrade (C) since antiquity. The human population had taken 200,000 years (more or less) to grow to one billion (1B), in 1804, within the natural and majestic evolution of global climates during those 2000 centuries, (1).

By 1927, the human population had increased to 2B. The 1920s were economic boom years in the Industrialized World (give or take some post WWI German misery, the Russian Revolution, and Chinese civil warfare) with the liquid petroleum replacing the solid coal as the fossil fuel of choice for transportation vehicles; and the explosion in the craving for, and manufacture and use of, internal combustion engines and the automobiles powered by them.

After 1927 the rate of population growth increased from what it had been on average during the previous 123 years (about 8 million per year, ~8M/yr) to an average rate of 29M/yr, to accumulate another 0.7B people in the 26 years up to 1953, when the population was 2.7B. Those 26 years between 1927 and 1953 spanned the crescendo of the Roaring ‘20s, the capitalist economic collapse of 1929, the Great Depression (1929-1942), World War II (1939-1945), the Second Sino-Japanese War (1937-1945), and the Chinese Communist Revolution and Civil War (1946-1949).

I estimate that the cumulative amount of petroleum produced (pumped out and used up) by 1953 was 98.6 billion barrels (98.6 giga-barrels, 98.6Gb), (2). This implies that since about 1900, when civilization’s use of petroleum as a fuel began in earnest, it consumed 602 giga-GJ (602 x 10^18 Joules) of energy (equivalent to 168 mega-GWh = 168 x 10^9 MWh = 168 giga-mega-watt-hours) to power itself up to 1953, (3).

By 1960, the world’s human population had reached 3B, and the rate of population growth was accelerating (having been about 43M/year during the previous 7 years). From 1960 to the present day, the trend of cumulative production of petroleum, Q, has been proportional to the rising trend of human population, in the ratio of 272 barrels of oil per person (272 b/p).

Specifically, my approximating formula for Q, the accumulated production of oil in giga-barrels (Q, in Gb), given as a function of the population in billions (P, in B) for a given year within the interval 1960 to 2025 is:

Q(year) = [P(year) – 2.7B] x (272 b/p).

This approximation gives an accumulated production up to 2015 (with population 7.35B) of

Q(2015) = 1265Gb, (approximation).

By integrating the actual production rate-per-year curve (the “Hubbert curve” for world production, in GB/yr) given by Laherrere (2), I find the actual accumulated production up to 2015 to be:

Q(2015) = 1258Gb, (actual).

The rate of oil production is now likely at its peak of between 25 Gb/yr to 35 Gb/yr during this 20 year interval between 2005 and 2025, (2),(4). Thereafter, it should drop rapidly since current oil fields have diminishing production, there have been no major oil field discoveries since the 1970s and the frequency of discovery has steadily diminished since then. That means that over half of Earth’s original total reserves, estimated at 2,200Gb (2), have already been extracted. The “end-of-oil” seems destined for the last two decades of the 21st century.

Assuming all that oil was burned, up to the year 2015 (115 years since 1900), civilization would have used 7,674GGJ, (7,674 x 10^18 Joules), equivalent to 2,139GMWh, (2,139 x 10^15 Watt-hours) of energy, derived from that 1258Gb of petroleum, to power itself.

That burning would have released 398,786Gkg (~4 x 10^14 kg = ~400 giga tonnes) of CO2, (5). At present (May 2019) there are about 3,250 giga tonnes of CO2 in the atmosphere, with an average concentration of 415 parts per million by volume (415ppmv), (6). 1228 G tonnes of that CO2 is excess above the pre-industrial amount in the atmosphere. The ~400 G tonnes estimated here as the accumulated emissions from the prior burning of petroleum (up to about 2015) is only about one-third of the excess atmospheric CO2.

There are numerous other processes in our civilization, as well as in the natural world, that cause the emission of carbon-dioxide and its atmospheric retention in excess amounts. The main sources of CO2 emissions are the exhalations from aerobic respiration by all of Earth’s living heterotrophs, decaying plants, and volcanic eruptions. Other sources include: the burning of coal and natural gas, forest and vegetation fires caused naturally and by slash-and-burn agriculture, the bubbling out of CO2 from warming oceans no longer able to dissolve as much of that gas as before, and the massive amount of past and continuing forest clearing that has reduced Earth’s natural system of CO2 uptake — photosynthesis. The cement industry is one of the two largest producers of anthropogenic carbon dioxide, creating up to 5% of worldwide man-made emissions of this gas, of which 50% is from the chemical process and 40% from burning fuel, (7).

Methane (CH4) is a very potent greenhouse gas, being 30 times more effective than CO2 at trapping heat. “For each degree that Earth’s temperature rises, the amount of methane entering the atmosphere from microorganisms dwelling in lake sediment and freshwater wetlands — the primary sources of the gas — will increase several times. As temperatures rise, the relative increase of methane emissions will outpace that of carbon dioxide from these sources.” (8) Other sources of methane emissions are: rotting organic wastes, termite colonies, and bovine flatulence from industrialized agricultural sites. The globally warmed thawing Arctic tundra is now a region of major methane eruptions.

Up until 1974, when the human population had reached 4B, Earth’s climate system had yet to become feverish over the previous 200,000 years of collective human activity. However, at about that time the average global temperature began increasing at a historically unprecedented rate because of civilization’s heated and organic outgassing, a process which continues today as anthropogenic global warming, (9).

In fact, the date at which collective human activity began to affect and alter Earth’s climate system has now been pinpointed to somewhere between October to December 1965. That date marks the end of the Holocene Epoch of geologic history (which began 11,700 years previously, after the last Ice Age), and the beginning of the Anthropocene Epoch — the epoch of human-affected climate, globally. The physical phenomenon marking this transition is that Carbon-14, a radioactive isotope released during open-air atomic and nuclear bomb explosions between 1945 and 1963, had finally dispersed uniformly around the globe, and become absorbed into tree tissues even in the remotest parts of the world, thus recording that uniformity (10).

Between 1960 and 2025, the three rising trends of: population (P), cumulative oil production (Q), and increase of average global temperature above baseline (T – 14.7C = delta-T), are all uniformly proportional to one another.

Specifically (for years between 1960 and 2025) T, P and Q are related to each other as follows:

[T(year) – 14.7C] = [P(year) – 2.7B]/3.3B = [Q(year)/(900 Gb)],

where the forms above are each equivalent to a temperature difference relative to the baseline of 14.7C (delta-T, in degrees C).

Notice that if T = 15.7C, and P = 6B, and Q = 900 Gb, then the equality above holds, with: 1 = 1 = 1. This particular condition actually occurred during 1999.

During this 65 year interval, a 1 degree C rise in temperature (above 14.7C) is coincident with a 3.3B increase in population (above its 1953 level of 2.7B), which in turn is coincident with a production (and use) of 900Gb of petroleum.

The population is growing from 3B in 1960 to an expected 8B in 2028 during this 68 year interval, with an average population increase of +73.5M/yr. Within these 68 years, and especially during the 55 years from 1970 to 2025, the rising trends of (T – 14.7C), (P – 2.7B)/3.3B, and Q/(900Gb) are in lockstep. This period — with explosive population growth, depletion of over half of the Earth’s petroleum endowment, and with an unprecedented rate of global warming — began in the last year of the Eisenhower Administration, 1960, when John Kennedy was elected US President, and extends right up to the present (and beyond it).

The average global temperature will have climbed up from ~15C to ~16.2C during this interval, a relative rise of 1.4C, and a rise of ~1.5C (delta-T = ~1.5C) above the pre-industrial temperature, defined here as 14.7C (58.46 degrees Fahrenheit). That 1.5C (2.7F) warming above the pre-industrial temperature represents a tremendous amount of heat energy diffused throughout the biosphere, and the deleterious effects of that excess heat are self-evident to all: the altering of climate; the powering of violent weather; the heating and acidifying (with absorbed CO2) of the oceans, sterilizing them of marine life; the melting of glaciers and thawing of tundras; the causing of carbon dioxide and methane to bubble out of solution and frozen capture in the natural world (in a vicious feedback loop); the expansion of disease pathogens and tropical parasites; and the added stresses to both wild and farmed vegetation, and increased desertification, which result in human hunger and desperate migrations of impoverished refugees.

Now, our civilization is starting to suffocate in the lingering heat of its previous exhalations. The singular challenge to our species and to our political economies is what to do, collectively, about global warming. That challenge remains largely unanswered, and tragically denied by too many people .


1. World population is estimated to have reached one billion for the first time in 1804. It was another 123 years before it reached two billion in 1927, but it took only 33 years to reach three billion in 1960. The global population reached four billion in 1974 (14 years later), five billion in 1987 (13 years later), six billion in 1999 (12 years later), and seven billion in October 2011 (12 years later), according to the United Nations, or in March 2012 (13 years later), according to the United States Census Bureau.

World population by year

2. Jean Laherrere, World Crude Oil Production, (brown line), April 2015

3. The energy released from combusting 1 barrel of oil is 6.1 giga-joules (6.1 GJ), which equals 1.7 MWh (1.7 mega-watt-hour).

4. Worldwide, around 92.6 million barrels of oil were produced daily in 2017.
~73 million barrels/day in 1998, rising since.
73 Mb/day = 26.7 Gb/yr (1998)
93 Mb/day = 34.0 Gb/yr (2017)
During 20 years of production (1998-2017) the rate rose 20 Mb/day = +1 MB/day/year

5. Burning one barrel of petroleum can produce between 317kg (realistically) to 433kg (theoretically) of CO2:
Therefore, the CO2 emitted by combusting 1b = 317kg CO2.

6. As of January 2007, the earth’s atmospheric CO2 concentration is about 0.0383% by volume (383 ppmv) or 0.0582% by weight. This represents about 2.996×10^12 tonnes (1 tonne = 1000kg), and is estimated to be 105 ppm (37.77%) above the pre-industrial average (~278 ppmv).

415 ppmv of atmospheric CO2, as of May 2019

(415/383) x 3000 G tonnes = 3,250 G tonnes, (May 2019).

7. Environmental impact of concrete

8. Methane is roughly 30 times more potent than CO2 as a heat-trapping gas

9. I first constructed the simplified plot of average global temperature in 2004, using data from public sources. Details about that construction and the data used are given at:
Population, Oil and Global Warming, 31 May 2019 (15 March 2004)

10. The Anthropocene Epoch began sometime between October and December 1965.


Population, Oil and Global Warming

Our ignorance is not so vast as our failure to use what we know.
—M. King Hubbert (1903-1989)


This article is identical to:

Oil, Population And Global Warming
15 March 2004

The only change is the addition of the graphs (below), which I made today (30 May 2019).

Numbers beyond the year 2020 are speculative (by the sources cited). Numbers for oil used to date (globally) are less certain than the numbers for population and average global temperature. The temperature history has been simplified (you can find very detailed data if you wish). Oil extraction by fracking since ~2000 (and since this article was originally published, in 2004), has drastically changed the numbers for oil production in the United States.


Future historians will look back on the 200 years of the 20th and 21st centuries as the Oil Period in world history. During this time, the latent heat of buried petroleum will have been mined and released into a dramatically warmed and crowded planetary surface. In the century from 1950 to 2050, the world will have shifted from one with 2.7 billion people, 96% of its petroleum reserves intact, and insignificant global warming, to one with perhaps over 9 billion people, less than 10% of its petroleum reserves left and a 2 °C average global temperature rise. For perspective, during the last Ice Age — about 16,000 years ago — the average global temperature was 4 °C (7 °F) below the 1860 to 1920 average of 14.7 °C (58.5 °F).

What will be the politics of a hot, crowded world without oil, and possibly on the brink of abrupt climate change?


Within the sixty years from 1970 to 2030, we will have used up about 80% of the world’s oil, the peak rate of production occurring now, during these few years about the turn from 20th to 21st century. Half of the world’s oil endowment has already been used. Efforts at conservation and improved extraction technology may extend till the years 2007 to 2013 when the oil production rate will peak (at about 26 billion barrels/year, or 70 million barrels/day). Inevitably, beyond this time the rate of oil extraction will diminish.

The bell-shaped curve of oil production rate variation over time is called the Hubbert Peak, in honor of the late geophysicist who — in 1949 — first predicted the brevity of the fossil fuel era. Hubbert’s 1956 prediction that US oil production would peak in 1970 and then decline was scoffed at, but he was proven exactly correct. (1), (2)

Today [15 March 2004], over 87% of the oil endowment in the continental U.S., and over 95% of that in Alaska have been consumed. America uses 28% of the world’s yearly oil production, producing 12% domestically, and importing the remaining 16%. Americans consume oil at six times the rate of the world average (25 versus 4 barrels/person/year). America imports oil to supply 29% of the energy it consumes, domestic oil supplying another 12%, so that 41% of our energy comes from oil. This fact is fundamental to national planning. (3), (4)

Oil used (accumulated giga-barrels, GB) by a given year (estimated)


World population increased at an accelerating rate until 1990 (when 85 million people joined us), and has continued increasing at a diminishing pace since. The world family was 2 billion people in 1930, 3 billion in 1959, 4 billion in 1974, 5 billion in 1987, and 6 billion in 1999. Estimates published by the US Census Bureau show a potential world population of 7 billion by 2013, 8 billion by 2028, and 9 billion by 2048. The future US population is estimated to be 4.5% of the world total, as it is today. (5)

World population (billions, B) vs. year


Instrumental records of global surface temperature begin in 1860. The average global surface temperature for the period between 1961 and 1990 was 15 °C (59 °F). The deviations of global surface temperature, relative to the reference temperature of 15 °C, are — very generally! — as follows: -0.4 °C prior to 1920, a rise to 0 °C by 1940 (being at 15 °C), a plateau at +0.1 °C during 1940-1945, a lower plateau at -0.05 °C during 1945-1975, a rise to +0.6 °C by 2000. The actual year-to-year variations within each of these five periods are within a swing of 0.2 °C either way. (6), (7)

The temperature rise after 1975 is unprecedented (averaging +0.03 °C/year). The temperature today is 1°C (1.8 °F) warmer than in the late 19th century. The initial 40% of this temperature rise took 55 years, while the final 60% only required 25 years.

It is interesting to view the finely-detailed temperature history presented by the United Nations Environment Programme, and to imagine the warming trend beginning in 1920 as reflective of the oil boom then underway, as the industrialized nations moved from coal to petroleum for their energy; and to the warmth during WWII, which was not equaled until the 1980s.

Predictions of global warming above the early 20th century temperature of 14.7 °C are +2.3 °C in 2050 (between +1.5 °C and +3 °C), and +3.3 °C in 2100 (between +2.1 °C and +6.5 °C). (8)

Average global temperature (degrees Centigrade, C) vs. year (simplified)

Is it possible to directly relate temperature rise with human activity? For example, linking fossil energy, greenhouse gases, and global warming? What about fossil energy, industrialized agriculture, energy-intensive social systems and human population? Finding causal links to global warming is a scientific problem of great complexity, and one that has engaged many scientists for at least two decades. (9), (10)

However, without appealing to causal arguments, it is sometimes possible to show that trends for two phenomena coincide. If so, some limited insight might be found by contemplating this.

Proportionality, people and oil

The growth of human population, the depletion of oil resources and the rise of global temperature each mirror one another to a remarkable degree, a result that can be arrived at from the data and projections already described.

The world population of 2.7 billion by 1953 can be taken as a base that required negligible petroleum energy to produce. The addition of people beyond this level is fueled at a rate of 264 barrels of oil per person.

So, population minus the base equals cumulative oil production in barrels divided by 264 (equation 1).

For example, today’s population of 6 billion required the expenditure of 871 Gb (Gb is for Giga-barrel, or 1 billion barrels); the actual consumption by January 1999 was 857 Gb. Similarly, a projected population in 2050 of 9 billion would coincide with an accumulated depletion of 1,663 Gb, or 95% of the estimated 1,750 Gb of the world’s oil endowment.

The actual population and cumulative oil production data between 1950 and 2000 correlate startlingly well with the proportionality and offset (base population) given here. The projections to 2050 also correlate extremely well, but of necessity they contain uncertainties only time can clarify.

Proportionality, people and temperature

By direct comparison, the trends of temperature rise above 14.7 °C (the pre-1920 plateau) and population growth mirror each other after 1975 with a proportionality of 3.3 billion people per °C.

So, the difference of population minus base, divided by 3.3 billion equals the temperature difference above 14.7 °C (equation 2).

For example, the 6 billion people of today coincide with a rise of 1 °C to 15.7 °C (60.3 °F), and the projected 9 billion people of 2050 would coincide with a rise of 1.9 °C to 16.6 °C (61.9 °F).

Proportionality, temperature and oil

By a ratio of the previous two proportionalities, one finds that for each 870 Gb of oil produced, the global surface temperature rises by 1 °C.

So, cumulative oil production in barrels divided by 870 Gb equals temperature rise above 14.7 °C (equation 3).

It has already been noted that today we have a global warming of about 1 °C above the 19th century level of 14.7 °C, and that just over 857 Gb of oil have been extracted; this matches the proportionality of 870 Gb/°C. The anticipated global warming in 2050, with 1663 Gb of oil having been extracted, would be 1.9 °C, for a temperature of 16.6 °C (61.9 °F).

Summary of proportionalities

Three proportionalities: 264 barrels/person, 3.3 billion people/°C, and 870 Gb/°C, correlate the data and projected trends in world population (above a base of 2.7 billion), cumulative oil production and global warming (above 14.7 °C). Population and oil production are correlated from 1950, while all three quantities are correlated after 1975.

Population (blue), oil (brown) scaled to match temperature rise (red) above 14.7 C, 1850-2050, (see text, proportionalities)

Population (blue), oil (brown) scaled to match temperature rise (red) above 14.7 C, 1950-2050, (see text, proportionalities)

Population (blue), oil (brown) scaled to match temperature rise (red) above 14.7 C, 1950-2020, (see text, proportionalities)

What’s Next?

Are we to believe that these correlations will remain intact until the world’s oil is exhausted? Will we really age to 2050 with an accumulation of 9 billion people, no petroleum, and unchanged climate despite a heating of unprecedented magnitude, comparable to the cooling of the Ice Ages?

Many find it easy to fantasize from this point: ice caps melt, oceans swell, shorelines recede so that countries like the Netherlands and Bangladesh disappear; jungles and deserts expand but in different locations than at present, waves of extinction and population-drop sweep the animal kingdom, equatorial zone agriculture collapses, massive migrations spark wars; America, Europe and Japan militarize heavily, including space, to capture foreign resources and repel invaders and refugees; America invades Canada because the ‘corn belt’ has moved north to the former tundra; the exploding price of oil spurs a frenzy of invention into synthetic fuels and alternate forms of energy, as well as a return to coal and a depletion of timber; sunny territory is invaded and conquered by foreign armies, and used for solar energy plantations by a colonial elite who export the accumulated energy to their imperial homelands.

Politics (finally!)

In fact, we don’t know what will happen, or when. But, we can “use what we know” to begin rational planning now for a transition to a new method of powering our society (particularly transportation systems), and of weaning ourselves from imported energy and the imperialism it seems to require. It would also be wise to rearrange our politics, that is to say remove the inequities between economic classes, so that our nation can retain its integrity while facing the environmental, economic and political pressures to be expected with a shift to a post-petroleum world. The added stress of a civil war during such a time would be tragically cruel.

Such planning is unlikely — at best very difficult — in America, because business has a quarterly-profits myopia, and the electorate in the suburban American “heartland” is thoroughly indoctrinated in capitalist ideology, with an anti-socialist “every man for himself (and women too)” attitude. The world’s revenge for our past imperialism may well be realized by our lack of social planning for the inevitable shocks of the collapse of the oil-powered economy, accompanied by a climate shift.

There are no physical reasons, no “laws of nature” that prevent us from devising an alternative way of organizing and powering our American society. There would certainly be many technical problems and intellectual challenges, but we have the means to prepare for what we can predict is likely to unfold. An enduring society would do this on a continuing basis. To me, that is socialism. Sometimes it’s as simple as seeing that everyone is in the boat, and they’re all rowing in the same direction.

In looking at our political figures, which ones seem to concern themselves with just the self-interest of one or another faction, and which ones seem to concern themselves with the good of the “whole boat?” We need leadership that can draw our involvement into long-term, democratic, social planning that achieves dependable commitments. We need such a process to bear fruit this decade, and we need a well-understood general plan for embarking on an intentional social transformation. If not, we will be the witless victims of a foreseeable catastrophe of our own making.


1.  “Hubbert Peak of Oil Production” – (as of 29 February 2004).

2.  James M. MacKenzie, “Oil as a finite resource: When is global production likely to peak?” World Resources Institute, 1996 & 2000 – (as of 24 February 2004).

3.  Energy Information Administration, U.S. Department of Energy – (as of 28 February 2004).
“Energy in the United States: 1635-2000” –
“25th Anniversary of the 1973 Oil Embargo” –
“U.S. Total Petroleum Consumption” –
“Imported Oil as a Percent of Total U.S. Consumption” –

4.  U.S. Department of Interior, Press Release, 19 March 2003 – (as of 28 February 2004).

5.  Bureau of the Census, U.S. Department of Commerce “Population Clock,” – (as of 28 February 2004).
“World Population Information” –
“Total Midyear Population for the World: 1950-2050” (table) –
“World Population: 1950-2050” (graph) –
“Historical Estimates of World Population” –
“Annual World Population Change: 1950-2050” –
“Methodology and Assumptions for the Population Projections of the United States: 1999 to 2100” –

6.  “Trend in global average surface temperature,” United Nations Environment Programme / GRID-Arendal – (as of 24 February 2004).

7.  Intergovernmental Panel on Climate Change (IPCC) of the United Nations Environment Programme (UNEP) – (as of 28 February 2004).
“Variations of Earth’s surface temperature for the past 140 years (global), and the past 1000 years (Northern Hemisphere)” –
“Variations of the Earth’s surface temperature: years 1000 to 2100” –

8.  The reference temperature in [6] is 15.08 °C (the 1961-1990 average), while in [7] it is 15.43 °C (the 1990 value). This article uses the 1860-1920 plateau (estimated average) of 14.7 °C as the reference for global warming. So, the data and projections of temperature “deviations” and “variations,” from [6] and [7], have been adjusted to ensure consistency in describing global warming.

9.  “Global Warming,” National Oceanic and Atmospheric Administration – (as of 24 February 2004)

10.  “What is Climate Change,” Government of Canada – (as of 24 February 2004).


The Latent Heat of Climate Change, Redux

The equations for the chemical-hydrodynamics and chemical-thermodynamics of global warming/climate change are non-linear. For this type of physics, the independent variables are (usually) time (t) and energy (h, enthalpy). So, a physical quantity like average global temperature (T) can be taken as related to average CO2 concentration (Xco2) as:


but it is not known if this is a single valued function (i.e., has a unique value of T for a unique value of Xco2). The graphs in the article below show examples of functions (curves) that are not single valued. Such multi-valued functions are non-linear. Non-linear functions (in math, and non-linear effects in physics) can exhibit “delays” and abrupt accelerations beyond some threshold value of the driving independent variable.

Now, in the case of our Earth’s climate, CO2 average concentration is a function of time; over time Nature and humanity release more CO2 into the atmosphere:


The rate at which these releases occur can vary (some sequence of decreases and increases) over time:

d(Xco2)/dt is itself a function of t.

So, T can be seen to be a nonlinear function explicitly of Xco2 and implicitly of t:


Now, realizing that there are hundreds (thousands?, more?) of “variables” that affect the momentary numerical value of T; and with many similar multi-variable — and nonlinear — dependencies of other significant physical and chemical quantities, it is easy to see that simple single-valued (and single independent variable) functional predictability just doesn’t exist for global warming. This is why the popular literature on global warming talks about “thresholds” and “tipping points” — unknown values of a driving independent variable, like Xco2, above which all hell breaks loose.

The purpose of The Latent Heat of Climate Change, is to give an inkling of the unpredictability of nonlinear, multi-variable phenomena, by describing a much simpler and well-known physical phenomena: the liquid-to-vapor phase change of water.

The Latent Heat of Climate Change
29 July 2013

Why is Global Warming stagnating? (1) I do not know the exact answer to this question. However, I do not see the lag of global warming relative to the increase in atmospheric CO2 during the last fifteen years as such a mysterious effect.

Why? Because the entire system of global heat balance and the chemical thermodynamics of the Earth’s atmosphere is extremely complicated, and multiply intertwined.

It is simple-minded to expect such a natural system (organism?, as in Gaia?) to behave mechanically and linearly. That is to say, it is naïve to expect that because data of climate history show that for a lower range of CO2 concentrations in the past the injection of X amount of CO2 into the atmosphere in any given brief period (a year or less) correlated with a parallel increase of Y amount of average temperature, that such a correlation will obtain at any higher level of CO2 concentration now and in the future.

There are so many possible feedback mechanisms and interconnections of chemistry, physics, and heat flow (chemical thermodynamics) in this earth atmosphere system that it is entirely possible for added heat energy to be stored, without temperature change, for a period of time while CO2 concentration increases above some threshold level, TL, until some higher level, TL + XX, at which point a new concentration-temperature correlation would exhibit itself.

I will give one example. When you heat ice water (but not solid ice, let us say liquid at 0 degrees Celsius) to boiling, there is a steady correlation of heat energy into the water (say in joules of energy per gram of H2O) with resultant water temperature: for every degree Celsius rise of water temperature, an amount of energy equal to 4.184 joules has infused each gram of the mass of liquid water. We know that water boils at a temperature of 100 degrees Celsius (at sea level), so we expect our (initially 0 degree C) water to boil — issue steam — once we have infused it with an amount of energy equal to its mass in grams times 418.4 joules (e.g., 418,400 joules for every kilogram). However, this is not the case.

Boiling is the condition where steam, vaporized water, can form and escape from the liquid mass because the vapor bubbles have sufficient energy to exert a comparable pressure to the liquid water from which they bubble out of, and against the atmosphere in which the heating takes place. (And, since atmospheric pressure is less at higher elevations as on the peak of Mount Blanc, the heat input required for boiling — and the resultant boiling temperature — are less than at sea level.)

A great deal of heat energy must be absorbed by the H2O molecules in liquid water that has just reached 100 degrees C, to agitate those molecules (speed up their kinetic motions) sufficiently so they separate widely (in localized spots) to make the “phase transition” from liquid to gas — steam — and then bubble out. This phase transition happens without an increase in temperature because the added energy is being absorbed into breaking the weak molecule-to-molecule attractive electromagnetic forces that make a liquid, and to agitate the molecular bonds of individual H2O molecules (which one can think of as springs between “billiard ball” atomic nuclei, and those springs are set into rotary and vibratory motions by the heat energy they absorb). The energy required to effect the phase transition of vaporization in water is 2260 joules per gram (this is called the “latent heat of vaporization”).

So, vaporizing our sample of water will require an additional 2260 joules of energy for each gram of liquid water that has just reached 100 degrees C. When we “boil water,” we take the first appearance of bubbling and steam emission as a sure sign that the liquid mass has reached 100 degrees C. Our water sample will be fully vaporized after every gram of the liquid (already at 100 C) has absorbed an additional 2260 joules of heat energy.

If we continue to heat our fully vaporized water mass, which is confined within an expanding balloon so its pressure remains constant (as its volume expands), then the steam will increase in temperature in a nearly proportional manner with respect to heat energy input, though not strictly linear (not exactly proportional).

Thus, a graph of water and/or steam temperature (at fixed pressure) with respect to energy input (per gram) would be a rising curve from ice water (0 C at 0 joules/gram of added heat) to the beginning of boiling (100 C at 418.4 joules/gram), then a flat line at 100 C from 418.4 joules/gram to 2678.4 joules/gram, and then a return to a rising trend of steam temperature with added heat energy. The following is a diagram of this process. (2)

Another representation of the thermodynamic data for water is the diagram of pressure-enthalpy at constant temperature. (3)

Note the line labeled “100 C” in the pressure-enthalpy diagram. You can see the flat part over the range of energy-per-gram during which water undergoes its phase transition from liquid to gas (vapor, dry steam). In this flat region, the mass of water is a mixture of liquid water and water vapor. At the left extreme of the flat line (418.4 J/g at 100 C) the sample is 100% liquid, while at the right extreme (2678.4 J/g at 100 C) it is 100% vapor (dry steam).

To keep water in a purely liquid state (no vapor) at a constant temperature requires a drastic increase of the pressure placed upon it (compression). Conversely, to keep water vapor (dry steam, that is to say without liquid droplets) at a constant temperature requires a drastic reduction of the pressure placed upon it (expansion, no condensation).

Each of the constant temperature lines in the pressure-enthalpy diagram shows a correlation of water pressure versus energy input (heating, energy-per-gram). For temperatures below 374.15 degrees C, there is a range of energy-per-gram in which a mixture of two phases of water — liquid and vapor — can coexist (the two phase “vapor dome”). Above 374.15 C, water exists only as vapor (gas) at any pressure.

Perhaps more than you want to know, but the example of a lag in temperature rise with heat input/content over a range of energy-per-mass in a “simple” single substance (a “pure substance” in thermodynamic parlance) like water should make us cautious about expecting an unvarying trend of any correlation between two variables, like CO2 concentration and global average surface temperature (indicative of tropospheric energy-per-mass), in a system (or substance) as incredibly complicated as the atmosphere (in its natural state, influenced by solar radiation and orbital effects).

Also, it is important to realize that global warming and the earth’s average temperature (particularly of the biosphere) is really an effect of the combined atmosphere-ocean system. The oceans are both chemical and heat sinks (they absorb gases, like CO2, and store heat, which is why polar ice shelves are melting). It is very likely that the energy-per-gram of the ocean-atmosphere system has reached some threshold that has triggered one or more unrecognized thermo-chemical cycles that are now absorbing heat and causing the lag we (i.e., climate scientists) observe between continuing CO2 emissions and global average temperature. Imagine an analogy to the vaporization of liquid water.

What is “fundamentally wrong” with climate models is that there is just too much going on in the natural system (Gaia, for romantics) for all of it to be known, or all the knowns-to-exist to be fully understood and mathematically abstracted and included in the computer simulations of the integrated reality of the atmosphere-ocean (and landmass surface) system. One hopes anomalies between theoretical results and measurements in the field, like those discussed by Hans von Storch (1), will enlighten scientists on the unrecognized phenomena and feedback mechanisms, so these processes can be included into new and improved climate models.

The models will never be “perfect” because the idea of being able to abstract all of nature in its expression as the earth’s biosphere, and simulate it computationally and exactly, is pure illusion. The full extent of natural reality is beyond the bounds of human intellect because human intellect is only a small subset of the full extent of natural reality: “Man is something nature is doing” (Alan Watts). However, the models could be refined to the point of being “good enough” — and probably already are — to guide us in making intelligent decisions about the conduct of globalized human social and economic activities. If and how we will are the real questions challenging us today.


1. Hans von Storch, Why Is Global Warming Stagnating?,

Also, previous difficulties in gathering geophysical data of climate history, and initial confusion in processing and analyzing it, could have made it seem that there was a “delay” in temperature rise for continuing CO2 input, until after resolution of such unrecognized errors would allow seeing a clear picture of the actual T-versus-CO2 relationship.

2. Temperature-Enthalpy at Constant Pressure

3. Pressure-Enthalpy at Constant Temperature


Originally published at on 29 July 2013, as:

Why Is Global Warming Stagnating?
Manuel García, Jr.


The context behind the argument made in The Latent Heat of Climate Change, Redux is given by the following two articles. The first is an outline of the scientific phenomena producing global warming, and the second describes, in general, how those phenomena are abstracted into computer codes, for the numerical simulation of the dynamics of Earth’s climate system.

Closing The Cycle: Energy and Climate Change
25 January 2014

Climate and Carbon, Consensus and Contention
18 September 2017, (4 June 2007)


The equivalent of “my book,” explaining global warming and climate change science, would be the totality of articles and blog posts collected here, under the title The Latent Heat of Climate Change, Redux. That collection (“my book”) including:

Energy for Society in Balance with Nature
8 June 2015 (27 February 2012)

The Atlantic Overturning Current Is Slowing
12 April 2018


Richard Dedekind & Irrational Numbers

This post is entirely the work of Patrick Weidhaas, a mathematician and friend.


Patrick Weidhaas: “I recently wrote a math article on the very successful definition of the real numbers by the German mathematician Richard Dedekind (1831-1916). He came up with the “Dedekind cuts.” I learned about this in college and never fully understood it — and wasn’t that interested in it. Only lately did I fully appreciate the significance of his attempt to define the real numbers purely through arithmetic — without any help from geometry.”

Patrick Weidhaas: “This is a photo I took in Berlin on September 11, 2010. It is one of my favorite shots. I still remember the late sunny afternoon as I encountered this blue bridge and the small lake (“Königssee”) below.”