Global Warming Prediction L. David Roper Professor Emeritus of Physics Virginia Polytechnic Inst. & St. Univ. [email protected] .

Global WarmingGlobal WarmingPredictionPrediction

L. David RoperL. David RoperProfessor Emeritus of PhysicsProfessor Emeritus of Physics

Virginia Polytechnic Inst. & St. Univ.Virginia Polytechnic Inst. & St. Univ.

[email protected]@vt.eduhttp://arts.bev.net/RoperLDavidhttp://arts.bev.net/RoperLDavid

http://www.roperld.com/science/GlobalWarmingPrediction.htmhttp://www.roperld.com/science/GlobalWarmingPrediction.htm

Global Warming and Peak Oil may be the greatest challenges that humans have encountered in the last

10,000 years.

Global Warming PredictionGlobal Warming Prediction It is very important to account for fossil-fuels It is very important to account for fossil-fuels

depletion when calculating Global Warming depletion when calculating Global Warming predictions.predictions.

Otherwise, it might be assumed that more Otherwise, it might be assumed that more carbon can be put into the atmosphere from carbon can be put into the atmosphere from burning fossil fuels than physically possible.burning fossil fuels than physically possible.

Calculating fossil-fuels depletion is not exact, Calculating fossil-fuels depletion is not exact, but can be estimated reasonably well.but can be estimated reasonably well.

Fossil Fuels Global WarmingFossil Fuels Global Warming Fit depletion curves to extraction data for coal, Fit depletion curves to extraction data for coal,

crude oil and natural gas using discoveries data crude oil and natural gas using discoveries data and reserves estimates.and reserves estimates.

Calculate the carbon emitted due to burning fossil Calculate the carbon emitted due to burning fossil fuels and the COfuels and the CO22 concentration in the concentration in the

atmosphere, accounting for residence time.atmosphere, accounting for residence time. Calculate the Earth temperature due to the COCalculate the Earth temperature due to the CO22 in in

the atmosphere, including time lag.the atmosphere, including time lag. Consider triggering of other effects that raise Consider triggering of other effects that raise

temperature, including temperature feedbacks temperature, including temperature feedbacks that increase COthat increase CO22 concentration. concentration.

12

1

12

2 1 exp

1 2 1 exp

nn

n

n

t t

QP t

n t t

Verhulst Function for resources depletion.

Verhulst Function: An asymmetric peaked curve.

Q = amount already extracted + amount left to be extracted =

total amount to be extracted

n ≠ 1 allows asymmetry.

Peak OilOil discoveries will not allow higher average

extraction.

Skewed toward later times.

You can’t extract it if you have You can’t extract it if you have not discovered it!not discovered it!

The areas under the two curves are the same: ~2x1012 barrels.

Areas under both curves are the same.That is, the amount discovered equals the amount extracted.

discoveries

extraction

Gas discoveries will not allow higher average

extraction.

Peak Gas

Skewed toward later times.

You can’t extract it if you have You can’t extract it if you have not discovered it!not discovered it!

The areas under the two curves are the same: ~8x1015 cu. ft.

Areas under both curves are the same.That is, the amount discovered equals the amount extracted.discoveries

Double known coal. Unlikely!

Known existent coal (EIA)

Peaks between 2060 & 2100

Factors and AssumptionsFactors and Assumptions Coal = 50% carbon, short ton = 0.907 tonnesCoal = 50% carbon, short ton = 0.907 tonnes Crude oil = 84% carbon, bbl = 0.136 tonnesCrude oil = 84% carbon, bbl = 0.136 tonnes Natural gas = 76% carbon, tcf = 0.0189 tonnesNatural gas = 76% carbon, tcf = 0.0189 tonnes COCO22 concentration in ppmv = concentration in ppmv = 0.470.47 x gigatonnes x gigatonnes

carbon emitted (may increase with high carbon emitted (may increase with high concentration; i.e., may be nonlinear; see later)concentration; i.e., may be nonlinear; see later)

Climate sensitivity = Climate sensitivity = 3°C3°C for doubling CO for doubling CO22

25% of fossil fuels are used to make useful 25% of fossil fuels are used to make useful materials or are lost instead of being burned.materials or are lost instead of being burned.

Background year 1700 COBackground year 1700 CO22 concentration = concentration = 280 280

ppmvppmv

20% left after 250 years

10% left after 2000 years

6% left after 10,000 years

Equation for CO2 left in nth year for emissions in all previous years.

1

0.0875exp 0.165exp 0.733exp35600 682 50.8

where factor (0.47x0.84 for crude oil) and amount burned at time in gigatonnes.

nn i n i n i

n ii

i i

t t t t t tC t g E t

g E t t

Coal CO2 emissions and CO2 concentration contribution.

Shift in ppmv is due to CO2 residence time.

Crude-oil CO2 emissions and CO2 concentration contribution.

Shift in ppmv is due to CO2 residence time.

Natural-Gas CO2 emissions and CO2 concentration contribution.

Shift in ppmv is due to CO2 residence time.

Fossil-Fuels CO2 emissions and CO2 concentration contribution.

CO2 concentration due to Fossil-Fuels burning

Peaks at about 2110.

CO2 concentration due to Fossil-Fuels burning + background

Below measured data, as it should be.

Non-Fossil-Fuels CONon-Fossil-Fuels CO22 Emissions Emissions

Assume that non-fossil-fuels COAssume that non-fossil-fuels CO22

concentration is proportional to concentration is proportional to concentration due to burning concentration due to burning fossil fuels.fossil fuels.

• Deforestation• Soil depletion• Cement production• Domestic animals

Fit of COFit of CO2 2 Concentration Data to Concentration Data to

Fossil-Fuels EmissionsFossil-Fuels Emissions

Pre-fossil-fuels industrialization

NFF=14% of FF

CO2 concentration due to Fossil-Fuels burning + Non-fossil-fuels sources;latter assumed proportional to fossil-fuels concentration.

CO2 concentration due to Fossil-Fuels burning + Non-fossil-fuels + background

465 ppmv

Carbon-dioxide concentration due to burning fossil fuels with non-fossil fuels emissions,

assuming that no Earth states are triggered.

It peaks at about 2100 instead of rising into the next century as many assume.

Climate Sensitivity (s)Climate Sensitivity (s)Earth average atmospheric temperature rise Earth average atmospheric temperature rise

due to doubling the carbon-dioxide due to doubling the carbon-dioxide concentration in the atmosphere. Accounts concentration in the atmosphere. Accounts for fast feedbacks, such as ice melting.for fast feedbacks, such as ice melting.

The average is The average is about 3 degrees Celsiusabout 3 degrees Celsius..

It must be applied each year using the carbon-It must be applied each year using the carbon-dioxide concentration for that year.dioxide concentration for that year.

CC00=concentration for =concentration for reference year (1700)reference year (1700)..

0

3ln

ln 2n

n

C tdT t

C

Climate-Response FunctionClimate-Response FunctionThere is a time lag for the atmospheric There is a time lag for the atmospheric

temperature after carbon emissions.temperature after carbon emissions.

Data errors are large.

Fit of two hyperbolic tangents to the data.

Due to energy absorbed and released later in mostly the oceans, but also in ice.

Climate-Response FunctionClimate-Response Function

The climate-sensitivity function is multiplied by a series of two hyperbolic tangents:

Temperature lag is due to energy absorbed and released later in mostly the oceans, but also in ice.

1 1

2773 0.6320.368 tanh 1 tanh ln

ln 2 10.5 2 524

nin i n i

ni i

C tt t t tdT t

C t

1.3 degrees C

Close to the current measured value.

Although the temperature is not extremely high, it hangs around for a long time.

Does not account for fluctuations due to global dimming.

Temperature & CO2 are mutually reinforcing (positive feedback).

8°C

Disaster region!Peak in this

calculation.

Ice age to current interglacial is about 8 degrees C in Antarctica and about half that in the temperate

regions.

Why such a high projection?!

Assume carbon sequestration or a coal-burning moratorium.

Probably optimistic!

1 20501 tanh

2 25

tf

Assume carbon sequestration or a coal-burning moratorium.

Coal

CO2 is somewhat reduced by carbon sequestration

or a coal-burning moratorium.

430 ppmv; reduced from 465

Temperature is somewhat reduced by carbon sequestration

or a coal-burning moratorium.

1.1 degrees C; reduced from 1.3

Will we have waited too late?!

Double the coal extracted.

Coal

CO2 concentration due to doubled coal extraction

490 ppmv

Temperature is increased due to doubled coal extraction.

1.65 degrees CInstead of 1.3

Temperatures for some of the cases considered

Coal Moratorium or Carbon Sequestration

Double Coal

Assumes that there is no triggering of Earth states.

!Some Nightmares!!Some Nightmares! Suppose concentration/emissions factor Suppose concentration/emissions factor

changes with increasing concentration from changes with increasing concentration from 0.47 to 0.94 (land and ocean become 0.47 to 0.94 (land and ocean become saturated with COsaturated with CO22).).

Suppose permafrosted tundra release of Suppose permafrosted tundra release of carbon during the next century (example of carbon during the next century (example of temperature feedback).temperature feedback).

Suppose climate sensitivity changes from 3 Suppose climate sensitivity changes from 3 to 4 over the next two centuries. (It is known to 4 over the next two centuries. (It is known that it changes to 6 over millennia because that it changes to 6 over millennia because of slow feedbacks.)of slow feedbacks.)

Suppose concentration/emissions factor changes Suppose concentration/emissions factor changes with concentration from 0.47 to 0.94 (doubled).with concentration from 0.47 to 0.94 (doubled).

Due to land and oceans being saturated with carbon dioxide.

820 ppmvAssumes hyperbolic-tangent change with 450 ppmv break

point and 50 ppmv width.Disaster Region!

Suppose emissions/concentration Factor changes Suppose emissions/concentration Factor changes with concentration from 0.47 to 0.94 (doubled).with concentration from 0.47 to 0.94 (doubled).

Dangerously high temperatures

2.7 degrees C

Assume permafrosted tundra release of carbon.

Total 400 gigatonnes

Example of temperature feedback; there are other temperature feedbacks.

CO2 concentration due to permafrosted tundra release of carbon

Total CO2 concentration including permafrosted tundra release of carbon

Disaster Region!

555 ppmv

Temperature including permafrosted tundra release of carbon.

Disaster Region!1.8 degrees C

Worst case CO2 concentration

Most likely fossil-fuels depletion, CO2 feedback & carbon release

in Arctic

1110 ppmv !Calamitous!

Worst case temperatureWill cause terrible catastrophes for human life. (See Six Degrees: Our Future on a Hotter Planet by Mark Lynas.)

4.5 degrees Cfor climate sensitivity

change to 4

3.5 degrees C for climate

sensitivity = 3

Approximately the same temperature change between the last glacial maximum and now!

Temperatures for some of the cases considered

Coal Moratorium or Carbon Sequestration

Double Coal

!Could a coal moratorium keep those disastrous

Earth states from triggering?!

Fossil Fuels Burning ReductionFossil Fuels Burning Reduction

Reduces temperature below now, which might keep from triggering carbon releases and other temperature-raising feedbacks.

ConclusionsConclusions Peaking fossil fuels keeps COPeaking fossil fuels keeps CO22

concentration from going extremely high, concentration from going extremely high, unless it triggers other effectsunless it triggers other effects..

Since temperature rise of about 0.8°C from Since temperature rise of about 0.8°C from 1818thth century is already causing disastrous century is already causing disastrous events, the continuing increase of another events, the continuing increase of another 1°C or more will cause even more disasters 1°C or more will cause even more disasters and may other Earth changes that will cause and may other Earth changes that will cause a higher temperature.a higher temperature.

The peaking of fossil fuels may be as large The peaking of fossil fuels may be as large immediate disaster as is global warming.immediate disaster as is global warming.

World Population ProjectionsWorld Population Projections

Fit of population to available fossil-fuels energy 1950-2006.Fit of population to available fossil-fuels energy 1950-2006.

Population without renewable energy

Population with renewable energy

Next Major Ice Age with Global Warming EffectNext Major Ice Age with Global Warming Effect

Accounting for claim that Earth average temperature changes are about half Antarctica average temperature changes.

This lecture is on the Internet, along with other This lecture is on the Internet, along with other related lectures:related lectures:

http://www.roperld.com/science/http://www.roperld.com/science/GlobalWarmingPrediction.pptGlobalWarmingPrediction.ppt

http://www.roperld.com/science/energy.ppt http://www.roperld.com/science/energy.ppt (Future Energy)(Future Energy)

http://www.roperld.com/science/http://www.roperld.com/science/energyGWNMIA.ppt (Energy, Global energyGWNMIA.ppt (Energy, Global Warming and the Next Major Ice Age)Warming and the Next Major Ice Age)