topic 8: energy, power, climate change 8.6 global warming

8.6.1 Describe some possible models of global warming.

8.6.2 State what is meant by the enhanced greenhouse effect.

Topic 8: Energy, power, climate change8.6 Global warming

Describe some possible models of global warming.

The Sankey diagram presented at the end of Topic 8.5 The greenhouse effect showed that overall, the intensity entering each interface balanced precisely with the intensity leaving each interface.

But if the input and output intensities are balanced the temperature remains constant. We show our first “model” for global warming here:


34075

30

165

195

70

350 40 325 100

520

GROUND

GREENHOUSE ATMOSPHERE490

Iin – Iout = 0 ∆T = 0 1st model constraint for temperature change


Our second model describes the temperature change when Iin – Iout 0…

Recall the concept of surface heat capacity.

Recall that intensity I = P/A and P = Q/∆t. Then Q = CsAT (surface heat capacity)

Qin – Qout = CsAT (net heat gain/loss)

(Pin – Pout)∆t = CsAT (Q = P∆t)

(Pin – Pout)∆t/A = CsT

(Iin – Iout)∆t = CsT (I = P/A)

Note: The 1st is just a special case of the 2nd.


Cs = Q / (AT) surface heat capacity

Cs = 4108 J K-1 m2 surface heat capacity

T = (Iin – Iout)∆t/Cs 2nd model constraint for temperature change



PRACTICE: Our equilibrium model has been adjusted as shown. Use the 2nd model constraint to find the change in temperature over one year.SOLUTION:At the interface of atmosphere and ground we have:

Iin = 165 + 335 = 500Iout = 360 + 20 + 110 = 4901 year is ∆t = 1(365)(24)(3600 s) = 3.15107 s.Thus T = (Iin – Iout)∆t/Cs

T = (500-490)(3.15107)/(4108) = 0.79 K

34075

30

165

195

70

360 20 335 110

540

GROUND

GREENHOUSE ATMOSPHERE500


Real global warming models are extremely complex, simply because the earth and all of its energy-exchanging and storing systems are extremely complex. Supercomputers are used with some success.

To gain some sort of insight into computer modeling, consider the following simple model:

5 kg of water is added to an aquarium once each second.

10% of the water is removed from the aquarium once each second.


FYIThe added water represents the incoming energy and the removed water is the outgoing energy.


At first glance it might appear that the water level will never stop increasing.

But consider the time when 5 kg is exactly 10% of the total water in the aquarium.

From that time on, the water will be removed exactly as fast as it is added.

Thus, at that time the “energy” represented by the water mass will have reached equilibrium.


FYI

The challenge is to find out how long it takes to reach equilibrium.

Hand calculations are tedious but possible:



PRACTICE: For the water model just proposed, complete the table:

SOLUTION:The next cell would be 8.55 + 5 = 13.55.The next cell would be 0.10(13.55) = 1.355.The next cell would be 13.55 – 1.355 = 12.195.

time / s in / kg pre-total / kg out / kg total/ kg

0 0 0.00 0.000 0.000

1 5 5.00 0.500 4.500

2 5 9.50 0.950 8.550

3 5 13.55 1.355 12.195



EXAMPLE: Create a spreadsheet to determine what the mass will be when the aquarium reaches equilibrium and how many seconds it will take.

SOLUTION: Create a new spreadsheet with five columns as shown here:

Highlight cell A3 and type in =A2+1 as shown.

This will increment the A cells by 1 second.




SOLUTION:

Highlight cell B2 and enter 5.Highlight cell C3 and type in =B3+E2 as shown.

This will add the new input of 5 to the previous total.




SOLUTION:

Highlight cell D3 and enter =0.1*C3.

Highlight cell E3 and enter =C3-D3.




SOLUTION:

Highlight cells A3 through D3 all the way down to about row 100.

Then select EditFillDown (or Ctrl+D) to copy down all of the formulas to each cell for all 100 rows.




SOLUTION:

Finally, make a graph or read the spreadsheet:

The graph shows that the mass of water will be 45 kg at equilibrium.

This will occur after about 45 seconds.

Water Vs. Time

0.0000

5.0000

10.0000

15.0000

20.0000

25.0000

30.0000

35.0000

40.0000

45.0000

50.0000

0 20 40 60 80 100 120

time / kg

wat

er /

kg

equilibrium



EXAMPLE: Compare the following two images showing the world weather for July 1, 1998:

Actual satellite view

Hadley Centre's computer simulation

0 90E 180 90W

60 N

30 N

0

30 S

60 S

60 N

30 N

0

30 S

60 S

Note the minor differences

State what is meant by the enhanced greenhouse effect.

Global warming (and cooling) are both natural processes and fluctuate in a periodic manner. The four causes of global warming and cooling are:

-The sun’s varying power output.

-The Milankovitch cycles.

-Greenhouse gas fluctuation.

-Radioactivity.

We will discuss each in turn on the following slides.

The enhanced greenhouse effect is that portion of the greenhouse effect that is caused by humans.



The sun’s varying power output

Because the sun is fluid rather than solid, different latitudes rotate at different rates in a process called differential rotation.

Differential rotation causes an 11-year sunspot and solar flare variation (with changing power output) and magnetic pole reversal.




The first animation shows sunspots during a single rotation of the sun on its axis.

The next animations show how far-reaching solar flares are.




There is also a centuries-long variation in overall power output of the sun, with the 11-year sunspot activity superimposed:


FYIThe Maunder Minimum was a mini ice-age.

1645 - 1715 Present

Centuries 11 years

The Maunder Minimum


The Milankovitch cycles

These extraterrestrial factors were enumerated in 1941 by Serbian Milutin Milankovitch in his great work on ice ages.

Factor 1: The elliptical cycle.-In a 100,000-year long cycle the earth's elliptical orbit changes its shape.

-Currently, our orbit is nearly circular: The fluctuation in the solar radiation reaching us between January and July is only 6%.

-When the orbit is at its most eccentric fluctuation can be as great as 30%.


http://www.wwnorton.com/college/geo/animations/milankovitch_cycle.htm




Factor 2: The tilt cycle.-In a 42,000-year long cycle the earth's rotational axis tilt varies between 21.8° and 24.4° (Currently, our tilt is 22.5°).

-Tilt determines at which latitude most of the solar radiation falls.


22.5° 24.4°21.8°


FYIWhen Vega marks true north the intensity of the seasons is much more extreme.




Factor 3: The wobble cycle.-In a 22,000-year long cycle the earth's rotational axis wobbles like a precessing top.

-Currently, our north pole is aimed at Polaris, the Pole Star.

-The axis can also point to Vega, and all points in between.


PolarisVega





Milankovitch’s work was not recognized until the late 1960s because it was in Serbian.

In the 60s just such cycles were being discovered in sediment and ice-core studies.


FYIAt their most extreme, Milankovitch cycles bring an annual variation of the sun’s power of less then 1/10th of 1 percent.Yet this seemingly trivial variation causes Earth’s average temperature to rise or fall by 9°F!



Greenhouse gas fluctuation

Both solar fluctuation and the Milankovitch cycles are extraterrestrial sources of global warming and cooling.

One of the two terrestrial causes are the greenhouse gases. (The other is the earth’s interior heat.)

Carbon dioxide, water vapor, methane, and nitrous oxide are all greenhouse gases which are capable of absorbing a portion of the IR energy emitted by the earth.


FYIThe enhanced greenhouse effect is caused by humans increasing their levels.


Radioactivity

The interior of the earth itself is quite hot.The two sources of internal heat are-radioactive minerals within the mantle, which provides about 80-90% of Earth’s internal heat,

-and accretion remnants, which is the energy left over from the forming of the earth through accretion.


FYIThese effects are quite minimal in the global warming scenario. Recall that volcanoes only add about 1% of the CO2 added yearly to the atmosphere as compared to human-added CO2.


The controversies

Data may or may not convince one of the first controversy but probably Earth is warming.

Given that humans produce greenhouse gases we can probably rule out the second controversy.

Extremely complex computer simulations are integral to deciding the third controversy, which helps to explain its divisiveness.


Global warming is really happening. Global warming is not really happening. Global warming is enhanced by man. Global warming is not enhanced by man. Enhanced greenhouse effect is a significant portion of the overall global warming. Enhanced greenhouse effect is not a significant portion of the overall global warming.

8.6.3 Identify the increased combustion of fossil fuels as the likely major cause of the enhanced greenhouse effect.

8.6.4 Describe evidence that links global warming to increased levels of greenhouse gases.

8.6.5 Outline some of the mechanisms that may increase the rate of global warming.

-Increased Greenhouse gases caused by burning fossil fuels.

-Decreased albedo caused by melting ice caps.


Identify the increased combustion of fossil fuels as the likely major cause of the enhanced greenhouse effect.

Note that deforestation accounts for only 8.1 / (29.2 + 8.1 + 8.4 + 3.7 + 0.5) = 16% of human-caused greenhouse gas production. Thus fossil fuels produce 84% of our greenhouse emissions.


Breakdown of world greenhouse gas

emissions in 2004 by gas (except ozone), in

billion tonnes CO2 equivalent. From IPCC,

2007.

Describe evidence that links global warming to increased levels of greenhouse gases.

The graph shows the seasonal variation of atmospheric CO2.

Note the seasonal fluctuations showing an increase in cooling months and a decrease in warming months.

Note the overall increase in CO2 levels.


cooling

months

warming

months

ftp://ftp.cmdl.noaa.gov/ccg/co2/trends/co2_mm_gl.txt

PRACTICE: Explain why the atmospheric concentration of CO2 increases in winter and decreases in summer.SOLUTION:It’s is all about living carbon sinks that store CO2 in the summer and release it in the winter: Namely- plants and their respiration and decomposition.



ftp://ftp.cmdl.noaa.gov/ccg/co2/trends/co2_mm_gl.txt


The previous data shows a steady increase in atmospheric CO2. But how does this correlate to average temperature? And how do we determine the geological correlations?

The answer is ice cores.From the concentration of the isotopes of hydrogen in the water we can determine the mean global temperature.

From the trapped air we can determine the greenhouse constituents of the atmosphere.


Ice core sections stored at the National Ice Core Laboratory in Colorado


Vostok ice core drilling site,

Antarctica

Analysis of the core has been completed to a depth of 3350 meters, representing about 440,000 years of climate history.


The graph shows the results of the Vostok ice core analyses, representing CO2 levels and temperatures going back 425,000 years (before present).

Note the very strong correlation between them.


Which Milankovitch cycle seems to be driving this variation? 100000 y The

elliptical variation.



The temperature and CO2 overlays show approximately that sometimes temperature change leads, and sometimes it follows change in CO2 levels:

So which change causes the other to change?


A more detailed plot shows perhaps that CO2 change leads temperature in change. But the overall percentages from the previous graph gives the lead slightly to temperature…


http://www.skepticalscience.com/pics/ShakunFig2a.jpg

Outline some of the mechanisms that may increase the rate of global warming.

Obviously, increased need for energy leads to increased burning of fossil fuels (or biomass) which leads to more greenhouse gases, which would increase the rate of global warming.FYIThis graph is compiled by the wishful thinkers located at http://www.via-azul.eu/



Another mechanism would be the decreased albedo caused by melting ice caps. Ice and snow have the highest albedo (0.6) of any terrestrial landscape. Less light would be reflected by snow and ice and more would be absorbed.


Anecdotal evidence -

Observations of changes in the environment in

our lifetimes...


Deforestation is also a factor. Forests are active carbon sinks, removing CO2 from the atmosphere during respiration.


8.6.6 Define coefficient of volume expansion.

8.6.7 State that one possible effect of the enhanced greenhouse effect is a rise in mean sea level.

8.6.8 Outline possible reasons for a predicted rise in mean sea level.


Define coefficient of volume expansion.Substances E X P A N D as they are warmed up according to the equation

where is the coefficient of volume expansion.The formula shows that the change in volume of an object is proportional to its original volume times the temperature change.This formula works for both solids and liquids.


V = V0T expansion due to ∆T

State that one possible effect of the enhanced greenhouse effect is a rise in mean sea level.

As the ocean warms up its seawater expands, taking up more volume. Thus global warming will cause the sea level to rise.

Furthermore as Earth warms up, landlocked glaciers will melt, adding to the rise in sea level.

FYIDuring ice ages when the land ice is enhanced by continental-sized glaciers, the sea level can decrease by 100 meters!The ice melt we are most concerned most with, in terms of present-day sea level rise, is glaciers and the Antarctic ice shield.


8.6.9 Identify climate change as an outcome of the enhanced greenhouse effect.

8.6.10 Solve problems related to the enhanced greenhouse effect. Problems could involve volume expansion, specific heat capacity and latent heat.


Done!

Solve problems related to the enhanced greenhouse effect.


V = V0T expansion due to ∆T

From the formula we can solve for : = V / V0T = (V2-V1)/V1(T2-T1).

PRACTICE: The land ice sheet consists of landlocked glaciers (in mountains) and the Antarctic ice shield. The north polar ice sheet is over water (floating). Explain why melting the north polar ice shield does not change the sea level, whereas melting the Antarctic ice shield does.SOLUTION:A floating object displaces water equal to its weight.Thus when floating ice becomes water, it just fills in the space in the ocean it already took up and doesn’t change its depth.



8.6.11 Identify some possible solutions to reduce the enhanced greenhouse effect.

-Increase power production efficiency.

-Replace coal and oil with natural gas.

-Use combined heating and power systems (CHP).

-Use renewable energy and nuclear power.

-Use CO2 capture and storage.

-Use hybrid vehicles.


8.6.12 Discuss international efforts to reduce the enhanced greenhouse effect.

-Intergovernmental panel on climate change (IPCC),

-Kyoto Protocol,

-Asia-Pacific Partnership on Clean Development and Climate (APPCDC).


topic 8: energy, power, climate change 8.6 global warming

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