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Hosted by Decisioneering, Inc.

July 19, 2007

Global Warming

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Guest SpeakerGaetan ‘Guy’ Lion

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Objective: simulate temperature increase over next century using IPCC timeframe

• Starting point: temperature 1980 – 1999 period.• Ending point: 2090 – 2099 period.

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Basic model structure

If not for IPCC timeframe intricacies, the model would be simple.

1. Record most current temperature (14.6 degree Celsius).

2. Next, simulate CO2 concentration by 2099 (i.e. 600 ppm)

3. Using regression, convert CO2 concentration into temperature level (16.3 degree Celsius).

4. Calculate temperature increase: 16.3 – 14.6 = 1.7 deg. Celsius.

Current temperature 14.6 Degree CelsiusSimulated CO2 concentr. 600.0 ppmFuture temperature 16.3 Degree CelsiusIncrease in temperature 1.7 Degree Celsius

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The Variables

Independent Variable Dependent Variable

CO2 concentration (parts per million)

300

310

320

330

340

350

360

370

380

390

Global average temperature (Land Ocean index)

13.8

13.9

14.0

14.1

14.2

14.3

14.4

14.5

14.6

14.7

De

gre

e C

els

ius

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Simulating CO2 concentration by 2099

CO2 %Year concentr. change2001 371.02002 373.1 0.56%2003 375.6 0.68%2004 377.4 0.48%2005 379.6 0.57%2006 382.2 0.68%2007 384.0 0.48%2008 384.7 0.19%2009 386.6 0.48%

Forecast

Annual growth in CO2 concentration (ppm)

0.00%

0.10%

0.20%

0.30%

0.40%

0.50%

0.60%

0.70%

0.80%

0.90%

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The Regression Models: Log & LinearCo2 concentration vs Temperature

Natural Log Model

y = 3.641Ln(x) - 7.1093

R2 = 0.82

13.8

13.9

14.0

14.1

14.2

14.3

14.4

14.5

14.6

14.7

310 320 330 340 350 360 370 380 390

CO2 parts per million concentration

Deg

ree

Cel

ciu

s

Co2 concentration vs Temperature. Linear Model

y = 0.0105074x + 10.5373318

R2 = 0.82

13.8

13.9

14.0

14.1

14.2

14.3

14.4

14.5

14.6

14.7

310 320 330 340 350 360 370 380 390

CO2 parts per million concentration

Deg

ree

Cel

ciu

sNatural Log model.

Regression StatisticsMultiple R 0.904

Adjust. R2 0.812Standard Error 0.091

Coeffi.Intercept -7.11Slope 3.64

Linear model.Regression Statistics

Multiple R 0.906

Adjust. R2 0.816Standard Error 0.090

Coeffi.Intercept 10.54Slope 0.01

Until recently, climatologists debated whether the relationship between CO2 and temperature was logarithmic or linear.

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The Natural Log Model Simulation

Year CO2 conc.

The model simulates temperature level by 2090 – 2099 two ways. One way just picks a year at random within the decade. The other way calculates the average over the decade.

Natural Log Model -Temperature increase

1980 - 1999 Temperature 14.24(mid point between Average & Median)

CoefficientsIntercept -7.11Slope 3.64St. error 0.09

Unadjusted Error AdjustedYear temp. term temp.

1 2090 15.88 0.11 15.992 2091 15.89 -0.09 15.803 2092 15.91 0.05 15.964 2093 15.93 -0.03 15.905 2094 15.95 -0.11 15.836 2095 15.97 -0.04 15.937 2096 15.98 -0.11 15.878 2097 16.00 -0.03 15.979 2098 16.01 0.09 16.10

10 2099 16.04 -0.11 15.93

Temperature levela) Using random funct. 7 15.87b) Using average 90 - 99 15.93

Temp. increase over 1980 - 1999 mediana) Using random function 1.63b) Using average 90 - 99 1.68

2090 552.0 0.32%2091 553.7 0.32%2092 556.8 0.56%2093 560.0 0.56%2094 562.5 0.46%2095 565.7 0.56%2096 567.4 0.32%2097 570.6 0.56%2098 572.6 0.35%2099 576.5 0.68%

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The Linear Model Simulation

Year CO2 conc.

Linear Model -Temperature increase

1980 - 1999 Temperature 14.24(mid point between Average & Median)

CoefficientsIntercept 10.54Slope 0.01St. error 0.09

Unadjusted Error AdjustedYear temp. term temp.

1 2090 16.34 0.11 16.442 2091 16.36 -0.11 16.253 2092 16.39 -0.14 16.254 2093 16.42 -0.03 16.395 2094 16.45 0.05 16.506 2095 16.48 -0.05 16.447 2096 16.50 -0.19 16.318 2097 16.53 -0.03 16.509 2098 16.55 -0.01 16.54

10 2099 16.60 0.13 16.72

Temperature levela) Using random funct. 10 16.72b) Using average 90 - 99 16.44

Temp. increase over 1980 - 1999 median Temp. increase over 1980 - 1999 mediana) Using random function 2.48b) Using average 90 - 99 2.19

2090 552.0 0.32%2091 553.7 0.32%2092 556.8 0.56%2093 560.0 0.56%2094 562.5 0.46%2095 565.7 0.56%2096 567.4 0.32%2097 570.6 0.56%2098 572.6 0.35%2099 576.5 0.68%

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Output: Temperature increase by end of 21st century

CO2 CO2 Temperature increaseConcentr. Concentr.in 2090 in 2099 Using avg. Random Using avg. Random

Average 553.3 576.1 1.71 1.71 2.23 2.22Median 553.0 575.8 1.71 1.71 2.22 2.22Stand. deviation 19.9 23.6 0.14 0.17 0.23 0.25Stand. error 0.6 0.7 0.00 0.01 0.01 0.01

Percentiles to study tails1.0% 508.0 521.1 1.38 1.33 1.73 1.652.5% 516.3 533.2 1.44 1.37 1.79 1.755.0% 522.9 540.1 1.49 1.42 1.88 1.82

95.0% 586.4 616.5 1.95 2.00 2.63 2.6697.5% 594.4 625.7 2.00 2.05 2.72 2.7699.0% 602.1 635.9 2.06 2.14 2.80 2.82

Log Model Linear Model

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IPCC Scenarios Definitions

Source: IPCC Summary for Policymakers.

Technological energy emphasis seems to be the most influential factor in determining CO2 concentration CAGR.

Scenario

CO2 concentration

CAGRTechnological

energy emphasis Economic growthPopulation

growth

B1 0.51% Clean & efficientRapid change towards a service and info economy

Population peaks mid century

A1T 0.68% Non-fossil based Very rapidPopulation peaks mid century

B2 0.83%More tech change than in A1s and B1

Less rapid than in A1s and B1.

Population continues to rise but slower than in A2

A1B 0.90%Balance across all sources

Very rapidPopulation peaks mid century

A2 1.33% Slow tech change Relatively slowerPopulation continues to rise

A1FI 1.58% Fossil intensive Very rapidPopulation peaks mid century

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Models vs IPCC Scenarios

Global temperature increase by end of centuryIn degree Celsius

Models Best est. Min. Max. VolatilityLinear 2.2 1.7 2.8 0.25LN 1.7 1.4 2.1 0.17

IPCCScenario Best est. Min. Max. Volatility

B1 1.8 1.1 2.9 0.46A1T 2.4 1.4 3.8 0.61B2 2.4 1.4 3.8 0.61

A1B 2.8 1.7 4.4 0.69A2 3.4 2.0 5.4 0.87

A1FI 4.0 2.4 6.4 1.02

95% C.I.

95% C.I.

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Are some IPCC scenarios higher because of other greenhouse gases? No.

Radiative Forcing componentUnit is watts per square meter

Anthropogenic effects:Carbon dioxide CO2 1.66 96.5%Methane CH4 0.48Nitrous oxide N2O 0.16Halocarbons 0.34Ozone - Stratospheric -0.05Ozone - Tropospheric 0.35Stratospheric water vapor from CH4 0.07Surface albedo - Land use -0.20Surface albedo - Black carbon on snow 0.10Aerosol - direct effect -0.50Aerosol - cloud albedo effect -0.70Linear contrails 0.01Subtotal* 1.60

Natural -solar irradiance 0.12

Total 1.72 100%

Source: IPCC Summary for Policy Makers* Does not sum up because of asymmetric uncertainties.

CO2 accounts for nearly 100% of the net radiative forcing from all sources.

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IPCC Scenarios are higher because of much higher CO2 concentration levels

CO2 concentration level in ppmHistoric.

rate B1 A1T B2 A1B A2 A1FI2005 380 380 380 380 380 380 3802010 387 389 393 396 397 406 4102015 395 399 406 412 415 433 4442020 403 410 420 430 434 463 4802025 411 420 435 448 454 495 5192030 419 431 450 467 475 529 5612035 428 442 465 487 497 565 6072040 436 454 482 507 519 603 6562045 445 465 498 529 543 645 7092050 454 477 515 551 568 689 7672055 463 490 533 574 594 736 8292060 473 502 552 599 621 786 8972065 482 515 571 624 650 840 9702070 492 528 591 650 679 898 10492075 502 542 611 678 711 959 11342080 512 556 632 707 743 1025 12262085 522 570 654 736 777 1095 13262090 533 585 677 768 813 1170 14332095 543 600 700 800 850 1250 1550

CAGR 0.40% 0.51% 0.68% 0.83% 0.90% 1.33% 1.58%

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IPCC Scenarios – CO2 concentration

IPCC scenarios - rise in CO2 concentration (ppm) by 2095

0

200

400

600

800

1000

1200

1400

1600

1800Hist. rate

B1

A1T

B2

A1B

A2

A1FI

A1FI

Historical rate

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Temp. Increase. Models vs 3 IPCC scenarios

Among the IPCC scenarios, B1 is the low scenario, A1B is the mid level one, and A1FI is the high one.

Watch carefully for the scale of the Y axes here.

Temperature increaseBest estimate

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

Year

Tem

per

atu

re in

cr.

Deg

ree

Cel

siu

s

LN

Linear

B1

A1B

A1FI

A1FI

Temperature increase Upper limit CI 95%

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

Year

Tem

per

atu

re in

cr.

Deg

ree

Cel

siu

s LN

Linear

B1

A1B

A1FI

Temperature increase Lower limit CI 95%

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Year

Tem

per

atu

re in

cr.

Deg

ree

Cel

siu

s LN

Linear

B1

A1B

A1FI

LN model

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Testing our regression coefficients vs IPCC scenarios

The coefficients of the natural log model replicate reasonably well the IPCC best estimates up to CO2 concentration of 850 ppm.

Difference be tween Mode ls and IPCC

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

600 700 800 850 1250 1550

CO2 concentration in ppm

Deg

ree

Cel

sius

Global temperature increase by end of centuryUnit is degree Celsius

IPCC CO2 LN IPCC Linear IPCCScenario Conc. model Best est. Differ. model Best est. Differ.

B1 600 1.94 1.80 0.14 2.60 1.80 0.80A1T 700 2.50 2.40 0.10 3.65 2.40 1.25B2 800 2.99 2.40 0.59 4.70 2.40 2.30

A1B 850 3.21 2.80 0.41 5.22 2.80 2.42A2 1250 4.61 3.40 1.21 9.43 3.40 6.03

A1FL 1550 5.39 4.00 1.39 12.58 4.00 8.58

Source: page 12 of IPCC Summary for Policymakers

Linear model

LN model

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Why is volatility so much higher for IPCC Scenarios?

Global temperature increase by end of centuryIn degree Celsius

Models Best est. Min. Max. VolatilityLinear 2.2 1.7 2.8 0.25LN 1.7 1.4 2.1 0.17

IPCCScenario Best est. Min. Max. Volatility

B1 1.8 1.1 2.9 0.46A1T 2.4 1.4 3.8 0.61B2 2.4 1.4 3.8 0.61

A1B 2.8 1.7 4.4 0.69A2 3.4 2.0 5.4 0.87

A1FI 4.0 2.4 6.4 1.02

95% C.I.

95% C.I.

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Another view of volatility. LN model vs B1

Volatility - the 95% Confidence Interval LN model vs IPCC - B1 scenario

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

2000

2010

2020

2030

2040

2050

2060

2070

2080

2090

Year

Tem

pera

ture

incr

. Deg

ree

Cel

sius

The natural log model and scenario B1 (IPCC) generate about the same best estimate in temperature increase (~ 1.8 degree Celsius). But, the confidence interval for the B1 scenario (green) is much wider at 1.8 degree Celsius vs only 0.68 degree Celsius for the log model (orange).

B1 scenario LN model

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Why volatility is higher in IPCC scenarios

• The IPCC estimates rely on numerous model sets that feed into each other.

• Algorithms capture all gases mentioned earlier. Each gas radiative forcing is associated with uncertainty (random variable).

• They capture many physical phenomenons such as cloud formation, precipitation, ice melting, ocean heat absorption, convection, radiation, etc…

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Generating higher Volatility

Natural Log Model -Temperature increase

1980 - 1999 Temperature 14.24(mid point between Average & Median)

Mean St. error Correl.Intercept -7.11 1.60Slope 3.64 0.27 -0.95

CO2concentr. Intercept Slope Temperature

2095 532.8 -7.11 3.64 15.74

Temperature increase 1.50

Volatility - the 95% Confidence Interval LN (high volatility) model vs B1 scenario

-4.0

-2.0

0.0

2.0

4.0

6.0

8.0

2000

2010

2020

2030

2040

2050

2060

2070

2080

2090

YearT

emp

erat

ure

incr

. Deg

ree

Cel

siu

s

LN model

B1

In this log model, I used the standard errors of the intercept and slope as random variables instead of the standard error of the regression. To moderate excessive volatility I used a high negative correlation (-0.95) between the two standard errors. But, resulting volatility was still way too high with a Confidence Interval that is too wide including large decrease in temperature.

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Thank you for attending the Web Seminar

Global Warming

Gaetan “Guy” LionE-mail: gaetanlion@gmail.com

July 19, 2007

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