GLOBAL WARMINGGLOBAL WARMING

Dr. Chris P. TsokosDistinguished University Professor

Vice President of IFNAJuly 03, 2008

KeynoteAddress: WCNA 2008

Orlando FloridaJuly 03, 2008

GLOBAL WARMINGGLOBAL WARMINGResearch Seminar Team

Chris P. TsokosGan LaddeRebecca WootenShou Hsing ShihBongjin ChoiYong XuDimitris Vovoras

Mathematical and Statistical Mathematical and Statistical Modeling of Global WarmingModeling of Global Warming

Do we scientifically understand the concept of “Global Do we scientifically understand the concept of “Global Warming”?Warming”?

Recent Definition: “GLOBAL WARMING- an increase Recent Definition: “GLOBAL WARMING- an increase in Temperature at the surface of the earth supposedly in Temperature at the surface of the earth supposedly caused by the greenhouse effects” (Greenhouse Effects- caused by the greenhouse effects” (Greenhouse Effects- Carbon Dioxide COCarbon Dioxide CO22 (greenhouse gas)) (greenhouse gas))

SupposedlySupposedly – assumed to be true without conclusive evidenceassumed to be true without conclusive evidence– Hypothetical, conjectural, etc.Hypothetical, conjectural, etc.

Wikipedia(on-line encyclopedia)

Defines the phenomenon of

“GLOBAL WARMING”

as the increase in the average temperature of the earth’s near-surface air and oceans in recent decades and its projected continuation.

MEDIA CHAOS: PRO AND MEDIA CHAOS: PRO AND CONCERNED (SKEPTICS)CONCERNED (SKEPTICS)

PRO - GLOBAL WARMINGPRO - GLOBAL WARMING *Intergovernmental Panel on Climate Change *Intergovernmental Panel on Climate Change

(IPCC) “Climate Change 2007”(IPCC) “Climate Change 2007” Increase in Temperature → Increase Sea LevelIncrease in Temperature → Increase Sea Level Unpredictable Pattern in RainfallUnpredictable Pattern in Rainfall Increase in Extreme Weather EventsIncrease in Extreme Weather Events Alterations in Agriculture YieldsAlterations in Agriculture Yields Increase in River FlowsIncrease in River Flows Etc.Etc.

PRO - GLOBAL WARMING PRO - GLOBAL WARMING (Continued)(Continued)

Award Winning Documentary–Vice President GoreAward Winning Documentary–Vice President Gore– Fiction VS. Reality / AwarenessFiction VS. Reality / Awareness– ABC: 20/20 / Give Me A Break!ABC: 20/20 / Give Me A Break!

A Number of Professional OrganizationsA Number of Professional Organizations– American Meteorological SocietyAmerican Meteorological Society– American Geographical UnionAmerican Geographical Union– AAASAAAS

National AcademiesNational Academies– Blame Human ActivitiesBlame Human Activities

CONCERNED / SKEPTICSCONCERNED / SKEPTICS Great Britain’s Channel 4 DocumentaryGreat Britain’s Channel 4 Documentary

– ““The Great Global Warming Swindle”The Great Global Warming Swindle” NASA ScientistsNASA Scientists

– Sun spots are hotter than previously thoughtSun spots are hotter than previously thought Danish National Space CenterDanish National Space Center

– Temperature changes are due to fluctuations in the Temperature changes are due to fluctuations in the sun’s output (NASA)sun’s output (NASA)

– (Stated: …there is absolutely nothing we can do to (Stated: …there is absolutely nothing we can do to correct the situation)correct the situation)

ABC – 20/20: Broadcast – “Give Me a Break”ABC – 20/20: Broadcast – “Give Me a Break”

CONCERNED / SKEPTICS CONCERNED / SKEPTICS (Continued)(Continued)

Times Washington Bureau Chief, Bill AdairTimes Washington Bureau Chief, Bill Adair– ““Global Warming has been called the most dire issue Global Warming has been called the most dire issue

facing the planet and yet, if you are not a scientist, it facing the planet and yet, if you are not a scientist, it can be difficult to sort out the truth”can be difficult to sort out the truth”

Finally, St. Pete Times, Jan 23, 2007Finally, St. Pete Times, Jan 23, 2007– ““Global Warming: Meet Your Adversary” By the Global Warming: Meet Your Adversary” By the

numbers: 9 out of 10 statistical Info. numbers: 9 out of 10 statistical Info. Not CorrectNot Correct

Wall Street JournalWall Street Journal“Global Warming is 300-years-old news”“Global Warming is 300-years-old news” ““The various kind of evidence examined by NRC – The various kind of evidence examined by NRC –

National Research Council, led it to conclude that National Research Council, led it to conclude that the observed disparity between the surface and the observed disparity between the surface and atmospheric temperature trends during the 20-year atmospheric temperature trends during the 20-year period is probably at least partially real”period is probably at least partially real”– Uncertainties in all aspects exist – can not draw any Uncertainties in all aspects exist – can not draw any

conclusions concerning “GW”conclusions concerning “GW”– NRC concludes that “Major Advances” in scientific NRC concludes that “Major Advances” in scientific

methods will be necessary before these questions methods will be necessary before these questions (GW) can be resolved.(GW) can be resolved.

… … spread fear of “Global Warming” demonizing, spread fear of “Global Warming” demonizing, hydrocarbon fuel.hydrocarbon fuel.

Do We Understand the Problem of Do We Understand the Problem of Global Warming?Global Warming?

Zero Legal Legislative Policies: Why?Zero Legal Legislative Policies: Why? Continental U.SContinental U.S

– Popular Claim to Global Warming: The Marriage of Popular Claim to Global Warming: The Marriage of Temperature and Carbon Dioxide (COTemperature and Carbon Dioxide (CO22))

Need to UnderstandNeed to Understand– Temperature Behavior (Type)Temperature Behavior (Type)– Carbon Dioxide (Type)Carbon Dioxide (Type)– Their RelationshipTheir Relationship

TemperatureTemperature

Atmospheric (2 or 3 Versions)Atmospheric (2 or 3 Versions) SurfaceSurface

– LandLand– Ocean (73%)Ocean (73%)

Historical Data: 1895-2007 / Daily, Historical Data: 1895-2007 / Daily, Weekly, Monthly, YearlyWeekly, Monthly, Yearly

Atmospheric Temperature DataAtmospheric Temperature Data

Version 1: United States Climate Division, Version 1: United States Climate Division, USCD, (1895-2007) 344 Climate DivisionsUSCD, (1895-2007) 344 Climate Divisions

Version 2: United States Historical Version 2: United States Historical Climatology Network, USHCN , (1895-2007) Climatology Network, USHCN , (1895-2007) 1219 Stations1219 Stations

Proposed Version: Stratified The Continental Proposed Version: Stratified The Continental U. S. in Equal SegmentU. S. in Equal Segment– Uniformly WeightedUniformly Weighted– Statistically Correct Statistically Correct

Creating Grid PointCreating Grid Point Select a random point in bottom left corner of map, Select a random point in bottom left corner of map,

use do loops to create points every x metersuse do loops to create points every x meters

Clipping Grid PointClipping Grid Point Clip the grids that fall within the boundary of the Clip the grids that fall within the boundary of the

polygonpolygon

Sampling Stations and Grid PointSampling Stations and Grid Point Output location of stations and grids in metersOutput location of stations and grids in meters

Sampling Stations and Grid PointSampling Stations and Grid Point Select sampling locations within a certain radius of Select sampling locations within a certain radius of

the grid pointsthe grid points

Comparison on Version 2 Temperature Comparison on Version 2 Temperature VS. Proposed VersionVS. Proposed Version

Version 2 * Proposed Version *

Year Temperature Year Temperature

1998 55.04 1934 56.0452266

2006 54.97 1921 55.32124871

1934 54.87 1931 55.1708375

1999 54.65 1998 55.16739946

1921 54.55 1939 55.07299072

2001 54.38 1953 54.96006998

1931 54.34 1938 54.92172591

2007 54.33 1954 54.90617377

2005 54.31 1999 54.83801259

1990 54.31 1946 54.77032593

Atmospheric TemperatureAtmospheric Temperature Descriptive AnalysisDescriptive Analysis

– Tabular, Graphical – Not Very UsefulTabular, Graphical – Not Very Useful Parametric Analysis / InferentialParametric Analysis / Inferential

– Temperature data follows 3-par. Lognormal pdfTemperature data follows 3-par. Lognormal pdf

– ScaleScale

– ShapeShape– – LocationLocation– X: TemperatureX: Temperature

Thus, we can probabilistically characterize the behavior of Thus, we can probabilistically characterize the behavior of temperature and obtain useful information.temperature and obtain useful information.

0,,;2)(

}]/))[(ln(21

exp{),,;(

2

x

x

xxf

59.3:

019.0:

195.0:

Temperature Forecasting ModelTemperature Forecasting Model

Version 2: ARIMA(2,1,1)×(1,1,1)Version 2: ARIMA(2,1,1)×(1,1,1)1212

Ref. (Shih & Tsokos, Vol. 16, March 2008, Ref. (Shih & Tsokos, Vol. 16, March 2008, NP&S Comp.)NP&S Comp.)

1312127

26252411514

1312321

9599.09741.09855.000014.0

0002.00916.00036.00395.00554.0

9009.09964.00396.00556.00952.1

tttt

ttttt

tttttt

x

xxxxx

xxxxxx

0131.0r 056.0SE

Estimated ValuesEstimated Values

Original Values Forecast Values Residuals

March 2006 43.45 44.1812 -0.7312

April 2006 56.12 53.2506 2.86942

May 2006 63.12 62.6351 0.48486

June 2006 71.55 70.7152 0.83478

July 2006 77.22 75.6947 1.52532

August 2006 74.19 74.3167 -0.1267

September 2006 63.86 66.8069 -2.9469

October 2006 53.13 55.6137 -2.4837

November 2006 44.58 43.3947 1.18529

December 2006 36.79 34.7224 2.06761

January 2007 31.46 32.6854 -1.2254

February 2007 32.86 36.3025 -3.4425

Monthly Temperature VS. Our Monthly Temperature VS. Our Predicted ValuesPredicted Values

Month

Te

mp

era

ture

0 2 4 6 8 10 12

30

40

50

60

70

80

0 2 4 6 8 10 12

30

40

50

60

70

80

Original Data Predicted Value

Yearly Temperature PatternsYearly Temperature Patterns

January

February

April

May

JuneAugust

September

October

November

December

July

March

Carbon Dioxide, COCarbon Dioxide, CO22

COCO22 – – – No Color, No Odor, No Taste No Color, No Odor, No Taste

– Puts Out Fire, Puts Fizz in Seltzer Puts Out Fire, Puts Fizz in Seltzer

– It is to plants what oxygen is to usIt is to plants what oxygen is to us

““It is hard to think of COIt is hard to think of CO22 as a poison” as a poison”

It is very important to understand its behaviorIt is very important to understand its behavior Atmospheric COAtmospheric CO22: 5.91221 billion metric tons in U.S, : 5.91221 billion metric tons in U.S,

Second to ChinaSecond to China COCO22 Emissions: Related to Gas, Liquid, Solid Fuels, Emissions: Related to Gas, Liquid, Solid Fuels,

Gas Flares, Cement ProductionGas Flares, Cement Production

Atmospheric Carbon DioxideAtmospheric Carbon Dioxide

CO2 in the Atmosphere

8 Contributable Variables

E CO2 emission (fossil fuel combustion)

D Deforestation and destruction

R Terrestrial plant respiration

S Respiration

O the flux from oceans to atmosphere

P terrestrial photosynthesis

A the flux from atmosphere to oceans

B burial of organic carbon and limestone carbon

To Understand COTo Understand CO22 - Atmosphere - Atmosphere We must analyze and model existing dataWe must analyze and model existing data

– To have a better understanding of the attributable variables To have a better understanding of the attributable variables (Rank)(Rank)

– To identify possible interactions of the attributable variablesTo identify possible interactions of the attributable variables– Parametric / Inferential Analysis To probabilistically Parametric / Inferential Analysis To probabilistically

understand the behavior of COunderstand the behavior of CO22

– Develop forecasting models to accurately predict CODevelop forecasting models to accurately predict CO22 in the in the futurefuture

– Identify the relationship between Temperature and COIdentify the relationship between Temperature and CO22

i.e., knowing Temperature predict COi.e., knowing Temperature predict CO22, etc., etc. Development of legal policiesDevelopment of legal policies

– Development of Economic models of Global Warming for Development of Economic models of Global Warming for implementing legal policiesimplementing legal policies

Atmospheric COAtmospheric CO22 (1958-2004) (1958-2004)Parametric Analysis / InferentialParametric Analysis / Inferential

– It is best characterized by the 3-par. Weibull, and its cumulative form is given by It is best characterized by the 3-par. Weibull, and its cumulative form is given by

– ScaleScale

– ShapeShape– – LocationLocation– X: Atmospheric COX: Atmospheric CO22

Thus, we can obtain, E[X], Var[X], S.D[X], Confidence limits, etc.Thus, we can obtain, E[X], Var[X], S.D[X], Confidence limits, etc.

0};)(exp{1)(

xx

xF

779.2:

029.23:

7.343:

})029.23

7.343(exp{1)( 779.2

x

xF

Trend Analysis: Determine If Trend Analysis: Determine If Atmospheric COAtmospheric CO22 Depends on Time Depends on Time

TheThe wherewhere gamma functiongamma function

ConsiderConsider Best FitBest Fit

Thus, F(x) as a function of time, isThus, F(x) as a function of time, is

Using this result we can obtain projections with a desired degree Using this result we can obtain projections with a desired degree of confidence, ten, twenty, fifty years from now.of confidence, ten, twenty, fifty years from now.

)1

1()(XE :

28107475.800225.028.314 ttt

)(tft

})092.17

)107475.800225.5534.354((exp{1)( 108.2

8

txxF

8857.0)108.2

11(;

8857.0;108.2

tt

Trend Analysis: Determine If Atmospheric Trend Analysis: Determine If Atmospheric COCO22 Depends on Time (Continued) Depends on Time (Continued)

That is, 10 years from now, 2018, at 95% That is, 10 years from now, 2018, at 95% level of confidence that the probable amount level of confidence that the probable amount of carbon dioxide in the atmosphere will be of carbon dioxide in the atmosphere will be between 381.35 and 410.11 ppm.between 381.35 and 410.11 ppm.

20 years, 2028, 95% CL, between 397.2 and 20 years, 2028, 95% CL, between 397.2 and 425.96 ppm, etc.425.96 ppm, etc.

Profiling: Ten Year ProjectionsProfiling: Ten Year Projections

Projections through 2018

Profiling: Fifty Year Projections

Projections through 2057

Confidence IntervalsConfidence Intervals

Time Series Plot on Monthly COTime Series Plot on Monthly CO22

Emissions 1981-2003Emissions 1981-2003

Month

CO

2 E

mis

sion

0 50 100 150 200 250

9010

011

012

013

014

015

0

The COThe CO22 Emissions Model Emissions Model

ARIMA(1,1,2)×(1,1,1)ARIMA(1,1,2)×(1,1,1)1212

After expanding the model and inserting the After expanding the model and inserting the coefficients, we havecoefficients, we have

tt BBBxBBBB )1)(1()1)(1)(1)(1( 121

221

121

121

141312

21262524

141312212

10517.08512772.08523.0

1234.09988.0002549.0007449.00049.0

5228495.0527749.10049.15203.05203.1

ttt

ttttt

ttttt

xxx

xxxxxCOE

Monthly COMonthly CO22 Emissions VS. Forecast Emissions VS. Forecast

Values for the Last 100 ObservationsValues for the Last 100 Observations

Month

CO

2 E

mis

sion

s

0 20 40 60 80 100

110

120

130

140

150

0 20 40 60 80 100

110

120

130

140

150

Original Data Predicted Value

COCO22 Emissions Forecast Emissions Forecast

  Original Values Forecast Values Residuals

Jan-03 147.6298 145.2361 2.3937

Feb-03 134.1716 132.6554 1.5162

Mar-03 133.6979 137.3912 -3.6933

Apr-03 121.0047 124.5518 -3.5471

May-03 120.4789 122.4091 -1.9302

Jun-03 120.7394 123.101 -2.3616

Jul-03 132.4187 129.3481 3.0706

Aug-03 135.1314 132.787 2.3444

Sep-03 121.7753 123.8295 -2.0542

Oct-03 125.2487 125.9811 -0.7324

Nov-03 126.2127 126.812 -0.5993

Dec-03 143.1509 141.1834 1.9675

Time Series Plot for Monthly COTime Series Plot for Monthly CO22 in in

the Atmosphere 1965-2004the Atmosphere 1965-2004

Month

Atm

osph

eric

CO

2 C

once

ntra

tion

0 100 200 300 400

320

330

340

350

360

370

380

The Atmospheric COThe Atmospheric CO22 Model Model

ARIMA(2,1,0)×(2,1,1)ARIMA(2,1,0)×(2,1,1)1212

After expanding the model and inserting the After expanding the model and inserting the coefficients, we havecoefficients, we have

tt BxBBBBBB )1()1)(1)(1)(1( 121

12221

242

121

123938

37362726

25241514

13123212

8787.000085.00015116.0

005234.00076.000768.0013585.0

047038.00683.012093.0213997.0

74097.00759.11124.01989.06887.0

ttt

tttt

tttt

ttttt

xx

xxxx

xxxx

xxxxxCOA

Monthly COMonthly CO22 in the Atmosphere VS. Forecast in the Atmosphere VS. Forecast

Values for the Last 100 ObservationsValues for the Last 100 Observations

Month

Atm

osph

eric

CO

2 C

once

ntra

tion

0 20 40 60 80 100

360

365

370

375

380

0 20 40 60 80 100

360

365

370

375

380

Original Data Predicted Value

Atmospheric COAtmospheric CO22 Forecast Forecast

  Original Values Forecast Values Residuals

Jan-04 376.79 376.7963 -0.0063

Feb-04 377.37 377.609 -0.239

Mar-04 378.41 378.1837 0.2263

Apr-04 380.52 379.6653 0.8547

May-04 380.63 380.8268 -0.1968

Jun-04 379.57 380.2339 -0.6639

Jul-04 377.79 378.3489 -0.5589

Aug-04 375.86 375.837 0.023

Sep-04 374.06 374.1871 -0.1271

Oct-04 374.24 374.1482 0.0918

Nov-04 375.86 375.6897 0.1703

Dec-04 377.48 377.2186 0.2614

Total Atmospheric CO2Total Atmospheric CO2EE CO2 emission (fossil fuel CO2 emission (fossil fuel

combustion)combustion)C1C1 Gas fuelsGas fuels

C2C2 Liquid fuel Liquid fuel

C3C3 Solid fuelSolid fuel

C4C4 Gas flaresGas flares

C5C5 Cement productionCement production

DD Deforestation and destructionDeforestation and destruction D1D1 deforestationdeforestation

D2D2 destruction of biomassdestruction of biomass

D3D3 destruction of soil carbondestruction of soil carbon

RR Terrestrial plant respirationTerrestrial plant respiration Only one variableOnly one variable

SS RespirationRespiration S1S1 respiration from soilsrespiration from soils

S2S2 respiration from decomposersrespiration from decomposers

OO the flux from oceans to atmospherethe flux from oceans to atmosphere Only one variableOnly one variable

PP terrestrial photosynthesisterrestrial photosynthesis Only one variableOnly one variable

AA the flux from atmosphere to oceansthe flux from atmosphere to oceans Only one variableOnly one variable

BB burial of organic carbon and burial of organic carbon and limestone carbonlimestone carbon

B1B1 the burial of organic carbonthe burial of organic carbon

B2B2 burial of limestone carbonburial of limestone carbon

Statistical Model for CO2 EmissionsStatistical Model for CO2 Emissions

CC22 & C & C44 alone contributions alone contributions CC11, C, C33, C, C55 Do not contribute alone, but their Do not contribute alone, but their

interactions contribute (Cinteractions contribute (C44CC55, C, C11CC33, C, C11CC55) )

2515

543

4316

2

255.10769.910228.5

529.571031.5289.807025

CCCCC

CCCCOE

Differential Equation of Differential Equation of Atmospheric COAtmospheric CO22

8 Contributable Variables

E CO2 emission (fossil fuel combustion)

D Deforestation and destruction

R Terrestrial plant respiration

S Respiration

O the flux from oceans to atmosphere

P terrestrial photosynthesis

A the flux from atmosphere to oceans

B burial of organic carbon and limestone carbon

),,,,,,,()( 2 BAPOSRDEf

dt

COd

Differential Equation of Differential Equation of Atmospheric COAtmospheric CO22

Note: B, P, R are constants, thusNote: B, P, R are constants, thus

dtBPAOSRDECOA

})({2

BdtkPdtk

tttk

tk

ttk

etk

CO

BP

OA

t

tt

S

D

E

t

32

82

12

3

12

4

12

2

9

2

0967.02665.4814.42

1031995315462

19954.10541995132.0

01625.05.10730

104755.2593503 1200

dtBkPkAOkSkRkDkEkCO BPAOSRDEA})({2