GLOBAL WARMING. Dr. Chris P. Tsokos. Distinguished University Professor Vice President of IFNA. July 03, 2008

Transcription

1 GLOBAL WARMING Keynote Address: WCNA 2008 Orlando Florida July 03, 2008 Dr. Chris P. Tsokos Distinguished University Professor Vice President of IFNA July 03, 2008

2 GLOBAL WARMING Research Seminar Team Chris P. Tsokos Gan Ladde Rebecca Wooten Shou Hsing Shih Bongjin Choi Yong Xu Dimitris Vovoras

3 Mathematical and Statistical Modeling of Global Warming Do we scientifically understand the concept of Global Warming? Recent Definition: GLOBAL WARMING- an increase in Temperature at the surface of the earth supposedly caused by the greenhouse effects (Greenhouse Effects- Carbon Dioxide CO 2 (greenhouse gas)) Supposedly assumed to be true without conclusive evidence Hypothetical, conjectural, etc.

4 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.

5 MEDIA CHAOS: PRO AND CONCERNED (SKEPTICS) PRO - GLOBAL WARMING *Intergovernmental Panel on Climate Change (IPCC) Climate Change 2007 Increase in Temperature Increase Sea Level Unpredictable Pattern in Rainfall Increase in Extreme Weather Events Alterations in Agriculture Yields Increase in River Flows Etc.

6 PRO - GLOBAL WARMING (Continued) Award Winning Documentary Vice President Gore Fiction VS. Reality / Awareness ABC: 20/20 / Give Me A Break! A Number of Professional Organizations American Meteorological Society American Geographical Union AAAS National Academies Blame Human Activities

7 CONCERNED / SKEPTICS Great Britain s Channel 4 Documentary The Great Global Warming Swindle NASA Scientists Sun spots are hotter than previously thought Danish National Space Center Temperature changes are due to fluctuations in the sun s output (NASA) (Stated: there is absolutely nothing we can do to correct the situation) ABC 20/20: Broadcast Give Me a Break

8 CONCERNED / SKEPTICS (Continued) Times Washington Bureau Chief, Bill Adair Global Warming has been called the most dire issue facing the planet and yet, if you are not a scientist, it can be difficult to sort out the truth Finally, St. Pete Times, Jan 23, 2007 Global Warming: Meet Your Adversary By the numbers: 9 out of 10 statistical Info. Not Correct

9 Wall Street Journal Global Warming is 300-years-old news The various kind of evidence examined by NRC National Research Council, led it to conclude that the observed disparity between the surface and atmospheric temperature trends during the 20-year period is probably at least partially real Uncertainties in all aspects exist can not draw any conclusions concerning GW NRC concludes that Major Advances in scientific methods will be necessary before these questions (GW) can be resolved. spread fear of Global Warming demonizing, hydrocarbon fuel.

10 Do We Understand the Problem of Global Warming? Zero Legal Legislative Policies: Why? Continental U.S Popular Claim to Global Warming: The Marriage of Temperature and Carbon Dioxide (CO 2 ) Need to Understand Temperature Behavior (Type) Carbon Dioxide (Type) Their Relationship

11 Temperature Atmospheric (2 or 3 Versions) Surface Land Ocean (73%) Historical Data: / Daily, Weekly, Monthly, Yearly

12 Atmospheric Temperature Data Version 1: United States Climate Division, USCD, ( ) 344 Climate Divisions Version 2: United States Historical Climatology Network, USHCN, ( ) 1219 Stations Proposed Version: Stratified The Continental U. S. in Equal Segment Uniformly Weighted Statistically Correct

13 Creating Grid Point Select a random point in bottom left corner of map, use do loops to create points every x meters

14 Clipping Grid Point Clip the grids that fall within the boundary of the polygon

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

16 Sampling Stations and Grid Point Select sampling locations within a certain radius of the grid points

17 Comparison on Version 2 Temperature VS. Proposed Version Version 2 * Proposed Version * Year Temperature Year Temperature

18 Atmospheric Temperature Descriptive Analysis Tabular, Graphical Not Very Useful Parametric Analysis / Inferential Temperature data follows 3-par. Lognormal pdf Scale Shape Location f ( x;,, ) : 3.59 : : exp{ [(ln( x ) ) / ] 2 ( x ) 2 } ; x,, 0 X: Temperature Thus, we can probabilistically characterize the behavior of temperature and obtain useful information. 2

19 Temperature Forecasting Model Version 2: ARIMA(2,1,1) (1,1,1) 12 x t x x t1 t x t x x t2 t t x t x t x t t x t x t25 t x t26 r SE Ref. (Shih & Tsokos, Vol. 16, March 2008, NP&S Comp.)

20 Estimated Values Original Values Forecast Values Residuals March April May June July August September October November December January February

21 Temperature Monthly Temperature VS. Our Predicted Values Original Data Predicted Value Month

22 Yearly Temperature Patterns December January February November October September March May April August July June

23 CO 2 Carbon Dioxide, CO 2 No Color, No Odor, No Taste Puts Out Fire, Puts Fizz in Seltzer It is to plants what oxygen is to us It is hard to think of CO 2 as a poison It is very important to understand its behavior Atmospheric CO 2 : billion metric tons in U.S, Second to China CO 2 Emissions: Related to Gas, Liquid, Solid Fuels, Gas Flares, Cement Production

24 Atmospheric Carbon Dioxide

25 CO 2 in the Atmosphere E D R S O P A B 8 Contributable Variables CO2 emission (fossil fuel combustion) Deforestation and destruction Terrestrial plant respiration Respiration the flux from oceans to atmosphere terrestrial photosynthesis the flux from atmosphere to oceans burial of organic carbon and limestone carbon

26

27 To Understand CO 2 - Atmosphere We must analyze and model existing data To have a better understanding of the attributable variables (Rank) To identify possible interactions of the attributable variables Parametric / Inferential Analysis To probabilistically understand the behavior of CO 2 Develop forecasting models to accurately predict CO 2 in the future Identify the relationship between Temperature and CO 2 i.e., knowing Temperature predict CO 2, etc. Development of legal policies Development of Economic models of Global Warming for implementing legal policies

28 Atmospheric CO 2 ( ) Parametric Analysis / Inferential It is best characterized by the 3-par. Weibull, and its cumulative form is given by x F( x) 1 exp{ ( ) }; x 0 Scale : Shape Location : : X: Atmospheric CO 2 x F( x) 1 exp{ ( ) Thus, we can obtain, E[X], Var[X], S.D[X], Confidence limits, etc. }

29 Trend Analysis: Determine If Atmospheric CO 2 Depends on Time The E (X ) (1 ) where : gamma function Consider Best Fit t 1 f (t) t t t t ; t ; (1 ) Thus, F(x) as a function of time, is 8 x ( t ) F( x) 1 exp{ ( ) } Using this result we can obtain projections with a desired degree of confidence, ten, twenty, fifty years from now.

30 Trend Analysis: Determine If Atmospheric CO 2 Depends on Time (Continued) That is, 10 years from now, 2018, at 95% level of confidence that the probable amount of carbon dioxide in the atmosphere will be between and ppm. 20 years, 2028, 95% CL, between and ppm, etc.

31 Profiling: Ten Year Projections Projections through 2018

32 Profiling: Fifty Year Projections Projections through 2057

33 Confidence Intervals

34 CO2 Emission Time Series Plot on Monthly CO 2 Emissions Month

35 The CO 2 Emissions Model ARIMA(1,1,2) (1,1,1) 12 ( B )(1 1B)(1 B)(1 B ) xt (1 1B 2B )(1 1 After expanding the model and inserting the coefficients, we have B 12 ) t CO2 E x x t1 t24 t x t x x t25 t13 t x x t26 t14 t x t t14 t2

36 CO2 Emissions Monthly CO 2 Emissions VS. Forecast Values for the Last 100 Observations Original Data Predicted Value Month

37 CO 2 Emissions Forecast Original Values Forecast Values Residuals Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

38 Atmospheric CO2 Concentration Time Series Plot for Monthly CO 2 in the Atmosphere Month

39 The Atmospheric CO 2 Model ARIMA(2,1,0) (2,1,1) (1 1B 2B )(1 1B 2B )(1 B)(1 B ) x t (1 1 B After expanding the model and inserting the coefficients, we have 12 ) t CO2 A x t x x x x t14 t26 t38 t x x t x x t27 t39 t x x t24 t x t12 t x x x t25 t37 t13

40 Atmospheric CO2 Concentration Monthly CO 2 in the Atmosphere VS. Forecast Values for the Last 100 Observations Original Data Predicted Value Month

41 Atmospheric CO 2 Forecast Original Values Forecast Values Residuals Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

42 E Total Atmospheric CO2 CO2 emission (fossil fuel combustion) C1 C2 C3 C4 C5 Gas fuels Liquid fuel Solid fuel Gas flares D Deforestation and destruction D1 deforestation D2 D3 Cement production destruction of biomass destruction of soil carbon R Terrestrial plant respiration Only one variable S Respiration S1 respiration from soils S2 respiration from decomposers O the flux from oceans to atmosphere Only one variable P terrestrial photosynthesis Only one variable A the flux from atmosphere to oceans Only one variable B burial of organic carbon and limestone carbon B1 B2 the burial of organic carbon burial of limestone carbon

43 Statistical Model for CO2 Emissions CO2 E C 4 C C C 1 1 C C C.255C 2 4 C 2 & C 4 alone contributions C 1, C 3, C 5 Do not contribute alone, but their interactions contribute (C 4 C 5, C 1 C 3, C 1 C 5 )

44 Differential Equation of Atmospheric CO 2 d( CO2 ) dt f ( E, D, R, S, O, P, A, B) E D R S O P A B 8 Contributable Variables CO2 emission (fossil fuel combustion) Deforestation and destruction Terrestrial plant respiration Respiration the flux from oceans to atmosphere terrestrial photosynthesis the flux from atmosphere to oceans burial of organic carbon and limestone carbon

45 Differential Equation of Atmospheric CO 2 Note: B, P, R are constants, thus dt B P A O S R D E CO A } ) ( { 2 Bdt k Pdt k t t t k t k t t k e t k CO B P O A t t t S D E t dt B k P k A O k S k R k D k E k CO B P A O S R D E A } ) ( { 2