Math 5490 9/8/2014 Math 5490 Math 5490 Topics in Applied - PDF document

Math 5490 9/8/2014 Math 5490 Math 5490 Topics in Applied Mathematics: Anthropogenic Warming Introduction to the Mathematics of Climate Mondays and Wednesdays 2:30 – 3:45 Is the globe warming? http://www.math.umn.edu/~mcgehee/teaching/Math5490-2014-2Fall/ Streaming video is available at What determines the Earth’s temperature? http://www.ima.umn.edu/videos/ Click on the link: "Live Streaming from 305 Lind Hall". What is the role of human activity? Participation: How big is the problem? https://umconnect.umn.edu/mathclimate Math 5490 9/8/2014 Anthropogenic Warming Anthropogenic Warming Is the Globe Warming? Global Mean Temperature Is the globe warming? What determines the Earth’s temperature? What is the role of human activity? How big is the problem? Technical Summary , IPCC AR4, p.37 http://ipcc-wg1.ucar.edu/wg1/Report/AR4WG1_Print_TS.pdf Math 5490 9/8/2014 Math 5490 9/8/2014 Anthropogenic Warming Anthropogenic Warming Is the Globe Warming? Is the Globe Warming? Antarctic Temperature Data 2 Antarctic Temperature Data 1.5 1 kiloyear bp 0.5 450 400 350 300 250 200 150 100 50 0 delta deg C 4 0 2 0 temperature -0.5 -2 -4 -1 -6 -8 -1.5 -10 -2 -8000 -7000 -6000 -5000 -4000 -3000 -2000 -1000 0 1000 2000 year Petit, et al, Nature 399 (June 3 1999), pp.429-436 Petit, et al, Nature 399 (June 3 1999), pp.429-436 Math 5490 9/8/2014 Math 5490 9/8/2014 Richard McGehee, University of Minnesota 1

Math 5490 9/8/2014 Anthropogenic Warming Anthropogenic Warming Is the Globe Warming? Is the Globe Warming? Benthic 18 O Data 2.5 3 Benthic Data ( δ 18 O) 3.5 4 4.5 5 5.5 ‐ 4500 ‐ 4000 ‐ 3500 ‐ 3000 ‐ 2500 ‐ 2000 ‐ 1500 ‐ 1000 ‐ 500 0 time (Kyr) Lisiecki, L. E., and M. E. Raymo (2005), A Pliocene-Pleistocene stack of 57 globally distributed benthic d18O Hansen, et al, Target atmospheric CO2: Where should humanity aim? Open Atmos. Sci. J . 2 (2008) records, Paleoceanography , 20 , PA1003, doi:10.1029/2004PA001071. Math 5490 9/8/2014 Math 5490 9/8/2014 Anthropogenic Warming Anthropogenic Warming What Determines the Earth’s Temperature? Heat Balance Is the globe warming?  T 4  (1   ) S outgoing (infrared) solar incoming (visible) Yes, but, from a geologic perspective, not so much. where T = surface temperature (Kelvin) What determines the Earth’s temperature? S = solar influx (W/m 2 ) What is the role of human activity? α = albedo (reflectivity) How big is the problem? σ = the Stefan-Boltzmann constant       T 255 K 18 C 0 F For current values , Why isn’t the Earth a Snowball? Math 5490 9/8/2014 Math 5490 9/8/2014 Anthropogenic Warming Anthropogenic Warming What Determines the Earth’s Temperature? What Determines the Earth’s Temperature? Heat Balance Historical Overview of Climate Change Science , IPCC AR4, p.96 Gary Stix, Scientific American September 2006, pp.46-49 http://ipcc-wg1.ucar.edu/wg1/Report/AR4WG1_Print_CH01.pdf Math 5490 9/8/2014 Math 5490 9/8/2014 Richard McGehee, University of Minnesota 2

Math 5490 9/8/2014 Anthropogenic Warming Anthropogenic Warming What Determines the Earth’s Temperature? What Determines the Earth’s Temperature? Atmospheric CO 2 (Vostok data) Atmospheric CO 2 (Vostok data) 400 400 350 350 atmos CO 2 (ppm) 300 atmos CO 2 (ppm) 300 250 250 200 200 150 150 100 100 ‐ 450 ‐ 400 ‐ 350 ‐ 300 ‐ 250 ‐ 200 ‐ 150 ‐ 100 ‐ 50 0 ‐ 450 ‐ 400 ‐ 350 ‐ 300 ‐ 250 ‐ 200 ‐ 150 ‐ 100 ‐ 50 0 time (Kyr) time (Kyr) Petit, et al, Nature 399 (June 3 1999), pp.429-436 Petit, et al, Nature 399 (June 3 1999), pp.429-436 Math 5490 9/8/2014 Math 5490 9/8/2014 Anthropogenic Warming Anthropogenic Warming What Determines the Earth’s Temperature? What Determines the Earth’s Temperature? Atmospheric CO 2 & Temperature (Vostok data) Vostok Data 12 10 Current 8 conditions 6 are well 4 outside the δ T ( ° C) 2 range 0 recorded in ‐ 2 ‐ 4 the ice core ‐ 6 data. ‐ 8 ‐ 10 150 200 250 300 350 400 450 CO2 (ppm) Pam Martin, University of Chicago, 2010 Math 5490 9/8/2014 Math 5490 9/8/2014 Anthropogenic Warming Anthropogenic Warming What Determines the Earth’s Temperature? What Determines the Earth’s Temperature? Vostok Data 12 10 8 6 Extrapolate 4 linear δ T ( ° C) 2 regression to 0 400 ppm ‐ 2 CO2. ‐ 4 ‐ 6 ‐ 8 ‐ 10 150 200 250 300 350 400 450 CO2 (ppm) http://www.carleton.edu/departments/geol/DaveSTELLA/Carbon/long_term_carbon.htm Math 5490 9/8/2014 Math 5490 9/8/2014 Richard McGehee, University of Minnesota 3

Math 5490 9/8/2014 Anthropogenic Warming Anthropogenic Warming What Determines the Earth’s Temperature? What Determines the Earth’s Temperature? Silicate Weathering Rainwater containing dissolved CO 2 falling on silicate rocks replaces a silicon atom with a carbon atom, ultimately producing calcium carbonate (limestone) and silicon dioxide (quartz). For example, calcium silicate (Wollastonite ):    CaSiO CO CaCO SiO 3 2 3 2 Under volcanic conditions, the carbon atom is replaced by a silicon atom, completing the long term carbon cycle.    CaCO SiO CaSiO CO 3 2 3 2 Hansen, et al, Target atmospheric CO2: Where should humanity aim? Open Atmos. Sci. J . 2 (2008) Math 5490 9/8/2014 Math 5490 9/8/2014 Anthropogenic Warming Anthropogenic Warming What Determines the Earth’s Temperature? Is the globe warming? Yes, but, from a geologic perspective, not so much. What determines the Earth’s temperature? Physics! Solar heating plus the carbon cycle. What is the role of human activity? How big is the problem? http://www.carleton.edu/departments/geol/DaveSTELLA/Carbon/long_term_carbon.htm Math 5490 9/8/2014 Math 5490 9/8/2014 Anthropogenic Warming Anthropogenic Warming What is the Role of Human Activity? What Determines the Earth’s Temperature? The Short-Term Carbon Cycle The Mauna Loa Observatory Couplings Between Changes in the Climate System and Biogeochemistry , IPCC AR4, p.513 http://ipcc-wg1.ucar.edu/wg1/Report/AR4WG1_Print_CH07.pdf http://www.climate.noaa.gov/images/about_climate/greenhouse_maunaloa.jpg Math 5490 9/8/2014 Math 5490 9/8/2014 Richard McGehee, University of Minnesota 4

Math 5490 9/8/2014 Anthropogenic Warming Anthropogenic Warming What is the Role of Human Activity? What is the Role of Human Activity? 400 350 atmos CO 2 (ppm) 300 250 200 150 100 ‐ 450 ‐ 400 ‐ 350 ‐ 300 ‐ 250 ‐ 200 ‐ 150 ‐ 100 ‐ 50 0 time (Kyr) http://scrippsco2.ucsd.edu/graphics_gallery/mauna_loa_record/mauna_loa_record.html Math 5490 9/8/2014 Math 5490 9/8/2014 Anthropogenic Warming Anthropogenic Warming What is the Role of Human Activity? What is the Role of Human Activity? Carbon isotope ratios and atmospheric oxygen depletion indicate that the increase in Models with and without atmospheric CO 2 comes from human activity. burning fossil fuels. Changes in Atmospheric Constituents and in Radiative Understanding and Attributing Climate Change , IPCC Forcing , IPCC AR4, Chap. 2, p.138 AR4, Chap. 9, p.684 http://ipcc- http://ipcc- wg1.ucar.edu/wg1/Report/AR4WG1_Print_Ch09. wg1.ucar.edu/wg1/Report/AR4WG1_Print_CH02. pdf pdf Math 5490 9/8/2014 Math 5490 9/8/2014 Anthropogenic Warming Anthropogenic Warming The IPCC Fourth Assessment Report Is the globe warming? Yes, but, from a geologic perspective, not so much. What determines the Earth’s temperature? Physics! Solar heating plus the carbon cycle. What is the role of human activity? How big is the problem? http://nobelprize.org/nobel_prizes/peace/laureates/2007/ Math 5490 9/8/2014 Math 5490 9/8/2014 Richard McGehee, University of Minnesota 5