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  • Math 5490 9/8/2014

    Richard McGehee, University of Minnesota 1

    Topics in Applied Mathematics: Introduction to the Mathematics of Climate

    Mondays and Wednesdays 2:30 – 3:45 http://www.math.umn.edu/~mcgehee/teaching/Math5490-2014-2Fall/

    Streaming video is available at http://www.ima.umn.edu/videos/

    Click on the link: "Live Streaming from 305 Lind Hall". Participation:

    https://umconnect.umn.edu/mathclimate

    Math 5490

    Is the globe warming?

    What determines the Earth’s temperature?

    What is the role of human activity?

    How big is the problem?

    Math 5490

    Anthropogenic Warming

    Math 5490 9/8/2014

    Is the globe warming? What determines the Earth’s temperature?

    What is the role of human activity?

    How big is the problem?

    Anthropogenic Warming

    Math 5490 9/8/2014

    Global Mean Temperature

    Technical Summary, IPCC AR4, p.37 http://ipcc-wg1.ucar.edu/wg1/Report/AR4WG1_Print_TS.pdf

    Is the Globe Warming?

    Anthropogenic Warming

    Math 5490 9/8/2014

    Petit, et al, Nature 399 (June 3 1999), pp.429-436

    Antarctic Temperature Data

    -2

    -1.5

    -1

    -0.5

    0

    0.5

    1

    1.5

    2

    -8000 -7000 -6000 -5000 -4000 -3000 -2000 -1000 0 1000 2000

    year

    de lta

    d eg

    C

    Is the Globe Warming?

    Anthropogenic Warming

    Math 5490 9/8/2014

    -10 -8 -6 -4 -2 0 2 4

    050100150200250300350400450

    kiloyear bp

    te m

    pe ra

    tu re

    Petit, et al, Nature 399 (June 3 1999), pp.429-436

    Antarctic Temperature Data

    Is the Globe Warming?

    Anthropogenic Warming

    Math 5490 9/8/2014

  • Math 5490 9/8/2014

    Richard McGehee, University of Minnesota 2

    Lisiecki, L. E., and M. E. Raymo (2005), A Pliocene-Pleistocene stack of 57 globally distributed benthic d18O records, Paleoceanography,20, PA1003, doi:10.1029/2004PA001071.

    Benthic 18O Data

    Is the Globe Warming?

    2.5

    3

    3.5

    4

    4.5

    5

    5.5

    ‐4500 ‐4000 ‐3500 ‐3000 ‐2500 ‐2000 ‐1500 ‐1000 ‐500 0

    Be nt hi c D

    at a  (δ

    18 O )

    time (Kyr)

    Anthropogenic Warming

    Math 5490 9/8/2014

    Is the Globe Warming?

    Hansen, et al, Target atmospheric CO2: Where should humanity aim? Open Atmos. Sci. J. 2 (2008)

    Anthropogenic Warming

    Math 5490 9/8/2014

    Is the globe warming?

    Yes, but, from a geologic perspective, not so much.

    What determines the Earth’s temperature? What is the role of human activity?

    How big is the problem?

    Anthropogenic Warming

    Math 5490 9/8/2014

    Why isn’t the Earth a Snowball?

    4 (1 )T S  

    where T = surface temperature (Kelvin)

    S = solar influx (W/m2)

    α = albedo (reflectivity)

    σ = the Stefan-Boltzmann constant

    For current values , 255 18 0T K C F     

    Heat Balance

    solar incoming (visible)outgoing (infrared)

    Anthropogenic Warming What Determines the Earth’s Temperature?

    Math 5490 9/8/2014

    What Determines the Earth’s Temperature?

    Gary Stix, Scientific American September 2006, pp.46-49

    Anthropogenic Warming

    Math 5490 9/8/2014

    Heat Balance

    Historical Overview of Climate Change Science, IPCC AR4, p.96 http://ipcc-wg1.ucar.edu/wg1/Report/AR4WG1_Print_CH01.pdf

    Anthropogenic Warming What Determines the Earth’s Temperature?

    Math 5490 9/8/2014

  • Math 5490 9/8/2014

    Richard McGehee, University of Minnesota 3

    Anthropogenic Warming What Determines the Earth’s Temperature?

    Petit, et al, Nature 399 (June 3 1999), pp.429-436

    100

    150

    200

    250

    300

    350

    400

    ‐450 ‐400 ‐350 ‐300 ‐250 ‐200 ‐150 ‐100 ‐50 0

    at m os  C O

    2 (p pm

    )

    time (Kyr)

    Atmospheric CO2 (Vostok data)

    Math 5490 9/8/2014

    Anthropogenic Warming What Determines the Earth’s Temperature?

    Petit, et al, Nature 399 (June 3 1999), pp.429-436

    Atmospheric CO2 (Vostok data)

    100

    150

    200

    250

    300

    350

    400

    ‐450 ‐400 ‐350 ‐300 ‐250 ‐200 ‐150 ‐100 ‐50 0

    at m os  C O

    2 (p pm

    )

    time (Kyr)

    Math 5490 9/8/2014

    Anthropogenic Warming What Determines the Earth’s Temperature?

    Pam Martin, University of Chicago, 2010

    Atmospheric CO2 & Temperature (Vostok data)

    Math 5490 9/8/2014

    Anthropogenic Warming What Determines the Earth’s Temperature?

    ‐10 ‐8 ‐6 ‐4 ‐2 0 2 4

    6 8

    10 12

    150 200 250 300 350 400 450

    δT  (° C)

    CO2 (ppm)

    Current  conditions  are well  outside the  range  recorded in  the ice core  data.

    Vostok Data

    Math 5490 9/8/2014

    Anthropogenic Warming What Determines the Earth’s Temperature?

    Vostok Data

    ‐10 ‐8

    ‐6 ‐4 ‐2 0 2 4 6 8

    10 12

    150 200 250 300 350 400 450

    δT  (° C)

    CO2 (ppm)

    Extrapolate  linear  regression to  400 ppm  CO2.

    Math 5490 9/8/2014

    Anthropogenic Warming What Determines the Earth’s Temperature?

    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 4

    Anthropogenic Warming What Determines the Earth’s Temperature?

    Rainwater containing dissolved CO2 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):

    3 2 3 2CaSiO CO CaCO SiO  

    Under volcanic conditions, the carbon atom is replaced by a silicon atom, completing the long term carbon cycle.

    3 2 3 2CaCO SiO CaSiO CO  

    Silicate Weathering

    Math 5490 9/8/2014

    Anthropogenic Warming What Determines the Earth’s Temperature?

    Hansen, et al, Target atmospheric CO2: Where should humanity aim? Open Atmos. Sci. J. 2 (2008)

    Math 5490 9/8/2014

    Anthropogenic Warming What Determines the Earth’s Temperature?

    http://www.carleton.edu/departments/geol/DaveSTELLA/Carbon/long_term_carbon.htm

    Math 5490 9/8/2014

    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?

    Anthropogenic Warming

    Math 5490 9/8/2014

    Anthropogenic Warming What Determines the Earth’s Temperature?

    The Short-Term Carbon Cycle

    Couplings Between Changes in the Climate System and Biogeochemistry, IPCC AR4, p.513 http://ipcc-wg1.ucar.edu/wg1/Report/AR4WG1_Print_CH07.pdf

    Math 5490 9/8/2014

    Anthropogenic Warming What is the Role of Human Activity?

    http://www.climate.noaa.gov/images/about_climate/greenhouse_maunaloa.jpg

    The Mauna Loa Observatory

    Math 5490 9/8/2014

  • Math 5490 9/8/2014

    Richard McGehee, University of Minnesota 5

    Anthropogenic Warming What is the Role of Human Activity?

    http://scrippsco2.ucsd.edu/graphics_gallery/mauna_loa_record/mauna_loa_record.html

    Math 5490 9/8/2014

    Anthropogenic Warming What is the Role of Human Activity?

    100

    150

    200

    250

    300

    350

    400

    ‐450 ‐400 ‐350 ‐300 ‐250 ‐200 ‐150 ‐100 ‐50 0

    at m os  C O 2 (p pm

    )

    time (Kyr)

    Math 5490 9/8/2014

    Anthropogenic Warming What is the Role of Human Activity?

    Carbon isotope ratios and atmospheric oxygen depletion indicate that the increase in atmospheric CO2 comes from burning fossil fuels.

    Changes in Atmospheric Constituents and in Radiative Forcing, IPCC AR4, Chap. 2, p.138

    http://ipcc- wg1.ucar.edu/wg1/Report/AR4WG1_Print_CH02.

    pdf

    Math 5490 9/8/2014

    Anthropogenic Warming What is the Role of Human Activity?

    Models with and without human activity.

    Understanding and Attributing Climate Change, IPCC AR4, Chap. 9, p.684

    http://ipcc- wg1.ucar.edu/wg1/Report/AR4WG1_Print_Ch09.

    pdf

    Math 5490 9/8/2014

    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?

    Anthropogenic Warming

    Math 5490 9/8/2014

    http://nobelprize.org/nobel_prizes/peace/laureates/2007/

    The IPCC Fourth Assessment Report

    Anthropogenic Warming

    Math 5490 9/8/2014

  • Math 5490 9/8/2014

    Richard McGehee, University of Minnesota 6

    Prediction Methodology

    Global Climate Projections, IPCC AR4, p.753 http://ipcc-wg1.ucar.edu/wg1/Report/AR4WG1_Print_CH10.pdf

    Anthropogenic Warming The IPCC Fourth Assessment Report

    Math 5490 9/8/2014

    Global Mean Temperature Predictions

    Summary for Policy Makers, IPCC AR4, p. 14 http://ipcc