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A Mathematical Tour of the State of the PlanetThomas J. PfaffIthaca College

M. King Hubberts (1903-1989), chief consultant-general geology- for shell development company, 1956 paper Nuclear Energy and the Fossil Fuels.Normal Density: 55% of all domestic oil was consumed from 1960 to 2000:

99% of all domestic oil is predicted to be consumed by 2036:

http://www.theoildrum.com/story/2006/1/22/04219/1102

"By 2012, surplus oil production capacity could entirely disappear, and as early as 2015, the shortfall in output could reach nearly 10 million barrels per day," says the report, which has a foreword by a senior commander, General James N Mattis

Joint Operating Environment report from the US Joint Forces Commandguardian.co.uk, Sunday 11 April 2010A Look at Global Temperature T(x)=0.0005x2 -0.00464x+57.133 FT(x)=0.001x-0.00464 F/yearx years after 1950

T(59)= 58.56 F and T(58)=0.05 F/yearIn 2009 the average global temperature was 58.56 deg F and increasing at a rate of 0.05 deg F per year.

Temperature PredictionsT(100)=61.55 F and T(150)=67.43 FThe model predicts that in 2050 the average temperature will be 61.55 deg F, and in 2100 it will be 67.43 deg F, an increase of 3.43 and 9.31 deg F, respectively, since 2000.

More Temperature PredictionsUsing T(58)=.0528 F/yearIf global temperatures continue to increase at current rates, then by 2050 there will be an increase of 2.61 deg F and by 2100 there will be an increase of 5.26 deg F since 2000. The average global temperature in those years will be 60.73 and 63.38, respectively.

-National Academies Report on Climate Change (March 2006)National Academies Report: Climate Change The rising temperature observed since 1978 are particularly noteworthy because the rate of increase is so high and because, during the same period, the energy reaching the Earth from the Sun had been measured precisely enough to conclude that Earths warming was not due to changes in the Sun.-March 2006

FAQ 3.1, Figure 1. (Top) Annual global mean observed temperatures1 (black dots) along with simple fi ts to the data. The left hand axis shows anomalies relative to the 1961to 1990 average and the right hand axis shows the estimated actual temperature (C). Linear trend fi ts to the last 25 (yellow), 50 (orange), 100 (purple) and 150 years (red) areshown, and correspond to 1981 to 2005, 1956 to 2005, 1906 to 2005, and 1856 to 2005, respectively. Note that for shorter recent periods, the slope is greater, indicating acceleratedwarming. The blue curve is a smoothed depiction to capture the decadal variations. To give an idea of whether the fl uctuations are meaningful, decadal 5% to 95% (lightgrey) error ranges about that line are given (accordingly, annual values do exceed those limits). Results from climate models driven by estimated radiative forcings for the 20thcentury (Chapter 9) suggest that there was little change prior to about 1915, and that a substantial fraction of the early 20th-century change was contributed by naturally occurringinfl uences including solar radiation changes, volcanism and natural variability. From about 1940 to 1970 the increasing industrialisation following World War II increasedpollution in the Northern Hemisphere, contributing to cooling, and increases in carbon dioxide and other greenhouse gases dominate the observed warming after the mid-1970s.

Figure 4.15. Cumulative mean specifi c mass balances (a) and cumulative total mass balances (b) of glaciers andice caps, calculated for large regions (Dyurgerov and Meier, 2005). Mean specifi c mass balance shows the strength ofclimate change in the respective region. Total mass balance is the contribution from each region to sea level rise.

Figure 5.13. Annual averages of the global mean sea level (mm). The red curve shows reconstructedsea level fi elds since 1870 (updated from Church and White, 2006); the blue curve shows coastal tidegauge measurements since 1950 (from Holgate and Woodworth, 2004) and the black curve is basedon satellite altimetry (Leuliette et al., 2004). The red and blue curves are deviations from their averagesfor 1961 to 1990, and the black curve is the deviation from the average of the red curve for the period1993 to 2001. Error bars show 90% confi dence intervals.17

Summary of Sea Ice1980Max: 16.13 msk, x=2.59Min: 7.86 msk, x=8.79Inf: -2.20 msk/month, x=6.44Melt Period: 6.20 months

2008Max: 15.11 msk, x=2.26Min: 5.40 msk, x=8.80Inf: -2.84 msk/month, x=6.77Melt Period: 6.54 monthsSlopes of LinesMarch: -0.043 msk/yr, (-0.054, -0.032)Sept: -0.079 msk/yr, ( -0.100, -0.057)

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19412004Muir Glacier, Alaska33Glacier Melting FactsTwo BILLION people in more than a dozen countries depend on rivers fed by the snow and ice of the plateau region. (Nat Geo, April 2010)The Tibetan Plateau as a whole is heating up twice as fast as the global average. (Nat Geo, April 2010)Snowpack too!Work with Brian McGauvran

Heat Index(F)Probability Above HI100 73%105 55%11038%11524%12014%1258%1304% Observed Ithaca Maxima Predicted Ithaca MaximaHeat Index(F)ProbabilityAbove HI10082%10570%11057%11543%12031%12522%13014%

THE ENDwww.ithaca.edu/tpfaff/sustainability.htmtpfaff@ithaca.eduPartly Supported by NSF DUE-0837721

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