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Global Change

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Math Behind the Rule of 70. The use of natural logs arises from ... Ecological (birds, mamals, plants, fish, coral) Polar regions (NW passage, permafrost) ... – PowerPoint PPT presentation

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Title: Global Change


1
Global Change
  • Mark Moldwin

2
What is changing?
  • Human Population
  • Land use
  • Water use
  • Pollution
  • Ecosystem exploitation/degradation

3
Human Population
  • 3.2 Billion to 6.1 Billion in my life so far
  • Expected to reach 10 Billion by my death (77
    million per year, 200,000 everyday)

4
Timescale Matters! (as does how the data are
presented!)
5
Exponential Growth
Penny exercise
Exponential and doubling are geometric series (a
series with a constant ratio between consecutive
terms - e 2.7)
6
Math Behind the Rule of 70 The use of natural
logs arises from integrating the basic
differential equation for exponential growth
dN/dt rN, over the period from t0 to t the
time period in question, where N is the quantity
growing and r is the growth rate. The integral
of that equation is   N(t) N(0) x ert where
N(t) is the size of a quantity after t intervals
have elapsed, N(0) is the initial value of the
quantity, e is the base of the natural
logarithm, r is the average growth rate over the
interval in question, and t is the number of
intervals. Natural logarithms (that is,
logarithms to the base e) come in from this
integration. Natural logs are sometimes
abbreviated ln to distinguish them from "common"
logarithms of base 10.   A special case is the
doubling time, which is the time when N(t)/N(0)
2, that is the quantity has doubled from its
initial value. At that point   rt ln 2 0.69
If one knows the growth rate as a decimal
fraction, then the doubling time t2 0.69 / r.
  If the growth rate is given in percent, then
0.69 must be multiplied by 100, and the doubling
time 69/r. This is the origin of the rule of
70, i.e., 69 is rounded up to 70.
7
Impacts of Population Growth
  • Energy Consumption
  • Carbon Cycle
  • Global Warming
  • Increased greenhouse gases
  • Increased greenhouse effect
  • Non-linear complex climate response

8
Greenhouse Effect
9
Equilibrium Temperature
  • Depends on (Energy output of Sun (S) at the
    planet and Albedo of planet)

For Earth A 0.3, S 241 W/m2 TE 255 K With
an atmosphere TE 277 K
10
Complex System
  • Atmosphere-Ocean system
  • Ice, snow, land cover
  • Aerosols (fires, volcanoes)
  • Clouds
  • Greenhouse gasses
  • Solar variability
  • Orbital variability
  • Asteroidal, cometary impacts

11
Chemistry Aside
  • What are greenhouse gasses and where do they come
    from?

12
Earth Science Aside
13
Evidence for Global Warming
14
Evidence of Global Warming
15
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16
Biology Aside
  • How does a tree grow from a seed? What material
    provides the mass of a tree? (What is plant
    food?)

17
Biological Implications
  • Plant growth

18
Recreated from a graph that orginally appeared in
an article written by Stephen H. Schneider called
"The Changing Climate" in Scientific American,
vol 261(3)70-80.
19
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20
This figure shows estimate of CO2 concentrations
(based on carbon-cycle and geochemical models,
along with estimates based on proxy data) at the
top and the resultant model-calculated average
global temperatures beneath. The bottom half of
the figure shows estimated actual tropical
temperatures (line C), and, beneath that, the
occurence of ice ages.. Figure reproduced from
Crowley Berner, Science 2001292(5518)870872.
21
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22
Evidence of Impact
  • Weather changes (El Nino/La Nina occurrence and
    amplitude)
  • Sea level
  • Ice caps and glacial melting
  • Ecological (birds, mamals, plants, fish, coral)
  • Polar regions (NW passage, permafrost)
  • http//www.climatehotmap.org/

23
June heat wave, 1998. Melbourne endured 24 days
above 95oF (35oC) nighttime temperatures in
Tampa remained above 80oF (26.6oC) for 12 days.
24
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25
Physics Aside
  • Blackbody Radiation
  • Electromagnetic Spectrum
  • Solar Energy

26
www.ess.ucla.edu/faculty/moldwin
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