Tools of the Trade math, physics, and chemistry for understanding and assessing environmental proble

1
Tools of the Trademath, physics, and chemistry
for understanding and assessing environmental
problems
2
Data Sources

• COW appendices for conversion factors, physical
  constants, data on earth, natural stocks/flows of
  air/water/nutrients/energy, biosphere, elements,
  chemical reactions
• World Resources for up-to-date data on
  population, economics, food, land use change,
  energy supply/consumption, emissions
• http//earthtrends.wri.org/

3
Whats wrong with this table?
4
Reporting Numbers

• Report only significant digits. This tells the
  reader how accurately the number is known.
• WR reports 1996 CO2 emissions as 23,881,952
  thousand tons (8 sig digits!). This implies an
  accuracy of 1000 tons, or 0.00001.
• The true accuracy of this estimate is about ?5
  (?1 billion tons) only 2 digits are significant
  and should be reported 24 billion tons
• Few estimates are accurate to more than 2 or 3
  significant digits

5
Significant Digits

• Results have as many significant digits as the
  least-significant number used in the calculation.
  
• Examples

Rounding should be the very last step. Keep at
least one more significant digit in intermediate
calculations.
6
Spurious Rounding
Physicist rounds on measurement boobs Monday
December 9, 2002 Large numbers of women are
wearing the wrong-sized bra because of a
mathematical error known as "spurious rounding"
claims a University of Southampton physicist. In
"Graphical Analysis of Bra Size Calculation
Procedures", published in the International
Journal of Clothing, Science and Technology, Dr
Matthew Wright has analysed the effects of small
errors in measurements. "To do this properly
requires making two measurements, one around the
rib cage and one around the bust. These two
numbers then have to be converted to an even
number and a letter, and this is where the
problem arises." The standard procedure for
making this calculation instructs the user to
convert the first number by adding four if it is
even and five if it is odd, effectively rounding
it to the nearest two inches. This rounded number
is then subtracted from the second number (also
rounded to the nearest inch) to give the cup
size. Because one rounded number is subtracted
from another any errors will accumulate. Dr
Wright explains "It's a well-known effect called
- perhaps somewhat unfortunately in this context
- 'spurious rounding'. It might seem surprising
but if this procedure was obeyed exactly then a
small error could, in principle, make the
difference between predicting a size of 36A and
one of 34D." His paper suggests an alternative
method of measurement for women fitting
themselves, which reduces the possibility for
error, where the subtraction is done before the
rounding.
7
Scientific Notation

• Because we will often deal with very small or
  very large numbers, we will sometimes use
  scientific notion
• Examples
• 1,000 10?10?10 103
• 2,000 2?103
• 321,000 3.21?105
• 0.0029 2.9?103
• 0.000006 6?106

8
Units of Measure

• We will use metric units in this course, also
  known as SI (international system) units
• Because English units are common in the US, we
  will convert from English to/from metric
• SI units have been officially adopted and steps
  have been taken to convert from older units of
  measure in all but three countries.
• Can you name the other two?

9
SI Base Units

• meter (m)
• kilogram (kg)
• second (s)
• kelvin (K)
• mole (mol) 6.02?1023 atoms or molecules
• nucleons (protons and neutrons) have a mass of
  1.67?1024 gram thus, 6.02?1023 nucleons have a
  mass of 1 gram (g)
• (1.67?1024 g/nucleon)(6.02?1023 nucleons) 1 g
• 6.02?1023 carbon atoms (each with 6 protons and
  6 neutrons) have a mass of exactly 12 g
• Also ampere and candela, but not used in this
  class

10
Derived Units
11
Other Units
12
Prefixes
13
Prefixes

• Examples
• kilogram kg 103 g
• kilometer km 103 m
• centimeter cm 102 m
• exajoule EJ 1018 J
• kilowatt kW 103 W 1 kJ/s
• teragram Tg 1012 g 109 kg 106 t 1 Mt
• 23,881,952 thousand tons 24 Gt 24 Pg

14
A Few Conversion Factors

• 1 foot 0.3048 m 1 mile 1609 m
• 1 acre 4047 m2 1 ha 2.47 acre
• 1 gal 3.785 L 1 bbl 42 gal 1 acre-ft 1234
  m3
• 1 year (y) 8766 hours (h) 3.15?107 s
• 1 pound 0.454 kg
• 1 BTU 1055 J 1 calorie 4.184 J
• 1 horsepower 746 W
• 1 K 1 ?C 1.8 ?F K 273 ?C

15
Other Useful Facts

• Density of water 1 t/m3 1 kg/L 1 g/cm3
• Density of air ? 1 kg/m3 1 g/L
• Density of any gas at STP 0.045 mol/L
• Acceleration of gravity 9.81 m/s2

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Unit Conversion

• Line up units so they cancel.
• Susquehanna River average discharge 27 million
  acre-feet per year to convert into m3/s

• Do it in your headits easier than you think!

17

• Earth is approximately a sphere with a radius of
  6370 km the surface area is therefore

• 510 million square kilometers 51 Gha
• Oceans cover 70 of this area. The mean depth is
  4 km, so the volume is

• The mass of the oceans is

18
Basic Physics

• The most important physics concepts in this
  course are energy (J) and power (W J/s)
• Energy comes in many forms
• Electromagnetic
• Chemical (stored in atomic bonds)
• Nuclear (stored in nuclear bonds)
• Mechanical (kinetic and potential)
• Thermal (heat)
• Power is a flow of energy

19
Dimensional Analysis

• Many problems can be solved by getting the units
  right you dont have to know physics.
• How much power can you generate with a dam
  10-meter-high across the Susquehanna?
• I want
• power W J/s kg?m2/s3
• I know
• average water flow 1100 m3/s
• water density 1 t/m3 1000 kg/m3
• head or distance water falls 10 m

20
Power in Susquehanna River
Turbines can convert 90 into electricity. The
16-m-high Holtwood dam in Lancaster County, PA,
has a capacity of 108 MW.
21
Holtwood dam, Lancaster, PA16 m, 108 MW
Conowingo dam, Cecil Co., MD32 m, 512 MW
22
Power in Susquehanna River
23
Power in the Wind

• A large wind turbine has 70-m rotor diameter. How
  much power generated in a 20 mph wind?
• We know
• area swept ?r2 ?(35 m)2 3848 m2
• density of air 1.3 kg/m3 (COW, p. 236)
• velocity of wind

24

• This omits a factor of ½, because kinetic energy
  is ½mv2. So the power in the wind is

• One cannot extract all this powerthe air would
  pile up! Theoretical maximum is 59 40-50 can
  be achieved in practice (800 kW).

25
44 1.5-MW turbines are being installed in Tucker
County, WVA Blades are 34 m long tower is 70 m
high
26
Chalk Point683 MW coal-fired electricity
27
Chalk Point How Much Coal?

• Chalk Points two coal-fired steam generators
  produce 683 MW of electricity
• Energy content of coal 29 MJ/kg 29 GJ/t (COW,
  p. 242)

28
Chalk Point How Much Coal?

• This assumes that 100 of the coal energy is
  converted into electrical energy
• In practice, only 35-40 is converted the rest
  is rejected as heat to the environment

At 55 t/car, this requires about one 100-car
train per day!
29
Thermal Efficiency

• Coal plants produce steam at ?840 K (570 ?C or
  1050 ?F) waste heat is discharged to the air or
  water at ?300 K (27 ?C or 80 ?F)
• Theoretical maximum (Carnot) efficiency

• Efficiency that maximizes power production

30
Thermal Efficiency

• As temperature difference between heat source and
  heat sink in reduced, efficiency is reduced
• Geothermal
• TH 520 K, TC 350 K, ?max 0.18
• (250 C, 480 F) (80 C, 170 F)
• Ocean thermal
• TH 300 K, TC 277 K, ?max 0.04
• (27 C, 80 F) (4 C, 40 F)

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Other Basic Physics

• Conservation of energy
• (potential kinetic internal) constant
• Example mgh ½mv2 mCT
• Conservation of mass
• total mass before total mass after
• Conservation of charge
• total charge before total charge after

32
Basic Chemistry

• Know how to read a periodic table
• How to read molecular formula
• How to determine molecular weight
• How to compute gas mixtures
• How to read basic chemical equations

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(No Transcript)
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Atomic number 6 All carbon atoms have six
protons
Atomic weight 12.01 One mole of carbon
(6.02x1023 atoms) has a mass of about 12
grams (not exactly 12 1.1 is carbon-13, which
has 7 neutrons the rest is carbon-12, with 6
neutrons (0.011)(13) (0.989)(12) 12.011)
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Periodic Tables on the Web

• http//pearl1.lanl.gov/periodic/
• http//www.webelements.com/
• http//www.chemicalelements.com/
• http//environmentalchemistry.com/
• http//www.chemicool.com/

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Molecular Weight

• Atomic weights H 1, C 12, N 14, O 16
• Molecular weights
• N2 2(14) 28 g/mol
• O2 2(16) 32 g/mol
• H2O 2(1) 16 18 g/mol
• CO2 12 2(16) 44 g/mol
• In 1996, 23.9 Gt of CO2 released how much C?

37
Average Molecular Weight

• A mole of any gas (6.02?1023 molecules) at a
  given T, P occupies the same V (22.4 L _at_ STP)
• Thus, gas mixtures are given in by volume
  molecules
• Air is 78 N2, 21 O2, 1 Ar, 375 ppm CO2
• 78 of air molecules are N2 molecules
• 375 of every million air molecules are CO2
• Average molecular weight of air
• (0.78)(28) (0.21)(32) (0.01)(40) 28.96

38
If you are fastidious about units
By knowing the pressure and composition of air at
sea level, one can estimate with fair accuracy
the total mass of the atmosphere and the number
of air molecules
39
Mass, Moles of Atmosphere

• Mass of atmosphere 5.14?1018 kg

• Number of moles of dry air 1.78?1020

40
CO2 Emissions

• CO2 emissions from fossil-fuels, 1996 23.9 Gt
• How many moles? How would CO2 concentration
  increase if all this stayed in atmosphere?

• Actual increase 1.5 ppmv ?50 absorbed by
  oceans, forest regrowth

41
Fraction by Weight

• CO2 is 27 C, 73 O by weight
• Very roughly, biomass is C6H12O6, or 40 C

1 t CO2 273 kg C
42
Estimation

• In addition to physics and chemistry,
  environmental science relies heavily on
  estimation and bookkeeping (stocks, flows)
• One would might prefer to look up the right
  answer or best value, but often this is not
  easily available and may not even exist
• This class will help you become comfortable with
  estimation, and better at it
• Sometimes called back-of-the-envelope
  calculations

43
Area, Volume of Chesapeake Bay

• How long is the Bay (north-south)?
• What is the average width?
• What is the average depth?

44
Chesapeake Bay
200 mi
25 mi
15 mi
100 miles
45
Area, Volume of Chesapeake Bay

• How long is the Bay (north-south)?
• What is the average width?
• (200 mi)(15 mi) 3,000 mi2
• actual area 3,238 mi2
• What is the average depth?

46
Volume of Chesapeake Bay
47
How Many Haircutters in CP?

• Population ? 25,000 8,000 students ??
• How many haircuts per person per year?
• How many haircuts per haircutter per day?

Yellow Pages lists 15 barbershops and hair salons
in College Park. Assuming an average of 4 cutters
per salon, there are 60 cutters.

• Average cost per cut?
• Average gross income per cutter per year?

48
How Many Rubber Bands?

• I used rubber bands in mail, food, etc. for 3 y
  to make a 3-lb ball 14 cm in diameter.
• How many rubber bands are in the ball?

• I estimated the number of rubber bands in four
  different ways. How many can you think of?
• Answers 1300, 1400, 1500, and 1600.

49
How Many Rubber Bands?

• Method 1 Rate of collection

Method 2 Mass ratio Using a postage scale, 28
RB weigh 1 oz
50
How Many Rubber Bands?

• Method 3 Volume ratio
• RB is 20 cm long, 0.5 cm wide, 0.1 cm thick
• (20 cm)(0.5 cm)(0.1 cm) 1 cm3

Method 4 Ratio to known standard A 12.7-lb ball
is known to contain 6,200 RB
51
Size of Asteroid

• The mass extinction 65 My BP probably was caused
  by asteroid impact. Geologists have discovered a
  65-My-old, 0.1-mm-thick, Ir-rich layer of dust
  everywhere on earth.
• About 20 of the asteroid ended up as fine dust
  in the upper atmosphere, eventually settling out
  uniformly over the earths surface.
• How large was the asteroid?

52
4 times the volume of Chesapeake Bay
5 miles in diameter!
53
For comparison, yield of combined US Russian
nuclear stockpiles ? 1019 J, so asteroid impact ?
10,000 x energy released in an all-out nuclear
war!
54
Drilling in ANWR

• USGS estimates that, if opened for drilling, ANWR
  would yield 6 to 16 billion barrels
• Is this a lot of oil? Most oil is used for
  gasoline. What is U.S. gasoline consumption?
• How many cars?
• What is the average miles/year?
• What is the average miles/gallon?

55
US Gasoline Consumption

• Actual gasoline consumption 126?109 gal/y

• Total oil consumption (diesel, fuel oil,
  lubricants, solvents, asphalt, etc.) 7.2
  Gbbl/y ANWR 0.8 to 2.2 y of US consumption at
  current rate

56
US Gasoline Consumption

• WRI gives US consumption of liquid fuels 855
  million metric tons oil equivalent (toe) using
  toe 41.868 GJ, and energy content of bbl oil
  from COW VII.4

57
Caesars Last Breath

• How likely is it that you will inhale, in your
  next breath, at least one of the air molecules
  exhaled by Julius Caesar in his dying breath?
• How many molecules are exhaled in one breath?
• What is the concentration of such molecules in
  the atmosphere?
• How many such molecules will I inhale in my next
  breath?

58
Molecules per Breath

• COW XV (p. 263) gives characteristics of a
  standard adult man
• Breathing rate, resting 6-8 breath/min 7.5
  L/min, so one breath ? 1 L
• One liter of any gas contains 0.045 moles at STP,
  but we also could compute this given the density
  and molecular weight of air

59
Concentration in Atmosphere

• The molecules Caesar exhaled are now uniformly
  mixed throughout the atmosphere. The
  concentration of cdb molecules is

Sometimes called the mixing ratio

• In your next breath, you inhale 1 L (0.045 mol)
  of air, with an average of 7 molecules exhaled by
  Caesar in his dying breath

60
Residence Time of Air Molecules

• Probability of inhaling no cdb molecules in
  your next breath
• POISSON(0,7,0) 0.0009
• Can we be sure that the air molecules that Caesar
  exhaled are still in the atmosphere, and that
  they are uniformly mixed?
• yes, well come back to this later

61
Nitrogen Runoff into Chesapeake

• Recall the discharge of the Susquehanna

• Lancaster County contains ?100,000 cows. Each cow
  produces ?120 lb/d wet manure (75 water). Dry
  manure is ?5 nitrogen.

62
Nitrogen Runoff into Chesapeake

• Half of the N produced runs off into the river

• Measured level ?3 ppm thus, Lancaster cows are
  about 1/10th of problem
• Other sources other farm animals (pigs,
  chickens) other counties human waste vehicle
  and power-plant emissions

63
Ecology USA (11 Nov 1996)

• The Biomass for Rural Development program
  centers on a 2600 acre tract where officials hope
  to develop hybrid, faster-growing willows that
  will produce between 3747 MW, or enough power to
  light 40,000 homes. Officials, who hope the
  willows will provide a viable energy source by
  2000, project willow-based sales could be as much
  as 20 million per year, which could lead to 135
  million worth of related energy sales.
• How much wood can be produced (t/yr)?
• How much is this wood worth (/yr)?
• How much electrical power (MW)?
• How many homes can this light?

64
How Much Wood?

• From Harte, NPP of temperate forests 0.56
  kg(C)/m2-yr biomass 37 carbon
• Compare to best average yields of 8 t/acre

65
How Much Is Wood Worth?

• As heating fuel, wood cannot be more valuable per
  J than other solid fuels coal
• Coal costs 30/t energy content is 29 GJ/t, v.
  15 GJ/t for dry wood

Compare to 20 million/y cited in article
66
How Much Electricity?

• 3 J of heat can produce 1 J of electricity
• Retail price of electricity ? 0.1/kWh

Compare to 37-47 MWe, 135 million/y cited in
article
67
How Many Homes?

• US residential sales 1.2?1012 kWh/y
• ?100 million households in US
• 1.2?1012/108 12,000 kWh/household?y
• Project can produce 30?106 kWh/y

33 of total
Article enough to light 40,000 homes Lighting
is ?10 of residential demand
68
Box Models

• Natural systems are characterized by the
  transport of substances (water, nutrients,
  toxics), organisms, and energy from one reservoir
  to another.
• Reservoirs can be physical (air, ocean), chemical
  (different chemical forms), or biological (live
  biomass, dead organic matter)
• Flows can be bulk motion, diffusion, convection,
  conduction and radiation, chemical or nuclear
  reactions, phase change

69
Uses of Box Models

• Predicting concentrations in organs after
  inhalation or ingestion of substance setting
  standards for exposure/intake of substances
• Water pollution, outdoor/indoor air pollution
  predicting concentrations in various
  environmental reservoirs as a function of time
• Population dynamics, predator-prey and food-chain
  models, fisheries, wildlife management
• Climate models (energy, air, water)

70
Box Models

• We represent the reservoirs with a box we
  usually assume the box is well-mixed, and we
  usually are not concerned with internal details

Stock, S
Inflow, Fin
Outflow, Fout

• Basic rule inflow outflow change in stock
• Flows (Fin, Fout) constant over small time ?t, so

71
Equilibrium

• If Fin Fout, then dS/dt 0 and the stock is
  constant with time a state of equilibrium.
• Most natural systems are in quasi-equilibrium
• Equilibrium means a particular quantity (stock)
  is not changing significantly over some time
• doesnt mean nothing is happening, every-thing is
  constant, or constancy is permanent
• equilibrium can be dynamic or static
• equilibrium can be stable or unstable

72
Equilibrium
Stable
Unstable
Neutral
Locally Stable
73
Residence Time

• If a quantity is near equilibrium, the
  characteristic response time of the system is

• Residence time is often the single most important
  characteristic of a natural system
• if ? large, system is resistant to change but,
  once perturbed, slow to return
• if ? small, system is quick to respond to
  perturbations, but quick to return

74
Hydrological Systemstocks and flows 1012 m3
103 km3 (COW, VI.2-3)
75
Hydrological System
76
Carbon(COW, XII.1)
77
Chesapeake Bay

• Stock of water 68 km3
• Flow in from Susquehanna 33 km3/y Susquehanna
  is about 50 of total flow in

• Ignores precipitation, evaporation, groundwater,
  tidal flows
• Not good example because not well-mixed

78
Mono Lake
79
Mono Lake

• High-altitude basin lake (no outflow, saline)
  brine shrimp and islands provide important
  habitat for migratory birds
• Before 1940, quasi-equilibrium (Fin ? Fout)
• Elevation 6417 ft
• Area 55,000 acres (55 kac)
• Volume 4300 kac-ft
• Fin streams (150 kac-ft/y) groundwater in
  (40 kac-ft/y) precipitation (8 in/y)
• Fout evaporation groundwater (25 kac-ft/y)

What is the average depth?
80
Evaporation 202 kac-ft/y
Precipitation 37 kac-ft/y
Stream Runoff 150 kac-ft/y Rush, Lee Vining, Mill
creeks
Mono Lake V 4,300 kac-ft A 55 kac
Groundwater out 25 kac-ft/y
Groundwater in 40 kac-ft/y plus non-stream runoff
81
Estimating Runoff

• In this example, stream flows were measured.
  For a watershed (drainage basin)
• Precip Evap Runoff Groundwater
• Average precipitation 21 in/y 1.74 ft/y
• Average evaporation 40 8.4 in/y
• Average groundwater recharge 35 7.3 in/y
• Average runoff 25 5.2 in 0.43 ft/y
• Watershed area 432 55 377 kac
• Runoff (377 kac)(0.43 ft/y) 160 kac-ft/y

82
Mono Lake Watershed
83
Residence Times

• Residence time of water in Lake Mono
• (and substances that co-distill with water, like
  DDT, PCBs)

• Residence time of other dissolved substances

84
Concentrations

• Suppose a toxic substance that co-distills with
  water flows into Mono Lake at a constant rate of
  1000 kg/y. What is the concentration?
• After a long time, fin fout f 1000 kg/y

85
Concentrations

• Most substances dont codistill with water in
  this case, ? 170 y and c 32 ppb.
• We could also get this answer by assuming that
  the toxic flow out is contained in the
  groundwater flow out

86
Concentration

• If we measure a concentration of 5 ppm in the
  lake water, then at what rate is the substance
  flowing into the lake?

87
Natural Sources of N2O

• Nitrous oxide is a greenhouse gas. The
  preindustrial concentration in the atmosphere was
  275 ppbv (v. 317 ppbv today)
• N2O is inert and nonreactive in the troposphere
  it diffuses to the stratosphere, where it is
  destroyed photochemically
• The residence time in the atmosphere is about 120
  years
• What is the natural (preindustrial) flow of N2O
  into the atmosphere?

88
Natural Sources of N2O
Photochemical destruction
Fout
c 275 ppbv ? 120 y
Natural Flow
Best estimates 9.6 and 10.8 TgN/y (with
uncertainties of ?5)
Fin
89
Great Lakes Watershed
90
Great Lakes A 5-Box Model
91
What If Flows Are Not Constant?

• If flows are not constant, then we must solve the
  differential equation

• Simplest case is when the difference between Fin
  and Fout is constant

92
Exponential Growth

• Next simplest is when flow in (or out) is
  directly proportional to the stock

• Put 100 in an account with r 0.1/y after 10
  years you have (100)e(0.1/y)(10y) 270

93
Doubling Time

• The time it takes for the stock to double when
  growing at a constant rate r is given by

• If a stock (e.g., US population) is growing 1/y
  (r 0.01/y), then it will double in 69 y
• At 3.5 (e.g., population of Saudi Arabia), it
  will double in 20 y at 7/y, T2x ? 10 y
• If St lt S0, r is negative and T½ is the halflife

94
Continuous v. Annual Rates

• Growth rate r is called the continuous growth
  rate. Most publications give annual yield i
  total percentage growth in one year.
• The relationship between r and i can be found by
  writing the equation for the stock after 1 y

95
If r lt 0.1, then i ? rBut i gt r always.S(t)
is given bySt S0(1 i)twhich is identical
to St S0 ertwhere r ln(1i)
96
Average Growth Rate

• If you know the stock at times t1 and t2, the
  average growth rate is given by
• US Pop S2000 281.4, S1990 248.7 million

? 1.2/y
? 1.2/y
97
Population Growth

• Populations have flows in (births) and out
  (deaths), which are proportional to population
• If b d, then r 0 and population is constant
  (ZPG)
• If b gt d, we have exponential growth at rate r
  b d
• If b lt d, we have exponential decay at rate r
• Somalia b 50/y per 1000, d 20/y per 1000
• r 0.05 0.02 0.03/y 3/y, T2x 23 y

98
Combining Rates

• If P is growing at rate rP, per-capita income is
  growing at rate rA, and emissions per dollar of
  economic activity at growing at rT, then impact
  is growing at rate r (rP rA rT)

99
Carbon Emissions
100
Carbon Emissions

• Often it is useful to break the IPAT identity
  down into more components
• For example, emissions intensity (tC/) is the
  product of energy intensity (GJ/) and carbon
  intensity (tC/GJ)

101
Carbon Emissions
102
Allocating Blame

• US energy use rose from 89 to 104 EJ/y from 1990
  to 2000 (r 0.0158/y). How much of this is due
  to population growth (r 0.0121/y)? Growth in
  per-capita consumption (r 0.0034/y)?

due to pop growth due to growth in
per-capita consumption
103
Exponential Growth of Flows

• We use growth rates for stocks (population) and
  flows (/y, energy/y, tons/y)
• When flows increase at a constant rate, we can
  integrate to find total amount consumed

between time 0 and T
104
Exponential Growth

• If consumption rate is growing exponentially,
  total consumption in next doubling time equals
  all previous consumption

105
In this chart, consumption is growing at 7/y
(doubling time 10 y) Consumption in the next
ten years (blue bars) equals total consumption
over all previous years
106
Exponential Depletion

• How long to consume a total amount of oil S?
• Suppose we have a 100-y supply of oil at current
  rate of consumption (S/F0 100 y), but
  consumption is growing 5/y (r 0.05/y)

107
Annual Consumption
108
Technical Note

• Note that this expression breaks down when r
  0, but thats ok because

109
Exponential Decay

• If the rate of consumption is decreasing at a
  constant rate, then total consumption for all
  time is finite
• If r 0.05/y, S8 20 F0

Suppose we reduced the annual consumption of a
resource (e.g., mercury) by 1/y forever. Total
consumption over the rest of human history would
be 100 times current annual consumption.
110
ANWR v. CAFE

• USGS estimates that, if opened to drilling, ANWR
  could produce ?10 billion barrels of oil over a
  20-year period, beginning 2010
• 95 confidence interval 6 to 16 Gbbl
• How does the amount of gasoline that could be
  produced from ANWR oil compare with
• the amount of gasoline that could be saved by
  increasing the average fuel economy of passenger
  vehicles by 5 mpg?

111
Gallons of Gasoline from ANWR

• 1 barrel (bbl) 42 gallons
• On average, ?20 gallons of gasoline are produced
  per barrel of oil
• the other 22 gallons are used to produce fuel
  oil, lubricants, solvents, asphalt, etc.

112
Gasoline Consumption 1

• In 2000 passenger vehicles drove 2,540 Gmi and
  consumed 126 Ggal of gasoline
• Average fuel economy 2540/126 20.1 mpg
• roughly constant since 1990
• each vehicle type is more efficient, but greater
  fraction of SUVs, minivans, trucks
• If fuel economy was 25.1 mpg, gasoline
  consumption would be

113
Gasoline Consumption 1

• Savings 126 101 25 Ggal/y
• Over 20 y (25 Ggal/y)(20 y) 500 Ggal
• Compare to ANWR 200 Ggal
• This assumes that VMT are constant, but VMT has
  increased steadily
• total vehicle miles in 1990 1,990 billion.
• what was average rate of growth?

114
Average Rate of Growth
T2X 69/2.5 28 y

• Better method regression with y ln(VMT), x
  t slope best-fit growth rate

115
Passenger VMT/y, 1966-2000
Passenger Vehicle Miles (Gmi/y)
116
Passenger VMT/y, 1966-2000
Passenger Vehicle Miles (Gmi/y)
117
Estimated VMT, 2010-2030
F(t) F2000e0.025(t-2000)
Passenger Vehicle Miles (Gmi/y)
Total VMT 2010-2030
118
Estimated VMT, 2010-2030
119
Gasoline Consumption 2

• Assuming average of 20 mpg
• Assuming average of 25 mpg
• Savings
• 4,250 3,400 850 Ggal

Compare to 500 Ggal, 200 Ggal from ANWR
120
DOE Projections
121
Logistic Growth

• Exponential growth cannot continue for more than
  10 (103) or 20 (106) doubling times
• As population grows, growth rate decreases
  simplest representation is a logistic function

S8 carrying capacity
exponential growth
no growth
122
Logistic Growth Total Stock
S(t) S0ert
S0 1 S8 100 r 0.1/y
123
Logistic Growth Annual Increment
S0 1 S8 100 r 0.1/y
124
Logistic Growth Rate
S0 1 S8 100 r 0.1/y
125
Other Uses for Logistic Equations

• Logistic equations have been used to model
• growth of populations (e.g., C in forest)
• relationships with dependent variable that is a
  proportion or a dichotomous variable
• spread of epidemics
• diffusion of innovations, market penetration,
  transition between industries, processes, fuels
  (e.g., percentage of final energy that is coal,
  oil, gas, or electricity)
• consumption of finite resources (fossil fuels)

126
Logistic Fit to SARS Cases
127
Oil Consumption

• There is a finite amount of oil that can be
  economically recovered S8
• When cumulative consumption, S(t), is small
  compared to S8, demand increases exponentially at
  rate r
• Cheapest, easiest deposits are exploited first
  as cumulative consumption increases, price
  increases (extraction more expensive, scarcity
  rents) and growth rate decreases
• When cumulative consumption ? ½S8, demand peaks
  and declines thereafter

128
US Oil Production
129
PA Coal Production
130
Three Facts and Some Speculation

• Current rate of oil consumption 163 EJ/y
• Average growth rate, 1990-2000 1.4/y
• Cumulative world consumption ? 6,000 EJ
• Estimates of total recoverable oil resources
  range from about 8,000 to 20,000 EJ remaining
  resource 2,000 to 14,000 EJ
• Lifetime assuming constant consumption
• (S8S0)/F0 12 to 86 y
• Lifetime assuming constant growth
• If r 0.014, T ln(1rS/F)/r 11 to 57 y

131
Cumulative Production
Best fit to 1980-2000 Cumulative Production
132
Annual Production
Best fit to 1980-2000 Cumulative Production
133
Year of Peak Production
134
Best-fit Logistic Curves simple method
Assume S8, compute ft St/S8, yt lnft/(1-ft)
135
Best-fit Logistic Curves
136
Best-fit Logistic Curves Rate Method
Can be rewritten as

• The derivative

The left-hand side, (dS/dt)/S, is the growth rate
of cumulative consumption. This is a linear
function of cumulative consumption, with an
intercept of r and a slope of r/S8. Growth is
zero when S S8 r/(r/S8)
137
Best Fit to Rate Curve 1929-2001
1970
95 CI (8,400, 11,000)
1983
95 CI (10,400, 13,000)
138
Best-fit to Rate Curves
139
Concentrations non-constant flows

• c concentration of contaminant (mg/L, ?g/m3)

140
Contamination and Clean-up
141
Simple Model v. Reality

• Caution reality is often more complicated!
• Stocks often are not well-mixed
• Stocks and flows may contain both dissolved and
  suspended contaminants
• Contaminants may precipitate at high
  concentrations and go back into solution at low
  concentrations
• Realistic models often subdivide physical
  reservoirs into several physical, chemical, or
  biological sub-compartments

142
Box Model of Human Body
143
Inhalation of 1-?m UO2 Aerosol
Fraction
Lung
Blood
Bone
Kidney
Time (hours)
144
Numerical Solutions

• If flows vary with time or if there are many
  different stocks, analytical solutions for S(t)
  for each box may be difficult or impossible
• Equations are solved numerically using
• custom program
• special systems modeling software (Stella)
• general-purpose equation-solving software
  (Mathematica, Maple, MathCad)
• spreadsheet (Excel Crystal Ball)

145
Mono Lake

• In 1941 Los Angeles began to divert water from
  the streams feeding Mono Lake
• Lake level drops, producing non-linear decrease
  in lake area, evaporation rate
• Lake volume decreases, salinity increases,
  evaporation rate decreases
• Runoff (precipitation) and diversions vary from
  year to year
• Numerical solution required! Mono Lake.xls

146
Mono Lake BOTE Calculation

• Always good to check detailed models with a quick
  back-of-the-envelope calculation
• What would happen if diversions continued at
  1962-85 average rate (?90 kac-ft/y)?
• In equilibrium, evaporation flow would decrease
  from 202 to 112 kac-ft/y
• Evaporation flow is proportional to lake area, so
  area reduced by factor of (112/202) 0.55, from
  55.2 to 30.6 kac
• Compare to spreadsheet answer 30.6 kac

147
Cost-Benefit Analysis

• Many environmental policy issues involve weighing
  costs and benefits of environmental protection
  measures or practices/projects that affect
  environmental quality
• Do the benefits of the policy or project outweigh
  the costs?
• What is the optimal solution? What level of
  pollution control or what size project is best?

148
Measuring Costs

• Costs of environmental protection generally are
  relatively easy to measure
• forgone industrial production or use of economic
  resources
• installing and operating pollution control
  devices, transition to more efficient and
  expensive technologies
• paying pollution taxes or purchasing permits
• verifying compliance
• lost markets

149
Measuring Benefits

• Benefits are often are avoided costs more
  difficult to measure difficult to monetize
• Deaths or illnesses avoided days of work
  quality-adjusted life-years saved (QALY)
• Dollar value of resources, ecosystem goods and
  services preserved or recovered
• Economic damages avoided (e.g., crops, timber,
  settlements, etc.)
• Recreational, aesthetic, and existence values of
  natural systems

150
Non-Market Valuation

• Value of wages lost due to death, illness cost
  of medical treatment for illness
• Travel costs, access fees for recreational value
• Willingness to pay (WTP) to preserve
  environmental goods and services contingent
  valuation (CV)
• Willingness to accept compensation (WTA) for
  illness, loss/damage to goods, services
• Differences, changes in property values
• Cost of compliance with existing laws (pollution
  control, taxes, permits)
• Cost of providing lost environmental goods and
  services with market goods and services

151
Discounting

• Usual procedure is to discount costs and benefits
  at the same rate and compare the present values
• Benefits in the distant future have little
  weight
• 1 billion today 20 billion in 2100 if r
  0.03/y
• 150 billion in 2100 if r 0.05/y
• 22,000 billion in 2100 if r 0.10/y
• 3,300,000 billion in 2100 if r 0.15/y

152
Incandescent v. Compact Fluorescent

• A 1200-lumen incandescent bulb uses 100 W,
  costs 1, and lasts 1000 h
• A 1200-lumen compact fluorescent uses 20 W,
  costs 10, and lasts 10,000 h
• Net benefit of CF bulb depends on discount rate,
  annual usage, cost of electricity, and
• cost of changing bulbs, space heating and
  cooling, aesthetics, externality costs of
  electricity generation and bulb manufacture and
  disposal

153
Other Examples

• Paper v. plastic grocery bags?
• Paper v. polystyrene coffee cups?
• Cloth v. disposable diapers?
• Glass v. plastic beverage containers?
• Heat pump v. gas furnace?

154
Economic Efficiency

• Costs are minimized (benefits maximized) when
• marginal cost marginal benefit
• costs of reducing the next unit of pollution
  benefits of the reduction

155
Theory Can Be Hard to Put into Practice
156
Cost-effectiveness Analysis

• Because benefits are difficult to measure and
  compare with costs, some are skeptical that CBA
  can be used to define policy goals
• The goal (e.g., the allowed level of pollution)
  is set externally through the policy problem
• The cost part of CBA analysis can be used to
  define the most cost-effective strategy to
  achieve the goal
• Like CBA, subject to problems facing discounting
  and uncertainties about technology, resources,
  etc.

157
Risk Analysis

• Costs and benefits often are not deterministic
  multiple outcomes are possible
• For a risk-neutral decisionmaker
• Ci is the cost of the ith possible outcome
• pi may be well-known (smoking), poorly known
  (reactor accidents), or completely unknown
• If risk-averse, event with Cipi (106)(106) 1
  is riskier than event with Cipi (1)(1) 1

158
Other Considerations

• Do same people pay as receive benefits?
• Are costs and benefits dispersed or concentrated
  (in space or in time)?
• How reversible is the damage? On what time scale?
• Is response linear or nonlinear, with or without
  a threshold?
• What is the quality of the evidence? How much
  uncertainty? How likely is it that uncertainties
  will be resolved or reduced?