Ehrlich equation
 I=P•A•T
Where
I = environmental Impact
P = Population
A = affluence (GDP/person)
T = Technology (impact/unit GDP)
Problems with Ehrlich Eq.
 This model, which drove
sustainability, has limitations.
many
developments
in
 Few consider reduction in population as a desirable approach
to sustainability
 Assumes technology is of the refining type – wherein
resources are converted to energy.
 New technologies can increase efficiency and reduce
resource impact, but this contradicts the Ehrlich equation.
 There is a need to re-write the Ehrlich equation and provide
a richer model of human impact on earth’s resources.
Population
 Population is growing
 For a local region, we usually consider the rate of
population growth to be
 R = [Rb – Rd] + [Ri – Re]
Where b = birth, d = death, i = immigation and e =
emmigration
Population
 Then, the population at some time t from the present is
given as
P = P0 eRt
Rewriting the Ehrlich
Equation
 Sustainability requires participation from the world
population as a whole.
 This challenge is addressed in terms of average
population response
 The goal is to shift resource consumption behavior.
Shift in Resource
Consumption
Total Consumption
 To measure the total consumption of the population,
the average (expected) value of the discrete
distribution can be computed as:
8
c   iPi
i1
Total Consumption
 There are more than 8 categories of consumption – perhaps
unique behavior per individual.
 Thus, consider the behavior as a continuous function rather
than a discrete one.
 If the probability distribution function is f, then the
continuous form of the expected value of the parameter, c,
is now written
E(c)  c 


cf

(c)dc
Modelling Sustainability
 Sustainability can be viewed as the intent to make the
expected value, E(c), as small as possible.
 With no outside constraints, f(c) may be chosen as an
impulse function at the origin - no consumption at all!
 However this is not a realistic situation and we will
introduce restrictions on the function, f(c).
Sustainability Distribution
Function
 We will assume that the distribution function f(c) is also
dependent on a finite number of side constraints;
 E = education and awareness of individuals
 A = Cost. Availability of resource intensive materials,
 T2 = Renewable technologies, (note that T2 is used to
differentiate renewable or environmentally friendly
technologies from those denoted as T in the Ehrlich
equation.)
 L = legislation that controls consumption
Differential Sustainability
 Now we would like to find a function, f(c) that
minimizes the average subject to the given side
constraints. Taking the variation of the expected value
equation results in
c 

c  f (c,E, A,T2 ,L....)dc
Variation of Distribution
Function
 The variation of the distribution function is given as:
 f 
f
E
E
f
 A
A
f
T2
 T2 
f
L
L
Sensitivity of Distribution
Function
 The variations on the right side of the equation
indicate changes in the constraints, E, A, T2, and L and
 the partial derivatives represent the sensitivity of f(c),
the number of individuals at a given level of
consumption, to the changes in the respective
constraints.
 For example, it is believed that ∂f/∂E is negative – as more
people are educated and aware of sustainability issues, the
function will be minimized.
 Only ∂f/∂A is considered positive in this research – increased
availability of resources likely results in reduced sustainability.
Implications
 Thus the following actions should result in a lowering of
mean expected consumption:
 increase E (educate and raise awareness)
 decrease A (increase cost, reduce availability of resource
intensive materials)
 increase T (increase renewable technologies)
2
 increase L (create legislation to penalize consumption).
Grand Objectives
 W1: Maintaining the existence of the human species
 W2: Maintaining the capacity for sustainable
development and the stability of human systems
 W3: Maintaining the diversity of life
 W4: Maintaining the aesthetic richness of the planet
W1: existence of the human species
 Global climate change
 Human organism damage
 Water availability and quality
 Resource depletion: fossil fuels
 Radionuclides
W2: Sustainable development
 Water availability and quality
 Resource depletion: fossil fuels
 Resource depletion: non-fossil fuels
 Landfill exhaustion
W3: biodiversity
 Water availability and quality
 Loss of biodiversity
 Stratospheric ozone depletion
 Acid deposition
 Thermal pollution
 Land use patterns
W4: Aesthetic richness
 Smog
 Aesthetic degradation
 Oil spills
 Odor
e.g. Climate Change
 Climate change ties into W1 and W3.
 Human activities that contribute to climate change
include (not limited to) greenhouse gas emissions
 Greenhouse gas emissions come from (not exclusive):
 Energy use, ruminants, refrigeration, farming,
transportation
Climate Change
 Targeted activity for
examination:







Fossil fuel combustion
Cement manufacture
Rice cultivation
Coal mining
Ruminant population
Waste treatment
Biomass burning
 Emissions of CFC,
HFC, N2O
Loss of Biodiversity
 Targeted activity for
examination:
 Loss of habitat
 Fragmentation of
habitat
 Herbicide, pesticide use
 Discharge of toxins to
surface waters
 Reduction of dissolved
oxygen in surface
waters
 Oil spills
 Depletion of water
resources
 Industrial development
in fragile ecosystems
Stratospheric Ozone Depletion
 Targeted activity for
examination:




Emission of CFCs
Emissions of HFCs
Emissions of halons
Emissions of nitrous
oxides
Human Organism Damage
 Targeted activity for
examination:








Emission of toxins to air
Emission of toxins to water
Emission of carcinogens to air
Emission of carcinogens to
water
Emission of mutagens to air
Emission of mutagens to water
Emission of radioactive
materials to air
Emission of radioactive
materials to water





Disposition of toxins in
landfills
Disposition of carcinogens in
landfills
Disposition of mutagens in
landfills
Disposition of radioactive
materials in landfills
Depletion of water resources
Water Availability and Quality
 Targeted activity for
examination:
 Use of herbicides and
pesticides
 Use of agricultural
fertilizers
 Discharge of toxins to
surface waters
 Discharge of carcinogens
to surface waters
 Discharge of mutagens to
surface waters
 Discharge of radioactive
materials to surface waters
 Discharge of toxins to
ground waters
 Discharge of carcinogens
to ground waters
 Discharge of mutagens to
ground waters
 Discharge of radioactive
materials to ground waters
 Depletion of water
resources
Resource Depletion: Fossil Fuels
 Targeted activity for examination:
 Use of fossil fuels for energy
 Use of fossil fuels as feedstock
Land Use Patterns
 Targeted activity for examination:
 Development of undisturbed land
 Emissions influencing sensitive ecosystems
 Restoration of disturbed land
Approach
Concern 1
Grand Objective
Activity 1
Remedy 1
Activity 2
Remedy 2
Activity 3
Remedy 3
Concern 2
Concern 3
Remedy 4
Coffee Cups
 What’s better for the environment?
 Ceramic cup
 Paper cup
 Styrofoam cup
Let’s simplify…
 Fossil fuel depletion
 Energy required to make the cup
 Energy required to reuse the cup
 -> Energy per usage
Energy to make
Material
Mass of Cup
(g/cup)
Embodied energy Embodied energy
of material
per cup
(MJ/kg)
(MJ)
Ceramic
290
48
14
Paper
8.3
66
0.55
Styrofoam
1.9
104
0.20
Energy to reuse
Material
Energy per wash (MJ/cup)
Ceramic
0.18
Paper
--
Styrofoam
--
Assumed that cups are washed in an energy efficient dishwasher, electrical power,
Canadian standards (1994).
Note that dishwashers are more energy efficient than washing by hand (Dep’t of
Energy).
Energy per usage
 Paper: 0.55 MJ
 Styrofoam: 0.20 MJ
 Ceramic: [14 + (n-1) * 0.18 ]/n
 The more you use your ceramic cup, the more efficient
it becomes.
Energy per Use
14
Paper
Energy per use (MJ)
12
Styrofoam
Ceramic
10
8
6
4
2
0
0
10
20
Number of uses
30
40
Energy per use
1
0.9
Paper
Styrofoam
Ceramic
Energy per use (MJ)
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
20
40
60
Number of uses
80
100
Comparison
 To be more efficient than a paper cup, you must use
your ceramic cup at least 39 times
 To be more efficient than a Styrofoam cup, you must
use your ceramic cup at least 1,006 times.
What’s missing
 ???