Ehrlich equation

I = P • A • TWhere

I = environmental Impact

P = Population

A = affluence (GDP/person)

T = Technology (impact/unit GDP)

Problems with Ehrlich Eq.

This model, which drove many developments in sustainability, has limitations. 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

0

0.05

0.1

0.15

0.2

0.25

0.3

1 2 3 4 5 6 7 8Level of Consumption

Frequency

CurrentSustainable

Total Consumption To measure the total consumption of the

population, the average (expected) value of the discrete distribution can be computed as:

€

c = iPi

i=1

8

∑

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

€

δc = cδ f (c,E ,A,T2,L....)dc∫

Variation of Distribution Function

The variation of the distribution function is given as:

€

δ f =∂f

∂Eδ E +

∂f

∂Aδ A+

∂f

∂T2δ T2 +

∂f

∂LδL

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 T2 (increase renewable technologies)

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

Grand Objective

Concern 1

Concern 2

Concern 3

Activity 1

Activity 2

Activity 3

Remedy 1

Remedy 2

Remedy 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 of material(MJ/kg)

Embodied energy per

cup(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

0 5 10 15 20 25 30 35 400

2

4

6

8

10

12

14

Paper

Styrofoam

Ceramic

Number of uses

En

erg

y p

er

use (

MJ)

Energy per use

0 10 20 30 40 50 60 70 80 90 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

PaperStyrofoamCeramic

Number of uses

En

erg

y p

er

use (

MJ)

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

???