Tofudi Com-population Models

7/30/2019 Tofudi Com-population Models

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IN T RO D U CT I O N TO E N G I N E E RIN GA N D T H E E N V IR O N M E N T

Edward S. Rubin

Cnrlzegie Mrllnn University

with Cliff I. Davidson

and other contributors

Boston Burr Ridge, lL Dubuqu e,lA Madison, WI New YorkSan Francisco St. Louis Bangkok Bog ota Caracas Kuala Lumpu r

Lisbon London Madrid MexicoCity Milan Montreal NewDelhiSantiago Seoul Singapore Sydney Taipei Toronto


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-CHAPTER 15 Environmental Forecasting

Populationgrowth

Changes il l Changes inenvironme~ltalj rowth i~npacta

Technologqchange

Figure 15.1 Basic elements of environmental forecas ting, illustrating the three main "drivers" ofpopulation growth, economic activity, and technological change: Future changesin environmental impacts also can feed back to and affect these processes.

reflect our current understanding of how the world works based on principles of

physics, biology, and chemistry. Many of these science-based models of environ-mental processes also are dynamic, meaning they can predict how factors like pol-lutant concentrations will change over time in response to a specified input or stim-ulus such as an increase or decrease in emissions from human activities.

The study of environmental eng ineering and science focuses mainly on develop-ing the science-based process models just described. Such models are essential forpredicting the environmental conscqucnces of changes in anthropogenic emissions,both now and in the future. In contrast, the study of population growth, economicactivity, and technological change lies primarily in fields of the social sciences, wheremathematical models also are used fo r prediction. Figure 15.1 illustrates some of thelinks between these social science models (reflecting hum an behavior) and the phys-ical science models of environmental processes. Both types of models are imp ortantfor environmental forecasting. The social science models emp hasized in this chapterprovide a b roader perspective on the factors affecting environmental futures.

15.4 POPULATION GROWTH MODELS

According to the United Nations, the world's population reached6 billion people onOctober 12 , 1999. The trend in world population grow th through the end of the 20thcentury A.D. is shown in Figure 15.2. Over the past 100 years, the world popu lation hasquadrupled. Although it took thousands of y ears for the population to grow to1 bil-lion, the last billion people arrived in only13 years! Several billion new neighbors areexpected to join us on the planet over the next several decades. Because pop ulationgrowth is a major determinant of environmental impacts, we look first at how suchgrowth can be expressed in mathematical tenns and used for environmental modeling.


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PART 4 Topics in Environmental Policy Analysis

7.000

6 billion on

1000 500 o 500 1000 1500 2000B C R C

Year ( A D )

Figure 15.2 World population growth, 1000 B.C . to 2000A . D . (Source: Based on USDOC, 19990)

Depending on the time frame and geographic region of concern, one could envi-sion a broad array of population trajectories, a s illustrated in Figure 15.3. Th ese includ epopulations that grow quickly or slowly, as well as populations that stabilize, or that

decline over time. The scope and purpose of an environmen tal analysis play a large rolein defining the importance and type of population prqjections needed.Each curve or trajectory in Figure 15.3 can be represented by an equ ation or math-

ematical model. Inde ed, virtually any path that can be envisioned can be representednumerically in an environmental forecast or scenario. The next sections present a setof population growth mod els that span a range of co mplexity. The param eters govern-ing the behavior of each model represent the variables of an environm ental forecast orscenario. The value of key variables is often guided by analysis of historical data, butit is up to the analyst to specify how the se parameters might change in the future.

1

15.4.1 Annual Growth Rate Model #1

One of the simplest and most common ways to quantify the growth of a populationis to assume a corzstont ariril~al rowth mte, r; expressed either as a percentage or as I

a fraction. For example, if a population grows at a rate of 2 percent per year, nextyear's pop ulation will be 1.02 times greate r than this year's popula tion, and the fol-lowing year it will be 1.02 times greate r than that (an overall incre ase of2.04 per-


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CHAPTER 15 Environmental Forecasting

Present FutureTime-igure 15.3 Possible trajectories of population change.

cent). If the annual growth rate, r, is expressed as a fraction (such as 0.02), a generalexpression for the total population, aftert years is

P = Po (1 + r ) ' [15.1]where Pu is the initial population at the timet = 0.

This equation has the identical form as the compound annual interest equationused in engineering econom ics to calculate monetary growth (s ee Chapter13j.The keycharacteristic of this equation is a nonlinear increase inthe total quantity over time (beit population, money, or any other quantity that grows at a constant annual rate). Fig-ure 15.4 llustrates thls trend for three different rates of annua l population growth. Thehigher the annual growth rate, the more dramatic the rise in population over time.

0

0 10 20 30 40 50Time (years)

Figure 15.4 Population increase for three annual growth rates based on acompound annual growth model.


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64 2 PART 4 Topics in Environmental Policy Analysis

Example 15.1Population growth of an urban area. The current population of an urban area is 1 million

people. The region has exp erienced rapid growth at an annual rate of 7 percentlyear. City plan-ners and environmental officials anticipate that this annual growth rate will continue for thenext 10 years. If so, what wou ld the population be 10 years from no w'?

Solution:

Assuming a constant annu al growth rate, use Equation (15.11 withPC ,= 1 million, r = 0.07.an d t = 10 years:

Thus the population would double in 1 0 years at a 7 percentlyear rate of growth.

The implication of a compound annual growth modelis an ever-rising popula-tion. This type of model is frequently used in environmental forecasts or scenariosto estimate future environmental emissions from hu man activity. The simplest typesof projections use population figures together with per capita measures of environ-mental impact, asin the next example.

Example 15.2Projected growth in municipal solid waste. Pleasantville is a city of 1 00,0 00 people that cur-rently collects 8 X lo 7 kg (80 ,000 metric tons) of municipal solid waste (MSW ) each year.The w aste is disposedof in a sanitary landfill the city owns. Bas ed on recent tren ds, the city'spopulation is projected to grow at a rate of3 percentlyear over the next 15 years. Assumingthat per capita waste production re mains co nstant over this period. how m uchadd i t i o r~n l wastewill the city have to collect and dispose of annually 15 years from now?

Solution:

First use Equation (1 5.1) to calculate the future population of the city 15 years from now,based on the 3 percentlyear annual growth rate:

P = 1 0 0 , 0 0 0 ( 1 . 0 3 ) ~ ~ 1 5 5 ,8 0 0 p e op le

The number of additional people is therefore

Added population = 155,800 - 100,000 = 55,800 peopleThe current annual waste generation per capita is

8 X 1 0 7 k gMSWlp er so n =

--800 kglperson-yr

100.000 people

Assum ing this rate remains constan t. the total additional waste generate d 1 5 years fro m nowwould be

Additional waste = (55 ,800 people) X (8 0 0 k g lp er so n -y r )

= 4. 5 X lo 7k g /y r

= 45,000 metric tons


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Estimates of this sort may be used to anticipate the magnitude of future environ-mental problcms. such as the n eed for additional landfill area or alternative method sof waste disposal. Because the futurei s always uncertain, a good analysis alsoemploys a range of assumptions fo r key p arameters that affect the outcomes of inter-est. In this case, both the annual population growth rate and the am ount of waste ge n-erated per person should be treated as uncertain. Similarly. different growth ratesmight apply to d iflerent time periods, yielding anulltiperiod growth model. Problemsat the end of the chapter include exam ples that illustrate these types of projections.

15.4.2 Exponential Growth Model

The annual growth models just described assunle that population increases occur inannua l spurts at the end of each year. a process know n as compou nd ann ual growth.This works well for compound annual interest added to a bank account, but a m orerealistic model for population increases would becontinuol~s. his can be modeledby shortening the t ime period for compound growth from annual to continuous. Theresult is an alternative model of puree.xporler~/icrlrowth:

P = Po e'" (15 .2)

This equation is based on the assumption that at any point in time the rate ofcha nge in population is proportional to the total population at that mom ent. Mathe -matically, this can be writtenas

wh ere the prvportionality constant,r is the growth rate express ed as a fraction of thccurrent population. The solution to this differential equation is Equation115.2).where Po is the original population at timer = 0.

Figure 15.5 compares the exponential growth model of E quation(15.2) with thecoinpound annual growth model of Equation(15.1).As you can see. the two modelsgivc very sirnilar results for low values of growth rates and time periods. But as r a n dtincrease, thcre is greater divergence, with the exponential m odel g rowin g more rapidly.

Example 15.3Exponential versus compound annual growth. In Examp le 15.2 the population of Plcasantvillewas assum cd to growat a compo und annual rateof 3 percentlyear for 15 years. Suppose insteadthat an exponential growth model had been used basedon the same3 pcrcent growth rate . Howwould ihis change the estimate of Plea~antville's opulation15 years from now.?

Solution:

Use Equation (15 .2) withP: , = 100.000 peuple,r = O.Oj/yr, and t = 15 years:

This compares to 155,800 people using the cu~n poun ii nnual growth model. The diffcl-cncein this caseis less than 1 percent. or an additional 1,00 0 people, assuming exp onen tial growth.


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PART 4 Topics i n Environmental Policy Analysis

Exponential growth

Compound annual growth

Figure 15.5 Comparison of two simple growth models.

Increases in the world's population over the past 5 ,000 years resemble an expo-j

nential growth function. ' Over the past 100 years the rate of increase has beenapproximately 1.3 percentlyear. We know. however, that exponential growth ca nnotcontinue indefinitely. In an env ironment with finite space an d finite resources to sup-port the needs of a population, growth eventually is curtailed. The next section pre-sents a mathem atical model that exhibits such characteristics.

15.4.3 Logistic Growth Model

Biologists have found that the population growth of many living organisms tends tofollow an S-shap ed curve like the one sketched in Figure 15.6, a shape known assig-moidal. Initially the population begins to grow exponentially, but over time thegrow th rate gradually slows until it finally reaches zero. At that point the populationstabilizes at the limit labeledP,,,, in Figure 15.6. This limit is known a s thecarry-ing capcrcih of the environment. It defines an equilibrium condition in which thetotal demands of the population f or food, water, waste disposal, and natural resourcesare in balance with the capability of the environment to supply those needs. That bal-ance defines a stable level of population with no further growth. T he result is knownas a logistic growth curve, represented by the sketch in Figure 15.6.

The leveling-off phenom enon in a logistic grow th model represents a resistanceto further growth as the population nears the carrying capacity of the environm ent.Mathematically, this can be represented by adding an "environmental resistance"term to the simple exponential growth mo del of Equation (15 .3):

1 1 Of course, over shorter periods and on smaller geogra phic scales, the population varies more erratically,especially due to catastrophes such as wars or famine.


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CHAPTER 15 Environmcntal Porecastirlg

Population

I Time

Figure 15.6 A logistic g rowth curve showing the characteristic S-shaped profile.Po is theinitial population and t , is the time needed to reach half of the carryingcapacity, P

Now instead o l population growth being proportional only to the current popu-lation, it dcpcnds also on the size of the current population relative to the carryingcapacity. P,,,,,,. When thc current population is small relative to the cax ~y ing apac-ity, the negative (resistance) tcrm in Equation (15.4) is also small, and we have anexponential grouath model as beforc. But asP gets larger and approachesPI,,,,, theenvironmental resistance increases and thc term in brackets approaches zero. Thepopulation growth rate (dP ldt) also then goes to zcro. Between these two extremesthe trend in total population transitions from an upward-bound curve to a horizontalasymptote. producing the S-shaped curve of a logistic growth modcl. Mathemati-

cally, the solution to Equation (15 .4)is

'The growth rate, r; in this equation represents a composite growth rate aver thesigmoidal shape of the logistic curve, so the value ofr differs from that of the sim-ple exponential growth model shown earlier. The two rates can be relatedif wedeline an initial exponential growth rate.r, , associated w ith an initial population.Po ,at t i~ i le = 0 . Then it can be shown that

Similarly, we can show that the constant t,, in Equation (15.5) represents thetime at which the population rcaches hulfthe carrying capacity (that is, the midpointof the growth curve). Thus

a t t = t,,,, P = ! P r,ial (15 )


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By manipulating Equation ( 15.5) we ca n further show thatt,, an d r are related by

A numerical example best illustrates the use of a logistic growth model for pop-ulation projections.

Example 15.4Estimating the world population in 2100. Assume that world population growth can bedescribed by a logistic zrowth model with a carrying capacity of 20 billion people. Estimatethe global population in 2100 based on a current population of 6 billion in 200 0 with an expo-nential growth rate of 1.5 percent. How wo uld you r answer differ if the carrying capacity were15 billion people?

Solution:

The desired population can be found using Equation (15.5) witht = 100 years. But first wemust find the logistic growth rate.K and the midpoint time,t,,,.From Equation (15.6).

From Equation (15.8).

Substituting these results into Equation (15.5) gives

p,,,,, -P = - 2 01 + r - r I + e - ~ , ~ ? ~ . ' i ~ ~ o - 3 ~ . 5 )15.7 billion

This is the projected population 100 years from now, assuming a carrying capacity of 20billion people. The value oft,, = 39.5 years indicates that a population of 10 billion people(half the carrying capacity) will be reached about 4 0 years from now. Repeating the calcula-tion for a global carrying capacity of 15 billion (instead of 20 billion), the estimated popula-tion in 2100 would be 13.4 billion people. By either estimate the world's population wouldmore than double over the next 1 00 years based on these assumptions.

nzizarantr j

t r jI m

rat

beThthe

a P

Estira cra ncperc

Logistic growth models are appealing because they reflect the type of long-termgrowth patterns that have actually been observed for n~ic roorga nisms, nsects, andother life forms.A logistic model further offers a simple way of representing a long-term limit to growth and a gradual stabilization of the population. For human popu- !lations, however, logistic models have been less successfulin predicting carryingcapacity and grow th rates in the past. Rather. the value of carry ing capacity se ems tobe a m oving target that changes ove r time. Th e unique human capability for techno-

2

i O n a

Solu

Becprob

logical innovation has led to developments such as modern medicine and fertilizers


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CHAPTER I5 Environ~nent;~lorecasting

for food production that continue to alter the apparent l imit to global population.Thu s a sinlple lvgistic model affords only a rough approximation based on assu mp-tions about key parameters. Because of the availability of detailed data on actualpopulation character ist ics, other types of models are more co mmon ly used to projectfuture population growth, as discussed next.

15.4.4 Demographic Models

Dernographj is the study of the character ist ics of human populations, including theirsize, age, gender. geograp hic distribu tion, and other statistics. The w ealth of data onpopulation characteristics allows much more detailed models to be developed forpopulation p rojections in lieu of the models discussed s o far.

Population stat ist ics are m ost com monly collected. analyzed, and reported on anational basis by individ ual countries, private org anizations, and international organ-izations like the United Nations. The basic data needed for population projectionsare currcnt rates of births and deaths. The difference between these two rates givesan approximate mcasure of the vverall population growth rate. In addition, a coun-try may gain or lose population via ~nigra tion.f mor e people regularly ent er a coun-try than leave, there is a net incrcase in the ove rall population grow th rate. If the netimmigratio n rate is negative (mor e people leaving than entering): the overall growthrate is reduced. In general, we c an write

Growth rate = (Bir th rate) - (Death rate) + (Immigration rate) ( 15 . 9 )The rate4 in Equ ation (15.9) are typically quantifiedin terms of the annual num-

bers of births, deaths, and immigrants per1,000 people in the overall population.The se overall statistics are referred toas th e crude rates, which means they apply tothe population as a whole. as oppoqed to specific segments of the population s uch asa particular ag e group.

Example 15.5Estimating population growth rate. A country with a total population of50 million peoplehasa crude birth rate of 2 0 births per year per 1.000 people, a crude dea th rate of9 per 1.000, anda net immigration rate of I per 1.000. What is the net population growth rate expressed asapercentage of thc total populatiuri?Solution:

Bccause we are nterested only inrates. the absolute size of the population d oes not enter this

problem. Using Equation(15.9). we have

Growth rate = Birth rate - Death rate + Immigration rate= 20 - 9 + 1 [per 1,000 people/yr)= 12 per 1.000 people/y r

On a percentage basis this annual growth rate is 1.2 percent of the population.


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PART 4 Topics in Environmental PolicyA~la lys i s

Age Structure of a Population Data on overall birth and death rates, plus imnligra-tion statistics, allow us to construct an overall picture of population dyna mics. Evenmore useful than the crude rates for the o~ e r a l l opulation are thea g e - s l ~ e r ~ f i crrtes

by gender. Combining such data with information on theo g e sti.zrc,tirlr of a popula-tion allows much more accurate projections of near-term population trends.Figur e 15.7 shows two exanlples of age-specific population distributions, illus-

trating the number of males and females in the population for various age intervals."For clarity of presentation an age intervalof five years is used in these fig ures, althougha one-year in ten al is com monly used in population statistics. Notice the bulge in theUnited States in the middle years: this represents the baby b oom cohort born after WorldWar 11. As this po pulation ag es; there will be an inc reasing perce ntage of people in thehigher age brackets. and the age distribution profile will flatten. In contrast, the shape

of the world population show s a predominan tly youn ger population. This implies a sub-stantial growth in future population as younger people enter their reproductive years.

Fertility Rates A key factor in population projections is thetotal fei-tilitj rate ofwomen in the population. A composite of the a ge-specific birth rates in a given year,this approximates the average num ber of children born to each wom an during her life-time. Th e higher the total fertility rate, the larger the future population is likely to be.

The r P ~ ~ l r r c e r ~ l e i ~ tertility rate is the average number of live births needed toreplace each female in the current population with one female in the next generation.In modern industrialized countries this number is about 2.1, reflecting the slightly

iLi

higher proportion of male s that are born each year (it's not exactly 50-50, as seen bythe higher number of males in the young er population in Figure 15.7) plus the num-ber of females who die before childbirth. An important factor here is the number ofnewborns who do not survive the first year of life. In poorer societies with littleaccess to the benefits of modern medicine and child care. theinfant morrcrlih rntcJhistorically has been high. Successful efforts to reduce infant mortality thus can sig-nificantly impact the replacement fertility rate and the total number of newborns

1i

who survive and contribute to the future population.Fertility rates that exceed the replacement rate create apop~ilatioiz iloinerltuin

that leads to a sustained increase in population. The highest fertility rates in theworld today are found am ong developing countries, whose populations are grow ingmost rapidly (for example, fertility rates are above 7 in some African nations). Incontrast. fertility rates in many industrialized countries (Western Europe) are cur-rently about l .5. well below the replacement rate. At this level the overall populationwill gradually decline over several decades (barring an increa se in immigration).

Projecting Future Population A simple example illustrates how population growthcan be mod eled using statistical data on age structure and age-specific birth rates anddeath rates. In order to simplify the arithmetic, the following example uses hypo-thetical data for a 10-year period rather than I-year intervals.

* Most textbooks display the number of males and females in each a ge gro up side b y side in the form of apopu la t ion tree centered about the vertical axis. The graphical presentation in Figure 15.7, however, showsmore clearly the differences in male and female pop ulations in each ag e grou p.


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Figure 15.7

I U emales 1Total = 273M

(mid-1999)

U.S. population (millions)

IMales

I 3 emale3

Total = 5.996M(mld- 1999)

0 100 200 300 400

World population (millions)

Ag e distribution of the U.S. and world populations in 1 99 9. The U.S. population has abulge in the m iddle age group, whereas the world popu lation is markedly younger. Thefigure also shows that females outnumber males aher age 30 in the U.S. population a ndaher age 55 in the world population. (Source: Based on USDOC, 19 99b and 1999c)

649


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650 PART 4 Topics in En~ironmental o l icy Analysis

A population projection based on age-specific data . Table 15.1 shows the current age distri-bution for a hypothetical p opulation of 50 0 million people. Th e age-specific birth rates anddeath rates also a re shoa.11 based on data for the prev ious 10 years. Assuming the se rates alsoapply for the next decade, calculate the total population and percentage of people in each age

E group expected 10 years froin now. Assume imm igrationis negligible.

pPC Table 15.1 Populat~on tat~st~cs or Example 15 6t

Births per Deaths perAge Group Current Population 1,000 People 1,000 People

(Years) (Rlillions) (During 10 Years) (During 10 Years)

0-5 100 0 20

10-19 95 200 30

20-29 90 600 30

30-39 80 300 40

4 0 4 0 6 0 100 50

50-59 40 0 100

60-69 2 0 0 300

70-79 1 0 0 500

80-89 4 0 70 0

50-09 1 0 1,000

Total 50 0 million

Solution:-- --2r First calculate the total number of births across all 'Ige g roups o \e r the 1 0-year period. Thi s-

% - ui ll de term ~n e he total number of children In the 0-9 ~I ge roup in the next time period a--.. dec'lde from non The reproductive ages In th ~ s xample are the four groups between I 0 ,~ nd I

= 8 49 bears o ld . For s~m plici ty,he r 'ites a re based on the to t ~ l opu lat~o n f each age grouprather than on the number of females. Thus

200 birthsBirths to people aged 10-1 9= 9 5 X 10"eople X - = 19 X 10' births

1.000 peop le

Similarly.

Births to people aged 20-29 = (9 0 X 10') (l!i:o)= 5 4 X 10 6Births to people aged 30-39 = (8 0 X 10") -- = 32 X 10"

Sum min g over a11 age grou ps, the total numbe r of children born over the next 10 yearswould be 19 i 5 4 + 32 + 6 = 1 I million. This would be the population in the 0-9 age group

I 10 years from now (that is, children who have not yet reached their 10th birthday). Note that 1


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'table 15.2 Summary of present and future popula tion for Example 15.6

Population (in Millions) Percentage of TotalAg e Group

(Years) Current In 10 Years Current In 10 Years

0-9

10-19

20-29

3 0-3 9

4 0 4 9

50-59

60-69

7U-79

SO-89

90-99

Total

the infant mortality rate (for age 0 to1 year) is not given separately in this example but ratheris accounted for in the overall death rate for the0- to 9-year-old population.

The remainder of the future population tree is quantified using the age-specific death ratesgiven in Table 15.1. For instance, Table 15.1 shows that the I0 0 million children currently in the0-9 age group will experience an average d eath rate of 20 per 1,0 00 (2.0 percent). This meansthat 98 percent of the 0-9 cohort will su ni ve and subsequently enter the 10-19 age group. Thus

Futur e population Current populationaged ) = ( aged 0-9 X (Fraction surviving)

Similar calculations apply to all other age groups. Notice that for the oldest group (90-99years) the 10-year death rate in this example is 100 percent. meaning that no on ein this agegroup survives past the 99th year.

Table 15.2 summarizes the results of these calculations. The table shows how each agegroup in the current population moves into the next age group 10 years from now. Also shownis the percentage of the total population in each age group now and in the future.

The result is a population of 5 78 million people 10 years from noM1. This represents a 16 per-cent increase over the current population. The percentage distributions also show an aging of thepopulation. with nearly 10 percent ovcr age 6 0 in the future compared to 7 percent cu rrently.

The preceding exam ple used a 10-year age interval to sirnplify the comp utations.Also, population migration was assumed to be negligible.A more refined analysis.done on a computer, would use one-year age categories and time steps, along withgender-specific and age-specific population figures, birth rates, and death rates. Exam-ples of such projections app ear in Figure 15.8(a),which shows the U.S. population pro-jected to the year 3050, as estimated by theU.S. Census Bureau for three scenarios(labeled low, middle, and high series). Figure 15.8(b ) shows how key parameters are


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assumed to change over time in the middle series Census Bureau projection. Differ-ent assumptions produced the higher and lower population projections.

Figure 15.8(c) shows the 2050 population distribution resulting from the middleseries projections. Note that the profile is much more uniform than the 1999 profile inFigure 15.7(a). These projections imply a higher percentage of older people in the p op-ulation than today: In the oldest groups the population ove r80 will have roughly tripled.Thes e results have important implications for public policy and the economy. For exam-ple, demand is likely to increase for health care services (as opposed to schools) and asmaller percentage of the population will be in the workforce. At the same time more

- - - - -1,200

- Low series- - - igh series /

//

//

/

Actual Forecast /0

Year

(a)

Year

(b )

Figure 15.8 U.S. population projections to 2 0 5 0 , showing [a] the low, middle, and highestimates of the U.S. Census Bureau, (b ) key assumptions behind the mid dle(best estimate) projec tion, a nd [c) the best-estimate age d istribu tion in 2 0 5 0 .(Source: Based on USDOC, 19 99 b and 199 9c)


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.niddle

-, )lilt in:? 2 pop-:sipled.

, ;Yam-. and a

..: {iiore

0 5 10 15 20U.S. p o p ~ ~ la t i o nmillions)

Figure 15.8 (continued) (c)

senior citizens will be collecting S ocial Security benefits. The im portance of popu lationprojections thus extends to a broad range of issues besides environmental impact$.

The procedure used in Example15.6 to calculate the total future population

based on age-specific birthrates and death rates can be expressed in general mathe-matical terms. A more detailed mathematical model also would divide the popula-tion into males and females and include separate data on the age-specific popula-tions, fertility rates, and d eath rates by g ender.

The writing of such equations is a bit tedious but essential for programmingadvanced models.A taste of this appears as an exercise for students in the p roblemsat the end of this chapter.

Limitations of Demographic Models Even when using detailed population data in

sophisticated demographic models, we m ust makeassumnprions about how far intothe future the current birth rates and death rates will prevail. In some cases mathe-matical models (including logistic models) have been proposed to estimate futurechanges in these parameters. But for the most part, assumptions about future fertil-ity rates, death rates. and imm igration patterns remain a matter of judgmen t becausethe future remains uncertain. Assumptions about demographic parameters are oftenlinked to assumptions about future economic development and standards of living.For instance. fertility rates and infant mortality rates are substantially lower amongwealthier populations than among poorer regions of the world.


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PART 4 Topics i n En v i ro n men tal Po l icy A n a l y s i~

Demographic models are thus limited in their ability tojb~*ecru t ong-termchang es in population. On the other hand. they can be very useful for analyzings c e -izarios of future population trends under different conditions. The detailed population

data of a demographic model also allow a richer set of "what if" questions to beasked, such as the effects of future changes in fertility rates and infant mortality rates.Such scenarios can reveal how policy actions might influence future populationtrends and hence environmental impacts. Dem ograph ic models also provide informa-tion on the size and age structure of the available labor force of the future. which pro-vides an important link to economic projections. as we shall discuss shortly.

At the same time! demographic models are not always necessary or suitable forall types of environmental projections. Rather, in many situations the results ofdemographic projections can be used to estimate the parameter values needed for

simpler models. Sucha case is illustrated in the next exam ple.

Example 15.7Estimating growth rates from population data . A demographic analysis projects the total pop-ulation of a region to grow from500 inillion to 7 7 2 million over the next30 years. If this pop -ulation increase were to be approximated by a simple exponential growth model. what is theimplied annual gro ath rate'?

Solution:

The exponential growth modelwas given earlier by Equation (15.2 ). In this case both the ini-tial and final populations are known. and we are solving for the growth rate.r; over a periodof 30 years. Thus

In most environmental forecast5 or scenarios. the size of the future population isonly one determinant of future env~ron menta lmpacts. A second. closely related factoris the standard of living or affluence of a population. We look next at how the effects ofeconomic development can be reflected in an analysis of environmental futures.

15.5 ECONOMIC GROWTH MODELS

Suppose you wanted to estimate the total mass of pollutant emissions from automo-biles 25 years from now. On e key factor in that analysis would be the num ber of carsin the future. That could depend on the future size of the popillation (the more peo-ple, the more cars), but it would also dep end on how affordable a car is for the aver-age citizen. In general, the mo re affluent the society. the more vehicles per cap ita as


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PART 4 Topics in Environmental P olicy Analysis

CO2 reduct~on:-1 = Stabilize at 1990 evels2 = 20% reduction below 1990

- 3 = 50% reduction below 1990-

Year

Fiaure 15.13 Macroeconomic model ~redic t io ns fU.S. GDP loss from a tax on ca rbonemissions to control g loba l warmin g. These average results across a large setof models predict that GDP losses will increase as C 0 2 emissions are reduced .[Source: IPCC, 1 996)

environmental analysis, considerable care and judgment are required to exercise andinterpret the results of such m odels.

15.6 TECHNOLOGICAL CHANGE

We have already touched on the importance of technological change to economicgrowth. Here we look at some of the more direct ways that technology change canaffect environmental forecasts or scenarios. Consider again, for example, the prob-lem of estimating air pollutant emissions from automobiles25 years from now. Oreven 10 years from now. Not only will the number of cars on the road have changed(due to changes in population and standards of living), bul vehicle designs also willhave chang ed. Ten years from now a portion of theU.S. auto fleet is expected to beelectric cars powered by batteries o r fuel cells, which emit no air pollution directly.The design of conventional gasoline-powered vehicles also will have improved to

emit fewer air pollutants than today's cars. Average energy consumption als o mighlchange significantly. Vehicles of the future might use more energy than today (froma continuing trend to large sports utility vehicles), or they might require less energy(from a transition to sm aller, fuel-efficient vehicles).

These are examples of technological changes that can influence an environ-mental forecast or scenario. In this section we examine some of the ways that tech-nological chang e can be considered analytically. Th e emphasis will be on relativelysimple approaches that can be used easily in environmental analysis.


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CHAP T E R 15 Environmental Forecasting 667

1 5.6.1 Types of Technology Change

Several types of technology c hanges can be im portant for environmental analysis:

Irnprnvernerzts to a current tecl~nologj esign. Incremental changes can reducethe environmental impacts of a current technology, typically via im provcmcntsin energy efficiency or a reduction in pollutant emission rates. An examplewould be an automobile with an improved catalyst or engine design emittingfewer hydrocarbons and nitrogen oxides per m ile of travel.

Substitz~tinn f an alternative technology. Replacing a current tcchnology witha different design often can provide the same basic se rvice with reduced envi-ronmental emissions-for instance. replacing a gasoline-powered car with anelectric vehicle, or an existing coal-fired pow er plant with an advanced pas-powered or wind-powered plant. However. the direct and indirect em ~ronmcn-tal impacts of the alternative technology mcs t be carefully evaluated relative tothe current technology design.

New classes o f teclznologq. This extension of the previous case encompassestechnologies that offer a whole new way of doin g things. For example, [heautomobile prov~ded new mode of pcrsonal transportation as an alternativeto bicycles or horsc-drawn buggies. Airplanes were a later example of an

cntirely new mode of transportation technology. The future environmentalimpacts of new classes of technology are inherently more difficult to cvaluatethan those of the technologies we know. Moreover, some indlrect environmen-tal impacts may be totally unforcscen (sucha5 the extensive urban sprawl pro-moted by thc growth of autom obiles).

Clzange irl tecl ~no log y tiliiatinn. Engineers are primarily concerned with thedesign of technology, but the deployrrlerlt an d utilization of technology deter-mine its aggregate environ~~lentalmpact. Environmental forecasts o r scenariosmust therefore con s~ de r ow technology utilization might change in the future.

Technological innovation has changed the face of personal transportation in the 20th century. Imag ine how things mightlook 5 0 or 100 years from now.


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For instance, will the future use of an automobile (average distance driven peryear) be the sam e or greater than today? O r might advances in air transporta-tion or a growth in electronic comme rce and telecommuting reduce the aver-age usage of automobiles in the future?

The answers to such questions, and the importance of technological change.depend on the tim e frame of interest and the scope or objectives of the analysis. Thefurther out in time we go, the m ore important these issues a re likely to become. N extwe discuss a few simple ways of incorporating technology ch ange into environmen-tal analysis.

15.6.2 Scenarios of Alternative Techn ologies

Perhaps the m ost direct way of modeling technological change is to postulate a tran-sition from current technology to some improved or alternative technology. Forinstance, to characterize future emissions from automobiles, we could ask what m ighthappen if x percent of future automobilesy years from now were battery-poweredelectric vehicles. What impact would this have on total air pollutant emissions andurban smog? A scenario of this type does not try to forecast the actual number ofelectric vehicles in the future. Rather. it asks a hypothetical question to assess thepotential air quality benefits of an alternative technology.

The m athematical model in this ca se would quantitatively characterize the alter-native technology. Key attributes of a technology for environmental analysis mightinclude the types and quantities of air emissions, water pollutants, and solid wastesthat are emitted: the fuel or energy consumption required for operation; and the nat-ural resource requirements and materials needed for construction and operation of thetechnology. The environmental analysis also should capture any important indirectimpacts of concern, such as em issions from the manufacturing or disposal of a newtechnology. Chapter 7 discussed this type of life cycle approach to environmentalanalysis, which applies to future technologies as well as to present-day systems.

Example 15.1 1Future C 0 2 reductions from a ne w technology. Coal-burning power plants in many develop-ing countries have an average efficiency of about30 percent and emit approximately 1.1 kgof carbon dioxide (CO z) for each kW-hr of electricity generated. C 0 2 s a greenhouse gas thatcontributes to global warming. The amount ofC 0 2 released is directly proportional to theamoun t of coal burned. What if all future coal plants in these countries utilized advanced coalgasification combined cycle technology with an efficiency of50 percent? How much w ouldthe CO, emission rate be reduced compared to plants uaing current technology?

Solution:

Recall that efficiency (p ) is defined as the useful energy output of a process (in this case,electricity from the power plan t) divided by the energy input ( in this case, the fuel energy incoal) . Thus

Electrical energy outputEfficiency (p) =

---oal energy input


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Perra -er-

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CHAP T E R 15 Environmental Foreca\ring

The higher efticiencq of the advanced power plant technology meansthat less coalenergy input is needed to achievea g i ~ e nlectrical output. Thus

Because C 0 2emissions are proportionalto the amountof coal burned,wc also havt:

Thus th e advanced plant uould emit10 percent lessC O , than the current plant design .It s C 0 2emission rate uould be

Scenarios like this can provide a simple way of estimating the potential envi-ronmental benefits of an advancedtechnology. IT the results loo k interesting. a moresophisticated analysis would be needed to assess the feasibility of actually achieving4uch a result.

15.6.3 Rates of Technology Adoption

An important question in environmental forecasts is how long it takes fora new orimproved technology to achieve widespread use. Chapter6, for exa~nple. iscussedthe design of m ore energy-efficient refrigerators that eliminate theCFCs (chloroflu-orocarhonsl responsible for stratospheric ozone depletion. Such refrigerators firstcam e on the markct in the mid-1990s. B ut how long will it take until all U.S. house-holds have these improved refrigerators? The answer is important for predictingat~rlosphericCFC levels, as well as energy-related environm ental impacts.

'Phe speed with which a new technology is adopted depends on many factors.Three of the most im portant are its price. its useful lifetime, and the number of com -peting options. High prices and many competing options inhibit the adoption of anew technolog y. So does a long useful lifelime because existing technologies a re notquickly replaced.A number of methods are used to model the rate of adoption of newtcchnology-some complex , others relatively simple. Threeof these methods are

highlighted here.

Specified Rate of Change The most direct method of introducinga new technologyis to ~pecifyts rate of adoption or diffusion into the economy. In general. that ratewill depend on the growth of new markets for the technology, plus the opportunityto replace cxisting technolog ies at the end of their useful lives. The expected usefullifetime is thus an important parameter controlling the rate of adoption of a newtechnology. Table 15.6 shows the typical life of several technologies relevant to envi-ronmental projections.



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Table 15.6 Typical technology lifetimes.

Technology

Light bulbsPersonal computersAutomobilesRefrigerators

Petrochemical plants

Power plants

Buildings

Typical Lifetime (year sy

1-23-8

10-1515-20

2 0 4 0

30-5050-100

" Some internal components or subsystems may be rep laced more frequently.

For the case of the household refrigerator, the expected useful life is about 18years. If we assume a constant rate of replacement, this means that 1118th(5.6 per-cent) of all current refrigerators must be replaced each year for the next18 years.This defines the maximum rate of introduction for the improved refrigerator designdiscuss ed earlier-at least in the replacement market. Th e grow thof new marketsoffers additional oppo rtunities for adopting the improved techn ology ; the size of thismarket depends mainly on population and econo mic growth.

Example 15.12Adoption of CFC-free refrigerators. Assume that all 120 million household refrigerators inthe United State s in 1995 are replaced with improved CFC -free refrigerators at the end of an18-year lifetime. Assum e further that population and econo mic growth increase the dem andfor new refrigerators by 2.0 million units per year over the next 10 years, and that all of theseunits are CFC-free. Estimate the percentage of all household refrigerators that are CFC -freein 2005.

Solution:

Since we are not given the age distribution of existing refrigerators. assume that each year1118th of all existing refrigerators die an d are replaced with C FC-free m odels. Thus

1Replacement units/yr = - 120 M ) = 6.67 million units/yr

18

In addition, there is new demand of 2.0 million unitslyear from population and economic

growth. ThusTotal new units/yr = Replacement units/yr + New demand/yr

= 6.67 M + 2.0 M = 8.67 M units/yrSo after 10 years (in 2005) the total number of CFC -free units will be 8.67X 10 = 86.7 M .The total number of refrigerators altogether will be

Total units in 2005 = 12 0M (as of 1995) + 20 M (new growth) = 14 0 M


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The fraction that are CFC-free in 2005 will be

bout 18I 5.6 per-18 years..rr design

markets7 5 of this

:-rators in2nd of an

- 2 demand:I1 of theseCFC-free

each year

86.7 M005 fraction of -

) - 140 M= 0.62 or 62%

CFC-free unilsThe fraction of CFC-free units will continueto grou for another eight years until it

reaches 100 percent.

Specified Market Share In Example 15.12 the only new refrigerator technologyavailable after 1995 was the CF C-free design. In this case environmental laws actu-ally prohibit the continued use of CFCs in new units. In general, though,a new or

improved technology must compete with alternative options in the marketplace. Inthat case the adoption rate of a new technology depends not only on the size of themarket, but also on its market share.

One way to model the diffusion of a new technology is tos p e r i ' the marketshare at different points in time. For instance, one couldassume that 10 percent ofall new cars sold in 2005 will be electric vehicles.A more detailed specificationmight take the shape of a logistic curve like the one s illustrated in Figure 15.14. Thistype of S-shaped curve is frequently used to model the gradual diffusion of a newtechnology into the marketplace. The mathematical form of a logistic model was

presented earlier in Section 15.4 .3, where it was used to approxim ate populationgrowth. Here we use it to represent the grow th in market share of a new technology.All we have to do is to redefine the variableP as percentage market share rather thanpopulation. So if we defineP(r) as the percentage share of the m arket at timet, andP,,, as the maximunl market share (up to 100 percent). then

Slow growthto 100%

Rapid growthto 70%

Moderate growthto 40%

I * Time0

Figure 15.14 Logistic models of growth in technology market share for three scenariosinvolving different growth rates and final market share.


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