Population

forecasting

Relation of Quantity of Water

and Population

Water consumption is influenced by the following

factors

Climate

Economic level

Population density

Degree of industrialization

Cost

Pressure

Quality of the supply

Analysis of the future demand begins by

considering the present use

Consumption is classified according to;

Classes of users (domestic, commercial,

industrial, public, etc)

Area of the city

Economic level of the users

Season of the year

On per capita consumption, applying the

procedure of dividing total use by the total

population should be applied with care, since

Entire population may not be served by the municipal

system

There may be large industrial users which will not

change with population

Characteristics and size of the population may be

changing

Population estimation

Since population is always a relevant

factor in estimating future use, it is

necessary to predict what the future

population will be

Arithmetic method

The assumption is that the rate of growth is

constant 𝑑𝑃

𝑑𝑡= 𝐾

where 𝑑𝑃

𝑑𝑡 is the rate of change of population and

K is a constant

The population in the future is estimated as; 𝑃𝑡 = 𝑃𝑜 + 𝐾𝑡

where 𝑃𝑡 is the population at some time in the

future, 𝑃𝑜 is the present population and t is the

period of the projection

Geometric or Uniform Percentage Method

The hypothesis of geometric or uniform

percentage growth assumes a rate of

increase which is proportional to population

𝑑𝑃

𝑑𝑡= 𝐾′𝑃

Geometric or Uniform Percentage Method

Thus, the population at some time is

estimated as; 𝑙𝑛𝑃 = 𝑙𝑛𝑃𝑜 + 𝐾′∆𝑡

𝑤ℎ𝑒𝑟𝑒 𝐾′ =ln (𝑃2) − ln (𝑃1)

𝑡2 − 𝑡1

Curvilinear Method This technique involves the graphical projection of the

past population growth curve, continuing whatever

trends the historical data indicate

Includes comparison of the projected growth to the

recorded growth of other cities of larger size

Geographical proximity, likeness of economic base,

access to similar transportation systems, and other

factors should be considered for comparison

Fig. Curvilinear method of projecting population growth

Logistic Method

The logistic curve used in modeling

population growth has an S shape –

combining a geometric rate of growth at low

population with a declining growth rate as the

city approaches some limiting population.

In the short term, a logistic projection can be

based on

𝑃 =𝑃𝑠𝑎𝑡

1 + 𝑒𝑎+𝑏∆𝑡

where 𝑃𝑠𝑎𝑡 is the saturation population of the

community and 𝑎 𝑎𝑛𝑑 𝑏 may be determined

from three successive census population

𝑃𝑠𝑎𝑡 =2𝑃𝑜𝑃1𝑃2 − 𝑃1

2(𝑃𝑜 + 𝑃2)

𝑃𝑜𝑃2 − 𝑃12

𝑎 = 𝑙𝑛𝑃𝑠𝑎𝑡 − 𝑃2

𝑃2

𝑏 =1

𝑛𝑙𝑛

𝑃𝑜(𝑃𝑠𝑎𝑡 − 𝑃1)

𝑃1(𝑃𝑠𝑎𝑡 − 𝑃𝑜)

where n is the time interval between succeeding censuses

Declining Growth Method

Assumes that the city has some limiting

saturation population, and that its rate of

growth is a function of its population deficit; 𝑑𝑃

𝑑𝑡= 𝐾"(𝑃𝑠𝑎𝑡 − 𝑃)

𝐾" =1

𝑛𝑙𝑛

𝑃𝑠𝑎𝑡 − 𝑃1

𝑃𝑠𝑎𝑡 − 𝑃𝑜

where 𝑃 𝑎𝑛𝑑 𝑃𝑜 re populations recorded in n

years apart

Future population can be estimated as;

𝑃 = 𝑃𝑜 + (𝑃𝑠𝑎𝑡 − 𝑃𝑜)(1 − 𝑒𝐾"∆𝑡)

Ratio Method

Relies on the population projections made by

professional demographers

Based on the assumption that the ratio of the

population of the city being studied to that of

the larger group will continue to change in the

future in the same manner that has occurred

in the past

The ratio is calculated for a series of

censuses, the trend line is projected into the

future, and the projected ratio is multiplied by

the forecast regional population to obtain the

city’s population in the year of interest

Use of good judgement in population

estimation is important

If the estimate is too low, the system will be

inadequate and redesign, reconstruction and

refinancing will be necessary

Overestimation will result in excess capacity

which must be financed by a smaller

population at a higher unit cost

Selection of an appropriate technique requires

testing all methods against recorded growth and

eliminate those which are not applicable

Growth of a community

with limited land area for future expansion may be

modeled by the declining growth or logistic technique

with large resources of land, power, and water and

good transportation may be predicted by the

geometric or uniform percentage growth

Example:

Given the population data as follows;

Population in 2000 = 76.5million

2010 = 92.3milliom

Estimate the population in 2020, 2030, 2040

using the arithmetic, geometric, logistic and

declining growth methods