# Population Forecasting For Water Supply And its Various Methods5 min read

## Population Forecasting

Population forecasting in environmental engineering is very important to know the growth rate and estimate the future population of a particular area.

The design population is estimated because of all the factors that control future growth and development. project areas in industrial, commercial, educational, social, and administrative sectors.

## Factor affecting population growth

1. Birth
2. Deaths
3. Migrations
• Besides these, some other factors like wars, nature havoc, and disasters may also bring about a sharp reduction in the population.

## Population Forecasting Methods

1. Arithmetical increase method
2. Geometrical increase method or Uniform increase method
3. Incremental increase method or Method of varying increment
4. Decreasing rate method
5. Simple graphical method
6. Comparative graphical method
7. Master plan method
8. Apportionment method or Ratio Method
9. Logistic curve method

### 1. Arithmetical increase method:

This method is based on the assumption that the population is increasing at a constant rate. The rate of change of population remains constant over time.

Pn = [Po + n x̄ ]

where, Pn = forecasted population after n decades from the present
Po = population at present (i.e. last known census)
n = number of decades between present and future
x̄ – average population increase in the known decades

### 2. Geometrical increase method or Uniform increase method

This method is based on the assumption that the percentage growth in the population remains constant from decade to decade. In this method the average percentage of growth of the last few decades is determined; Population is predicated on the basis that the percentage growth per decade will be the same.

In the arithmetic method, no compounding is done but, in the geometric method, compounding is done every decade.

$\huge Pn=Po(1+\frac{r}{100})n$

where Po = initial population
Pn = future population after n decades
r = assumed growth rate (%)

Computation of assumed growth rate (r) from the last known population data.

$\huge r\ =\ ^t\sqrt{\frac{P2}{P1}}-1$

where P1 = initial known population

P2 = final known population

t = number of decades between P1 and P2

Note: Arithmetic mean,

Geometric mean,

where r1, r2, r3 ….rt are % growth rates of the several known decades of past.

The arithmetic mean is slightly higher than the geometric mean.

Also, r can be calculated as

$\huge r\ =\frac{increase\ in\ population}{original\ population}\cdot100$

Note: In the geometric method, computing is done every decade

### 3. Incremental increase method or Method of varying increment

This method is an improvement over the above two methods. Average growth in population is determined by the arithmetic method and the average of net incremental growth is added once for each future decade.

The incremental increase method is the best method for population forecasting.

Pn = Po + nx¯ + n(n+1)/2*ȳ

where Pn = population after n decades front pre^nt
Po = present population
x̄  = average increase of population of known decades.
ȳ = average incremental increase of the known decades.

• Population obtained by

Arithmetic increase method < Incremental increase method < Geometrical increment method.

• The incremental method gives quite satisfactory results.
• For new younger cities expanding at faster rates —> Geometric increment method is applied.
• For old cities —> Arithmetic method is better.
• The incremental method is applied for any type of city.

### 4. Decreasing rate method

It has been observed that all life develops in a confined space. If the full growth of a very old city is plotted, it will be seen that the curve has an S-shape, which indicates that the initial growth is at an increasing rate, the later growth is at a decreasing rate which indicates That the saturation limit has been reached.

In this method, the average decrease in the percentage increases is worked out and is then subtracted from the latest percentage increase for each successive decade.

This method is applicable only in cases where the rate of growth shows a downward manner.

### 5. Simple graphical method

In this method, a graph is plotted from the available data, between time and population. The curve is then smoothly extended up to the desired year.

### 6. Comparative graphical method

In this method, cities with similar conditions and characteristics to the city whose future population is to be estimated are first selected. It is then assumed that the city in question will develop as selected similar cities have developed in the past. This method has a logical background, and fairly accurate and reliable results can be obtained if development data for similar cities are available.

### 7. Master plan method

It is very easy to access precisely the design population because the master plan will give us when and where the given number of houses, industries, and commercial establishments would be developed.

A master plan is prepared for the development of cities for 25-30 years. The population density is also determined for different zones of the cities to be developed. Now that the population of a particular area is fixed, it is very easy to design water supply plans for particular areas. The future development of the waterworks is also designed based on the master plan.

### 8. Apportionment method or Ratio Method

The local population and the country population for the last four or five decades are obtained from the census method.

### 9. Logistic curve method

The equation of the logistic curve is

$\huge P=\frac{Ps}{1+m\log^{-1}e(nt)}$

where P = population at any time t from the origin A
Ps = saturated population
m = (Ps* Po)/Po (a constant)
n = kps (another constant)
Po = population at the start point of the curve.
k = constant

• If only three pairs of characteristic values Po, P1, P2 at time t = t0 = 0, t1and t2 = 2t1 extending over the useful range of the census population are chosen, then

$\huge Ps=\frac{2PoP1P2-P1^2(Po+P2)}{PoP2+P1^2}$

m = (Ps* Po)/Po

$\huge n=\frac{1}{t1}\log e[\frac{Po(Ps-P1)}{P1(Ps-Po)}]$

Note:
(i) Methods 1 to 5 are based on the assumption that factors and conditions which were responsible for population increase in the past and continue even in the future also, with the intensity. This is a vague assumption.

(ii) Methods 6 to 9 are advanced and time-consuming methods that give fair results.

(iii) None of these methods is exact, and they are all based on the laws of probability, and thus, only for possible future approximate estimation population can be made.