Population forecasting is defined as the method of determining the expected population for a particular design period of a water supply system with the help of the study and analysis of future events and available records.

The population is an important parameter that is determined for the design of the water system of a particular area. Water supply systems are designed for a population expected for a certain design period instead of taking into consideration the present population of the area.

There are several mathematical methods that can be used to determine the population for a design period.

## Population Forecasting Methods

The population forecasting methods require the values of present and past population records to undergo the calculation. The local census records of a particular area provide the value of present and past populations.

The two categories of methods used for population forecasting are:

- Short Term Methods
- Long Term Methods

The short term methods include:

- Arithmetic Progression
- Geometric Progression
- Iller Bankasi Method
- Decreasing Rate of Growth method
- Graphical Extension Method

The long term methods include:

- Comparative Method
- Ratio and Correlation Method
- Component Method
- Logistic Method

## Short Term Methods for Population Forecasting

The different short term methods for forecasting population are:

### 1.Arithmetic Increase Method

This method is applied to areas where it is found that the rate of increase of population with time is constant i.e. dP/dt = Constant;

If, Pn = Population of an area after any time ‘t’ or Population after ‘n’ decades, Po = Last known Population of that area; n = number of decades ( 10 years = 1 decade); X’ = average increase in population.

**Pn = Po + nX**‘ (Eq.1)

### 2. Geometric Progression Method

The method is used for the condition dP/dt = Kg. P. Where, Kg is called as the geometric constant, P is the population.

**Kg = [(LnP” -LnP’)/(t” – t’)]** (Eq.2)

Then the future population Pn is given by,

**Ln Pn = Ln Po + K’ _{g}(tn – to);** (Eq.3)

K’g is Average of Kg which is equal to below relation.

### 3. Iller Bankasi Method or Geometric Increase Method

This method is employed in a area where the population is rapidly increasing. Here the future population Pn is given by,

Here, r = Assumed growth rate in percentage, n is in decades and Po is the last known population of the city.

The value of ‘r’ is calculated differently based on the data available.

**1.If Initial Population P’ and Final Population P” are given, then**

2. **Arithmetic Increase method**

r = ( r1 + r2 + …. rn)/n Eq.7

**3. Geometric Method**

### 4. Decreasing Rate of Growth Method

The method is applied to a city that owns a limiting saturation population. In this type, the rate of growth is a function of its population deficit. That means,

** dP/dt = Kd(S-P)** Eq.9

Where, P is the population, S is the saturation population and Kd is the constant.

Then, Kd and Kd average is given by,

Then, future population is given by,

### 5. Graphical Extension Method

In this method, the population of the past few decades is plotted in the graph correctly following a proper scale. The obtained population curve is extended to obtain the future population. The extension of the curve is performed by a person who has proper experience and judgement.

## Long Term Methods for Population Forecasting

The long term methods for forecasting population are:

### 1. Comparative Method

In this method, population curve of different cities with similar population growth is studied. The different factors that are taken into consideration are:

- The likeness of Economic Base
- Proximity of geography
- Access to similar transportation systems

### 2. Ratio and Correlation Method

The method works based on the concept that the ratio of the population of the city studied compared to a larger group continues to change in the future similar to the manner that has occurred in past years. The concept is explained in the figure below.

### 3. Component Method

The population change is observed due to birth, death and migration. So estimation of these factors helps to understand the increase or decrease of the population. During calculation, migration is estimated first followed by the estimation of births and deaths.

### 4. Logistic Method

This method is also called as mathematical curve fitting. The method follows an assumption that the rate of growth at low population with a rate that is declining as the given city approach some value of limiting population.

In order to proceed with this method, last three census is taken. If so the population is calculated by the formula,

S is the saturation population and m and c are constants

The Saturation population is calculated by the formula,

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