Population forecasting is a method to predict or forecast the future population of an area. Design of water supply and sanitation scheme is based on the projected population of a particular city, estimated for the design period. Any underestimated value will make system inadequate for the purpose intended; similarly overestimated value will make it costly. Change in the population of the city over the years occurs and the system should be designed taking into account of the population at the end of the design period. Factors affecting changes in population are given below.
- Increase due to births
- Decrease due to deaths
- Increase/ decrease due to migration
- Increase due to annexation
The present and past population record for the city can be obtained from the census population records. After collecting these population figures, the population at the end of design period is predicted using various methods as suitable for that city considering the growth pattern followed by the city. The various population forecasting methods are mentioned below.
1) Arithmetical Increase Method
The arithmetical Increase Method is mainly adopted for old and developed towns, where the rate of population growth is nearly constant. Therefore, it is assumed that the rate of growth of the population is constant. It is similar to simple interest calculations. The population predicted by this method is the lowest of all. If it is used for small, average or comparatively new cities, it will give low result than actual value. In this method the average increase in population per decade is calculated from the past census reports. This increase is added to the present population to find out the population of the next decade.
Hence,
i.e. rate of change of population with respect to time is constant.
Pn = Po + n x̄
where,
Po - last known population
Pn - population (predicted) after 'n' number of decades
n - number of decades between Po and Pn
x̄ - the rate of population growth
Example Question
Predict the population for the year 2021, 2031 and 2041 from the following population data.
|
Year |
1961 |
1971 |
1981 |
1991 |
2001 |
2011 |
|
Population |
8,58,545 |
10,15,672 |
12,01,553 |
16,91,538, |
20,77,820, |
25,85,862 |
Solution
|
Year |
Population |
Increment |
|
1961 |
858545 |
- |
|
1971 |
1015672 |
157127 |
|
1981 |
1201553 |
185881 |
|
1991 |
1691538 |
489985 |
|
2001 |
2077820 |
386282 |
|
2011 |
2585862 |
508042 |
|
| Average increment, x̄ | 345463 |
Population after nth decade is Pn = Po + n x̄
Population in year 2021 is, P2021 = 2585862 + 345463 x 1
= 2931325
Similarly, P2031 = 2585862 + 345463 x 2
= 3276788
P2041 = 2585862 + 345463 x 3
= 3622251
2) Geometrical Increase Method or Geometrical Progression Method
This method is adopted for young and developing towns, where the rate of growth of population is proportional to the population at present (i.e., dP/dt ∝ P). Therefore, it is assumed that the percentage increase in population is constant. It is similar to compound interest calculations. The population predicted by this method is the highest of all. Geometric mean increase is used to find out the future increment in population. Since this method gives higher values and hence should be applied for a new industrial town at the beginning of development for only few decades.
The population at the end of nth decade ‘Pn’ can be estimated as
where,
Po - last known population
Pn - population (predicted) after 'n' number of decades
n - number of decades between Po and Pn
r - growth rate in percentage
r could be found as
a) Arithmetic Mean Method
b) Geometric Mean Method
Note: According to Indian standards 'r' should be calculates using geometric mean method.
Example Question
Considering data given in above example predict the population for the year 2021, 2031 and 2041 using geometrical progression method. Solution
Solution
|
Year |
Population |
Increment |
Geometrical increase Rate of growth |
|
1961 |
858545 |
- |
|
|
1971 |
1015672 |
157127 |
(157127/858545) = 0.18 |
|
1981 |
1201553 |
185881 |
(185881/1015672) = 0.18 |
|
1991 |
1691538 |
489985 |
(489985/1201553) = 0.40 |
|
2001 |
2077820 |
386282 |
(386282/1691538) = 0.23 |
|
2011 |
2585862 |
508042 |
(508042/2077820) = 0.24 |
By Geometric Mean Method
Population in year 2021 is, P2021 = 2585862 x (1+ 0.235)1
= 3193540
Similarly, for year 2031 and 2041 can be calculated by,
P2031 = 2585862 x (1+ 0.235)2
= 3944021
P2041 = 2585862 x (1+ 0.235)3
= 4870866
3) Incremental Increase Method
This method is adopted for average sized towns under normal conditions, where the rate of population growth is not constant i.e., either increasing or decreasing. It is a combination of the arithmetic increase method and geometrical increase method. Population predicted by this method lies between the arithmetical increase method and the geometrical increase method. While adopting this method the increase in increment is considered for calculating future population. The incremental increase is determined for each decade from the past population and the average value is added to the present population along with the average rate of increase.
Hence, population after nth decade is
where,
Po - last known population
Pn - population (predicted) after 'n' number of decades
n - number of decades between Po and Pn
x̄ - mean or average of increase in population
ȳ - algebraic mean of incremental increase (an increase of increase) of population
Example Question
Considering data given in the above example, predict the population for the year 2021, 2031 2041 using incremental increase method.
|
Year |
Population |
Increase (X) |
Incremental Increase (Y) |
|
1961 |
858545 |
- |
- |
|
1971 |
1015672 |
157127 |
- |
|
1981 |
1201553 |
185881 |
+28754 |
|
1991 |
1691538 |
489985 |
+304104 |
|
2001 |
2077820 |
386282 |
-103703 |
|
2011 |
2585862 |
508042 |
+121760 |
|
|
Total |
1727317 |
350915 |
|
|
Average |
345463 |
87729 |
Population in year 2021 is P2021 = 2585862 + (345463 x 1) + {(1 (1+1))/2} x 87729
= 3019054
For year 2031 P2031 = 2585862 + (345463 x 2) + {((2 (2+1)/2)}x 87729
= 3539975
P2041 = 2585862 + (345463 x 3) + {((3 (3+1)/2)}x 87729
= 4148625
4) Decreasing Rate of Growth Method
Since the rate of increase in population goes on reducing as the cities reach towards saturation, this method is suitable. In this method, the average decrease in the percentage increase is worked out and is then subtracted from the latest percentage increase for each successive decade. This method is applicable only when the rate of growth shows a downward trend.
Decreasing Rate of Growth Method Formula
where,
Pn - population at required decade
P(n-1) - population at previous decade (predicted or available)
r (n-1) - growth rate at previous decade
S - average decrease in growth rate
Due to the very nature of the formula, which requires population data at the previous decade i.e., P(n-1), this method requires the calculation of population at each successive decade (from the last known decade) instead of directly calculating population at the required decade.
Example Question
Considering data given in the above example, predict the population for the year 2021, 2031 2041 using incremental increase method.
|
Year |
Population |
Increase in population |
Growth rate
(r) (%) |
Decrease in
Growth rate (%) |
|
1961 |
858545 |
- |
- |
- |
|
1971 |
1015672 |
157127 |
18 |
- |
|
1981 |
1201553 |
185881 |
18 |
0 |
|
1991 |
1691538 |
489985 |
40 |
-22 |
|
2001 |
2077820 |
386282 |
23 |
17 |
|
2011 |
2585862 |
508042 |
24 |
-1 |
Average of decrease in growth rate
S = (0-22+17-1)/4
= -1.5 S
= 0.015%
By using the equation,
= 3206081
(Here r(2031) is directly found as (24 - 0.015) i.e., r(2021) - S, which equals to 23.985.
r(2041) = 23.985 - 0.015
= 23.97
= 4926689
5) Graphical Method
In this method, the population of last few decades are correctly plotted to a suitable scale on a graph. The graph is plotted from the available data between time and population, the curve is then smoothly extended up to the desired year. It is to be done by an experienced person and is almost always prone to error. As per the graph shown in Fig.1, the population up to the year 2001 is known and the population of the year 2021 can be found by smoothly extending the graph.
6) Comparative Graphical Method
Cities of similar conditions and characteristics are selected which have grown in similar fashion in the past and their graph is plotted and then mean graph is also plotted. This method gives quite satisfactory results. In this method, the population of a town is predicted by comparing it with a similar town. The advantage of this method is that the future population can be predicted from the present population even in the absence of some of the past census report.
Example Question
Let the population of a new city ‘X’ be given for decades 1970, 1980, 1990 and 2000 were 32000, 38000, 43000 and 50000 respectively. The cities A, B, C and D were developed in similar conditions as that of city X. It is required to estimate the population of the city X in the years 2010 and 2020. The population of cities A, B, C and D of different decades were given below.
- City A was 50000, 62000, 72000 and 87000 in 1960, 1972, 1980 and 1990 respectively.
- City B was 50000, 58000, 69000 and 76000 in 1962, 1970, 1981 and 1988 respectively.
- City C was 50000, 56500, 64000 and 70000 in 1964, 1970, 1980 and 1988 respectively.
- City D was 50000, 40000, 58000 and 62000 in 1961, 1973, 1982 and 1989 respectively.
Population curves for the cities A, B, C, D and X were plotted. Then an average mean curve is also plotted by dotted line as shown in the Fig.2. The population curve X is extended beyond 50000 matching with the dotted mean curve. From the curve the populations obtained for city X are 58000 and 68000 in year 2010 and 2020.
7) Master Plan Method
The big and metropolitan cities are generally not developed in haphazard manner, but are planned and regulated by local bodies according to master plan. The master plan is prepared for next 25 to 30 years for the city. According to the master plan, the city is divided into various zones such as residence, commerce and industry. The population densities are fixed for various zones in the master plan. From this population density total water demand and wastewater generation for that zone can be worked out. So by this method it is very easy to access precisely the design population.
8) The Ratio Method or Apportionment Method
In this method, the city’s census population record is expressed as the percentage of the population of the whole country, in order to do so, the local population and the country’s population for last 4 - 5 decades is obtained from the census records. The ratios of local population to national population is worked out a graph is then plotted between those ratios and time and extended up to the design period and then ratio is multiplied by expected national population at the end of design period. This method does not take into consideration abnormalities in local areas.
9) The Logistic Curve Method
This method is given by P.F. Verhulst. This method is mathematical solution for logistic curve. This method is used when the growth rate of population due to births, deaths and migrations takes place under normal situation and it is not subjected to any extraordinary changes like epidemic, war, earth quake or any natural disaster etc. the population follow the growth curve characteristics of living things within limited space and economic opportunity. If the population of a city is plotted with respect to time, the curve so obtained under normal conditions is look liked ‘S’ shape curve and is known as logistic curve.
The population at any time t from the start is given by
where,
PS = Saturation population
P = Population at any time ‘t’ from start point
PO =Population at the start point of the curve
PO, P1, P2 are
population at times t0, t1, t2 and t2 =
2 t1.
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