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Chapter 3 Graphical Representation Of Data
Representation Of Data
You have previously learned about collecting, compiling, and processing data. Data itself describes the characteristics of phenomena. While data can be presented in tabular or descriptive forms, graphical representation offers a powerful visual method to understand complex information quickly and easily.
Graphs, diagrams, and maps are visual tools used to transform data into a more comprehensible format. This transformation allows for easier understanding of patterns, distributions, and comparisons of geographical phenomena like population growth, density, sex ratio, or occupational structures.
As the Chinese proverb suggests, "a picture is equivalent to thousands of words." Visual representations enhance understanding, facilitate comparisons, save time, and create a lasting mental imprint of the presented characteristics.
General Rules For Drawing Graphs, Diagrams And Maps
To ensure effective graphical representation, certain general rules should be followed:
Selection Of A Suitable Method
The choice of the graphical method depends on the type of data and the theme being represented. For example:
- Time series data (showing changes over time, like temperature, rainfall, population growth) are often best represented using line graphs.
- Data for comparison across different categories (like rainfall in different months, production of various commodities) are well-suited for bar diagrams.
- Spatial distribution of phenomena (like population distribution, crop areas) can be effectively shown on dot maps.
- Showing variations in density or rates across administrative units (like population density, literacy rates) is ideal for choropleth maps.
Selection Of Suitable Scale
Choosing an appropriate scale is critical for representing data accurately on diagrams and maps. The scale acts as the measure that translates data values into visual lengths or areas. The chosen scale should accommodate the entire range of data without making the diagram too large or too small, ensuring clarity and readability.
Design
Effective cartographic design enhances the clarity and impact of graphs, diagrams, and maps. Important design components include:
- Title: Clearly indicates the subject matter of the diagram/map, including the area covered and the reference year(s) of the data. The title should be prominently placed, often at the top center.
- Legend: Also called an index or key, it explains the meaning of all colours, shades, symbols, and signs used in the representation. The legend should be accurately drawn and clearly visible, usually placed at the bottom left or right of the map/diagram.
- Direction: Maps representing geographical areas should include a direction symbol, typically indicating North, to orient the viewer.
Construction Of Diagrams
Diagrams are used to represent data based on measurable characteristics like length, width, or volume. Diagrams can be one-dimensional (using lines or bars), two-dimensional (using areas like circles or rectangles), or three-dimensional (using volumes like cubes or spheres).
We will focus on the construction methods for some commonly used one-dimensional and two-dimensional diagrams:
Line Graph
Line graphs are particularly useful for representing time series data, showing trends or changes in variables over a continuous period (e.g., monthly temperature, annual population growth rate, birth/death rates over decades).
Construction Steps:
- Simplify data if necessary (e.g., round numbers).
- Draw the horizontal (X) and vertical (Y) axes. The X-axis typically represents the time variable (years, months), and the Y-axis represents the data quantity/value.
- Select an appropriate scale for the Y-axis based on the range of data values. Label the axis and indicate the units (e.g., %, °C, cm). If data includes negative values, the scale should extend below zero.
- Plot each data point on the graph according to its time period on the X-axis and its value on the Y-axis, marking the location with a dot.
- Connect the plotted dots with a free-hand drawn line to show the trend over time.
Example 3.1: Construct a line graph to represent the annual growth rate of population in India from 1901 to 2011, as given in Table 3.1:
| Year | Growth rate in percentage |
|---|---|
| 1901 | - |
| 1911 | 0.56 |
| 1921 | -0.30 |
| 1931 | 1.04 |
| 1941 | 1.33 |
| 1951 | 1.25 |
| 1961 | 1.96 |
| 1971 | 2.20 |
| 1981 | 2.22 |
| 1991 | 2.14 |
| 2001 | 1.93 |
| 2011 | 1.79 |
Answer:
Using the steps above, plotting the years on the X-axis and growth rate percentages on the Y-axis results in the following line graph:
Polygraph
A Polygraph is a type of line graph used to display and compare two or more sets of related variables simultaneously. For example, it can show the growth rate of different crops, or trends in birth rates, death rates, and life expectancy for a region over time. To distinguish between the different variables, various line patterns (solid, dashed, dotted, different colours) are used for each line on the graph.
Example 3.2: Construct a polygraph to compare the growth of sex ratio in selected states of India from 1961 to 2011, as given in Table 3.2:
| States/UT | 1961 | 1971 | 1981 | 1991 | 2001 | 2011 |
|---|---|---|---|---|---|---|
| Delhi | 785 | 801 | 808 | 827 | 821 | 866 |
| Haryana | 868 | 867 | 870 | 860 | 846 | 877 |
| Uttar Pradesh | 907 | 876 | 882 | 876 | 898 | 908 |
Answer:
Plotting the sex ratio values for each state against the years on the X-axis, using different line patterns for each state, results in the following polygraph:
Bar Diagram
Bar diagrams, also known as columnar diagrams, use columns of equal width to represent data for comparison. They are suitable for discrete data or categories.
Rules for Construction:
- All bars must have the same width.
- There should be equal intervals or spacing between bars.
- Bars can be shaded or coloured distinctly for visual appeal and clarity.
Bar diagrams can be simple, multiple, or compound, depending on the number of variables and components being represented.
Simple Bar Diagram
A simple bar diagram is used to represent a single set of variables for immediate comparison across different categories or time points. For categories, arranging data in ascending or descending order before plotting is often helpful. For time series data, bars are plotted according to the chronological sequence.
Example 3.3: Construct a simple bar diagram to represent the average monthly rainfall data of Thiruvananthapuram as given in Table 3.3:
| Months | J | F | M | A | M | J | J | A | S | O | N | D |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Rainfall in cm | 2.3 | 2.1 | 3.7 | 10.6 | 20.8 | 35.6 | 22.3 | 14.6 | 13.8 | 27.3 | 20.6 | 7.5 |
Answer:
Plotting months on the X-axis and rainfall in cm on the Y-axis, using vertical bars of equal width and equal spacing, results in the following simple bar diagram:
Line And Bar Graph
This method combines a line graph and a bar diagram in a single representation, typically used for showing two different but related variables over the same period, such as climatic data like mean monthly temperature and rainfall. Months are shown on the X-axis, while one variable (e.g., temperature) is plotted as a line on one Y-axis (say, on the right), and the other variable (e.g., rainfall) is plotted as bars on the other Y-axis (say, on the left).
Example 3.4: Construct a combined line graph and bar diagram to represent the average monthly rainfall and temperature data of Delhi as given in Table 3.4:
| Months | Jan. | Feb. | Mar. | Apr. | May | June | Jul. | Aug. | Sep. | Oct. | Nov. | Dec. |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Temp. in °C | 14.4 | 16.7 | 23.30 | 30.0 | 33.3 | 33.3 | 30.0 | 29.4 | 28.9 | 25.6 | 19.4 | 15.6 |
| Rainfall in cm. | 2.5 | 1.5 | 1.3 | 1.0 | 1.8 | 7.4 | 19.3 | 17.8 | 11.9 | 1.3 | 0.2 | 1.0 |
Answer:
Plotting months on the X-axis, temperature as a line graph on the right Y-axis, and rainfall as a bar diagram on the left Y-axis, using appropriate scales, results in the following combined graph:
Multiple Bar Diagram
Multiple bar diagrams are used for comparing two or more variables across different categories or time points. For example, comparing male, female, and total literacy rates over different census years or irrigation sources across states. Bars for each category at a given point are placed next to each other, grouped together, and distinguished by different shading or colours.
Example 3.5: Construct a suitable bar diagram to show decadal literacy rate in India during 1951–2011 for Total population, Male, and Female literacy as given in Table 3.5:
| Year | Total population | Male | Female |
|---|---|---|---|
| 1951 | 18.33 | 27.16 | 8.86 |
| 1961 | 28.3 | 40.4 | 15.35 |
| 1971 | 34.45 | 45.96 | 21.97 |
| 1981 | 43.57 | 56.38 | 29.76 |
| 1991 | 52.21 | 64.13 | 39.29 |
| 2001 | 64.84 | 75.85 | 54.16 |
| 2011 | 73.0 | 80.9 | 64.6 |
Answer:
Plotting the years on the X-axis and literacy percentages on the Y-axis, grouping the bars for Total, Male, and Female literacy for each year, and using different shading for each category, results in the following multiple bar diagram:
Compound Bar Diagram
A compound bar diagram is used to show the components of a variable or different variables within a single bar. The bar represents the total value, and different sections within the bar, distinguished by shading or colour, represent the value of each component or variable. For example, showing the breakup of total electricity generation by source (thermal, hydro, nuclear) for different years.
Example 3.6: Construct a compound bar diagram to depict the Gross Generation of Electricity in India by source (Thermal, Hydro, Nuclear) as shown in Table 3.6:
| Year | Thermal | Hydro | Nuclear | Total |
|---|---|---|---|---|
| 2008-09 | 616.2 | 110.1 | 14.9 | 741.2 |
| 2009-10 | 677.1 | 104.1 | 18.6 | 799.8 |
| 2010-11 | 704.3 | 114.2 | 26.3 | 844.8 |
Answer:
For each year, a single bar representing the total electricity generation is drawn. This bar is then divided into segments corresponding to the values for Thermal, Hydro, and Nuclear generation, using different shading for each segment. The segments are stacked within the bar. This results in the following compound bar diagram:
Pie Diagram
A Pie Diagram, also called a Divided Circle Diagram, is a two-dimensional graphical method using a circle to represent the total value of an attribute. The circle is divided into sectors, where the angle of each sector is proportional to the share or percentage of a sub-set of the data. This diagram is best used for showing the proportion of different components that make up a whole.
The angle for each variable is calculated based on its proportion of the total, typically using the following formula:
$ \text{Angle for Category } x = \left( \frac{\text{Value of Category } x}{\text{Total Value of All Categories}} \right) \times 360^\circ $
If data is in percentage form, the formula is simpler:
$ \text{Angle for Category } x = \text{Percentage of Category } x \times 3.6^\circ $ (since $360^\circ / 100 = 3.6^\circ$)
Example 3.7: Represent the percentage share of India's export to major regions/countries of the world in 2010–11 as given in Table 3.7 (a) with a suitable diagram (Pie Diagram):
| Unit/Region | % of Indian Export |
|---|---|
| Europe | 20.2 |
| Africa | 6.5 |
| America | 14.8 |
| Asia and ASEAN | 56.2 |
| Others | 2.3 |
| Total | 100 |
Answer:
Calculate the angle for each region by multiplying the percentage share by 3.6°:
| Countries | % | Calculation (Degree) | Rounded Degree |
|---|---|---|---|
| Europe | 20.2 | $20.2 \times 3.6 = 72.72$ | 73° |
| Africa | 6.5 | $6.5 \times 3.6 = 23.4$ | 23° |
| America | 14.8 | $14.8 \times 3.6 = 53.28$ | 53° |
| Asia and ASEAN | 56.2 | $56.2 \times 3.6 = 202.32$ | 202° |
| Others | 2.3 | $2.3 \times 3.6 = 8.28$ | 8° |
| Total | 100 | 360 | 360° |
Construction Steps:
- Choose a suitable radius for the circle.
- Draw a circle and a radius line from the center to the edge.
- Starting from the radius line, measure and draw the angle for each category. It is advisable to plot angles in ascending order clockwise, starting with the smallest angle, to minimise error accumulation.
- Distinguish each sector using different shading, colours, or patterns.
- Add title, subtitle, and a legend explaining what each sector represents.
Following these steps results in the following pie diagram:
Precautions: Ensure the circle size is appropriate. Plotting smaller angles first helps maintain accuracy.
Other types of diagrams mentioned but not detailed in construction include Wind Rose (for showing wind direction and frequency) and Star Diagram.
Flow Maps/Chart
A Flow Map or Flow Chart is a visual representation used to show the movement or flow of phenomena (commodities, people, vehicles) between different locations or along routes. These maps are also called Dynamic Maps because they depict movement. They use lines or bands of varying width to represent the quantity or volume of flow. The width of the line is proportional to the quantity being transported or the number of entities moving along the route. Flow maps are commonly used to show traffic density on transport routes or the movement of goods between production and consumption centers.
Flow maps generally represent data related to:
- The number and frequency of vehicles moving along routes.
- The number of passengers or the quantity/volume of goods transported between origin and destination.
Requirements for Preparation:
- An outline map showing the relevant transport routes and connecting stations/locations.
- Statistical data on the flow (quantity, number of vehicles/passengers) between specific origin and destination points.
- A suitable scale to convert data quantities into proportional line widths on the map.
Example 3.10: Construct a flow map to represent the number of trains running in Delhi and adjoining areas as given in Table 3.8:
| S. No. | Railway Routes | No. of Trains |
|---|---|---|
| 1. | Old Delhi – New Delhi | 50 |
| 2. | New Delhi-Nizamuddin | 40 |
| 3. | Nizamuddin-Badarpur | 30 |
| 4. | Nizamuddin-Sarojini Nagar | 12 |
| 5. | Sarojini Nagar – Pusa Road | 8 |
| 6. | Old Delhi – Sadar Bazar | 32 |
| 7. | Udyog Nagar-Tikri Kalan | 6 |
| 8. | Pusa Road – Pehladpur | 15 |
| 9. | Sahibabad-Mohan Nagar | 18 |
| 10. | Old Delhi – Silampur | 33 |
| 11. | Silampur – Nand Nagari | 12 |
| 12. | Silampur-Mohan Nagar | 21 |
| 13. | Old Delhi-Shalimar Bagh | 16 |
| 14. | Sadar Bazar-Udyog Nagar | 18 |
| 15. | Old Delhi – Pusa Road | 22 |
| 16. | Pehladpur – Palam Vihar | 12 |
Answer:
Construction Steps:
- Obtain an outline map of Delhi and adjoining areas showing railway lines and stations (nodes).
- Select a scale to represent the number of trains by line width. For example, if 1 cm line width = 50 trains, then:
- 50 trains = 1 cm (or 10 mm) wide line
- 40 trains = $ (40/50) \times 10 = 8 $ mm wide line
- 30 trains = $ (30/50) \times 10 = 6 $ mm wide line
- etc., down to 6 trains = $ (6/50) \times 10 = 1.2 $ mm wide line.
- Draw the railway lines on the map with widths corresponding to the number of trains on each route segment, as per the selected scale.
- Include a terraced scale as a legend to show the relationship between line width and the number of trains. Also, use symbols to represent the nodal stations.
Following these steps results in a traffic (Railway) flow map of Delhi:
Example 3.11: Construct a water flow map of Ganga Basin as shown in Fig. 3.11.
Answer:
Construction Steps:
- Obtain an outline map of the Ganga Basin showing the river and its tributaries and relevant locations/points.
- Select a scale to represent the volume of water flow (e.g., 1 cm width = 50,000 cusecs).
- Draw lines along the river courses with widths proportional to the water flow data at different points, according to the selected scale.
- Include a scale and legend to explain the width representation.
The construction results in a water flow map like this (based on the data represented in Fig. 3.11 and Fig. 3.12):
Other flow maps can represent movement of people (e.g., migration), goods, etc.
Thematic Maps
While graphs and diagrams effectively compare data and show internal variations, they often lack a regional perspective. Thematic maps are specifically designed to show the spatial distribution patterns or variations of a particular theme or phenomenon over a geographical area. These maps are also known as distribution maps.
Requirements For Making A Thematic Map
To create a thematic map, you generally need:
- Statistical data for the chosen theme, corresponding to specific administrative units (state, district, etc.) or point locations.
- An outline map of the study area showing the administrative boundaries or the relevant physical features.
- A physical map (e.g., physiographic, relief, drainage) of the region can be helpful for accurately depicting distributions influenced by physical factors (e.g., placing dots in population distribution maps considering mountains, deserts).
Rules For Making Thematic Maps
Thematic map creation requires careful planning and execution:
- The map should clearly display essential components: Name of the area, Title of the subject, Source of data and year, Legend explaining symbols/shading/colours, and Scale.
- Select a suitable thematic mapping method based on the nature of the data (e.g., dot map for distribution, choropleth for density/rates, isopleth for continuous data).
Classification Of Thematic Maps Based On Method Of Construction
Thematic maps are broadly classified into quantitative and non-quantitative types.
- Quantitative Maps (Statistical Maps): Show variations in data values. They use visual techniques (dots, shading, lines) where the quantity or intensity corresponds to the data value (e.g., map showing rainfall categories: >200cm, 100-200cm).
- Non-quantitative Maps (Qualitative Maps): Depict non-measurable characteristics or categories in distribution (e.g., map showing areas of high vs. low rainfall, different types of vegetation).
We will focus on the methods for constructing quantitative thematic maps:
Dot Maps
Dot maps are used to show the distribution of phenomena where individual units can be represented by dots of a specific value (e.g., population, cattle, crop production). Dots of the same size are placed within administrative units or over point locations on the map according to a chosen scale. The total number of dots within an area represents the total quantity of the phenomenon in that area. The visual density of dots highlights the distribution patterns.
Requirements:
- Administrative map with boundaries.
- Statistical data for the chosen theme for each administrative unit.
- A suitable scale determining the value represented by a single dot.
- Physiographic map to guide accurate placement of dots, especially in areas where distribution is influenced by terrain (e.g., avoiding placing dots in mountainous regions if representing population).
Precautions: Use thin lines for boundaries. All dots must be of uniform size.
Example 3.12: Construct a dot map to represent the population data of India from 2001 as given in Table 3.9:
| Sl. No. | States/Union Territories | Total Population | |
|---|---|---|---|
| 1. | Jammu & Kashmir | 10,069,917 | |
| 2. | Himachal Pradesh | 6,077,248 | |
| 3. | Punjab | 24,289,296 | |
| 5. | Uttarakhand | 8,479,562 | |
| 6. | Haryana | 21,082,989 | |
| 7. | Delhi | 13,782,976 | |
| 8. | Rajasthan | 56,473,122 | |
| 9. | Uttar Pradesh | 166,052,859 | |
| 10. | Bihar | 82,878,796 | |
| 11. | Sikkim | 540,493 | |
| 12. | Arunachal Pradesh | 1,091,117 | |
| 13. | Nagaland | 1,988,636 | |
| 14. | Manipur | 2,388,634 | |
| 15. | Mizoram | 891,058 | |
| 16. | Tripura | 3,191,168 | |
| 17. | Meghalaya | 2,306,069 | |
| 18. | Assam | 26,638,407 | |
| 19. | West Bengal | 80,221,171 | |
| 20. | Jharkhand | 26,909,428 | |
| 21. | Odisha | 36,706,920 | |
| 22. | Chhattisgarh | 20,795,956 | |
| 23. | Madhya Pradesh | 60,385,118 | |
| 24. | Gujarat | 50,596,992 | |
| 25. | Maharashtra | 96,752,247 | 968 |
| 26. | Andhra Pradesh | 75,727,541 | 757 |
| 27. | Karnataka | 52,733,958 | 527 |
| 28. | Goa | 1,343,998 | 13 |
| 29. | Kerala | 31,838,619 | 318 |
| 30. | Tamil Nadu | 62,110,839 | 621 |
| Total | 1,028,610,328 | 10,286 |
Let's assume a scale of 1 dot = 100,000 persons.
Answer:
Construction Steps:
- Obtain an outline map of India showing state boundaries.
- Select the size and value of a dot (here, 1 dot = 100,000 persons).
- For each state, calculate the number of dots needed by dividing the state's population by the value of one dot (e.g., for Maharashtra: 96,752,247 / 100,000 = 967.52, rounded to 968 dots). Table 3.9 part 2 shows the calculated number of dots for each state.
- Place the calculated number of dots within the boundaries of each state. Dots should be placed where people actually live, considering physiographic features. Fewer dots should be placed in mountainous areas, deserts, and snow-covered regions (referencing a physiographic map) than in plains or populated areas.
- Include a legend showing the value of a dot and other standard map design elements (title, source, year).
Following these steps results in the following dot map of India's population:
Choropleth Map
Choropleth maps are used to represent data that are related to administrative units (states, districts, blocks). They are suitable for showing variations in density, rates, or percentages across these units (e.g., population density, literacy rates, sex ratio, percentage of area under a crop). The administrative units are shaded or coloured with different patterns or hues, where the intensity of the shading/colour corresponds to the data value within that unit. Higher data values are typically represented by darker shades or more intense colours.
Requirements:
- An outline map showing the boundaries of administrative units.
- Appropriate statistical data (density, rate, percentage) for each administrative unit.
Steps for Construction:
- Arrange the statistical data for all administrative units in ascending or descending order.
- Group the data into a suitable number of categories, typically 5 (e.g., very high, high, medium, low, very low concentration).
- Determine the class intervals for these categories. A common method is to divide the range of the data (maximum value minus minimum value) by the number of categories (e.g., Range/5). Adjust the intervals to convenient round numbers if necessary.
- Assign different patterns, shades, or colours to each category. The patterns or shades should be arranged in a logical sequence (e.g., from light to dark) corresponding to the order of categories (e.g., lighter shades for lower values, darker for higher values).
- On the map, shade or colour each administrative unit according to the category its data value falls into.
- Add a legend clearly showing the categories and their corresponding shades/patterns. Include all other standard map design elements (title, source, year, name of area).
Example 3.13: Construct a Choropleth map to represent the literacy rates in India in 2001 as given in Table 3.10:
| S. No. | States / Union Territories | Literacy Rate |
|---|---|---|
| 1. | Jammu & Kashmir | 55.5 |
| 2. | Himachal Pradesh | 76.5 |
| 3. | Punjab | 69.7 |
| 4. | Chandigarh | 81.9 |
| 5. | Uttarakhand | 71.6 |
| 6. | Haryana | 67.9 |
| 7. | Delhi | 81.7 |
| 8. | Rajasthan | 60.4 |
| 9. | Uttar Pradesh | 56.3 |
| 10. | Bihar | 47.0 |
| 11. | Sikkim | 68.8 |
| 12. | Arunachal Pradesh | 54.3 |
| 13. | Nagaland | 66.6 |
| 14. | Manipur | 70.5 |
| 15. | Mizoram | 88.8 |
| 16. | Tripura | 73.2 |
| 17. | Meghalaya | 62.6 |
| 18. | Assam | 63.3 |
| 19. | West Bengal | 68.6 |
| 20. | Jharkhand | 53.6 |
| 21. | Odisha | 63.1 |
| 22. | Chhattisgarh | 64.7 |
| 23. | Madhya Pradesh | 63.7 |
| 24. | Gujarat | 69.1 |
| 25. | Daman & Diu | 78.2 |
| 26. | Dadra & Nagar Haveli | 57.6 |
| 27. | Maharashtra | 76.9 |
| 28. | Andhra Pradesh | 60.5 |
| 29. | Karnataka | 66.6 |
| 30. | Goa | 82.0 |
| 31. | Lakshadweep | 86.7 |
| 32. | Kerala | 90.9 |
| 33. | Tamil Nadu | 73.5 |
| 34. | Puducherry | 81.2 |
| 35. | Andaman & Nicobar Islands | 81.3 |
Answer:
Construction Steps:
- Obtain an outline map of India showing state boundaries.
- Arrange the literacy rate data for all states/UTs in ascending order (as provided in Table 3.10 part 2).
- Identify the range: Minimum literacy rate = 47.0% (Bihar), Maximum literacy rate = 90.9% (Kerala). Range = $90.9 - 47.0 = 43.9$.
- Decide on the number of categories (here, 5). Calculate the approximate interval width: Range / 5 = $43.9 / 5 = 8.78$. Round this to a convenient number, like 9.0.
- Determine the class intervals and assign categories (e.g., Very Low, Low, Medium, High, Very High):
- 47.0 - 55.9: Very Low (approx. 47-56)
- 56.0 - 64.9: Low (approx. 56-65)
- 65.0 - 73.9: Medium (approx. 65-74)
- 74.0 - 82.9: High (approx. 74-83)
- 83.0 - 91.9: Very High (approx. 83-92)
- Assign shading patterns or colours to each category, ranging from light for the 'Very Low' category to dark for the 'Very High' category.
- On the map, shade each state/UT according to the category its literacy rate falls into.
- Add a legend showing the categories and their corresponding shades/patterns. Include title, source, year, and name of area.
Following these steps results in the following Choropleth map:
Isopleth Map
Isopleth maps are used to represent the spatial variations of continuous data that are not tied to administrative boundaries, such as temperature, pressure, rainfall, or elevation. These maps depict variation by drawing lines (isopleths) that connect places of equal value for the specific phenomenon. The word "Isopleth" comes from "iso" (equal) and "pleth" (lines).
Common examples of isopleths include Isotherms (equal temperature), Isobars (equal pressure), Isohyets (equal rainfall), Contours (equal height), Isobaths (equal depth), etc.
Requirements:
- A base map showing the locations where data was collected (point locations).
- Appropriate data values (temperature, rainfall, etc.) recorded at these point locations.
- Drawing instruments, especially a French Curve for drawing smooth lines.
Rules for Drawing:
- Select an equal interval between the values of consecutive isopleths (e.g., lines for 10°C, 20°C, 30°C). Intervals of 5, 10, or 20 are often considered ideal.
- Write the value of the isopleth along the line, either by the side or by breaking the line.
Interpolation
Drawing isopleths often requires interpolation, which is the process of estimating the intermediate values between known data points. Specifically, it involves locating the exact point on a map between two known data points where a particular isopleth value would pass.
Method of Interpolation:
- Determine the minimum and maximum data values on the map.
- Calculate the range: Range = maximum value - minimum value.
- Based on the range, determine the suitable interval for drawing isopleths (e.g., every 5 units, 10 units).
- To find the exact point where an isopleth passes between two known points, assume a linear relationship between the two points. Measure the distance between the two points on the map. Calculate the difference in data values between the two points. Then, for the desired isopleth value, determine its "interval" or difference from one of the known points. Use a formula to find the distance from that known point where the isopleth should be drawn.
- For example, if Point A is 28°C and Point B is 33°C, and the distance between them is 1 cm (10 mm). To draw the 30°C Isotherm:
- Difference between values = $33 - 28 = 5$.
- Desired isopleth value = 30°C.
- Interval from Point A (28°C) to 30°C = $30 - 28 = 2$.
- Use proportionality: If 5 units difference spans 10 mm, then 2 units difference spans $ (2/5) \times 10 \text{ mm} = 4 \text{ mm} $.
- So, the 30°C isotherm passes 4 mm away from Point A (28°C) along the line towards Point B. Alternatively, the interval from Point B (33°C) to 30°C is $33 - 30 = 3$. Distance from B is $ (3/5) \times 10 \text{ mm} = 6 \text{ mm} $. The point is 4 mm from A and 6 mm from B, summing to the total distance of 10 mm.
- After locating points for the same isopleth value based on interpolation between multiple pairs of points, connect these points with a smooth curve using a French Curve.
- Start by drawing the isopleth with the minimum value first, then proceed to higher values at the selected intervals.