8. TOPOGRAPHICAL SURVEYS - DIRECT LEVELLING

8.0 Introduction

What are elevation and altitude?

2. You have learned what the height of a ground point is. Now, however, you will need to know a more accurate definition of this term.

• When the height of a point is its vertical distance above or below the surface of a reference plane* you have selected, it is called the elevation* of that point.
• When the height of a point is its vertical distance above or below mean sea level (as the reference plane), it is called the altitude* of the point.

3. The vertical distance between two points is called the difference in elevation , which is similar to what you have learned as the difference in height (see Section 5.0). The process of measuring differences in elevation is called levelling , and is a basic operation in topographical surveys.

What are the main levelling methods?

4. You can level by using different methods, such as:

• direct levelling, where you measure differences in elevation directly. This is the most commonly used method;
• indirect levelling, where you calculate differences in elevation from measured slopes and horizontal distances.

You have already learned about indirect levelling in Section 5.0, when you learned to calculate differences in elevation from slopes or from vertical angles. Now you will learn about direct levelling.

Differential levelling

8.1 How to level by differential

What is differential levelling?

1. You can best understand differential levelling by first considering only two points, A and B , both of which you can see from one central levelling station, LS .

• Sight with a level from LS at the levelling staff on point A. The point where the line of sight meets the levelling staff is point X. Measure AX. This is called a backsight (BS).

• Turn around and sight from LS at the levelling staff on point B. The point where the line of sight meets the levelling staff is point Y. Measure BY. This is called a foresight (FS).

• The difference in elevation between point A and point B equals BC or (AX- BY) or (backsight BS - foresight FS).

• If you know the elevation of A, called E(A), you can calculate the elevation of B, called E(B), as BS -FS + E(A).
• But BS + E(A) = HI, the height of the instrument or the elevation of the line of sight directed from the level.

• Therefore,

What are backsights and foresights?

It is important for you to understand exactly what "backsight" and "foresight" are in direct levelling.

2. A backsight (BS) is a sight taken with the level to a point X of known elevation E(X), so that the height of the instrument HI can be found. A backsight in direct levelling is usually taken in a backward direction, but not always. Backsights are also called plus sights (+ S), because you must always add them to a known elevation to find HI.

3. A foresight FS is also a sight taken with the level, but it can be on any point Y of the sight line where you have to determine the elevation E(Y). You will usually take it in a forward direction, but not always. Foresights are also called minus sights (-S) , because they are always subtracted from HI to obtain the elevation E of the point. Remember:

Surveying two points with one turning point

7. Move to a second levelling station, LS2, about halfway between C and B. Set up the level and measure BS = 1.96 m, and then FS = 0.87 m. Calculate HI = BS + E(C) = 1.96 m + 101.17 m = 103.13 m. 0btain E(B) = HI- FS = 103.13 m - 0.87 m = 102.26 m.

8. You can make the calculations more easily if you record the field measurements in a table , as shown in the example. You will not make any intermediate calculations. All BS's and all FS's must be added separately. The sum FS is subtracted from the sum BS to find the difference in elevation from point A to point B.

• A positive difference means that B is at a higher elevation than A.
• A negative difference means that B is at a lower elevation than A.

Knowing the elevation of A, you can now easily calculate the elevation of B. In this case, E(B) = 100 m + 2.26 m = 102.26 m; this is the same as the result in step 7, which required more complicated calculations. This kind of calculation is called an arithmetic check.

Example
Table form for differential levelling with one turning point.

Example
Table form for differential levelling with several turning points.

Example
Differential levelling with several turning points

Making topographical surveys by straight open traverses

13. By now, you have learned enough to make a topographical survey of two distant points by measuring the horizontal distance between them and the difference in their elevation.

When you survey a future fish-farm site, you will use a very similar method. You can then prepare a topographic map of the site (see Chapter 9), which will become a useful guide for designing the fish-farm.

14. This is a survey method using straight open traverses , that is, several intermediate stations along one straight line. You know for example the elevation of starting point A, E(A) = 63.55 m. You want to know the distance of point B from point A, and its elevation. Because of the type of terrain on which you are surveying, you cannot see point B from point A, and you need two turning points , TP1 and TP2 , for levelling. Measure horizontal distances as you move forward with the level, from point A toward point B; try to progress along a straight line. If you cannot, you will need to use the broken open traverse survey method, which involves measuring the azimuths of the traverse sections as you move forward and change direction (see step 17).

Example
Topographical survey of a straight open traverse by differential levelling

Making topographical surveys by broken open traverses

18. You need for example to survey open traverse ABCDE from known point A. You require four turning points, TP1, TP2, TP3 and TP4. You want to know:

• the elevations of points B, C, D and E;
• the horizontal distances between these points;
• the position of each point in relation to the others, which will help you in mapping them.

Example

Topographical survey of a broken open traverse by differential levelling

Checking on levelling errors

Example

From point A of a known elevation, survey by traversing through five turning points, TP1 ... TP5, and find the elevation of point B. To check on the levelling error, survey by traversing BA through four other turning points, TP6 ... TP9; then calculate the elevation of A. If the known elevation of starting point A is 153 m, and the calculated elevation of A at the end of the survey is 153.2 m, the closing error is 153.2 m - 153 m = 0.2 m.

Making topographical surveys by closed traverses  

23. If you do not know the exact elevation of starting point A, you can assume its elevation, for example E (A) = 100 m. Start the survey at point A , and proceed clockwise along the perimeter of the area. Take levelling staff readings at TP1, TP2, B, TP3, etc., until you reach starting point A again and close the traverse. At the same time, make any necessary horizontal distance and azimuth measurements. Record your measurements either in two separate tables , one for plan surveying and one for levelling, or in one table which includes distance measurements. From the (BS-FS) columns, you can easily find the elevation of each point on the basis of the known (or assumed) elevation at point A. Make all the checks on the calculations as shown in steps 15 and 16. Find the closing levelling error at point A (see step 20). This error should not be greater than the maximum permissible error (see step 21).

Example

Topographical survey of a closed traverse by differential levelling

 Making topographical surveys by the square grid

24. The square-grid method is particularly useful for surveying small land areas with little vegetation. In large areas with high vegetation or forests, the method is not as easy or practical. To use the method, you will lay out squares in the area you are surveying, and determine the elevation of each square corner.

25. The size of the squares you lay out depends on the accuracy you need. For greater accuracy, the sides of the squares should be 10 to 20 m long. For reconnaissance surveys, where you do not need to be as accurate, the sides of the squares can be 30 to 50 m long.

27. Working uphill, chain along this baseline from the perimeter of the area, and set stakes at intervals equal to the size you have chosen for the squares, such as 20 m. Clearly number these stakes 1, 2, 3, . . . n.

• a letter (A, B, C, etc.) which refers to the line, running parallel to the base line, to which the point belongs;
• a number (1, 2, 3.... n) which refers to the perpendicular, laid out from the base line, to which the point belongs.

Example

20 m from point A1, perpendicular 2 crosses line AA at point A2.
20 m to the left of point A2 lies point B2 , on line BB.

30. Now that you have laid out the square grid on the ground, you need to find the elevation of each corner of the squares , which you have marked with stakes. First establish a bench-mark (BM) on base line AA near the boundary of the area and preferably in the part with the lowest elevation (see steps 42-44). This bench-mark can be either at a known elevation (such as one point on a previously surveyed traverse), or at an assumed elevation (such as 100 m) (see step 45).

31. You will level the square grid points in two stages.

• Starting from the bench-mark, measure the differences in elevation for all the base points A1, A2, A3, ... An. This is called longitudinal profile levelling (see Section 8.2).
• Then, starting at these base-line points with known elevations, measure the differences in elevation for all points of each of the perpendiculars, on each side of the base line (for example, B2, C2 and D2 followed by E2, F2 and G2). This is called cross-section levelling (see Section 8.2).

Example

Topographical survey by square grid with a sighting level

Enter all your measurements in a table, and find the elevation of each point of the square grid (see steps 38-41 for a further explanation).

You can check calculations and survey measurements at the bottom part of the table (see this Section, step 41).

  Making topographical radiating surveys

34. When you make a radiating survey (see Section 7.2), you first need to determine the height of the instrument HI at levelling station 0. Sight at a point X of known elevation E(X), and find a backsight (BS). Then,

35. Then you need to find the elevation of each of the points A, B, C and D. Sight at each of them in turn. You will find a foresight (FS) for each. Calculate their elevations as

36. Record all your measurements in a table. This table may also include plan-surveying information, such as azimuths and horizontal distances. You might also use two different tables as explained in step 23. The first line of the table will refer to the known point X . This point can be one of the perimeter points which you have already determined, or it can be a benchmark (see step 42). You find the position of point 0 from the azimuth of line OX and the horizontal distance OX.

Example

Topographical radiating survey

Combining traversing and composite radiating

(e) Now you are ready to start the detailed topographical survey, proceeding from each known levelling station in turn. From station 1, set up a series of radiating straight lines at a fixed-angle interval (such as 20�). This means that each radiating line will be 20� from the next. Use your magnetic compass and ranging poles or stakes. Mark on the ground the north-south line. You will call this the zero-degree line . Standing on this line at station 1, measure and mark a line with a 20� azimuth. Then, moving around in a clockwise direction on the same point, measure and mark in turn lines with azimuth 40�, 60�, ... 340�.

Note: the fixed-angle interval you use depends on how accurate a survey you need. Smaller angles will help you make a more accurate map of the site.

(h) Record all the measurements in a table, and calculate the elevations of all the surveyed points (see this section, step 36). You will need two additional columns in this table:

• one column marked "Line" , where you will record the azimuth of each line;

• one column marked "Cumulative distances" . In this space, you can separately calculate the distance from the levelling station to the points surveyed for each line.

Example

Topographical survey of partial area by composite radiating

Making topographical surveys with non-sighting levels

38. You can also make topographical surveys along straight lines by using non-sighting levels , such as the line level (see Section 5.2) or the flexible-tube water level (see Section 5.3). You have already learned how to measure height differences by using the square-grid method with such levels (see this section, step 33).

Remember , when you lay out your grid, that the distance between points cannot be more than the length of your level.

Example

Topographical survey with a line level (20 m)

Note : you have seen in previous examples that some surveys are related to previously surveyed points, This means that the measurements in the survey are based on these points. These points then become turning-point bench-marks . You find their elevations by levelling, and these then become known elevations.

8.2 How to level by profile

What is the purpose of profile levelling?

Ground line AB
 

  What does profile levelling consist of?

3. When you profile level, you are determining a series of elevations of points which are located at short measured intervals along a fixed line . These elevations determine the profile of the line.

4. There are two kinds of profiles which are commonly used in fish culture: longitudinal and cross-section profiles.

• You survey longitudinal profiles by profile levelling along a line which is the main axis of the survey. This can be the centre-line of a water canal or the base line of a square grid.

• You usually survey cross-section profiles along a line which is perpendicular to a surveyed longitudinal profile, using its points of known elevation as bench-marks. Cross-sections of valleys are useful in helping you locate a good fish-farm site. On a smaller scale, you can also survey cross-sections for water-supply canals, for dam construction, and for pond construction. You have already learned how to use cross-section profiles when surveying by the square-grid method (see Section 8.1, step 31).

Longitudinal profile levelling by radiating

6. Set up your level at LS1. Take a backsight BS on a bench-mark of elevation E(BM) to determine the height of the instrument

8. When you need to move the level to a new station so that you can take readings on the points ahead:

• first, choose a turning point TP and take a foresight FS to find its elevation from LS1;
• move to the next levelling station LS2, from which you can see the turning point TP;
• take a backsight BS on this turning point to find the new height of the instrument HI.

Take foresights at the points you have marked

Example

Longitudinal profile levelling with a sighting level in a radiating survey

Longitudinal profile levelling by traversing

11. You need to survey the same line AB, the centre-line of a water canal, for profile levelling. You will use a non-sighting level, such as the flexible tube water level (see Section 5.3). Since you are using this kind of level, you will survey by traversing. Mark the line AB with stakes driven into the ground at regular intervals. The length of these intervals depends on the working length of your level (in this case, 10 m). Where there are marked changes in slope, add intermediate stakes. On each stake, mark its distance from the initial point A.

12. Level a tie-in line between bench-mark BM and the initial point A (see Section 5.3, steps 6-12). This will give you the elevation of point A, through intermediate point 1.

13. Proceed with the levelling of the marked points along the line, using this method. At each point, you will make two scale readings, one rear and one forward, except at the final point where you will take only one height measurement.

14. One person should be responsible for recording the measurements in a field book, using a table similar to the one in Section 8.1, step 41. But, in this case, you will not need to enter the distances in the table, since they identify the surveyed points. Checks are made at the bottom of the table as usual. Remember that in this type of survey there is no need for turning points.

Example

Longitudinal profile levelling by traversing with a flexible tube water level (10 m)

Cross-section profile levelling

15. After you have found the elevations of points along a longitudinal profile, you can proceed with the survey of perpendicular cross-sections . These cross-sections can pass through as many of the points as necessary. Cross-sections are commonly used for contouring long, narrow stretches of land (see Section 8.3).

16. You will need to have more information on some of the longitudinal profile points. Choose these points and mark them. Then, set out and mark perpendicular lines at these points (see Section 3.6), and extend these perpendiculars on both sides of the traverse as far as you need to. In this type of levelling, such perpendiculars are called the cross-section lines .

17. Choose and clearly mark the points you want to survey on each cross-section line. In this case, these points do not have to be regularly spaced. Rather, they should be at places where the terrain changes since they should mark changes in slope.

18. As you know the elevations of the traverse points from a previous survey, you may treat these points as bench-marks. Proceed with the profile levelling of selected points along the cross-section lines as explained earlier. You may survey them:

• by radiating, with a sighting level (see this section, steps 5-10); or
• by traversing, with a non-sighting level (see this section, steps 11-14).

Note : you can also survey by traversing using a simple sighting level such as a bamboo sighting level (see Section 5.6) or a hand level (see Section 5.7).

8.3 How to contour

What is a contour?

Example

When you pour water into a hole in the ground, you will see that the surface of the water forms a continuous line made up of the water's points of contact with the sides of the hole. This line shows one contour for this particular water depth in the hole. A lake or a reservoir also has a surface contour which depends on its water level.

What is contouring?

2. Contouring means surveying to identify the contours on the ground, lay them out with markers, and plot them on a plan or map. You will learn more about planning and mapping contours in Section 9.4.

3. Contouring is used in fish culture to solve two kinds of problem:

• if you have fixed the location of a point, you may have to identify the contour passing through that point;

Example

You have chosen the end-point of your water-supply canal on a fish-farm site. Now you have to identify the canal's centre-line, which usually follows a contour back to the water source (which may be a point along a river, or the outlet pipe of a pump).

• If you need to prepare a plan or map showing the ground relief of an area, you must find out the location of contours on the ground and be able to transfer them onto paper.

Example

You have chosen a fish-farm site. Before you can plan, design and build the farm, you will need to make a topographical map showing the location of a series of contours from which you will be able to define the ground relief of the site.

4. You have already learned how to find a contour on the ground from a fixed point, in the sections on contouring devices (see Sections 6.2-6.8).

5. In the following steps, you will learn how to survey contours over a land area so that you can prepare a topographical map (see Section 9.4).

What are the main methods for contouring?

6. It would be an impossible task to identify all the contours in one area. Therefore, you will have to decide how many contours you need to identity in each area. You will have to fix the difference in elevation between contours which are next to each other. This is called the contour interval .

7. Choosing which contour interval to use depends mainly on the accuracy you need, on the scale of the map you will prepare (see Section 9.1) and on the kind of terrain you are surveying. Contour intervals usually vary from 0.25 m to 1 m . This range of intervals allows good accuracy, and makes it possible to produce large-scale topographical maps for flat or slightly sloping ground (which is usually the type of ground used for fish-culture sites). Since smaller contour intervals make contouring much more difficult, you will usually make reconnaissance and preliminary surveys with a contour interval greater than the one you use for later, more detailed surveys.

Example

Relationship between the size of contour intervals and various factors

8. There are two main methods of surveying contours:

• a direct method; in which you trace and mark the line of each contour on the ground, and then plan survey these lines so that they can be mapped,
• an indirect method; in which you make a topographical survey of the area to find a series of points of known elevation. Then you enter them on a map and determine the contours from this map.

Selecting the contouring method

9. When selecting the method you will use for contouring, remember that:

• the direct method is much slower, but is more accurate. Use it only to contour a relatively small area which you need to map in detail, on a large scale;
• the indirect method is faster, but it is not so accurate. Use it to contour large areas that you will map on a medium or small scale. It should preferably be combined with plane-tabling (see Section 7.5).

Laying out contours on the ground with a sighting level

You will now learn the direct method of contouring which will enable you to lay out a number of points on the ground which have exactly the same elevation.

10. Start your contouring survey of site ABCDEA at a point of known elevation, such as an existing bench- mark BM . If there is no such point of known elevation in the area, you can establish one:

• either by differential levelling from a bench-mark outside the area to a point within the area;
• or by assuming a convenient elevation for your bench-mark (such as 100 m) so that you will not have points with negative elevation later.

Note : try to establish this bench-mark in the middle of the lowest ground of the area, so that you can survey uphill.

11. Through this bench-mark BM at point F, lay out and mark a straight line FG . Make sure you follow the direction of the greatest ground slope . The line should cross the entire site.

12. At regular intervals, set out a series of lines parallel to FG. To choose the interval between parallels, use:

• 10 m or less , if the contour interval is to be 0.25 to 0.50 m;
• 25 to 30 m , if the contour interval is to be 1 to 1.5 m;
• 50 m , if the terrain has a very gentle or regular slope.

Example

• BM is at elevation 59.36 m.
• With a sighting level set up at LS1 and a levelling staff held on BM, read BS = 3.23 m.
• Choose the contour interval, for example Cl = 0.25 m.
• Calculate the multiple of Cl (= nCl) closest to E(BM) = 59.36 m as follows:
  (a) E(BM) � Cl = 59.36 m � 0.25 m = 237.44 ... or the round number n = 238;
  (b) n x Cl = 238 x 0.25 m = 59.50 m.
• The difference between E(BM) and n(Cl) equals 59.50 m - 59.36 m = 0.14 m.
• Set the target on a target levelling staff at the height of BS minus this difference or
  3.23 m - 0.14 m = 3.09 m.
• Find the position of the first contour at the elevation 59.50 m.

16. To determine the next contour, you must change the position of the target on the staff. As you are moving uphill , using a selected contour interval of 0.25 m, you will lower the target by 0.25 m to a height of 3.09 m - 0.25 m = 2.84 m. In this position, the target will show the ground points at elevation 59.50 m + 0.25 m = 59.75 m, if you continue surveying from the same levelling station LS1 .

17. From LS1, find all the points on the parallel lines at elevation 59.75 m, and mark a second contour on the ground. Again lower the target by 0.25 m to the height of 2.84 m - 0.25 m = 2.59 m to determine points at the next elevation of 60 m.

18. If you need to change the levelling station but continue to survey the same contour:

• ask your assistant to hold the levelling staff on one of the points of that contour;
• move the level to a new, more convenient levelling station;
• tell your assistant to adjust the target height until it lines up with the line of sight of the level;
• continue to survey the same contour.

19. If you need to change the levelling station at the same time you are ready to determine another contour:

• ask your assistant to keep the levelling staff on a point of the last surveyed contour;
• move the level to its new station; adjust the target height to the new line of sight;
• change this target height to determine the new contour (by lowering it 0.25 m, for example, see step 16).

...Find the new contour

Laying out contours with a non-sighting level

21. When you use a non-sighting level (such as a line level or an A-frame level) to lay out contours over an area of land, you first need to establish a bench-mark BM near the boundary of the area. As usual, this bench-mark may be either of known elevation or of assumed elevation. It should also be located in the part of the area with the lowest elevation (see Section 8.1, steps 42-44).

22. Set out a line FC through BM , and set out lines parallel to it at a selected distance, as described in steps 11- 12 above.

Example

Selected distance between parallels = 10 m.

Set out a line through the bench-mark,
and parallels at regular intervals

23. If you are using a bench-mark with a known elevation , proceed as shown above in step 13 to calculate the elevation of the first contour you will survey near the bench-mark. Also calculate the difference between the elevation of this first contour and the elevation of the bench-mark.

Example

• BM elevation E(BM) = 127,85 m
• Selected contour interval = 0.50 m
• Multiple of E(BM): 127.85 m � 0.50 m = 255.7 and therefore you choose n = 256
• First contour will be at elevation 256 x 0.50 m = 128 m
• Difference in elevation between E(contour) and E(BM): 128 m - 127.85 = 0.15 m.

24. Then, next to the bench-mark , place some objects (such as bricks, stones, wooden planks, a tin or a box) that will provide the elevation calculated for the first contour.

Example

Next to BM, place some bricks and adjust their top height at 0.15 m higher than E(BM), using a straight-edge and a mason's level (see Section 5.1). The top of these bricks will be at the 128 m elevation.

25. Find a ground point X which is near BM, is located on the line CF passing through BM, and has the same elevation as the objects piled near BM. To do this, use one of the methods described earlier (see Sections 5.1, 6.2-6.4 and 6.6). This ground point X is the first point of the contour 128 m.

Example

Using a straight-edge level, transfer the level 128 m from the top of the bricks to a ground point X on the line CF passing through BM.

26. If you are using a bench-mark with an assumed elevation , and are working uphill, determine the point X of the line passing through BM in the same way. The elevation of this point will equal assumed E(BM) plus the contour interval Cl.

Example

• If E(BM) = 100 m and Cl = 0.50 m, pile bricks 0.50 m high at BM.
• Locate nearby point X where E(X) = 100 m + 0.50 m = 100.50 m.

27. Start contouring from point X using one of the methods described in Chapter 6. With a stake , mark each point where the contour you are following intersects with one of the parallel lines . On each stake, clearly indicate the elevation of the ground point.

28. Each time you finish laying out a contour, determine the first point Z, of the next contour by using a method like the one described in step 24. At known point X, where the last contour line crosses central line CF, place objects with a total height equal to the contour interval . Transfer this new level horizontally along line CF to point Z on the next contour. If the contour interval is large, you may have to use intermediate points to do this in stages.

Example

• Cl = 0.50 m.
• Transfer first E(contour) by + 0.25 m, from X to Y.
• Repeat again from Y to Z, to total + 0.50 m = 2 x 0.25 m.

29. When you have laid out all the contours on the ground with stakes, measure, from stake to stake, the horizontal distances along the parallel lines. This will help you to prepare a topographical map (see Section 9.4).

Contouring by the indirect method

30. You can also contour by the indirect method . In this method, you make a topographical survey of the area, using a definite pattern, such as..

• a square grid to determine elevations for points located at the intersections of a grid made of square or rectangular blocks;
• radiating to determine elevations for random points located on lines which radiate at a selected angle interval from a known point;
• cross-sections to determine elevations for points located on short lines laid out at right angles to a surveyed base line.

31. You learned earlier that the square-grid pattern is commonly used to contour relatively small areas, particularly if their perimeters have already been surveyed (see Section 8.1, steps 24-33).

32. You also learned about the radiating pattern , which is particularly useful for large areas (see Section 8.1, steps 34-36).

Cross-sections