E.3.5 Line, or Differential, Levelling

To determine the difference in elevation between two widely separated bench marks, a level circuit is run between the two stations (e.g., Geodetic Survey of Canada bench mark to a hydrometric gauging station). A number of intermediate instrument set-ups are selected, so that sighting distance for backsights and foresights are approximately equal (range 50 to 90 m). At the first instrument set-up, the rod is held vertically on the bench mark of known elevation with its face turned to the instrument. The backsight (BS) reading on the rod is added to the known elevation to obtain the height of instrument (HI). Next, the rodperson carries the rod to the instrument, counting the number of paces from the bench mark to the instrument. He/she then proceeds the same number of paces away from the instrument and finds or establishes a suitable turning point (TP1) (e.g., a hub driven into the ground or a high point on a rock). The HI minus the foresight (FS) rod reading at the turning point is the elevation of the turning point (TP1).

When the turning point has been established, the instrument is carried to the next set-up. The distance to the next set-up is determined in the same manner as the distance to the first turning point. The reason for balancing backsights and foresights is to eliminate instrument and physical errors (see two-peg test). (If it is not possible to balance the backsights and foresights when using the Wild N2 level, the rod should be read in both positions of the telescope [bubble right and bubble left] and the two readings averaged to eliminate the instrument error.) When sighting distance is over 70 m, influences of the earth's curvature and refraction may be noticeable, and they are not eliminated by reading the rod in two positions. The difference in elevation of the two bench marks should equal the difference in the sum of all backsight readings minus the sum of all foresight readings (from the first bench mark to the second bench mark).

Some of the turning points can be temporarily marked and used again when returning from the circuit to the original bench mark. If there is an error in the levels, only a portion of the circuit may have to be re-run. Refer to Figure E-11 for a schematic of the level run, and Figure E-12 for differential level notes.

In all cases the circuit must be closed, even when it involves only one set-up to check gauge movement, to do a bench mark tie, or to obtain a direct water level.

Figure E-11. Differential leveling.

Figure E-12. Level note for differential leveling.

E.3.6 Reciprocal Levelling

Occasionally it is necessary to transfer a known elevation from one side of a large river channel to the other. This may result from the need to relocate an existing gauging station with a known datum or to carry a line of levels from an established bench mark when installing a new gauging station. The continuation of an existing datum and the transfer of an established elevation for a gauging station site are essential parts of hydrometric work.

The procedure to perform reciprocal leveling is as follows:

1. Set up the instrument near the point of known elevation (point A). Observe and record backsight readings at point A and foresight readings at the point across the channel to which the elevation is to be transferred (point B).
2. Now set up the instrument near point B. Observe and record backsight readings at point A and foresight readings at point B.
3. Often the horizontal distance between points is large, making it necessary to fit a rod target on the distant rod. To obtain precise results, take a series of foresight readings, re-centering the bubble and re-setting the target after each observation.
4. The difference between the mean value of the backsight readings and the mean value of the foresight readings is the difference in elevation of the two points.

This method of reciprocal leveling assumes that the conditions under which observations are taken remain unchanged during the procedure. When leveling points are far apart, two factors may affect the accuracy of readings: unequal expansion of the instrument parts and variations in atmospheric refraction. It is best to carry out this task on a cloudy day when temperature and atmospheric conditions remain constant; otherwise protect the instrument from the sun's rays. Complete the procedure in as short a time period as possible.

E.3.7 Adjustment of Elevation

It can be assumed that the principal errors of leveling are accidental and that most of the level circuits run in hydrometric surveys are relatively short.

When a line of levels makes a complete circuit, almost invariably the final elevation of the initial bench mark as computed from the notes does not agree with the initial elevation. The difference in value between the bench mark's known elevation and its computed elevation according to the level circuit is known as the error of closure. This is the true error value incurred while running the level circuit. It is obvious that the elevation of the intermediate points established while running the circuit will also be in error.

When significant errors of closure are experienced in level circuits over small distances such as the immediate vicinity of a hydrometric station, the survey should be repeated. In the case of a long distance circuit, there are statistical techniques for computing corrections to intermediate points. These can be found in surveying texts.

E.3.8 Levelling Errors

One of the most important factors required to achieve accurate leveling is the skill of the field technician. Field technicians must be aware of potential problems that will produce errors in leveling and the steps necessary to limit them. The following list discusses many of the common errors committed while performing leveling work:

1. Improper Adjustment of Instrument. This condition occurs when the line of sight is not parallel to the axis of the level tube. This error can be minimized by careful adjustment of the instrument and by balancing backsight and foresight distances.
2. Parallax. The eyepiece of the telescope must be adjusted until the crosshairs appear sharp and distinct. If there is an apparent movement of the crosshairs on the target with a corresponding slight movement of the observer's eye (vertically or horizontally), the condition of parallax exists. This condition can be reduced to a negligible quantity by careful focusing of the eyepiece on the objective lens.

Alternate procedure:

• Focus the telescope to the greatest distance.
• Tilt the level to view the sky.
• Adjust eyepiece until crosshairs are as sharp as possible.
• Note the reading on the dioptric refraction scale for further checks.
• Proceed to use the instrument.

3. Inaccurate Reading of Rod. This error can be greatly reduced by using shorter sights and by checking each reading before recording it.

4. Rod Not Plumb. A rod level can be used or the rod can be waved to eliminate this type of error. When the rod is tipped backward, ensure that it still rests on the front edge of the base.

5. Improper Turning Points. Turning points that are not both well defined and stable are potential sources of error. If reasonable care is exercised when selecting turning points that are both solid and have rounded tops, this error can be kept to a minimum.

6. Tubular Bubble Not Centered. The magnitude of this error will vary with the distance between the instrument and the rod. It follows that the greater the distance to be sighted, the greater the care that should be exercised when leveling the instrument.

7. Settlement of the Instrument Tripod. Some settlement of the tripod is likely to occur when leveling over soft, muddy, or thawing ground. Under these conditions backsight and foresight observations should be made in quick succession in order to minimize any effect from the instrument settling.

8. Incorrect Rod Length. Level rod lengths should be checked periodically with a steel tape. Dirt or snow can become trapped in the sleeve of sectional rods which may prevent sections from fitting together properly. Rods should be assembled and carried so that the upper portion is never in contact with the ground.

9. Mud, Snow, or Ice Accumulation on Base of Rod. Mud, snow, or ice accumulations on the rod must be removed before each reading is taken so that level circuits will close. Note that ice accumulation is sometimes unavoidable when obtaining direct water levels in the winter. Uniform wear of the rod base causes no error.

---