1. Sources

a. Personal

(1) Instrument set up

Incorrectly leveling the instrument, not seating the legs firmly, setting up in an adverse location (e.g. blacktop on a sunny day). Setting up on or near roads can cause the compensator to "bounce" when vehicles go by; this can also happen on construction sites near heavy equipment.

(2) Parallax

Parallax was discussed in I. Basic Principles Chapter E. Parallax is affected by malfocus and observer's eye geometry. It results in image separation, Figure D-1, and can cause error unless removed. Every time the instrument operator changes, parallax should be cleared.
Figure D-1
Parallax Error

(3) Sight distance

Accurate rod readings are more difficult at longer sight distances. This is not only because the rod and its divisions become visually smaller, but also because the relative size of the crosshairs become larger on the rod. Figure D-2 shows the same rod and reading at two difference distances: the rod in (b) is twice as far away as the rod in (a).

 d 6
Figure D-2
Reading Difficulty at Longer Distances

 Add to that wind and atmospheric anomalies along the line of sight. All these conspire to introduce reading errors, and they can be substantial. Most manufacturers will specify a maximum working range for an instrument (check the manual) but consider this being for ideal conditions. Shorter sights may mean more setups but the trade off is more reliable readings.

(4) Rod

Modern rods generally use a multi-part telescoping design. The first section may be 0 to 4 feet, the second 4 to 8, and a third 8 to 12. On some, it is easy to telescope the incorrect section resulting in a 8 foot tall rod which is graduated from 0 to 4 ft followed by a 8 to 12 ft section. Any reading above 4 ft on the rod would have a 4 ft error.

A traditional wooden Philadelphia rod is usually a two-section sliding design with each section approximately 7 ft long. When extending the rod, the rod person must be careful of two things:

1. To extend the rod all the way until it locks, and,

2. To face the correct side to the instrument. The bottom of the back side is blank, but the upper back side is numbered in decreasing fashion.

(5) Reading or recording errors

The first time a surveyor reads a level rod can be confusing. A common mistake is a reading that is exactly one foot off. This happens when the sight through the telescope looks like Figure D-3.

d 7
Figure D-3
Limited Field of View

The novice surveyor may concentrate on interpreting the hundredths and tenths, coming up with .93, and then subconsciously grab 5 for the foot reading because it's in the field of view. He'll report a reading of 5.93 when it should be 4.93.

If the distance is short, the foot number may not appear in the field of view. In that case, after obtaining the hundredths and tenths, the surveyor should tell the rod person to "raise for red." The rod person then raises the rod slowly and the instrument person reads the first red number which appears.

Most modern rods have small red foot numbers between the normal ones for these situations.

(6) Reading the wrong crosshairs

Most instrument telescopes have two stadia crosshairs equally spaced above and below the horizontal crosshair. These are used for horizontal distance determination as well as for precise Three-Wire Leveling. They are also used for LoS collimation which will be discussed in a later chapter.

A common mistake by a new surveyor is to read the level rod using one of the stadia hairs resulting in a reading that is either too high or too low, Figure D-4.

 d 8
Figure D-4
Stadia Hairs

(7) Computation errors

It's important to compute EIs and point elevations as the data are collected and that a page check be done immediately at the completion of a page. Sometimes, a large rod reading mistake (see above) can be identified right away when the elevation is computed and checked visually. Running calculations are needed to determine closure at network completion and the page check helps identify and correct math errors.

 b. Instrument

(1) Compensator

Reliable readings are not possible if the compensator is sticking or jammed. Testing the compensator is quick and simple.

1. Set up and level the instrument.

2. Clear parallax. 

 d 9
 Figure D-5

3. Sight a level rod and note the reading.

d 14
 Figure D-6

 4. While sighting the rod, use a finger to firmly and gently press down on the forward end of the telescope.

This will deflect the line of sight changing the reading.

d 11
 Figure D-7

5. While holding the telescope depressed, the crosshairs should return to the initial reading.

This is the compensator reacting as it should.

d 12
 Figure D-8

 6. Remove pressure from the telescope front; the line of sight will go up and then... 

d 13
 Figure D-9

7.  ... should return to the inital rod reading.

d 14
 Figure D-10
  Checking Compensator Operation

 Another way to check the compensator is to take a reading with the circular bubble centered, turn one of the leveling screws making the instrument slightly out of level, and check the reading again. If the second reading matches the first then the compensator is operating correctly. This must be done with care as turning a level screw too much can change the instrument’s elevation which can affect the second rod reading.

A level with a sticky or inoperable compensator cannot be reliably used. If the compensator does not respond correctly, it should be sent in for repair. The internal mechanism is delicate and sealed from dust and should only be adjusted by a qualified service technician.

(2) Horizontal crosshair

On an adjusted level, the horizontal crosshair is truly horizontal when the instrument is correctly set up. This allows accurate rod reading using any part of the crosshair.

d 15
Figure D-11
Horizontal Crosshair

 To check the horizontal crosshair:

1. Set up and level the instrument.

2. Clear parallax. 

3. Sight a rod with one end of the horizontal crosshair and note the rod reading. 
d 16
Figure D-12

4. While sighting through the telscope, use the slow motion to horizontally scan across the rod.

If the reading doesn't change. the horizontal crosshair is in adjustment.

 d 17
Figure D-13
  Checking Horizontal Crosshair

(3) Collimation

On an adjusted instrument which is correctly set up, the Line of Sight (LoS) should be horizontal and perpendicular to the Vertical Axis (VA). If that isn't the case, then the instrument has a collimation error: the LoS is inclined or depressed with respect to horizontal, Figure D-18. This introduces a rod reading error when leveling. 

d 18
Figure D-14
Collimation Error

 Collimation error is caused by the vertical position of the crosshairs: if they are too low then the LoS is inclined; if they are too high, the LoS is depressed.

The amount of reading error caused by collimation is a function of distance, Figure D-15. The error increases linearly as distance increases, e.g., the error at 200 ft is twice that at 100 ft.

d 19
Figure D-15
Collimation Error Effect

 The error amount can be determined by performing a collimation check (the procedure is explained in a later chapter). The error can then be corrected by adjusting the crosshairs or applying it mathematically to each reading. Or the error can be removed procedurally. How? By balancing BS and FS distances, that is, making them equal, Figure D-16.

d 20
Figure D-16
Collimation Error Compensation

 If the BS and FS distances are equal, then the reading error in both will be the same: eBS=eFS. Because ElevB = ElevA + BS - FS, the BS error (eBS) is added and the FS (eFS) error is subtracted so the collimation error cancels. That means that the elevation of B is correct with respect to A if the BS and FS distances are equal. However, the EI is incorrect since it is subject only to the BS error. That's why in differential leveling we have one BS and one FS per setup and make sure their distances are approximately equal.

How close must the BS and FS distances be? It depends on the accuracy level of the survey. Table D-1 shows the maximum allowable BS and FS distance difference (as well as maximum distance) for First, Second, and Third Order geodetic leveling.

Table D-1
table d 1
units are meters
per setup is for each instrument setup
per section is cumulative difference for each closed network
 From Standards and Specifications for Geodetic Control Networks, FGCS, 1984; Section 3.5 Geodetic Leveling.

Considering that Third Order allows a 10 meter (~33 ft) differential, keeping distances balanced within several paces for local projects should be sufficient. Yes, pacing is an acceptable way to balance distances.

By balancing BS and FS distances the readings can be used without having to determine the collimation error because it cancels.

(4) Rod bubble

A rod bubble is used to keep the rod vertical for readings. If the rod bubble is off, then the rod will not be vertical and reading errors will be introduced. Because a rod bubble lives a hard life, it should be checked at the beginning of each leveling day. A rod bubble can be checked and adjusted using a prism pole having an adjusted bubble. For two methods to adjust a prism pole bubble, see Chapter B of Topic III. Distances.

(5) Waving (rocking) a rod

If the rod is slowly waved back and forth, the instrument person will see the reading rise and fall; the rod is vertical when the reading is lowest. An error could be introduced, however, if the rod is sitting on a hard flat surface. On older Philadelphia rods which have sliding sections, the bottom of the rod is deep enough to support the upper section when collapsed. This gives the rod a larger footprint than a telescoping rod. When the rod is rock backward, the pivot point is at the back of this footprint and it actually raises the rod a little.

In Figure D-17, each division line represents a tenth of a foot. When the rod is vertical, it reads 1.00 ft. When tipped back approximately 5 degrees, the reading is below 1.00 ft. The lowest reading, in this situation, is not the correct one. Here it appears to introduce an error of about 0.014 ft in the first foot on the rod. Readings higher up on this tipped rod will have slightly increasing error.

To avoid this error, a rod bubble should be used. If this is a turning point, a pin or turtle should be used since both have a rounded top to avoid this problem.

d 21
Figure D-17
Potential Error Waving a Rod

 c. Natural

(1) Climate

Weather can have various detrimental effects on leveling accuracy:

(2) Curvature and Refraction

(a) Curvature

Recall that a level line is curved and the LoS is horizontal. They coincide at the instrument but separate as the distance from the instrument increases. Figure D-18 shows that curvature causes the rod reading to be too high. 

 d 22
Figure D-18
Curvature Error

 Its effect is:

c = -0.667M= -0.0239F2    Equation D-1
c: reading correction, ft
M: distance to rod, miles
F: distance to rod, 1000s of ft 

 Note: F in 1000s of feet means, for example, that for 100 ft, F = 100/1000 = 0.1

Curvature can be accounted for by computing and applying the correction, Equation D-1, to the rod reading, or, because it is a function of distance, balancing BS and FS distances, Figure D-19, will allow it to cancel.

d 23
Figure D-19
Curvature Error Compensation
(b) Refraction

Even if there are no atmospheric anomalies, the fact that the LoS has to pass thru atmosphere causes it to bend, introducing a reading error. Refraction causes the LoS to be bent downward, Figure D-20, resulting in a rod reading that is too low.

 d 24
Figure D-20
Refraction Error

 The error can be determined from:

R = +0.093M= +0.0033F2  Equation D-2
R: reading correction, ft
M: distance to rod, miles
F: distance to rod, 1000s of ft 

 Refraction can be accounted for by computing and applying the correction, Equation D-2, to the rod reading, or, because it is a function of distance, balancing BS and FS distances allowing it to cancel, Figure D-21.

d 25
Figure D-21
Refraction Error Compensation
(c) Combined

The effect of curvature is greater than, and opposite to, refraction. The two are generally combined with the resulting equation:

(c+R) = -0.574M= -0.0206F2  Equation D-3
(c+R): reading correction, ft
M: distance to rod, miles
F: distance to rod, 1000s of ft 

 How significant is the combined corrections? Table D-2 shows the correction for various sight distances, 

Table D-2
Distance, ft  (c+R), ft
100 -0.000206
200 -0.000824
300 -0.00185
400 -0.00330
500 -0.00515
1000 -0.0206


Not much, huh? Especially considering how hard it is to read a rod at distances greater than 400 ft.

Regardless, the combined effect of refraction and curvature can be accounted for by computing and applying the correction to the rod reading, or,

Balancing BS and FS distances allowing it to cancel

2. Errors Summary

Although we could go on (and on) digging up more leveling errors from each source, we've identified and described the major ones having the greatest impact. Table D-3 categorizes each by Source and identifies their Type (behavior).

Table D-3
Source Error Type
Personal   Set up Random
  Parallax  Random
  Sight distance  Random
  Rod leveling Random
  Reading or recording  Random/Mistake
 Instrumental Compensator  Random
  Horizontal crosshair Systematic
  Collimation Systematic
  Rod bubble Systematic
Natural Climate Random
  Curvature Systematic
  Refraction Systematic 


Some systematic errors are compensated by balancing BS and FS distances. The distances need only be within several paces of each other in order to remove the error effects. While point elevations are correct when BS and FS distances are balanced, the EI (elevation of the instrument) is still subject to error since the BS error is present without the compensating FS error.

To minimize most systematic errors when differential leveling:

• Always balance BS and FS distances within a few paces, and,

• Each instrument set up should have a single BS and a single FS - do not take multiple FS readings off a single BS reading.

What's left after systematic errors (and mistakes) have been eliminated? Random errors. Recall that random errors tend to be small and compensate. These are the only things which prevent perfect closure on a closed level network.

3. Misclosure

a. Determining

A closed level network is either a loop or link which begins and ends on a known elevation, Figure D-22.

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Figure D-22
Closed Network


In the process of running the network, new elevations are measured including that of the known ending elevation. The difference between the known and measured ending elevation allows us to determine the amount of error, or misclosure, in the network:

M =(Known End Elev) - (Meas'd End Elev)  Equation D-4
M: misclosure

 Misclosure should be the result of accumulated random errors. Systematic errors and mistakes must be eliminated first in order to judge quality of the newly created elevations. Random errors, while they can't be entirely eliminated, can be minimized by knowledgeable personel using the appropriate equipment and procedures under the best conditions.

b. Allowable

How much misclosure is acceptable? It depends on the purpose of the network. The allowable misclosure should be consistent with how random errors accumulate. Differential leveling consist of a series of instrument setups at which two rod readings are made. This is repeated throughout the entire network. If we assume that each time the process is performed we expect a certain error behavior then we can consider the total misclosure to behave like an Error of a Series.

eqn d 5 Equation D-5

c: total error
E: expected error for a condition
n: number of times the condition occurs

(1) Formal standards

Table D-4 is taken from Standards and Specifications for Geodetic Control Networks, FGCS, 1984; Section 3.5 Geodetic Leveling.

Table D-4
table d 4

 The Loop misclosure not to exceed (mm) row identifies the network misclosure using a form of the Error of a Series equation. The allowable misclosure is based on the loop length (that is, the total of all the BS and FS distances) instead of instrument set ups. Consider the greater difficult reading a level rod at twice the distance - not only are rod divisions smaller but other environmental factors add to the difficulty as well. Assuming error accumulates as a function of distance is reasonable.


The distance around a level network is approximately 1800 ft. What is the allowable misclosure, in feet, if the network is to meet Second Order Class II standards?

Convert the distance to km

d 3 1

Compute the misclosure, m, and convert to feet

(2) Informal standards

Informal standards can also be based on the Error of a Series. However, the error accumulation could be presumed based on distance surveyed or number of instrument setups.


A survey crew ran a level network consisting of seven set ups. If they have an expected error of ±0.005 ft for each set up, what is their expected network misclosure?

Using Equation D-5:

d 3 3

Whether using formal or informal standards, remember that the final results are affected by errors from the different sources. Controlling those errors is paramount to meeting misclosure standards by design, not by mistake.

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