U.S. Department of the Interior

U.S. Geological Survey

Techniques and Methods 3-A19

Levels at Gaging Stations

Chapter 19 of 

Section A, Surface-Water Techniques 

Book 3, Applications of Hydraulics
Cover: View of levels being run at U.S. Geological Survey streamflow-gaging 

station 10156000, Snake Creek near Charleston, Utah. 

Photograph taken by K. Michael Nolan, U.S. Geological Survey, June 30, 2010. 

Back Cover: USGS topographic field party, circa 1925, with a Wye level on a 

tripod and two stadia rods. Photograph by U.S. Geological Survey.
Levels at Gaging Stations

By Terry A. Kenney 

Chapter 19 of

Section A, Surface-Water Techniques

Book 3, Applications of Hydraulics

Techniques and Methods 3–A19

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia: 2010

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Although this report is in the public domain, permission must be secured from the individual copyright owners to 

reproduce any copyrighted materials contained within this report.

Suggested citation:

Kenney, T.A., 2010, Levels at gaging stations: U.S. Geological Survey Techniques and Methods 3-A19, 60 p.
iii

Preface

This series of manuals on techniques and methods (TM) describes approved scientific and datacollection procedures and standard methods for planning and executing studies and laboratory 

analyses. The material is grouped under major subject headings called “books” and further 

subdivided into sections and chapters. Section A of book 3 is on surface-water techniques.

The unit of publication, the chapter, is limited to a narrow field of subject matter. These 

publications are subject to revision because of experience in use or because of advancement 

in knowledge, techniques, or equipment, and this format permits flexibility in revision and 

publication as the need arises. Chapter A19 of book 3 (TM 3–A19) deals with levels at gaging 

stations. The original version of this chapter was published in 1990 as U.S. Geological Survey 

(USGS) Techniques of Water-Resources Investigations, chapter A19 of book 3. New and 

improved equipment, as well as some procedural changes, have resulted in this revised second 

edition of “Levels at gaging stations.”

This edition supersedes USGS Techniques of Water-Resources Investigations 3A–19, 1990, 

“Levels at streamflow gaging stations,” by E.J. Kennedy.

This revised second edition of “Levels at gaging stations” is published on the World Wide Web 

at http://pubs.usgs.gov/tm/tm3A19/ and is for sale by the U.S. Geological Survey, Science 

Information Delivery, Box 25286, Federal Center, Denver, CO 80225.
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v

Contents

Preface ...........................................................................................................................................................iii

Abstract...........................................................................................................................................................1

Introduction.....................................................................................................................................................1

Purpose and Scope .......................................................................................................................................1

Differential Leveling and Leveling Equipment ..........................................................................................2

Level Instruments..................................................................................................................................2

Optical Levels ...............................................................................................................................3

Electronic Digital Levels .............................................................................................................3

Parallax..........................................................................................................................................4

Checking the Engineer’s Level ...........................................................................................................4

Fixed-Scale Test ..........................................................................................................................6

Peg Test.........................................................................................................................................6

Manufacturer-Recommended Collimation Test......................................................................7

Collimation Error and Balanced Sightline Distances .....................................................................8

Leveling Rods.........................................................................................................................................9

Inspection of Leveling rod .......................................................................................................10

Proper Care and Use of a Rod Level.......................................................................................11

Correcting for Rod Scale Expansion or Contraction Due to Temperature Variations ....11

Considerations for Secondary Devices Used for Vertical Measurements ......................13

Establishment of Gage Datum ...................................................................................................................13

Installation of Reference Marks.......................................................................................................14

Referencing a Gage Datum to an Established Datum ..................................................................16

Frequency of Gaging-Station Levels ........................................................................................................17

Preparation for Running Levels.................................................................................................................18

Determining the Need for Levels .....................................................................................................18

Compiling Historic Level Notes and Site Sketch Maps................................................................19

Considerations for Site Conditions ..................................................................................................19

Running Levels ............................................................................................................................................19

Standards and Requirements for Gaging-Station Levels....................................................20

Circuit-Closure Error ................................................................................................................20

Assessing a Level Circuit and Adjusting Elevations .....................................................................25

Methods for Taking Foresights on Gages and the Water Surface .............................................27

Vertical Staff Gage ....................................................................................................................27

Electric Tape Gage.....................................................................................................................27

Wire-Weight Gage.....................................................................................................................30

Crest-Stage Gage ......................................................................................................................32

Inclined Staff Gage....................................................................................................................33

Water Surface ............................................................................................................................36

Resetting Gages Based on the Results of Levels..........................................................................36

Methods for Simplifying Complex Level Circuits...........................................................................36

Separating Complex Level Circuits into a Set of Sequentially Closed Simple 

Level Circuits ................................................................................................................37
vi

Running Levels—Continued ......................................................................................................................19

Methods for Simplifying Complex Level Circuits—Continued ....................................................36

Using a Suspended Weighted Steel Tape to Carry Elevation to or from a Bridge 

Structure .......................................................................................................................39

Bridge-Down Method .....................................................................................................44

Ground-Up Method ..........................................................................................................44

Office Procedures .......................................................................................................................................45

Applying Datum Corrections to Gage Height Time Series ..........................................................45

Developing a Site-Specific Historical Level Summary.................................................................45

Developing a Site Sketch Map .........................................................................................................45

Auxiliary Data to be Obtained During Level Runs ..................................................................................46

Summary........................................................................................................................................................46

References Cited..........................................................................................................................................46

Glossary.........................................................................................................................................................49

Appendix A. Fixed-Scale Test Form.......................................................................................................51

Appendix B. Peg Test Form ....................................................................................................................53

Appendix C. Level Notes Form ...............................................................................................................55

Appendix D. Historical Level Summary Form ......................................................................................57

Appendix E. Summary of Selected Requirements and Tolerances for Gaging Station Levels....59

Contents—Continued

Figures

Figure 1. Diagram of differential leveling using an engineer’s level and leveling rods......... 2

Figure 2. Photographs of optical levels ............................................................ 3

Figure 3. Photographs of electronic digital levels ................................................ 4

Figure 4. Photographs of bar-code leveling rods ................................................... 5

Figure 5. Diagram of an engineer’s level and rod scales set up for the fixed-scale test ...... 7

Figure 6. Diagram of an engineer’s level and leveling rods set up for the two-peg test ...... 7

Figure 7. Photographs of self-reading leveling rods................................................ 10

Figure 8. Scale of a self-reading Philadelphia rod ................................................ 11

Figure 9. Photographs of stand-alone and permanently attached rod levels .................. 12

Figure 10. Photograph of a steel tape with 1 pound of tension .................................... 13

Figure 11. Diagram of gage datum at a station ...................................................... 14

Figure 12. Typical reference marks .................................................................. 15

Figure 13. Extreme depth of frost map ............................................................... 16

Figure 14. Decision tree for determining if levels are needed .................................... 17

Figure 15. Complete set of level notes for a level circuit with two instrument setups ......... 21

Figure 16. Complete set of level notes for a level circuit with eight instrument setups ......... 23

Figure 17. Photographs of foresights being taken on staff plates by holding leveling rods

on nails driven into backing boards ...................................................... 28

Figure 18. Picture of an electric tape gage with a pocket rod held on a stack of coins at

the elevation of the index .................................................................. 29

Figure 19. Photographs of a wire-weight gages mounted on bridges ........................... 31
vii

Conversion Factors

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

foot (ft) 0.3048 meter (m)

Temperature in degrees Fahrenheit (°F) may be converted to degrees Celsius (°C) as follows:

°C = (°F - 32)/1.8

Figure 20. Photograph of a cantilevered wire-weight gage located to the left of a 

stilling well.................................................................................... 32

Figure 21. Stage-related wire-weight corrections determined from levels ..................... 33

Figure 22. Photograph of a crest-stage gage where the index is the bottom cap ............... 34

Figure 23. Photograph of a crest-stage gage where the index is a bolt installed through

the pipe ....................................................................................... 35

Figure 24. Photograph of an inclined staff gage installed on a streambank ..................... 35

Figure 25. Leveling diagram showing objective points in a complex circuit and level notes

for a complex leveling circuit ............................................................ 37

Figure 26. Leveling diagram and level notes showing 3 simple level circuits used to

replace 1 complex level circuit ............................................................ 39

Figure 27. Leveling diagram and level notes illustrating the use of a suspended steel tape

to carry elevations from a bridge down to a streamside gage location and from

a streamside gage location up to a bridge ............................................. 41

Figures—Continued

Tables

Table 1. Notes for gaging station levels run when all sightline distances are equal and

the instrument used has a collimation error of 0.01 foot per 100 feet ............... 9

Table 2. Notes for gaging station levels run when sightline distances between the

instrument and objects vary in the same order for two setups and the

instrument used has a collimation error of 0.01 foot per 100 feet ..................... 10

Table 3. Notes for gaging station levels run when sightline distances between the

instrument and objects vary inversely for two setups and the instrument used

has a collimation error of 0.01 foot per 100 feet.......................................... 11

Table 4. Approximate coefficients of thermal expansion for common leveling rod-scale

materials .................................................................................... 15

Table 5. Requirements for demonstrating gaging station stability .............................. 21

Table 6. Example summary of levels where the stability criterion is not met .................. 21

Table 7. Standards and select requirements for leveling ....................................... 28

Table 8. Standards and adopted requirements for gaging station levels ..................... 28

Table 9. Computed adjustment values for each instrument setup of a four-instrument

level circuit with a closure error of –0.005 foot .......................................... 30

Table 10. Technique for rounding off numbers ...................................................... 30
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Abstract

Operational procedures at U.S. Geological Survey gaging 

stations include periodic leveling checks to ensure that gages 

are accurately set to the established gage datum. Differential 

leveling techniques are used to determine elevations for 

reference marks, reference points, all gages, and the water 

surface. The techniques presented in this manual provide 

guidance on instruments and methods that ensure gagingstation levels are run to both a high precision and accuracy. 

Levels are run at gaging stations whenever differences in gage 

readings are unresolved, stations may have been damaged, or 

according to a pre-determined frequency. Engineer’s levels, 

both optical levels and electronic digital levels, are commonly 

used for gaging-station levels. Collimation tests should be 

run at least once a week for any week that levels are run, and 

the absolute value of the collimation error cannot exceed 

0.003 foot/100 feet (ft). 

An acceptable set of gaging-station levels consists of a 

minimum of two foresights, each from a different instrument 

height, taken on at least two independent reference marks, all 

reference points, all gages, and the water surface. The initial 

instrument height is determined from another independent 

reference mark, known as the origin, or base reference mark. 

The absolute value of the closure error of a leveling circuit 

must be less than or equal to 0.003 n ft, where n is the total 

number of instrument setups, and may not exceed |0.015| ft 

regardless of the number of instrument setups. Closure error 

for a leveling circuit is distributed by instrument setup and 

adjusted elevations are determined. Side shots in a level 

circuit are assessed by examining the differences between the 

adjusted first and second elevations for each objective point 

in the circuit. The absolute value of these differences must be 

less than or equal to 0.005 ft. Final elevations for objective 

points are determined by averaging the valid adjusted first and 

second elevations. If final elevations indicate that the reference 

gage is off by |0.015| ft or more, it must be reset. 

Introduction

At gaging stations where water-surface elevation or 

stage is measured, the U.S. Geological Survey (USGS) sets 

gages to read the stage above a specified reference surface 

called the gage datum (Kennedy, 1990). Equipment in most 

gaging stations measures and records stage at a frequency 

of 15 minutes. At streamflow gaging stations, discrete 

measurements of streamflow, made by hydrographers, are 

paired with a representative stage value. Over time, these 

pairings define a site-specific stage-discharge relation to 

which recorded stage values are applied to obtain a continuous 

streamflow record. To provide accurate and relevant data, it is 

imperative that gages agree with the established gage datum 

for the life of the station. To check and ensure that gages are 

properly set to gage datum, differential leveling techniques are 

used. Levels are run at gaging stations according to a standard 

set of frequency requirements, when unresolved gage reading 

differences have been identified, or when the station has been 

damaged. 

Purpose and Scope

The purpose of this manual is to document the 

procedures that should be followed when running levels 

to check that gages are set to the established gage datum. 

Leveling equipment is discussed, along with specific precision 

requirements, desired accuracy, and calibration requirements. 

The required frequency for running gaging-station levels is 

outlined and presented in an easy to follow decision tree. The 

procedure for running levels at gaging stations is described 

in detail and illustrated in example level circuits. Specific 

error tolerances for both circuit closure and objective-point 

elevation differences are presented. Methods for taking 

foresights to various types of gages are discussed, and finally, 

office procedures associated with gaging-station levels are 

outlined. This manual describes new procedures for running 

levels at gaging stations that supersede those described by the 

previous USGS Techniques of Water-Resources Investigations 

Report “Levels at Streamflow Gaging Stations” by E.J. 

Kennedy (1990). 

Levels at Gaging Stations

By Terry A. Kenney 
2 Levels at Gaging Stations

Differential Leveling and Leveling 

Equipment 

Differential leveling is the process of measuring the 

vertical difference between a point of unknown elevation and 

a point of known elevation (McCormac, 1983). By measuring 

this difference, an elevation can be determined for the point 

of unknown elevation. At gaging stations, this measurement 

is most commonly made using an engineer’s level and a 

calibrated leveling rod (fig. 1). The engineer’s level is set up 

about equidistant from the point of known elevation and the 

point(s) of unknown elevation. A shot from the engineer’s 

level is first made to a leveling rod that is held on the known 

elevation point. This reading on the leveling rod is called 

a backsight (BS). The BS, which is the vertical distance of 

the engineer’s level above this point, is added to the known 

elevation of that point to determine the elevation of the 

engineer’s level, or the height of the instrument. Shots are then 

made from the engineer’s level to the leveling rod that is held 

on point(s) of unknown elevation. These readings are called 

foresights. A foresight (FS) is the distance of the engineer’s 

level above the point and is subtracted from the instrument 

height to determine elevation. 

Differential leveling techniques are used at gaging 

stations to determine elevations for reference marks, reference 

points, gages, and the water surface. Reference marks are 

objects (for example, brass tablets, steel rods, or bolts) that 

are installed in the most stable locations near the gage and 

are used to adjust the gages as necessary to keep them in 

agreement with the gage datum (Kennedy, 1990). Reference 

points are objects (for example, bolts, nails, or screws) that 

are installed in locations to facilitate the determination of 

gage heights by measuring their distance from the water 

surface. A variety of engineer’s levels and leveling rods can be 

used to run levels at streamflow-gaging stations. The USGS 

reports stage at most gaging stations in increments of 0.01 ft. 

Therefore, gaging-station levels, which are used to verify 

that gages agree with the gage datum, must be measured at 

a higher level of precision and accuracy. Precision describes 

the closeness of one measurement to another while accuracy 

describes how close a given measurement is to the true value 

(McCormac, 1983). The precision required of gaging-station 

levels is 0.001 ft, while the desired accuracy is less than 

0.010 ft. Instruments selected for running levels at gaging 

stations must be capable of meeting these precision and 

accuracy requirements. 

Level Instruments

Many surveying instruments are available that have 

several different equipment options and can perform 

a variety of surveying tasks. Levels at gaging stations 

require measurements of vertical distance and do not need 

measurements of horizontal distance or horizontal angle. 

Engineer’s levels are the most common instruments used for 

running levels at gaging stations. Most engineer’s levels meet 

the desired accuracy of less than 0.010 ft and the required 

precision of 0.001 ft for gaging-station levels. Surveying 

technology is continually changing, and other types of 

surveying instruments, such as tilting instruments, may be 

capable of meeting these accuracy and precision standards. 

Point of

known elevation 

Point of

unknown elevation 

BS

BS Backsight

FS Foresight

FS

Leveling rod 

Instrument

EXPLANATION

Figure 1. Differential leveling using an engineer’s level and leveling rods.
Differential Leveling and Leveling Equipment 3

The techniques and methods presented in this manual provide 

guidance on using engineer’s levels that ensures gaging-station 

levels are run to a high level of precision and accuracy. Before 

other types of surveying instruments are used for running 

gaging-station levels, techniques and methods specific to those 

instruments that ensure precision and accuracy requirements 

are met must be rigorously documented. Engineer’s levels, 

which are sometimes referred to as line or spirit levels, can 

be classified in two general categories: optical levels and 

electronic digital levels. 

Optical Levels

Optical levels (fig. 2) are used to manually read the 

leveling rod that is held on an objective point. When using 

an optical level, the operator reads the value off the rod at the 

cross hair of the level. Self-reading rods used in gaging-station 

levels are graduated to 0.01 ft. Precision requirements call 

for the operator of an optical level to estimate measurements 

within 0.001 ft. The ability to accurately estimate to 0.001 ft is 

determined by the distance from the instrument to the rod, the 

magnification power of the level’s optics, and environmental 

conditions, such as the presence of heat waves. In general, the 

magnification of optical levels is about 30 times and allows 

readings as precise as 0.001 ft up to a distance of about 150 ft. 

Most modern optical levels are automatic, or self-leveling 

— the instrument levels itself precisely after being leveled 

manually with its circular (bull’s eye) level (Kennedy, 1990). 

Many older optical levels, such as the Dumpy level, are not 

self-leveling and are time-consuming to set up and level. 

These older instruments are also easily knocked out of level, 

which can introduce unquantified errors into the leveling 

circuit. 

Electronic Digital Levels

Electronic digital levels (fig. 3) automatically read a 

bar-code leveling rod (fig. 4) held on an objective point. 

When using an electronic digital level, the operator sights in 

the bar-code leveling rod using the optical view finder and 

then interrogates the instrument to make a measurement. The 

instrument then shows the value on its digital display screen. 

Many electronic digital levels are equipped with logging 

and computational functions that can be used when running 

levels. Electronic digital levels contain optical systems that 

also allow the level to be used manually. Like optical levels, 

distances to objective points and environmental conditions 

can limit the utility of electronic digital levels. Electronic 

digital levels provide some distinct advantages over optical 

levels; for example, because the instrument automatically 

reads the leveling rod, any subjectivity in manually estimating 

the measurement to 0.001 ft is removed. Similarly, the 

potential for misreading the leveling rod is eliminated when 

using electronic digital levels. When using data-logging 

features common to many electronic digital levels, errors 

associated with manually transcribing measurements can 

also be eliminated. A disadvantage of electronic digital levels 

is that the electronic nature of these instruments introduces 

the potential for system failures to occur while in the field. 

Fortunately, the optical capability serves as a backup to the 

electronic system. It is common when running levels at gaging 

stations to use a secondary device, such as a steel tape, to 

take shots on objects located in places where a rod cannot 

be placed. Further, FSs to some objects (such as wire-weight 

gages) are made by sighting in the object at the cross hair of 

the instrument. Digital systems, which require a bar-code rod, 

cannot be used for such shots. For these reasons, both the 

optical and the digital systems of electronic digital levels must 

be maintained and tested frequently. 

Figure 2. Optical levels. 
4 Levels at Gaging Stations

Figure 3. Electronic digital levels.

Parallax

A sharply focused level is important for accurate readings 

of the leveling rod. A properly focused instrument locates the 

graduations of the leveling rod at the plane of the cross hairs. 

Parallax is the relative movement of the image of the leveling 

rod with respect to the cross hairs as the observer’s eye moves. 

This is caused by the objective lens not being focused on the 

leveling rod (Kennedy, 1990). To check for parallax, slightly 

move your eye up and down while sighting in a leveling rod. If 

the rod appears to move with respect to the cross hair, parallax 

is present. Parallax usually can be eliminated by adjusting the 

objective focus. Diligence in refocusing the instrument for all 

readings and checking for parallax will eliminate erroneous 

measurements associated with improper focus. 

Checking the Engineer’s Level 

An engineer’s level is set up to measure the vertical 

distance from objective points to the level plane of the 

instrument. When applying the techniques of differential 

leveling, a properly leveled instrument is assumed to be on a 

horizontal plane at the determined elevation of the instrument 

or instrument height. Collimation error is a measurement of 

the inclination of a level’s line of sight (Breed and others, 

1970; McCormac, 1983; Kennedy, 1990), or the deviation 

from the horizontal plane. Collimation error is reported as 

a vertical deviation over a set distance, such as 0.xxx ft per 

100 ft. If horizontal distances from the instrument to each 

object that a FS or BS is taken on are known, collimation 

corrections can be computed and applied. However, levels 

at gaging stations do not require measurements of horizontal 

distance, and therefore, the collimation error of the instrument 

is preserved in all measurements and is not corrected for. 
Differential Leveling and Leveling Equipment 5

A

B

IP021599_Figure 4. Rods

Figure 4. Bar-code leveling rods. A. separated multi-section rod 

showing the self-reading rod scale on the second side.

Collimation error of an engineer’s level is determined by 

running a fixed-scale test, a two-peg test, or another accepted 

collimation test. These tests check how true the instrument 

is sighting on a horizontal plane. Given the precision with 

which gaging-station levels are run (0.001 ft) and the criteria 

that determine a valid level run at a gaging station (these are 

outlined in detail in the section on “Assessing a Level Circuit 

and Adjusted Elevation”), the tolerance for the collimation 

error of an instrument cannot exceed the absolute value (| |) 

of 0.003 ft/100 ft. Instruments possessing collimation errors 

greater than |0.003| ft/100 ft should be adjusted by qualified 

personnel or by a certified facility. Following any adjustments 

made to an instrument, a collimation test must be performed 

and documented to verify that the instrument was adjusted 

correctly. 

The criteria for an acceptable level run include a limit 

on circuit-closure error and a maximum difference between 

the first and second elevations of any objective point in the 

level circuit. Conditions exist that can cause an instrument 

with a collimation error greater than |0.003| ft/100 ft to yield 

results that meet the criteria for an acceptable level circuit and 

yet still produce final elevations that are incorrect because of 

the collimation error (see section on “Collimation Error and 

Balanced Sightline Distances”). In order to minimize errors 

associated with instrument calibration, a collimation test 

(fixed-scale, peg, or other accepted test) must be performed 

and documented at least once per week (National Oceanic 

and Atmospheric Administration, 1981; Federal Geodetic 

Control Committee, 1984) for each week that gaging-station 
6 Levels at Gaging Stations

levels are run. There should not be more than 7 days between 

a collimation test and a set of levels. If a level is found to 

have a collimation error greater than |0.003| ft/100 ft, all 

gaging-station levels run since the previous collimation 

test must be discarded and re-run. For this reason, it is 

recommended to run collimation tests more frequently. When 

electronic digital levels are used, these tests should be done for 

both the optical and digital systems. 

Fixed-Scale Test 

A fixed-scale test uses two mounted rod scales set to 

the same datum and spaced about 120 ft apart to determine 

the collimation error of an instrument (fig. 5). A fixed-scale 

test can be set up outdoors between trees, deeply set posts, 

or buildings at a reasonably level location, or can be set up 

indoors; for example, between columns or doorframes in a 

long corridor of a large building (Kennedy, 1990). To install 

the scales, place the instrument equidistant from the mounting 

locations. Install each scale such that the readings from the 

level to each scale are equal. To test the collimation of the 

level, set it up as close as possible to one scale. Read each 

scale from this location, and measure the horizontal distances 

to each scale. The length of d2 should not exceed 110 ft to 

avoid curvature and refraction effects. Horizontal distances 

can be determined using the stadia hairs of the level, the 

distance reported by an electronic digital level, or a measuring 

tape. From these readings, the collimation error can be 

computed using the equation (Kennedy, 1990):

1 2

2 1

1

2

( ) 100* , ( )

where

is the collimation error, in unit length 

per 100 unit lengths,

is the reading obtained from the near 

rod scale, in unit length,

is the reading obtained from the far 

R R

c

d d

c

R

R

  − =     −

1

2

rod scale, in unit length,

is the distance to the near rod scale,

in unit length, and

is the distance to the far rod scale, in 

unit length, which should be less 

than 110 ft.

d

d

(1)

If the absolute value of the collimation error is greater than 

0.003 ft/100 ft, the level must be adjusted. A diagram of a 

fixed-scale test showing the variables of equation 1 is shown 

in figure 5. A fixed-scale test form is provided in appendix A. 

Peg Test

A peg test does not require scales to be mounted and 

can be run with the instrument and rod in any reasonably 

level location. Several versions of peg tests are used. The 

one described here, commonly referred to as a two-peg test, 

was adapted from the USGS Geography Discipline, formerly 

known as the USGS Survey and National Mapping Division 

(Kennedy, 1990). Two pegs or marks should be established 

and spaced about 120 ft apart (fig. 6). The instrument is set up 

as close as possible to one of the pegs. Shots are taken to the 

rod held on the near peg and the far peg. Distances from the 

instrument to the pegs are measured, using the stadia hairs, 

the digital system, or a measuring tape. The instrument is then 

moved as near as possible to the other peg, and again shots 

are taken to each and distances are measured. From these 

measurements the collimation error can be computed using the 

equation (Kennedy, 1990):

1 3 2 4

2 4 1 3

1

2

( ) ( ) 100* , ( ) ( )

where

is the collimation error, in unit length 

per 100 unit lengths,

is the reading taken on the near peg 

from the first instrument setup, 

in unit length,

R R R R

c

d d d d

c

R

R

 + − +  =    + − + 

3

4

is the reading taken on the far peg 

from the first instrument setup, 

in unit length,

is the reading taken on the near peg 

from the second instrument 

setup, in unit length,

is the reading taken on th

R

R

1

2

e far peg 

from the second instrument setup, 

in unit length,

is the distance to the near peg 

from the first instrument setup, 

in unit length,

is the distance to the far peg from 

the first instrument 

d

d

3

4

setup, in unit 

length,

is the distance to the near peg from 

the second instrument setup, in 

unit length, and

is the distance to the far peg from the 

second instrument setup, in unit 

length.

d

d

(2)
Differential Leveling and Leveling Equipment 7

The average of d2 and d4 should be less than 110 ft to avoid 

curvature and refraction effects. If the absolute value of the 

collimation error is greater than 0.003 ft/100 ft, the instrument 

must be adjusted. A diagram of a peg test showing the 

variables of equation 2 is shown in figure 6. A peg test form 

is provided in appendix B and is also contained in the Gaging 

Stations Level Notes form (appendix C). 

Manufacturer-Recommended Collimation Test

Some manufacturers of level instruments provide 

a recommended method for testing and adjusting for 

collimation error. Some of the electronic digital levels 

contain preprogrammed tests and adjustment routines 

that provide for efficient and convenient collimation 

checks. Some preprogrammed checks may require the 

instrument to be located a specified distance from the rod. 

If manufacturer-recommended methods meet the 0.001-ft 

precision and the less than 0.010-ft accuracy requirements for 

gaging-station levels and report collimation error as a vertical 

deviation over a specified distance, they can be used as the 

weekly collimation test. Weekly tests are required for both the 

optical and digital systems of the electronic instruments. 

Figure 5. Engineer’s level and rod scales set up for the fixed-scale test. R, the reading obtained from a rod scale; d, the distance 

to a rod scale. Modified from Kennedy (1990). 

R1 R2

d1 d2

Fixed scale Fixed scale 

Instrument

Figure 6. Engineer’s level and leveling rods set up for the two-peg test. R, the reading obtained from a leveling rod; d, the 

distance to a peg. Modified from Kennedy (1990). 

R1

R3

R2

R4

d1 d2

d3 d4

1 Instrument

position

st

2 Instrument

position

nd

Leveling rod Leveling rod 

Peg Peg
8 Levels at Gaging Stations

Collimation Error and Balanced Sightline 

Distances 

Collimation error is a measure of the inclination of a 

level’s line of sight. Unless corrected using measurements of 

horizontal distance, this systematic error is preserved in all 

measurements made with the level. Balancing the sightline 

distances to all objects to which shots are taken minimizes 

the effects of collimation error on final elevations. However, 

balancing sightline distances in a gaging-station level circuit 

is often not feasible. Under ideal conditions when sightline 

distances are perfectly balanced, collimation error preserved 

in FSs and BSs does not affect the final computed elevations. 

An example is an instrument that has a high collimation error 

of 0.010 ft/100 ft and sightline distances that equal 100 ft 

(table 1). Each BS and FS shows an error of 0.010 ft, because 

the instrument has a collimation error of 0.010 ft/100 ft and 

the distances are all 100 ft. Even though each shot contains 

collimation error, because the horizontal distances are equal, 

the error in each shot is equal. The collimation error indicates 

that the line of sight of the level is angled downwards causing 

readings of the leveling rod to be 0.010 ft low. Because the 

errors are equal for each shot, the true differences in elevation 

between the objective points can be accurately determined, and 

therefore, the final elevations of the objective points are the 

true elevations and the circuit-closure error is 0.000 ft. If this 

were a level circuit, ideally the level would not be used because 

the absolute value of the collimation error is greater than 

|0.003| ft; however, because the sightline distances are perfectly 

balanced, the collimation error does not adversely affect 

the final elevations because the true differences in elevation 

between the objective points are determined in this circuit. 

Collimation error begins to have a profound effect 

on final elevations when sightline distances are extremely 

unbalanced. However, the effect of collimation error can be 

masked when the distances between the instrument and the 

objective points remain the same for the second instrument 

setup. Table 2 provides an example of how the effects of 

collimation error can go unnoticed. This example uses the 

same level circuit as the previous example, but sightline 

distances range from 10 to 200 ft. In this circuit, the distance 

to each of the objects remained the same for the second 

instrument setup. Errors contained in each BS and FS ranged 

from 0.001 to 0.020 ft. In a real gaging-station level circuit, 

these errors would not be known because horizontal distances 

are not measured. The two elevations acquired for each 

objective point differ from the true elevations, yet the closure 

error is 0.000 ft. In this example circuit, an instrument with 

a large unknown collimation error was used, and unless a 

comparison was made with the historical elevations, one 

would assume that the level circuit met the criteria for a 

valid level circuit of closure error and the difference between 

adjusted first and second objective point elevations (discussed 

in detail below). This introduces the potential for gages to be 

set or adjusted incorrectly during a level run. 

The sightline distances should be inverted in order to 

reveal collimation errors in a circuit consisting of unbalanced 

sightline distances, which, as shown above, can produce 

erroneous final elevations. In the previous example with 

unbalanced sightline distances, the second instrument setup 

was located in the same position as the first instrument setup. 

The level circuit appeared to be valid, as evidenced by a 

closure error of 0.000 ft and no differences between first 

and second elevations for each objective point, yet the final 

Object

Distance 

from 

instrument 

to object

BS 

error 1 BS HI FS 

error 1 FS Elevation Closure error

1st and 2nd 

elevation 

differences

True 

elevations

Difference 

from true 

elevation

RM1 (origin) 100 0.010 5.260 105.260 0.010 NA 2 100.000 NA NA 100.000 NA

RM2 100 NA NA NA 0.010 7.121 98.139 NA NA 98.139 0

RM3 100 NA NA NA 0.010 2.042 103.218 NA NA 103.218 0

TP 100 NA NA NA 0.010 3.343 101.917 NA NA 101.917 0

Instrument moved and re-leveled

TP 100 0.010 4.343 106.260 0.010 NA 101.917 NA NA 101.917 0

RM3 100 NA NA NA 0.010 3.042 103.218 NA 0 103.218 0

RM2 100 NA NA NA 0.010 8.121 98.139 NA 0 98.139 0

RM1 100 NA NA NA 0.010 6.260 100.000 0.000 NA 100.000 0

Table 1. Notes for gaging station levels run when all sightline distances are equal and the instrument used has a collimation error of 

0.01 foot per 100 feet. 

[All values are given in feet. Elevations are referenced to an arbitrary gage datum. BS, backsight; HI, height of instrument; FS, foresight; RM, reference mark; 

TP, turning point; NA, not applicable]

1

 Computed from the collimation error and the distance from the instrument to the object.

2

 Given elevation in the level circuit.
Differential Leveling and Leveling Equipment 9

Object

Distance 

from 

instrument 

to object

BS 

error 1 BS HI FS error 1 FS Elevation Closure error

1st and 2nd 

elevation 

differences

True 

elevation

Difference 

from true 

elevation

RM1 (origin) 10 0.001 5.251 105.251 0.001 NA 2 100.000 NA NA 100.000 NA

RM2 100 NA NA NA 0.010 7.121 98.130 NA NA 98.139 –0.009

RM3 150 NA NA NA 0.015 2.047 103.204 NA NA 103.218 –0.014

TP 200 NA NA NA 0.020 3.353 101.898 NA NA 101.917 –0.019

Instrument moved and re-leveled

TP 200 0.020 4.353 106.251 0.020 NA 101.898 NA NA 101.917 –0.019

RM3 150 NA NA NA 0.015 3.047 103.204 NA 0.000 103.218 –0.014

RM2 100 NA NA NA 0.010 8.121 98.130 NA 0.000 98.139 –0.009

RM1 10 NA NA NA 0.001 6.251 100.000 0.000 NA 100.000 0.000

Table 2. Notes for gaging station levels run when sightline distances between the instrument and objects vary in the same order for 

two setups and the instrument used has a collimation error of 0.01 foot per 100 feet. 

[All values are given in feet. Elevations are referenced to an arbitrary gage datum. Distances from the instrument to each object remained the same after the 

instrument was moved. BS, backsight; HI, height of instrument; FS, foresight; RM, reference mark; TP, turning point; NA, not applicable]

1

 Computed from the collimation error and the distance from the instrument to the object.

2

 Given elevation in the level circuit.

elevations were incorrect, because the FS errors caused by 

the collimation error of the instrument were equal for the two 

shots taken to each objective point. 

Table 3 shows an example of the same level circuit 

run with an instrument with the same collimation error of 

0.010 ft/100 ft, but with the sightline-distances inverted so that 

the object farthest from the initial instrument setup is closest 

to the instrument for the second setup. The range of error 

contained in the FSs and BSs associated with the collimation 

error of the instrument is similar to those in the previous 

example because the same distances were used. Again, these 

errors would not be known because the horizontal distances 

are not measured when levels are run at gaging stations. By 

inverting the sightline distances a significant closure error 

is revealed. If this example were an actual level circuit and 

the instrument had a large (unknown) collimation error, 

the sightline distances were unbalanced, but the sightline 

distances were inverted for the second instrument setup, the 

closure error criterion for a valid level circuit would have 

indicated a problem with the circuit. By inverting the sightline 

distances in a circuit that has unbalanced sightline distances, 

unknown collimation errors of an instrument can be reflected 

in the closure error. If the location of objective points and 

the locations for setting up the instrument cause unbalanced 

sightline distances to be unavoidable, it is recommended that 

these distances be inverted so that the object that was farthest 

from the first instrument setup becomes closest to the second 

instrument setup. The technique of inverting the sightline 

distances is designed to expose any unknown instrument error 

in the circuit closure error, thus alerting the user of possible 

systematic instrument error. 

Leveling Rods

Many kinds of leveling rods are available for use in 

running levels at gaging stations. Rods come in different 

lengths, many are expandable, and they are made of different 

materials. Many rods, such as the “Philadelphia” or “Chicago” 

style rods, are made of a structural material, often wood or 

fiberglass, and a rod-scale material, such as Invar or steel. 

Invar is a nickel steel alloy, commonly used for precise 

measuring equipment and has a very low coefficient of thermal 

expansion (CTE). Self- reading rods with numeric scales 

(fig. 7) are used with optical engineer’s levels, while electronic 

digital levels use leveling rods with bar-code scales (fig. 4). 

The scales of self-reading rods are typically divided into feet 

and tenths and hundredths of feet by means of alternating 

black and white spaces (McCormac, 1983) (fig. 8). Bar-code 

leveling rods often have a self-reading scale on the second 

side of the rod to use with the optical system of the instrument 

(fig. 4A). For gaging-station levels, self-reading rods must 

be graduated to 0.01 ft and readings are visually interpolated 

in order to meet the measurement-precision requirement of 

0.001 ft. Regardless of the type of engineer’s level, when 

running levels at gaging stations, it is good practice to not 

extend a rod more than about 16 ft because of the difficulty 

in holding a tall rod steady and level on an objective point. A 

leveling rod should always be used in conjunction with a rod 

level.
10 Levels at Gaging Stations

Inspection of Leveling rod 

Leveling rods should be examined regularly to ensure 

that their scales are set correctly and that their structure, 

specifically the bottom surface, is free of damage or debris. If 

a leveling rod is found to be damaged it should be removed 

from service. Thermal expansion or contraction of the material 

of the rod scale should be considered when the rod is used 

for gaging-station levels. The most common materials for 

leveling-rod scales include Invar, fiberglass, steel, and wood. 

Most rod scales are calibrated at the standard temperature of 

68°F. The entire scale length for a self-reading rod should 

be verified with an independent measuring tape from the 

bottom of the rod. Similar independent verification checks of 

all other measuring devices used when running levels should 

also be done. All verifications should be made indoors at the 

standard temperature of 68°F. Rods should be checked with 

a measuring tape at each foot marking along the length of the 

scale and at both sides of any joints between scale sections. 

If all graduations are accurate to within |0.002| ft, the rod is 

satisfactory (Kennedy, 1990). If a rod scale is found to be 

outside of the |0.002|-ft tolerance, adjust the scale if possible 

or remove the leveling rod from service. At temperatures 

greater than the calibration or standard temperature, the rod 

scale will expand causing measurements to be lower than 

they actually are, and at temperatures less than the calibration 

temperature, contraction of the rod scale will have the opposite 

effect. To minimize both errors in shots taken to leveling 

rods, and the need to apply corrections to measurements due 

to thermal expansion or contraction, it is recommended that 

leveling rods (including all devices used as rods during level 

Object

Distance 

from 

instrument 

to object

BS 

error 1 BS HI FS error 1 FS Elevation Closure error

True 

elevations

Difference 

from true 

elevation

RM1 (origin) 200 0.020 5.270 105.270 0.020 NA 2 100.000 NA 100.000 NA

RM2 150 NA NA NA 0.015 7.126 98.144 NA 98.139 0.005

RM3 100 NA NA NA 0.010 2.042 103.228 NA 103.218 0.010

TP 10 NA NA NA 0.001 3.334 101.936 NA 101.917 0.019

Instrument moved and re-leveled

TP 200 0.020 4.353 106.289 0.020 NA 101.936 NA 101.917 0.019

RM3 150 NA NA NA 0.015 3.047 103.242 NA 103.218 0.024

RM2 100 NA NA NA 0.010 8.121 98.168 NA 98.139 0.029

RM1 10 NA NA NA 0.001 6.251 100.038 -0.038 100.000 0.038

Table 3. Notes for gaging station levels run when sightline distances between the instrument and objects vary inversely for two setups 

and the instrument used has a collimation error of 0.01 foot per 100 feet. 

[All values are given in feet. Elevations are referenced to an arbitrary gage datum. BS, backsight; HI, height of instrument; FS, foresight; RM, reference mark; 

TP, turning point; NA, not applicable]

1

 Computed from the collimation error and the distance from the instrument to the object.

2

 Given elevation in the level circuit.

Figure 7. Self-reading leveling rods.
Differential Leveling and Leveling Equipment 11

runs) be used at temperatures near the calibration temperature 

of the rod scale whenever possible. Determining the need 

for and computing temperature corrections is discussed 

in the section on “Correcting for Rod Scale Expansion or

Contraction Due to Temperature Variations.”

Proper Care and Use of a Rod Level

It is important that the leveling rod be held vertical 

when levels are run at gaging stations. To ensure that the 

leveling rod is vertical, a rod level should always be used. 

Rod levels are either stand alone (fig. 9A) and are used with 

multiple leveling rods, or permanently attached and dedicated 

to a single leveling rod (fig. 9B). The stand-alone rod levels 

consist of a bull’s eye bubble level mounted on a 90-degree 

or square channel material. The 90-degree channel allows the 

rod level to be held along the vertical axis of either a square or 

round leveling rod. Rod levels should be checked for plumb 

regularly and adjusted if necessary. To test the rod level, any 

corner such as a wall corner that has been verified to be level 

Figure 8. Scale of a self-reading Philadelphia rod.

This reading is 2.140 ft

Feet are marked by

red numbers. 

Tenths of feet are

represented by

black numbers. 

The x.x00 and x.x50

marks on strips are

pointed. 

This reading is 2.050 ft

Small red numbers 

indicate the 

associated foot 

sections

This reading is 2.127 ft

Foot marks are represented

with long strips 

Hundredths of feet are represented 

by the top and bottom of black 

strips. The top of strips represent 

even numbers and the bottom of 

strips represent odd numbers.

IP021599_Figure 8. Reading the rod.

using a carpenter’s level can be used. Most rod levels have 

screws that are used to adjust how the bubble level is seated 

in its mount. When checking for plumb, the bubble should be 

examined for expansion. If the bubble has expanded beyond 

the circular level indicator line, the rod level should be 

discarded. 

Correcting for Rod Scale Expansion or 

Contraction Due to Temperature Variations

At constant temperatures, measurements can be precisely 

corrected for expansion and contraction of the rod-scale 

material due to temperature variation. All materials have 

a determined coefficient of thermal expansion (CTE), and 

the CTE for the rod scale should be readily available from 

the manufacturer of the rod. Material compositions of rod 

scales vary, particularly for fiberglass rods; therefore, it is 

recommended that the rod scale CTE be obtained directly 

from the manufacturer. For reference, CTE ranges for some 

common leveling rod-scale materials are provided in table 4. 
12 Levels at Gaging Stations

The rod-scale material-specific CTE, the standard temperature, 

and the rod-scale temperature at the time the leveling rod is 

used for a measurement are used in the following equation to 

determine the correction for expansion or contraction due to 

temperature variation: 

CTE * ( ),

where

is the correction for expansion or 

contraction due to temperature 

variation,in unit length,

CTE is the rod scale material specific 

coefficient of thermal expansion,

in 1/ degrees Fah

t o

t

C L T T

C

= −

− −

renheit or 

1/ degrees Celsius (examples 

contained in table 4),

is the length of the measurement, 

in unit length,

is the rod scale temperature at the 

time of the measurement, in 

degrees Fahrenheit or de

L

T −

grees 

Celsius, and

is the standard temperature, in 

degrees Fahrenheit (usually 68 F)

or degrees Celsius (usually 20 C).

To

°

°

(3)

The rod-scale temperature, T, can be measured directly by an 

infrared thermistor, or if the rod is not in the direct sun, air 

temperature can be used as a surrogate for the rod temperature. 

To determine whether corrections are needed for a given level 

circuit, first compute or estimate the maximum elevation 

difference between the origin reference mark and any point in 

the level circuit. This is the difference between the elevation 

of the origin and either the highest or the lowest point that a 

FS will be taken on. Substitute this difference for L in equation 

3 and compute Ct. If the absolute value of Ct is greater than 

0.003, all FSs and BSs of the circuit should be corrected for 

temperature-related expansion or contraction. Individual FSs 

and BSs taken during a level run can be corrected by adding 

the rod reading to the computed expansion or contraction 

correction value by using the equation

corrected read read

corrected

read

(CTE * ( )),

where

is the sight (backsight or foresight) 

corrected for expansion or contraction 

due to temperature variation, in unit 

length,

is the sight (backsight

o S S S T T

S

S

= + −

 or foresight) 

obtained from the leveling rod, in 

unit length,

CTE is the rod-scale material-specific 

coefficient of thermal expansion, in 

1/degrees Fahrenheit or 1/degrees 

Celsius (examples contained in table 4),

is the rod-scale temperature at the time 

of the measurement, in degrees 

Fahrenheit or degrees Celsius, and

is the standard temperature, in degrees 

Fahrenheit (usually 68°F) or degrees 

Cel

o

T

T

sius (usually 20°C).

(4)

A B

Figure 9. Stand-alone A. and permanently attached B. rod levels. 
Establishment of Gage Datum 13

Rod-scale 

material

Approximate coefficient of thermal expansion 

in length/length/degree 

Fahrenheit (1/°F) 

in length/length/degree Celsius 

(1/°C)

Invar 1 0.8 × 10–6 1.4 × 10–6

Wood 1 2.1 × 10–6 to 2.8 × 10–6 3.8 × 10–6 to 5 × 10–6

Steel tape 2 6.45 × 10–6 12 × 10–6

Fiberglass 1 17 ×10–6 to 22 × 10–6 30.6 ×10–6 to 39.6 × 10–6

Table 4. Approximate coefficients of thermal expansion for 

common leveling rod-scale materials.

1

 From http://www.engineeringtoolbox.com/linear-expansioncoefficients-d_95.html.

2

 From Breed, Hosmer, and Bone (1970).

Considerations for Secondary Devices Used for 

Vertical Measurements

When running levels at gaging stations, a secondary 

measuring device other than a leveling rod might be required 

to take FSs on gages or to carry elevations over a large vertical 

distance. The CTE for the materials that compose secondary 

devices used in a level circuit should be obtained and used to 

correct FSs and BSs when appropriate. Any secondary devices 

used must meet the precision and accuracy requirements of 

gaging-station levels. When using a measuring tape to carry 

elevations between a bridge deck and a low water bank, 

the tape should be weighted so that the tape is not stretched 

and the tension applied by the weight should ensure that the 

tape is suspended vertically. Figure 10 is a photograph of 

a steel tape with a 1-pound weight that is commonly used 

for measuring water levels in wells. This same equipment 

can be used for tape-down measurements or for carrying 

elevations over a large vertical distance. The practical limit of 

measurement precision for this tape-down method is ±0.01 ft 

(U.S. Geological Survey, 1980). If used when running levels 

at gaging stations to carry elevations between a bridge deck 

and a low water bank, the FSs or BSs should be estimated to 

0.001 ft. 

Wind can have a profound effect on suspended measuring 

devices, particularly those suspended from a bridge. Wind 

will cause a suspended tape to bend and artificially increase 

the vertical distance the tape is spanning. Wind effects cannot 

be accounted for, so vertical measurements using a suspended 

measuring tape affected by wind should be avoided. 

Establishment of Gage Datum

The gage datum is the reference surface at a gaging 

station to which all gages are set (Corbett and others, 1943) 

(fig. 11). The reference surface is represented by the 0.000‐ft 

mark on the gages and should be located well below the 

streambed, below any likely gage height of zero flow (GZF). 

The gage datum is usually an arbitrary reference but it can 

be tied to an established datum, such as the North American 

Vertical Datum of 1988 (NAVD 88), through the use of 

established benchmarks. When a gaging station is being 

established where no station has existed previously, the gage 

datum should be set low enough to ensure that the lowest 

gage height ever likely to be recorded while the stream is 

flowing is at least 1 ft (Kennedy, 1990). When establishing 

the gage datum, the current water depth over the hydraulic 

control of the gage pool should be known and the potential 

maximum streambed scour should be considered. Experience 

with stream channels of similar materials, geometry, and 

basin characteristics may provide some indication of the 

potential magnitude of streambed scour. Because negative 

gage heights are undesirable, the gage datum reference surface 

that is selected should be well below the estimated maximum 

scour depth to avoid negative gage heights over the life of the 

station. 

Figure 10. Steel tape with 1 pound of tension.

IP021599_Figure 10. Steel weight tape
14 Levels at Gaging Stations

Gage datum, 0.000 feet 

Gage height 

Elevation of

reference mark 

ELEVATION IN GAGE DATUM 

IP021599_Figure 11. Gage datum 

Staff

gage

Water

surface

Reference mark

Figure 11. Gage datum at a station.

Installation of Reference Marks

Reference marks are installed and elevations are 

determined in the gage datum when gaging stations are 

established. Stable and permanent reference marks facilitate 

maintaining that the gages at a station are set to the gage 

datum over the life of the station. Typical reference marks 

include gaging-station tablets cemented and drilled into rock 

outcrops, bolts drilled into masonry walls, steel rods driven 

and cemented into stable ground, and other earth anchors 

located below frost lines (fig. 12). Reference marks provide 

a means for recovering the gage datum if the gaging station 

is destroyed or is removed and reactivated sometime later. 

The most stable locations for reference marks are often rock 

outcrops and substantial masonry structures. Bridges often 

provide a stable environment for reference marks; however, 

bridges that sway or have a high traffic volume may not be 

desirable because precise measurements are difficult to make 

with a level and rod. In the absence of rock outcrops and 

stable masonry structures, reference marks can be anchored at 

depths below the local frost depth in stable soils (fig. 13). The 

methods used by the U.S. Department of Commerce, National 

Oceanic and Atmospheric Administration, and National Ocean 

Survey for establishing geodetic benchmarks (Floyd, 1978) 

can provide guidance for installing reference marks. Clay soils 

that expand and contract during seasonal variations in soil 

moisture should be avoided (Kennedy, 1990).

Gaging stations should have a minimum of three 

independent reference marks; more than three are 

recommended whenever possible in case one (or more) 

proves to be unstable or is destroyed. These marks should be 

located independently of one another. For example, if one or 

more reference marks are installed on a bridge structure, at 

least two others should be installed somewhere away from 

(and independent of) the bridge. Furthermore, reference 

marks should be located independently of any gage, gage 

infrastructure, or instream control structure, because reference 

marks are used to track vertical changes over time to the gages 

and to the other marks. If reference marks and gages are not 

independent of one another, determining vertical differences 

becomes difficult. 

When locating reference marks, other considerations 

should be made. Access to reference marks during flood 

conditions is important to verify that the recorder is 

accurately set to the gage datum in case the reference gage 

is inaccessible. Ideally, at least one reference mark should 

be located outside of the floodplain. When determining 

the locations of reference marks, running levels should be 

considered and, if possible, marks should be located so that 

sightline distances are balanced and levels can be run in an 

efficient manner. The potential for damage or destruction 

of reference marks related to construction, specifically road 

construction or future land development, should be considered. 

Finally, reference marks should be easily found from 

descriptive statements in the station description document. As 

discussed later, site sketches showing the location of reference 

marks should be prepared. If vegetation is likely to obscure 

marks over time, exact measurements from local objects 

should be provided and a witness post should be installed. 
Establishment of Gage Datum 15

Figure 12. Typical reference marks.

IP021599_Figure 12. Setting marks

Modified from Kennedy (1990).

Gaging-station tablet

cemented in hole drilled

in rock outcrop

3/8-inch brass bolt and washer

in masonry wall

3/8-in. reinforcing

steel

Steel rod in

concrete base

Earth anchor

4-inch PVC pipe

4-inch PVC pipe

lining

Concrete

base

3-4 inches 

Below frost

line or at

a minimum

of 3 feet deep

Below frost

line or at

a minimum

of 3 feet deep

gravel

Clean gravel
16 Levels at Gaging Stations

Referencing a Gage Datum to an Established 

Datum

It is desirable to reference an arbitrary gage datum to 

a commonly used established datum, such as NAVD 88, at 

all gaging stations. This is especially important at stations 

used by the National Weather Service for flood forecasting 

or at locations where flood profiles are likely to be needed 

(Kennedy, 1990). Generally, two methods are used to tie a 

gage datum to an established datum - running a traditional 

survey line and using a survey grade Global Positioning 

System (GPS). 

The first method is to run a traditional survey line 

consisting of a closed level circuit or a series of closed 

level circuits from an established survey control point to 

the origin or base reference mark of a gaging station. The 

National Geodetic Survey (NGS) maintains a database 

of established and maintained survey control points or 

benchmarks throughout the United States that are available 

at http://www.ngs.noaa.gov/cgi-bin/datasheet.prl. This 

database can be used to find the location of the nearest 

control point and its elevation in NAVD 88. The distance 

between the gaging station and an established survey control 

point may be considerable and therefore the survey line 

will consist of a number of different instrument setups and 

turning points. Techniques for running survey lines from 

established benchmarks outlined by the National Oceanic and 

Atmospheric Administration (Schomaker and Berry, 1981) 

should be used to tie gage datums to established datums. 

The second method is to use a survey-grade GPS to 

determine the elevation of a gaging station reference mark 

above an established datum. Usually, the GPS is set up 

over the reference mark of interest and allowed to collect 

positional data over a set time interval. The uncertainty of 

the positional data decreases with increased occupation time 

over the reference mark. GPS technology and therefore the 

recommended methods for collecting positional data using 

a GPS, is continually changing. Follow currently accepted 

agency guidelines and methods for determining elevations 

with a survey-grade GPS. 

After determining the elevation of a gaging station 

reference mark above an established datum, the gage datum 

can then be referenced, or tied, to the already established 

datum. The gage datum is the 0.000 ft reference surface at 

a gaging station. To determine the elevation of this surface 

above the desired established datum, subtract the elevation of 

the reference mark above the gage datum from the elevation 

for the same reference mark above the established datum. All 

other reference marks, reference points, and gages can then be 

assigned elevations above the established datum by adding the 

elevation of the gage datum above the established datum to 

their elevation above the gage datum. 

Figure 13. Extreme depth of frost map. 

0.49 0.82 1.64 2.46 3.28 4.10

4.92 5.74

5.74

4.92

4.10

3.28

3.28

2.46

1.64

0.82

0.49

0

0

0

0

4.10

7.38 7.38

7.38

7.38

8.20 8.20

8.20

8.20

6.56 6.56

EXPLANATION

Line of equal depth

of possible frozen

soil during winter 

Modified from Floyd (1978).

CARIBOU

AUGUSTA

CONCORD

BOSTON

NEW YORK

PHILADELPHIA

WASHINGTON

NORFOLK ROANOKE

RALEIGH

WILMINGTON

COLUMBIA

ATLANTA

ALBANY

MACON

MIAMI FT MEYERS

ORLANDO

GAINSVILLE

PENSACOLA TALLAHASSEE

BILOXI

MERIDIAN

EL DORADO OXFORD

LITTLE ROCK

FAYETTEVILLE

SPRINGFIELD

COLUMBIA

OTTUMWA

CEDAR

RAPIDS

MASON

CITY

MANKATO

DULUTH

BEMIDJI

DEVILS

LAKE

FARGO

MINOT

WILLISTON GLENDIVE

HAVRE

MILES CITY BILLINGS

GREAT

FALLS HELENA

BUTTE SALMON

LEWISTON

SPOKANE

OMAK

MISSOULA

KALISPELL

MINNEAPOLIS

DES MOINES

FORT

DODGE

JACKSON

BATON

ROUGE

CORPUS

CHRISTI

GALVESTON

SHREVEPORT

DEL RIO

AUSTIN

WACO

DALLAS

LAWTON

TULSA

WICHITA

TOPEKA

ST JOSEPH

ENID

HAYS

LINCOLN

NORFOLK

MITCHELL

PIERRE

ABERDEEN

BISMARK

LEAD

NORTH PLATTE

CHADRON CHEYENNE

CASPER

GILLETTE

CODY SHERIDAN

JACKSON

ROCK SPRINGS

DODGE CITY

LAMAR

DENVER CRAIG

PUEBLO

GRAND

JUNCTION

DURANGO

ABILENE

PECOS

TUCSON

MIAMI

PHOENIX

PRESCOTT

FLAGSTAFF KINGMAN

LAS VEGAS

ELY

RENO AUSTIN

REDDING

LAKEVIEW

LONGVIEW YAKIMA

SEATTLE

BEND

SALEM

BURNS

BAKER

PENDLETON

MEDFORD

ELKO

WINNEMUCCA

TONOPAH

GRAND CANYON

CEDAR CITY

SAN DIEGO

LOS

ANGELES

BAKERSFIELD

SAN FRANCISCO

SACRAMENTO

FRESNO

SAN

BERNARDINO

GREEN

RIVER

IDAHO

FALLS

TWIN

FALLS

BOISE

PROVO

LOGAN

RICHFIELD

LAS CURCES

ROSWELL

PORTALES

ALBUQUERQUE

GALLUP SANTA FE

RATON

SILVER

CITY

LUBBOCK

AMARILLO

MONTGOMERY

BIRMINGHAM

FLORENCE

NASHVILLE

KNOXVILLE

LOUIS VILLE 

DAYTON 

COLUMBUS 

CANTON LIMA 

KALAMAZOO 

DETROIT 

GRAND

RAPIDS 

GRAYLING

MARQUETTE

WAUSAU

ELY

EAU CLAIRE

LA CROSSE

MADISON

CHICAGO

AURORA

PEORIA

DECATUR

MT VERNON

MARION

INDIANAPOLIS 

BOWLING GREEN

LEXINGTON

CHARLESTON

ASHEVILLE

RICHMOND

ALBANY SYRACUSE

BUFFALO

MONTPIELIER

SCRANTON

READING ERIE

PITTSBURGH

CLARKSBURG

CLARKSBURG

CHARLESTON
Frequency of Gaging-Station Levels 17

Frequency of Gaging-Station Levels

Gaging-station locations and environments vary widely 

as do the factors affecting the stability of reference marks and 

gages. The relative stability of a gaging station needs to be 

considered when determining the frequency at which levels 

should be run. For example, a station affected by ground 

freezing and thawing may require levels to be run annually 

in the spring, while a station with gages and reference 

marks fixed to bedrock that has demonstrated stability may 

require levels to be run only every 5 years. Gaging-station 

levels should be run frequently enough to capture any gage 

movement that may occur. A decision tree is provided (fig. 14) 

to help determine when levels need to be run at a gaging 

station. 

Are there unresolved gage

reading differences? 

Has stability at the station

been demonstrated and

documented (see table 5)? 

Did the level run from last year

show that the primary reference

gage elevation differs from the

gage datum enough to

require a correction? 

Have more than 3 years passed

since the last complete set

of levels were run?

Are less than 3 sets of

annual levels associated with

the current reference gage?

Has an event occurred that

may have disturbed the gaging

station (flood, construction,

vandalism, other)? 

Have more than 5 years passed

since the last complete set

of levels were run?

Run levels 

Levels are

not needed

YES 

YES 

YES 

YES 

YES 

YES 

YES 

NO 

NO 

NO 

NO 

NO 

NO 

NO 

Figure 14. Decision tree for determining if levels are needed.
18 Levels at Gaging Stations

In addition to running levels according to the sitespecific determined frequency, levels should be run whenever 

a difference in gage readings cannot be resolved or damage 

is suspected. Suspected damage to a gage may be associated 

with flooding, ice, vandalism, nearby construction, or other 

events that may disturb some part of the gaging station. A new 

gage installation (including the installation of a new reference 

gage at an existing station) should have three sets of annual 

levels, including the initial establishment set, acquired during 

the first 3 years of operation. After the first three sets of levels 

are acquired, a level frequency of once every 3 years may be 

adopted. A level frequency of at least every 5 years may be 

adopted if stability is shown to exist. Stability is demonstrated 

if the maximum elevation difference from the initial elevations 

for the primary reference gage and three reference marks is 

less than |0.015| ft for a minimum of five sets of levels and a 

period of at least 10 years (table 5). This means that for any 

set of levels run during a 10-year period, the elevations for 

the primary reference gage and the three reference marks 

(these must be the same three marks measured over the 

minimum five consecutive sets of levels) cannot differ from 

the initial elevation (as determined at the beginning of that 

10-year period) by |0.015| ft or more. If elevations for any 

of these four objective points change by |0.015| ft or more, 

the site is not considered stable and the frequency that levels 

are run cannot exceed 3 years. An example of a summary of 

levels for a station where the stability criterion was not met 

is shown in table 6. If during any level run, regardless of the 

determined frequency of levels, the elevation of the primary 

reference gage differs from the gage datum by |0.015| ft or 

more (requiring the gage to be reset and the recorded and 

(or) observed stage values to be corrected), levels must be 

run again the following year. If no correction is required the 

following year, the level frequency can be reset to a 3-year 

cycle, until stability can be demonstrated. 

Preparation for Running Levels

Running levels at gaging stations is important for 

accurate measurements of stage and subsequent computation 

of streamflow over the life of the station. Uncertainties related 

to measurement error during the leveling process can be 

minimized if adequate preparations are made. Equipment 

should be properly tested and calibrated, and site-specific 

information important to the leveling process should be 

gathered. Crews assigned to run levels should be properly 

trained in the procedures explained in this manual and be 

familiar with the equipment they will be using. Levels should 

be run in favorable weather conditions and site-specific 

environmental conditions; safety hazards that may be 

encountered should be understood and discussed before 

traveling to the site. 

Determining the Need for Levels

The first step in preparing to run levels is to determine 

whether or not levels are needed at a specific gaging station. 

The need for levels should be assessed using the decision 

tree (fig. 14) at least once a year for each station and more 

frequently if differences in gage readings cannot be resolved 

or damage to the gage is suspected. Offices are encouraged to 

implement a tracking system to determine when levels are due 

to be run at each of their stations. It is beneficial operationally 

Minimum years that a reference gage and three 

reference marks have been active

10

Minimum number of sets of levels 5

Maximum difference in elevation from the initial 

elevation (as determined at the beginning of a 

10-year time period), in feet, of a reference gage 

and three reference marks 

<|0.015|

Table 5. Requirements for demonstrating gaging station stability.

Date

Elevations

Differences in elevation 

Remarks

Reference gage

RM1 

(given) RM2 RM3

Water 

surface 

found

Water 

surface 

left

Adj. 

made

RM1 

(given) RM2 RM3

04/01/1999 12.525 8.623 10.226 4.234 4.234 NA NA NA NA

04/14/2000 12.525 8.621 10.228 4.325 4.325 0 0 –0.002 0.002

03/28/2001 12.525 8.622 10.224 3.999 3.999 0 0 –0.001 –0.002

04/02/2004 12.525 8.635 10.242 4.177 4.177 0 0 0.012 0.016 RM3 different by 0.016 ft

04/15/2007 12.525 8.635 10.240 4.440 4.440 0 0 0.012 0.014

04/02/2010 12.525 8.635 10.244 4.013 4.013 0 0 0.012 0.018 RM3 different by 0.018 ft

Table 6. Example summary of levels where the stability criterion is not met.

[All values are given in feet. Elevations are referenced to an arbitrary gage datum. RM, reference mark; adj., adjustment; NA, not applicable; ft, foot]
Running Levels 19

for an office to schedule level runs for about one-third of its 

stations each year. This will ensure that the leveling workload 

in an office is balanced and will allow additional stations 

that have an immediate need for levels to be run to be more 

readily incorporated. The time of year that levels are run at 

stations should follow the likely factors that cause changes 

to the reference gage. For example, if stations are susceptible 

to frost heave, it is best to run levels as soon as possible after 

the spring thaw, ideally at temperatures near the standard 

temperature of the leveling rod-scale material (usually 68°F). 

Compiling Historic Level Notes and Site Sketch 

Maps

Past level notes for the station where levels are to be 

run should be reviewed. These notes show the previous 

composition of the level circuit(s), which can assist in 

planning the new level circuit(s). The past level notes can be 

used to determine the maximum elevation difference between 

the origin and any point in the circuit (L in equation 3). 

This information is needed to determine whether or not 

the leveling-rod scale must be corrected for expansion or 

contraction. The historic level summary should be examined 

for any stability issues related to reference marks and 

reference points. Finally, copies of the past set of level notes 

and the site sketch map should be made and taken to the site. 

Considerations for Site Conditions

The expected environmental conditions at the site where 

levels are to be run should be considered. The river stage 

should be amenable to determining accurate water-surface 

elevations from the low water bank and taking FSs to all 

reference marks, reference points, and gages. Levels should 

be run in favorable weather conditions; wind, rain, and 

snow should be avoided if at all possible. Air temperature 

and its affect on leveling-rod scales needs to be considered. 

Vegetation located in sightlines is undesirable and may be 

avoided through maintenance or running levels during times 

when leaves are off trees and shrubs. The survey crew should 

be briefed on all safety hazards specific to the site where the 

levels are to be run. These hazards should be documented and 

available in the site-specific job hazard analysis document. 

Running Levels 

After determining that levels are needed at a gaging 

station and making the necessary preparations, levels should 

be run following the procedures outlined below. Ideally, the 

leveling instrument should be set up in a location that allows 

for balanced sightline distances to the objects to be shot from 

this instrument setup. The instrument should be placed upon 

a firmly set tripod in a stable location at a height that allows 

for a comfortable position for the instrument operator and 

accurate readings of the rod on the objects to be shot. The 

instrument should be properly leveled using the leveling 

tools of the instrument. Before beginning the level run, the 

time should be noted and all of the gages and recorders at the 

station should be read. The temperature of the leveling rod 

should be equilibrated to the air temperature. Rod-scale and 

air temperatures should be measured and noted. The rod-scale 

temperature can be measured directly using an infrared 

thermistor, or if the rod is not in the direct sun, air temperature 

can be used for the rod-scale temperature. Equation 3 should 

be used to determine the maximum expansion or contraction 

correction for the level circuit. For this determination, L in 

equation 3 should be set equal to the maximum elevation 

difference expected between the origin and either the highest 

or the lowest point to be surveyed. If the absolute value of the 

correction for expansion or contraction due to temperature 

variation is greater than 0.003 ft, all FSs and BSs of the level 

circuit should be corrected using equation 4. 

To describe the procedures for running levels at a gaging 

station, a very simple level circuit with two instrument 

setups is presented here. Determine the order in which the 

reference marks, reference points, gages, water surface, and 

other objects are to be shot. The initial instrument height 

is determined from a BS to the origin, as determined from 

historical levels at the station. The BS value, measured to 

the nearest 0.001 ft, should be corrected for expansion or 

contraction of the rod scale if needed and then added to the 

given elevation of the origin reference mark to obtain the 

instrument height. Foresights read to the nearest 0.001 ft 

should then be taken to the reference marks, reference points, 

gages, water surface, and other objects that were planned 

to be shot from the current instrument setup. If appropriate, 

FSs should be corrected for temperature-related expansion or 

contraction of the rod scale. The corrected FS values should be 

subtracted from the corresponding instrument height to obtain 

elevations in the gage datum. All gages and recorders should 

be read and noted with corresponding times just before or 

immediately after the FS on the water surface. 

After taking a FS on all objective points that were 

planned to be shot from the current instrument setup, a turning 

point should be established. The turning point should be a 

stable, independent object that is not an objective point of 

the level circuit. This point will be used to establish a new 

instrument height from which second elevations will be 

determined for the objects previously shot. Take a FS on 

the turning point, and if necessary, correct for expansion 

or contraction, and then determine its elevation. Following 

this FS, the instrument should be moved and re-leveled in 

a location that again balances the distances to the objective 

points. However, if the sightline distances to the objective 

points were unbalanced in the initial instrument location, the 

new instrument location should invert the sightline distances 

by being set up closer to the objective point that was farthest 

from the initial setup. Take a BS to the turning point, and if 

required, correct for expansion or contraction of the rod scale 
20 Levels at Gaging Stations

and add it to the determined elevation of the turning point to 

determine a new instrument height. From this new instrument 

height, take FSs to the same objective points, correcting for 

expansion or contraction if conditions require it, and obtain 

second elevations for each. To close the leveling circuit, 

the final shot should be a FS taken on the origin reference 

mark that, if necessary, should be corrected for expansion or 

contraction of the rod scale. 

If a FS on the water surface cannot be taken directly 

using the leveling rod, a measurement using a measuring tape 

may be made from a reference point from which two FSs 

were taken. The length of the tape up or down measurement 

should be as short as possible by measuring from a temporary 

or permanent reference point on the low water bank from 

which two FSs were taken. Tape downs from a bridge or 

similar structure should not be used to obtain the water-surface 

elevation during a level run. 

The procedure presented above describes a simple gaging 

station level circuit in which all FSs to objective points can 

be taken from a single instrument setup. To help illustrate the 

procedures for running levels at gaging stations, a complete 

set of level notes from a level circuit that required only two 

instrument setups is shown in figure 15. The turning point 

that was used to determine the second instrument height was 

not an objective point of the circuit. In order to ensure that 

two FSs were taken on each objective point of the circuit, an 

independent turning point was required. If an objective point 

was used as the turning point in this circuit, that objective 

point would not have two FSs taken from two different 

instrument heights from which elevations could be compared. 

Quite often, level circuits are more complex than the one 

presented above and require multiple instrument setups, and 

thus more than one turning point, to be able to take two FSs 

on all objective points. Intermediate turning points, those used 

to carry elevations to different instrument setup locations on 

either the “out” or the “back” parts of the level circuit, can 

be objective points if, when the circuit is completed, they 

have two FSs taken on them. Because these objective points 

are being used as turning points, they will also have at least 

one BS taken on them as well. However, regardless of circuit 

complexity, the turning point ascertained after determining 

all first elevations and before determining second elevations 

must be independent (not one of the objective points). This 

independent turning point marks the termination of the out 

part and the beginning of the back part of the level circuit, or 

loop. To help illustrate the procedures for running levels at 

gaging stations using multiple turning points, a complete set of 

level notes from a level circuit that required eight instrument 

setups is provided in figure 16. A level notes form, available 

for printing and downloading, is provided in appendix C. 

Standards and Requirements for Gaging-Station 

Levels

Three orders of vertical control classification are accepted 

by the Federal Geodetic Control Committee (1984). In 

this classification scheme, first- and second-order leveling 

can be applied to the vertical control for National geodetic 

surveys, and second- and third-order leveling can be applied 

to engineering projects of varying size and scope. Selected 

requirements associated with the three classifications that 

are pertinent to gaging-station levels are presented in table 7. 

Gaging-station levels generally are classified as thirdorder levels with the adoption of some first- and secondorder requirements. Table 8 shows adopted standards and 

requirements for gaging-station levels. 

Circuit-Closure Error 

The closure error of a leveling circuit is the difference 

between the given elevation for the origin reference mark 

and the elevation for that reference mark associated with the 

final instrument height of the level circuit. Closure error is 

computed as the given elevation minus the final elevation. 

Assigned vertical closure-error limits define the desired 

and acceptable accuracy, or error, for the intended use of 

the survey data. The random acquisition of error in a level 

circuit tends to vary with the square root of the number of 

opportunities or instrument setups (Davis and others, 1966). 

Therefore, a vertical closure-error limit for differential levels 

can be determined by multiplying an acceptable uncertainty 

constant by the square root of the total number of setups. This 

acceptable uncertainty depends on how the data will be used 

and should be amenable to the desired accuracy and precision 

requirements of the levels. For gaging-station levels, the 

uncertainty constant is 0.003 ft (Kennedy, 1990). The vertical 

closure-error limit for gaging station level circuits is computed 

using the equation

limit

limit

0.003 ,

where

is the closure-error limit, in feet, and

is the total number of instrument 

setups in a level circuit.

CE n

CE

n

= (5)
Running Levels 

21

Figure 15. Complete set of level notes for a level circuit with two instrument setups.

System type(s) circle: optical digital

Party (inst.) (rod)

INSTRUMENT

Make/Model:Serial Number:Collimation (optical):

Average of d2 and d4 should be less than 110 ft Collimation test date:

d R Collimation (digital):

1 Collimation test date:2 ROD3 Scale material: ______ CTE ___________ 1/F° or 1/C°

CTE conversions: (1/°F * 1.8 = 1/°C) and ((1/°C)/1.8 = 1/°F) 4

Temperature (T): Rod:___ °F or °C; Air:___ °F or °C d RStandard temp (To): 68°F or 20°C or other: ____ 1

Given/Origin elevation: _________ 2Max elevation of objective point: ________ 3

Min elevation of objective point: _______

c = _______________ft/100ftc = _______________ft/100ft

as foundas found 4

Max elevation difference (L): _____ ADJUSTMENT (level remains set up at 2 and sighted at R4) Ct = CTE * L(T-To) C = ________ t

Other devices used as rod (list): Repeat collimation test

after adjustment Adjust cross hair to: Time WS Ref. Rod taped (circle): yes no

NOTES or SKETCHES: Rod level used (circle): yes no

GAGE RESET

Ref.

FoundLeft

WEATHER:NOTES:

Circuit

No.

No. of

Inst.

Setups

(N) 

Allowable

closure

0.003 *

(N)^.5 

Closure

Error

(CE)

CE/N

(take to

0.0001)

CLOSURE ERROR COMPUTATIONS

Computed by: Checked by: Date: 

SUMMARY OF OBJECTIVE POINTS

Object Diff. (1st Elev. - 2nd

Elev.) 

Final Elev.

(Ave. of

Adj. Elev.)

GAGE READINGS

Station Name

Date

Station Number:

U.S. DEPARTMENT OF THE INTERIOR

U.S. Geological Survey

Gaging Station Level Notes

R1

R3

R2

R4

d1 d2

d3 d4

1

2

Collimation = c = 100 * ( R1 + R3 ) - ( R2 + R4 ) ( d2 + d4 ) - ( d1 + d3 )

c = 100 * ( 4.930 + 5.415 ) - ( 5.772 + 4.572 ) ( 137.5 + 73.5 ) - ( 10 + 74 )c = 100 * ( + ) - ( + ) ( + ) - ( + )

PEG TEST OF ENGINEER'S LEVEL

Make/Model:

OPTICAL SYSTEM

DIGITAL SYSTEM

Adj. 1st

Elev. 

Adj. 2nd

Elev. 

IP021599_Fig15_Simple notes_FB

Strawberry River at Pinnacles near Fruitland, UtahApril 20, 2009 MLF RJE

RM2 Given 4.160

4.930 10 RM1 2.788 2.785 0.003 2.786

5.772 137.5 RM4 6.200 6.197 0.003 6.198

5.415 74 CSG 3.820 3.821 -0.001 3.820 Invar 0.8*10^-6

0.0008 4.572 73.5 OG 2.552 2.548 0.004 2.550

75 75

4.160

6.200

1.520

3.157

<0.0001

none

DCP OG

OG

13:05 1.52

13:15 1.517 1.52

13:25 1.515 1.52 DCP

13:30 1.52

1.52

1.52

1.521.52 1.52 1.52

1.52 1.52

1 2 0.0042 -0.003 -0.0015 Clear, sunny, warm

No changes needed or made.

MLF RJE April 22, 2009

Leitz Sokkisha Optical 

354635

0.0008

April 20,2009

09285900
22

Levels at Gaging Stations

CORRECTED CORRECTED

BS FS

BS+(CTE*

BS*(T-T0))

FS+(CTE*

FS*(T-T0))

CLOSUREERROR

ADJUSTMENT

TO HI

ADJUSTED

1st

ELEVATION 

ADJUSTED

2nd

ELEVATION 

OLD

ELEVATION

Remarks ELEVATION Remarks OBJECT BS FS HEIGHT

OF 

INSTRUMENT

(HI)

FINAL

ELEVATION

DIFFERENCE

(AE1

-AE2)

5.0178.335

9.177

6.388

4.160

2.7886.200

2.7886.200

3.8202.552

2.786

4.160

6.1983.820 3.8222.550 2.550

1.516

1.5122.5483.8216.1972.785

2.7896.2013.8212.5531.5170.982

2.9765.3566.6247.6608.195

7.8026.7665.4933.1176.5295.154

1.5152.5513.8246.2002.7884.163

9.317

RM2RM1RM4CSGOG

@13:15@13:25

WS

TP1

Moved Instrument

TP1WSOGCSGRM4RM1RM2

CLOSURE ERROR = 4.160 - 4.163 = -0.003

CElimit = |0.003*(√2setups)| = |0.004| 

Given; Cap 15' NE gage

Cap in concrete pier 

Bolt in tree 10' SE gage

Index top lower cap

Given, OriginNail at 2.55 Ref. gage (staff plate)

Held on rock, +/-.01 OG=1.52, DCP=1.52

Held on rock, +/-.01Nail at 2.55

OG=1.52, DCP=1.52

-0.0015-0.0030

-

0.0030.003

0.001

0.004

IP021599_Figure 15 Simple notes_IS Figure 15. Continued.
Running Levels 

23

Figure 16. Complete set of level notes for a level circuit with eight instrument setups.

System type(s) circle: optical digital

Party (inst.) (rod)

INSTRUMENT

Make/Model:Serial Number:Collimation (optical):

Average of d2 and d4 should be less than 110 ft Collimation test date:

d R Collimation (digital):

1 Collimation test date:2 ROD

3 Scale material: ______ CTE ___________ 1/F° or 1/C°

CTE conversions: (1/°F * 1.8 = 1/°C) and ((1/°C)/1.8 = 1/°F) 4

Temperature (T): Rod:___ °F or °C; Air:___ °F or °C d RStandard temp (To): 68°F or 20°C or other: ____ 1

Given/Origin elevation: _________ 2Max elevation of objective point: ________ 3

Min elevation of objective point: _______

c = _______________ft/100ft as foundc = _______________ft/100ft as found 4

Max elevation difference (L):_________ ADJUSTMENT (level remains set up at 2 and sighted at R4) Ct = CTE * L(T-To) C = ________ t

Other devices used as rod (list): Repeat collimation test

after adjustment Adjust cross hair to: Time WS Ref. Rod taped (circle): yes no

NOTES or SKETCHES: Rod level used (circle): yes no

GAGE RESET

Ref.

FoundLeft

WEATHER:NOTES:

Circuit

No.

No. of

Inst.

Setups

(N) 

Allowable

closure

0.003 *

(N)^.5 

Closure

Error

(CE)

CE/N

(take to

0.0001)

CLOSURE ERROR COMPUTATIONS

Computed by: Checked by: Date: 

SUMMARY OF OBJECTIVE POINTS

Object Diff. (1st Elev. - 2nd

Elev.) 

Final Elev.

(Ave. of

Adj. Elev.)

GAGE READINGS

Station Name

Date

Station Number:

U.S. DEPARTMENT OF THE INTERIOR

U.S. Geological Survey

Gaging Station Level Notes

R1

R3

R2

R4

d1 d2

d3 d4

1

2

Collimation = c = 100 * ( R1 + R3 ) - ( R2 + R4 ) ( d2 + d4 ) - ( d1 + d3 )

c = 100 * ( 4.834 + 4.715 ) - ( 2.643 + 6.901 ) ( 109.4 + 108.9 ) - ( 9.6 + 10.2 )

( 4.940 + 4.559 ) - ( 2.748 + 6.747 )

( 109.1 + 108.7 ) - ( 9.9 + 10.2 ) c = 100 * 

PEG TEST OF ENGINEER'S LEVEL

Make/Model:

OPTICAL SYSTEM

DIGITAL SYSTEM

Adj. 1st

Elev. 

Adj. 2nd

Elev. 

IP021599_Fig16_Simple notes_FB

Green River near Jensen, Utah

April 19, 2009 MLF TAK

15.410

25.68516.29026.471

25.68816.29026.472

-0.003-

0.0000.001

25.68616.29026.472

Given RM1

RM3RM4

ChkBar Fiberglass 20*10^-6

0.0025 6.901 108.9

4.715 10.22.643 109.44.834 9.6

--

70 70

4.940 9.9

15.410

2.748 109.1

26.472

4.559 10.2

3.114 0.002 6.747 108.7

12.296

<0.0005

none

DCP WW

WW DCP

12:05

12:30

3.11 3.113.11 3.11

1 8 0.008 -0.004 Clear, sunny, warm

No changes needed or made.

TopCon DL-102C

1202

09261000

MLF TAK April 22, 2009

0.0025

April 19, 2009

0.0020

April 19, 2009

3.11 3.11

12:55 3.11 3.11

3.11 3.11 3.114

12:35 3.11 3.11 3.114

-0.0005
24

Levels at Gaging Stations

CORRECTED CORRECTED

BS FS

BS+(CTE*

BS*(T-T0))

FS+(CTE*

FS*(T-T0))

CLOSUREERROR

ADJUSTMENT

TO HI

ADJUSTED

1st

ELEVATION 

ADJUSTED

2nd

ELEVATION 

OLD

ELEVATION

Remarks ELEVATION Remarks OBJECT BS FS HEIGHT

OF 

INSTRUMENT

(HI)

FINAL

ELEVATION

DIFFERENCE

(AE1

-AE2)

15.410

16.290 16.290 16.290

10.02616.29015.410

25.685

25.688

26.471

25.68626.472

25.69026.470

26.472

9.9633.113

3.112

0.000

-0.0005-0.0010

-0.003-0.001

-0.0020-0.0040-0.0025-0.0035-0.0030-0.0015

15.410 3.111

1.5524.6169.8808.6705.0692.4171.682

18.521

9.964

10.028

10.109

18.292

25.46428.59028.69221.344

RM1

16.291 2.230 RM4

8.412 TP19 WW

3.114 6.850 @12:30

@12:35

WS

5.412 4.552 TP2

3.114 6.914 WS

10.028

0

0 WW

8.412 1.616 TP1

16.292 2.000 RM4

16.794 1.498 TP323.521 1.943 TP4

25.688 2.902 RM3

26.474 2.116 CHKBR26.27526.475

2.315 TP52.217 CHKBR

25.691 3.001 RM319.662 9.030 TP6

15.414 5.930 RM1

Closure Error is (15.410-15.414) =-0.004

Acceptable closure is 0.003*√8 = |0.008| ft

Brass cap rt. Anchor blockTop of bolt d/s leg A-framescrewdriverDirect read 

+/- 0.02

Given, OriginDial =9.96Dial =10.03

WW(ref) = 3.11, DCP=3.11WW(ref) = 3.11, DCP=3.11

Direct read

+/- 0.02

Brass cap us right brdg abutDial = 26.47Dial = 26.47

.964

IP021599_Figure 16 Comp notes_IS Figure 16. Continued.
Running Levels 25

Order First Second Third

Class I II I II

Recommended uses Basic framework of the National 

Network and metropolitan 

area control. Regional crustal 

movement studies. Extensive 

engineering projects. Support for 

subsidiary surveys.

Secondary framework of the 

National Network 

and metropolitan 

area control. Local 

crustal movement 

studies. Large 

engineering 

projects. Tidal 

boundary reference. Support 

for lower order 

surveys.

Densification within 

the National 

Network. Rapid 

subsidence studies. 

Local engineering 

projects. 

Topographic 

mapping. 

Small-scale 

topographic 

mapping. 

Establishing 

gradients in 

mountainous areas. 

Small engineering 

projects. May 

or may not be 

adjusted to the 

National Network.

Maximum collimation error 

(ft/100 ft)

0.005 0.005 0.005 0.005 0.01

Maximum time interval (days)

between collimation error 

determinations

1 1 1 1 7

Rod level verticality maintained 

to within (ft)

10 10 10 10 10

Maximum sight length (ft) 164 197 197 230 295

Minimum ground clearance of 

line of sight (ft)

1.6 1.6 1.6 1.6 1.6

Maximum circuit misclosure 

(circuit-closure error limit) (ft)

|0.010√D| |0.013√D| |0.020√D| |0.026√D| |0.039√D|

Table 7. Standards and select requirements for leveling. 

[Modified from Federal Geodetic Control Committee (1984) and McCormac (1983). D is distance in kilometers. ft, foot]

Adopted 

standards and 

requirments

Order Third

Use Gaging station 

levels

Maximum collimation error (ft/100 ft) |0.003|

Maximum time interval (days) between 

collimation error determinations

7

Rod level verticality maintained to within (ft) 10

Maximum sight length (ft) 164

Minimum ground clearance of line of sight (ft) 1.6

Maximum circuit misclosure (circuit-closure 

error limit) (ft)

|0.003√n|

Table 8. Standards and adopted requirements for gaging station 

levels. 

[n is the total number of instrument setups in a circuit. ft, foot]

Assessing a Level Circuit and Adjusting 

Elevations

An acceptable set of gaging-station levels has two FSs, 

each from a different instrument height, to a minimum of 

two independent reference marks, all reference points, all 

gages, and the water surface. A third independent reference 

mark is the origin, or starting point, with a given elevation 

from which the initial instrument height is determined. The 

origin reference mark is considered to be the most stable and 

should be explicitly identified as such in the current station 

description for the gaging station. The first criterion for a valid 

level circuit is that the absolute value of the closure error for 

the leveling circuit must be less than or equal to the closure 

error limit computed using equation 5 and must not exceed 

|0.015| ft regardless of the number of instrument setups. If the 

closure error exceeds the closure error limit, the entire level 

circuit must be re-run. 
26 Levels at Gaging Stations

Following the completion of a level circuit for which 

the closure error falls within the specified limit, elevations of 

objective points are adjusted by distributing the determined 

closure error of the circuit to each instrument setup. Closure 

error is associated with instrument setups made throughout 

a leveling circuit and instrument (collimation) error if 

present and sightline distances are not balanced. Closure 

error is introduced into a circuit during the determination of 

instrument heights because of errors in FS readings taken 

on the turning points, or errors in BS readings taken on the 

turning points or origin. Closure error is not affected by side 

shots, shots taken on objective points from a given instrument 

setup. In the levels methods and techniques presented in 

this manual, the specific instrument setup(s) where error is 

incurred cannot be determined; therefore, closure error is 

distributed in a manner that assumes the error accumulates 

with each instrument setup. The methods described by Thomas 

and Jackson (1981) should be used to adjust the elevations 

of objective points by distributing the circuit closure error 

uniformly to the different instrument setups of the level 

circuit. To determine adjusted elevations for any objective 

point in a circuit, use the equation 

[( )( / )] ,

where

is the adjusted elevation of an objective 

point,

is the sequential instrument setup 

number associated with the 

foresight taken to that objective 

point (the fir

adj seq unadj

adj

seq

E HI CE n E

E

HI

= +

st instrument setup is 1,

second instrument setup is 2),

is the closure error for the circuit 

computed as the given origin 

elevation minus the final elevation 

of the origin from the final 

instrument s

CE

etup,

is the total number of instrument setups

in the circuit, and

is the unadjusted elevation of the 

objective point.

unadj

n

E

(6)

Table 9 gives an example of a four-instrument setup level 

circuit where a closure error of -0.005 ft is distributed to the 

four instrument setups and the applied error is accumulated 

with the sequence of instrument setups. The absolute value of 

the closure error of the circuit, 0.005 ft, is less than the closure 

error limit, |0.006| ft, computed using equation 5. The closure 

error of -0.005 ft shows that the final elevation of the origin 

reference mark was 0.005 ft higher than the given elevation. 

The adjustment, calculated by dividing the closure error by the 

number of instrument setups and multiplying by the sequential 

instrument setup number should be rounded to a precision of 

0.0001 ft. This adjustment should be added to the unadjusted 

elevations to obtain adjusted elevations that should then be 

rounded to a precision of 0.001 ft. Rounding should follow the 

technique shown in table 10 (U.S. Geological Survey, 1991). 

The closure-error criterion of a valid level circuit 

discussed above ensures that systematic errors associated with 

instrument setups are not introduced into a leveling circuit. 

The second criterion of a valid level circuit is that the absolute 

value of the difference between the adjusted first and second 

elevations for each objective point must be less than or equal 

to 0.005 ft. This criterion, based on the examination of side 

shots, ensures that systematic errors specific to each objective 

point are not present in their final elevations. If the absolute 

value of the difference between the adjusted first and second 

elevations for an objective point is greater than 0.005 ft, two 

new FSs, each from independent instrument heights, must 

be taken. A new closure error for this abbreviated circuit 

is determined, and the closure error must fall within the 

previously specified tolerance. The new elevations of the 

objective points are adjusted, as described above, and the 

absolute value of the difference between the adjusted first and 

second elevations must be less than or equal to 0.005 ft. 

Elevations for some objects are determined by sighting 

them in at the cross hair of the level, such as the bottom of a 

wire weight or an electric tape gage weight. When running 

levels to these types of objects, they are either lowered or 

raised until they are at the cross hair of the level. Therefore, 

determined elevations, which are equal to the instrument 

height, vary from one instrument setup to another. For this 

reason, these types of objects are not subject to the elevation 

difference criterion. Although it may be possible to compare 

the difference between the height of the instrument and the 

dial reading for the 2 FSs, the 0.01 ft precision of the gages 

prohibits a comparison that can be held to the |0.005| ft 

tolerance. Because taking precise FSs on the water surface is 

often difficult, water-surface elevations are not subject to the 

|0.005| ft elevation difference criterion as long as uncertainties 

in the water-surface measurements are noted (for example, 

Sequential 

instrument 

setup 

Amount to add 

to initial elevations 

(foot)

1 –0.0012

2 –0.0025

3 –0.0038

4 –0.0050

Table 9. Computed adjustment values for each instrument setup 

of a four-instrument level circuit with a closure error of –0.005 

foot.

[Closure error of circuit: –0.005 foot. The final elevation of the origin 

reference mark was 0.005 foot higher than the given elevation]
Running Levels 27

± 0.01). Final elevations for objective points are calculated 

by averaging the adjusted first and second elevations. The 

elevation for the origin reference mark is still the given value. 

To properly determine whether a gage needs to be reset, and 

if it is reset, to ensure that it is reset correctly, levels must 

be computed and checked in the field. The level note form 

provided in appendix C adheres to the gaging-station levels 

procedures and requirements presented here. 

Methods for Taking Foresights on Gages and the 

Water Surface

Two FSs must be taken to all gages and the water surface 

from two different instrument heights when levels are run at a 

gaging station. Levels are run at gaging stations to make sure 

that all gages are properly set and accurately reporting watersurface elevation in the gage datum. Therefore, these FSs 

are the most important shots taken. When gages do not agree 

with the gage datum, the survey crew must accurately reset 

the affected gages. Many different types of gages are used at 

gaging stations, and various techniques are used to take a FS 

on each gage type and the water surface. Some of the more 

common techniques for taking a FS on gages and the water 

surface are presented below. 

Vertical Staff Gage 

Vertical staff gages are perhaps the type of gage most 

commonly found at gaging stations. Staff gages are placed 

in direct contact with the water. They can be placed inside 

stilling wells or attached to various objects on the banks of a 

stream. Stations on streams that have a large range in stage 

often have a series of staff plates that are installed in vertical 

intervals along a sloping bank. While it is feasible to directly 

read staff plates using an engineer’s level, this technique is 

usually not practical. The most common method for taking a 

FS on a staff plate is to establish a reference point by partially 

driving a nail or screw into the staff plate backing next to the 

plate. The elevation of the reference point, in relation to the 

staff plate, should be read from the plate and noted. To take the 

FS, a rod should be held level on the reference point (fig. 17). 

For the staff plate to agree with the gage datum, the elevation 

of the reference point, read using the plate, should equal the 

elevation computed from the FS. Staff gages consisting of 

multiple plate sections should have a FS taken on all sections 

or a measuring tape can be used to measure from a location 

where the FSs have been taken on one plate section, such as a 

reference point, to each of the other plate sections. For obvious 

reasons, staff plates must be installed vertically. A carpenter’s 

level should be used to verify that plates are vertical when 

levels are run. 

Electric Tape Gage

Electric tape gages (ETG) are used in stilling wells to 

safely measure the water surface inside the well without 

entering the confined space. Electric tape gages are 

permanently mounted on a shelf inside the stilling well. 

These gages consist of a spooled graduated steel tape with an 

attached weight and an analog voltage readout (fig. 18). The 

gage is connected to a battery terminal, and a lead wire from 

another battery terminal is extended below the water surface in 

the well. To obtain a gage reading, the ETG weight is spooled 

down to the water, and when the bottom of the weight contacts 

the water surface, the circuit is closed and the voltage dial 

responds. The graduated tape is read at a reading index, called 

the ETG index, marked by a line and located just above the 

surface on which it is mounted. 

Example Original number Rounded number

1 0.32891 0.329 If the first of the discarded digits is greater than 5, add 1 to the digit representing the 

third significant figure

2 47,543 47,500 If the first of the discarded digits is less than 5, leave the digit representing the third 

significant figure unchanged

3 11.65 11.6 If the first of the discarded digits is 5, all the following digits are zero, and the digit 

representing the third significant figure is even, leave the digit unchanged. 

4 22.75 22.8 If the first of the discarded digits is 5, all the following digits are zero, and the digit 

representing the third significant figure is odd, round the digit up to the next even 

number. 

5 18.05 18.0 If the first of the discarded digits is 5, all the following digits are zero, and the digit 

representing the third significant figure is zero, leave the digit unchanged.

6 18.051 18.1 If the 5 is followed by any of the digits 1 through 9, add 1 to the digit representing the 

third significant figure

Table 10. Technique for rounding off numbers. 

[Modified from Hansen (1991)]
28 Levels at Gaging Stations

Figure 17. Foresights being taken on staff plates 

by holding leveling rods on nails driven into backing 

boards.
Running Levels 29

Figure 18. Electric tape gage with a pocket rod held on a stack of coins at the elevation of 

the index.

IP021599_Figure 18. ETC_coins

Electric tape gage

index
30 Levels at Gaging Stations

When running levels at a station with an ETG, FSs 

should be taken on the ETG index, and when feasible, FSs 

should also be taken on the bottom of the weight. A slight gap 

exists between the ETG index and the object on which it is 

mounted. When taking a FS on the ETG index, be sure that the 

rod, which is likely a carpenter’s ruler, a measuring tape, or a 

“pocket rod,” is set at the level of the ETG index. A stack of 

coins on the shelf can usually be used as a stable place to hold 

the rod and obtain an accurate FS (fig. 18). 

Foresights taken on the bottom of the ETG weight should 

be taken with the weight as close to the water surface as 

possible. However, unless the stilling well is equipped with a 

clean-out door, the FS on the bottom of the weight will likely 

be taken with the weight located just below the instrument 

shelf. The level should be set up so that the instrument height 

is at least one length of the weight lower than the ETG index. 

To take a FS, the ETG weight should be lowered until the 

bottom of the weight is at the cross hairs of the level. While 

the weight is at this location, the gage height should be read 

at the ETG index. If the ETG agrees with the gage datum, the 

instrument height will equal the reading at the ETG index. 

Electric tape gages are susceptible to any movement of the 

shelter they are installed in. They are also sensitive to any 

movement of the shelf that they are mounted on. Adding 

weight, such as a larger battery, to an instrument shelf may 

cause the shelf to flex downwards, which could change the 

elevation of the ETG index and cause incorrect gage height 

readings. 

Wire-Weight Gage

Wire-weight gages are most often installed on bridge 

structures (fig. 19), but can also be installed on a cantilever on 

a stream bank (fig. 20). Suspended above the water surface, 

wire-weight gages are weighted cables that are spooled on 

a calibrated drum. To take a gage reading, the weighted 

cable is lowered until the bottom of the weight contacts the 

water surface. The gage-height value is read from the digital 

counter and the calibrated drum of the wire-weight gage. The 

contact with the water surface is determined visually, which 

introduces uncertainty associated with the sightline distance, 

lighting, and the surface characteristics of the water. When 

running levels to a wire-weight gage, a FS should be taken on 

both the check bar (fig. 19) and the bottom of the weight near 

the water surface. For cantilever installations (only), FSs on 

the check bar are not required as they are not associated with 

the elevation of the weight of the wire-weight gage; however, 

tracking elevations of the check bar of a cantilevered wireweight gage may be useful in determining stability of the 

cantilever structure. 

Foresights taken on the check bar of a traditional wireweight gage are taken with the check bar in its outer position 

(away from the object it is mounted on) using a leveling rod. 

Foresights taken on the bottom of the weight for all wireweight gages should be taken from an instrument set up on 

the low water bank, such that the FS is taken with the wire 

weight as close to the water surface as possible. The wire 

weight should be lowered until the bottom of the weight is at 

the cross hairs of the level. With the weight at this location, 

the gage height should be read from the digital counter and 

the calibrated drum. If the wire-weight gage agrees with the 

gage datum, the instrument height will equal the reading of the 

wire-weight gage. 

A wire-weight gage has several potential sources of error 

to be considered when checking it (Kennedy, 1990). The drum 

is calibrated so that every rotation accounts for a distance 

traveled by the weight. For this reason, the cable should be 

evenly spooled on the drum. Wire weights tend to spin as 

they are lowered and raised. If the cable is not allowed time 

to unwind, it will be twisted and thus shorter. This can lead 

to incorrect gage heights. After the cable reaches its proper 

length, the wire weight should be spooled back up onto the 

drum. The weight should be placed on the check bar, and the 

associated check bar reading should be noted. The weight can 

then be lowered to the water surface to determine the gage 

height. These procedures should be followed when taking a FS 

on the bottom of the weight as well. 

Variations in the drum and the cable diameter of a wireweight gage can cause calibration errors (Kennedy, 1990). 

Gage height readings from a wire-weight gage represent a 

count of the number of revolutions made by the calibrated 

drum before the weight contacts the water surface. Any 

differences between the actual diameters of the drum and 

the cable, and the diameters programmed into the revolution 

counter will accumulate as the drum revolves. Fortunately, 

because of this accumulation, these calibration errors are linear 

and can be corrected for once recognized and documented. 

At most gaging stations, wire-weight gages should be 

set to accurately read low water elevations. If a wire-weight 

gage is properly set to read low water elevations, a calibration 

error can be recognized if the check bar reading differs from 

the check bar elevation determined from levels. By preparing 

a graph of the wire-weight gage readings for the bottom of 

the weight and the check bar and the elevations from levels, 

corrections for gage height readings at different stages can be 

determined (fig. 21). The equation for this linear relation is 

shown in figure 21 and can be used to compute the correction 

to the gage reading by inputting the wire-weight reading. 

When such corrections are defined, a plot and an equation 

similar to these should be prepared and stored at the gaging 

station. The sources of error for wire-weight gages discussed 

here are usually negligible for wire-weight gages mounted less 

than 15 ft above the water, and increase with greater distances 

(Kennedy, 1990). 
Running Levels 31

Digital

counter

Calibrations

on drum

Drum with

spooled

cable

Check bar

Weight

Figure 19. Wire-weight gages mounted on bridges.
32 Levels at Gaging Stations

Figure 20. Cantilevered wire-weight gage located to the left of a stilling well.

IP021599_Figure 20. Cantilever wire-weight.

Crest-Stage Gage

Crest-stage gages (CSG) record the peak water-surface 

elevation, or gage height, as a high water mark consisting 

most often of a cork line on a stick inside a pipe. A vertically 

installed pipe, which is capped on the top and bottom, 

communicates with stream water by a set of holes drilled into 

a cap on the bottom of the pipe. As the water-surface elevation 

decreases, the maximum level of the water is recorded by a 

cork line on a stick contained within the pipe. To recover the 

recorded maximum instantaneous gage height, the stick is 

removed from the pipe and the distance from the bottom or the 

top of the stick to the cork line is measured. If the index of the 

CSG is located at the bottom, the stick is measured up from 

the bottom. If the index is at the top, the stick is measured 

from the top. 

Foresights taken on the index of a CSG can usually be 

taken with a leveling rod. The location where the leveling rod 

is held depends on location of the index. Often, the bottom 

cap has a metal stud attached in the center where the stick 

rests (fig. 22 inset). The elevation of this stud is equal to the 

cap surface where the threads begin, and the FS is taken by 

holding the rod on the top of the bottom cap (fig. 22). A bolt 

installed through the pipe near the bottom provides a surface 
Running Levels 33

Figure 21. Stage-related wire-weight corrections determined from levels.

Correction value = 0.024 - 0.0024*Wire-weight gage reading 

5

-0.1 -0.08 -0.06 -0.04 -0.02 0.0 0.02

10

15

20

25

30

35

40

45

50

IP021599_Figure 21. WW correction

WIRE-WEIGHT GAGE READING, IN FEET

CORRECTION TO WIRE-WEIGHT GAGE READING, IN FEET

46.27 46.182 -0.088

9.89 9.890 0

Object Wire-weight

gage reading,

in feet

Wire-weight

checkbar

Wire-weight

at height of

instrument

Elevation

from levels,

in feet

Correction to

wire-weight gage

reading, in feet

for the stick to rest on and is an excellent index to hold a rod 

on to take a FS (fig. 23). For both of these CSG configurations, 

the maximum stage is determined by measuring from the 

bottom of the stick to the cork line high water mark and then 

adding that value to the elevation of the CSG index. Some 

CSGs have the index on the top of the stick. Foresights are 

taken by holding the leveling rod on top of the stick at the 

index, and the maximum stage is determined by measuring 

from the top of the stick down to the cork line high water mark 

and then subtracting that value from the elevation of the CSG 

index.

Inclined Staff Gage

Inclined staff gages are permanent structures that are 

installed at about the same slope as the streambank (fig. 24). 

The scale along the incline is set to represent the water-surface 

elevation. The slope of these gages minimizes damage caused 

by debris and ice. The permanence of the inclined staff gages 

makes them very difficult to adjust if they disagree with 

the gage datum. Foresights are taken on several foot marks 

throughout the gage’s range, from one or more instrument 

heights (Kennedy, 1990). If the inclined staff gage is a 

composite of multiple slopes, at least 2 FSs must be taken on 

each slope. 
34 Levels at Gaging Stations

Figure 22. Crest-stage gage where the index is the bottom cap. Inset 

photograph of the bottom cap showing the internal stud.

IP021599_Figure 22. Rising level auto gages.
Running Levels 35

Figure 23. Crest-stage gage where the index is a bolt 

installed through the pipe.

Figure 24. Inclined staff gage installed on a streambank.

IP021599_Figure 23. Rising level auto gages.

Bolt

8.30 feet

8.20 feet

8.10 feet

8.00 feet
36 Levels at Gaging Stations

Water Surface

Traditional gaging stations are established to measure the 

elevation of the water surface. When running levels at gaging 

stations, two FSs are required to be taken on the water surface. 

These FSs can be difficult to obtain because the water surface 

is not a firm object and therefore a rod cannot be held directly 

on it. Also, the water surface may not be vertically stable at 

the time and (or) location of the measurement. There are three 

techniques that can assist in taking precise and accurate FSs 

on the water surface. For streams that are shallow along the 

banks, a stable object such as a rock, a stake, or a screwdriver 

driven to the water surface, or even the wading boot of the 

rod man can be used as a stable location to hold a leveling 

rod. These objects will have to be positioned in a manner 

that allows a visual determination of the water surface and 

firm placement of the bottom of the leveling rod. A second 

technique that can be used if stream conditions (including 

depth and velocity) allow is to hold the rod on the streambed, 

take a FS of the elevation of the streambed, and manually 

read the depth of the water off of the rod. To determine the 

elevation of the water surface, compute the elevation of 

the streambed and add the water depth to it. Finally, if the 

conditions of the stream do not allow both of these techniques, 

a reference point (either a temporary or a permanent one) can 

be established as close as possible to the water surface. From 

this reference point, a measuring tape can be used to tape 

down to the water surface. An estimate of the uncertainty in 

the FS taken on the water surface should always be provided 

by the rod man and included in the remarks on the level notes. 

Resetting Gages Based on the Results of Levels

The main purpose of running levels at gaging stations is 

to verify that gages, specifically the primary reference gage, 

are properly set to read the stage in the gage datum. The 

primary reference gage should be reset if the absolute value of 

the difference between the elevation reading of the reference 

gage and the gage datum is greater than or equal to 0.015 ft. 

Before the gage is reset, the level circuit containing the gage 

must be completed. A complete level circuit is one in which 

circuit closure error is less than or equal to the established 

limit, adjustments associated with closure error have been 

applied, differences between the adjusted first and second 

elevations of objective points have been computed, and it 

has been verified that these differences meet the established 

criteria. Final elevations for all gages are determined and the 

computations for the circuit are checked. If the reference gage 

needs to be reset, it should be reset on the basis of the final 

computed elevation. 

The survey crew must verify and document that the gage 

was reset correctly. There are three verification methods: (1) 

an abbreviated level circuit consisting of a closed objective 

point (part of a completed and valid level circuit), the gage, 

and a turning point (2) a tape down from a reference point 

that was part of a completed and valid circuit; and (3) an 

independent check of the water-surface elevation and gage 

reading. Resetting auxiliary gages (those other than the 

primary reference gage) also is recommended when the 

difference between the elevation reading of the auxiliary gage 

and the gage datum is greater than or equal to |0.015| ft. 

Methods for Simplifying Complex Level Circuits

Complex level circuits for the purposes of this discussion 

are level circuits that require more than two instrument 

setups to obtain two independent FSs for all objective points. 

In a complex circuit, elevation must be carried from one 

instrument setup location to another by using intermediate 

turning points to establish more than two instrument heights. 

After obtaining all first FSs and before obtaining second FSs, 

an independent turning point that is not an objective point is 

required to establish the first instrument height from which 

second FSs will be taken. In contrast, simple level circuits 

have only two instrument setups, with the second instrument 

height being established from an independent turning point 

that is not an objective point to take second FSs. 

The error tolerances set forth for circuit closure and for 

differences between adjusted first and second elevations are 

strict. The method described by Thomas and Jackson (1981) 

for distributing closure error by instrument setup assumes that 

error is evenly accumulated through the level circuit. While 

this assumption may not always be true, this method provides 

the best means available for distributing closure error because 

it is difficult, if not impossible, to determine the specific 

instrument setups where errors are incurred within a leveling 

circuit. Unfortunately, this method of error distribution, and 

its underlying assumption, can lead to incorrect adjustments to 

valid elevations. 

Level circuits with more than two instrument setups 

have more opportunity to incur error in both closure and final 

elevations. By limiting the number of instrument setups in a 

circuit, the potential for error can be minimized. In most cases, 

by implementing some of the techniques discussed below, a 

level circuit consisting of more than two instrument setups 

can be broken down into a series of independent level circuits, 

each having a minimum of two instrument setups. 
Running Levels 37

Separating Complex Level Circuits into a Set of 

Sequentially Closed Simple Level Circuits 

Most complex level circuits can be broken down into 

a series of simple level circuits that are closed in sequence. 

A simple level circuit requires a turning point that is not an 

objective point, and a complex level circuit needs to carry 

elevation using an objective point(s) or an intermediate turning 

point(s), and requires at least one turning point that is not an 

objective point. 

Level notes and a leveling diagram for a complex level 

circuit are shown in figure 25. Shots from a single instrument 

setup cannot be taken on all of the objective points of this 

circuit: RM1, RM2, RM3, the ETG index, the bottom of the 

ETG weight, the outside staff gage, and the water surface. 

RM1 (the origin) and RM2 are located up a slope above the 

other objective points at the site. This level circuit uses an 

intermediate turning point (TP1) to carry elevation down to 

the remaining part of the circuit. From the second instrument 

setup, FSs are taken on the ETG index, the outside staff 

gage, the water surface and RM3. RM3 is then used as an 

intermediate turning point to establish the third instrument 

height, which is needed to take a FS on the bottom of the ETG 

weight. An independent turning point is established (TP2) and 

the circuit is shot in reverse order back to RM1. 

The complex level circuit described above can be broken 

down into three simple level circuits that are sequentially 

closed. Level notes and a leveling diagram for the three simple 

level circuits are shown in figure 26. The first simple circuit 

consists of objective points RM1, RM2, and TRM1. RM1 

is the origin and is used as the starting point to set the initial 

instrument height. A temporary reference mark, TRM1, is 

established in the first simple level circuit to carry elevation 

to the second circuit. Note that the location of TRM1 is the 

same as that of the first turning point in the complex leveling 

circuit diagram discussed above. An independent turning 

point (TP1) is established to ensure that two FSs are taken on 

each of the objective points for the first level circuit, which 

includes RM2 and TRM1. This first circuit is closed with the 

second FS taken on RM1. The second simple circuit consists 

of objective points TRM1, RM3, the ETG index, the outside 

staff gage, and the water surface. The initial height of the 

instrument for the second circuit is determined from TRM1 

which had two FSs taken on it in the first circuit. The second 

instrument height is determined from an independent turning 

point (TP2). This circuit is closed with the second FS taken on 

TRM1. Finally, the shots to the bottom of the ETG weight are 

made from a final simple circuit in which the initial instrument 

height is determined from RM3, which had two FSs taken on 

it in the second circuit. The second instrument height for the 

third simple circuit is determined from an independent turning 

point (TP3), and the circuit is closed with the second FS taken 

on RM3

Figure 25. A. Leveling diagram showing objective points in a complex circuit and B. level notes for a complex leveling circuit. 

2,5 3,4

1,6

RM3

RM2

RM1

TP1,

TP3

TP2

Staff

gage

Gaging

station

Water

Surface

ETindex

EXPLANATION

RM

TP

Reference mark

Turning point

ETindex

ETweight

1,2

Electric tape index

Electric tape weight

Represents the sequential

 instrument setup number

ETWeight

A
38

Levels at Gaging Stations

DIFFERENCE

(AE1

-AE2)

CORRECTED CORRECTED

BS FS

BS+(CTE*

BS*(T-T0))

FS+(CTE*

FS*(T-T0))

CLOSUREERROR

ADJUSTMENT

TO HI

ADJUSTED

1st

ELEVATION 

ADJUSTED

2nd

ELEVATION 

OLD

ELEVATION

Remarks ELEVATION Remarks OBJECT BS FS HEIGHT

OF 

INSTRUMENT

(HI)

FINAL

ELEVATION

4.655

17.023

14.144

14.14412.23312.300

14.14617.10329.499

14.146

30.666 26.011 26.011

25.23515.47015.21010.34012.30010.34015.21015.47025.23526.011

9.550

25.235

14.144

25.235 25.235

15.21010.34012.300

15.21010.34012.300

15.21010.34012.300

9.550

9.550

14.146

12.300

10.34015.21025.235

9.550

1.553

1.844

1.846

7.553

6.7631.8931.6334.2643.488

1.913

14.029

4.803

5.431

1.813

6.6837.4734.723

1.911

15.196

RM1RM2TP1

Moved Instrument

TP1

0.00000.00000.0000

0.0000.0000.0000.000

OG

@13:20

@13:30

WSRM3

Moved Instrument

RM3TP2

Moved Instrument

TP2RM3

Moved Instrument

RM3 0.0000WSOG

3PT

Moved Instrument

TP3 0.0000RM2RM1

CLOSURE ERROR = 26.011- 26.011 = 0.000

+/- 0.01, DCP = 9.55

+/- 0.01, DCP = 9.55

ETG (ref)=9.55, OG=9.55 nail @ 10.34

ETG reads 14.15 Ref. gage , Direct ReadETG reads 14.14

Mounted on shelfStaff, Nail @ 10.34ETG(ref)=9.55, OG=9.55Brass cap 12' E 

Ref. gage, Direct Read

Given, Origin Brass cap upslope 50' E

Brass cap upslope 35' E

CElimit = |0.003*(√6setups)| = |0.007| 

00

ETGIndexETGIndex

ETGWeightETGWeight

B

Figure 25. Continued.
Running Levels 39

5,6 3,4

1,2

RM3

RM2 RM1

TRM1

Staff TP2

gage

Gaging

station

Water

Surface

ETindex

TP1

TP3

EXPLANATION

RM

TP

TRM

Reference mark

Turning point

Temporary reference mark

ETindex

ETweight

1,2

Electric tape index

Electric tape weight

Represents the sequential

 instrument setup number

ETWeight

A

Figure 26. A. Leveling diagram and B. level notes showing 3 simple level circuits used to replace 1 complex level circuit.

Both the complex level circuit and the set of three 

simple circuits have a total of six instrument setups. A distinct 

difference is that in the complex circuit, elevation is carried 

through the six instrument setups consecutively, whereas in 

the simple circuits, elevation is carried through two setups 

at a time. The six setups in the complex circuit represent 

six opportunities where errors can occur. We assume that if 

present, these errors accumulate and will be represented in the 

closure error for the circuit. Where these types of errors occur 

within the circuit cannot be determined, and in a case such as 

this one, the closure error is distributed evenly to each of the 

six instrument setups. In the set of three simple level circuits, 

only two instrument setups were needed in each circuit to 

take FSs on the objective points and close the circuit. That 

created only two locations in each circuit where error could be 

introduced. All three simple circuits were closed sequentially, 

which ensured that elevations assigned to TRM1 and RM3, 

used to determine instrument heights for the second and third 

circuits, respectively, were valid before running those circuits. 

If an error is introduced into one of the simple circuits, that 

error can be recognized and rectified before shooting all 

objective points twice at the site. The above examples also 

demonstrate that sequentially closing the simple circuits 

eliminates the need to go back up the slope to the origin 

reference mark, RM1. The accuracy and efficiency in running 

levels at gaging stations can be improved by breaking down 

a complex level circuit into a series of simple level circuits. 

Strategic placement of permanent reference marks, such as in 

locations where elevation has to be carried up or down a slope, 

would reduce the need to establish temporary reference marks 

or intermediate turning points for every level run. 

Using a Suspended Weighted Steel Tape to Carry 

Elevation to or from a Bridge Structure 

Many gaging stations are separated by a range in 

elevation that is greater than the length of one extended 

leveling rod. This often happens when reference marks, 

reference points, and (or) the wire- weight gage are located 

on a bridge that is relatively high above the stream, and 

other reference marks, reference points, various gages, and 

the water surface are located well below the bridge deck. 

Kennedy (1990) describes how a weighted steel tape can be 

suspended from a bridge and be used as a long leveling rod 

to carry elevation from a lower streamside level circuit to a 

higher level circuit on the bridge deck (and vice versa). This 

method incorporates running a series of simple level circuits. 

The effects of thermal expansion and contraction, tension, 

and wind must be understood and the precision and accuracy 

requirements attainable before using a suspended steel tape 

for levels (see section on “Leveling Rods”). Two sets of level 

notes, one presenting the bridge-down method and the other 

the ground-up method, and a leveling diagram are provided as 

an example of how to use a suspended weighted steel tape to 

run a series of simple level circuits at a gaging station (fig. 27). 
40

Levels at Gaging Stations

Figure 26. Continued.

CORRECTED CORRECTED

BS FS

BS+(CTE*

BS*(T-T0))

FS+(CTE*

FS*(T-T0))

ELEVATION Remarks OBJECT BS FS HEIGHT

OF 

INSTRUMENT

(HI)

DIFFERENCE

(AE1

-AE2)

CLOSUREERROR

ADJUSTMENT

TO HI

ADJUSTED

1st

ELEVATION 

ADJUSTED

2nd

ELEVATION 

OLD

ELEVATION

Remarks FINAL

ELEVATION

B

30.666

30.750

26.011 26.011

25.23516.51425.235

26.011

25.23516.514

25.235 25.23516.514

16.514 16.514

25.235

25.00216.51412.30015.210

10.34016.52410.340

15.21012.30016.51412.300

11.455

12.300

4.655

5.4315.664

5.5154.7395.8002.8907.7608.550 9.550

12.30015.210

10.340

12.89015.210

10.340

12.89015.210

10.340

9.550

9.550

10.340

15.21012.300

9.550

1.576

8.6137.8232.9532.6551.855

00

5.8631.649

14.152

14.236

18.100

18.163

5.748

RM1RM2TRM1TP1TP1

Moved Instrument

0.00000.00000.00000.00000.00000.0000

0.0000.0000.0000.0000.000

TRM1RM2RM1

CE = 26.011-26.011 = 0.000 CElimit =|0.003*(√2setups)|=|0.004|

1.5861.639

TRM1RM3

ETGIndexETGIndex

ETGWeightETGWeight

OG

@13:25@13:30

WS

TP2TP2

Moved InstrumentMoved Instrument

WSOGRM3TRM1

CE=16.514-16.514=0.000 CElimit=|0.003*(√2setups)|=|0.004|

14.10014.155

14.155 14.155

14.100 14.100

1.800

2.710

RM3TP3TP3RM3

CE=12.300-12.300=0.000 CElimit=|0.003*(√2setups)|=|0.004|

ETG reads 14.16 Ref gage, direct readETG reads 14.10 Ref gage, direct read+/Given

- 0.01, DCP = 9.55

ETG(ref) = 9.55, OG=9.55ETG(ref) = 9.55, OG=9.55

Nail @ 10.34

+/- 0.01, DCP = 9.55

Brass cap 12' E 

Given

Mounted on shelfStaff, Nail @ 10.34

Given, Origin Brass cap upslope 50' E

Brass cap upslope 35' E
Running Levels 

41

Figure 27. A. Leveling diagram and B., C. level notes illustrating the use of a suspended steel tape to carry elevations from a bridge down to a streamside 

gage location and from a streamside gage location up to a bridge.

RM1

RM2

RM4

Water

surface RP1

Electric-tapegage

Electric-tapeweight

Wire-weight

gage Check-bar

Suspended steel tape Index

IP021599_Figure 27a. Suspended tape

Modified from Kennedy (1990).

Leveling rod

Leveling rod

Leveling rod

Leveling rod

EXPLANATION

RMRP

Reference markReference point

A
42

Levels at Gaging Stations

DIFFERENCE

(AE1

-AE2)

CORRECTED CORRECTED

BS FS

BS+(CTE*

BS*(T-T0))

FS+(CTE*

FS*(T-T0))

CLOSUREERROR

ADJUSTMENT

TO HI

ADJUSTED

1st

ELEVATION 

ADJUSTED

2nd

ELEVATION 

OLD

ELEVATION

Remarks ELEVATION Remarks OBJECT BS FS HEIGHT

OF 

INSTRUMENT

(HI)

FINAL

ELEVATION

B

3.410

4.3024.0893.1970.8735.6518.0086.909

0

8.142

0

3.3652.462

0

1.4562.3283.2316.195

0

1.4752.8951.262

42.84342.630

2.6826.2346.0617.043

@10:15@10:20

46.216 42.806 42.806

41.91444.74141.91442.80620.131

41.91444.741

41.91444.741

44.74124.909 24.909 24.909 24.90924.909 24.909

3.373

41.91444.741

3.373

3.373

44.74141.914

3.373

3.3733.373

43.321 46.003

22.409 25.782

26.365

22.992

9.434 3.373

7.1069.4346.2039.434

3.3736.203 6.203

1.4262.5259.5686.2039.5687.1063.373

3.3739.4346.2031.4269.434

1.426

9.5681.4266.2039.5687.106

9.568

RM2RM4WWCBTapeTP1TapeWWCBRM4RM2

CE = 42.806

TapeTapeTapeRM1RP1RP1RM1Tape

- 42.806 = 0.000 CElimit = |0.003*(√2setups)|=|0.004|

CE = 3.373- 3.373 = 0.000 CElimit = |0.003*(√2setups)|=|0.004|CE = 3.373- 3.373 = 0.000 CElimit = |0.003*(√2setups)|=|0.004|

0 ft mark on clamped tape is 3.373 ft gage datum

ETGIndexETGIndex

ETGWeightETGWeight

TP2WS

WWbottom

WWbottom

TP3WS

Brass cap right abutmentBrass cap on sidewalk 75'NClamped @ 40', rod=2.843

Moved InstClamped @ 40', rod=2.630

Direct read Moved InstDirect read Direct read Bolt E side Rt Pier@ HI

Nail @ 6.20 ft

ETG(ref) = 1.43, WW=1.43

@ HIMoved Inst@ HIETG(ref) = 1.43, WW=1.43

nail @ 6.20 ft@ HIDirect read 

Given, OriginCheck bar reads 44.74Bottom of tapeCheck bar reads 44.74GivenGivenETG reads 9.43+/-0.01, DCP=1.43WW reads 9.43WW reads 9.57+/-0.01, DCP=1.43ETG reads 9.57

0.0000

0.0000.0000.0000.0000.000

0.00000.00000.00000.00000.0000

Figure 27. Continued.
Running Levels 

43

DIFFERENCE

(AE1

-AE2)

CORRECTED CORRECTED

BS FS

BS+(CTE*

BS*(T-T0))

FS+(CTE*

FS*(T-T0))

CLOSUREERROR

ADJUSTMENT

TO HI

ADJUSTED

1st

ELEVATION 

ADJUSTED

2nd

ELEVATION 

OLD

ELEVATION

Remarks ELEVATION Remarks OBJECT BS FS HEIGHT

OF 

INSTRUMENT

(HI)

FINAL

ELEVATION

2.328 9.434 7.106 7.106

9.4346.2033.3733.3736.2037.1063.373

24.909 24.909 24.909

20.13124.909 24.909

1.4269.4341.4263.373

9.4346.2033.373

6.2033.373

6.203

1.4269.434

2.5259.5689.568

9.5681.4263.3736.2039.568

3.231

0

9.568

6.0618.0086.9098.142

0

0

6.1953.3652.462

0

7.0436.2342.682

5.6511.456

1.4753.4104.3022.8954.0893.1971.262

42.630

44.74142.80641.914

44.74142.80641.914

44.74142.80641.914

24.909

44.74142.80641.914

43.32141.91442.80644.741

41.91442.80644.741

3.3733.373

22.992

0.873

22.40942.843

25.78226.36546.21646.003

RM1

ETG

RM1

Weight

ETGWeight

ETGIndexETGIndex

RP1TapeTapeRP1TapeTapeTapeTape

@ 10:15@ 10:20

WSWWbottomWWbottomTP1WSTP2

Bottom of tape = 3.373

WWCBRM2RM4TP3RM4RM2WWCB

Bolt E side Rt Pier@ HInail @ 6.20 ft Direct read ETG(ref)=1.43, WW=1.43@ HIMoved Inst@ HIETG(ref)=1.43, WW=1.43Direct read @ HIDirect read Moved InstDirect read 

Clamped @ 40', rod=2.843Brass cap right abutmentBrass cap on sidewalk 75'N

Moved Inst

Clamped @ 40', rod=2.630

Given, OriginETG reads 9.43+/WW reads 9.43

-0.01, DCP=1.43

Bottom of clamped tapeWW reads 9.57+/-0.01, DCP=1.43ETG reads 9.57GivenGivenCheck bar reads 44.74Check bar reads 44.74

0.00000.00000.00000.00000.00000.0000

0.0000.0000.0000.0000.0000.000

CE = 7.106- 7.106 = 0.000 CElimit = |0.003*(√2setups)|=|0.004|CE = 3.373- 3.373 = 0.000 CElimit = |0.003*(√2setups)|=|0.004|CE = 3.373- 3.373 = 0.000 CElimit = |0.003*(√2setups)|=|0.004|

C

Figure 27. Continued.
44 Levels at Gaging Stations

Bridge-Down Method 

The diagram in figure 27 shows a weighted steel tape 

clamped at its 40.000-ft marking to the bridge deck rail. The 

first level circuit is on the bridge deck and the objective points 

are RM2, RM4, the wire-weight check bar, and the clamped 

steel tape (noted as “tape” in the level notes). RM2 is the 

origin and is used to establish the initial instrument height. 

Foresights are taken on the wire-weight check bar and the 

bridge deck rail where the tape is clamped. The FS to the top 

of the deck rail at the tape is 2.843 ft, noted in the remarks 

column in the level notes. The tape is being used as a long 

leveling rod; therefore, the FS to the rod at the tape, 2.843 ft, 

is added to the suspended length of the tape, 40.000 ft, to 

get the representative FS, 42.843 ft. An independent turning 

point, TP1, is established and a second instrument height is 

determined from which second FSs are taken on the tape, 

wire-weight check bar, and RM4. The circuit associated with 

the bridge deck is completed by taking a second FS on the 

origin, RM2. The first and second elevations of the 0.000-ft 

mark on the suspended tape are determined by subtracting the 

representative FSs for the tape from the instrument height. 

Both representative FSs for the tape are used to determine that 

the elevation at the 0.000-ft mark on the suspended tape is 

3.373 ft. The closure error for this circuit is 0.000 ft, elevations 

do not need to be adjusted, and the differences between 

first and second elevations for all of the objective points are 

0.000 ft. 

A second level circuit is about half the distance from the 

bridge deck to the low-water bank, and the objective points 

are the tape and the ETG index. The instrument height is 

established with a BS taken on the tape, which is a direct read 

of 22.409 ft. This BS is added to the determined elevation 

for the 0.000-ft mark of the tape, 3.373 ft, to determine an 

instrument height of 25.782 ft. A FS is taken on the ETG 

index and an independent turning point, TP2, is established 

to determine the second instrument height. A second FS is 

taken on the ETG index and this circuit is completed by taking 

a second FS on the suspended tape, which again is a direct 

read of the tape. This circuit has a closure error of 0.000 ft, 

elevations do not need to be adjusted, and the difference 

between first and second elevations for the ET index is 

0.000 ft.

The final level circuit is on the low-water bank and the 

objective points are the tape, RM1, the bottom of the electric 

tape weight (ETG weight), RP1, the water surface, and the 

bottom of the wire weight (noted as “WW bottom” in the level 

notes). Again, the instrument height is established with a BS 

taken on the tape, which is a direct read of 6.061 ft. This BS is 

added to the determined elevation for the 0.000-ft mark of the 

tape, 3.373 ft, to determine an instrument height of 9.434 ft. 

From this instrument height, first FSs are taken on RM1, the 

ETG weight through the cleanout door, RP1, the water surface, 

and the bottom of the wire weight near the water surface. An 

independent turning point is established, TP3, to determine the 

second instrument height from which second FSs are taken. 

This final circuit is completed by taking a second FS on the 

suspended tape. This circuit has a closure error of 0.000 ft, 

elevations do not need to be adjusted, and differences between 

first and second elevations for each of the objective points are 

0.000 ft. By using a weighted suspended steel tape clamped 

to the bridge deck rail to carry elevation from the bridge 

down to the low-water bank, levels can be run at a gaging 

station with an elevation difference of over 35 vertical ft using 

three sequentially closed level circuits that have a total of six 

instrument setups and three turning points. 

Ground-Up Method 

The ground-up method reverses the procedure for the 

bridge-down method and begins from the low-water bank. 

A weighted steel tape is clamped at its 40.000-ft marking to 

the bridge deck rail. The first level circuit is on the low-water 

bank and the objective points are RM1, the bottom of the 

electric tape weight (ETG weight), RP1, the steel tape, the 

water surface, and the bottom of the wire weight. The initial 

instrument height is established with a BS taken on RM1. 

Foresights are taken on the ETG weight through the cleanout 

door, RP1, the steel tape, the water surface, and the bottom 

of the wire weight near the water surface. An independent 

turning point is established, TP1, to determine the second 

instrument height from which second FSs are taken on the 

objective points. The circuit is completed by taking a final FS 

on the origin, RM1. The elevation of the 0.000-ft mark on the 

suspended tape is determined by subtracting the FSs for the 

tape from the associated instrument heights. Both FSs taken 

on the tape determined that the elevation of the 0.000-ft mark 

on the suspended tape is 3.373 ft. The closure error of this 

circuit is 0.000 ft, elevations do not need to be adjusted, and 

the differences between first and second elevations for all of 

the objective points are 0.000 ft. 

A second level circuit is about half the distance from the 

low-water bank to the bridge deck, and the objective points 

are the tape and the ETG index. The instrument height is 

established with a BS taken on the tape, which is a direct read 

of 22.409 ft. This BS is added to the determined elevation 

for the 0.000-ft mark of the tape, 3.373 ft, to determine an 

instrument height of 25.782 ft. A FS is taken on the ETG 

index and an independent turning point, TP2, is established 

to determine the second instrument height. A second FS is 

taken on the ETG index and this circuit is completed by taking 

a second FS on the suspended tape, which again is a direct 

read of the tape. This circuit has a closure error of 0.000 ft, 

elevations do not need to be adjusted, and the difference 

between first and second elevations for the ETG index is 

0.000 ft.

The final level circuit is on the bridge deck and the 

objective points are the steel tape, wire-weight check bar, 

RM2, and RM4. The instrument height is established with a 

BS of 2.843 ft, taken on the top of the deck rail at the tape, 
Office Procedures 45

and noted in the remarks column in the level notes. The 

tape is being used as a long leveling rod; therefore, the BS 

to the rod at the tape is added to the suspended length of 

the tape, 40.000 ft, to get the representative BS, 42.843 ft. 

The determined elevation for the 0.000-ft mark of the tape, 

3.373 ft, is added to the BS to determine an instrument 

height of 46.216 ft. From this instrument height, first FSs 

are taken on the wire-weight check bar, RM2, and RM4. An 

independent turning point, TP3, is established and a second 

instrument height is determined from which second FSs are 

taken on RM4, RM2, and the wire-weight check bar. The 

circuit associated with the bridge deck is completed by taking 

a second FS on the deck rail at the tape. The closure error for 

this circuit is 0.000 ft, elevations do not need to be adjusted, 

and the differences between first and second elevations for 

all of the objective points are 0.000 ft. By using a weighted 

suspended steel tape clamped to the bridge deck rail to carry 

elevation from the low-water bank to the bridge deck, levels 

can be run at a gaging station with an elevation difference of 

over 35 vertical ft using three sequentially closed level circuits 

that have a total of six instrument setups and three turning 

points. 

Office Procedures 

The task of running levels at gaging stations includes 

some important office-related activities. A final check of the 

computations made during the level run that were first checked 

in the field should be made and documented. Following a level 

run, any adjustments made to the elevation of the reference 

gage need to be applied to the time series record of gage 

height and any other affected measurements of the reference 

gage. The field notes, which include digital files, original 

hand written documents, and photographs taken during field 

work, should be stored according to office specifications. The 

historical level summary and station description should be 

updated to reflect the elevations found during the level run. 

Finally, if needed, the site sketch should be updated along with 

any descriptions of reference marks that may have changed or 

been added since the last level run. 

Applying Datum Corrections to Gage Height 

Time Series 

The primary reference gage at a continuously recording 

gaging station is used to set the gage height on the data logger 

and to determine the representative gage heights for discharge 

measurements. If the level run finds that the absolute value of 

the difference between the elevation reading of the reference 

gage and the gage datum is greater than or equal to 0.015 ft, 

the recorded stage record must be corrected. Corrections 

of this type are referred to as datum corrections. Similarly, 

observed gage height measurements made during the time 

period affected by the datum correction should be adjusted 

accordingly. The datum correction applied to the time series 

of recorded stage values should be applied in a manner that 

is consistent with what caused, or was assumed to cause, the 

reference gage elevation to be different from the gage datum. 

For example, if the reference gage is damaged during a flood, 

the datum correction should be applied at the time the damage 

occurs and held constant until the time levels are run and the 

reference gage is adjusted. If the reference gage is assumed 

to have been heaved by frozen ground during the winter, the 

datum correction should be held constant back to the winter 

period. If the gage remains ice-free during the winter and 

it is believed the reference gage was heaved slowly during 

the winter, the datum correction may then be prorated back 

through the winter period. 

Developing a Site-Specific Historical Level 

Summary

A historical level summary that contains the final 

elevations of all objective points from every level run should 

be maintained for all gaging stations. The level summary also 

should contain descriptions of all reference marks, reference 

points, and gages. Other objects of interest that were shot 

during a level run, such as the gage height of zero flow or 

the orifice line terminus, can also be included in the level 

summary. The primary reference gage should be explicitly 

noted. The level summary provides a way to track elevations 

and thus, vertical stability of all objective points over the life 

of the station. The stage that each of the various gages at the 

station was found to be reading at the beginning of a level run 

should be noted as well as the stage each gage was reading at 

the end of a level run. The origin reference mark for each of 

the level runs should be noted. The historical level summary 

should be updated immediately every time levels are run at 

the gaging station. A digital summary file provides the best 

means for storage and retrieval and can easily be updated. A 

form template for the historical level summary for printing or 

download is provided in appendix D.

Developing a Site Sketch Map

A sketch map of the site will help anyone who runs 

levels at the station. This is especially true for someone who 

is unfamiliar with a particular station. This map should show 

the locations of the reference marks, reference points, and all 

gages with respect to the gaging station structure and other 

prominent objects. The location of the low-water control along 

with the direction of flow should be included. Recommended 

instrument setup locations that provide ideal shot distances are 

useful as well. Site sketch maps are best maintained and stored 

in digital format. 
46 Levels at Gaging Stations

Auxiliary Data to be Obtained During 

Level Runs

Running levels at gaging stations provides an opportunity 

to acquire other useful elevation-related information. Fresh 

high-water marks, if present, should be surveyed and 

compared later to recorded gage heights. A cross section of the 

hydraulic control(s) (including section, channel, and bank-full 

elevations), surveyed in the gage datum, is easy to obtain and 

can aid in developing the stage-discharge rating for the site. 

The gage height of zero flow associated with the hydraulic 

control that defines the low-water stage-discharge relation can 

be easily measured when the instrument is set up to measure 

the water-surface elevation during levels. Documenting 

the elevation, or gage height, at which flow overtops either 

bank can assist the USGS and other agencies during flood 

conditions. Determining the minimum elevation of a bridge 

or road deck in the gage reach can be very useful during 

flood events. Measurements of the elevations of various gage 

components, such as the orifice line terminus or stilling well 

intakes, can assist in determining the gage height at which the 

gage is out of communication with the stream. A measurement 

of the elevation of the instrument shelf provides an estimate of 

the likely maximum gage height the data logger can record. In 

short, the efficiency with which engineer’s levels can obtain 

accurate vertical measurements presents opportunities to 

acquire auxiliary data when running levels at gaging stations. 

Summary

Levels are run at gaging stations to ensure gages are 

accurately set to the established gage datum. Differential 

leveling techniques are used to determine elevations for 

reference marks, reference points, all gages, and the water 

surface to a precision of 0.001 foot (ft). Desired accuracy for 

a set of station levels is less than 0.010 ft. Precision describes 

the closeness of one measurement to another while accuracy 

describes how close a given measurement is to the true value. 

The techniques presented in this manual provide guidance on 

instruments and methods that ensure gaging-station levels are 

run to both a high precision and accuracy. 

Levels are run at gaging stations whenever unresolved 

gage reading differences are identified, damage is suspected 

to have occurred to the station, or according to a frequency 

recommended for a given station. Engineer’s levels, optical 

levels and electronic digital levels, are commonly used for 

running levels at gaging-stations. Collimation tests should 

be run at least once during any week that levels are run. 

Collimation error for an instrument cannot exceed the 

absolute value of 0.003 ft/100 ft. Instruments exceeding 

this collimation tolerance should be adjusted, and another 

collimation test must be run before it is used for gaging-station 

levels. If an instrument fails a collimation test, all levels run 

since the prior passing collimation test cannot be used and 

must be re-run.

An acceptable set of gaging-station levels consists of a 

minimum of two foresights, each from a different instrument 

height, to at least two independent reference marks, all 

reference points, all gages, and the water surface. The initial 

instrument height is determined from a third independent 

reference mark, known as the origin, or base reference mark. 

The absolute value of the closure error of a leveling circuit 

must be less than or equal to 0.003 n ft, where n is the 

total number of instrument setups. The entire level circuit 

must be re-run if closure error exceeds this threshold; closure 

error may not exceed |0.015| ft, regardless of the number 

of instrument setups. Closure error for a leveling circuit is 

distributed by instrument setups in a manner that assumes 

error accumulates linearly and elevations for objective points 

are adjusted accordingly. Absolute differences between the 

adjusted first and second elevations for the objective points 

in the circuit must be less than or equal to 0.005 ft. Objective 

points with absolute differences between adjusted first and 

second elevations exceeding 0.005 ft require two more 

foresights from different instrument heights. Final elevations 

of objective points are determined by averaging the valid 

adjusted first and second elevations. Reference gages should 

be reset if the absolute value of the difference between the 

elevation reading of the reference gage and the gage datum 

is greater than or equal to 0.015 ft. A summary of selected 

requirements and tolerances for gaging-station levels is 

provided in appendix E. 

References Cited

Breed, C.B., Hosmer, G.L., and Bone, A.J., 1970, The 

principles and practice of surveying—Vol. 1., Elementary 

surveying (10th ed.): London, Wiley and Sons, 717 p.

Corbett, D.M., and others, 1943, Stream-gaging procedure; a 

manual describing methods and practices of the Geological 

Survey: U.S. Geological Survey Water-Supply Paper 888, 

245 p. 

Davis, R.E., Foote, F.S., and Kelly, J.W, 1966, Surveying 

theory and practice (5th ed.): New York, McGraw-Hill, 

1096 p. 

Federal Geodetic Control Committee, 1984, Standards and 

specifications for geodetic control networks: National 

Oceanic and Atmospheric Administration, accessed on 

March 9, 2010, at http://www.ngs.noaa.gov/FGCS/tech_

pub/1984-stds-specs-geodetic-control-networks.htm
References Cited 47

Floyd, R.P., 1978, Geodetic bench marks: National Oceanic 

and Atmospheric Administration Manual, National Ocean 

Survey, National Geodetic Survey 1, 52 p., accessed on 

March 6, 2010, at http://www.ngs.noaa.gov/PUBS_LIB/

GeodeticBMs/

Hansen, W.R., ed., 1991, Suggestions to authors of the 

reports of the United States Geological Survey (7th ed.): 

Washington, D.C., U.S. Government Printing Office, 289 p.

Kennedy, E.J., 1990, Levels at streamflow gaging stations: 

U.S. Geological Survey Techniques of Water-Resources 

Investigations, book 3, chap. A19, 31 p., available online at 

http://pubs.usgs.gov/twri/twri3-A19/pdf/twri_3-A19_a.pdf

McCormac, J.C., 1983, Surveying fundamentals: Englewood 

Cliffs, New Jersey, Prentice-Hall, 522 p.

Schomaker, M.C., and Berry, R.M., 1981, Geodetic leveling: 

National Oceanic and Atmospheric Administration Manual, 

National Ocean Survey, National Geodetic Survey 3, 

accessed on March 6, 2010, at http://www.ngs.noaa.gov/

PUBS_LIB/Geodeticleveling_nos_3.pdf

Thomas, N.O., and Jackson, N.M., Jr., 1981, Manual 

for leveling at gaging stations in North Carolina: U.S. 

Geological Survey Open-File Report 81-1104, 37 p., 

available online at http://pubs.usgs.gov/of/1981/ofr81-1104/

pdf/ofr81-1104.pdf

U.S. Geological Survey, 1980, Ground water: National 

handbook of recommended methods for water-data 

acquisition: Office of Water Data Coordination, 149 p.
48 Levels at Gaging Stations

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Glossary 49

Glossary

Backsight (BS). The reading on a leveling 

rod held on a point of known elevation that is 

used to establish a height of an instrument. 

Benchmark . A permanent marker with 

known survey control of vertical and (or) 

horizontal coordinates in an established 

geodetic system, such as the North American 

Vertical Datum of 1988.

Closure error. The difference between the 

elevation of the starting point, or origin, of a 

closed level circuit and the elevation of that 

same point from the final instrument setup; 

computed as the given elevation minus the 

final elevation. 

Collimation. Agreement of a surveying 

instrument’s line of sight with its horizontal 

axis.

Collimation error. The deviation or 

inclination of a level’s line of sight from 

horizontal, often given in a vertical deviation 

per horizontal distance such as feet per 100 

feet; positive when the line of sight points 

downward from the instrument.

Curvature and refraction effect. The 

increase in a leveling rod’s reading caused by 

the combination of the Earth’s curvature and 

atmospheric refraction effects.

Datum. A level surface that represents zero 

elevation.

Differential leveling. The determination of 

the difference in elevation of two points using 

a surveying instrument and a leveling rod.

Elevation. The vertical distance from a 

point to the datum.

Engineer’s level. A surveying instrument 

consisting of a minimum of a telescopic sight 

and a sensitive leveling device to make the 

line of sight horizontal.

Optical level. An engineer’s level that 

is used to manually read a leveling rod.

Electronic digital level. An engineer’s 

level with an automated system that reads 

a leveling rod. 

Foresight (FS). The reading on a leveling 

rod held on a point whose elevation is to be 

determined.

Gage datum. The zero elevation reference 

surface at a gaging station to which all gages 

are set.

Gage height. The elevation of the 

water surface at a gaging station, used 

interchangeably with stage.

Gage height of zero flow. The gage height 

at which streamflow ceases. Associated with 

the elevation of the lowest point on the lowwater hydraulic control of a gaging station.

Gaging-station levels. Differential levels 

run (that is, carried out) at a gaging station to 

define and maintain a constant gage datum for 

all gages.

Height of instrument (HI). The elevation 

of the horizontal line of sight of a surveying 

instrument.

Horizontal. A direction that is perpendicular 

to the force of gravity.

Parallax. The relative movement of the 

image of a leveling rod with respect to 

the cross hairs of a surveying instrument 

as the observer’s eye moves, caused by 

improper focusing of the objective lens of the 

instrument.

Reference mark (RM). A permanent marker, 

installed in the ground or on a structure, 

whose elevation above a set datum is known. 

Used to check and make sure that all gages 

and reference points are properly set to gage 

datum. 

Reference point (RP). Objects, often bolts 

or screws that are assigned an elevation in 

the gage datum. Used to obtain gage heights 

when necessary by measuring their distance to 

the water surface. 

Stage. The elevation of the water surface 

at a gaging station, used interchangeably with 

gage height.

Temporary reference mark (TRM). A 

temporary point of reference that was treated 

as an objective point in a previously closed 

level circuit that is used to carry elevations to 

other instrument setups. 

Turning point (TP). A temporary point of 

reference in an open level circuit that is used 

to carry elevations to other instrument setups 

in the level circuit. 

Vertical. The direction of the force of 

gravity. 
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50 Levels at Gaging Stations
Appendix A 51

Date: _____________________________________ 

d2 should be less than 110 ft. 

R d

1

2

R d

1

2

c = _______________ft/100ft as found

c = _______________ft/100ft as found

ADJUSTMENT (level remains set up at ORIGINAL LOCATION)

To adjust level, set R2 to read R1

To test collimation after adjustment, set up near other scale and repeat measurements.

R System adjusted: optical digital 1 = ______________

NOTES or COMMENTS:

Collimation = c = 100 * ( R1 - R2 )

( d2 - d1 )

( - )

( - ) c = 100 * 

( - )

( - ) c = 100 * 

( - )

( - ) c = 100 * 

FIXED SCALE COLLIMATION TEST OF ENGINEER'S LEVEL

Tested by: _________________________________

OPTICAL SYSTEM

DIGITAL SYSTEM

Make/Model: Circle system type(s): optical digital

R d

1

2

IP021599_FigA01_Fixed scale_B

R1 R2

d1

d2

Fixed scale Fixed scale 

Instrument

R2 R1

d1 d2

Fixed scale Fixed scale 

Instrument

Appendix A. Fixed-Scale Test Form
52 Levels at Gaging Stations

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Appendix B 53

Appendix B. Peg Test Form 

Circle system type(s): optical digital

Average of d2 and d4 should be less than 110 ft. 

R d

1

2

3

4

R d

1

2

3

c = _______________ft/100ft as found

c = _______________ft/100ft as found

c = _______________ft/100ft as found

4

ADJUSTMENT (level remains set up at 2 and sighted at R4)

Repeat collimation test

after adjustment. Adjust cross hair to

NOTES or COMMENTS:

R1

R3

R2

R4

d1 d2

d3 d4

1 2

Collimation = c = 100 * ( R1 + R3 ) - ( R2 + R4 )

( d2 + d4 ) - ( d1 + d3 )

c = 100 * ( + ) - ( + )

( + ) - ( + )

c = 100 * ( + ) - ( + )

( + ) - ( + )

( + ) - ( + )

( + ) - ( + ) c = 100 * 

PEG TEST OF ENGINEER'S LEVEL

Make/Model:

Tested by: ______________________________ Date: ____________________________________

OPTICAL SYSTEM

DIGITAL SYSTEM

COLLIMATION TEST AFTER ADJUSTMENT

IP021599_Figure B01 Peg Test
54 Levels at Gaging Stations

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Appendix C

55

Appendix C. Level Notes Form(Full-size form [8” x 10”] is available for download at http://pubs.usgs.gov/tm/tm3A19)

Circle system type(s): optical digital

Party (inst.) (rod)

INSTRUMENT

Make/Model: _______________________Serial Number: ________________________Collimation (optical): ___________________

Average of d2 and d4 should be less than 110 ft. Collimation test date: ___________________

d R Collimation (digital): ___________________

1 Collimation test date: ___________________2 ROD

3 Scale material: ________ CTE _________ 1/F° or 1/C°

CTE conversions: (1/°F * 1.8 = 1/°C) and ((1/°C)/1.8 = 1/°F) 4

Temperature (T): Rod:_____ °F or °C; Air:_____ °F or °C d RStandard temp (To): 68°F or 20°C or other: _______ 1

Given/Origin elevation: ______________ 2Max elevation of objective point: ______________ 3

Min elevation of objective point: ______________

c = _______________ft/100ft as foundc = _______________ft/100ft as found 4

Max elevation difference (L): ______________ _ ADJUSTMENT (level remains set up at 2 and sighted at R4) Ct = CTE * L (T-To) C= ____________ t _

Other devices used as rod (list): Repeat collimation test

after adjustment. Adjust cross hair to Time WS Ref. Rod taped (circle): yes no

NOTES or SKETCHES:

Rod level used (circle): yes no

GAGE RESET

Ref.

FoundLeft

WEATHER:NOTES: Circuit

No.

No. of

Inst.

Setups

(n) 

Allowable

closure

0.003 √ n

Closure

Error

(CE)

CE/(n)

(take to

0.0001)

CLOSURE-ERROR COMPUTATIONS

Computed by: Checked by: Date: 

SUMMARY OF OBJECTIVE POINTS

Object Difference (AE1

-AE2)

Final

Elevation

((AE1+

AE2)/2)

GAGE READINGS

Station Name

Date

Station Number:

U.S. DEPARTMENT OF THE INTERIOR

U.S. Geological Survey

Gaging Station Level Notes

R1

R3

R2

R4

d1 d2

d3 d4

1

2

Collimation = c = 100 * ( R1 + R3 ) - ( R2 + R4 ) ( d2 + d4 ) - ( d1 + d3 )

c = 100 * ( + ) - ( + ) ( + ) - ( + )c = 100 * ( + ) - ( + ) ( + ) - ( + )

PEG TEST OF ENGINEER'S LEVEL

Make/Model:

OPTICAL SYSTEM

DIGITAL SYSTEM

COLLIMATION TEST AFTER ADJUSTMENT d R

1234

c = _______________ft/100ft as found

c = 100 * ( + ) - ( + ) ( + ) - ( + )

Adjusted

 1st

Elevation

(AE1) 

Adjusted

 2nd

Elevation

(AE2) 
56 Levels at Gaging Stations DIFFERENCE (AE1

-AE2)

CORRECTED CORRECTED

BS FS

BS+(CTE*

BS*(T-T0))

FS+(CTE*

FS*(T-T0))

CLOSUREERROR

ADJUSTMENT

TO HI

ADJUSTED

1st

ELEVATION 

ADJUSTED

2nd

ELEVATION 

OLD

ELEVATION

Remarks ELEVATION Remarks OBJECT BS FS HEIGHT

OF 

INSTRUMENT

(HI)

FINAL

ELEVATION
Appendix D

57

HISTORICAL LEVEL SUMMARY

(Given)

Descriptions of objective points:

RM1 —RM2 —RM3 —RP1 —RP2 —RP3 —

CSG Index —ORIFICE —REF GAGE —GZF —

STATION NUMBER

Reference Marks and Reference Points

Primary Reference Gage

DATE PARTY

Wire-weight gage Staff gage

Water

surface

by

levels

Water

surface

found

Water

surface

left

Water

surface

found

Water

surface

left

Check

bar(Aux

wireweight)

Orifice

line

terminus

Gage

height of

of zero

flow

Datum

correction Remarks

Btm of

weight

nr water

surface

Check

bar

Electric

tape

index

Index

found

Index

left Found Left

Adjust.

made

Auxillary gage Crest Stage gage Recorder

STATION NAME

Appendix D. Historical Leval Summary Form(Digital Excel format is available for download at http://pubs.usgs.gov/tm/tm3A19)
58 Levels at Gaging Stations

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Appendix E 59

[n is the number of instrument setups in level circuit. ft, foot; <, less than; | |, absolute value]

Requirements and tolerances

Precision of gaging station levels 0.001 ft

Accuracy of gaging station levels <0.01 ft

Maximum number of days since the last collimation test 7

Maximum collimation error of level instrument |0.003| ft/100 ft

Maximum allowable difference between rod scale and tape check |0.002| ft

Minimum number of reference marks in a level run 3

Maximum temperature correction, Ct, computed using maximum 

vertical distance from origin (equation 3) that does not require 

correcting all shots for thermal expansion or contraction 

|0.003| ft

Maximum allowable closure error |0.003√n| and not to exceed |0.015| ft

Minimum number of foresights to 

 at least two reference marks 2

all reference points 2

all gages 2

the water surface 2

the origin reference mark 1

Minimum number of non-objective point turning points 1

Maximum allowable difference between the adjusted first and the 

adjusted second elevations of objective points

|0.005| ft

Maximum allowable difference between the elevation reading of the 

reference gage and the gage datum

<|0.015| ft

Appendix E. Summary of Selected Requirements and Tolerances for Gaging 

Station Levels
60 Levels at Gaging Stations

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For more information concerning the research in this report, contact the

 Chief, Office of Surface Water

U.S. Geological Survey

12201 Sunrise Valley Drive

Reston, Virginia 20192

http://water.usgs.gov/osw/
Kenney—Levels at Gaging Stations—Techniques and Methods 3-A19