Crossing wide rivers or steep wide valleys while performing precise differential leveling has been a challenge for surveyors and engineers for as long as we have been performing differential leveling. Rivers and valleys impact surveying and engineering projects where precise elevations are required on both sides, such as bridge construction.

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Today’s modern equipment takes much of the reading error and transposition of numbers out of the equation when performing differential leveling. Digital bar code reading levels together with precise invar bar code staffs make achieving Second Order leveling almost easy if the several guidelines and procedures are carefully followed. There have been many very precise levels available before the days of the digital bar code level. The manufacturers and designs of precise levels are varied. From highly-precise automatic levels like the Zeiss Ni 002 to the early spirit levels like the Fischer level of the U.S. Coast and Geodetic Survey (USC&GS), precise differential leveling has a place in our history. Countless thousands of miles of First Order leveling have been carried out across the nation.

Despite all the precision and technology available today, differential leveling campaigns all suffer from the same limitations when crossing rivers or valleys. Length of site is certainly not the only limitation with respect to precise leveling, but it is a significant challenge to overcome for several reasons.

Length of site, or sighting distance, not only limits one’s ability to read a rod, but also introduces yet another set of errors that must be accounted for. Leveling errors that are dependent on sighting distance are magnified when long sights must be taken. Crossing a river or valley significantly impacts the errors, because the sights, fore and aft, are usually not balanced and typically by a great amount. Thus, curvature and collimation cannot be accounted for in the usual manner. Further, refraction errors can be large and variable, especially passing over water.

In 1929, the Coast and Geodetic Survey, later USC&GS, now National Geodetic Survey (NGS), developed and published a routine suitable for performing river crossings. The effectiveness of the crossing routine is founded in the principle of Simultaneous Reciprocal Observations, outlined in detail in the publication “NOAA Manual NOS NGS 3 Geodetic Leveling.” It should be noted that NGS is currently in the process of developing a new procedure that will allow river crossings to be made using very precise digital theodolites; it is soon to be approved and published by NGS.

The Challenge

American Surveying & Engineering has had the good fortune of having played a significant role in the Illinois Height Modernization Program over the past six years. Each year, we have been contracted to set NGS 3D rod monuments as benchmarks and run Second Order, Class 1 levels over hundreds of miles of leveling corridor.

To date, we have performed nine separate leveling campaigns, recovering 354 existing Second Order, Class 1 or better benchmarks, setting 957 new 3D rod marks and run more than 2,340 miles of Second Order double-run leveling. In years prior to 2014, we were always able to run digital levels over waterways or valleys using railroad or highway grade separation structures or bridges. Our assignment for 2014 was not much different than prior years except for crossing the Illinois River.

Our 2014 assignment included Line 4 West of the Illinois Height Modernization leveling campaign. This line is comprised of 130 miles one way of Second Order, Class 1 leveling through central Illinois, running from Decatur west to Plainville. All leveling was performed with digital bar code levels, specifically Leica DNA 03 models, along with certified invar digital bar code staffs and appropriate peripherals, turning pins, turtles and thermistors. A portion of the leveling line crossed the Illinois River at Meredosia. Originally, the Illinois River was also crossed in this vicinity by NGS (then USC&GS). The river was crossed by USC&GS via a railroad bridge; the railroad no longer exists and the bridge is gone as well. The east abutment of the bridge is the only remaining evidence of the railroad in the area. The abutment contains a benchmark from the original level line, a First Order, Class II BM, KC0286, found by Coast and Geodetic Survey dated 1933.

There is an existing highway bridge in the vicinity of the crossing, carrying Illinois State Route 104 over the Illinois River at Meredosia. This bridge, in our original assignment, was to be used to cross the river. The existing river bridge profile is steep and has a navigation channel center span of over 650 feet in length. Preliminary inquiries indicated that the bridge could not be closed to traffic except in one direction at a time with flagmen and proper maintenance of traffic signage. Additionally, initial testing showed the kinetic dynamics of the bridge might impair the ability of the levels compensator to adequately perform to the criteria of Second Order, Class 1 specifications.

The river in the vicinity of the crossing is approximately 700 feet wide from bank to bank. The east floodplain rises from the bank at a moderate rate, approximately 6 percent. The west floodplain is not as steep and remains more flat, approximately 2 percent until reaching a levee 800 feet west of the river’s edge. The distance from the top of the levee on the west to the approximate top of the floodplain of the east spans 1,900 feet. 

The methodology we employed to cross the river follows “NOAA Manual NOS NGS 3,” specifically Chapter 4, Section 4.4, “Instructions for Ordinary Leveling Instruments.” This procedure is suitable “when less than First Order precision” is allowable. The NGS-recommended procedure suitable for First Order work is to use the Zeiss river crossing equipment. This equipment is discussed in detail in Section 4.3 of the NOAA manual. The equipment is not presently commercially available and, after two years of searching worldwide, we were not able to locate a system, except those owned by NGS. 

A slight modification was made with respect to the procedure for ordinary leveling instruments. Section 4.4.1 requires that a leveling rod (staff) be set on a benchmark on each side of the river and “intercepting targets” be placed on the rod at even marks on the rod scale. The alternate method we used for this crossing was to use “target stations” constructed in accordance with Section 4.3.2, Figure 4-9, consisting of intercepting targets mounted on a target column. Target stations are routinely employed when the Zeiss river crossing equipment is used. The target station has many advantages over placing intercepting targets on the face of a rod scale, not the least of which is greater precision and minimizing error in placing the targets caused by misreading the scale or parallax aligning the target to the scale.

The Equipment     

Two matched Wild N3 First Order precision levels were employed in the procedure. The new-style Wild N3 is a spirit level — sometimes referred to as a tilting level — that has many advantages with respect to geodetic leveling. It is still widely used in industrial and laboratory applications for its high precision. Prior to the advent of digital bar code leveling instruments, it was used for high-order geodetic surveys, deformation surveys and other applications requiring high order control. The manufacturer’s quoted standard deviation for this instrument over a one mile double run is ±0.0008 feet. 

In 1929, the Coast and Geodetic Survey published a routine suitable for performing river crossings with the then current Fischer level. The Fischer spirit level was the workhorse of the national geodetic leveling network. The Fischer level is purported to have a “setting precision” of ±0.5 seconds (0.5”) of arc. It did not have an internal micrometer, but did have a micrometer tilting screw. The 1934 Fischer level tilting micrometer was divided into 100 intervals with 0.000025 radians per interval, which equates to approximately 5 arc seconds (5”) per interval. It was estimated that the micrometer tilting screw could be read by estimation to 0.1 interval (0.5”). 

By contrast, the Wild N3 employed for this project uses a similar tilting screw — “gradienter screw” — and has a tilting interval of 2.06 seconds (2.06”) of arc. By estimation, 0.1 interval may be read yielding 0.2 seconds of arc (0.2”). The Wild N3 is listed in Table 3-2 of the “NOAA Manual NOS NGS 3.” The new-design Wild N3 has a frictionless tilting axis free from wear and tear that sometimes plagued other spirit level designs. The Wild N3 also has an integral parallel plate micrometer to facilitate precise measurements from a standard invar rod.

Target stations are comprised of a column that fits into a tribrach from which at least two targets can be affixed. A height stud is also fixed to the target column in precise relation to the targets. Our target stations were manufactured using computer numerical control precision machine operations, ensuring dimensions in the range of ±0.001 inch (0.025 mm) with respect to target separation and reference to the height stud. Intercept targets are spaced two at a time on the target column at uniform spacing of 0.00, 40.00, 80.00 120.00 or 160.00 half-centimeters, not exceeding 1 meter overall. Note that half-centimeters are the customary graduation for conventional precision invar rods. Targets are white isosceles triangles on a black background measuring approximately 20 by 30 centimeters. Repeatability of the tilting screw of less than half an interval has been confirmed at distances exceeding 3,280 feet (1 km) for this size target.

Customary digital bar code levels and full-length invar rods, in addition to Leica 60-centimeter invar scale strips, were used to transfer the elevation to the respective height stud on the target stations. Auxiliary invar scale strips were also used to establish the instrument height during the river crossing measurements.

Field Setup

Care was taken to ensure the river crossing location met the criteria outlined in “NOAA Manual NOS NGS 3” with respect to height above the water surface and uniformity of the simultaneous reciprocal observations.

The instrument and target location on each side of the river were uniform with respect to length of site for each instrument and the geometry of the target stations with respect to the instruments. The primary impact of refraction for long sights is based on the density gradient. Practically, the density gradient is in fact heavily reliant on the temperature gradient for terrestrial refraction. Care was taken to ensure uniform refraction on each side of the river would be met.

The instrument location and the target station were of uniform geometry on both sides of the river. That is, careful attention was made to form a uniform rectangle or parallelogram. Temporary stakes were marked in the field for positional accuracy. As quality control on the orientation and configuration, the dimensions between instrument stations and target stations across the river and adjacent to one another were measured with conventional total stations. This ensured the simultaneous reciprocal observations accomplished the goals of canceling curvature and refraction errors. In addition, when the levels were swapped to the opposite side of the river, the focus was not changed before performing the second set of tilt measurements, thereby retaining the previous collimation for each level, allowing for approximate reciprocal collimation.

The Wild N3s were always shaded from direct sunlight. Before removing the levels from their cases, a shade tent was erected over the instrument location on each side of the river to ensure uniform thermal expansion of the levels. During the daily collimation checks, a portable umbrella was used to shade the instruments. After performing a collimation check and ensuring collimation was acceptable, the levels were placed over each respective level station to acclimate to current temperatures, and the target stations were set up. Meanwhile, digital bar code levels were used on each side of the river to establish the elevation of the height studs on the respective target stations. Thermistors — aspirated thermometers — were placed on each tripod of the levels to record temperature gradients during the observations.


The river crossing site was selected and prepared for the crossing well in advance of the observations. The leveling crew, while performing daily digital bar code leveling, monitored the weather and atmospheric conditions daily to select the ideal conditions to perform the river crossing observations.  The crossing observations needed to be performed when refraction effects were small and uniform in nature.  Overcast days with slight to moderate wind and median temperatures are customarily ideal. Care was taken to avoid bright sun, wind, fog or temperature inversions.

The leveling crew members had already been carefully trained and experienced in the river crossing techniques. The river crossing crews were made up of an observer and a recorder on each side of the river. After each collimation check and each party was ready to begin observations, communication between the two recorders was initiated. The first running commenced with a backsight on the target station height stud and a pointing to the opposite target station on the other side of the river, foresight, together with recording upper and lower thermistor temperatures. The recorders then communicated with both observers to simultaneously commence the series of three sets of 25 tilt measurements, performed as follows:

  1. Tilt the line of sight using the tilting screw and align the middle reticle line to intercept the upper target. Read the tilting screw and estimate the nearest tenth of an interval. Announce the value to the recorder. The recorder repeats the value to the observer and the observer confirms.
  2. Center the split bubble in the level vial by use of the tilting screw. Read and record the tilting screw value using the same protocol as in Step 1 above.
  3. Tilt the line of sight using the tilting screw and align the middle reticle line to intercept the lower target. Read the tilting screw and estimate the nearest tenth of an interval. Announce the value to the recorder. The recorder repeats the value to the observer and the observer confirms.
  4. This series is repeated 25 times. The recorders announce the commencement of each set of triple readings to the other recorder to ensure that the simultaneous readings remain in sync.
  5. At the end of the 25th set of readings, the levels are carefully removed from the tripods, leaving the tripods in place. It is very important to not change the focus of the instruments and carefully transport them to the opposite side of the river. 
  6. Once the instruments are set and leveled, the second series of 25 foresight measurements are performed first, exactly as in Steps 1-4 above.
  7. At the end of this series, the backsight is made to the adjacent target station height stud to establish the instrument height of the level. The upper and lower thermistor readings are also recorded at this time.

This concludes the first running of the river crossing. The second can be commenced immediately from the same setup in the identical but opposite sequence if time and weather allows. If not, the second running should occur on an alternate day starting from the same side of the river where the first running ended.

The first and second runnings comprise the river crossing. The data should be computed in accordance with “NOAA Manual NOS NGS 3.” The two runnings should meet the required closure for the order and class of the entire level line. If the closure is not met, additional runnings should be performed until two runnings yield the required closure.


The numerous observations were input into a spreadsheet to facilitate ease of computation. The spreadsheet also recorded other important observation aspects, such as date, time, instrument serial number, target system serial number, observer, recorder, wind code, sun code, and upper and lower temperature readings using a thermistor.

The raw data measurements consist of 25 tilt measurements each of the upper target, horizontal and lower target observed at the same time on each side of the river. Run 1 Set 1 Side A and Side B along with Run 1 Set 2 Side A and Side B consist of 300 tilt measurements, which comprise one running. The second running consists of another 300 tilt measurements, totaling 600 measurements. The spreadsheet checks the residuals of the measurements and means the results.

Where the lower target elevation is known, the computation of the horizontal elevation is easily computed as a simple ratio of the distance between the upper and lower target and the tilt measurement between the lower target to the horizontal compared to the tilt measurement between the lower target to the upper target. 

Where “D” is the distance between the lower and upper target, “b” is the tilt measurement to the lower target, “r” is the tilt measurement to the horizontal and “a” is the tilt measurement to the upper target, then “h” is the distance from the lower target to the horizontal is computed by:

h = D x (b-r)/(b-a)

The difference in height between the lower target on Side A was compared to the lower target on Side B to determine the height difference for the level run. The difference between Run 1 and Run 2 is used to compute the height difference closure error. For this campaign, the distance across the river from each instrument to the corresponding target station was 540.72 meters (1,774.01'). The actual achieved error of closure was 2.92 mm (0.0096') compared to the allowable Second Order, Class 1 error of 4.41 mm (0.0145').


Precision leveling over wide rivers or valleys can successfully be employed using conventional instruments and techniques developed more than 86 years ago. Numerous civil applications such as building bridges struggle with carrying precise elevations over wide bodies of water or deep valleys even in today’s world of great advances in technology.

By following well developed procedures, using carefully trained field staff and precise instruments, we have successfully established Second Order, Class 1 benchmarks on each side of a river, allowing us to complete the 130-mile level line to modern survey accuracies.