Surveying and geomatics: an overview

Every civil engineering project starts and ends with measurement. Before a road can be designed, someone has to measure the shape of the ground, the location of property lines, the elevations of existing pipes and the positions of buildings that must be avoided. During construction, someone has to put the design back on the ground, marking where each footing, curb and manhole belongs. After construction, someone has to measure what was actually built so that the owner has a reliable record. Surveying is the science and practice of making those measurements and turning them into positions, maps and plans. Geomatics is the broader modern term that covers surveying together with satellite positioning, mapping, remote sensing and geographic information systems.

This course follows Coulee Geomatics Inc., a surveying and mapping firm in Great Falls, Montana. The firm's work this year includes control and topographic surveys for the Coulee Ridge subdivision, a new 36-lot residential development on the edge of the city; design and construction surveys for the extension of Coulee Ridge Drive, including a horizontal curve and a sag vertical curve; and earthwork volume surveys for a stormwater pond. The team includes Ruth Albrecht, a Professional Land Surveyor licensed in Montana who signs the boundary surveys and plats; Grant Okonkwo, the party chief who leads the field crew; Leah Tran, a civil engineering co-op student spending her term with the firm; and Theo Martel, a geomatics technologist who runs the drone and GIS work. Each lesson uses their projects to show how surveying measurements are made, checked and used.

What surveyors measure

At its core, surveying measures only a few quantities: horizontal distances, vertical distances (differences in elevation), horizontal angles and vertical angles. Modern instruments add a fourth kind of measurement, satellite positioning, which delivers three-dimensional coordinates directly. Everything else, including coordinates, areas, volumes, curve layouts and maps, is computed from these basic observations. A surveyor's skill lies less in pressing buttons than in choosing the right measurements, making them carefully, building in checks, and knowing how good the result is.

Positions are usually expressed as coordinates in a defined system. Horizontal positions are given either as latitude and longitude on a mathematical model of the Earth, or as grid coordinates called northing and easting on a map projection. Vertical positions are given as elevations above a defined reference surface, close to mean sea level, called a vertical datum. Lesson 9 explains these reference systems in detail; for now it is enough to know that every coordinate belongs to a particular system, and mixing systems is one of the most common and expensive mistakes in geomatics.

Kinds of surveys

Surveys are often grouped by purpose. The same instruments are used across all of them, but the accuracy needed, the legal weight of the result and the deliverables differ.

• Control surveys establish a framework of accurately positioned points, called control points or monuments, that later surveys tie to. A project control network for a subdivision might consist of a dozen points set with GNSS and traverses, tied to the national or state reference system.
• Topographic surveys measure the shape of the ground and the location of natural and built features, such as trees, fences, buildings, utilities and drainage ditches, to produce a base map for design.
• Boundary or cadastral surveys establish or re-establish property boundaries, create new parcels, and prepare plats for recording with the county. In Montana, only a licensed Professional Land Surveyor may carry out these surveys.
• Construction or layout surveys place stakes, marks and offsets on the ground so that contractors can build what the designers drew, and check grades and alignments as work proceeds.
• As-built surveys measure completed work, such as the actual location and invert elevations of pipes, so that the record drawings reflect reality.
• Monitoring surveys measure small movements over time, for example settlement of a bridge pier, movement of a landslide or deformation of a dam.
• Hydrographic surveys map the bottoms of lakes, rivers and harbours, and mine surveys measure underground workings.

Plane and geodetic surveying

The Earth is roughly an ellipsoid about 6,371 km in mean radius. Over a small area, such as a building site or a subdivision, the curved surface can be treated as a flat plane without significant error. Surveys computed this way are called plane surveys. Over larger areas, or where high accuracy matters, the curvature of the Earth must be considered, and the survey is called geodetic. The difference is small horizontally: over a distance of 10 km, the arc along the Earth's surface and the straight chord differ by less than 1 cm. Vertically the effect is much larger, because the Earth's surface curves away from a horizontal line of sight by about 7.8 cm over 1 km and about 7.8 m over 10 km. Lesson 4 shows how leveling procedures cancel this effect.

In practice, almost every modern project is a hybrid. Control is established in a geodetic reference system with GNSS, then projected onto a map projection so that day-to-day computations can be done in plane coordinates. The projection introduces small, predictable scale distortions that surveyors correct for, as lesson 9 explains.

Units and conventions

In the United States, surveys use feet for most construction and property work, with distances usually recorded to the hundredth of a foot, areas in square feet or acres, and volumes in cubic yards. Angles are measured in degrees, minutes and seconds, where one degree equals 60 minutes and one minute equals 60 seconds. Road alignments are described by stations measured along a centerline in hundreds of feet: station 12+50.00 is 1,250 ft from the start of the alignment. Older plats and legal descriptions use chains (66 feet) and links, which are still found when retracing original township surveys of the Public Land Survey System that covers most of the country west of the original colonies. Federal mapping and GNSS work use meters.

American surveyors must watch for the two feet that have been used in the country. The international foot is defined as exactly 0.3048 m. The US survey foot, defined as 1200/3937 m, is longer by about 2 parts per million, which amounts to about 2 ft in a State Plane coordinate of 1,000,000 ft. The National Geodetic Survey and the National Institute of Standards and Technology deprecated the US survey foot at the end of 2022, so new work uses the international foot, but decades of older coordinates and plans still use the survey foot, and the definition must be checked whenever coordinates in feet are exchanged.

# Unit conversions used throughout the course
US_FT = 1200 / 3937          # metres per US survey foot
INT_FT = 0.3048              # metres per international foot
CHAIN_FT = 66                # one Gunter's chain in feet

value_ft = 1_524_000.00
m_us = value_ft * US_FT
m_int = value_ft * INT_FT
print(f"{value_ft:,.2f} US survey ft = {m_us:,.3f} m")
print(f"{value_ft:,.2f} international ft = {m_int:,.3f} m")
print(f"difference = {m_us - m_int:.3f} m ({(US_FT/INT_FT - 1)*1e6:.2f} ppm)")

# A distance of 20 chains 35 links from an old township plan
chains, links = 20, 35
feet = (chains + links / 100) * CHAIN_FT
print(f"20 chains 35 links = {feet:.2f} ft = {feet * INT_FT:.3f} m")

# Earth curvature drop over a horizontal sight
R = 6_371_000
for d in (100, 1000, 10_000):
    print(f"curvature drop over {d:>6} m = {d**2 / (2*R):.4f} m")

1,524,000.00 US survey ft = 464,516.129 m
1,524,000.00 international ft = 464,515.200 m
difference = 0.929 m (2.00 ppm)
20 chains 35 links = 1343.10 ft = 409.377 m
curvature drop over    100 m = 0.0008 m
curvature drop over   1000 m = 0.0785 m
curvature drop over  10000 m = 7.8481 m

Who does surveying

Surveying work in the United States is done by several groups. Professional Land Surveyors are licensed by state boards, which in Montana is the Board of Professional Engineers and Professional Land Surveyors, and only a licensed surveyor may establish property boundaries or sign a plat. Licensure typically requires education, experience under a licensed surveyor, and passing the national Fundamentals of Surveying and Principles and Practice of Surveying examinations plus any state-specific examination. Geodesists and geomatics specialists in agencies such as the National Geodetic Survey maintain the national reference system. Survey technicians, often trained in two-year programs, run instruments, process data and draft plans under the direction of licensed professionals. Civil engineers also need a working knowledge of surveying, because they design from survey data, specify the accuracy of layout and judge whether construction meets tolerances.

On the Coulee Ridge project, the division of responsibilities is typical. Ruth is responsible for the legal survey of the subdivision boundary and new lots, and she signs the plan. Grant runs the field crew, sets control and does the construction layout. Theo flies the drone and builds the surface model and GIS deliverables. Leah's job this term is to learn each task, check computations and, by the end of the course, compute a traverse adjustment and stake out a curve on her own.

Field procedure and good practice

Good surveys share some habits that matter more than any particular instrument.

• Work from the whole to the part. Establish accurate control first, then fill in detail from it. Errors in detail then stay local instead of spreading across the project.
• Build in independent checks. Close traverses back on known points, run level loops back to the starting benchmark, measure distances in both directions, and observe angles on both faces of the instrument. A survey with no redundancy can hide a blunder.
• Keep complete, original field records. Whether the notes are handwritten or stored in a data collector, they must show what was measured, when, by whom, with what instrument, and any sketches and remarks needed to understand them later. Legal surveys may be examined in court decades after they were made.
• Calibrate and adjust equipment regularly. A level with a tilted line of sight, a total station with collimation error or a tape that has stretched produces systematic errors that repeat in every measurement.
• Think about safety. Survey crews work near traffic, heavy equipment, excavations, water and overhead power lines. Traffic control plans, high-visibility clothing, awareness of equipment swing radius and care around trenches are part of every field day.

Accuracy and tolerances

No measurement is exact. Each survey must be accurate enough for its purpose, and achieving more accuracy than needed wastes time and money. Construction layout tolerances depend on what is being built: anchor bolts for structural steel may need to be placed within a few millimeters, while rough grading stakes may be acceptable within a few centimeters. Control surveys are specified by accuracy classes or standards that state the maximum allowable error at a given confidence level. Lesson 2 introduces the vocabulary of errors and the statistics surveyors use to describe accuracy.

How the course is organized

The course moves from basic measurements to complete projects. Lessons 2 and 3 cover errors and distance measurement. Lessons 4 and 5 cover leveling, profiles, cross-sections and earthwork volumes. Lessons 6 to 8 cover angles, total stations, traverses and coordinate geometry. Lesson 9 explains datums, map projections and coordinate systems, lesson 10 covers satellite positioning, and lesson 11 covers GIS, lidar, photogrammetry and drones. Lesson 12 brings everything together in construction layout, including the horizontal and vertical curves for the Coulee Ridge Drive extension.