How to:
Some Basic
Principles for
Leveling
Tilo Schöne
GFZ, Germany
tschoene@gfz-potsdam.de
Lecture Overview
• Equipment
• Introduction to Leveling
• Observation, Field Notes, and
Computation
• Errors and their effects
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Equipment
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Equipment
•
•
•
•
•
•
Level Instrument
Tripod
Staff/Pole
Change plate (German: Frog/Frosch)
Pole staff bubble (bull eye)
Marker
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Equipment: Level Instrument
• Automated Levels



Easy to use (not power!)
Needs experience
Robust even in hostile environment
• Digital Levels



Push-button technique
No reading errors, special staff
Readings are stored and analyzed digitally
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Automated Levels (Compensator)
Bull Eye
Pendulum
Tribrach
Courtesy: Deumlich, Vermessungskunde
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Digital Levels
• Uses Barcode staffs
• Internal storage of data




Download to the computer
Automated height computation + adjustment
No feeling for quality anymore
You frequently need power plugs
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Equipment
•
•
•
•
•
•
Level Instrument
Tripod
Staff/Pole
Change plate (German: Frog/Frosch)
Pole staff bubble (bull eye)
Marker
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Equipment: Tripod
• Wooden design or aluminum

From “easy to sit”
to
“ops, this is high”
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Equipment
•
•
•
•
•
•
Level Instrument
Tripod
Staff/Pole
Change plate (German: Frog/Frosch)
Pole staff bubble (bull eye)
Marker
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Equipment: Staff/Pole
• Wood, aluminum
• INVAR type for high precision leveling
Conventional (“E”-type)
Barcode
for Digital Levels
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Equipment
•
•
•
•
•
•
Level Instrument
Tripod
Staff/Pole
Change plate (German: Frog/Frosch)
Pole staff bubble (bull eye)
Marker
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Equipment: Change Plate
• For long survey lines
• Allows change of instruments



Best is a metal change plate
Screws e.g. at fences
Sharp stones or nails
• Beware of dark colors
It’s not the
IndonesianGerman Dictionary,
It’s the nail!
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Equipment
•
•
•
•
•
•
Level Instrument
Tripod
Staff/Pole
Change plate (German: Frog/Frosch)
Pole staff bubble (bull eye)
Marker
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Equipment: Bubble
• Keep the pole upright

Any tilt will disturb your readings
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Equipment
•
•
•
•
•
•
Level Instrument
Tripod
Staff/Pole
Change plate (German: Frog/Frosch)
Pole staff bubble (bull eye)
Marker
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Survey Markers
• Gives you a fixed point




Should be of good quality
Should be long-term
Preferable in bedrock, settled buildings, or bridges
Do not use fences or walls
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Introduction to Leveling
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Some Basic Definitions
• Level surface (e.g. the geoid)



A water surface with no motion
Gravity gradient is the normal to the level surface
The Instrument’s Bubble is in the normal (!)
• Horizontal surface



At the instruments axis, the horizontal surface is tangent
to the level surface
Over short distances (<100 m) the horizontal surface
and the level surface will coincide
For long leveling lines the effects of the gravity field
must be considered
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Basic Principle of Leveling
• Measures height differences between points

Along a line

Several points from one occupation
Leveling rods
Line of sight
Back sight
Fore sight
fs
bs
Dh = bs - fs
Gravity Gradient
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Definitions
• Back sight (BS)

The first reading from a new instrument stand
point (i.e. take the height to the instrument)
• Fore sight (FS)

The last reading from the current instrument
station (i.e. give the height to a benchmark)
• Intermediate sight (IS)

Any sighting that is not a back sight or fore sight
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Reading a Staff
• Read the [m], [dm] & [cm]
• Estimate the [mm]
1422
• Check yourself for frequent
used numbers (2/3) or (7/8)
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Basic Rules for Leveling
• Always start and finish a leveling run on a
Benchmark (BM or TGBM) and close the loops
• Keep fore sight and back sight distances as equal
as possible
• Keep lines of sight short (normally < 50m)
• Never read below 0.5m on a staff (refraction)
• Use stable, well defined change points
• Beware of shadowing effects and crossing waters
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Observation, Field Notes, and
Computation
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
How to: A sample loop
New Benchmark
NB2
S2
New Benchmark
NB1
Tidal Hut
TH
S1
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
How To: Field Notes
New Benchmark
NB2
Back
S2
Inter
Fore
TH
1327
New Benchmark
NB1
Point
2365
3982
NB1
2347
0986
NB2
3753
3724
1101
NB1
TH
Tidal Hut
TH
S1
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Date, Observer,
Instrument
SD
Fore
Back
Instrument Check
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Compute levels
Back
Inter
Fore
dh
Comment
100 000
1327
2365
2347
H
+1
3753
9792
IST
SOLL
3982
´7345
97 345
0986
1379
98 724
3724
´8624
97 348
1101
2652
100 000
9793
0
TH
BM1
BM2
?
BM1
TH
0
-0001
0000
0001 (SOLL – IST)
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Loop misclosure
• Misclosure Error

The difference of the measured height difference
(DHmeas) to the known height (closed loops = 0,
known benchmarks = height difference)
Misclosure = DHSOLL – DHIST
• Point errors at double observed points
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Achievable Accuracy
• Instrument dependent

Roughly from the instrument
 NI002 = 0,2mm/km (doubled line)
 NI025 = 2.5mm/km (doubled line)
• Survey line length dependent


ms = m1km s, s in km
mH = (m1km/2) s, s in km #(middle of the line)
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
An acceptable misclose?
• Small misclosures in closed level loops are
expected because of the accumulation of
random errors and can be adjusted
• If the misclosure is large, the loop (or part of
it) must be repeated
• Misclosures can also result from errors in published
BM levels and from BM instability
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Testing the misclose
• The amount of misclosure acceptable using a
specific instrument and survey line length
• For our example, a second order leveling
standard is adopted*…
misclosure  2,5s mm
• where s is the length of the line in km
*Dependent on your contry’s rules and the instrument used
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Our example
• The misclosure is +1 mm
• The length of the loop is 0.4 km
• Acceptable error is
2.5(0.4) = ±1.6 mm
• The misclosure of +1 mm is within the limit
• Mean error for NB1 = 2.5/2* (0.4)
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Errors and their effects
(many, but only a few addressed)
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Errors in leveling, e.g.
•
•
•
•
•
•
•
Collimation, Parallax
Change point / staff instability
Instrument or Benchmark instability
Refraction
Uncalibrated staff or levels
Reading, booking, or computation errors
Fore- and backsight distances different
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Systematic and Random Errors
• Earth curvature
• Refraction
• Collimation errors
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Effect of Earth Curvature
Horizontal Level
(r +Dh)2 = r2 + s2
=>
Dh  s2/(2r)
Distance (s) in m
10
20
50
100
1000
Effect (Dh) in mm
0,008
0,03
0,2
0,8
80
www.fh-oow.de/institute/ima/personen/weber/VK_12/VL_VK1/geo_niv_6.htm
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Refraction
Mean Gradient: 0,2 °C / m
www.fh-oow.de/institute/ima/personen/weber/VK_12/VL_VK1/geo_niv_6.htm
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Collimation error
• Occurs when the line of sight (as defined by
the lens axis and cross-hairs) is not
horizontal
• Leads to an incorrect staff reading
error
horizontal line
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Instrument test: Nähbauer
´
´
´
´
Stand point 1
Stand point 2
a′2 = a2+2e
a′1 = a1+e
b′2 = b2+e
b′1 = b1+2e
Δh = a2−b2
Δh = a1−b1
Δh′2 = a′2−b′2 = a2+e−b2 = Δh+e
Δh′1 = a′1−b′1 = a1−b1−e = Δh−e
Δh =Δh′2−e
With Δh′1+e = Δh′2−e
Δh′2−Δh′1
e=
2
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Summary
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Procedure of leveling
1. The instrument must be check before use! (see lecture)
2. The instrument and level must be stable settled-up
3. The bubble tube must be leveled before the reading
•
Beware of sun exposure (will wander)
•
Ensure the instruments pendulum is in-limit
4. The instrument must be set up in the middle between two
staffs
•
Prevents curvature effects
•
If impossible, use the same distances, but opposite for the
next readings
5. You must not use the parallax screw between the backsight
and foresight readings
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Procedure of Leveling
6. Readings must be taken 30-50 cm above the ground
•
•
Surface refractions
Beware also of temperature gradients (inside/outside
buildings) !!!!
7. Staff should be set up vertically
8. A change plate should be used
9. Leveling must be done in two opposite directions but the
same line (beware of gravity gradients)
10. Staff should be calibrated, especially if INVAR
11. Be careful when crossing rivers (large water surfaces)
•
•
Use “same-time” (mutual) observations
Repeat it during different times of the day
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
An Unhappy Surveyor
… having a 2 centimeter difference
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006