How to: Some Basic Principles for Leveling

1
How toSome Basic Principles forLeveling

• Tilo Schöne
• GFZ, Germany
• tschoene_at_gfz-potsdam.de

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Lecture Overview

• Equipment
• Introduction to Leveling
• Observation, Field Notes, and Computation
• Errors and their effects

3
Equipment
4
Equipment

• Level Instrument
• Tripod
• Staff/Pole
• Change plate (German Frog/Frosch)
• Pole staff bubble (bull eye)
• Marker

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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

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Automated Levels (Compensator)
Pendulum
Bull Eye
Tribrach
Courtesy Deumlich, Vermessungskunde
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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

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Equipment

• Level Instrument
• Tripod
• Staff/Pole
• Change plate (German Frog/Frosch)
• Pole staff bubble (bull eye)
• Marker

9
Equipment Tripod

• Wooden design or aluminum
• From easy to sit to ops, this is
  high

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Equipment

• Level Instrument
• Tripod
• Staff/Pole
• Change plate (German Frog/Frosch)
• Pole staff bubble (bull eye)
• Marker

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Equipment Staff/Pole

• Wood, aluminum
• INVAR type for high precision leveling

Barcode for Digital Levels
Conventional (E-type)
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Equipment

• Level Instrument
• Tripod
• Staff/Pole
• Change plate (German Frog/Frosch)
• Pole staff bubble (bull eye)
• Marker

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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

Its not the Indonesian- German Dictionary, Its
the nail!
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Equipment

• Level Instrument
• Tripod
• Staff/Pole
• Change plate (German Frog/Frosch)
• Pole staff bubble (bull eye)
• Marker

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Equipment Bubble

• Keep the pole upright
• Any tilt will disturb your readings

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Equipment

• Level Instrument
• Tripod
• Staff/Pole
• Change plate (German Frog/Frosch)
• Pole staff bubble (bull eye)
• Marker

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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

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Introduction to Leveling
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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 Instruments Bubble is in the normal (!)
• Horizontal surface
• At the instruments axis, the horizontal surface
  is tangent to the level surface
• Over short distances (lt100 m) the horizontal
  surface and the level surface will coincide
• For long leveling lines the effects of the
  gravity field must be considered

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Basic Principle of Leveling

• Measures height differences between points
• Along a line
• Several points from one occupation

fs
bs
Dh bs - fs
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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

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Reading a Staff

• Read the m, dm cm
• Estimate the mm
• Check yourself for frequent used numbers (2/3)
  or (7/8)

1422
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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 lt 50m)
• Never read below 0.5m on a staff (refraction)
• Use stable, well defined change points
• Beware of shadowing effects and crossing waters

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Observation, Field Notes, and Computation
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How to A sample loop
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How To Field Notes
S2
1327
3982
2365
2347
0986
3753
3724
1101
S1
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Date, Observer, Instrument
Instrument Check
SD
Back
Fore
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Compute levels
100 000
1327
3982
2365
97 345
7345
1
0986
98 724
2347
1379
8624
3724
3753
97 348
1101
2652
100 000
9793
0
0
9792
-0001
0000
0001 (SOLL IST)
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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

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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)

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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

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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 contrys rules and the
  instrument used

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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)

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Errors and their effects(many, but only a few
addressed)
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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

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Systematic and Random Errors

• Earth curvature
• Refraction
• Collimation errors

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Effect of Earth Curvature
Horizontal Level
Curvature effect
(r Dh)2 r2 s2 gt Dh ? s2/(2r)
www.fh-oow.de/institute/ima/personen/weber/VK_12/V
L_VK1/geo_niv_6.htm
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Refraction
Mean Gradient 0,2 C / m
www.fh-oow.de/institute/ima/personen/weber/VK_12/V
L_VK1/geo_niv_6.htm
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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

line of sight
error
horizontal line
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Instrument test Nähbauer
a'2 a22e b'2 b2e ?h a2-b2 ?h'2
a'2-b'2 a2e-b2 ?he ?h ?h'2-e
a'1 a1e b'1 b12e ?h a1-b1 ?h'1
a'1-b'1 a1-b1-e ?h-e With ?h'1e ?h'2-e
?h'2-?h'1 2
e
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Summary
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Procedure of leveling

• The instrument must be check before use! (see
  lecture)
• The instrument and level must be stable
  settled-up
• The bubble tube must be leveled before the
  reading
• Beware of sun exposure (will wander)
• Ensure the instruments pendulum is in-limit
• 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
• You must not use the parallax screw between the
  backsight and foresight readings

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Procedure of Leveling

• Readings must be taken 30-50 cm above the ground
• Surface refractions
• Beware also of temperature gradients
  (inside/outside buildings) !!!!
• Staff should be set up vertically
• A change plate should be used
• Leveling must be done in two opposite directions
  but the same line (beware of gravity gradients)
• Staff should be calibrated, especially if INVAR
• Be careful when crossing rivers (large water
  surfaces)
• Use same-time (mutual) observations
• Repeat it during different times of the day

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An Unhappy Surveyor

• having a 2 centimeter difference