how to: some basic principles for leveling tilo schöne gfz, germany [email protected]
TRANSCRIPT
How to:Some Basic Principles forLeveling
Tilo SchöneGFZ, [email protected]
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
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)
Pendulum
Tribrach
Courtesy: Deumlich, Vermessungskunde
Bull Eye
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 Indonesian-German 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
Leveling rods
Line of sight
Back sight Fore sight
Gravity Gradient
Basic Principle of Leveling• Measures height differences between
points Along a line Several points from one occupation
bs
fs
h = bs - fs
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
1422
• Read the [m], [dm] & [cm]
• Estimate the [mm]
• 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
S2
S1
New BenchmarkNB1
Tidal HutTH
New BenchmarkNB2
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
How To: Field Notes
Back Inter Fore Point
TH
NB1
NB2
NB1
TH
1327
3982
S2
S1
New BenchmarkNB1
Tidal HutTH
New BenchmarkNB2
2365
09862347
37243753
1101
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Date, Observer,Instrument
Instrument Check
Fore
Back
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Compute levels
Back Inter Fore dh H Comment
TH
BM1
BM2
BM1
TH
IST
SOLL
1327
3982
0986
3724
2365
2347
3753
1101
1379
2652
9792 9793
-0001
+1
100 000
100 000
0000
0001 (SOLL – IST)
´7345
´8624
0
97 345
98 724
97 348
?
0
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Loop misclosure
• Misclosure Error The difference of the measured height
difference (Hmeas) to the known height (closed loops = 0, known benchmarks = height difference)
Misclosure = HSOLL – HIST
• 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 2,5s 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
Curva
ture
effec
t
Distance (s) in m 10 20 50 100 1000
Effect (h) 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
Horizontal Level
(r +h)2 = r2 + s2
=>h s2/(2r)
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Refraction
www.fh-oow.de/institute/ima/personen/weber/VK_12/VL_VK1/geo_niv_6.htm
Mean Gradient: 0,2 °C / m
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
horizontal line
line of sighterror
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
Stand point 1
Stand point 2
´ ´
´ ´
Instrument test: Nähbauer
a′1 = a1+e
b′1 = b1+2e
Δh = a1−b1
Δh′1 = a′1−b′1 = a1−b1−e = Δh−e
With Δh′1+e = Δh′2−e
Δh′2−Δh′12
a′2 = a2+2e
b′2 = b2+e
Δh = a2−b2
Δh′2 = a′2−b′2 = a2+e−b2 = Δh+e
Δh =Δh′2−e
e =
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 leveling1. 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
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
Procedure of Leveling
ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006
An Unhappy Surveyor
… having a 2 centimeter difference