Lecture 1: Levelling
➢ Fundamental concepts
➢ Determining height differences using
differential levelling
➢ Instrumentation
➢ Reductions & operations
➢ Testing & limitations
➢ Chap. 2 (Uren & Price) 5th Ed.
Levelling
C. Roberts, Surveying & Geospatial Engineering, UNSW, Bruce Harvey (c)
Basic Survey Measurements
➢ Height differences
➢ Levelling
➢ Angles
➢ Theodolite
➢ Distances
➢ Tape, EDM
In combination gives 3-D position (coordinates) of points…
What is the appropriate technique & technology?
Levelling
C. Roberts, Surveying & Geospatial Engineering, UNSW, Bruce Harvey (c)
What is the Shape of the Earth?
Levelling
C. Roberts, Surveying & Geospatial Engineering, UNSW, Bruce Harvey (c)
What is the Mathematical Shape of the
Earth?
Levelling
C. Roberts, Surveying & Geospatial Engineering, UNSW, Bruce Harvey (c)
But what about height ?
Where is sea
level?
Mt Everest is 8848m ± 1m
Above sea level
Levelling
C. Roberts, Surveying & Geospatial Engineering, UNSW, Bruce Harvey (c)
Geoid – like sea level …
… but actually the gravity field
http://grace.jpl.nasa.gov/resources/6/
Principles: Earth's Gravity Field & Survey
Operations (1)
➢ Gravity --> LOCALLY - horizontal lines & surfaces
➢ Pendulums, liquid surfaces & bubbles
➢ Direction of gravity force defines vertical line or
'plumbline'
➢ Direction of gravity changes about 1" for a horizontal
distance of every 30m due to Earth curvature
Levelling
C. Roberts, Surveying & Geospatial Engineering, UNSW, Bruce Harvey (c)
Datum
Plumblines
➢ Plumblines have twist
and torsion due to the
curve of the Earth
➢ For most engineering
projects covering small
portions of the Earth, this
effect can be ignored!
Levelling
C. Roberts, Surveying & Geospatial Engineering, UNSW, Bruce Harvey (c)
Diagram courtesy Stolz
courtesy Stolz
Principles: Earth's Gravity Field & Survey
Operations (2)
➢ Gravity equipotential surfaces are approx.
'horizontal’ - locally
➢ Local variations in 'plumbline' due to Earth's
non-sphericity and local mass anomalies.
➢ Elevation datum surface often referred to as
the 'geoid'.
Levelling
C. Roberts, Surveying & Geospatial Engineering, UNSW, Bruce Harvey (c)
AUSGEOID2020 Geoid Model
Ranges from -35 to +75 m across Australia with a NE slope
Geoid contours relative to GDA2020 datum at geocentre
What is Levelling?
➢ 'Levelling' is process of measuring or setting out a
difference in height between two or more points.
➢ In engineering surveying, levelling is used at all stages
in construction projects, from the initial site survey
through to the final setting out.
➢ Most accurate and commonly used technique is 'spirit
levelling'.
Levelling
C. Roberts, Surveying & Geospatial Engineering, UNSW, Bruce Harvey (c)
Hydrostatic Levelling
Fix tube on datum
Use other end of
tube as a roving
check
Plastic tube with
water in it
PS used food colouring
to see the water
If water level the
same = level.
If out, it will be out
by twice as much.
Hydrostatic Levelling - Obsolete
Applications
➢ Contour plans
➢ Construction of level surfaces, e.g. setting out
floor levels, etc
➢ Long sections and cross sections for roads,
drainage design, etc
➢ Subsidence and deformation monitoring
➢ Determine as-built (work as executed) or natural
surface levels
Levelling
C. Roberts, Surveying & Geospatial Engineering, UNSW, Bruce Harvey (c)
Long Section (courtesy Uren & Price)
Levelling
C. Roberts, Surveying & Geospatial Engineering, UNSW, Bruce Harvey (c)
Cross Section (courtesy Uren & Price)
Levelling
C. Roberts, Surveying & Geospatial Engineering, UNSW, Bruce Harvey (c)
Principles of Spirit Levelling
➢ Optical instrument able to define a 'horizontal' line (or
surface)
➢ Graduated staff, held vertically
➢ 'Absolute height' benchmark
➢ Operational procedure to determine height difference
between two points
Levelling
C. Roberts, Surveying & Geospatial Engineering, UNSW, Bruce Harvey (c)
Datum
Types of Level Instruments
Types of Modern Levels
➢ Dumpy Level - obsolete
➢ Tilting Level
➢ Automatic Level
➢ Digital Level
Tilting
Level
Split Bubble Image
(for tilting level)
VERY OLD – YOU MAY ONLY SEE THIS IN A MUSEUM
Automatic Level
Automatic Level
➢ No precise spirit bubble
attached. The telescope
need only be
approximately levelled by
means of circular bubble
and a 'compensating
device' inside the
telescope will correct for
any residual
mislevelment.
Compensator
Components of an Automatic Level
1. Base plate
2. Footscrew (3 of them)
3. Horizontal circle
4. Reading index for circle
5. Press button for compensator
6. Telescope eyepiece
7. Protective cover for adjustment screw
8. Telescope focusing knob
9. Gunsight
10. Telescope objective
11. Horizontal drive screw
12. Dots marking 0o, 90o, 180o, 270o (whole circle)
Digital Level
➢ An automatic level which
allows measurements to be
made electronically to a
levelling staff on whose
face is a bar code scale.
➢ Manual measurements to a
classic staff also possible.
(Optical) Bar
Code
Reading
Note: Passive system.
Digital Level does not
emit a beam.
Digital Level measures staff intercept (H).
Horizontal distance to front of staff (D).
Rotating Laser
Levels
Lenses on
pendulum
wires
Hold Levelling Staff Vertical!
Staff reading is greater
when the staff is inclined
1.067
1.050
1.030
1.000
0.973
0.950
Levelling
C. Roberts, Surveying & Geospatial Engineering, UNSW, Bruce Harvey (c)
U&P Fig 2.5 pp33
Some instruments give inverted image!
Also important for inverted staff readings (book as -ve number)
Telescopes
➢ Focus / Parallax
U&P Fig 2.6
Adjusting Eyepiece for Parallax
Height Datums
➢ There was no national height datum prior to
proclamation of the Australian Height Datum (AHD)
in 1972 → AHD71.
➢ Most height datums are based on local mean sea
level (MSL).
➢ Variety of project-based (or institutional) height
datums → “local datum”.
➢ Offshore (chart) datums (hydrographic surveying)
B&R p72-73
typicallyReference:
different
from onshore (land map) datums.
Height Datums - OLD
Prior to 1971, Standard Datum was used.
Defined by value for MSL at Fort Denison,
accessed via a survey plug, north wall of the
Dept of Lands Bldg in Bridge St, Sydney.
Reference: B&R p72-73
Australian Height Datum (AHD) proclaimed in 1972 → AHD71.
Height - from Tide Gauges
The observations for MSL spanned 3 years (between 1 January 1966 and 31 December 1968)
Australian Height Datum
AHD was realised by setting MSL to zero at 30 tide gauges distributed around the coast of
mainland Australia and adjusting 97,320 km of 2-way spirit levelling across the country.
Field Booking and Calculations
➢ 'Rise and Fall' method
➢ 'Height of Collimation' method
HoC = RLA + R1
HoC = RLB + R3
R2
R1
R4
R3
RLB
B
RLA
I1
I2
RLC
A
C
U&P Fig 2.22
Calculating Height Difference
Height difference from A to B = 1.234 - 0.567
= 0.667
Height difference from B to C = 0.123 - 1.123
= -1.000
0.567
0.123
1.123
B
A
C
Some Terminology
Backsight (BS)
Foresight (FS)
/ Backsight
Foresight
0.567
0.123
1.123
B
Change Point (CP)
A
C
Some Terminology
➢ Back Sight (BS) is the first staff reading
observed after setting up of the level.
➢ Fore Sight (FS) is the staff reading
observed before shifting of the level.
➢ Intermediate Sights (IS) are staff
reading observed after BS but before FS.
➢ Change Point (CP) is the staff position
at which the position of the level is being
changed.
Change Plates
RL of Change point
Reduced Levels and Bench Marks
➢ Reduce Level (RL) of a point is its height above
the level datum (eg AHD71).
➢ Bench Marks (BMs) are marks with known RLs:
– Temporary Bench Marks (TBMs) are stable but not
permanent marks established close to construction
site.
– Precise Bench Marks are stable and permanent
marks.
'Rise and Fall' Method
C
B
BMA
BS
2.191
IS
D
FS
Rise
0.453
0.627
1.111*
1.564
0.342
1.845
2.533
2.587
-0.054
* Note IS-FS
2.134
2.587
1.738
1.792
-0.054
Fall
BME
RL Remark
1.243 BMA
1.870 B
2.981 C (CP)
1.503 1.478 D
0.289* 1.189 BME
1.792 1.189 Arithmetic
1.243 Checks!
-0.054
Height of Collimation
Ht of Collimation = RL of Collimation Axis
= 1.243 + 2.191
= 3.434
RL= 1.243
Height of Collimation Method
3.434
3.323
C
B
BMA
BS
2.191
IS
1.564
0.342
1.845
2.533
2.587
-0.054
D
BME
FS Ht of Collimation RL Remark
1.243 BMA
3.434
1.870 B
0.453
2.981 C (CP)
3.323
1.478 D
2.134
1.189 BME
2.587
1.189
1.243
-0.054
Height of Collimation method
BS
IS
FS
2.857
HoC
RL
Remarks
48.425 45.568
BM
46.437
CP1
1.988
K
L
M
N
K
CP1
BM
BM
Plan
CP1
Height of Collimation method
BS
IS
FS
HoC
RL
Remarks
2.857
48.425 45.568
BM
0.356
1.988 46.793 46.437
CP1
0.65
46.143
K
2.11
44.683
L
3.04
43.753
M
43.668
N
3.125
N
K
Intermediate
sights
L
CP1
BM
K
Plan
CP1
M
Height of Collimation method
BS
IS
FS
HoC
RL
Remarks
2.857
48.425 45.568
BM
0.356
1.988 46.793 46.437
CP1
0.65
46.143
K
2.11
44.683
L
3.04
43.753
M
3.125 47.993 43.668
N
46.143
K
46.437
CP1
4.325
1.85
1.556
N
BM
L
K
Plan
CP1
M
Height of Collimation method
BS
IS
FS
HoC
RL
Remarks
2.857
48.425 45.568
BM
0.356
1.988 46.793 46.437
CP1
0.65
46.143
K
2.11
44.683
L
3.04
43.753
M
3.125 47.993 43.668
N
46.143
K
1.556 50.474 46.437
CP1
4.907
BM
4.325
1.85
4.037
45.567
RL45.568
Plan
Things to Watch!
➢ Instrument not level – (bubble in centre of bulls eye?)
➢ Misreading staff - perform backward/forward level runs
➢ Instrument out of adjustment (collimation error)
- equal FS & BS/ perform '2 peg test'
➢ Acceptable misclose - (within tolerance?)
➢ Don’t bump the legs
➢ Don’t adjust bubble between BS and FS observations
➢ Invert levels - (book as –ve value)
Misclose = RL obs – RL given (= Error)
Error = - Corrections
Accuracy Specification
The tolerance for levelling is usually
expressed in the form:-
E = C K
where E = allowable misclose in mm
C = constant in mm (3rd order = 12mm)
K = total length of the level circuit in kms
Levelling
C. Roberts, Surveying & Geospatial Engineering, UNSW, Bruce Harvey (c)
Adjustment of Levelling Misclose
RL
Remarks
23.456
Corr Adj RL
mm
23.456
21.906
-2
21.904
Cp1
24.342
-4
24.338
Cp2
22.456
-6
22.450
Cp3
28.317
-8
28.309
Cp4
32.166
-10
32.156
BM2
32.156
BM1
given
Instrumental Errors - '2 peg test'
True horizontal plane
Line of collimation
error
error
X
X
S2
S1’
S2’
A
B
C
L/2
L/2
error
S4
U&P Fig
2.19
S3
S4’
S3’
A
B
L
<L/10
S1
'2 peg test' Example
L = 50m
True horizontal plane
Line of collimation
S2
S2 = 1.258
X
X
S1’
S2’
A
L/2
S1 = 1.237
true H = 0.021
B
C
S1
L/2
S3 = 1.332  S3’
error
S4
S4 = 1.363 S4’=1.353
S3
H’ = 0.031
S4’
S3’
A
B
L
error = 0.031-0.021
<L/10
= + 0.010 / 50
Curvature and
Refraction
Curvature (m)  0.0785 D2
(D sight distance in kms)
Refraction bends line of sight
 1/7th of curvature effect in
opposite direction (up)**
Combined effect:
 1mm in 120m
(and 69.4 mm in 1 km)
Reciprocal Levelling U & P pp 58
➢ It is beneficial to maintain equal sight distances
(ie BS & FS) in levelling to eliminate collimation
error and the effect of atmospheric refraction and
curvature (for long levelling line).
➢ For levelling across wide gap, such as river, sea
channel or canyon, the technique of reciprocal
levelling is applied to eliminate the systematic
errors → RARE!
Reciprocal Levelling
E
A
R1
L
True Ht Diff, dH1 = R1 - E - R2
Used for
connection to Fort
Denison Tide
gauge
R2 B
5m
(1)
Fort Denison Schematic
Grade
U & P pp 684
➢ The results of a levelling run can be used to
determine grade.
➢ Grade = Rise / Run = Change in height / Distance
Rise = 2m
Run = 100m
Grade = Rise / Run = 2 / 100 = 0.02
Use 1/x => 1 / 0.02 = 50
Therefore Grade can be expressed as 1:50
Subsidence Issue for Jakarta
VISIT
2050
What’s JAKARTA
New and What’s
Next?
by Heri Andreas
2050
2025
2012
2007-2008
2008-2009
2009-2010
“visual” Evidence!
Pictures of PLTGU Building in year 1977
Pictures of PLTGU Building in year 2011
Roof 2nd floor
Roof 1st floor
Ground floor
~ 2 meter
Sea level in 2011
Sea level in 1977
“From 1977 to 2011 (~35 years), the sea level seems to have
risen about 2 metres”
Andreas, 2013
Less Influence from Global Warming!
“Sea Rising ~0.5 cm/year”
MSL (cm)
Perairan Utara Jakarta
15 mm/tahun
“The ground subsiding ~2-15 cm/year”
24.100
24.000
23.900
23.800
23.700
23.600
23.500
23.400
23.300
2005.5
2006
2006.5
2007
2007.5
2008
2008.5
2009
2009.5
2010
2010.5
Andreas, 2013
Measuring the Subsidence
Subsidence map of Jakarta 1974-2010:
Total subsidence -25 up to -400 cm ; rate -0.5 up to -17 cm/year
First record of leveling
data was in 1974. Based
on accumulated data,
interpolation and
extrapolation with GPS
data, we can make
subsidence map of
Jakarta from year 1974 up
to 2010.
-4,1 meter
-2,1 meter
-1,4 meter
-0,7 meter
-0.25 meter
Base on latest analysis of piezometric
surface data it was found that the
initial condition of subsidence was
probably around 1965.
Andreas, 2013
Warta Informasi Geospasial di DKI
Sign of Sinking is real!
Pluit, 26 November 2007
JCDS
Andreas, 2014
Warta Informasi Geospasial di DKI
Sign of Sinking is real!
Pluit, 26 November 2007
JCDS
Andreas, 2014
Warta Informasi Geospasial di DKI
Sign of Sinking is real!
Pluit, 15 November 2008
JCDS
Andreas, 2014
Warta Informasi Geospasial di DKI
Sign of Sinking is real!
Pluit, 15 November 2008
JCDS
Andreas, 2014
Warta Informasi Geospasial di DKI
Sign of Sinking is real!
Pluit, Februari 2011
JCDS
Andreas, 2014
Warta Informasi Geospasial di DKI
Sign of Sinking is real!
Pluit 18 Oktober 2013
JCDS
Andreas, 2014
Discussion
Pluit, 5 December 2017
Andreas, 2018
Sign of Sinking is real!
Muara Baru January 14, 2003
Muara Baru February 15, 2010
The Harbor in Muara Baru has disappeared
Andreas, 2013
Sign of Sinking is real!
Northern Kamal Muara March 24, 2004
Northern Kamal Muara February 15, 2010
Rice field in Northern Kamal Muara has disappeared
Andreas, 2013
Sign of Sinking is real!
Ancol March 24, 2004
Ancol February 15, 2010
Break water in Ancol has slowly been disappeared
Andreas, 2013
Model the Sinking of Jakarta
Area bellow the Sea Level
Area above the Sea Level
Around 26.86%
of Jakarta
maybe flooded
by the sea in
year 2025
Around 10.53%
of Jakarta
maybe flooded
by the sea in
year 2000
Around 15.58%
of Jakarta
maybe flooded
by the sea in
year 2007
Around 35.61%
of Jakarta
maybe flooded
by the sea in
year 2050
Around 18.78%
of Jakarta
maybe flooded
by the sea in
year 2012
The DEM Model derived form LiDAR data, rates of subsidence from GPS
and leveling Surveys, Sea level Rise from Satellite Altimetry
Andreas, 2013
Closing Remarks
Subsidence in Java
Amelung et.al 2010
University of Miami
Semarang area
Jakarta area
Bandung area
LUSI area
Kelompok Keilmuan Geodesi et.al
Institute of Technology Bandung
Andreas, 2013
Georges
River,
Sydney
Summary
➢ Principles of height difference measurement.
➢ Types of instrumentation.
➢ Field booking & calculations for 'Rise and Fall'
method.
➢ Height datums.
➢ Errors in levelling and how to guard against them.
➢ Application of levelling for flood modelling.
Levelling
C. Roberts, Surveying & Geospatial Engineering, UNSW, Bruce Harvey (c)
Things to do
➢ Read textbook (Uren & Price)
➢ Practice 'Rise & Fall' calculations
➢ Prac 1 next week
➢ Workshop exercise – week 2 – can start now
Levelling
C. Roberts, Surveying & Geospatial Engineering, UNSW, Bruce Harvey (c)