How to: Some Basic Principles for Leveling Tilo Schöne GFZ, Germany

ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium Nov Lecture Overview Equipment Introduction to Leveling Observation, Field Notes, and Computation Errors and their effects

ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium Nov Equipment

ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium Nov 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 Nov 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 Nov Automated Levels (Compensator) Pendulum Tribrach Courtesy: Deumlich, Vermessungskunde Bull Eye

ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium Nov 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 Nov 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 Nov Equipment: Tripod Wooden design or aluminum From “easy to sit” to “ops, this is high”

ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium Nov 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 Nov 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 Nov 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 Nov 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 Nov 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 Nov Equipment: Bubble Keep the pole upright Any tilt will disturb your readings

ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium Nov 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 Nov 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 Nov Introduction to Leveling

ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium Nov 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 Nov 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 Nov 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 Nov 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 Nov 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 Nov Observation, Field Notes, and Computation

ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium Nov How to: A sample loop S2 S1 New Benchmark NB1 Tidal Hut TH New Benchmark NB2

ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium Nov How To: Field Notes BackInterForePoint TH NB1 NB2 NB1 TH S2 S1 New Benchmark NB1 Tidal Hut TH New Benchmark NB

ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium Nov Date, Observer, Instrument Instrument Check Fore Back 

ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium Nov Compute levels BackInterForedhHComment TH BM1 BM2 BM1 TH IST SOLL (SOLL – IST) ´7345 ´ ? 0

ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium Nov Loop misclosure Misclosure Error The difference of the measured height difference (  H meas ) to the known height (closed loops = 0, known benchmarks = height difference) Misclosure =  H SOLL –  H IST Point errors at double observed points

ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium Nov Achievable Accuracy Instrument dependent Roughly from the instrument  NI002 = 0,2mm/km (doubled line)  NI025 = 2.5mm/km (doubled line) Survey line length dependent m s = m 1km  s, s in km m H = (m 1km /2)  s, s in km # (middle of the line)

ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium Nov 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 Nov 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 Nov 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 Nov Errors and their effects (many, but only a few addressed)

ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium Nov 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 Nov Systematic and Random Errors Earth curvature Refraction Collimation errors

ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium Nov Effect of Earth Curvature Curvature effect Distance (s) in m Effect (  h ) in mm 0,0080,030,20,880 Horizontal Level (r +  h) 2 = r 2 + s 2 =>  h  s 2 /(2r)

ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium Nov Refraction Mean Gradient: 0,2 °C / m

ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium Nov 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 sight error

ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium Nov Stand point 1 Stand point 2 ´ ´ ´ ´ Instrument test: Nähbauer a′ 1 = a 1 +e b′ 1 = b 1 +2e Δh = a 1 −b 1 Δh′ 1 = a′ 1 −b′ 1 = a 1 −b 1 −e = Δh−e With Δh′ 1 +e = Δh′ 2 −e Δh′ 2 −Δh′ 1 2 a′ 2 = a 2 +2e b′ 2 = b 2 +e Δh = a 2 −b 2 Δh′ 2 = a′ 2 −b′ 2 = a 2 +e−b 2 = Δh+e Δh =Δh′ 2 −e e =

ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium Nov Summary

ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium Nov 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 Nov Readings must be taken 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 Nov An Unhappy Surveyor … having a 2 centimeter difference