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) Pendulum Bull Eye 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 Barcode for Digital Levels Conventional (“E”-type) 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

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 Gravity Gradient fs bs Dh = bs - fs ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006

Definitions Back sight (BS) Fore sight (FS) Intermediate sight (IS) 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) 1422 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 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 S2 Back Inter Fore Point TH NB1 1327 2365 3982 2347 0986 3753 3724 New Benchmark NB1 1101 Tidal Hut TH S1 ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006

SD Date, Observer, Instrument Instrument Check Back Fore ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006

Compute levels TH BM1 BM2 ? IST SOLL Back Inter Fore dh H Comment 1327 100 000 2365 3982 ´7345 ? 97 345 +1 0986 2347 1379 98 724 3753 3724 ´8624 97 348 1101 2652 100 000 9792 9793 -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 Survey line length 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 Curvature effect (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 line of sight 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′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′1 2 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 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 ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006

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 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