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How to: Some Basic Principles for Leveling

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. Equipment. Equipment. Level Instrument Tripod Staff/Pole

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How to: Some Basic Principles for Leveling

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  1. How to:Some Basic Principles forLeveling Tilo Schöne GFZ, Germany tschoene@gfz-potsdam.de

  2. 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

  3. Equipment ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006

  4. 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

  5. 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

  6. Automated Levels (Compensator) Pendulum Bull Eye Tribrach Courtesy: Deumlich, Vermessungskunde ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006

  7. 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

  8. 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

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. 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

  15. Equipment: Bubble • Keep the pole upright • Any tilt will disturb your readings ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006

  16. 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

  17. 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

  18. Introduction to Leveling ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006

  19. 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

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

  21. 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

  22. Reading a Staff • Read the [m], [dm] & [cm] • Estimate the [mm] • Check yourself for frequent used numbers (2/3) or (7/8) 1422 ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006

  23. 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

  24. Observation, Field Notes, and Computation ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006

  25. New Benchmark NB2 S2 New Benchmark NB1 Tidal Hut TH S1 How to: A sample loop ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006

  26. New Benchmark NB2 New Benchmark NB1 Tidal Hut TH How To: Field Notes S2 1327 2365 3982 2347 0986 3753 3724 1101 S1 ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006

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

  28. ? Compute levels 100 000 1327 2365 3982 97 345 ´7345 +1 0986 98 724 1379 2347 ´8624 3724 3753 97 348 1101 2652 100 000 9793 0 0 9792 -0001 0000 0001 (SOLL – IST) ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006

  29. 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

  30. 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

  31. 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

  32. 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

  33. 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

  34. Errors and their effects(many, but only a few addressed) ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006

  35. 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

  36. Systematic and Random Errors • Earth curvature • Refraction • Collimation errors ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006

  37. Effect of Earth Curvature Horizontal Level Curvature effect (r +Dh)2 = r2 + s2 => Dh  s2/(2r) 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

  38. 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

  39. 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

  40. Stand point 2 ´ ´ Stand point 1 ´ ´ Instrument test: Nähbauer 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 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 e = ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006

  41. Summary ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006

  42. 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

  43. 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

  44. An Unhappy Surveyor … having a 2 centimeter difference ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006

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