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

2. 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

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

4. 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

5. 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

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

7. 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

8. 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

9. 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”

10. 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

11. 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

12. 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

13. 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!

14. 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

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

16. 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

17. 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

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

19. 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

20. 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

21. 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

22. 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)

23. 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

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

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

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

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

28. ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006 Compute levels BackInterForedhHComment TH BM1 BM2 BM1 TH IST SOLL 1327 3982 0986 3724 2365 2347 3753 1101 1379 2652 9792 9793 +1 100 000 0000 0001 (SOLL – IST) ´7345 ´8624 0 97 345 98 724 97 348 ? 0

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

30. 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 m s = m 1km  s, s in km m H = (m 1km /2)  s, s in km # (middle of the line)

31. 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

32. 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

33. 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)

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

35. 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

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

37. ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006 Effect of Earth Curvature Curvature effect Distance (s) in m1020501001000 Effect (  h ) in mm 0,0080,030,20,880 www.fh-oow.de/institute/ima/personen/weber/VK_12/VL_VK1/geo_niv_6.htm Horizontal Level (r +  h) 2 = r 2 + s 2 =>  h  s 2 /(2r)

38. 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

39. 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 sight error

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

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

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

43. 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

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