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) Bull Eye Pendulum 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 Conventional (“E”-type) Barcode for Digital Levels 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 IndonesianGerman 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 fs bs Dh = bs - fs Gravity Gradient 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 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) 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 New Benchmark 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 Back S2 Inter Fore TH 1327 New Benchmark NB1 Point 2365 3982 NB1 2347 0986 NB2 3753 3724 1101 NB1 TH Tidal Hut TH S1 ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006 Date, Observer, Instrument SD Fore Back Instrument Check ODINAFRICA/GLOSS Sea Level Training Course - Oostende, Belgium - 13-24 Nov. 2006 Compute levels Back Inter Fore dh Comment 100 000 1327 2365 2347 H +1 3753 9792 IST SOLL 3982 ´7345 97 345 0986 1379 98 724 3724 ´8624 97 348 1101 2652 100 000 9793 0 TH BM1 BM2 ? BM1 TH 0 -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 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 2,5s 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 (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 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′2 = a2+2e a′1 = a1+e b′2 = b2+e b′1 = b1+2e Δh = a2−b2 Δh = a1−b1 Δh′2 = a′2−b′2 = a2+e−b2 = Δh+e Δh′1 = a′1−b′1 = a1−b1−e = Δh−e Δh =Δh′2−e With Δh′1+e = Δh′2−e Δh′2−Δh′1 e= 2 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 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 - 13-24 Nov. 2006 Procedure of Leveling 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 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