Reduction of Field Observations

Transcription

1 Reduction of Field Observations GNSS/GPS measurements or Latitudes, Longitudes, HAE: We re interested in projected coordinates, e.g., State Plane Survey measurements in a projected coordinate system, on a surface: we must adjust, or reduce the measurements for accurate planar and geodetic coordinates

2 Now: Accurate, anytime, anywhere positioning

3 surface GNSS/GPS Measures X,Y,Z, then converted to latitude, longitude, and ellipsoid height ITRF08 l,f h ITRF08 l,f are provided at the ellipsoid surface

4 Data collected with GNSS - lat, lon, HAE Positions initally computed in WGS84/ITRF coordinates Z λ, φ ITRF/WGS84 Y [ [-R x y z Datum transformation WGS84ver1 to NAD83ver2 X = T +srx ] = [ ][ x ] y Tz z T x 1 -R Zt R Yt T y ]+ R Zt 1 -R Xt Yt R Xt 1 X WGS84/ITRF system Z' λ', φ' NAD83(...) Y' X' NAD83 system

5 surface NAD83(2011) h NAD83(2011) l,f A datum transformation converts these to values relative to our NAD83xx (here 2011) datum

6 GNSS Gives Ellipsoidal Height We typically want orthometric height, so we need to subtract geoidal height orthometric height = ellipsoidal height - geoidal height H = h - N surface ellipsoidal height h H geoid orthometric height ellipsoid N geoidal height

7 Finally, project from lat/lon to State Plane geographic coordinates, NAD83 (2011) projected coordinates, e.g. Iowa State Plane North, NAD83(2011)

8 Conversions supported in most professional GPS/GNSS software e.g., Trimble export

9 The Other (and older) Way Surveying - Used for small-area and cadastral layers, we must reduce surface measurements, first to adjust for local slope, then for orthometric heights and grid/ geographic axis divergence. Why? Because our measurements are on the Earth surface, in a rectangular coordinate system, but our geographic coordinates and map projections are at the ellipsoid surface - then projected to the grid. Also, our optical survey measurements are usually relative to geographic north, and not grid north Finally, surface horizontal is define relative to a surface gravity normal, which is deflected from the ellipsoid vertical

10 Measuring up here Coordinate system defined down here

11 Long Distance Surveys Start at known location (Bench Mark) Determine Geographic North direction Measure azimuths and distances on the surface Calculate arc distance on the ellipsoid, known as the geodetic distance Calculate corrected azimuth, for deflection of the vertical Calculate new position on ellipsoid from reduced distance, adjusted azimuth

12 Determine Geographic North In practice, measure magnetic north with a compass, use NGS program to find magnetic declination, and adjust accordingly

13 Conduct field survey - distances and azimuths

14 Calculate arc distance on the ellipsoid, known as the geodetic distance h 1 = h1 + hi Dh = h 2 - h 1 Ra is earth radius at the measured point, calculated as per formulas given last week Law of cosines: S 2

15 Calculate arc distance on the ellipsoid, known as the geodetic distance

16 Azimuth,deflection of the vertical Vertical, direction of gravity Ellipsoid normal, right angle to ellipsoid

17 Calculate corrected azimuth, for deflection of the vertical

18 Calculate corrected azimuth, for deflection of the vertical z is the zenith angle, 90 - latitude, f j is the deflection in the meridian direction h is the deflection in the prime vertical direction How do we determine deflection?

19 Determine Deflection From the Vertical In practice, use starting or approximate latitude/longitude, use NGS program to find deflection

20 Calculate new position on ellipsoid from adjusted distance, bearing Remember from Week 3? If I leave a point on a given azimuth, and travel a given distance, where will I end up? Wikimedia commons

21 Computations on an Ellipsoid Surface Bowring Equations pg 78, here Remember, e = second eccentricity = [(a 2 -b 2 )/b 2 ] 1/2 where a and b are semi-major and minor axes pg 78, E & F

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24 Reduction of Survey Measurements in State Plane We could do all our calculations for survey points using these equations, and measuring distances and heights. Shorter way if we are doing small area, plane surveying, e.g., in the state plane, but especially county coordinate systems These are short cuts, that allow fewer steps, while maintaining accuracy (but only over short distances, e.g., 10 s of miles at most)

25 Field Survey in State Plane or MCC Length Adjustment Can substitute mean earth radius for Ra, Rm= 6,371,000 m

26 Also, scale variation adjustment

27 Adjusting for Projection Scale in State Plane LCC Lp = Le. k, where

28 Our grid north diverges from geographic north Where n is as defined on the previous page, lo is the Central Meridian, and l is the longitude at the measurement point