WISCONSIN COORDINATE SYSTEMS

Transcription

1 Pdf versions of the Handout and Powerpoint slides are on jerrymahun.com. Follow the USPLSS Forum link and use the password: WildT2 WISCONSIN COORDINATE SYSTEMS CONCEPTS & IMPLEMENTATION Jerry Mahun, PLS, Semi-retired UW-Platteville

2 I. REFERENCE MODELS A. THREE TO TWO DIMENSIONS B. DATUM C. CREATING A GRID

3 I. REFERENCE MODELS A. Three to Two Dimensions 1. Distortions Grid Coordinate System 1. Orthogonal 2. Parallel north lines 3. Uniform scale in both directions

4 I. REFERENCE MODELS A. Three to Two Dimensions 1. Distortions

5 I. REFERENCE MODELS A. Three to Two Dimensions 2. Direction Distortion Smaller Area N g g E True (Geodetic): Grid: A-B geodetic E/W A-C grid E/W

6 I. REFERENCE MODELS A. Three to Two Dimensions 3. Distance Distortion Scale < 1.0 Scale > 1.0

7 I. REFERENCE MODELS B. Datum 1. Surfaces

8 I. REFERENCE MODELS B. Datum 2. What s a datum? Measurement reference surface Math model and measurements Ex: Vertical Datum Elev NGVD

9 I. REFERENCE MODELS B. Datum 2. What s a datum? a: semi-major axis b: semi-minor axis f: flattening e: first eccentricity f e a b a a b a 2 2

10 I. REFERENCE MODELS B. Datum 2. What s a datum? a: semi-major axis b: semi-minor axis f: flattening e: first eccentricity f e a b a a b a 2 2

11 I. REFERENCE MODELS B. Datum 2. What s a datum? Geoid Regional ellipsoids are fit to a part of the geoid

12 I. REFERENCE MODELS B. Datum 2. NAD -From 1927 to 1983 a. Redefinition... Clarke 1866 GRS80 Name a (m) / b (m) 1/f Comments Clarke 1866 GRS80 6,378,206.4* 6,356,583.8* 6,378,137.0* 6,356, / / * Regional fit for NAD27; No ellipsoid-geoid separation Global fit for NAD83; ellipsoidgeoid separation included *defining parameters GRS Geodetic Reference System

13 I. REFERENCE MODELS B. Datum 2. NAD -From 1927 to 1983 a.... and Readjustment 1927 Network: ~27,000 points 1983 Network: ~270,000 points

14 I. REFERENCE MODELS B. Datum 2. NAD -From 1927 to 1983 b. Position shifts Longitude (m) Latitude (m)

15 I. REFERENCE MODELS B. Datum 2. NAD -From 1927 to 1983 c. Continued Readjustment Lead to better earth modeling Measurements exceed accuracy of control Individual state initiatives HARNs Patchwork readjustments Border area issues Sufficient densification for entire network to be adjusted

16 I. REFERENCE MODELS B. Datum 2. NAD -From 1927 to 1983 d. NAD Summary Datum New England Datum Adopted Pre-1901 US Standard Datum 1901 North American Datum 1913 North American Datum of 1927: NAD 27 North American Datum of 1983: NAD 83 (1986) Post-NAD83(86) States with HARNs had their own readjustments NAD 83 (1991) 1991 NAD 83 (1997) 1997 Starting with NAD(07) the readjustment included the entire network NAD 83 (NSRS2007) 2007 NAD 83 (NSRS2011) 2012

17 I. REFERENCE MODELS B. Datum 2. NAD -From 1927 to 1983 e. Multiple Positions OM1168 DESIGNATION - MAZOMANIE OM1168 PID - OM1168 OM1168 STATE/COUNTY- WI/DANE OM1168 COUNTRY - US OM1168 USGS QUAD - MAZOMANIE (1962) OM1168 OM1168 *CURRENT SURVEY CONTROL OM1168 OM1168* NAD 83(2011) POSITION (N) (W) ADJUSTED OM1168* NAD 83(2011) ELLIP HT (meters) (06/27/12) ADJUSTED OM1168* NAD 83(2011) EPOCH OM1168* NAVD 88 ORTHO HEIGHT (meters) 995. (feet) VERTCON OM1168 OM1168 GEOID HEIGHT (meters) GEOID12B OM1168 NAD 83(2011) X - 17, (meters) COMP OM1168 NAD 83(2011) Y - -4,659, (meters) COMP OM1168 NAD 83(2011) Z - 4,341, (meters) COMP OM1168 LAPLACE CORR (seconds) DEFLEC12B OM1168 OM1168 Network accuracy estimates per FGDC Geospatial Positioning Accuracy OM1168 Standards: OM1168 FGDC (95% conf, cm) Standard deviation (cm) CorrNE OM1168 Horiz Ellip SD_N SD_E SD_h (unitless) OM OM1168 NETWORK OM OM1168 Click here for local accuracies and other accuracy information. OM1168 OM1168 OM1168.The horizontal coordinates were established by GPS observations OM1168.and adjusted by the National Geodetic Survey in June 2012.

18 I. REFERENCE MODELS B. Datum 2. NAD -From 1927 to 1983 e. Multiple Positions OM1168 SUPERSEDED SURVEY CONTROL OM1168 OM1168 NAD 83(2007) (N) (W) AD( ) 0 OM1168 ELLIP H (02/10/07) (m) GP( ) OM1168 NAD 83(1997) (N) (W) AD( ) 2 OM1168 ELLIP H (06/17/02) (m) GP( ) 4 1 OM1168 ELLIP H (10/21/99) (m) GP( ) 4 1 OM1168 NAD 83(1991) (N) (W) AD( ) 2 OM1168 NAD 83(1986) (N) (W) AD( ) 2 OM1168 NAD (N) (W) AD( ) 2 OM1168 NGVD 29 (07/12/88) (m) RAPSU86 model used GPS OBS OM1168 OM1168.Superseded values are not recommended for survey control.

19 I. REFERENCE MODELS B. Datum 2. NAD -From 1927 to 1983 e. Multiple Positions From-To Lat Diff (sec) Long Diff (sec) N Diff (m) E Diff (m) NAD27-NAD83(86) NAD83(86)-NAD83(91) NAD83(91)-NAD83(97) NAD83(97)-NAD83(07) NAD83(07)-NAD83(11) x enlargement NAD27 NAD83(86)

20 I. REFERENCE MODELS C. Creating a Grid 1. Relating surfaces: heights Ground Geoid h H h: Orthometric height N: Geoid height H: Ellipsoidal height Ellipsoid N H = h + N

21 I. REFERENCE MODELS C. Creating a Grid 2. Projection Surface Tangent Secant Plane Tangent Secant Cylinder Tangent Secant Conic

22 I. REFERENCE MODELS C. Creating a Grid 2. Projection Surface Select appropriate projection Fit to area

23 I. REFERENCE MODELS C. Creating a Grid 2. Projection Surface Example: conic projection g: convergence angle Grid North Grid N True North Grid N g Project Superimpose Grid Grid East

24 I. REFERENCE MODELS C. Creating a Grid 2. Projection Surface Distance Ground Geoid Ellipsoid Grid k < 1.0 k > 1.0 From Ground through h and H to Ellipsoid(geodetic dist) From Ellipsoid through scale factor (k) to Grid.

25 II. WISCONSIN - A WELL-COORDINATED STATE A. STATE PLANE COORDINATES B. UNIVERSAL TRANSVERSE MERCATOR C. WIS TRANSVERSE MERCATOR D. WIS COUNTY COORD SYSTEMS E. WIS COORD REFERENCE SYSTESM F. SUMMARY

26 II. WISCONSIN - A WELL-COORDINATED STATE A. State Plane Coordinate (SPC) System Projection Conic Zones 3 NAD27 Yes NAD83( ) Yes Maximum distance distortion: 1/10,000 (ellipsoid-grid)

27 II. WISCONSIN - A WELL-COORDINATED STATE B. Universal Transverse Mercator (UTM) System Projection Cylindric Zones 2 NAD27 Yes NAD83( ) Yes Maximum distance distortion: 1/2,500 (ellipsoid-grid)

28 II. WISCONSIN - A WELL-COORDINATED STATE C. Wisconsin Transverse Mercator (WTM) System Projection Cylindric Zones 1 NAD27 Yes NAD83( ) Yes Maximum distance distortion: 1/2,500 (ellipsoid-grid)

29 II. WISCONSIN - A WELL-COORDINATED STATE D. Wisconsin County Coordinate System (WCCS) Projection Cylindric& Conic Zones 58 NAD27 NAD83( ) No Yes Conic Cylindric Maximum distance distortion: (ground-grid) Rural: 1/30,000 Urban 1/50,000

30 II. WISCONSIN - A WELL-COORDINATED STATE D. Wisconsin County Coordinate System (WCCS) Projection Cylindric& Conic Zones 58 NAD27 NAD83( ) No Yes Counties sharing coordinate systems. Maximum distance distortion: (ground-grid) Rural: 1/30,000 Urban 1/50,000

31 II. WISCONSIN - A WELL-COORDINATED STATE E. Wisconsin Coordinate Reference System (WisCRS) Projection Cylindric& Conic Zones 59 NAD27 NAD83( ) No Yes Counties systems remained the same. Maximum distance distortion: (ground-grid) Rural: 1/30,000 Urban 1/50,000

32 II. WISCONSIN - A WELL-COORDINATED STATE WCCS WisCRS difference WCCS used raised ellipsoid: GRS80 + h d + N d Raised Ellipsoid h d N d

33 II. WISCONSIN - A WELL-COORDINATED STATE WCCS WisCRS difference WCCS used raised ellipsoid: GRS80 + h d + N d Projection fit to raised ellipsoid Raised Ellipsoid A A' B B' Grid Advantage: Ellipsoid is closer to ground minimizing distance distortions h d N d Disadvantage: Nonstandard ellipsoid; software issues. Raised Ellipsoid b+(h d +N d ) b GRS 80 a a+(h d +N d )

34 II. WISCONSIN - A WELL-COORDINATED STATE WCCS WisCRS difference WisCRS uses GRS80 ellipsoid.

35 II. WISCONSIN - A WELL-COORDINATED STATE WCCS WisCRS difference WisCRS uses GRS80 ellipsoid. Projection fit to GRS80 ellipsoid. A A' B B' Grid Advantage: Grid close to ground minimizing distortions. GRS80 ellipsoid so fewer software issues. Disadvantage: Ellipsoid and fit differences meant some WCCS-WisCRSpositional error would result. Design goal -<±3 mm diff Req ddifferent projection equations and defining parameters.

36 II. WISCONSIN - A WELL-COORDINATED STATE WCCS WisCRS difference WisCRS uses GRS80 ellipsoid. Projection fit to GRS80 ellipsoid. A A' B B' Grid Advantage: Grid close to ground minimizing distortions. GRS80 ellipsoid so fewer software issues. Disadvantage: Ellipsoid and fit differences meant some WCCS-WisCRSpositional error would result. Design goal -<±5 mm diff Req ddifferent projection equations and defining parameters.

37 II. WISCONSIN - A WELL-COORDINATED STATE WCCS WisCRS State Cartographer s Office Publications

38 II. WISCONSIN - A WELL-COORDINATED STATE F. Summary of Wisconsin Systems Coordinate System Datum Distance distortion * NAD27 NAD83 Maximum Scale Range SPC y y 1/10, UTM y y 1/2, WTM y y 1/2, WCCS n y rural: 1/30,000 WisCRS n y urban: 1/50, * Ellipsoid-to-Grid except WCCS & WisCRSwhich are Ground-to-Grid. A B A' B' Grid A' B' Grid A B

39 II. WISCONSIN - A WELL-COORDINATED STATE G. Distance Comparison Systems: UTM, SPC, WTM, WisCRS WCCS System d H d H d G Grid d G d L Grid d E R E de dh RE havg N RE hc N C dl dh RE havg N d d k G E d d k G L R E -earth radius h avg -mean elevation of line N -geoid height of line h C -median county elevation N C -mean county geoid height

40 II. WISCONSIN - A WELL-COORDINATED STATE G. Distance Comparison Corner Elev (ft) S22 T28N R7E Marathon County ft ft SE 1590 S1/ SW 1180 For WCCS: h C = ft N C =-32.64m Line d H d E UTM SPC C WTM WisCRS d L WCCS SE-S1/ SE-SW WCCS-WisCRS Difference SE-S1/ ft 0.09 mm 1/8,600,000 SE-SW ft 0.15 mm 1/10,300,000 d E -distance on GRS80 ellipsoid d L -distanceonraised(local)ellipsoid.

41 II. WISCONSIN - A WELL-COORDINATED STATE G. Distance Comparison S22 T28N R7E Marathon County ft ft Ground to Grid Difference SE-S1/4 SE-SW UTM /13, /11,000 SPC C /8, /9,000 WTM /2, /2,000 WisCRS /90, /800,000 WCCS /91, /860,000

42 III. MOVING DATA BETWEEN SYSTEMS A. TRANSFORMATIONS AND CONVERSIONS B. DATUMS AND ADJUSTMENTS C. APPLICATION D. SOFTWARE

43 III. MOVING DATA BETWEEN SYSTEMS A. Transformations and Conversions We have coordinates of a point in one system. How to determine its coordinates in a different system? Are any errors introduced? North Both answers depend on mathematical relationship between the two systems. East

44 III. MOVING DATA BETWEEN SYSTEMS A. Transformations and Conversions For purposes of this discussion: Moving points from one system to another by either 1. Transformation approximate 2. Conversion - exact (N, E) (X±, Y±)

45 III. MOVING DATA BETWEEN SYSTEMS A. Transformations and Conversions 1. Transformation No rigorous math relationship between the two systems. (N, E) (X±, Y±)

46 III. MOVING DATA BETWEEN SYSTEMS A. Transformations and Conversions I. Transformation No rigorous math relationship between the two systems. Create math model - Complexity dependent on a number of factors. Final position errors depend on model. (N, E) (X±, Y±)

47 III. MOVING DATA BETWEEN SYSTEMS A. Transformations and Conversions 2. Conversion There is an exact rigorous math relationship between the systems. Conversion does not introduce additional error in point position. (N, E) (X±, Y±)

48 III. MOVING DATA BETWEEN SYSTEMS A. Transformations and Conversions Error, Exact No error, or an exact relationship, means no additional error is introduced than already exists in a position. Any projection errors are below measurement threshold. In a transformation, more error can be introduced than already exits in the position.

49 III. MOVING DATA BETWEEN SYSTEMS B. Datums and Adjustments NAD27 to NAD83(86) Redefinition (different ellipsoid with different fit) Readjustment (27,000 points vs 270,000 points) No exact relationship between them. Transformation NAD83(86) to NAD83(91) to... Same ellipsoid, but observations removed/added and readjusted. No exact relationship between the adjustments. Transformations but typically smaller errors that NAD27 to NAD83(86)

50 III. MOVING DATA BETWEEN SYSTEMS C. Application 1. When to Use Which a. Conversion Within a datum-adjustment Rigorously Defined Local System State Plane System Universal Transverse Mercator System Geodetic System Datum-Adjustment Arrows define error-free conversion paths.

51 III. MOVING DATA BETWEEN SYSTEMS C. Application 1. When to Use Which b. Transformation Between datum-adjustments Datum- Adjustment Datum- Adjustment NAD 27 Transformation NAD 83 (1986) Transformation NAD 83 (1991) Transformation NAD 83 (1997) Transformation NAD 83 (2007) Transformation NAD 83 (2011)

52 III. MOVING DATA BETWEEN SYSTEMS C. Application 1. When to Use Which c. Combination Example: NAD27 UTM to NAD83(91) SPC Rigorously Defined Local System State Plane System Universal Transverse Mercator System Geodetic System (1) Convert UTM to LL NAD 27 Rigorously Defined Local System (2) Transform NAD27 LL to NAD83(91) LL State Plane System Geodetic System Universal Transverse Mercator System (3) Convert LL to SPC NAD83(91)

53 III. MOVING DATA BETWEEN SYSTEMS D. Software 1. Conversion Most GIS, Design, Mapping software have built-in conversions. Many include WisCRS or WCCS NGS Geodetic Toolkit GPPCGP State Plane to/from Geodetic on NAD27 SPCS83 State Plane to/from Geodetic on NAD83 (on same adjust) UTMS Universal Trans Mercator to/from Geodetic on NAD83 (on same adjust) or on NAD27

54 III. MOVING DATA BETWEEN SYSTEMS B. Datums and Adjustments 2. Transformations a. User Models Average Shift Conformal Transformation Affine Transformation Limited to smaller areas where shift behavior is more consistent.

55 III. MOVING DATA BETWEEN SYSTEMS B. Datums and Adjustments 2. Transformations b. Software Most GIS, Design, Mapping software have various transformation models. NGS deprecated packages NADCON 1-4 GEOCON 1 & 2

56 III. MOVING DATA BETWEEN SYSTEMS B. Datums and Adjustments 2. Transformations b. NGS Coordinate Conversion and Transformation Tool (NCAT) Newly release tool allows users to easily convert between different coordinate systems and/or transform between different datums, in a single step. For coordinate conversion, NCAT allows conversion between lat/long/height, SPC, UTM, XYZ, and USNG systems. For coordinate transformations, NCAT uses NADCON 5.0 to perform three-dimensional (latitude, longitude, ellipsoid height) coordinate transformations for a wide range of datums and regions in the National Spatial Reference System. NADCON 5.0 provides local error estimates for each transformation,

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58 IV. CONSIDERATIONS A. COORDINATE MISAPPROPRIATION B. BEST PRACTICES

59 IV. CONSIDERATIONS A. Coordinate Misappropriation Coordinates make mapping and computations easier But, because we have so many systems on so many datum-adjsin Wisconsin, that can cause serious problems. Consider the following description on this deed recorded in 2005 in Monroe Count (handout page 21).

60 IV. CONSIDERATIONS A. Coordinate Misappropriation This particular description presents a number of issues, one of which affects surveyors and non-surveyors alike: the GPS positions. A few questions should immediately come to mind: (1) To what datum-adj are the latitude and longitude referenced? (2) What are the resolutions in linear terms on the ground of the latitude and longitude values? (3) What are the latitude and longitude accuracy (which is a direct function of the type of GPS used)?

61 IV. CONSIDERATIONS A. Coordinate Misappropriation What kind of GPS was used? Probably not survey-grade or done by a land surveyor -why not? GIS grade: ±(1 to 2 m) Civilian grade: ±(2 to10 m) Survey grade: ±(< 1 cm) Big error - centering over point.

62 IV. CONSIDERATIONS A. Coordinate Misappropriation Mapping this description in a GIS may be problematic Re-Surveyor is caught in a legal dilemma. Description terms weigh heavily on the GPS values as controlling terms: there are few supportive traditional measurements and almost no physical monument calls. How does the surveyor determine legal corner locations in light of the three questions? Does inclusion of these coordinates benefit this parcel?

63 IV. CONSIDERATIONS B. Best Practices 1. Don t mix datum-adj control values on a project. 2. Use the latest data available. If using NSRS control be sure to get the latest data sheet (from the NGS website or using SCO s ControlFinder) and check the Current Survey Control section. Use only points that are ADJUSTED 3. Do not use transformed positions as control Remember the accuracy limitations of transformations like NADCON. 4. Don t use coordinates of unknown quality Survey maps with notes like Coordinates are from the Badger County GIS. What does that mean in terms of their quality? Is the note intended to be a disclaimer?

64 IV. CONSIDERATIONS B. Best Practices 5. Readjusting original data to updated control is always better that transforming it. You ran a high precision survey & adjusted to NAD27 control Now the control has NAD83(91) positions. How do you bring your survey positions from NAD27 to NAD83(91)?

65 IV. CONSIDERATIONS B. Best Practices 5. Readjusting original data to updated control is always better that transforming it. You could use NCAT to transform your points, but they would have transformation error. (N±, E±) (N±, E±) (N±, E±)

66 IV. CONSIDERATIONS B. Best Practices 5. Readjusting original data to updated control is always better that transforming it. Or you could readjust original measurements using the NAD83(91) control values. Measurements are independent of datum or coordinate system untilthey are reduced and adjusted to a specific control network. (N, E) (N, E) (N, E) Errors in the positions are from the measurements, not the transformation.

67 IV. CONSIDERATIONS B. Best Practices 6. Document: datum-adjand, if possible, accuracy, methodology, and software used. Explicitly state coordinate system & datum-adj reference. Would that help with the Monroe Co description? Express consistent realistic resolution in conventional form. If a transformation is used, identify it so coordinate lineage & dependency can be understood.

68 IV. CONSIDERATIONS B. Best Practices 7. Test before assuming something can be ignored. Transformation: use transformed control to check transformation results. Do ground measequal grid measat extreme elevin a county? Check worse case scenario: If it passes, then the rest of the survey should be all right. If it doesn t, should give you an idea where the ground-grid relationship starts to fall apart.

69 IV. CONSIDERATIONS B. Best Practices 7. Test before assuming something can be ignored. Commercial software and County Coordinate system. Does it support WCCS or WisCRS? WisCRSdesigned to be accuracy compatible (±5mm) with WCCS so both won t always appear.

70 Questions? Comments? Observations?