The Future of SPCS in Charles Chuck Ghilani, Ph.D. Professor Emeritus Pennsylvania State University

Transcription

1 The Future of SPCS in 2022 Charles Chuck Ghilani, Ph.D. Professor Emeritus Pennsylvania State University

2 Class Etiquette Turn off all cell phones Or set them to vibrate Go out of the room to answer any calls You can ask questions at any point during the class. Simply speak up so that all can hear your question If you can t hear, ask me to repeat the question.

3 What You Will Learn The reason for changing NAD83 NGS s plans for future changes in datums and SPCS Options NGS is providing to states Dual and/or single zones Zones designed at heights to reduce/no remove distortion to distances Differences in current systems and proposed system for 2022 Single parallel versus two standard parallels

4 Discussion Topics Future plans by NGS for SPCS in PA Needs agreement of any change from constituents PennDOT PSLS PSPE Geospatial consortium (GIS community) Others?

5 Surfaces of the Earth Topographic (4 in picture) Geoid (aka Spheroid) (5 in picture) Equipotential (based on gravity) surface (H) Geoid model (Geoid 12B) Ellipsoid (2 in picture) Mathematical surface GRS 80, WGS 84 Geodetic coordinates (φ, λ, h) Map surface (6 in picture) Plane surface SPCS Allows plane computations 2 5 6

6 Topographic Surface The physical surface of the Earth on which measurements are made 4 in drawing Unfortunately, this surface is complicated, constantly changing, and difficult to mathematically model Thus there is no recognized coordinate system on the surface of the Earth!

7 Geoid An arbitrarily selected equipotential surface on which gravity is perpendicular everywhere 5 in drawing, which is known as spheroid May be modeled to an accuracy of 1 2 cm, but model is complicated. In PA 3 6 cm. GRAV-D Program for U.S. Geoid12B, Deflec12, and so on at

8 Geoid Models

9 Interactive Geoid12B Web Page

10 Results of Request

11 Process a File of Points Reads common text file File is deciphered using columns Free format type 2 requires latitude and longitude in columns 1 32 Western longitude can be positive. Set at upload Example file format for Type 2 Latitude Longitude ID

12 Example File Results

13 Geoid/Spheroid Coordinates Coordinates of points on spheroid are given by astronomic latitude (Φ), astronomic longitude (Λ), and orthometric height (H). Orthometric height also known as the elevation of the point Latitude and longitude differ from their geodetic values by functions of the deflection of the vertical This is also true for our vertical (zenith) angles

14 Deflection of the Vertical plumb line normal to ellipsoid Shown by 3 in drawing Ellipsoid

15 Difference Between Geoid and Ellipsoid

16 Ellipsoid An ellipse rotated about its semiminor axis that is designed to closely approximate the geoid A simple mathematical surface Does not coincide with geoid Surface observations must be reduced to the ellipsoid to perform geodetic computations Geodetic Reference System of 1980 (GRS80) World Geodetic System of 1984 (WGS84) Clarke 1866 (SPCS 27) PZ 90 (GLONASS ellipsoid)

17 Ellipsoid Coordinates on ellipsoid are given by latitude (φ), longitude (λ), and height (h) above the ellipsoid Results of GNSS survey in point positioning mode Note: h is not H! h is geodetic height of point height of point above ellipsoid H is the orthometric height (aka elevation) Height of point above the geoid

18 The Earth Using plane computations on surface of Earth results in Errors in computed positions of stations Distances that are relevant to a station's elevation Not on the ellipsoid Not on a mapping (plane) surface For directions (geodetic versus plane direction) Grid norths are parallel whereas geodetic norths converge Tangent to meridian at A A Az AB B C θ D Difference between geodetic and grid north E F Tangent to meridian at F Az FG G

19 Convergence of Meridians Assume that you traverse 1 mi in the eastwest direction with a traverse at a mean latitude of 41. How far off will your final azimuth in your traverse be if you use plane computations? θ = 206,265 D EW where tan φ = R e 206, tan 41 20,902,000 D EW is the east-west departure of traverse φ is the average latitude of the traverse 46 R e is the average radius of the Earth (20,902,000 ft) Tangent to meridian at A A Az AB C θ B D E F θʺ Tangent to meridian at F Az FG G

20 Most Surveyors Compute surveys in arbitrary coordinate systems that are not on the 1. Geoid 2. Ellipsoid 3. Any map projection 4. Thus coordinates are arbitrary and lost when survey markers are lost

21 Advantages of Map Projections Map projections provide a Systematic representation of a round body on a flat surface. Mapping surface is a plane surface We do not need geodetic computations to maintain survey accuracies However, we need to Convert all geodetic/magnetic directions to grid directions Reduce distance observations to the mapping surface

22 Disadvantage All map projections introduce some form of distortion Designer of a map projection tries to minimize some distortions at the expense of others In SPCS angle distortions are limited at the expense of distances Distortion sizes are minimized by limiting size of projection and by raising mapping surface to an average height of terrain Distortions can be compensated by using proper distance and azimuth reduction procedures

23 Some Software Packages Unclear Example: Partial listing of adjusted observations from 1 GNSS package So what type of distance/azimuth is listed? Grid? Mark-to-Mark? Geodetic? Should be determined by options selected for adjustment but Linear unit: Meters Projection: SPC83-Pennsylvania (North) Mark-to-mark distance Distance Observations Name Distance (m) Res D (m) Azimuth Res A (m) Elevation Angle Duration 1A ' " ' " 0:14:05 1A ' " ' " 0:16: ' " ' " 0:15: ' " ' " 0:14: ' " ' " 0:16: ' " ' " 0:15:20

24 How can we check? Using geodetic values for adjusted coordinates: 1A 10 distance values: Reported distance = m Grid distance = m Mark-to-Mark distance = m Geodetic distance = m Reported azimuth: Grid azimuth = (Note: Convergence angle = ) Geodetic forward azimuth = ? Geodetic back azimuth =

25 INVERSE/FORWARD/INVERS3D/FORWRD3D Computation Utilities Available at

26 Obtained using NGS Tool Kit Why doesn t BkAz = FwAz ± 180?

27 What is wrong with NAD 83? NAD 83 based on a nongeocentric reference system Off by about 2.2 m Note this is the best they could do with observations available in the early 80 s Not a mistake. Just a reality of not having GNSS GNSS works in a geocentric reference system relatable to a geocentric ITRF coordinate system

28 What is wrong with NAVD 88? NAVD 88 is both biased (by about one-half meter) and tilted (about 1 meter coast to coast) relative to the best global geoid models available today U.S. uses a hybrid geoid today Not a best fit to the topographic surface for the U.S.

29 What is being done? Geometric model has New geometric 4D horizontal datum based on GRS 80 ellipsoid Latitude, φ Longitude, λ Geodetic height, h Time, t 0 Geometric model relies on the CORS network

30 What is being done? Why time, t 0? Because plate tectonics, coordinates of stations change over time GNSS can detect these motions Why CORS stations have velocity vectors related to them In this area, coordinates change by a few centimeters each year

31 WIL1 Position and Velocity

32 Approximate Shifts in Horizontal Datum Horizontal coordinates will change from 0.5 m to 1.5 m across the U.S. New horizontal datum in PA will be called the North American Terrestrial Reference Frame of 2022 (NATRF2022) Three others will be created according to tectonic plates in 2022

33 Approximate Shifts in Heights Can vary from 0 m to 1.3 m in U.S. New vertical datum will be called the North American- Pacific Geopotential Datum of 2022 (NAPGD2022) Will use GEOID 2022

34 What is being done? Ellipsoid is a best fit of geopotential (gravitybased) model of Earth Vertical model Geopotential model closely aligns with surface of Earth Based on variations in gravity Relies on spaceborne gravity observations (long wavelength) GRAV-D program, (medium wavelegth) terrestrial gravity observations (short wavelength)

35 A New State Plane Coordinate System State Plane Coordinate System of 2022 Referenced to a 202x Terrestrial Reference Systems (TRFs) Based on the same ellipsoid of GRS 80 Same three conformal mapping systems Lambert Conformal Conic (LCC) used in PA Transverse Mercator (TM) Oblique Mercator (OM) Will be set to fit topographic surface

36 A New State Plane Coordinate System From International Earth Rotation and Reference /ITRF/itrf.html IERS is a international consortium using GNSS, VLBI, and other techniques to define worldwide coordinate systems NGS plans to align new reference system to current at the time of creation of NA

37 Current Map Projection Systems used in SPCS 83

38 Surfaces in SPCS Note: Surface secant at standard parallels TM secant along two meridians Standard parallels Meridians where surface is secant to ellipse Scale exact means geodetic distance equal to grid distance

39 Components of Current LCC Map Projection Ellipsoidal parameters for GRS 80 Semimajor axis, a = 6,378,137.0 m Flattening factor, f = 1/ Eccentricity, e = Current zonal constants (Lambert conformal conic) Grid origin (φ 0, λ 0 ) Latitude of standard parallels North φ N and south φ S Origin offsets False easting, E 0, and false northing, N b

40 Components of the Secant Lambert Conformal Conic Projection Note: Zone limits only define extents where distance distortion is limited to some factor such as 1:10,000 or better Zones do not stop at limits! φ S φ N Standard Parallels

41 Secant to ellipsoid! Current Projection Distance distortions refer to a comparison between the grid (map) distance and the geodetic (ellipsoid) distance However we work on the ground So distance distortion can be very large due to elevations (orthometric heights) of stations

42 Distance Reductions Must reduce horizontal distances to ellipsoid (geodetic) Horizontal distance ellipsoid Called elevation factor (EF) hi A A H 1 S D 1 Geoid B B h r From ellipsoid mapping surface Called scale factor (k) Combined factor = EF k = (CF) map distance = (horizontal distance)cf horizontal distance = map distance/cf h 1 N 1 N 2 D 2 D 3 h 2 θ O R

43 A New State Plane Coordinate System Based on same three map projection systems But a single-parallel system for Lambert Conformal Conic So mathematics slightly different

44 How Will They Do It? Instead of making developable surface secant to ellipsoid Increase radius of cone to bring it closer to topographic surface of Earth Elevation variation still limits its precision

45 SPCS 2022 Surface By increasing radius of cone, the mapping surface approaches the topographic suface Due to elevation variations in PA and size of PA, the fit to the surface is limited Ellipsoid Mapping surface

46 Does a Single Parallel LCC equal the Current System? Can check by determining scale factor at current central parallel in SPCS 83 PA North zone Defining parameters South standard parallel, φ S = North standard parallel, φ N = Grid origin, (φ 0, λ 0 ) = (N40 10, W77 45 ) False northing and easting: (0.000 m, 600, m)

47 Example In PA North zone for SPCS 83 Station A: (N , W ) Computed Northing Easting are: N = 127, m E = 745, m Can this be matched with a single-parallel LCC?

48 Example Equivalent single parallel system relies on scale factor at central parallel Central parallel for the PA SPCS 83 North zone of N Computed as φ CP = sin 1 2 ln cos φ S cos φ N 1 e 2 sin 2 φ N 1 e 2 sin 2 φ S ln 1+sin φ N 1 sin φ N ln 1+sin φ S 1 sin φ S +e ln 1+e sin φ S 1 e sin φ S ln 1+e sin φ N 1 e sin φ N SPCS 83, PA North zone scale factor at central parallel is This will be limited to 6 decimals in SPCS 2022 and will be > 1 in most cases This computation is only for the example and will be defined as part of SPCS 2022

49 Example So defining parameters for single parallel system are Central parallel, φ CP = N Grid origin, (φ 0, λ CM ) = (N 40 10, W ) Note that φ 0 = φ CP in SPCS 2022 Scale factor at φ CP, k 0 = False northing, N 0, and easting, E 0 : (0.000 m, 600, m) Note The NGS plans on placing the grid origin at the central parallel, thus reducing the number of defining parameters to five. This will result in a large False northing to remove possibility of negative coordinates.

50 Example Common functions for single parallel LCC map projection W φ = 1 e 2 sin 2 φ M φ = cos φ W(φ) T φ = 1 sin φ 1+sin φ 1+e sin φ 1 e sin φ e

51 Example Zone computations for PA North zone using single parallel w CP = W φ CP = m CP = M φ CP = t 0 = T φ 0 = ; Needed since SPCS83 origin not at CP t CP = T φ CP = n = sin φ CP = F = m CP nt n = CP R b = ρ t 0 = k CP aft n 0 = 7,379, m = k CP a m n Reduces number of zone constants from 11 to 5

52 Example Station computations t = T = m = M = R = ρ t = k 0 aft n = 7,252, m γ = n = N = R b R cos γ + N b = 127, m (Check!) E = R sin γ + E 0 = 745, m (Check!)

53 SPCS 2022 Defining parameters Only change to inverse computations will be to compute radius to station as R = N k CP cos γ = E 2 +N 2 k CP

54 SPCS 2022 Defining parameters So defining parameters will be Grid origin: (φ CP, λ CM ) Scale factor: k CP False Northing and Easting, N 0 and E 0 Note that N 0 will need to be large to avoid negative coordinates With fewer defining parameters and fewer computations

55 Preliminary Design for PA North Zone Grid Origin: (N 41 25, W ) k CP = (exact) False northing and easting? Unknown at this time, assume (600,000 m, 600,000 m)? For your consideration Going from to the western border, is about 232,752 m Offsets could be (350,000 m, 350,000 m) and still provide overlap with southern zone and western states

56 Comparison of Zone Constants Current North Zone Prelim. SPCS 2022 North Zone Parameter Value Parameter Value w w m m t t W M T N R b 7, m F t n F R b 7,379, m

57 Given: (φ, λ) Find: (N, E), k, γ Solution: n R = r ( ) = aft ( ) n 0 = N = R R cos + E k b = R sin + E Rn = = am m t mt n 1 n 1 0 Direct Problem Nb

58 Direct Problem Given: (N , W ) Find: (N, E), k, γ Solution: Parameters Values R 7,253, γ N 589, m E 745, m K

59 Distance Precision SPCS 2022 will use PPM s rather than distance precisions Converting Precision = PPM E.g. 100 PPM yields Precision = 100 1,000,000 = 1 10,000 Scale Factor = 1 PPM = 1 Precision E.g. 400 mm yields Scale factor = ,000,000 =

60 Examples PPM Precision Scale Factor 400 1: : :10, :12, :16, :25, :50, :

61 Distance Reductions Will 100, 80, 60, 40, be good enough? Depends on accuracy necessary for job Also may depend on equipment 1:10,000 is well below what today s instruments can achieve Today s instruments capable of 40 ppm or lower (better)

62 FGDC Control Standards For engineering and construction control surveys Engr & Constr Order Precision PPM 2 nd order, class 1 1:50, nd order, class 2 1:20, rd order, class 1 1:10, rd order, class 2 1:5, th order (Construction) 1:2,

63 What Reductions Will Be Necessary? Reduction of Distances Depends on required accuracy of survey and its location in zone Azimuths Definitely, due to convergence of the meridians Angles 1 mile east-west traverse at yields a 46 convergence in directions Depends on length of sight distance but probably not

64 Distance Reduction Elevation Factor Nothing changes: To reduce an observed horizontal distance to a geodetic distance, we need the elevation factor (EF) L e L m = R e R e +H+N = R e R e +h Then L e = R e R e +H+N L m = R e R e +h where R e = Radius of the Earth So EF = R e R e +H+N = R e R e +h L m

65 Distance Reduction Combining elevation factor with scale factor yields a combined factor CF = EF k L g = EF k L m = CF L m Using a project factor will yield better results Project factor is an average combined factor for project Project factor can be entered in controller as project scale factor

66 Direction Reduction All grid north are parallel to central meridian All geodetic north converge at the pole Convergence of meridians must be corrected when using grid or geodetic azimuths γ γ γ γ

67 Direction Reduction Computing a grid azimuth from a geodetic azimuth Az grid = Az geodetic γ γ Geodetic azimuth from a grid azimuth Az geodetic = Az grid + γ γ

68 Arc-to-Chord Correction A small correction that accounts for the projection of an arc on a plane surface Also known as the second-term correction Should be applied to all directions In SPCS 83 NGS recommended this correction for line over 8-km in length Dated: To match 1 -instrumentation lines over 2 km but where can you see that far anyway?

69 Planning for Upcoming Changes NGS will provide transformation tools but Accuracy of transformation tools based on heights dependent on GPS on Benchmarks program Horizontal accuracies will always be better by readjusting the original data Learn to save the observations What will it take for you to change an existing project?

70 Planning for Upcoming Changes State and local laws and contracts may require SPCS 83 (NAD 83 positions) or NAVD 88 heights These must be changed By 2022 Suggest change it so that it says the most recent nationally recognized state plane coordinate system and height systems rather than a specific item such as SPCS 2022 What will it take to change these in your locality?

71 Things that need our attention Definition of the foot Survey foot? 1 ft = ത3 m This definition has led to multiple errors since its creation International foot? 1 ft = m States in green adopted international foot in SPCS 83 Meters?

72 Planning for Upcoming Changes Number of Zones? Currently there are north (3701) and south (3702) zones North zone extends to international border in Lake Erie. Why? Does not support a statewide GIS nor a statewide coordinate system PA about mi from Mason- Dixon line to PA North border Approximately 158 mi yields 1:10,000 ~ 175 mi to very tip of Erie county ~157.2 mi

73 Planning for Upcoming Changes Number of Zones? Maintain current 1:10,000 precision? Precision compares ellipsoid versus map distance Not ground versus map Heights of lines require distance reductions Enlarge cone to achieve precisions closer to ground distances? NGS default

74 Planning for Upcoming Changes Number of Zones? State and local organizations will benefit by having only 1 zone Will provide a common map coordinate system for the Commonwealth Create three different systems? Two-zone North-South system (NGS) Statewide

75 Prelimnary SPCS 2022 System Default design will mimic current two-zone system However, designed with respect to topographic surface North zone has a range of +102 to 99 ppm Or about 1/10,000 with topographic surface

76 Planning for Upcoming Changes NGS allows two different state plane coordinate systems for each state Currently being done in KY That is, a multiple-zone (North-South in PA) system To support local surveying and engineering projects And a single-zone system To support statewide mapping and planning projects

77 Planning for Upcoming Changes Note danger of two different systems is confusion about basis for a set of coordinates E.g. (203, , 634, ) Are these from the single- or multi-zone system??? Thus documentation(meta data) will be paramount May be also handled by designing a system that will make the origin of the coordinates by using very different offsets. i.e. false northing and easting E.g. (350,000 m, 350,000 m) for dual-zone Single-zone (600,000 m, 600,000 m)

78 Planning for Upcoming Changes Two well-designed systems should satisfy all users However, two different systems will not occur without consensus and input from stakeholders!

79 Planning for Upcoming Changes Stakeholders that can give input to desired changes or not in SPCS 2022 when compared to SPCS 83 State organization such as PennDOT, surveying and engineering societies such as the PSLS, professional geospatial organizations such as the GEOSPATIAL Consortium, and universities that perform geospatial education or research such as Penn State

80 Poll Questions? Definition of length unit Survey foot? International foot? International system (metric) Who has legislation that specifies SPCS 83 or NAD 83? How many have contacted the appropriate people to change this?

81 Poll Questions How many systems should we have? Dual- and single-zone system Dual-zone system only Single-zone system only False northing and easting values?

82 Poll Questions Has your Chapter discussed this? Is PSLS leadership actively pursuing 1. Forming a consortium of people to discuss changes Who is working on modifying legislation? Yes No 1. Yes No Don t know Know Don t Are you concerned about upcoming changes? Yes No

83 Poll Questions How prepared are you for the upcoming changes? Prepared Somewhat prepared Unprepared How prepared is your company for the upcoming changes? Prepared Somewhat prepared Unprepared Prepared Somewhat Unprepared Prepared Somewhat Unprepared

84 Further Study Ghilani, C Elementary Surveying: An Introduction to Geomatics,16 th Edition Chapter 20. Prentice Hall, Upper Saddle River, NJ. Observation reductions Low-distortion projections Single project factor Crossing zones

85 If a man empties his purse into his head, no man can take it away from him. An investment in knowledge always pays the best interest. - Benjamin Franklin 86

86 End of Class!!!