The Future of SPCS in 2022

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

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 Multi and/or single zones Zones designed at heights to reduce/no remove distortion to distances Differences between current systems and proposed systems for 2022 Single parallel versus two standard parallel system 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 such as county mapping offices? Computations 2

Surfaces of the Earth Topographic (4 in picture) Geoid (aka Spheroid) (5 in picture) Equipotential (based on gravity) surface (H) (surface = g dh) Geoid model (e.g. Geoid 12B) Astronomic coordinates: (Φ,Λ,H) Ellipsoid (2 in picture) Mathematical surface GRS 80, WGS 84, PZ 90 Geodetic coordinates: (φ, λ, h) Map surface (6 in picture) 2 5 Ellipsoid projection to a plane surface SPCS Provides simpler plane computations 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! Computations 3

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 http://www.ngs.noaa.gov/tools/ Geoid Models Computations 4

Interactive Geoid12B Web Page Results of Request Computations 5

Reads common text file Process a File of Points 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 41 17 36.66999 76 18 07.72000 2 41 17 54.43988 76 18 01.19911 3 41 18 01.88975 76 17 53.08841 4 Example File Results 41 17 36.66999 76 18 7.72000-31.872 0.0315 2 41 17 54.43988 76 18 1.19911-31.847 0.0315 3 41 18 1.88975 76 17 53.08841-31.834 0.0315 4 41 18 4.07950 76 17 42.62683-31.828 0.0315 5 41 18 10.33935 76 17 37.37638-31.818 0.0315 6 41 18 32.32973 76 17 39.27630-31.787 0.0315 7 41 18 44.85003 76 17 41.09654-31.770 0.0314 8 41 18 49.76001 76 17 47.08707-31.765 0.0314 9 41 18 54.56944 76 18 5.36963-31.763 0.0312 10 41 18 58.13958 76 18 8.31017-31.759 0.0312 11 41 19 10.52001 76 18 7.62996-31.746 0.0311 12 Computations 6

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 This is the system that optical surveying measurements are observed in Deflection of the Vertical plumb line normal to ellipsoid Shown by 3 in drawing Ellipsoid Computations 7

Difference Between Geoid and Ellipsoid 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) Computations 8

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 This is the system that GNSS observations are made in 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 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 θ C D Difference between geodetic and grid north E F Tangent to meridian at F Az FG G Computations 9

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,, 46,, where D EW is the east-west departure of traverse φ is the average latitude of the traverse 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 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 Computations 10

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 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 Computations 11

How much does a new total station cost? This Photo by Unknown Author is licensed under CC BY Why are you paying for a geodetic quality instrument and then settling for traverse precisions of 1:10,000 or less? 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 ~ geodetic Microsoft Excel Worksheet Distance Observations Name Distance (m) Res D (m) Azimuth Res A (m) Elevation Angle Duration 1A 10 51.207-0.001 274 49'21.8169" -0.001-4 04'27.6201" 0:14:05 1A 11 55.584-0.001 311 33'08.0960" 0.001-4 18'41.9336" 0:16:20 4 10 54.883-0.003 243 44'14.4457" -0.002-2 18'25.9048" 0:15:05 4 10 54.887 0.001 243 44'25.3306" 0.001-2 18'27.0676" 0:14:20 4 11 40.695 0.001 281 39'24.1935" -0.001-3 52'04.0925" 0:16:35 4 11 40.695 0.001 281 39'22.4856" -0.001-3 52'18.9718" 0:15:20 Computations 12

How can we check? Using geodetic values for adjusted coordinates and enter them into a geodetic inverse package 1A 10 distance values: Reported distance = 51.207 m Grid distance = 51.073 m Mark-to-Mark distance = 51.2075 m Geodetic distance = 51.075 m Reported azimuth: 274 49 21.8169 Grid azimuth = 273 40 39.6 (Note: Convergence angle = 1 08 45.2 ) Geodetic forward azimuth = 274 49 24.8? Geodetic back azimuth = 94 49 23.3 INVERSE/FORWARD/INVERS3D/FORWRD3D Computation Utilities Available at http://www.ngs.noaa.gov/tools/inv_fwd/inv_fwd.html Computations 13

Obtained using NGS Tool Kit Why doesn t BkAz = FwAz ± 180? 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 Computations 14

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. 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 Computations 15

What is being done? Why time, t 0? Because plate tectonics, coordinates of stations change over time GNSS can detect these motions This is why CORS stations have velocity vectors related to them In this area, coordinates change by a few centimeters each year However, most of the motion is captured by a rotation about an Euler pole Euler Pole In geometry, Euler's rotation theorem states that, in three-dimensional space, any displacement of a rigid body such that a point on the rigid body remains fixed, is equivalent to a single rotation about some axis that runs through the fixed point. The theorem is named after Leonhard Euler, who proved it in 1775 by means of spherical geometry. - Wikipedia U.S. Naval Academy https://www.usna.edu/users/oceano/pguth/md_help/geology_course/euler_poles.htm Computations 16

WIL1 Position and Velocity Approximate Shifts in Horizontal Datum in 2022 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 Computations 17

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 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) Computations 18

A New State Plane Coordinate System State Plane Coordinate System of 2022 Referenced to a 20xx 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 better fit the topographic surface A New State Plane Coordinate System From International Earth Rotation and Reference System @ https://www.iers.org/iers/en/dataproducts /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 NATRF Computations 19

Current Map Projection Systems used in SPCS 83 Cone.wrl Cylinder.wrl Note: Surface secant at standard parallels Surfaces in SPCS TM secant along two meridians Standard parallels Meridians where surface is secant to ellipse Scale exact means geodetic distance equal to grid distance Computations 20

Components of Current LCC Map Projection Ellipsoidal parameters for GRS 80 Semimajor axis, a = 6,378,137.0 m Flattening factor, f = 1/298.25722210088 Eccentricity, e = 0.081819191043 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 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! False Origin N R b φ N φ S False easting P R Origin P Zone limit False northing Standard Parallels Zone limit E Computations 21

Current Projection Secant to ellipsoid! 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 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 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 h r θ O R Computations 22

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 How Will They Do It? Instead of making developable surface secant to ellipsoid Raise cone increase radii to bring it closer to topographic surface of Earth That is, bring up to some height above/below ellipsoid Elevation variation still limits its precision Computations 23

SPCS 2022 Surface By raising the tip of cone, the mapping surface approaches the topographic surface Due to elevation variations in PA and size of PA, the fit to the surface is limited Ellipsoid Mapping surface 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 = 40 53 North standard parallel, φ N = 41 57 Grid origin, (φ 0, λ 0 ) = (N40 10, W77 45 ) False northing and easting: (0.000 m, 600,000.000 m) Computations 24

Example In PA North zone for SPCS 83 Station A: (N41 18 20.25410, W76 00 57.00239 ) Computed Northing Easting are: N = 127,939.400 m E = 745,212.637 m Can this be matched with a single-parallel LCC? Example Equivalent single parallel system relies on scale factor at central parallel Central parallel for the PA SPCS 83 North zone of N 41 25 02.66745 Computed as φ sin SPCS 83, PA North zone scale factor at central parallel is 0.9999568402 Scale factor 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 Computations 25

Example So defining parameters for single parallel system are Central parallel, φ CP = N 41 25 02.66745 Grid origin, (φ 0, λ CM ) = (N 40 10, W 77 45 ) Note that φ 0 = φ CP in SPCS 2022 Scale factor at φ CP, k 0 = 0.9999568402 False northing, N 0, and easting, E 0 : (0.000 m, 600,000.000 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. Example Common functions for single parallel LCC map projection W φ 1 e sin φ M φ T φ Computations 26

Example Zone computations for PA North zone using single parallel w W φ 0.9985340786 m M φ 0.7510110381 t T φ 0.4665502273; Needed since SPCS83 origin not at CP t T φ 0.4533396213 n sinφ 0.6615397338 F 1.9159306051 R ρ t k aft 7,379,348.367 m k CP a m n Reduces number of zone constants from 11 to 6 Station computations Example t T 41 18 20.25410 0.4545150743 m M 41 18 20.25410 0.7522972496 R ρ t k aft 7,252,862.7946 m γ n 77 45 76 00 57.00239 1 08 49.991 N R Rcosγ N 127,939.400 m E Rsinγ E 745,212.637 m Computations 27

SPCS 2022 Inverse Computations Only change to inverse computations will be to compute radius to station as R where N N N and E E E 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 Computations 28

Preliminary Design for PA North Zone Grid Origin: (N 41 25, W 77 45 ) k CP = 1.00001 (exact) False northing and easting? Unknown at this time, assume (600,000 m, 600,000 m)? For your consideration Going from 77 45 to the western border, 80 31 is about 232,752 m Offsets could be (350,000 m, 350,000 m) and still provide overlap with southern zone and western states We could set these! Preliminary Design for PA North Zone Grid Origin: (N 41 25, W 77 45 ) Computations 29

Comparison of Zone Constants Current North Zone Parameter Value w 1 0.99856504 w 2 0.99850313 m 1 0.75713034 m 2 0.74484340 t 0 0.46655023 t 1 0.45896491 t 2 0.44775285 n 0.66153973 F 1.91584791 R b 7,379,348.367 m Prelim. SPCS 2022 North Zone Parameter Value W 0.998534121652 M 0.751019573405 T 0.453347409647 N 0.661530035807 R b 7,421.022.1315 m F 1.9159439932 Direct Problem Given: (φ, λ) Find: (N, E), k, γ Solution: R k aft cos N R b 0 n R E R sin E k Rn am m t mt 0 Nb N R b P R P E 0 N b E Computations 30

Given: (φ, λ) Find: (N, E), k, γ Solution: R ρ φ aft 0 n N R R cos b E R sin E Rn k am m t mt n 1 n 1 0 Direct Problem Nb N R b P R P E 0 N b E Direct Problem Given: (N41 18 20.25410, W76 00 57.00239 ) Find: (N, E), k, γ Solution: N P Parameters Values R 7,253,354.523 γ 1 08 49.9304 N 589,121.492 m E 745,220.353 m K 1.0000118698 R b R P E 0 N b E Computations 31

Distance Precision SPCS 2022 will use PPM s rather than distance precisions Converting Precision PPM E.g. 100 PPM yields Precision,, Scale Factor 1 PPM 1 Precision E.g. 400 ppm yields Scale factor 1,,, 0.9996 Examples PPM Precision Scale Factor 400 1:2500 0.99960 200 1:5000 0.99980 100 1:10,000 0.99990 80 1:12,500 0.99992 60 1:16,667 0.99994 40 1:25,000 0.99996 20 1:50,000 0.99998 0 1:1 1.00000 Computations 32

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) FGDC Control Standards For engineering and construction control surveys Engr & Constr Order Precision PPM 2 nd order, class 1 1:50,000 20 2 nd order, class 2 1:20,000 50 3 rd order, class 1 1:10,000 100 3 rd order, class 2 1:5,000 200 4 th order (Construction) 1:2,500 400 Computations 33

Computations 34

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 1 mile east-west traverse at 41 25 yields a 46 convergence in directions Angles Depends on length of sight distance but probably not Distance Reduction Elevation Factor Nothing changes: To reduce an observed horizontal distance to a geodetic distance, we need the elevation factor (EF) Then L L where R e = Radius of the Earth So EF L Computations 35

Distance Reduction Combining elevation factor with scale factor yields a combined factor CF = EF k L g EF k L CF L 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 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 Computations 36

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 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 in PA can you see that far anyway? Computations 37

Planning for Upcoming Changes NGS will provide transformation tools but Accuracy of height transformation tools based dependent on GPS on Benchmarks program Horizontal transformation tools will have limited accuracy Horizontal accuracies will always be better by readjusting the original data Learn to save your observations What will it take for you to change an existing project? Why save observations? Transformations between one coordinate system and another are always best-fit approximations That is, take stations known in both coordinate systems and do leastsquares fit of this limited set of coordinates To precisely change all station coordinates from SPCS 83 to SPCS 2022 simply modify control stations coordinates and directions to SPCS 2022 and rerun adjustment with original observations, which have been reduced where necessary Computations 38

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? Things that need our attention Definition of the foot Survey foot (sft)? 1 ft = 0.3048006069 m This definition has led to multiple errors since its creation International foot (ift)? 1 ft = 0.3048 m States in green adopted international foot in SPCS 83 Meters? Computations 39

Problem with Foot Conversion SI (m) SI (ft) U.S. (sft) Northing 589,121.492 1,932,813.29 1,932,809.43 Easting 745,220.353 2,444,948.66 2,444,943.77 This conversion is the reason our first Mars lander crashed into its surface! 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? Considerable zone overlap. Southern standard parallel of north zone south of north standard parallel of south zone Does not support a statewide GIS nor a statewide coordinate system Computations 40

Planning for Upcoming Changes Number of Zones? PA about 157.2 mi from Mason- Dixon line to PA North border Approximately 158 mi yields 1:10,000 ~ 175 mi to very tip of Erie county ~ 175 mi ~157.2 mi 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 but due to Appalachian mountains, will only be better Computations 41

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 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 Computations 42

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 Planning for Upcoming Changes Note danger of two different systems is confusion about basis for a set of coordinates E.g. (203,972.974, 634,038.083) Are these from the single- or multi-zone system??? Thus documentation (meta data) is 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) Computations 43

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! 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 Computations 44

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? 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? N 0 E 0 Computations 45

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 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 Computations 46

Poll Questions Does your company save the original observations or just the coordinates? Yes No Don t know Further Study Ghilani, C. 2021. Elementary Surveying: An Introduction to Geomatics,16 th Edition Chapter 20. Prentice Hall, Upper Saddle River, NJ. Observation reductions http://www.xyht.com/professional-surveyor-archives/3088/ Low-distortion projections http://www.xyht.com/surveying/transformation-observations-2/ Single project factor http://www.xyht.com/surveying/transformation-of-observations-part-3/ Crossing zones http://www.xyht.com/professional-surveyor-archives/where-theory-meets-practicespcs-zone-conversions/ Computations 47

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 95 End of Class!!! Computations 48