An Illustrated Guide to Geodesy for Engineering, Surveying, and GIS

An Illustrated Guide to Geodesy for Engineering, Surveying, and GIS

Michael Dennis, RLS, PE [email protected]

Esri AEC Summit Manchester Grand Hyatt July 12-15, 2014 • San Diego, CA

® Why should we care about geodesy?

7/13/2014 2014 Esri AEC Summit 2 The Plan • Introducing the National Geodetic Survey • GIS and the National Spatial Reference System (NSRS) • Geodetic concepts – illustrated! • Focus today is on geometric (“horizontal”) datums – Connecting data to the Earth: Datums – A complicated topic: Datum transformations – Nothing is constant except change: Time dependence – Specific example: “WGS 84” ßà “NAD 83” • Other topics of Great Interest (pursue as time allows) – How data are displayed and analyzed: Map projections – How high? How deep? Where will water go? Gravity and heights – How good is it? How do you know? Accuracy (vs. precision) – Putting it all together: Metadata

7/13/2014 2014 Esri AEC Summit 3 NGS: Who we are is where you are • Been around a long time (since 1807) – Became National Geodetic Survey in 1970 (when NOAA created) • Keepers of the National Spatial Reference System (NSRS) – Define, maintain, provide access for US and territories – Position, height, scale, gravity, orientation – …and how they change with time • Products & Services – Geodetic control (active and passive) – Data, models, and imagery (gravity, geoid, aerial imagery) – Tools and services (online and desktop software and services) – Standards, specifications, guidelines, and education

7/13/2014 2014 Esri AEC Summit 4 The NSRS is the foundation for GIS

Land Ownership

Transportation

Surface Waters

Boundaries Elevation Aerial Imagery NSRSGeodetic Control What is a (geometric) “datum”? • Geometric (“horizontal”) datums – a.k.a. “geographic coordinate systems” – Basis for determining positions on the Earth – Modern ones are 4-D (time is 4th dimension) • Lat, lon, height (or Earth-Centered, Earth-Fixed XYZ) + velocities – Ellipsoid (“spheroid”) by itself is NOT a datum • ~Same ellipsoid for NAD 83 and WGS 84, but differ by ~2 m • Includes “local” and “global” datums – “Local” (regional) datums (e.g., NAD 83) – “Global” datums (e.g., WGS 84) • Vertical datums another topic for another time…

7/13/2014 2014 Esri AEC Summit 6 “The Figure of the Earth” Best-fit spherical Too big by 9 miles Earth model at the poles

Point #1 San Diego

Too small by Earth mass center Too small by 4 miles at 4 miles at the equator the equator Mean Earth radius, R ≈ 3959 miles Equatorial plane Geoid Too big by 9 miles (“mean sea level”) at the poles Earth model: Ellipsoid of revolution Best-fit ellipsoid a = 6,372,137.000 m ≈ 3963 mi (e.g., GRS-80, WGS-84) b = 6,356,752.314 m ≈ 3950 mi Ellipsoid flattening f = (a – b)/a ≈ 0.335% 1/f ≈ 298.25722 b = semi-minor axis Point #1 (polar radius) San Diego

Earth mass center

a = semi-major axis (radius of equatorial plane) Equatorial plane

Ellipsoid fits geoid to Geoid within about ±100 m worldwide (“mean sea level”) Geospatial Codependence the first step is admitting you have a problem

• Datums must be “realized” – Connected to Earth by observations (e.g., GNSS) – New realizations improve accuracy of coordinates – A single datum can have multiple realizations • Interrelationships given by “datum transformations” – Mathematical methods for converting between datums – Needed if combining data based on different datums – There are many different kinds and they can vary greatly • Modern datum definitions are accurate but complex – Will focus on two here: NAD 83 and WGS 84.

7/13/2014 2014 Esri AEC Summit 9 A (very) brief history of NAD 83 datum • Original realization completed in 1986 – Almost entirely classical (optical) observations • “High Accuracy Reference Network” (HARN) realizations (1990s) – Done essentially state-by-state – Based on GNSS but classical stations included • National Re-Adjustment of 2007 – NAD 83(NSRS2007/CORS96) epoch 2002.00 – Nationwide adjustment (GNSS only) • NAD 83 (2011/PA11/MA11) epoch 2010.00 – Also nationwide GNSS-only adjustment – This is NOT a new datum! (still NAD 83)

7/13/2014 2014 Esri AEC Summit 10 Alaska

CONUS Pacific (MA11)

Pacific (PA11)

GIS is only for low spatial accuracy?

Median accuracy (95% conf.): 0.9 cm horiz, 1.5 cm height 7/13/2014 2014 Esri AEC Summit 11 A (very) brief history of WGS 84 datum • Original realization completed in 1987 – “Same” as original NAD 83 (to within ±1-2 m) • WGS 84 (G730) — adopted Jan 1994 – Aligned with ITRF91 • WGS 84 (G873) — adopted Sep 1996 – Aligned with ITRF94 • WGS 84 (G1150) — adopted Jan 2002 – Aligned with ITRF2000 (at epoch 2001.00) • WGS 84 (G1674) — adopted Feb 2012 – Aligned with ITRF2008 (at epoch 2005.00) • WGS 84 (G1762) — adopted Oct 2013 – Also aligned with ITRF2008 (at epoch 2005.00) – Note that current NAD 83 is epoch 2010.00 7/13/2014 2014 Esri AEC Summit 12 Understanding geodetic coordinates • Positions for entire Earth (or large part of Earth) – For modern datums these are 3-D • With velocities they are 4-D – Here concerned with geometric coordinates • Two main types: – Latitude, longitude, and ellipsoid height: φ, λ, h – Earth-Centered, Earth Fixed (ECEF) Cartesian: X, Y, Z • Used for many types of geodetic computations – Can covert between both types without error

7/13/2014 2014 Esri AEC Summit 13 Earth-Centered Earth-Fixed (ECEF) coordinates Ellipsoid (e.g., GRS-80, WGS-84) +Z axis (parallel to axis of rotation)

+Y axis (90°E) Point #1, San Diego +Z1 Coordinates:

(–X1, –Y1, +Z1)

(φ1, λ1, h1)

h1 Earth mass center +X axis –X axis –X 1 (Prime (180° φ1 W) meridian) 1 –Y1 λ Equatorial plane

Geoid –Y axis (90°W) (“mean sea level”) –Z axis Earth-Centered Earth-Fixed (ECEF) coordinates Ellipsoid (e.g., GRS-80, WGS-84) +Z axis (parallel to axis of rotation)

+Y axis (90°E) Point #1, San Diego +Z1 Coordinates:

(–X1, –Y1, +Z1)

(φ1, λ1, h1)

h1 Earth mass center +X axis –X axis –X 1 Where is San Diego Conference Center?(Prime (180° φ1 X = -2,451,510 m W) meridian) Y = -4,780,1001 m –Y1 λ Equatorial Z = +3,426,640 m plane …is the same as: Latitude, φ = 32°42’ 25” N Longitude, λ = 117°09’Geoid 05” W –Y axis (90°W) Ellipsoid height, h = -30(“mean m sea level”) –Z axis Datum transformations

• Typical datum transformations – 3-parameter: 3-dimensional translation of origin as ΔX, ΔY, ΔZ – 7-parameter: 3 translations plus 3 rotations (one about each of the axes) plus a scale – 14-parameter: A 7-parameter where each parameter changes with time (each has a velocity) – Transformations that model tectonic displacement and other distortion (e.g., NGS models in HTDP, GEOCON, and NADCON) • Vertical datum transformations – Can be simple shift or complex operation that models distortion (e.g., GEOCON, VERTCON)

7/13/2014 2014 Esri AEC Summit 16 Datum transformations

b2 b1

a1

a2

3-parameter datum transformation

7/13/2014 2014 Esri AEC Summit 17 Datum transformations If datum changes with time, each rotZ component has a b1 velocity…

a1

b2

rotX a2

rot 1437--parameterparameter Y datum transformation scale What to do…?

7/13/2014 2014 Esri AEC Summit 19 Based on 7 constant transformation parameters published by NGS (7 time- dependent parameters ignored), at input time = output time of 1997.0 (so tectonic velocities irrelevant).

This is how the transformation is implemented in most commercial geospatial software.

7/13/2014 2014 Esri AEC Summit 20 Based on 14 transformation parameters published by NGS at input time = output time of 2010.0 (so tectonic velocities irrelevant)

7/13/2014 2014 Esri AEC Summit 21 Based on 14 transformation parameters published by NGS at input time = output time of 2005.0 (so tectonic velocities irrelevant)

7/13/2014 2014 Esri AEC Summit 22 Based on 14 transformation parameters published by NGS at input time of 2005.0 ≠ output time of 2010.0 (5 years of tectonic movement).

This much more complex case is the “correct” transformation.

7/13/2014 2014 Esri AEC Summit 23 7/13/2014 2014 Esri AEC Summit 24 7/13/2014 2014 Esri AEC Summit 25 This 7-parameter transformation is equivalent to the following commercial vendor transformations: n ESRI: “WGS_1984_(ITRF08)_To_NAD_1983_2011” (108363) • NOT “WGS_1984_(ITRF00)_To_NAD_1983_2011”, or the ~25+ other NAD 83ßàWGS 84 transformations in ArcGIS 10.x n Trimble: “ITRF to NAD 1983 (2011)” • NOT “NAD 1983 (Conus)”, a “zero” transformation (used automatically with State Plane) n Topcon: “NAD83” • NOT “NAD83_NO_TRANS”, another “zero” transformation

7/13/2014 2014 Esri AEC Summit 26 Where do you get “WGS 84” coordinates? • Autonomous positions (~3 – 5 m accuracy) • Satellite Based Augmentation Systems (SBAS) – WAAS solutions (1 – 2 m accuracy) – OminStar HP (10 cm) • Various GNSS positioning services (~1 cm) – OPUS (on right side of solution report) – AUSPOS – CSRS-PPP 7/13/2014 2014 Esri AEC Summit 27

How to check transformation: HTDP

7/13/2014 2014 Esri AEC Summit 28 Does this stuff really matter? • Significant for accuracies better than ~1-2 m – Can be problem for combining accurate datasets – Requires understanding of modern datums – Be careful when using “WGS 84” • Which realization? At what epoch? At what level of accuracy? • Things are moving, and it can make a difference – e.g., San Diego moving 4.0 cm/yr NW w.r.t. Phoenix, AZ • GNSS becoming more precise – Autonomous positions soon better than 1-2 m – But accuracy another issue… with respect to what?

7/13/2014 2014 Esri AEC Summit 29 New Datums for the U.S.

• Planned release in 2022 – Geometric datum: Aligned with ITRF/WGS 84 – Vertical datum: Based on gravimetric geoid • How much will NSRS coordinates change? – North America plate (CONUS and AK): Approx 0.8 to 1.6 m – Pacific plate: Approx 3.4 (Midway) to 4.3 m (American Samoa) – Mariana plate: Approx 1.1 to 1.4 m • How much will NSRS ellipsoid height change? – Approx -1.9 m (Puerto Rico) to +2.0 m (Guam) • How much will NSRS CONUS orthometric height change? – Approx +0.1 m (Florida) to -1.3 m (Washington)

7/13/2014 2014 Esri AEC Summit 30 NAD 83(2011) to IGS08 at epoch 2022.0 NAD 83(PA11) to IGS08 at epoch 2022.0 NAD 83(2011) to IGS08 at epoch 2022.0 Differential Tectonic Displacement

7/13/2014 2014 Esri AEC Summit 34

NAD 83(2011) coordinate shifts

7/13/2014 2014 Esri AEC Summit 37 Grid-based transformations

7/13/2014 2014 Esri AEC Summit 38

7/13/2014 2014 Esri AEC Summit 39 Different Flavors of NAD 83

7/13/2014 2014 Esri AEC Summit 40 GEOCON and GEOCON11 • Transformation grids for latest realizations of NAD 83 – GEOCON: NAD 83 “HARN” ßà NAD 83(NSRS2007/CORS96) – GEOCON11: NAD 83(NSRS2007/CORS96) ßà NAD 83(2011) – Both horizontal AND “vertical” (i.e., ellipsoid height) – 1 arc-minute spatial resolution – Include output that indicates “quality” of transformation • Quantified using station within grid cell that is worst match with model • Complication: Some states have > 1 HARN realization • Current release only uses Bluebook format as input/output – Difficult to use because format not readily available – Will provide more flexible input and output soon

7/13/2014 2014 Esri AEC Summit 41

GEOCON and GEOCON11 (beta) GEOCON and GEOCON11 (beta) GEOCON and GEOCON11 (beta)

7/13/2014 2014 Esri AEC Summit 44 GEOCON and GEOCON11 (beta) GEOCON and GEOCON11 (beta) GEOCON and GEOCON11 (beta) GEOCON and GEOCON11 (beta)

7/13/2014 2014 Esri AEC Summit 48 GEOCON and GEOCON11 (beta) Map Projections

• GPS yields geodetic coordinates – Usually given as latitude, longitude, and ellipsoid height • Usually must be “projected” to be useable – “Map projection” used to convert to “grid” coordinates • i.e., Northing, Easting, “Elevation” (y, x, “z”) – Essential for printed maps, computer display, CAD – Projected coordinates are always distorted • There is no way around this — it is a Fact of Life • Cannot be eliminated — it can only be reduced • Effect is computable — it is NOT the same as “error

7/13/2014 2014 Esri AEC Summit 50

State Plane (AZ zone C) “linear distortion” (feet/mile)

+3.0 ft/mile

-3.0 ft/mile

State Plane (AZ zone C) “linear distortion” (feet/mile)

+3.0 ft/mile

-3.0 ft/mile

State Plane (AZ zone C) “linear distortion” (feet/mile)

Central meridian

Zero Zero distortion distortion

W 1/6 2/3 1/6 E

Zone width to balance positive and negative distortion (with respect to the ellipsoid) Gravity, Heights, and Vertical Datums

• How high is it? • How deep is it? • Where will water go? • What kind of heights (“elevations”) to use? – Orthometric? – Dynamic? – Ellipsoid?

7/13/2014 2014 Esri AEC Summit 54 The ellipsoid, the geoid, and you Deflection of the vertical

You are here Earth surface Ellipsoid height, h Orthometric height, H Mean sea level Geoid height, NG

h ≈= H + NG

Note: Geoid height is negative everywhere in the coterminous US (but it is positive in most of Alaska) 7/13/2014 2014 Esri AEC Summit 56 7/13/2014 2014 Esri AEC Summit 57 Experimental NGS geoid models (beta)

• xGEOID14A and xGEOID14B • xGEOID14B includes aerial GRAV-D data • Covers nearly one quarter of Earth

7/13/2014 2014 Esri AEC Summit 58

7/13/2014 2014 Esri AEC Summit 59 Orthometric height change (meters)

NAVD 88 to new vertical datum Estimated as NAVD 88 "zero" (datum) surface minus NGS gravimetric geoid

Spatial Accuracy (vs. Precision)

• How good is your data? • How do you know?

7/13/2014 2014 Esri AEC Summit 62 NAD 83(2011) epoch 2010.00 Horizontal accuracy, cm (95% confidence)

7/13/2014 2014 Esri AEC Summit 63 NAD 83(2011) epoch 2010.00 Vertical accuracy, cm (95% confidence)

7/13/2014 2014 Esri AEC Summit 64 7/13/2014 2014 Esri AEC Summit 65 Some “accuracy” results to consider (all from same set of actual GPS data) • Horizontal “accuracy” computed as: – ±0.6 feet – ±0.8 feet “Torture numbers, and they'll confess – ±1.4 feet to anything.” ~Gregg Easterbrook – ±1.8 feet – ±2.7 feet “Statistics are like bikinis. What they – ±3.8 feet reveal is suggestive, but what they – ±6.5 feet conceal is vital.” ~Aaron Levenstein – ±9.4 feet • Is it “accuracy” or is it “precision”? • What is the “confidence level”? 7/13/2014 2014 Esri AEC Summit 66 Scatter plot with respect to known coordinates

8.0 Sample size n = 130

4.0

0.0 Delta north (ft) Delta

-4.0

-8.0 -8.0 -4.0 0.0 4.0 8.0 Delta east (ft) Scatter plot showing standard precision (39% confidence)

8.0

Circular precision =

4.0 0.6 ft

0.0

Precision ellipse Delta north (ft) Delta a = 0.8 ft -4.0

-8.0 -8.0 -4.0 0.0 4.0 8.0 Delta east (ft) Scatter plot showing scaled precision (95% confidence)

8.0

Circular precision =

4.0 1.4 ft

0.0

Precision ellipse Delta north (ft) Delta a = 1.8 ft -4.0

-8.0 -8.0 -4.0 0.0 4.0 8.0 Delta east (ft) Scatter plot showing standard accuracy (39% confidence) 8.0

Circular 4.0 accuracy = 2.7 ft

0.0

Delta north (ft) Delta

-4.0 Accuracy ellipse a = 3.8 ft

-8.0 -8.0 -4.0 0.0 4.0 8.0 Delta east (ft) Scatter plot showing scaled accuracy (95% confidence) 8.0 Circular

accuracy = 6.5 ft (NSSDA)

4.0

0.0

Delta north (ft) Delta

-4.0

Accuracy ellipse a = 9.4 ft -8.0 -8.0 -4.0 0.0 4.0 8.0 Delta east (ft) Some “accuracy” results to consider (all from same set of actual GPS data) • Horizontal “accuracy” computed as: – ±0.6 feet Accuracy(precision percircle NMAS at 39% (circular) confidence) = 5.7 ft (90% confidence) – ±0.8 feet (precision ellipse at 39% confidence) Accuracy RMSE (radial) = 3.9 ft – ±1.4 feet (precision circle at 95% confidence) (~66% confidence) – ±1.8 feet (precision ellipse at 95% confidence) ± Razzle-dazzle accuracy = 0.4 ft – 2.7 feet (1%(accuracy confidence) circle at 39% confidence) – ±3.8 feet (accuracy ellipse at 39% confidence) – ±6.5 feet per NSSDA (95% confidence) – ±9.4 feet (accuracy ellipse at 95% confidence) • Is it “accuracy” or is it “precision”? • What is the “confidence level”? 7/13/2014 2014 Esri AEC Summit 72 Accuracy scatter plot (95% confidence)

8.0 Circular

accuracy = 6.5 ft (NSSDA)

4.0

0.0

Delta north (ft) Delta

-4.0

Accuracy ellipse a = 9.4 ft -8.0 -8.0 -4.0 0.0 4.0 8.0 7/13/2014 2014Delta Esri AEC Summiteast (ft) 73 Transformed accuracy scatter plot (95% confidence)

8.0 Circular

accuracy = 1.4 ft (NSSDA)

4.0

Applied published “CORS96”datum 0.0 transformation (ITRF 00 to NAD 83 at time 1997.0) Delta north (ft) Delta

-4.0

Accuracy ellipse a = 1.8 ft -8.0 -8.0 -4.0 0.0 4.0 8.0 Delta east (ft) Spatial Data Requirements

• Completely define the coordinate system – Linear unit (meter, foot, what kind of foot?) – Geodetic and vertical datums – Map projection parameters • Is “distortion” an issue for your project . . . ? • Require ties to published control – Best source for control: National Geodetic Survey (NGS) • But control must be more accurate than surveying or mapping method used

7/13/2014 2014 Esri AEC Summit 75 Spatial Data Requirements

• Specify accuracy requirements – Use objective, robust, defensible methods • Make use of published standards (e.g., NSSDA) • Least-squares network adjustment (but no cheating!) – Remember: Accuracy may not be same as precision • Documentation is essential (metadata!) – Report methods, procedures, and results for creating final deliverables – Must include any coordinate transformations • E.g., datum transformations, “rubber sheeting”

7/13/2014 2014 Esri AEC Summit 76 Documentation (metadata!)

• Essential for correctly georeferencing data – Especially important if a “custom” coordinate system is used – Should rarely have to resort to approximate methods (e.g., “best-fit ”, “rubber sheeting”) • Metadata needs to be AVAILABLE and kept with the data! – Best is to embed it with the data so that it cannot be lost or easily ignored – Also helpful if it is CORRECT • Consistent with spirit of “leaving footsteps…” – Others should be able to retrace the original surveying or mapping product (without having to contact the person who created it!)

7/13/2014 2014 Esri AEC Summit 77 Example of typical geospatial metadata . . .

7/13/2014 2014 Esri AEC Summit 78

7/13/2014 2014 Esri AEC Summit 79 Conclusions

• Geodetic knowledge needed for correct georeferencing – Becomes more important as spatial accuracy increases – Driven by high precision and low cost of GNSS (a geodetic tool) • High-accuracy geodetic transformations are complicated – Time-dependence especially complex for differential tectonic motion – Datasets representing different times difficult to spatially align • Metadata (documentation) is essential – Improves reliability and accuracy of data – Increases value and usefulness of spatial data – Needed all geospatial data (GIS, surveying, engineering, etc.)

7/13/2014 2014 Esri AEC Summit 80 More information… geodesy.noaa.gov

7/13/2014 2014 Esri AEC Summit 81 An Illustrated Guide to Geodesy for Engineering, Surveying, and GIS

Questions?

7/13/2014 2014 Esri AEC Summit 82