# Presentation: 526714

## Technical Issues in Establishing Heights 

- Donald.Mulcare@noaa.gov
- NOAA, National Geodetic Survey

**Notes:**
Introduce Cliff and myself.  We are available for discussions about the NSRS and contributing data to it.

## Definitions

- Height
- The distance measured along a perpendicular between a point and a reference surface.
- Raw leveled heights
- Non-unique.  Depending on the path taken a different height will be determined for the same point.  They have NO *physical* relevance.

**Notes:**
To elaborate on yesterday’s discussion.  No significance if we do not subsequently link our observations to the gravity field (we need to know where we are).

## Slide 3

**Notes:**
Precise leveling includes techniques and additional data acquisition that permit correction of most systematic errors.  

## Slide 4

**Notes:**
It is time consuming, rigorous and linked to standards (here second order class I).  These observations were made to determine a height for TULLS a Maryland HARN point.  Note that four (4) benchmarks were used to establish the new height.  We verify the relationship between fixed control as part of the process.

## Geometric to Physical

- Geopotential numbers
- Unique, path-independent
- Geopotential number at a point of interest is the difference between the potential on the geoid and potential at the point.

**Notes:**
Since we want to make the observations meaningful and repeatable, we introduce geopotential numbers.

## Orthometric Height

- Orthometric height
- Is the length of the plumbline between a point on a surface and the geoid.
- It is the geopotential number divided by mean gravity along plumbline between point and geoid.
- Helmert orthometric heights NAVD 88
- Use certain assumptions to compute gravity effect.

**Notes:**
Assumptions relate to gravity density.  NAVD 88 heights are Helmert orthometric heights.

## Slide 7

**Notes:**
These are the values as adjusted by NGS.  Note the use of geopotential numbers.  The Helmert height equation is also shown.

## Observed difference in orthometric height, H, depends on the leveling route.

- Equipotential Surfaces

**H****C**

**H****A**

- Reference Surface (Geoid)

******H****AC****  ******** ********h****AB**** + ********h****BC**** **

**Observed difference in orthometric height, ********H, depends on the leveling route.**

**A**

**C**

**B**

**Topography**

****** ****h****AB**

****** ****h = local leveled differences**

**Leveled Height vs. Orthometric Height**

**= ******** h****BC**

******H = relative orthometric heights**

## Relationship between height systems

**h-H-N=0**
**where:**
**h is ellipsoid height**
**H is NAVD 88 height**
**N is geoid separation (height)**

**Notes:**
Of course they sum to zero only if all components are without error.  Each has error.  

## Texas Points in NGS Data Base

**Notes:**
This file was created from the state-level control shapefile available from the NGS.  It includes every point in our database including intersection stations, horizontal and vertical control.  Undoubtedly, it includes points that are inaccurate and no longer existing.

## Texas FBN and HARN

**Notes:**
This is the highest level of monumented points.  Points determined rigourously as part of a project.  The most recent campaign, FBN, included three days of observations with session lengths of 5.5 hours.  One session was offset by 4 hours from the other two.  The FBN accuracy goal was 2cm ellipsoid height.

## Texas GPS on BM Points

**Notes:**
These points were used in the creation of the hybrid geoid, GEOID 2003.  

## Benchmarks (all orders)

## Slide 14

## Slide 15

## Slide 16

## Benchmarks recovered since 2000

**Notes:**
While useful, recovery information is of varying quality.  Also a number of points are not recovered though they still exist.  We do have a tool on the NGS web page that facilitates the submission of recovery information.

## Heights, once determined, never change????

## Vertical Velocities: Not dominated by tectonics!  GIA is the issue.

**Notes:**
Global Isostatic Adjustment ... looking at the graph there are other problems.  This graph was taken from a presentation on SNARF (Stable North American Reference Frame).

## Rare photo of early GPS surveyors

**Rare photo of early GPS surveyors**

## GPS

**Notes:**
While it may seem otherwise, NGS is not the acronym for National GPS Survey.  GPS is the primary tool in geodesy.  Not the only.

## Slide 22

**Notes:**
Point P our GPS antenna is positioned in 3-D Cartesian coordinates.  We link it to an ellipsoid (point positioning) to calculate latitude longitude and ellipsoid height. 

## Slide 23

## Slide 24

**Notes:**
Over time a greater understanding of error sources has been obtained.  Networks like CORS operate 24/7 and provide the data we need to model these error sources.  

## Slide 25

## Slide 26

## Slide 27

## Texas CORS

## Slide 29

## Slide 30

## Slide 31

## Slide 32

## OPUS and OPUS-RS

## H = 1.422 m

- h = -24.93 m
- N = -26.34 m

- h(1996) = -24.92
- h(1995) = -24.82

## H = 1.005

- h = -25.35
- N = -26.34

- h(1996) = -25.34
- h(1995) = -25.24

## Slide 36

## ARANSAS A USCG

**ARANSAS A USCG**
- H = 1.378 m (OPUS)
- H =  1.422 m (published)
- diff = 0.044m
- h  = -24.958 m (OPUS)
- h = -24.93 m (published)
- diff = 0.03 m

## ARANSAS B USCG

**ARANSAS B USCG**
- H = 0.961 m (OPUS)
- H =  1.005 m (published)
- diff = 0.044m
- h  = -25.381 m (OPUS)
- h = -25.35 m (published)
- diff = 0.03 m

## OPUSA – OPUSB = 0.417 m

- H = 1.378 m (OPUS)
- H =  1.422 m (published)
- diff = 0.044m
- h  = -24.958 m (OPUS)
- h = -24.93 m (published)
- diff = 0.03 m

**ARANSAS B USCG**
- H = 0.961 m (OPUS)
- H =  1.005 m (published)
- diff = 0.044m
- h  = -25.381 m (OPUS)
- h = -25.35 m (published)
- diff = 0.03 m

**OPUS****A**** – OPUS****B**** = 0.417 m**
**Published****A**** – Published****B**** = 0.417 m**

**Your results may vary ...**

## Bad ant choice: 869.338

- Good:                869.420
- Published:         869.468

## Exchanging Data

## Slide 42

## Slide 43

## Establishing NAVD 88 Heights for CORS

- Recover or establish two first-order (NGS-published) benchmarks within 1 mile of CORS antenna.  Second-order points can be used.
- 	If none are found establish them.
- Run differential levels between CORS reference monuments
- Observe two independent GPS sessions to determine dh
- 		use dh – dN = dH

## Data reductions

- The leveled difference between benchmarks should be used to verify the quality of the GPS vector reduction.
- Incorrectly fixed integer/s will result in wrong height!
-  Geoid heights should be examined to insure consistency among points occupied.

## Submitting this data

- A project proposal must be submitted and approval obtained from NGS
- Check level observations must be submitted to NGS
- New leveling must be done to minimum of NGS second-order.
- Data must be “Blue-Booked!”
- B,A,G and D files as well as all adjustments

## Slide 47

## Questions?

- Donald M. Mulcare
- donald.mulcare@noaa.gov
- 361.825.6064