# Presentation: 488527

## VERTICAL DATUMS 

- APRIL 08, 2008
- By
- Ronnie L. Taylor
- Chief, Geodetic Advisor Branch
- NOAA, National Geodetic Survey

**Notes:**
Geodetic Leveling is more than just “really good” leveling.  It is grounded in the Theory of Error Propagation.  What will be taught here represents NGS’ leveling requirements since the 1970’s.  Yes, NGS has been performing Geodetic Leveling since the 1800’s, calling the Quality Standard by similar sounding names, e.g.. First-order, Second-order, Third-order, but what we will be teaching are the requirements for performing Geodetic Leveling according to the latest Standards, which NGS expects of all Leveling projects included in its Data Base holdings since the mid 1970’s

## VERTICAL DATUMS

**Local/Regional**
**Assumed**
**City, County**
**International Great Lakes Datum 1955  (IGLD55)**
**International Great Lakes Datum 1985  (IGLD85)**
**National**
**Sea Level Datum 1929 (SLD29)**
**National Geodetic Vertical Datum of 1929  (NGVD29) **(As of July 2, 1973)
**North American Vertical Datum of 1988  (NAVD88) **(As of  June 24, 1993)
**Tidal Datums**

## VERTICAL DATUMS

**What types of heights are there?**
**	****	****•   ****Orthometric heights**
**	****	****•   ****Ellipsoid heights**
**	****	****•   ****Geoid heights**

## NATIONAL SPATIAL REFERENCE SYSTEM(NSRS)

- The National Spatial Reference System (NSRS) is the name given to all geodetic control contained in the National Geodetic Survey (NGS) Data Base.  This includes:  A, B, First, Second and Third-Order horizontal and vertical control, Geoid models such as GEOID 99, precise GPS orbits and Continuously Operating Reference Stations (CORS), observed by NGS as well as data submitted by other Federal, State, and local agencies, academic institutions and the private sector

## NATIONAL SPATIAL REFERENCE SYSTEM(NSRS)

**ACCURATE**** ****-- CM accuracy on a global scale**
**MULTIPURPOSE**** ****--  Supports Geodesy, Geophysics, Land Surveying, Navigation, Mapping, Charting and GIS activities and derived products**
**ACTIVE**** ****-- Accessible through Continuously Operating Reference Stations (CORS)**
**INTEGRATED**** ****-- Related to International services and standards (e.g. International Earth Rotation and Reference System Service, International GPS Service etc.)**

## WHAT IS A GEODETIC DATUM?

- Geodetic Datum
- “A set of constants specifying the coordinate system used for geodetic control, i.e., for calculating coordinates of points on the Earth”*
- “[above] together with the coordinate system and the set of all points and lines whose coordinates, lengths, and directions have been determined by measurement or calculation.”*
-  *Definitions from the Geodetic Glossary, September 1986
**Characterized by:**
**A set of physical monuments and**
**Published coordinates (horizontal and/or vertical) on                                                                the monuments**

**Notes:**
Understanding what a datum is will help in understanding where the heights come from and the differences between the heights.

## GEODETIC DATUMS

- Classical
- Horizontal – 2 D (Latitude and Longitude, e.g. NAD 27, NAD 83(1986))
- Vertical – 1 D (Orthometric Height, e.g. NAVD 88)
- Contemporary
- 	Practical – 3 D (Latitude, Longitude and Ellipsoid Height) Fixed and Stable – Coordinates seldom change, e.g. NAD 83 (1991)
-   Scientific
- 	4 D (Latitude, Longitude, Ellipsoid Height, Velocities) – Coordinates change with time, e.g. ITRF00

## VERTICAL CONTROL DATUMS

- A set of fundamental elevations to which other elevations are referred.
- _Datum Types_
**Assumed** – As the name implies
**Geodetic** – Either directly or loosely based on Mean Sea Level at one or more points at some epoch
- (NGVD 29, NAVD 88, IGLD85 etc.)
**Tidal** – Defined by observation of tidal variations over some period of time
- (MSL, MLLW, MLW, MHW, MHHW etc.)

## VERTICAL DATUMS OF THE UNITED STATES

**Second General Adjustment - 1903**

**	****Mean Sea Level 1929**
**National Geodetic Vertical Datum of 1929 (NGVD 29)**

**North American Vertical Datum of 1988 (NAVD 88)**

**First General Adjustment - 1899**

**Third General Adjustment - 1907**

**Fourth General Adjustment - 1912**

**Notes:**
There have been several different ellipsoids used for the horizontal datums of the United States.  The Bessell 1841 ellipse was used from approximately 1845 until 1879.  Clarke 1866, developed by the English Geodesist A. R. Clarke was adopted in 1879 following the completion of the great Transcontinental Arc of Triangulation as it most closely approximates the size and shape of North America.  As part of the activity to complete the North American Datum of 1983 (NAD 83), In 1979, the National Geodetic Survey decieded to adopt the Geodetic Reference System 1980 (GRS 80) as recommended by the International Association of Geodesy, as it most closely reflects the size and shape of the entire globe.  It should be noted that GRS80 is for all practical purposes, the same size and shape as the World Geodetic System of 1984 (WGS 84) ellipsoid used with the Global Positioning System (GPS).  The small numerical differences in the flattening (1/f) amount to less than 0.1 millimeter from the most northern part of Alaska to the southern tip of Florida!!

## 
      DATUMS 		
NAD 27, NAD 83(1986), NAD83 (199X), NGVD29, NAVD88, MLLW, MSL, MHW etc.

                               UNITS
Meters, U.S. Survey Feet, International Feet, Chains, Rods, Poles, Links, Varas (CA or TX), Smokes, Smoots.

                        ACCURACY
      A, B, 1st, 2nd, 3rd, 3cm, Scaled etc.

**      **_**DATUMS**_** **
**NAD 27, NAD 83(1986), NAD83 (199X), NGVD29, NAVD88, MLLW, MSL, MHW etc.**
**                               **_**UNITS**_
**Meters, U.S. Survey Feet, International Feet, Chains, Rods, Poles, Links, Varas (CA or TX), Smokes, Smoots.**
**                        **_**ACCURACY**_
**      ****A, B, 1st, 2nd, 3rd, 3cm, Scaled etc.**

**METADATA****Data About Data**

## METADATA??

**METADATA??**

**Horizontal  & Vertical Datums??**

**Plane Coordinate System ??**

**Units of Measure ??**

**How Accurate ??**

## METADATA??

**METADATA??**

## NGVD 29 Versus NAVD 88

_**Datum Considerations:**_**             **_**NGVD 29**_**	****     **_**NAVD 88**_
**   ****Defining Height(s)****	****           26 Local MSL****	****     ****1 Local MSL**
**   ****Tidal Epoch****	****	****	****Various****	****       ****	****       ****1960-78**
**                                                              ****(18.6 years)**

_**Treatment of Leveling Data:**_
**   ****Gravity Correction****	****       Ortho Correction ****	****  ****Geopotential Nos.**
**	****	****	****       ****(normal gravity)             ****(observed gravity)**
**   ****Other Corrections****	****       Level, Rod, Temp.       ****Level, Rod, Astro,**
**	****	****	****	****	****	****  ****Temp, Magnetic,**
**	****	****	****	****	****	****  ****and Refraction**
**                                                      **

**Notes:**
Differences between NGVD29 and NAVD88 - summation of defining characteristics.

Basis for defining heights; biases and tidal epochs used, treatment of data, adjustment considerations, adjustment statistics, and published information.

## NGVD 29 Versus NAVD 88 (continued)

_**Adjustments Considerations:**_**   **_**NGVD 29**_**	****     **_**NAVD 88**_
**   ****Method****	****       ****	****        Least-squares****	****     ****Least-squares**
**   ****Technique****	****	****        Condition Eq.****	****    ****Observation Eq.**
**   ****Units of Measure****	****             Meters****	****                 ****Geopotential Units**
**   ****Observation Type****	****        Links Between****	****   ****Height Differences**
**                      ****Junction Points          ****Between Adjacent BMs**

**Notes:**
Differences between NGVD29 and NAVD88 - summation of defining characteristics.

## NGVD 29 Versus NAVD 88 (continued)

_**Adjustments Statistics :**_** ****	****       **_**NGVD 29**_**	****	****     **_**NAVD 88**_
**   ****No. of Bench Marks****	****       100,000 (est) ****	****  ****450,000 (US only)**
**   ****Km of Leveling Data****	****         75,159 (US)****	****	****        ****1,001,500**
**	****	****	****         ****31,565 (Canada)**

_**Published Information:**_
**   ****Orthometric Height Type****	****Normal****	****	****       ****Helmert **
**   ****Orthometric Height Units****	****Meters****	****	****        ****Meters**
**   ****Gravity Value****	****	****	****Normal****	****	****       ****“Actual”****  **

**Notes:**
Differences between NGVD29 and NAVD88 - summation of defining characteristics.

## First-Order Leveling Network NGVD 29

**First-Order Leveling Network NGVD 29**

**Notes:**
Levels and tide station connections included in NGVD29. 

## NGVD 29 TIDE CONTROL

**Notes:**
As much as 5 feet – or a meter and a half, even 2 meters in some areas, with most of it in the Rockies.

## Slide 18

## NAVD 88 Origin Point

**Notes:**
As much as 5 feet – or a meter and a half, even 2 meters in some areas, with most of it in the Rockies.

## PRESENT NETWORK FOR NAVD 88

- ORIGINAL LEVELING                  700,000 KM
- REPEAT LEVELING                     200,000 KM
- NEW BNA LEVELING                    81,500 KM
- NEW OUTSIDE LEVELING           20,000 KM
- TOTAL FOR NAVD 88              1,001,500 KM
-                                          (620,000 MILES)

## National Geodetic Vertical Datum 1929(NGVD 29)

**Defined by heights of 26 tidal stations in U.S. and Canada**
**Tide gages were connected to the network by leveling from tide gage staffs to bench marks**
**Water-level transfers used to connect leveling across Great Lakes**
**Normal Orthometric Heights:**
**H* =  C / ******
**C   =  model (“normal”) geopotential number**
******    ****=  from normal gravity formula**
**H*  =  0 level is NOT a level surface**

**Notes:**
Vertical Datums - heights relative to defined datum.

NGVD 29 - 0 height (mean sea level) - not true level surface due to inherent problems; normal heights (averaged gravity).  NGVD29 “warped” to fit 26 tide gages; disparity between Pacific and Atlantic Oceans, mean sea level ... geoid.

Individual tide gages are not the same; affected by sea surface topography due to currents, salinity, temperature, weather patterns, etc.; USC&GS forced heights to tide gages creating biases; knew bad but presented a fair approximation.

Normal heights + bias ... level surface.

## Slide 22

## Slide 23

## NORTH AMERICAN VERTICAL DATUM 88

- WHAT IS A VERTICAL CONTROL NETWORK?
- An  Interconnected System of Bench Marks
- Each Bench Mark Is Assigned A height Referenced To A Common Surface

## VERTCON - Vertical Datum Transformations

- Published = 4.896 m
- Difference = 0.000 m / 0.00 ft

## HEIGHT SYSTEMS DATUMS

- INTERNATIONAL Great Lakes Datum (IGLD) 1985
- Same as NAVD 88, except published in Dynamic Heights
- Dynamic Heights
- Hdym = C/Go;  Go = 980.6199 gals
- (Normal gravity at 45 degrees latitude as defined in 1985)

## WHY DO WE NEED A VERTICAL CONTROL NETWORK?

Reduces The Amount Of Future Leveling Required

Enables Surveyors To Check Their New Leveling

Provides Backups For Destroyed Or Disturbed Bench Marks

Assists In Monitoring Changes In Local Areas

Provides A Common Framework

- Reduces The Amount Of Future Leveling Required
- Enables Surveyors To Check Their New Leveling
- Provides Backups For Destroyed Or Disturbed Bench Marks
- Assists In Monitoring Changes In Local Areas
- Provides A Common Framework

**NORTH AMERICA VERTICAL**** ****DATUM 88**

## Vertical Datums

**Notes:**
The topographic surface is the actual visible surface of the Earth. To represent horizontal positions on maps and charts, we need a mathematical model of the Earth which includes a set of numbers for the size and shape of the Earth. Because the Earth is slightly flattened at the poles, a sphere won't work. A flattened sphere, which is called an ellipsoid, is used to represent the geometric model of the Earth. As mentioned earlier the geoid, which is approximated by MSL, is the zero surface as defined by the Earth's gravity. The answer to the question posed in the diagram is, "Depending on the application, the ellipsoid, the geoid, and the center of the Earth are all used." In fact, for the standard GPS receiver to output MSL elevation all three of these zero references must be used! 

## Vertical Datums

- MSL elevation is roughly equivalent to orthometric height (H), the technical name for height above the geoid.
- Geoid height (N) is the separation between the geoid and the ellipsoid. It can be plus or minus.
- Ellipsoid height (h) is the distance above or below the ellipsoid (plus or minus). Ellipsoid height is also called geodetic height.

**Vertical Datums**

**H**

**H = Orthometric Height**  **(NAVD 88)**

**H** ** = ****h**** - ****N**

- TOPOGRAPHIC SURFACE

**h = Ellipsoidal Height (NAD 83)**

**N = Geoid Height (GEOID 03)**

**Ellipsoid****, ****Geoid****, and Orthometric Heights**

## What is the GEOID?

- “The *equipotential surface* of the Earth’s gravity field which best fits, in the least squares sense, mean sea level.”*
- Can’t see the surface or measure it directly.
- Modeled from gravity data.
-                          *Definition from the Geodetic Glossary, September 1986

## Slide 32

**Notes:**
Plot of 6169 GPS/levels bench marks used in Geoid99 model; overrides gravity information by computing model relative to GPS/NAVD88 bench marks.

NAVD88 to Geoid99 -  comparisons between level surfaces; 31 cm NAVD88 bias is consistent around U.S. reflecting the difference determined at Father Point, Rimouski.  This shows that the error at any given point is fairly relative to the error at another point.

## Slide 33

## Level Surfaces and Orthometric Heights

**Level Surfaces and Orthometric Heights**

**Level Surfaces**

**Plumb**

**Line**

**“****Geoid”**

**P****O**

**P**

**Level Surface = Equipotential Surface (W)**** **

**H (Orthometric Height) = Distance along plumb line (P****O**** to P)**

**Earth’s**

**Surface**

**Ocean**

**Geopotential Number (C****P****) = W****P**** -W****O**

**W****O**

**W****P**

**Mean**
** ****Sea**
**Level**

**Notes:**
Level surfaces - imagine earth standing still - ocean standing still; no effects such as currents, tides, winds;  except for slight undulations created by gravity effects = level surface.
Geoid is this level surface relating to today’s mean sea level surface - this does not truly coincide with mean sea level because of the non-averaging effects of currents, tides, water temperatures, salinity, weather, solar/lunar cycle, etc.  The geoid is a best fit mean sea level surface.
Equipotential surfaces - add or subtract water and level surface changes parallel to previous surface = infinite number of possible level surfaces.  Each equipotential surface has one distinct potential quantity along its surface.
Point on earth’s surface is the level surface parallel to the geoid achieved by adding or subtracting potential.  Lines don’t appear parallel; they are based on the gravity field and are affected by mass pluses and minuses.
Geopotential number is the numerical difference between two different equipotential surfaces. W = potential along a level surface.  CP = geopotential number at a point.
Plumb line (over exaggerated in drawing) - is a curved distance due to effects of direction of gravity- known as deflection of the vertical.
Orthometric height is exactly the distance along this curved plumb line between the geoid and point on the earth’s surface.  We can make close approximations but to be exact we would need to measure gravity along this line requiring a bored hole which is impractical.

##        Orthometric Heights

**A**

**C**

**B**

**Topography**

- Adjusted to Vertical Datum using existing control
- Achieve 3-10 mm relative accuracy

-        Orthometric Heights

- Using Optical or Digital/Bar Code Leveling

**Notes:**
Begin our understanding of orthometric heights.

Heights & Datums  - traditionally orthometric heights meant above sea level.  Now we must be aware of factors affecting our understanding and use of height interpretations.

Determining elevation differences through use of conventional leveling procedures.  Conventional spirit-leveled height from points A to B and B to C.

Differential leveling surveys, being a “piecewise” metric measurement technique, accumulate local height differences (dh).

## NATIONAL TIDAL DATUM EPOCH

**A specific 19 year period that includes the longest periodic tidal****	****	****	****	****	****variations caused by the astronomic tide-producing forces.**
**Averages out long term seasonal meteorological, hydrologic, ****	****and ****	****oceanographic fluctuations.**
** ****Provides a nationally consistent tidal datum network (bench ****	****marks) by accounting for seasonal and apparent environmental ****	****trends in sea level that affects the accuracy of tidal datums.**
**The NWLON provides the data required to maintain the epoch                                                                                                                                                                                        ****	****and make primary and secondary determinations of tidal ****	****datums.**

**NATIONAL TIDAL DATUM EPOCH**

**Notes:**
To begin to understand datums, you need to understand what an epoch is and why we have them.  
Epoch is how long it takes for the Sun, Moon, & Earth complete epoch tidal cycle
This takes 18.6 yrs, so we use 19 yrs (because statistically the 0.4 is not significant out of the 19 yr avg.)
What this means is that the NOS has a standard for creating 19 year means.

## Slide 37

## National Water Level Observation Network (NWLON)

**National Water Level Observation Network (NWLON)**

**175 Permanent Stations**

**Notes:**
All datums are based on this network of stations.
As Todd stated earlier, most of these stns have at least 19 yrs of data.
It is these stations that are used to calculate a Tidal Datum Epoch.
What is a ...?  Next slide...

## Slide 39

**Notes:**
#rising 1-3
#rising 3-5&5-10
#falling all
What do we see nationally?  
MSL on east coast is rising while west is mix depending on the tectonic location.  
Note, almost everywhere in CA is rising with the exception of LA 
remember falling MSL= land rising
                    rising MSL= land falling
AK is falling at least 5mm/yr more like 8 or more/yr

## GENERALIZED ACCURACY OF TIDAL DATUMS 

**FOR SHORT SERIES (BASED ON ONE STD DEV)**
**       ****Series****	****       East****	****       Gulf****	****      ****West**
**       ****Length****	****       Coast****	****       Coast****	****      ****Coast**
**        **_**# Mo**__**	**__**         FT**__**	**__**         FT**__**	**__**       **__** FT**_
**          ****1****	****	****        0.13****	****        0.18****	****       ****0.13**
**          ****3****	****	****        0.10****	****        0.15****	****       ****0.11**
**          ****6****	****	****       **** ****0.07****	****        0.12****	****       ****0.08**
**         ****12****	****	****       **** ****0.05****	****        0.09****	****       ****0.06**

**Notes:**
Sigma= std dev/statistics (standard deviation is a measure of how widely values are dispersed from the mean) 
basically these numbers tell us how close the MLLW of a short series is to the MLLW of a 19 yr series
diffs are due to shallow waters and meteorological events.

## Slide 41

**Notes:**
Note differences along coasts and that there is a slope to LMSL (local mean sea level).

## Slide 42

**Notes:**
Chart illustrating relationship of tidal information, vertical datums, and bench marks.

## Slide 43

## Boston Harbor, Massachusetts

**MHHW****	****= 10.27 feet (3.130 meters)**

**MHW****	****=   9.83 feet (2.996 meters)**

**NAVD88****	****=   5.51 feet (1.679 meters)**

**MTL****	****=   5.08 feet (1.548 meters)**

**NGVD29****	****=   4.70 feet (1.433 meters)**

**MLW****	****=   0.34 feet (0.104 meters)**

**MLLW****	****=   0.00 feet (0.000 meters)**

**Feet**

## Slide 45

## Slide 46

## Importance of Shoreline

**AL, AK, CA, CT, FL, GA, LA, MD, MS, NJ, NY, NC, OR, RI, SC, WA**

**Privately Owned**
**Uplands**

**State Owned**
**Tidelands**

**Territorial Seas**

**State Submerged Lands**

**Contiguous Zone**

**Exclusive Economic Zone**

**Federal Submerged Lands**

**High Seas**

**Privately**
** ****Owned**

**State**
** ****Owned**

**TX**

**3 n. mi.**

**12 n. mi.**

**200 n. mi.**

**Privately**
** ****Owned**

**State**
** ****Owned**

**DE, MA, ME, NH, PA, VA**

**MHHW**

**MHW**

**MLLW**

**Importance of Shoreline**

**Chart Datum**

**Notes:**
State define boundaries by statute which varies around the United States.

Changes in sea level will affect these boundaries.

## Vertical Datum Relationships

**Vertical Datum Relationships**

**3-D Datums**

**Orthometric Datums**

## Leveling and Datum’s

**Leveling and Datum’s**

**Notes:**
All tide stns have a benchmark network associated with them.  
The reason being that they are a stability check for the stn and the bm’s themselves. 
benchmarks are all related to where the acoustic sensor sits on the well.  
Some of the bm’s are part of NGS’s National Spatial Reference System (NSRS).  
From these bm’s we can derive a land based datum (NAVD88) that the tide can be related to. 
 BM’s are also related to CO-OPS’s final water level product called the “Published Benchmark Sheet.”  

## National Spatial Reference System(NSRS)

**Consistent National Coordinate System**
** ****Latitude **
** ****Longitude **
** ****Height **
** ****Scale **
** ****Gravity**
** ****Orientation**** **
**and how these values change with time****.**

**Notes:**
 NSRS is a consistent national coordinate system that defines 
latitude, 
longitude,
height, 
scale, 
gravity, and 
orientation 
throughout the Nation, and how these values change with time.

## Before you build . . .

**. . . inspect your foundation.**

** ****D E F I N I T I O N**

**Notes:**
Just like building a house, having a strong, well-planned, standardized foundation for surveying, engineering, GIS, etc., geospatial referencing is critical.  Otherwise, what you “build” on top of it won’t hold up or “fit in.”

## Questions?

**Questions?**

**Ronnie L. Taylor****	**
**Chief, Geodetic Advisor Branch**
**301-713-1054**
**Ronnie.Taylor@noaa.gov**