The Right Place

*GPS, Geodesy, and the Perils of Modern Positioning*

*National Geodetic Survey Convocation, October 2005*

+-----------------------------------+-----------------------------------+
| Michael L. Dennis, P.E.           | Prepared in cooperation with the  |
|                                   |                                   |
| Shephard-Wesnitzer, Inc.          | Geospatial Committee of the       |
|                                   | Arizona Professional Land         |
| E-mail: *mdennis@swiaz.com*       | Surveyors Association             |
+-----------------------------------+-----------------------------------+

The Global Positioning System (GPS) has become a dominant technology for
positioning. GPS is used for a wide variety of mapping and surveying
applications and is often employed for populating, verifying, and
controlling Geographical Information System (GIS) databases. The
software has also become easier to use, so that it is now possible for a
user with minimal training to collect and process GPS data. Such
"user-friendly" software has made GPS a much more accessible technology,
yet this ease of use has come at a price: It is also easy for users with
little geodetic knowledge to unwittingly generate erroneous coordinates.

Modern technology is characterized by rapid change, and GPS is no
exception. The pace of change has made it difficult to establish GPS
positioning standards and specifications. Many users find themselves
struggling to understand a tool that is both highly complex and
unnervingly easy to use. GPS vendors have attempted to fill this void by
developing their own specifications and methods, including their own
jargon. While this has propelled the use of GPS, it has also led to
confusion about procedures, accuracy, performance, and terminology. This
has made it problematic for those seeking positioning services to write
meaningful project specifications. The end result of all this is a
greatly increased risk for creating or receiving a product that is not
correctly georeferenced --- that is, not in the right place.

The positioning precision of GPS varies greatly, by as much as a factor
of a thousand depending on the types of equipment and procedures used.
Regardless of the precision, derivations and manipulations of GPS
coordinates are based on the science of geodesy. While poor field
procedures can and do contribute to positioning errors, the largest
errors, both in number and magnitude, are a consequence of neglecting
the geodetic principles behind GPS.

To illustrate this problem, several examples of GPS positioning errors
are listed in Table 1. This table was prepared for the situation as it
exists in Arizona, but most of the examples apply to other areas in the
country, and even elsewhere in the world. Although the list is intended
to be comprehensive, it does not cover all possible permutations. It is
important to realize that these tabulated errors are not hypothetical;
they actually do occur. This fact alone should give pause to surveyors
and GIS managers.

Two things in Table 1 specifically warrant comment. One is the large
variety of positioning errors, which can occur from diverse sources, and
can range from a fraction of a foot to many miles. The other is that the
table is dense with arcane terminology and abbreviations. Indeed, most
of the error descriptions in the table are probably unfamiliar to many
readers (a list of definitions below the table should help in
deciphering it). This is a cogent demonstration of what is arguably the
central problem of GPS positioning: It is a highly complex technology
that requires considerable geodetic knowledge to ensure consistent and
correct results. This problem remains despite the efforts of vendors to
streamline and simplify the GPS positioning process.

The required positional accuracy of data used to populate a GIS can vary
widely. For example, mapping of utilities might require positions
accurate to ±5 feet horizontally (with no vertical accuracy specified).
In contrast, control for a flood hazard mapping project could require
positions accurate to better than ±0.1 foot, both horizontally and
vertically. At the other end of the spectrum, mapping of wildlife
habitat might only need to achieve a horizontal accuracy of ±100 feet.
Despite this wide range, all positioning has some accuracy associated
with it, and this accuracy should always be part of the GIS metadata.
Even positions with relatively low accuracy requirements can be
adversely affected by some of the errors listed in Table 1.

A major challenge facing the geospatial community is the problem of
establishing appropriate mapping standards and specifications. In many
cases existing standards are preliminary; if not well written or if
overly prescriptive they can quickly become obsolete; they may be
excessively long and complex; and in some cases they are too
vendor-specific to be generally useful. Because of such problems with
existing standards, a goal of the geospatial community should be to
develop spatial data standards that will enable them to unambiguously
define project requirements, whether they are seeking or providing
mapping and surveying services. Given the pace of technological change,
it is vitally important that any new standards be flexible enough to
allow for the inevitable advances in theory and technology. Another
critical element of modern standards is that they should be explicitly
integrated with current realizations of the National Spatial Reference
System (NSRS). The NSRS was developed and is maintained by the National
Geodetic Survey (NGS) to provide a uniform and reliable framework for
positioning throughout the US. As an illustration of its importance to
positioning, consider that most of the errors listed in Table 1 can be
attributed to incorrect use of the NSRS.

Although recent high-profile developments (such as Homeland Security)
have highlighted the need for consistent and correct spatial
information, the problem has existed for some time. The cost for
developing a sophisticated GIS is quite high, but it is false economy to
attempt to save money by populating a GIS with data of dubious origin
--- it can be more expensive to evaluate and fix positioning problems
than it is to initially capture and document the data correctly. This is
not to say that all GIS data should be highly accurate, but rather that
*realistic* and *reliable* accuracy estimates (regardless of magnitude)
be explicitly linked to the data. It is moreover poor practice to rely
solely on the equipment and software vendors for ensuring spatial
integrity. In the end, this is the duty of the professional in
responsible charge, which also best serves the public welfare. Simply
put, geospatial professionals who use GPS should be conversant with
geodesy, a point persuasively articulated by Jan Van Sickle (2001, p.
126):

> *Today, GPS has thrust surveyors into the thick of geodesy which is no
> longer the exclusive realm of distant experts. Thankfully, in the age
> of microcomputers, the computational drudgery can be handled with
> software packages. Nevertheless, it is unwise to venture into GPS
> believing that knowledge of the basics of geodesy is, therefore,
> unnecessary. It is true that GPS would be impossible without
> computers, but blind reliance on the data they generate eventually
> leads to disaster.*

Table 1. Examples of various positioning error sources and their
magnitudes for Arizona. Abbreviations and technical terms are defined in
the "Abbreviations and definitions" section following this table.

+---+-----------------------------------------------+---------------------+
| P |                                               | Error magnitudes    |
| o |                                               |                     |
| s |                                               |                     |
| i |                                               |                     |
| t |                                               |                     |
| i |                                               |                     |
| o |                                               |                     |
| n |                                               |                     |
| i |                                               |                     |
| n |                                               |                     |
| g |                                               |                     |
| e |                                               |                     |
| r |                                               |                     |
| r |                                               |                     |
| o |                                               |                     |
| r |                                               |                     |
| s |                                               |                     |
| a |                                               |                     |
| n |                                               |                     |
| d |                                               |                     |
| e |                                               |                     |
| x |                                               |                     |
| a |                                               |                     |
| m |                                               |                     |
| p |                                               |                     |
| l |                                               |                     |
| e |                                               |                     |
| s |                                               |                     |
| f |                                               |                     |
| o |                                               |                     |
| r |                                               |                     |
| A |                                               |                     |
| r |                                               |                     |
| i |                                               |                     |
| z |                                               |                     |
| o |                                               |                     |
| n |                                               |                     |
| a |                                               |                     |
+---+-----------------------------------------------+---------------------+
| G |                                               |                     |
| e |                                               |                     |
| o |                                               |                     |
| d |                                               |                     |
| e |                                               |                     |
| t |                                               |                     |
| i |                                               |                     |
| c |                                               |                     |
| d |                                               |                     |
| a |                                               |                     |
| t |                                               |                     |
| u |                                               |                     |
| m |                                               |                     |
| d |                                               |                     |
| e |                                               |                     |
| f |                                               |                     |
| i |                                               |                     |
| n |                                               |                     |
| i |                                               |                     |
| t |                                               |                     |
| i |                                               |                     |
| o |                                               |                     |
| n |                                               |                     |
| s |                                               |                     |
| a |                                               |                     |
| n |                                               |                     |
| d |                                               |                     |
| r |                                               |                     |
| e |                                               |                     |
| f |                                               |                     |
| e |                                               |                     |
| r |                                               |                     |
| e |                                               |                     |
| n |                                               |                     |
| c |                                               |                     |
| e |                                               |                     |
| c |                                               |                     |
| o |                                               |                     |
| o |                                               |                     |
| r |                                               |                     |
| d |                                               |                     |
| i |                                               |                     |
| n |                                               |                     |
| a |                                               |                     |
| t |                                               |                     |
| e |                                               |                     |
| s |                                               |                     |
+---+-----------------------------------------------+---------------------+
|   | Using NAD 27 when NAD 83 required             | Varies from \~210   |
|   |                                               | to                  |
|   |                                               |                     |
|   |                                               | 230 feet            |
|   |                                               | (horizontal)        |
+---+-----------------------------------------------+---------------------+
|   | Using "WGS 84" when NAD 83 required (e.g., by | \~4 feet            |
|   | using WAAS corrections or CORS ITRF           | (horizontal)        |
|   | coordinates)                                  |                     |
|   |                                               | \~3 feet (vertical) |
+---+-----------------------------------------------+---------------------+
|   | Using published three-parameter datum         | \~2 to 16 feet      |
|   | transformation between NAD 27 and WGS 84 for  | (horizontal)        |
|   | NAD 83 projects                               |                     |
+---+-----------------------------------------------+---------------------+
|   | Using NADCON to transform coordinates between | \~0.5 to 1 foot     |
|   | NAD 27 and NAD 83                             | (horizontal)        |
+---+-----------------------------------------------+---------------------+
|   | Using 1986 adjusted coordinates when 1992     | Up to 3.8 feet      |
|   | HARN required                                 | (horizontal)        |
+---+-----------------------------------------------+---------------------+
|   | Using NAD 83 1992 HARN when CORS 2002.0 or    | Up to 0.2 foot      |
|   | 1999 Arizona FBN unpublished coordinates      |                     |
|   | required                                      | (horizontal and     |
|   |                                               | vertical)           |
+---+-----------------------------------------------+---------------------+
|   | Using reference coordinates found in the      | Varies from zero to |
|   | header records of CORS raw GPS data files     | over 100 feet       |
|   |                                               | (horizontal and     |
|   |                                               | vertical)           |
+---+-----------------------------------------------+---------------------+
|   | Autonomous (uncorrected) GPS single-point     | \~10 to 20 ft       |
|   | positioning precision (at 95% confidence)     | (horizontal)        |
|   |                                               |                     |
|   |                                               | \~20 to 50 ft       |
|   |                                               | (vertical)          |
+---+-----------------------------------------------+---------------------+
| G |                                               |                     |
| r |                                               |                     |
| i |                                               |                     |
| d |                                               |                     |
| c |                                               |                     |
| o |                                               |                     |
| o |                                               |                     |
| r |                                               |                     |
| d |                                               |                     |
| i |                                               |                     |
| n |                                               |                     |
| a |                                               |                     |
| t |                                               |                     |
| e |                                               |                     |
| s |                                               |                     |
| y |                                               |                     |
| s |                                               |                     |
| t |                                               |                     |
| e |                                               |                     |
| m |                                               |                     |
| s |                                               |                     |
| a |                                               |                     |
| n |                                               |                     |
| d |                                               |                     |
| c |                                               |                     |
| o |                                               |                     |
| m |                                               |                     |
| p |                                               |                     |
| u |                                               |                     |
| t |                                               |                     |
| a |                                               |                     |
| t |                                               |                     |
| i |                                               |                     |
| o |                                               |                     |
| n |                                               |                     |
| s |                                               |                     |
+---+-----------------------------------------------+---------------------+
|   | Using SPCS 27 projection parameters for SPCS  | 37.9 *miles*        |
|   | 83 projects                                   | (horizontal)        |
+---+-----------------------------------------------+---------------------+
|   | Determining State Plane coordinates in US     | Up to 5 feet        |
|   | Survey Feet when International Feet are       | (horizontal)        |
|   | required                                      |                     |
+---+-----------------------------------------------+---------------------+
|   | Determining UTM coordinates in US Survey Feet | Up to 27 feet       |
|   | when International Feet are required          | (horizontal)        |
+---+-----------------------------------------------+---------------------+
|   | Using linear coordinates from a geographic    | Up to \~1000 feet   |
|   | "projection" to compute distances             | horizontal per mile |
+---+-----------------------------------------------+---------------------+
|   | Using SPCS grid distances when "ground"       | \~2.3 feet          |
|   | distances are required (example here is for   | horizontal per mile |
|   | Flagstaff)                                    | at elevation of     |
|   |                                               | 7000 feet           |
+---+-----------------------------------------------+---------------------+
|   | Using UTM grid distances when "ground"        | \~3.6 feet          |
|   | distances are required (example here is for   | horizontal per mile |
|   | Flagstaff)                                    | at elevation of     |
|   |                                               | 7000 feet           |
+---+-----------------------------------------------+---------------------+
|   | Using planar computation methods to transform | Varies, but         |
|   | geodetically-derived horizontal coordinates   | increases rapidly   |
|   | (example here is for converting from UTM to   | with size of area   |
|   | SPCS over a 10 mi × 10 mi area in Phoenix     | (\~1 foot           |
|   | using planar scaling, rotation, and           | horizontal for this |
|   | translation based on two common points)       | example)            |
+---+-----------------------------------------------+---------------------+

*continued on next page*

Error Table. (*continued*)

+---+-----------------------------------------------+--------------------+
| P |                                               | Error magnitudes   |
| o |                                               |                    |
| s |                                               |                    |
| i |                                               |                    |
| t |                                               |                    |
| i |                                               |                    |
| o |                                               |                    |
| n |                                               |                    |
| i |                                               |                    |
| n |                                               |                    |
| g |                                               |                    |
| e |                                               |                    |
| r |                                               |                    |
| r |                                               |                    |
| o |                                               |                    |
| r |                                               |                    |
| s |                                               |                    |
| a |                                               |                    |
| n |                                               |                    |
| d |                                               |                    |
| e |                                               |                    |
| x |                                               |                    |
| a |                                               |                    |
| m |                                               |                    |
| p |                                               |                    |
| l |                                               |                    |
| e |                                               |                    |
| s |                                               |                    |
| f |                                               |                    |
| o |                                               |                    |
| r |                                               |                    |
| A |                                               |                    |
| r |                                               |                    |
| i |                                               |                    |
| z |                                               |                    |
| o |                                               |                    |
| n |                                               |                    |
| a |                                               |                    |
+---+-----------------------------------------------+--------------------+
| V |                                               |                    |
| e |                                               |                    |
| r |                                               |                    |
| t |                                               |                    |
| i |                                               |                    |
| c |                                               |                    |
| a |                                               |                    |
| l |                                               |                    |
| d |                                               |                    |
| a |                                               |                    |
| t |                                               |                    |
| u |                                               |                    |
| m |                                               |                    |
| s |                                               |                    |
| a |                                               |                    |
| n |                                               |                    |
| d |                                               |                    |
| h |                                               |                    |
| e |                                               |                    |
| i |                                               |                    |
| g |                                               |                    |
| h |                                               |                    |
| t |                                               |                    |
| s |                                               |                    |
| y |                                               |                    |
| s |                                               |                    |
| t |                                               |                    |
| e |                                               |                    |
| m |                                               |                    |
| s |                                               |                    |
+---+-----------------------------------------------+--------------------+
|   | Using NGVD 29 when NAVD 88 required           | 1.2 to 4.5 feet    |
|   |                                               | (vertical)         |
+---+-----------------------------------------------+--------------------+
|   | Using ellipsoid heights for elevations        | Varies from 63 to  |
|   |                                               |                    |
|   |                                               | 113 feet           |
|   |                                               | (vertical)         |
+---+-----------------------------------------------+--------------------+
|   | Neglecting geoid slope when transferring      | Up to 0.7 foot     |
|   | elevations with GPS                           | vertical per mile  |
|   |                                               | horizontal         |
+---+-----------------------------------------------+--------------------+
|   | Using leveling without orthometric            | Can exceed 0.05    |
|   | corrections to "correct" GPS-derived          | foot vertical per  |
|   | elevations                                    | mile horizontal    |
+---+-----------------------------------------------+--------------------+
| A |                                               |                    |
| c |                                               |                    |
| c |                                               |                    |
| u |                                               |                    |
| r |                                               |                    |
| a |                                               |                    |
| c |                                               |                    |
| y |                                               |                    |
| e |                                               |                    |
| s |                                               |                    |
| t |                                               |                    |
| i |                                               |                    |
| m |                                               |                    |
| a |                                               |                    |
| t |                                               |                    |
| i |                                               |                    |
| o |                                               |                    |
| n |                                               |                    |
| a |                                               |                    |
| n |                                               |                    |
| d |                                               |                    |
| r |                                               |                    |
| e |                                               |                    |
| p |                                               |                    |
| o |                                               |                    |
| r |                                               |                    |
| t |                                               |                    |
| i |                                               |                    |
| n |                                               |                    |
| g |                                               |                    |
+---+-----------------------------------------------+--------------------+
|   | Using precision as an accuracy estimate with  | Accuracy estimate  |
|   | data containing systematic errors (e.g.,      | is meaningless     |
|   | incorrect reference coordinates)              |                    |
+---+-----------------------------------------------+--------------------+
|   | Reporting horizontal error using unscaled     | Gives error        |
|   | standard deviation, rather than at the 95%    | estimates at 39%   |
|   | confidence level (as specified by the FGDC)   | confidence level   |
+---+-----------------------------------------------+--------------------+
|   | Reporting vertical error using unscaled       | Gives error        |
|   | standard deviation, rather than at the 95%    | estimates at 68%   |
|   | confidence level (as specified by the FGDC)   | confidence level   |
+---+-----------------------------------------------+--------------------+
|   | Using radial and circular estimates for       | Typically makes    |
|   | horizontal error rather than semi-major axis  | errors appear less |
|   | of horizontal error ellipse                   | than actual        |
+---+-----------------------------------------------+--------------------+
|   | Using trivial vectors in GPS network          | Varies, but always |
|   | adjustments                                   | makes errors       |
|   |                                               | appear less than   |
|   |                                               | actual             |
+---+-----------------------------------------------+--------------------+

**Abbreviations and definitions**

Below is an alphabetical list of the abbreviations and terms used in
this handout. In the interest of brevity, the definitions are highly
general and simplified. Please note also that this list gives only a
portion of the terms and abbreviations frequently encountered in GPS
positioning and geodesy. Terms in *italics* within the definitions are
defined in this list. Cited references are listed at the end of this
document.

Autonomous position. A *GPS* position obtained with a single receiver
using the ranging capability of the single frequency code (i.e., the
Standard Positioning Service).

Confidence interval or level. A computed probability that the "true"
value will fall within a specified region (e.g., 95% confidence level).
Applies only to randomly distributed errors.

CORS (Continuously Operating Reference Stations). A nation-wide system
of permanently mounted *GPS* antennas and receivers that collect *GPS*
data continuously. The CORS network is extremely accurate and
constitutes the primary survey control for the US. CORS data can be used
to correct *GPS* survey and mapping results, and is freely available
over the Internet.

Datum transformation. Mathematical method for converting one *geodetic
datum* to another (there are several types, and they vary widely in
accuracy).

Differential correction. A method for removing much of the error in an
*autonomous GPS* position. Typically requires at least two
simultaneously operating *GPS* receivers, with one of the two at a
location of known geodetic coordinates.

Ellipsoid height. Straight-line height above and perpendicular to the
*ellipsoid*. This is the type of height determined by *GPS*, and it does
not equal elevation. Can be converted to orthometric heights
(elevations) using a *geoid* model.

Ellipsoid. A simple mathematical model of the Earth corresponding to
mean sea level (the *geoid*) and used as part of a *geodetic datum*
definition. Constructed by rotating an ellipse about its semi-minor
axis. Also referred to as a spheroid.

FBN (Federal Base Network). Nationwide network of *GPS* control stations
observed and adjusted by the NGS. A nation-wide readjustment of the FBN
is scheduled for 2007.

FGDC (Federal Geographic Data Committee). Develops and promulgates
information on spatial data formats, accuracy, specifications, and
standards. Widely referenced by other organizations. Includes the
Federal Geodetic Control Subcommittee (FGCS) and the *NSSDA*.

Geodetic datum. Reference frame for computing geodetic coordinates
(latitude, longitude, and *ellipsoid height*) of a point. A datum always
refers to a particular *ellipsoid* and a specific adjustment (e.g. the
1992 adjustment of *NAD 83* for the Arizona *HARN*).

Geographic "projection". This is not a true *map projection* in the
sense that it does not transform geodetic coordinates into linear units.
However, it is a projection in the sense that it represents geodetic
coordinates on a regular flat grid, such that the difference in angular
units (e.g., decimal degrees) is equal in all directions. Because of
meridian convergence, this results in a coordinate system that is
extremely distorted, especially at high latitudes, and the distortion
varies greatly with direction.

Geoid. Surface of constant gravitational equipotential (a level surface)
that best corresponds to global mean sea level. Used as a reference
surface for modern *vertical datums*, such as *NAVD 88*.

GPS (Global Positioning System). A constellation of (currently) 29
satellites used for navigation, mapping, surveying, and timing.
Microwave signals transmitted by the satellites are observed by GPS
receivers to determine a three-dimensional position. Accuracy varies
greatly depending on the type of receiver and methods used.

Grid distance. The horizontal distance between two points on a flat
plane. This is the type of distance obtained from map projections.

Ground distance. The horizontal distance between two points as measured
on the curved surface of the Earth.

GRS-80 (Geodetic Reference System of 1980). The reference *ellipsoid*
currently used for many *geodetic datums* throughout the world,
including *NAD 83* and *ITRF*.

HARN (High Accuracy Reference Network). Network of *GPS* stations
adjusted by the NGS on a state-by-state basis. The Arizona HARN was
adjusted in 1992. In some states it is referred to as a High Precision
GPS (or Geodetic) Network (HPGN).

International Foot. Linear unit adopted by the US in 1959, and defined
such that one foot equals exactly 0.3048 meter. Shorter than *US Survey
Foot* by 2 *parts per million (ppm)*.

ITRF (International Terrestrial Reference Frame). Global geodetic
reference system that takes into account plate tectonics (continental
drift) and is used mainly in scientific studies. A new ITRF "epoch" is
computed periodically and is referenced to a specific time (e.g., ITRF
2000 1997.0). Each epoch is a realization of the International
Terrestrial Reference System (ITRS). See Soler (2004), and Soler and
Snay (2004) for information on its relationship to *NAD 83*.

Map projection. A functional (one-to-one) mathematical relationship
between geodetic coordinates (latitude and longitude) on the curved
surface of the Earth, and grid coordinates (northings and eastings) on a
planar (flat) map surface. All map projections are distorted, in that
the relationship between the projected grid coordinates differs from
that between their respective geodetic coordinates. See Snyder (1987)
for details.

NAD 27 (North American Datum of 1927). Geodetic datum of the US prior to
*NAD 83*. Superseded by *NAD 83* in 1986. This is the datum of *SPCS 27*
and *UTM 27*.

NAD 83 (North American Datum of 1983). Current official geodetic datum
of the US. Replaced *NAD 27* in 1986, which is the year of the initial
NAD 83 adjustment. This is the datum of *SPCS 83* and *UTM 83*. See
Schwarz (1986) for details.

NADCON. *Datum transformation* computer program developed by the NGS for
transforming coordinates between *NAD 27* and *NAD 83*, and also between
the *NAD 83* 1986 adjustment and the various *HARN* adjustments. See
Dewhurst (1990) for details.

NAVD 88 (North American Vertical Datum of 1988). Current official
vertical datum of the US. Replaced *NGVD 29* in 1991. See Zilkoski et
al. (1992) for details.

NDGPS (National Differential GPS). A nation-wide system of "beacons"
(permanently mounted *GPS* receivers and radio transmission equipment)
that transmit real-time *differential corrections* which can be used by
GPS receivers equipped with the appropriate radio receivers. Operated
and maintained by the US Coast Guard. See US Coast Guard (2004) for
details.

NGS (National Geodetic Survey). Federal agency within the Department of
Commerce responsible for defining, maintaining, and promulgating the
*NSRS* within the US and its territories.

NGVD 29 (National Geodetic Vertical Datum of 1929). Previous vertical
datum of the US, superseded by *NAVD 88* in 1991. Not referenced to the
*geoid* or mean sea level, and not as compatible with GPS-derived
elevations as *NAVD 88*. Called "Mean Sea Level" (MSL) datum prior to
1974.

NSRS (National Spatial Reference System). The framework for latitude,
longitude, height, scale, gravity, orientation and shoreline throughout
the US. Consists of geodetic control point coordinates and sets of
models describing relevant geophysical characteristics of the Earth,
such as the *geoid* and surface gravity. Defined, maintained, and
promulgated by the *NGS* (see Doyle, 1994, for details).

NSSDA (National Standard for Spatial Data Accuracy). *FGDC* methodology
for determining the positional accuracy of spatial data (see Federal
Geographic Data Committee, 1998).

OPUS (Online Positioning User Service). A free *NGS* service that
computes *NSRS* and *ITRF* coordinates with respect to the *CORS* using
raw *GPS* data submitted via the Internet.

Orthometric correction. A correction applied to leveled height
differences which reduces systematic errors due to variation in
gravitational potential. See Dennis (2004) for details.

Parts per million (ppm). A method for conveniently expressing small
numbers, accomplished by multiplying the number by 1 million (e.g.,
0.00001 = 10 ppm). Exactly analogous to percent, which is "parts per
hundred".

SPCS (State Plane Coordinate System). A system of standardized *map
projections* covering each state with one or more zones such that a
specific distortion criterion is met. Projection parameters (including
units of length) are independently established by the legislature of
each state. Can be referenced to either the *NAD 83* or *NAD 27* datums
(SPCS 83 and SPCS 27, respectively). See Stem (1989) for details.

Trivial vector. A *GPS* vector (computed line connecting two GPS
stations) that is not statistically independent from other *GPS* vectors
observed at the same time.

US Survey Foot. Linear unit of the US prior to 1959, and defined such
that one foot equals exactly\
1200 / 3937 meter. Longer than *International Foot* by 2 *parts per
million (ppm)*.

UTM (Universal Transverse Mercator). A grid coordinate system which
divides the Earth (minus the polar regions) into 120 zones to allow
creation of maps that meet a specific distortion criterion using the
Transverse Mercator *map projection*. Can be referenced to either the
*NAD 83* or *NAD 27* datums (UTM 83 and UTM 27, respectively). See Hager
et al. (1989) for details.

Vertical datum. Reference system for determining "elevations", typically
through optical leveling. Modern vertical datums use the *geoid* as a
reference surface and allow elevation determination using *GPS* when
combined with a *geoid* model.

WAAS (Wide Area Augmentation System). A system of geosynchronous
satellites and ground *GPS* reference stations developed and managed by
the Federal Aviation Administration and used to provide free real-time
*differential corrections*. See Federal Aviation Administration (2003)
for details.

WGS 84 (World Geodetic System of 1984). Reference *ellipsoid* and
*geodetic datum* of *GPS*, defined and maintained by the US Department
of Defense. Current realizations of WGS 84 are considered identical to
*ITRF* 2000 at the 2 cm level. See National Imagery and Mapping Agency
(2000) for details, and Merrigan et al. (2002) for information on the
most recent realization.

**Surveying & mapping spatial data requirements & recommendations**

***These should be explicitly specified in surveying and mapping
projects***

1.  **[Completely define the coordinate system]{.underline}**

    a.  Linear unit (e.g., International foot, U.S. Survey foot, meter)

        i.  Use same linear unit for horizontal and vertical coordinates

    b.  Geodetic datum (recommend North American Datum of 1983)

        i.  Should include datum "epoch" (date), e.g., 1986, 1992
            (HARN), 2002.0 (CORS)

        ii. WGS 84, ITRF, and NAD 27 are **NOT** recommended

    c.  Vertical datum (e.g., North American Vertical Datum of 1988)

        i.  If GPS used for elevations, recommend using a modern geoid
            model (e.g., GEOID03)

        ii. Recommend using NAVD 88 rather than NGVD 29 when possible

    d.  Map projection type and parameters (e.g., Transverse Mercator,
        Lambert Conical)

        i.  Special attention required for low-distortion grid (a.k.a.
            "ground") coordinate systems

            1.  Avoid scaling of existing coordinate systems (e.g.,
                "modified" State Plane)

2.  **[Require *direct* referencing of the NSRS (National Spatial
    Reference System)]{.underline}**

    a.  Ties to published control strongly recommended (e.g., National
        Geodetic Survey control)

        i.  Relevant component of control must have greater accuracy
            than positioning method used

            1.  E.g., B-order (or better) stations for GPS control,
                2^nd^ order (or better) for vertical control

    b.  NGS Continuously Operating Reference Stations (CORS) can be used
        to reference the NSRS

        i.  Free Internet GPS post-processing service: OPUS (Online
            Positioning User Service)

3.  **[Specify *accuracy* requirements (*not* precision)]{.underline}**

    a.  Use objective, defensible, and robust methods (published ones
        are recommended)

        i.  Mapping and surveying: National Standard for Spatial Data
            Accuracy (NSSDA)

            1.  Require occupations ("check shots") of known
                high-quality control stations

        ii. Surveys performed for establishing control or determining
            property boundaries:

            1.  Appropriately constrained and over-determined
                least-squares adjusted control network

            2.  Beware of "cheating" (e.g., using "trivial" GPS vectors
                in network adjustment)

4.  **[Documentation is *essential* (metadata!)]{.underline}**

    a.  Require a report detailing methods, procedures, and results for
        developing final deliverables

        i.  This must include any and all post-survey coordinate
            transformations

            1.  E.g., published datum transformations, computed
                correction surfaces, "rubber sheeting"

    b.  Documentation should be complete enough that someone else can
        reproduce the product

    c.  For GIS data, recommend that accuracy and coordinate system
        information be included as feature attributes (not just as
        separate, easy-to-lose and easy-to-ignore metadata files)

**Example of surveying and mapping documentation (*metadata*)**

**[Basis of Bearings and Coordinates]{.underline}**

[Linear unit]{.underline}: International foot

[Geodetic datum]{.underline}: North American Datum of 1983 (1992)

[Vertical datum]{.underline}: North American Vertical Datum of 1988 (see
below)

[System]{.underline}: Shephard-Wesnitzer

[Zone]{.underline}: Sedona

[Projection]{.underline}: Transverse Mercator

Latitude of grid origin: 34° 44' 00" N

Longitude of central meridian: 111° 48' 00" W

Northing at grid origin: 0.000 ft

Easting at central meridian: 50,000.000 ft

Scale factor on central meridian: 1.000206 (exact)

All distances and bearings shown hereon are grid values based on the
preceding projection definition. The projection was defined such that
grid distances are equivalent to "ground" distances in the project area.

The basis of bearings is true geodetic north. Note that the grid
bearings shown hereon (or implied by grid coordinates) do not equal
geodetic bearings due to meridian convergence.

Orthometric heights (elevations) were transferred to the site from NGS
control station "Y 492" (PID ES0652) using GPS with NGS geoid model
"GEOID03" referenced to the published NAVD 88 height of this station.

The survey was conducted using GPS referenced to the National Spatial
Reference System. A partial list of point coordinates is given below
(additional coordinates are available upon request). Local network
accuracy error estimates are given at the 95% confidence level and are
based on an appropriately constrained least-squares adjustment of
over-determined and statistically independent observations.

[Point #28 "VORTEX" (PID AJ5367), fixed NGS control (off
site)]{.underline}

Latitude: 34° 50\' 46.53509" N (fixed)

Longitude: 111° 49\' 41.94400" W (fixed)

Ellipsoid height: 4384.121 ft (fixed)

[Point #2019, 1/2" rebar with aluminum cap, derived coordinates (on
site)]{.underline}

Latitude: 34° 51\' 47.13683\"N (±0.035 ft)

Longitude: 111° 47\' 07.78081\" W (±0.028 ft)

Ellipsoid height: 4343.842 ft (±0.056 ft)

[Point #3006, 1/2" rebar with plastic cap, derived coordinates (on
site)]{.underline}

Latitude: 34° 51\' 50.45539\" N (±0.046 ft)

Longitude: 111° 47\' 10.25560\" W (±0.039 ft)

Ellipsoid height: 4353.976 ft (±0.067 ft)

**Selected GPS and Geodesy resources and references**

***(includes references cited in preceding definitions)***

**Primary resource: The National Geodetic Survey
(<http://www.ngs.noaa.gov/>)**

*Some NGS web pages of particular interest*

Control station datasheets:
<http://www.ngs.noaa.gov/cgi-bin/datasheet.prl>

The Geodetic Tool Kit: <http://www.ngs.noaa.gov/TOOLS/>

Online Positioning User Service (OPUS): <http://www.ngs.noaa.gov/OPUS/>

Continuously Operating Reference Stations (CORS):
<http://www.ngs.noaa.gov/CORS/>

The Geoid Page: <http://www.ngs.noaa.gov/GEOID/>

**Documents (categorized as *introductory*, *intermediate*, *advanced*,
or *reference*)**

American Congress on Surveying and Mapping and The American Society of
Civil Engineers, (1978) *Definitions of Surveying and Associated Terms*,
American Congress on Surveying and Mapping and The American Society of
Civil Engineers, 210 pp. *\[reference\]*

American Land Title Association, American Congress on Surveying &
Mapping, and National Society of Professional Surveyors (1999) *Minimum
Standard Detail Requirements for ALTA/ACSM Land Title Surveys*, 9 pp.,
<http://www.acsm.net/alta99.pdf>. *\[reference\]*

American Society for Photogrammetry and Remote Sensing (2001) *Digital
Elevation Model Technologies and Applications: The DEM Users Manual*,
539 pp. *\[reference\]*

Anderson, M.A., D'Onofrio, D., Helmer, G.A. and Wheeler, W.W. (1996)
Specifications for geodetic control networks using high-production GPS
surveying techniques, version 2. California Geodetic Control Committee,
<http://www.rbf.com/cgcc/hpgps21.htm>. *\[reference\]*

Bomford, G. (1980) *Geodesy* (4^th^ Edition), Oxford University Press,
Great Britain, 855 pp. *\[advanced\]*

Bureau of the Budget (1947) *National Map Accuracy Standards*, Office of
Management and Budget, Washington, D.C., 1 p.
<http://rockyweb.cr.usgs.gov/nmpstds/acrodocs/nmas/NMAS647.PDF>.
***\[Note: These standards have been superseded by the FGDC 1998
standards and are NOT recommended for use\]*** *\[reference\]*

Dana, P. H. (2000) Global Positioning System Overview, University of
Colorado at Boulder website,
<http://www.colorado.edu/geography/gcraft/notes/gps/gps_f.html>
(includes links to related overview sites on map projections, geodetic
datums, and coordinate systems) *\[introductory\]*

Defense Mapping Agency (1984) *Geodesy for the Layman*, DMA Technical
Report 80-003, U.S. Defense Mapping Agency, Washington D.C., USA, 96
pp., <ftp://164.214.2.65/pub/gig/geo4layman/Geo4lay.pdf>
*\[introductory\]*

Dennis, M.L. (2002) When is control really *control*? Things to be aware
of when using NGS survey control for high accuracy GPS surveys in
Arizona, *The Arizona Surveyor*, Arizona Professional Land Surveyors
Association, Vol. 1, No. 4, pp. 6-8,
<http://www.azpls.org/displaynewsletter.cfm> *\[intermediate\]*

Dennis, M.L. (2004) A question of gravity: What effect does gravity have
on elevations determined by differential leveling?, *The Arizona
Surveyor*, Arizona Professional Land Surveyors Association, Vol. 4, No.
1, p. 6, <http://www.azpls.org/displaynewsletter.cfm>\]
*\[intermediate\]*

Dewhurst, W.T. (1990) NADCON: The application of
minimum-curvature-derived surfaces in the transformation of positional
data from the North American Datum of 1927 to the North American Datum
of 1983, *NOAA Technical Memorandum NOS NGS-50*, National Geodetic
Survey, Silver Springs, MD, USA, 32 pp.,
<http://www.ngs.noaa.gov/PUBS_LIB/NGS50.pdf> *\[advanced\]*

Doyle, D.R. (1994) *Development of the National Spatial Reference
System*, National Geodetic Survey, Silver Spring, Maryland,.
<http://www.ngs.noaa.gov/PUBS_LIB/develop_NSRS.html> *\[intermediate\]*

Federal Aviation Administration (2003) FAA Wide Area Augmentation
System, *Fact Sheets*, <http://gps.faa.gov/Library/indexWAAS-f.htm>
*\[introductory\]*

Federal Emergency Management Agency (2003) *Guidelines and
Specifications for Flood Hazard Mapping Partners*, FEMA Map
Modernization Program, April 2003 version. Consists of 3 volumes (337
pp.), 13 appendices (1207 pp.), and 5 supporting documents (85 pp.), for
a total of 1629 pp., <http://www.fema.gov/fhm/dl_cgs.shtm>.
*\[reference\]*

Federal Geographic Data Committee (1998) *Geospatial Positioning
Accuracy Standards*, FGDC-STD-007.2-1998, Federal Geographic Data
Committee, Reston, Virginia, USA, 128 pp.,
<http://www.fgdc.gov/standards/documents/standards/accuracy/>,
\[includes National Standard for Spatial Data Accuracy (NSSDA), Chapter
3\]. *\[reference\]*

Hager, J.W., Behensky, J.F., and Drew, B.W. (1989) The Universal Grids:
Universal Transverse Mercator (UTM) and Universal Polar Stereographic
(UPS), *DMA Technical Manual 8358.2*, Defense Mapping Agency, Fairfax,
Virginia, USA, 49 pp.,
<ftp://164.214.2.65/pub/gig/tm8358.2/TM8358_2.pdf>. *\[reference\]*

Hager, J.W., Fry, L.L., Jacks, S.S. and Hill, D.R. (1990) Datums,
Ellipsoids, Grids, and Grid Systems, *DMA Technical Manual 8358.1*,
Edition 1, Defense Mapping Agency, Fairfax, Virginia, USA, 150 pp.,
<http://earth-info.nga.mil/GandG/tm83581/toc.htm>. *\[reference\]*

Heiskanen, W.A. and Moritz, H. (1967) *Physical Geodesy*, WH Freeman &
Co, San Francisco, USA, 364 pp. *\[advanced\]*

Hoffman-Wellenhoff, B., Lichtenegger, H. and Collins, J. (2001) *Global
Positioning System: Theory and Practice* (5^th^ Edition),
Springer-Verlag, New York, USA, 382 pp. *\[advanced\]*

Leick, A. (2003) *GPS Satellite Surveying* (3^rd^ Edition), John Wiley &
Sons, New York, New York, USA, 464 pp. *\[advanced\]*

Merrigan, M.J. et al. (2002) A Refinement to the World Geodetic System
1984 Reference Frame, *Annual Meeting Proceedings: 58^th^ Annual
Meeting*, ION GPS 2002, September 24-27, Portland, Oregon, USA, pp.
1519-1529,
<http://earth-info.nga.mil/GandG/sathtml/IONReport8-20-02.pdf>
*\[advanced\]*

National Digital Elevation Program (2004) *Guidelines for Digital
Elevation Data*, version 1.0, 93 pp.,
<http://www.ndep.gov/NDEP_Elevation_Guidelines_Ver1_10May2004.pdf>.
*\[reference\]*

National Geodetic Survey (1998) *National Height Modernization Study:
Report to Congress*, National Geodetic Survey, Rockville, MD, USA, 181
pp., <http://www.acsm.net/heightmod.pdf>. *\[reference\]*

National Geodetic Survey (1986) *Geodetic Glossary*, National Geodetic
Survey, Rockville, Maryland, USA, 274 pp. *\[reference\]*

National Imagery and Mapping Agency (2000) *Department of Defense World
Geodetic System of 1984: Its Definition and Relationships with Local
Geodetic Systems* (3^rd^ Edition), Amendment 1, NIMA Technical Report
8350.2, National Imagery and Mapping Agency (now the National
Geospatial-Intelligence Agency), 175 pp.,
<http://earth-info.nima.mil/GandG/tr8350_2.html>. *\[reference\]*

National Ocean Service (2004) Geodesy, *NOS Education* website, National
Oceanic and Atmospheric Administration,
<http://oceanservice.noaa.gov/education/geodesy/welcome.html>
*\[introductory\]*

National Ocean Service (2004) Global Positioning, *NOS Topics* website,
National Oceanic and Atmospheric Administration,
<http://oceanservice.noaa.gov/topics/navops/positioning/welcome.html>
*\[introductory\]*

Schwarz, C.R. (ed.) (1989) North American Datum of 1983, *NOAA
Professional Paper NOS 2*, U.S. Department of Commerce, National Oceanic
and Atmospheric Administration, National Geodetic Survey, Rockville,
Maryland, USA, 256 pp.,
<http://www.ngs.noaa.gov/PUBS_LIB/NADof1983.pdf>\] *\[advanced\]*

Smith, J.R. (1997) *Introduction to Geodesy: The History and Concepts of
Modern Geodesy*, John Wiley & Sons, New York, USA, 224 pp.
*\[introductory\]*

Snyder, J.P. (1987) *Map Projections ─ A Working Manual*, U.S.
Geological Survey Professional Paper 1395, U.S. Government Printing
Office, Washington, D.C., USA, 383 pp. *\[reference\]*

Soler, T. (2004) *CORS Coordinates*, National Geodetic Survey, Silver
Spring, Maryland, <http://www.ngs.noaa.gov/CORS/metadata1/>\]
*\[advanced\]*

Soler, T. and Snay, R.A. (2004) Transforming Positions and Velocities
between the International Terrestrial Reference Frame of 2000 and North
American Datum of 1983, *Journal of Surveying Engineering*, American
Society of Civil Engineers, Vol. 130, No. 2, pp. 49-55. *\[advanced\]*

Stem, J.E., (1990) State Plane Coordinate System of 1983, *NOAA Manual
NOS NGS 5*, U.S. Department of Commerce, National Oceanic and
Atmospheric Administration, National Geodetic Survey, Rockville,
Maryland, USA, 119 pp.,
<http://www.ngs.noaa.gov/PUBS_LIB/ManualNOSNGS5.pdf>. *\[reference\]*

Torge, W. (2001) *Geodesy* (3^rd^ Edition), W de Gruyter, Berlin, New
York, USA, 416 pp. *\[advanced\]*

U.S. Army Corps Of Engineers (2002) *Geodetic and Control Surveying*,
Engineer Manual No. 1110-1-1004, 101 pp.,
<http://www.usace.army.mil/publications/eng-manuals/em1110-1-1004/toc.htm>.

U.S. Army Corps Of Engineers (2003) *NAVSTAR Global Positioning System
Surveying*, Engineer Manual No. 1110-1-1003, 468 pp.,
<http://www.usace.army.mil/publications/eng-manuals/em1110-1-1003/toc.htm>.
*\[reference\]*

U.S. Coast Guard (2004) *GPS*, U.S. Coast Guard Navigation Center
website, <http://www.navcen.uscg.gov/gps/default.htm> *\[introductory\]*

U.S. Forest Service and Bureau of Land Management (2001) *Standards and
Guidelines for Cadastral Surveys Using the Global Positioning System*,
U.S. Department of Agriculture and U.S. Department of the Interior, 18
pp., <http://www.blm.gov/nhp/efoia/wo/fy01/im2001-186attach1.pdf>.
*\[reference\]*

Van Sickle, J. (2001) *GPS for Land Surveyors* (2^nd^ Edition), Ann
Arbor Press, Chelsea, Michigan, USA, 284 pp. *\[intermediate\]*

Wolf, P.R. and Ghilani, C.D. (1994) *Elementary Surveying* (9^th^
Edition), Harper-Collins, New York, USA, 760 pp. *\[intermediate\]*
*Note:* 10^th^ Edition published in 2001.

Wolf, P.R. and Ghilani, C.D. (1997) *Adjustment Computations: Statistics
and Least Squares in Surveying and GIS*, John Wiley & Sons, New York,
USA, 564 pp. *\[advanced\]*

Zilkoski, D. B., D'Onofrio, J. D. and Frakes, S. J. (1997) Guidelines
for Establishing GPS-Derived Ellipsoid Heights (Standards: 2 cm and 5
cm), version 4.3, *NOAA Technical Memorandum NOS NGS-58*, National
Geodetic Survey, Silver Springs, MD, USA, 22 pp.,
<http://www.ngs.noaa.gov/PUBS_LIB/NGS-58.html>. *\[reference\]*

Zilkoski, D. B., Richards, J.H. and Young, G.M. (1992) Special Report:
Results of the General Adjustment of the North American Vertical Datum
of 1998, *Surveying and Land Information systems*, Vol. 52, No. 3, pp.
133-149, <http://www.ngs.noaa.gov/PUBS_LIB/NAVD88/navd88report.htm>\]
*\[advanced\]*