__implications of geodesy, spatial reference systems

8/12/2019 __Implications of Geodesy, Spatial Reference Systems

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Implications of Geodesy, Spatial Reference Systems,and Map Projections in Processing, Conversion,

Integration, and Management of GIS Data

Larry ZHANG

eMap Div., Integrated Solution Services Dept, Saudi Aramco

C-121 West Park #1, Dhahran 31311, Saudi ArabiaPhone: (966 3) 874-8187; Fax: (966 3) 874-8339

Email: [email protected]

Copyright Saudi Aramco 2005

Keywords: geodesy, datum, coordinate system, map projection, engineering

surveying, CAD drawing, GIS, RS, GPS measurements, data processing,conversion, integration, management

Abstract

Geospatial datasets are collected from a huge variety of sources, including field

surveying, spatial-enabled CAD drawings, GIS; GPS measurements, satellite

sensors or airborne missions, with an equally large variety in quality,

accessibility, confidence, and references. Most engineering surveying

traditionally was carried out on local scales using terrestrial equipment such as

theodolites and levels to establish positions with respect to nearby control

stations (points). Similarly, most CAD drawings requiring access to spatial data

are usually through a published local map. Even though the map projection was

usually a consideration, the question of the datum was of minimal importance.

Moreover, rapid development of GIS, GPS, and spaceborne (airborne) remote

sensing is changing this state of affairs. Due to their global and space-based

nature, these are techniques that have broken free completely of the localized

survey. Presenting the data in an almost infinite variety of ways and scales, as

defined by an increasingly varied set of users in multifunctional teams, is an

equally daunting challenge. Consequently, more and more confusion potentially

http://www.saudigis.org/fckfiles/file/saudigisarchive/1stgis/papers/10.pdf


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exists, which can cause unreliable spatial analysis, even totally misplaced

decisions.

This paper focuses on the practical considerations of correctly using datum and

map projections in processing, conversion, integration, and management ofgeospatial datasets in order to minimize planimetric distortion and reach

reasonable accuracy of heights for GIS data management.

Introduction

It is well known that the earth is not quite round. And because the earth's not

round, we need to clearly define that shape so that we can make maps as

accurate as possible. In order to make larger and better maps, we need to use

something called a spatial reference system. A spatial reference system defines

the way that any landmark (trees, houses, roads, buildings etc.) can have its own

unique address. To have a good spatial reference system, engineers really need

to need to know about the shape of the earth, that is, geodesy. Quite simply,

geodesy is the study of the shape and size of the earth, and its gravity fields.

More strictly, geodesy is the discipline that deals with the measurement and

representation of the earth, its gravity field and geodynamic phenomena (polar

motion, earth tides, and crustal motion) in three-dimensional time varying space.

Obviously, to correctly determine positions of geographical features on the

surface of the Earth, spatial datasets must all be related to a single, common

'reference system', that is, to the same or consistent datum.

Coordinates, Datums, and Map Projections

The shape of the earths surface is quite complicated. But, the easiest way to

represent the shape of the earth mathematically is by using an ellipsoid or

spheroid. An ellipse rotated on its minor axis (b) generates an ellipsoid.

Therefore, the most common way of stating terrestrial position is with two angles,

latitude and longitude. These define a point on the globe. More correctly, they

define a point on the surface of an ellipsoid which approximately fits the globe.


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The relationship between the ellipsoid and latitude and longitude is simple. North-

south lines of constant longitude are known as meridians, and east-west lines of

constant latitude are parallels. One meridian of the ellipsoid is chosen as the

prime meridian and assigned zero longitude. The longitude of a point on the

ellipsoid is the angle between the meridian passing through that point and the

prime meridian. Usually the scale of longitude is divided into eastern and western

hemispheres (hemi-ellipsoids, actually!) from 0 to 180 degrees west and 0 to 180

degrees east. The equator of the ellipsoid is chosen as the circle of zero latitude.

The latitude of a point is the angle between the equatorial plane and the line

perpendicular to the ellipsoid at that point. Latitudes are reckoned as 0 to 90

degrees north and 0 to 90 degrees south, where 90 degrees either north or south

is a single point - the pole of the ellipsoid.

So latitude and longitude give a position on the surface of the stated ellipsoid.

Since real points on the ground are actually above (or possibly below) the

ellipsoid surface, we need a third coordinate, the so-called ellipsoid height, which

is simply the distance from the point to the ellipsoid surface along a straight line

perpendicular to the ellipsoid surface. The term ellipsoid height is actually a

misnomer, because although this is an approximately vertical measurement, it

does not give true height because it is not related to a level surface. It does

however unambiguously identify a point in space above or below the ellipsoid

surface in a simple geometrical way, which is its purpose. In order to use

latitudes and longitudes with any degree of certainty we must know which

ellipsoid we are dealing with.

Cartesian coordinates are a very simple system of describing position in three

dimensions, using three perpendicular axes X, Y and Z. Three coordinates

unambiguously locate any point in this system. It can be used as a very usefulalternative to latitude, longitude and ellipsoid height to convey exactly the same

information. Using a Cartesian coordinate system, any point on the earth's

surface has an x, y, z coordinate value, and that coordinate value can be

translated into an ellipsoid coordinates, that is, Latitude, Longitude, and an

ellipsoid height.


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Figure 1. The position of point (P) stated as either geodetic coordinates (latitude, longitude,

and ellipsoid height) or geocentric coordinates (Cartesian coordinates X, Y and Z) (Ordnance

Survey, 2005)

In practice, the ellipsoid height is traditionally referred to as mean sea level, that

is, geoid height, rather than ellipsoid height. Geoid is essentially the real shape of

the earth, without accounting for the topographic features. It is an idealized

equilibrium surface of gravity field. It is called orthometric height, or geoid

height, i.e., elevation.

Different Geoid models will give different orthometric heights for a point, even

though the ellipsoid height (determined by GPS) might be very accurate. The

geoid, unlike the ellipsoid, is too complicated to serve as the computational

surface on which to solve geometrical problems like point position. Therefore

orthometric height should never be given without also stating the Geoid model

used.


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Figure 2. The relationship among the surfaces associated with the ellipsoid, the geoid (local and

global), mean sea level (MSL), sea surface topography (SST), and the continent (Ordnance

Survey, 2005)

As mentioned above, one or more of these coordinate types are used to state the

positions of points and features on the surface of the Earth by introducing various

types of coordinates. However, no matter what type of coordinates used, a

suitable origin with respect to the stated coordinates must be known, called the

geodetic datum.

The term geodetic datum is usually taken to mean the ellipsoidal type of datum

just described: a set of 3-D Cartesian axes plus an ellipsoid, which allows

positions to be equivalently described in 3-D Cartesian coordinates or as latitude,

longitude and ellipsoid height. The datum definition consists of eight parameters:

the 3-D location of the origin (three parameters), the 3-D orientation of the axes(three parameters), the size of the ellipsoid (one parameter) and the shape of the

ellipsoid (one parameter).

There are, however, other types of geodetic datum. A local datum is defined by

selecting an origin for national or regional surveying or mapping. At this point,


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geoid-ellipsoid separation and the vertical deviation are chosen, usually, as zero.

Almost by definition, a local datum approximates the geoid in the region much

more closely than does the global datum, or a datum optimized for a wider

region. A local datum for orthometric height measurement is very simple. It

usually consists of the stated height of a single fundamental bench mark (FBM).

However, modern height datums are becoming more and more integrated with

ellipsoidal datums through the use of Geoid models. In engineering surveying

and GIS, the ideal is a single datum definition for horizontal and vertical

measurements, locally rather than globally.

The plane coordinates, that is, grid coordinates or map coordinates (also called

eastings and northings), are commonly used to locate position with respect to a

map, which is a two-dimensional plane surface depicting features on the curved

surface of the Earth. Map coordinates use a simple 2-D Cartesian system in

which the two axes are known as eastings and northings. Map coordinates of a

point are computed from its ellipsoidal latitude and longitude by a standard

formula known as a map projection. Obviously, a map projection cannot be a

perfect representation. Therefore, different datasets should be projected into the

same map frame.

In geodesy, when computations with coordinates are needed, latitude and

longitude or Cartesian coordinates are used, then the results are converted to

map coordinates as a final step if necessary. Map coordinates only tend to be

used for visual display purposes.

Impacts of Datums and Map Projections on Processing,

Integration, and Management of Spatial Datasets

In GIS, geospatial data is an integration of data from different sources and

datasets. An integrated GIS dataset may need to combine datasets having

different reference systems from differing surveying organizations in cross-border

neighboring regions; to georeferencing an image with ground control points using

GPS, to cooperating with others from a published map; to carrying out a survey


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with high precise GPS, or bringing it into sympathy with existing mapping in a

local coordinate system.

In effect, even if each "sub" data set is intrinsically correct, there is still a major

design effort just to bring the datasets together in a common reference frame(datum realization). Geologists and drilling engineers using GIS databases with

inconsistent datums or different map coordinates have potential significant risks.

For example, in oil exploration:

1. Potential failure to match seismic data with well surface location (wrongdatums)

2. Missing geological horizons and encroaching on other horizontally

deviated wells (wrong positioning because of wrong horizontal datum and

vertical reference, or different map projections).

In fact, the worst case is to carry out computation using datasets with incorrect

reference systems. In GIS, for example, determining the optimum route on a

transportation network or computing the area of land parcels. The same adverse

impact will result if it is just too difficult to manipulate the data to the desired

output in GIS (Figure 3). Therefore, different datasets should be projected into

the same map frame in a GIS project.

In GIS, map coordinates with varied map projections are used directly for many

computational tasks because projected coordinates are easily calculated. A map

projection can not be a perfect representation because it is not possible to show

a curved surface on a flat map without creating distortions and discontinuities.

This working procedure is in contrast to the practice in geodesy, where latitude

and longitude or Cartesian coordinates are used directly.

Dengerous!


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Figure 3. Showing 70 m offset between layers using inconstant datum (local datum

Ain_el_ABD_1970 and global datum WGS84) in 1:2500 map of a town

In practice, Universal Transverse Mercator (UTM) and Lambert Conformal Conic

(LCC) projections account for 90% of base maps worldwide (J. Illife, 2000). In

theory, a UTM projection can allow minimum distortion in an area that is

predominately north-south in extent, while a LCC does the same for areas that

predominately east-west extent. LCC is similar to the Albers Conic Equal-Area

projection except that it portrays shape more accurately than area (Table 1).

Table 1 LCC Properties

Shape:All graticular intersections are 90 degrees. Small shapes are

maintained.

Area:Minimal distortion near the standard parallels. Arial scale is

reduced between standard parallels and increased beyondthem.

Direction:Local angles are accurate throughout because ofconformity.

Distance:Correct scale along the standard parallels. The scale is

reduced between the parallels and increased beyond theparallels.

Limitations:Best results are for regions predominantly east-west in

extent and located in the middle, north, or south latitudes.Total range in latitude should not exceed 35 degrees.


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Applications:Saudi national projection of LCC is widely used for varied

GIS mapping in Saudi Arabia. It makes use of the followingparameters:

Map Projection: Lambert Conformal Conic

Ellipsoid: International 1909 (1924)

Datum: Ain_el_ABD_1970 Longitude of Origin: 45 (Central Meridian)

Latitude of Origin: 24 Degrees North

Standard Parallel 1: 27 Degrees North

Standard Parallel 2: 21 Degrees North

Central Meridian: 45 Degrees East

False Easting: 1,000,000

False Northing: 3,000,000

Unit of Measurement: meter

It is worth noting that integration of data from digitized historical paper maps,

CAD drawing, GPS measurements, traditional airphotos, or engineering

surveying into a spatial database or a GIS project requires special attention to

spatial information and accuracy.

The CAD map projection is firstly determined when the data is created and must

be supplied from the vendor of the data. Knowing this information is very

valuable for referencing with any other geospatial data. Generally, there are three

types of XY referenced CAD files that the vendor of CAD data provides for GIS

integration: spatially-enabled CAD, pseudo-projection, and non-projected (lost inspace).

Spatially-enabled CAD file has its projection/coordinate system and mapping unit

stored in a format that can be easily read by GIS software like ArcGIS or

GeoMedia. Generally speaking, when digitizing paper maps in CAD environment,

it is the first step to correctly use a grid system to reference all locations of paper

maps to a specific point, that is, the origin in Cartesian coordinate system. If

CAD-based GIS like AutoCAD Map or MicroStation GeoGraphics are available, itis necessary to firstly georeference scanned maps to available georeferenced

vector or raster data because historical paper maps usually do not conform to a

scaled grid system. And then, digital vector layers can be obtained through

digitizing the georeferenced maps.


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Pseudo-projected XY CAD coordinates have been set up to correlate to a

particular coordinate system (UTM, for example). The actual names of the

projection, units of measurements (feet, meter), and datum would have to be

obtained from the creator of the data. Once those data are available, pseudo-

projected CAD files can be easily defined in GIS system.

Non-projected CAD files have no projection, which is lost in space. The XY

readouts from MicroStation or AutoCAD do not correspond to any real-world

latitude/longitude or easting/northing coordinates. In practice, most engineering

CAD drawings belong to this category. For integration of those digital CAD

drawings into GIS, spatial adjustment on CAD drawing data is firstly required in

order to spatially register the CAD drawings to reliable raster or vector data in

GIS project. Spatial adjustment on CAD drawings must be carefully taken

because all adjusted vectors must be consistent in order to avoid different errors

in different locations. In other word, it is necessary to analyze adjusted vectors

for acceptance or rejection (Wolf & Ghilani, 1997).

In addition to spatial references of CAD files, an accuracy expectation will help to

determine whether digitizing hardcopy data or CAD drawings are acceptable for

a GIS project. The highest accuracy obtainable from digitized hardcopy maps is

0.25 mm at scale. For example, the data digitized from a 1:10000 paper map will

allow an accuracy of 2.5 meters (offset). It is possible for CAD drawing to have

an accuracy of 0.625 m if digitized from a 1:2500 QuickBird image for example.

Finally, most spatially-enabled CAD drawings often provide a very dirty vector

base for a GIS project or spatial database. It is mandatory to simplify and clear

them before integrating into GIS projects in order to improve display

performance and make accurate analysis in GIS.

For the past decades, significant progress of GPS have now made the global

positioning system convenient and practical for use in all type of local and

regional surveying, including property surveys, topographical mapping, and

construction projects. However, GPS measurement contains errors. Adjustment

computations have to be done in order to provide the required accuracy of the


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certain applications (Wolf & Ghilani, 1997). During adjustment computations,

three reference systems are involved, including satellite reference system,

geocentric coordinate system, and geodetic system. In order for the results of the

baseline computations to be useful to regional GIS or local surveying, GPS

measurements are finally provided in geodetic coordinates (latitude, longitude,

and ellipsoid height), which are referenced to WGS84 ellipsoid. From latitude and

longitude of geodetic coordinates, local projected map coordinates like UTM 39

with Saudi national datum (Ain_el_ABD_1970) can be computed. It is critical to

note that, to convert ellipsoid heights to elevations, local geoid heights (vertical

distances between the ellipsoid and geoid) must be subtracted from ellipsoid

heights.

Managing spatial datasets, especially in an enterprise environment is critical to

successful applications and core missions of GISenabled integration. It is

significant important to plan ahead and inspect project field operations and

delivered data, and ensure proper spatial continuity between projects. Workflows

in GIS and remote sensing are daily tasks. Therefore, it is recommended to store

all spatial data in spatial database systems in the planned datum. And design all

GIS systems to transfer or reproject data automatically to a user-defined or

default datum. The transformation approaches taken are very much dependent

on the accuracy requirements. In a 2D GIS and remote sensing project, the data

accuracy is usually up to 1 meter horizontally. With this range of accuracy

requirement, all spatial data must be properly referenced by specifying the datum

because spatial analysis and mapping missions are fully based on single datum

and map coordinate. Obviously, considering spatial data has many unique

characteristics and management requirements; GIS and remote sensing data

management requires more than DBMS technology. Otherwise, mismanagement

of spatial data is likely to be very costly both in operational and corporate value.

Conclusions

Presenting geospatial data in a GIS system can be done in many ways, so any

location-based systems will be significantly impacted if system analysts and


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__implications of geodesy, spatial reference systems

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