Survey, Mapping and GIS Principles

An overview of Survey, Mapping and GIS principles

Written by Wynand Mulder – Copyright

INDEX
  1. Co-ordinate Systems Explained
  2. Transformations
  3. Geo-referencing Explained
  4. CAD vs Database vs GIS
  5. South African Co-ordinate Systems
  6. Elevations, heights and Geoids
  7. GPS Accuracies
  8. Rules and Principles
1.   Co-ordinate Systems Explained

A Co-ordinate System is a set of mathematical formulae used to transfer a point on the irregular surface of the earth onto a planar surface.

A Co-ordinate System consists of 3 elements:

1.   Ellipsoid

This is the smooth mathematical surface that best fits the earth, described with either a and b values or often an a-value and flattening or sometimes inverse flattening (1/f). Examples: Clarke 1880, WGS-84 ellipsoid, etc.

2.   Projection

This is a set of mathematical functions used to convert the co-ordinates to “grid values”, i.e. co- ordinates meaningful for calculations. Once projected, x,y,z co-ordinates or e,n,z co-ordinates are obtained. Examples : Transverse Mercator, Lambert, etc.

The projection definition depends on the type of projection (for example cylindrical, conical etc.), but typical parameters are central meridian, latitude of origin, scale factor and false easting and northern values.

Note – Geographical co-ordinates (latitude and longitude), are not projected. It is a way to reference position on the earth without a projection. Co-ordinates are measured on a given ellipsoid in degrees South or North of the equator, and East or West of Greenwich. Geographical co-ordinates are often written as decimal degrees, or degrees minutes and seconds.

3.  Datum

Datum transformations were introduced to enable easy conversion between co-ordinates on a given co-ordinate system to and from the GPS co-ordinate system. All GPS receivers adopted the WGS-84 ellipsoid with no projection nor datum. Transformation parameters can be calculated between the GPS WGS-84-system and any other system

Examples :

  • Cape datum (South Africa)
  • Arc 1950 datum (used in some African countries) Tete datum (Mosambique)
2.   Transformations

A transformation is the mathematical process of converting co-ordinates / plans / data from one Co-ordinate System to another. Data is often converted from some older co-ordinate system to the GPS-friendly WGS-84 system. There are 2 main types of transformations :

  1. Transformations with pre-calculated parameters – Many software packages contain pre- programmed general Co-ordinate System parameters. These could be used to convert data between systems, but is very often not accurate enough for high-precision work. In South Africa, the older Cape Datum was established using a combination of stellar surveys (observations to the stars) and observations using manual optical survey instruments. Errors were propagated through the country as the network was extended through triangulation. The modern Hartbeeshoek datum was established using GPS technology. The pre-programmed Cape datum contains the average shift in x,y and z co- ordinates between the 2 systems and is therefore not accurate. Discrepancies of up to 50m could be found when converting Cape co-ordinates to WG co-ordinates using the standard datum transformation.

  2. Transformations by calculating best parameters – When we have common points on 2 co-ordinate systems a transformation could be calculated. The accuracy of the transformation depends on the precision of the co-ordinates on the 2 systems, the type of transformation used, the number of common points and the position of the common points. Ideally, points should be spaced equally around the area of interest (interpolating rather than extrapolating) Various transformations could be used :
  • In small areas the average plane difference in x, y and z could be used to shift a dataset from one system to another.
  • A 3-parameter Molodensky transformation could be calculated. This transformation is a dx, dy and dz transformation taking reference ellipsoids into account.
  • A 4-parameter affine transformation calculates dx, dy and scale factor in x and y directions
  • A 7-parameter transformation calculates dx, dy, dz and rotation in x,y,z and scale factor.
3.   Geo-referencing Explained

Geo-referencing is the process during which a digital raster image is spatially positioned. Raster data is commonly obtained by scanning maps, collecting aerial photographs, and obtaining raw satellite images. Scanned map datasets don’t usually contain information (either embedded in the tile or as a separate file) about where the area fits on the surface of the earth.

The location information delivered with raw aerial photographs and satellite imagery is often inadequate to perform analysis or display in proper alignment with other data. Thus, to use these types of raster data in conjunction with your spatial data, you often need to align it, or geo- reference it, to a map co-ordinate system.

When geo-referencing the raster dataset, you define how the data is situated using map co- ordinates. Geo-referencing is specified by “from” points linked to “to” points. This process includes assigning a co-ordinate system that associates the data with a specific location on the earth. Geo-referencing raster data allows it to be viewed, queried, and analyzed with other geographic data.

4.   CAD vs Database vs GIS

CAD (Computer Aided Design) is software packages used for drafting, design and displaying graphical information. CAD systems are most commonly used for engineering and planning purposes. A CAD drawing normally consists of a combination of various feature types, lines, polylines, polygons, text etc. Features may contain attributes such as color, line type, fill color and style, text font etc.

A Database is one or more structured sets of data, managed and stored as a unit, and generally associated with software to update and query the data. A Database could also be described as the digital representation of physical file cabinets containing files with records of a specific nature. Examples of database systems are Dbase, Access and SQL.

GIS is a system that presents data in a database spatially to aid in decision making. It is a visual representation of the numbers and datafields in a database. A GIS is typically used to represent maps as data layers that can be studied and used to perform analyses. Modern GIS systems can incorporate a huge variety of different data types, including various types of database datasets, CAD and Raster data sets.

5.   Elevations, heights and Geoids

Heighting carried out in survey operations normally refers to Mean Sea Level. The Geoid is an equipotential surface which approximates Mean Sea Level and also has its origin at the true centre of the earth. The Geoid surface is perpendicular to the force of gravity and is therefore also the reference datum referred to by spirit leveling. The Geoid cannot be mathematically defined like the ellipsoid, since it is gravity dependant. The Mean Sea Level determined as the Datum reference for a region is used as the reference for the geoid.

To convert the GPS derived heights (ellipsoidal) into Geoidal heights it is therefore necessary to know the separation between the ellipsoid and the geoid. Geoidal separation could be calculated using complex mathematics based on actual gravity surveys, or could be interpolated from pre- calculated published tables (for example Egm96, Osu91, Dma10x10 etc)

6.   South African Co-ordinate Systems

In South Africa we mainly use the following 2 systems :

  1. Lo-System : This is a co-ordinate system with
    • Ellipsoid = Clarke 1880,
    • Projection = Gauss Conform,
    • Datum = CAPE.
  2. Hartbeeshoek : In 2000 South Africa switched to this system with
    • Ellipsoid = WGS-84,
    • Projection = Gauss Conform
    • Datum = 0,0,0

These systems differ with roughly 30m in Y and 300m in X co-ordinates. Both these systems have grid X-values that increase from North to South (0 being on the equator), and grid Y-values that increase from East to West. Northern Hemisphere co-ordinate systems (for example UTM) have grid X values that increase from South to North, and grid Y values that increase from West to East.

Goldfields is a local grid system used in South Africa prior to the 1960`s. Goldfield X-grid values increase to the West, and Y-grid values increase to the North.

Most modern software packages were programmed to only work on Northern Hemisphere Co- ordinate Systems. An easy solution if you are working on a Southern Hemisphere system is to multiply the grid values with -1. One will notice that in Arcgis, Autocad, Microstation and many others, the co-ordinates are inverted. Often the CAD axis labels are also inverted, i.e. the x-axis describes the E-W direction and y-axis N-S. This could sometimes lead to some confusion.

Sketches below show a graphical summary of the correct signs :

Northern Hemisphere (for example UTM) :

Southern Hemisphere (for example LO)

And Goldfields :

7.   GPS Accuracies

It should be understood that GPS`s calculate elevations above the mathematical ellipsoid, and not Mean Sea Level as often needed. (see heading 6 : Elevations, heights and Geoids). Due to satellite geometry GPS elevations are approximately half as accurate as x and y coordinates.

The GPS market can be divided into three major categories :

  1. Handheld Devices
  2. Differential sub 1m devices
  3. Survey Grade Differential devices

Handheld GPS`s are relatively small, easy to use standalone devices that calculates positions accurate to approximately 10 metres (sigma 1, i.e. 68% of the positions will be more accurate than 10m). In practice these devices often gives a position more accurate than 3 metres. Examples are the various Garmin handheld devices and various different car navigation systems.

There are many factors that influence the accuracy of the GPS :

  1. Satellite Geometry and number of Satellites (measured in PDop)
  2. Time Synchronization between GPS device and satellites
  3. Multipathing (signals reflecting of other surfaces before hitting the GPS antenna)
  4. Atmospheric Influence on incoming GPS signals (signals bend when entering earths thick ionosphere and troposphere)

Some of the factors can be minimized when using a Differential GPS set. Sub 1m differential GPS`s receive correction signals from a geostationary satellite to improve overall position to within 1m. The correctional signal is hired on a time basis from service providers (Omnistar or Landstar).

Survey Grade GPS receivers is a set of two receivers. One receiver is based on a known point and transmits correction signals via radio transmitters. The signal is received at a roving receiver and corrected in Real Time to achieve accuracies of often better than 0,05m.

8.   Rules and Principles

From the above it should be clear that co-ordinates can only be referenced to a true position on earth if the parameters of the Co-ordinate System are known. The same y and x values for 2 co- ordinates on Wg27 and Wg29 would represent two positions that is approximately 200km`s from each other.

For this reason it is vital that all spatial datasets (cad drawings, raster maps, Co-ordinate lists etc.) must have the Reference Co-ordinate System attached. The reference could be shown as a header, or could be attached in a separate file (metadata). Abbreviations are often used and are quite acceptable. (For example : Wg29 refers to Hartbeeshoek Datum, WGS-84 ellipsoid with Transverse Mercator Projection with central meridian of 29 degrees East longitude. Likewise, Lo29 refers to Cape Datum, Clarke1880 ellipsoid with a Transverse Mercator Projection with central meridian of 29 degrees East longitude).

In South Africa the convention is to write Co-ordinates in the following sequence : Y-Co-ordinate, X-Co-ordinate, Z-Co-ordinate (grid system), or Latitude, Longitude, Z (geographical system)

The South African Co-ordinate Systems have x-values that increase from 0 at the equator towards the South. The x-value will therefore always be positive. However, as previously mentioned, some software packages invert the Co-ordinate sign to allow functionality with Southern Hemisphere Co-ordinate Systems. If negative x-values are encountered the y-Co- ordinate will also be inverted.

The Central Rand Gold exploration area ranges from approximately

  • Wg27 and Wg29 :         X = +2 896 000m to x= +2 905 000m
  • Wg27 :                            Y = -89 000m to -115 000m
  • Wg29 :                          Y = +110 000m to +85 000m

For quality control purposes, it is important that Co-ordinate lists should be accompanied with a brief report stating the method and equipment used to obtain co-ordinates as well as reference co-ordinates used.

Written by Wynand Mulder – Copyright

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