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Abstracted from: Environmental Mapping Systems - Locationally Linked Databases
Bryan Hall. University of Western Sydney (1994).
Including The Australian Geodetic Datum and The Accuracy of Map Overlays
The accuracy required for survey data is that there be no plotable error in the survey data (Bannister and Raymond; 1984). A line can be hand drawn on a sheet of paper to within 0.25 millimetres and consequently if a survey is to be undertaken at 1 in 2000 scale all measurements must be sufficiently accurate to ensure that the relative positions of any point with respect to any other point in the survey can be stated to an accuracy within 0.25 millimetres at survey scale, at 1:2000 this represents 50 centimetres.
The zero dimension of any conventional paper map is defined as 0.25 millimetres, however, it is not feasible to scrutinise a map at this level of detail and extract reliable information.
| Map Scale | 1:1,000 | 1:4,000 | 1:10,000 | 1:25,000 | 1:50,000 | 1:100,000 |
| Minimum mapping unit. (metres) | 0.25 | 1 | 2.5 | 6.25 | 12.5 | 25 |
In 1966, all the geodetic surveys in Australia and New Guinea were adjusted and placed on a new Australian Geodetic Datum (AGD). The new grid was named The Australian Map Grid and is frequently denoted and referred to as the AMG. At the time, the Australian map grid covered Australia and it's territories, with the exception of the Australian Antarctic Territory and sub-antarctic islands. The AMG is based on the metric UTM system and coordinates on the AMG are derived from the projection of the Transverse Mercator lines of latitude and longitude onto the Australian Geodetic Datum. In 1966 the coordinates were known to be correct to less than 1 mm anywhere in a grid zone (National Mapping Council of Australia; 1972).
Grid Zones, AMG Eastings And Northings.
In the AMG each zone is 6 degrees wide and contains 1/2 degree overlaps at each intersection. These zones are numbered from 47, with central meridian 99 degrees east to zone 58 with central meridian 165 degrees east. Each zone has a true origin, defined by the intersection of its central meridian with the equator and a false origin from which AMG eastings and northings are quoted. The false origin is defined to be 500,000 metres west of the true origin and 10,000,000 metres south of the true origin (National Mapping Council of Australia; 1972).
A pair of grid coordinates on any given datum and grid may be used to uniquely define a point on the earths' surface. It is necessary to specify the Grid zone, the easting, and the northing of the location. The Australian Geodetic Datum Special Publication number 10 sites the AMG coordinates for "the Lion" survey station as being:
| Station | Zone | Eastings | Northings |
|---|---|---|---|
| LION | 56 | 497 345.431 | 6 852 369.368 |
The eastings and northings are stated in metres. This location is in New South Wales, approximately 19 kilometres north west of Kyogle. From the coordinates of "The Lion" it is apparent that it is approximately 3150 kilometres south of the equator and 6950 kilometres north of the false origin.
Each zone of the AMG is divided into 100 kilometre squares. The AMG holds the convenience of rectangular coordinates by restricting the size of grid squares.
The Australian National Standards of Map Accuracy are reproduced below.
National Mapping Council of Australia. Standards of Map Accuracy.
First Edition February 1953. Second Edition December 1975.
1. Horizontal Accuracy.
The horizontal accuracy of standard published maps shall be consistent within the criterion that not more than 10% of points tested shall be in error by more than 0.5 millimetres.
This limit of accuracy shall apply in all cases to positions of well defined points only. "Well defined" points are those that are easily visible or recoverable on the ground. In general what is "well defined" will also be determined by what is plotable on the scale of the map within 0.25 millimetres.
2. Vertical Accuracy.
Vertical accuracy, as applied to the contours of standard published maps shall be consistent with the criterion that not more than 10% of elevations tested shall be in error by more than one-half the contour interval. In checking elevations taken from the map, the apparent vertical error may be decreased by assuming a horizontal displacement with the permissible horizontal error for a map of that scale.
The following quote is recorded in the minutes of the First Meeting of the working party to deal with standard topographic mapping specifications for all scales. 5-7/9/1982 (CMA Bathurst, 1982):
"Lt Col Harrison pointed out to the delegates the importance of the map accuracy statement as a quality control device in mapping and as an aid to the map user. He stressed that its inclusion on maps should be considered a professional obligation."
The errors in maps produced in accordance with the above standard are, in general, normally distributed. It should also be noted that the error in the horizontal position of contours on the flat two dimensional map is not independent of the "lie of the land". For a fixed contour interval the horizontal error associated with contour location depends on the rate of change of land elevation in any particular direction. Consequently, it follows that contour lines are subject to greater horizontal locational errors in flat and undulating country than in steep mountainous terrain.
Macdougal (1975) explained that in maps where characteristic regions are represented at least two types of accuracy are important, the precision (the upper bound on accuracy) with which the boundary lines are located and the extent to which the soils on the ground represent the regions coded.
The lower limit to the accuracy of a map overlay operation consists of the sum of the allowable positioning errors and the product of the purities of the constituent factor maps, plus errors which are introduced in the assembly of the final overlay. The sum can be expressed as:
Amin = f(SH(i),PPi,e); where:
Amin is the probability that a specified combination actually occurs at the indicated location on the overlay map, H is the allowable positioning error, P is the purity on the ith map, e is the error introduced in the assembly of the overlay.
The possible magnitude of each of these terms in a typical application can be quite large. For example, in an overlay of six maps, each with an allowable horizontal error of 0.5 mm (equivalent to Australian Topographic National Map Accuracy Standards) and a purity of 0.8 (a good soils map), the possible horizontal error in the location of boundaries is 3 mm, and the purity of the overlay is 0.806, or 0.21. On the basis of purity alone, one could argue that such an overlay map is not significantly different from a random map. The soil mapping criteria of the US Soil Conservation Service explicitly states that regions on detailed large scale maps may include up to 15% of a substantially different soil type, and over 15% may be soils with different management requirements (Macdougal; 1975). However Macdougal (1975) does claim that it is unlikely that the errors in the constituent maps are so independent and systematic that map overlays are this inaccurate, particularly in the location of boundaries. In optimal circumstances it may be reasonable to assume that the purity of the overlay is that of the least accurate map in the combination and the inaccuracy in boundary location is the average boundary error (H(bar)). In this case the upper limit to the overlay accuracy is
Amax = f( H(bar),Pmin ,e)
If the errors in the source maps (for example vegetation and soils maps) do not occur independently, in this case possibly because the vegetation determines the characteristics of the soils and the soil in turn directs the growth of vegetation, then the categories are not independent. Information in the vegetation map makes it possible to infer and recover information about soil properties. Consequently, the amount of new information gained by overlaying a soils map is significantly less than may have at first been expected. Additionally, the fact that maps contain information that is not independent of other maps immediately imposes constraints on the types of questions that one can expect to get meaningful answers to. Without knowing how the information contained in each map is linked to the information in other maps it may be quite simple for an operator to ask a wrong question1. Finally, because not all biological sets are well defined, maps in which regions are coded, such as soils maps, often do not have precise boundaries between regions.
Macdougal (1975) concludes by saying:
"It is clear from this discussion that some overlay maps may indeed differ little from random maps, and that most overlay maps contain more error than their compilers probably realise. ... Most important, the compilers of overlay maps should attempt to estimate their accuracy, and present this in the legend or the accompanying text."
To interrogate a soil series map with logical (Boolean) operators it is essential to invoke the erroneous assumption that the soil series is a homogeneous unit of productivity exhibiting consistent properties with respect to other soil series. It has been demonstrated that this assumption may lead to significant errors in estimates of potential productivity and according to Gersmehl (1980) this has profound implications for prime land delimitation, tax assessment, zoning administration, and other policies that presently rely on published soil productivity ratings.
In order to test the question: can soil series serve as a functional unit for comparisons of productivity; Gersmehl (1980) selected pairs of counties for which soil surveys were completed within a few years of each other (so chosen to minimise the effect of historical changes or soil survey methods). For an arbitrarily selected pair of common soils, tables of estimated yields in the County soil surveys were used to prepare a table of average yields for the major crops in the region. Comparisons were made only after controlling for slope, erosion, class, surface texture, and level of management.
A summary of Gersmehl's (1980) conclusions follows:
"The obvious conclusion is that an attempt to use the relative productivity of two soil series in one place as a predictor of yields elsewhere is likely to yield considerable error. Any regional map of soil productivity that uses a series as a unit should therefore be viewed with suspicion, if not rejected outright.
....
All ... sources of environmental variation may contribute to differences in the estimation of relative productivity of two soils in different places. Attempts to determine the precise reason for a given discrepancy are undoubtably significant but are beside the point of this paper, which is simply to demonstrate that maps of soil productivity based upon relative rankings of soil series in one place are inevitably questionable in other places.
...
To summarise, any regional map of soil productivity that uses the series as a unit is on methodological quicksand. Moreover any policy of tax assessment, zoning, or land-use planning that depends on such general indices of productivity may inflict serious inequity on property holders. Finally, any regional assessment of land-use potential that is based on such an inequitable map may lead to significant misallocation of public resources."
1 It is possible to ask a wrong question if a false assumption is implicit in the statement of the question.
References:
A Review Of The Environmental Resource Mapping System and A Proof That It Is Impossible To Write A General Algorithm For Analysing Interactions Between Organisms Distributed At Locations Described By A Locationally Linked Database and Physical Properties Recorded Within The Database. University of Western Sydney 1994.Bryan Hall
http://au.riversinfo.org/library/1994/masters_thesis/
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