This explanation assists with using our map co-ordinate converters. Also read our FAQs.
In principle there is a mathematical basis for the Alberta Township System (ATS) variant of the Dominion Land Survey (DLS) system as implemented in Canada. In fact, the implementation in Western Canada reflects a number of slightly different approaches, as well as a large number of errors.
Below is a brief description of how to lay out the DLS grid for Alberta.
Lay off six-mile ticks from the 49th parallel of latitude to the 60th parallel. This gives you 127 township lines.
The 49th parallel of latitude is the first base line of the ATS system. On it lay off six-mile ticks westwards starting at the 110th line of longitude (4th DLS meridian). Start over at the 114th and 118th lines of longitude (5th & 6th DLS meridians). Extend these ticks 12 miles due north (following a line of constant longitude) to the first correction line. This gets you your first set of range lines.
Starting at the 49th parallel (first base line) go 24 miles directly north. This gets you to the second base line. At the latitude corresponding to this distance from the 49th parallel lay off six-mile ticks westwards from 110th merdian as you did at the 1st base line. The circumference of the earth has decreased as you went northwards, so there will be fewer full ticks than there were one base line south. Extend 12 miles north and 12 miles south from these ticks. This gets you your next set of range lines. You will note there is an offset between the range lines extending north from the lower base line and those extending south from the current ones. This offset occurs along what is called a correction line.
Repeat the base line process every 24 miles northwards (to the 32nd).
All this will result in a mesh of cells nominally six miles on a side. Each such cell is called a Township (not to be confused with the township lines we laid off earlier). Subdivide the Township into 36 sections by laying off ticks of one sixth of each Township side and connecting them by north-south and east west lines. The sections are numbered sinusoidally starting from the southeast corner of the Township.
Sections can be similarly subdivided into quarters by placing and connecting ticks at the half waypoint on each section side. Use the same process to subdivide sections into legal subdivisions (LSD) except place the tick at the one-quarter waypoints. LSDs are numbered sinusoidally starting at the southeast corner of the section.
Note that this method of determining subdivision of the Section is approximate in that it ignores complexities introduced by the placement of road allowances and differences in road allowance widths within Alberta.
The publication "Understanding Western Canada's Dominion Land Survey System" published by the Division of Extension and Community Relations, University of Saskatchewan, provides a readable, fairly detailed description of how things are laid out.
Alberta Geological Survey's approach is pragmatic. We use a form of the ATS grid, available from AltaLIS, to construct a spatially indexed ISAM-like set of files containing the section corner co-ordinates. These are used to perform quick forward and inverse lookups. Bilinear interpolations are applied to handle quarters, LSDs and residuals.
What is the formula/algorithm to make these conversions? Can we download it to use offline?
The conversion is not based on a formula. The basis of the conversion is
an ISAM file of section corner co-ordinates. We have implemented spatial
indices to these to allow rapid lookups. The co-ordinate resolution below
one section is handled through bi-linear interpolation. However, the
section corner co-ordinates are not ours. These must be purchased from AltaLIS.
What mode should my GPS be in (NAD83 or WGS84) in the field so it is compatible with your GIS conversion tools?
The control we started with was NAD83. It is our understanding that the difference in the two ellipsoids results in a miniscule difference on the ground.
Is there a public domain conversion formula to convert lat/long XY co-ordinates into metres (the local UTM system for W5 area in Alberta)?
The conversion between ATS and geographic co-ordinates is based
on spatial indices to a very large database of section corners. It is not
based on a formula. The conversion between geographic and planimetric co-ordinates
is done using public domain algorithms. These are available as
C and Fortran source codes from the United States Geological Survey.
Search for general cartographic transformation package.
Is there a way to enter the Legal SubDivision (LSD) starting with the least
significant digit? For instance, all of the documentation given to me from my customers lists
the locations as LSD, section, township, range then meridan; e.g., 7-18-65-08W6.
Yes, use our unique well identifier order
converter.
Are you aware of any links that will take lat/long co-ordinates and convert them into legal land descriptions?
If you are referring to ATS/DLS, our converters will do this. If you are referring to Lot, Block, etc, then we are not aware of such a program.
I'm using ESRI ArcGIS and was hoping to implement the conversion from Township System to Geographic Degrees algorithm within a VBA application. Is this algorithm available for download or is there any way I can expose the code?
The algorithm will do you no good as it just looks up values in a large data set. However, GeoAnalytic may have DLS functions of use for your purposes.
Where does each UTM zone begin and end?
UTM zones are 6 degrees of longitude wide. The table below lists some of the zones. Simply continue the process to figure out the other zones.
| Zone | |
| 7 | 144 - 138 |
| 8 | 138 - 132 |
| 9 | 132 - 126 |
| 10 | 126 - 120 |
| 11 | 120 - 114 |
| 12 | 114 - 108 |
| 13 | 108 - 102 |
| 14 | 102 - 96 |
Do you have converters that convert to the NAD27 datum?
There is one available from Natural Resources Canada.
Last modified: November 19, 2009
