Wednesday, September 12, 2012

How to Determine Magnetic Declination Information for a Topographic Map


This post is a companion to my How to Create and Print Custom Canadian Topographic Maps with Quantum GIS post.

The grid printed on a Canadian Topographic map is a UTM grid.  UTM Grid North (GN) is not the same as Magnetic North (MN), so to conveniently and accurately use the map with a compass; the grid declination (angle between MN and GN) must be documented on the map.  This value is constantly changing so the year it was determined and the estimated annual change should also be recorded on the map.  Annual declination change predictions are not accurate over more than a few years so if the declination information for a map was calculated using a magnetic model more than about 5 years old, it should be recalculated with a declination calculator that is using an up to date magnetic model, not just adjusted by the old annual change amount.  Declination varies by location, but for a large scale map (like 1:50,000) the convention is to document the declination for the centre of the map sheet as the change over the sheet is too small to be significant for compass work.

The UTM map grid doesn’t point to True North (TN) except in the centre of a UTM zone and can point +/- several degrees off of TN at the edge of a zone.  Declination calculators provide the declination from TN so the grid convergence angle (angle between GN and TN) for the location the declination was calculated for should also be determined to accurately determine the grid declination for that location.  The grid convergence angle should also be documented on the map in case a TN reference is required.

One way to determine the declination information is to look at a printed topo map or download a print ready topo map file and determine the information from it.  The disadvantages of this are that the map must be available, is should be reasonably current, and the information from it must be manually transcribed.  The declination on older maps, even corrected for annual change, will not be as accurate as it could be so really should be re-calculated.  The UTM grid convergence angle does not change over time so this value will always be current.  This information is provided in Degrees and decimal Minutes (DM.M) on Canadian topo maps.

A more accurate way to determine the declination information is to use one of the readily available free on-line declination calculators such as the US NOAA Estimated Value of Magnetic Declination calculator.  Enter the desired date and the Latitude and Longitude values from QGIS Coordinate Capture, removing the minus (-) from the Longitude value.  For Canada, Latitude will always be N (North) and Longitude will always be W (West).  The NOAA calculator displays the Declination and Annual Change.  The declination provided is the angle between MN and TN and should be corrected by subtracting the UTM grid convergence angle for the location.

Formulas for manual UTM grid convergence angle calculations are available on-line but are complex and not feasible for most people. Fortunately, the UTM grid convergence angle can readily be determined by using one of several free on-line coordinate conversion calculators that provide it, such as the US NGS Geodetic Tool Kit UTM Coordinate calculators. The NGS Latitude/Longitude to UTM calculator requires Latitude/Longitude in DMS format but QGIS directly provides D.D format, so it is easier to use the NGS UTM to Latitude/Longitude calculator rather than converting to DMS.  Enter the UTM zone and the UTM coordinates from QGIS (Easting, Northing); adding a decimal point at the end of the Northing and Easting values if they don’t already include one since this calculator requires a decimal point be present. For Canada, select Northern Hemisphere, NAD83 (in most cases) and WEST. The grid convergence angle is provided in DMS.S which will likely need to be converted to decimal degrees (D.D); an on-line Latitude/Longitude coordinate conversion calculator can be used to do this.

There are also several free GUI or command line computer applications that will calculate convergence and declination.  A good option for Windows or Linux users are the MagneticField and GeoConvert command line utilities supplied with GeographicLib. MagneticField requires that the GeographicLib wmm2010 magnetic field model also be installed.  If a number of maps are being produced, these utilities can be provided with a file containing multiple coordinates and process many in one execution, potentially saving quite a bit of work compared to manually processing each individually using GUI utilities.

I am not a mapping expert so please comment on this post to correct any errors or suggest better ways to do things.

Given a date and Lat/Long, MagneticField can calculate the magnetic declination angle and the annual change for that date and location.  Example:

> magneticfield -r -t 2012-06-01 --input-string "44.80023 -62.69268"   <--- Given Date, Lat and Long, calculate the Magnetic Declination angle and Annual Change
-18.25 67.51 19900.4 18899.6 -6231.4 48078.0 52033.8   <--- The first number is the magnetic declination angle in decimal degrees
0.14 -0.10 47.7 60.4 30.8 -118.6 -91.4   <--- The first number is the magnetic declination angle annual change in decimal degrees

Given UTM or Lat/Long coordinates, GeoConvert can calculate the UTM convergence angle for that location.  Example:

>geoconvert -c --input-string "44.80023 -62.69268"   <--- Given Lat and Long, calculate the UTM Grid Convergence angle
0.21655 0.9996073   <--- The first number is the grid convergence angle in decimal degrees

The Grid Declination angle that should be recorded on the map is the Magnetic Declination angle less the UTM Grid Convergence angle.  Example:

-18.25° - 0.22° = -18.47° (in 2012, plus 0.14° annually)   <--- This can also be stated as 18.47°W (2012) decreasing 0.14° annually or 18.47°W (2012), annual change 0.14°E, either of which are probably less confusing

Latitude and Longitude may be expressed in Degrees Minutes Seconds (DMS) or decimal Degrees (D.D) or Degrees and decimal Minutes (DM.M) and also N/S/E/W or +/- may be used for direction so some geographic coordinate conversion may be required while working with these values.  A number of online coordinate conversion calculators are available; the GeoConvert utility can also perform many of these conversions.

Click here for some links to useful mapping information and calculators.

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