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Meaning of the North arrow on (excavation) maps

Introduction

There are several North arrows that can be used in maps (see also Ghilani [2004], page 1-2):
In many instances the North arrow is not labelled, so one can't determine how to orient a map. This page tries to determine what recommendations are being used. And it proposes some guidelines (based on existing survey guidelines/recommendations).

This web page does not cover the measurement of the below directions, see for the ins and outs another page.

Astronomic North

The Astronomic (or Astronomical) North is defined by the direction of gravity (vertical) and the Earth's rotation axis (Brinker, [1995], page 416). The Earth's rotation axis points in present days close to Polaris, the so called North star. The direction of the Earth's rotation axis changes over time due to the Precession of the equator.

Geodetic North

The Geodetic (or Geographic) North is determined by the mean rotational axis of the earth which is known as the Conventional Terrestrial
Pole (CTP) (Ghilani [2004], page 1).
The difference between Geodetic North and Astronomic North is the Laplace correction, which is the angular deflection between the plumb line and a line perpendicular to the utilised mathematical Earth's model at the location (Brinker, [1995], page 463):
Laplace correction = η cos (φ) [deg]
η is deflection of the vertical in the prime vertical (east-west) component (depending on the mathematical Earth's model)
φ the latitude of the location

The Laplace correction is not large (upto 20 arcsec).

True North

This is a term that is being used for Astronomic or Geodetic North; so it can be seen as ambiguous. As the accuracies of equipment and measurement method increase, the term True North should be replaced with Astronomic or Geodetic North (Brinker, [1995], page 459). The difference between Astronomical and Geodetic North (can be up to ~20 arcsec) can be in the same order as the measurement error of a theodolite (~10 arcsec).
The small difference between Geodetic and Astronomic North can not really be depicted on a physical map (due to humidity) or on a (small) digital map (due to pixel resolution). So the usage of True North is a compromise, but keep in mind these two different meanings.

True North is Geodetic North for the Irish and UK OS maps (pers. comm. Ordnance Survey [2012]); Google Earth; and USGS (UTM) maps (even though True North is depicted with a star).

Grid North

The Grid North defines the North direction of the map grid being used. This depends on the projection of the Earth on a flat surfaces (like Mercator projection). The difference between Grid North and Geodetic North is called Convergence angle (Brinker, [1995], page 462). For instance an approximation of: the Convergence angle for the Irish and UK OS map projection (transverse Mercator) is (Thom, [1967], page 168):
Convergence angle = γ = Δλ sin (φ) [deg]
Δλ is longitude difference from the central longitude (for UK OS map; the central longitude is 2 [deg] west and for Irish OS map; the central longitude is 8 [deg] west)
φ the latitude of the location

Magnetic North

This is the north that is shown by a compass. The difference between Geodetic North and Magnetic North is called Magnetic declination.
There is different usages of the Magnetic declination:
The Magnetic North is depending on the year (due to the so called Magnetic variation). So beside showing the Magnetic North Arrow, it is essential to state the year the Magnetic North was measured.

North arrow on excavation maps

If one sees an excavation map there is normally one North arrow (possibly without any proper labelling). In that case once can't assume that the North arrow depicts Astronomic, Geodetic, True, Grid or Magnetic North. Check if somewhere in the text there is a statement on the North arrow, if not: don't assume and look for other excavation reports or redo the measurement.

What is being used:
 So the message is: Don't assume anything if North Arrow is not properly labelled/stated.

Checking North arrow with Google Earth

Google Earth (GE) uses a variant of the Mercator projection and in the middle of GEs window, Grid North is the same as Geodetic North.
By adding an Image overlay in GE one now can overlay an excavation map on the surface of GE. If GE has for the location a high resolution image, one can easily determine the angular difference (using the Ruler Tool) between Geodetic North and North arrow on the map.

Guidelines for the North arrow

Beside following existing archaeological survey guidelines (Georgia Council of professional archaeologist in USA ([2012], page 20); English Heritage ([2007], page 31); and Karachorov [2006]), additional guidelines can be made when documenting excavation sites that could be important for archaeoastronomy work (although is it really additional? As it is in general important info):

Deriving one direction from another direction

As one can see in the above sections, one can derive a direction in a certain reference north from a direction in another reference north. When doing this, one needs to be careful how the derivation is done: please see the plus/minus signs and positive/negative values as different things! Check and re-check this, as an error is easily made with regard to adding instead of subtracting (or other way around).

The below table will help with this derivation:

 Starting direction referenced to
Astronomic North
 Geodetic North
 Grid North
 Magnetic North
Resulting
direction
referenced to
 Astronomic North
 none
 -Laplace correction
 +Convergence angle-Laplace correction +Magnetic declination-Laplace correction
Geodetic North
 +Laplace correction
 none
 +Convergence angle
 +Magnetic declination
Grid North
 -Convergence angle+Laplace correction -Convergence angle
 none
 +Magnetic declination-Convergence angle
Magnetic North
 -Magnetic declination+Laplace correction
 -Magnetic declination -Magnetic declination+Convergence angle none

Remark: The Laplace correction, Convergence angle and Magnetic declination values can be positive or negative! In case the term west is used, the value is negative and in case east is used the value is positive.

References

Russell C. Brinker, and Roy Minnick. The Surveying Handbook: Chapman & Hall, 1995.
Georgia Council of Professional Archaeologists. "Georgia standards and guidelines for archaeological surveys.", accessed on Sept. 30, 2012.
Charles D. Ghilani. "Astronomical Observation Handbook." The Pennsylvania State University, 2004
English Heritage. Understanding the archaeology of landscapes: A guide to good recording practice, Guidelines / Standards: English Heritage, 2007.
Karacharov KG, and Aref VA. "Manual for archaeological surveys of heritage sites." 2006.
Alexander Thom. Megalithic Sites in Britain: Oxford University Press, 1967.

Acknowledgements

I would like to thank the following people for their help and constructive feedback: archaeocosmology e-group, Richard Bartosz, Alison Betts, HASTRO-L list, Paul Hirose, Kim Marville, Manoj Nair, Michael Nickiforov, Frank Prendergast and all other unmentioned people. Any remaining errors in methodology or results are my responsibility of course!!! If you want to provide constructive feedback, let me know.
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Major content related changes: Oct. 20, 2012