PBSmapping: calcGCdist – R documentation

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calcGCdist

Calculate Great-Circle Distance

Description

Calculate the great-circle distance between geographic (LL) coordinates. Also calculate the initial bearing of the great-circle arc (at its starting point).

Usage

calcGCdist(lon1, lat1, lon2, lat2, R=6371.2)

Arguments

`lon1`	Longitude coordinate (degrees) of the start point.
`lat1`	Latitude coordinate(degrees) of the start point.
`lon2`	Longitude coordinate(degrees) of the end point.
`lat2`	Latitude coordinate(degrees) of the end point.
`R`	Mean radius (km) of the Earth.

Details

The great-circle distance is calculated between two points along a spherical surface using the shortest distance and disregarding topography.

Method 1: Haversine Formula

a = sin^2((phi2-phi1)/2) + cos(phi1) cos(phi2) sin^2((lambda2-lambda1)/2)

c = 2 * atan2(sqrt(a), sqrt(1-a))

d = R * c

where
phi = latitude (in radians),
lambda = longitude (in radians),
R = radius (km) of the Earth,
a = square of half the chord length between the points,
c = angular distance in radians,
d = great-circle distance (km) between two points.

Method 2: Spherical Law of Cosines

d = acos(sin(phi1) sin(phi2) + cos(phi1) cos(phi2) cos(lambda2-lambda1)) * R

The initial bearing (aka forward azimuth) for the start point can be calculated using:

theta = atan2( sin(lambda2-lambda1) cos(phi2), cos(phi1) sin(phi2) - sin(phi1) cos(phi2) cos(lambda2-lambda1) )

Value

A list obect containing:
a – Haversine a = square of half the chord length between the points,
c – Haversine c = angular distance in radians,
d – Haversine d = great-circle distance (km) between two points,
d2 – Law of Cosines d = great-circle distance (km) between two points,
theta – Initial bearing theta (degrees) for the start point.

Note

If one uses the north geomagnetic pole as an end point, theta crudely approximates the magnetic declination.

Author(s)

Rowan Haigh, Program Head – Offshore Rockfish
Pacific Biological Station (PBS), Fisheries & Oceans Canada (DFO), Nanaimo BC
opus locus: Institute of Ocean Sciences (IOS), Sidney BC
Last modified Rd: 2017-06-22

References

http://www.movable-type.co.uk/scripts/latlong.html

Examples

local(envir=.PBSmapEnv,expr={
  #-- Distance between southern BC waters and north geomagnetic pole
  print(calcGCdist(-126.5,48.6,-72.7,80.4))
})

PBSmapping

Mapping Fisheries Data and Spatial Analysis Tools

v2.73.0

GPL (>= 2)

Authors

Jon T. Schnute [aut], Nicholas Boers [aut], Rowan Haigh [aut, cre], Alex Couture-Beil [ctb], Denis Chabot [ctb], Chris Grandin [ctb], Angus Johnson [ctb], Paul Wessel [ctb], Franklin Antonio [ctb], Nicholas J. Lewin-Koh [ctb], Roger Bivand [ctb]

Initial release

2021-01-12