calcGCdist: Calculate Great-Circle Distance

Description Usage Arguments Details Value Note Author(s) References See Also Examples

View source: R/extraFuns.r

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

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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

See Also

addCompass, calcArea, calcCentroid, calcLength

Examples

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

PBSmapping documentation built on Jan. 15, 2021, 3:41 p.m.