calcGCdist: Calculate Great-Circle Distance

In PBSmapping: Mapping Fisheries Data and Spatial Analysis Tools

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	numeric – Longitude coordinate (degrees) of the start point.
lat1	numeric – Latitude coordinate(degrees) of the start point.
lon2	numeric – Longitude coordinate(degrees) of the end point.
lat2	numeric – Latitude coordinate(degrees) of the end point.
R	numeric – 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((\phi_2 - \phi_1)/2) + \cos(\phi_1) \cos(\phi_2) \sin^2((\lambda_2 - \lambda_1)/2)

c = 2~\mathrm{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 = \mathrm{acos}(\sin(\phi_1)\sin(\phi_2) + \cos(\phi_1)\cos(\phi_2)\cos(\lambda_2 - \lambda_1)) R

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

\theta = \mathrm{atan2}(\sin(\lambda_2-\lambda_1)\cos(\phi_2), \cos(\phi_1)\sin(\phi_2) - \sin(\phi_1)\cos(\phi_2)\cos(\lambda_2-\lambda_1))

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
locus opus: Offsite, Vancouver BC
Last modified Rd: 2023-11-03

References

Movable Type Scripts – Calculate distance, bearing and more between Latitude/Longitude points

See Also

In package PBSmapping:
addCompass, calcArea, calcCentroid, calcLength

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 documentation built on Nov. 4, 2023, 9:08 a.m.