Latitude and Longitude GEO426/526 Principles of GIS

Earth Properties Starting point of any map is the actual earth Natural starting place to measure North/South –Equator –Latitude is angular distance from center of earth to point north or south of equator –Parallels connect points of equal latitude No natural place to measure East/West –Prime Meridian –Longitude is angular distance from axis of rotation to point east or west of Greenwich, England –Meridians connect points of equal longitude

Earth Reference Grid

Graticule Campbell, Map Interpretation…, 2006

Degrees, minutes, and seconds Each degree ° is divided into 60 minutes ' Each minute is divided into 60 seconds " There are 3600 seconds in one degree Mostly commonly in GIS, decimal degrees are used instead of degrees, minutes, and seconds –38° 25 ' 25 " N latitude = / /3600 = –1° 1 ' 1 " S latitude = / /3600 = –N and E are positive numbers in a GIS –S and W are negative numbers is a GIS How to convert from decimal degrees to ° ' " ?

Measuring Latitude and Longitude on the sphere Campbell, Map Interpretation…, 2006

Degrees, minutes, seconds and distance Typically measure distance in miles/feet not degrees, minutes, seconds Latitude distances remain relatively constant –Polar circumference of earth (24,863 miles) ÷ 360° ≈ 69 miles per degree –Miles per minute? –Feet per second? Longitude distances decrease from 69 miles at Equator to 0 miles at the poles –Cosine of latitude x 69 miles = miles per degree of longitude –Miles per minute? –Feet per second?

Globe Properties Globe is best model of earth, but infrequently used in GIS (2- dimensional) Latitude/longitude describe 3D earth and are ALWAYS distorted when displayed in 2D. Can only see half at any time Parallels are equally spaced and always parallel Meridians are farthest apart at the Equator and converge at the poles –Meridians are ½ the distance apart at 60°N as at the Equator Parallels and meridians cross at right angles The shortest distance between two points is an arc of a great circle. –Only parallel = the Equator –All meridians –Great circles appear as straight lines when viewed orthogonally

Latitude and Longitude “unprojected” or GCS = the Plate Carree projection

Globe scale and measurements Scale is the ratio of globe (or map) distance to ground distance Three ways to represent scale: –Word/verbal statement –Graphic –Representative fraction Divide earth diameter (7,927 miles) by globe diameter = globe scale Use string, ruler, calculator to measure distances –Stretch string –Compare to ruler –Multiply by scale Shortest distance is rarely a cardinal direction Use spherical trigonometry to measure distances (or areas); distance calculation:

Spherical Distance example What is the distance between Huntington, WV and London, UK? –Huntington, WV 38.41°N, 82.43°W –London, UK 51.53° N, 0.08°W

Radians and degrees One radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle. One radian = 57.3°. One circle = 2π radians. Microsoft Excel works in radians by default. A calculator will work with degrees.

Solution Formula stepDegrees (calculator)/Radians (Excel) (sin a sin b).486 (cos a cos b cos |Δλ|).065 Sum of the products.551 Arccosine of the sum degrees Times 69 miles/degree miles