Where am I? Lecture 3 CONS 340

Learning Objectives Explain map scale Define geodesy Compare geographic and projected coordinate systems Define spheroids and datums Datum transformations

 Linear (also called graphic)   Verbal  20cm = 4.8km  Representative fraction 1:24,000 Conversion Example 20cm = 4.8km (original verbal scale) 20cm = 480,000cm (convert all units to a common metric) 1cm = 24,000cm (make the left side equal to one by dividing) 1 / 24,000 or 1:24,000 (remove the unit designation) Map Scale

Large vs. small scale maps Because it is a ratio, scale is unitless and large and small scale varies according to project 1:1 is the largest scale 1:24,000 is large scale for Conservation 1:500,000 is a small scale for Conservation Scale is inversely proportional to area given the same size map (display)

You will want to pay attention to map scale, because there are always questions on the exams dealing with scale. For example: Which of these is the larger scale? 1:24,000 or 1:100,000 Map Scale and You

What is Geodesy? Geodesy is the study of: The size, shape and motion of the earth The measurement of the position and motion of points on the earth's surface, and The study of the earth's gravity field and its temporal variations Types of Geodesy terrestrial or classical geodesy space geodesy theoretical geodesy

Basic Geodesy Facts Geographic/true directions determined by the orientation of the graticule on the earths' surface

Basic Geodesy Facts Magnetic directions must take into account the compass variation (magnetic declination)

Basic Geodesy Facts Great circle – arc formed by the intersection of the earth with a plane passing through any two surface points and the center of the earth

Basic Geodesy Facts Rhumb line, loxodrome or constant azimuth – line which makes a fixed angle with all meridians; spirals to pole Conic projection Mercator projection

The Earth is Not Round First the earth was flat 500 BC Pythagoras declared it was a sphere In the late 1600’s Sir Issac Newton hypothesized that the true shape of the earth was really closer to an ellipse More precisely an Oblate Ellipsoid (squashed at the poles and fat around the equator) And he was right!

Geoid, Ellipsoid & Sphere Geoid - estimates the earth's surface using mean sea level of the ocean with all continents are removed It is an equipotential surface - potential gravity is the same at every point on its surface Ellipsoid - It is a mathematical approximation of the Geoid Authalic Sphere - a sphere that has the same surface area as a particular oblate ellipsoid of revolution representing the figure of the Earth

Shape of the Earth Earth as sphere simplifies math small- scale maps (less than 1: 5,000,000) Earth as spheroid maintains accuracy for larger- scale maps (greater than 1: 1,000,000)

Spheroid or Ellipsoid? What is a Spheroid anyway? An ellipsoid that approximates the shape of a sphere Although the earth is an ellipsoid, its major and minor axes do not vary greatly. In fact, its shape is so close to a sphere that it is often called a spheroid rather than an ellipsoid. ESRI calls it a spheroid but the two can be used interchangeably For most spheroids, the difference between its semi-major axis and its semi-minor axis is less than 0.34 percent.

How About a Few Ellipsoids

Why Do We Need More Than One Spheroid (Ellipsoid)? The earth's surface is not perfectly symmetrical the semi-major and semi-minor axes that fit one geographical region do not necessarily fit another one.

After James R. Smith, page 98 What is the best Ellipsoid for you?

Shape of the Earth

From James R. Smith, page 34 Relation of Geoid to Ellipsoid

Vertical Deflection Important to surveyors Deflection of the Vertical = difference between the vertical and the ellipsoidal normal Described by the component tilts in the northerly and easterly directions.

Measuring Height Traditionally measured as height above sea level (Geoid) but is changing due to GPS The distance between the geoid and the spheroid is referred to as the geoid- spheroid separation or geoidal undulation Can convert but it is mathematically complex

Coordinate Systems

Cartesian Coordinate System  Used for locating positions on a flat map  Coordinates tell you how far away from the origin of the axes you are  Referenced as (X,Y) pairs  In cartography and surveying, the X axis coordinates are known as Eastings, and the Y axis coordinates as Northings.  False easting and northings are typically added to coordinate values to keep coordinates in the upper right hand quadrant of the ‘graph’ – positive values

3D Cartesian Coordinates Cartesian Coordinates can define a point in space, that is, in three dimensions. To do this, the Z axis must be introduced. This axis will represent a height above above or below the surface defined by the x and y axes.

Local 3D Cartesian Coordinates This diagram shows the earth with two local coordinate systems defined on either side of the earth. The Z axis points directly up into the sky. Instead of (X,Y) it is (X,Y,Z)

Geographic Coordinate System The Equator and Prime Meridian are the reference points Latitude/ longitude measure angles Latitude (parallels) 0 º - 90 º Longitude (meridians) 0 º º Defines locations on 3- D surface Units are degrees (or grads) Not a map projection!

Prime Meridians Origin of Longitude lines Usually Greenwich, England Others include Paris, Bogota, Ferro CityMeridian Athens, Greece23° 42' "E Bern, Switzerland7° 26' 22".5E Bogota, Colombia74° 04' 51".3W Brussels, Belgium4° 22' 04".71E Ferro (El Hierro)17° 40' 00"W Jakarta, Indonesia106° 48' 27".79E Lisbon, Portugal9° 07' 54".862W Madrid, Spain3° 41' 16".58W Paris, France2° 20' 14".025E Rome, Italy12° 27' 08".4E Stockholm, Sweden18° 03' 29".8E

Latitude/ Longitude Not uniform units of measure Meridians converge near Poles 1° longitude at Equator = 111 km at 60° lat. = 55.8 km at 90° lat. = 0 km

Decimal Degrees (DD) Decimal degrees are similar to degrees/minutes/seconds (DMS) except that minutes and seconds are expressed as decimal values. Decimal degrees make digital storage of coordinates easier and computations faster.

Conversion from DMS to DD: Example coordinate is 37° 36' 30" (DMS) Divide each value by the number of minutes or seconds in a degree: 36 minutes =.60 degrees (36/60) 30 seconds = degrees (30/3600) Add up the degrees to get the answer: 37° +.60° ° = DD

Datums

Datums (simplified) Reference frame for locating points on Earth’s surface Defines origin & orientation of latitude/ longitude lines Defined by spheroid and spheroid’s position relative to Earth’s center

Creating a Datum Pick a spheroid Pick a point on the Earth’s surface All other control points are located relative to the origin point The datum’s center may not coincide with the Earth’s center

Datums, cont. 2 types of datums Earth- centered (WGS84, NAD83) Local (NAD27, ED50)

Why so many datums? Many estimates of Earth’s size and shape Improved accuracy Designed for local regions

North American Datums NAD27 Clarke 1866 spheroid Meades Ranch, KS 1880’s NAD83 GRS80 spheroid Earth- centered datum GPS- compatible

GPS Uses WGS84 datum Other datums are transformed and not as accurate Know what transformation method is being used

Relationship between 2 datums

Transformation method accuracies NADCON HARN/ HPGN CNT (NTv1) Seven parameter Three parameter 15 cm 5 cm 10 cm 1- 2 m 4- 5 m

International datums Defined for countries, regions, or the world World: WGS84, WGS72 Regional: ED50 (European Datum 1950) Arc 1950 (Africa) Countries: GDA 1994 (Australia) Tokyo