planet earth is a potato...different results at different places of the earth: newton (1643-1727)...

Planet Earth is a Potato

Uta Griwodz, con terra GmbH

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Shape of the Earth Different map projections Measuring distances Area calculation Buffering Résumé

Agenda

Shape of the Earth

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The earth in the bible: a round disc

Source: http://glauben-und-wissen.de/M2.htm#b

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Already the Greeks (Eratosthenes about 200 B.C.) measured the circumference of the Earth

But it’s not a disc

Source: http://www.grenzstein.de/era/eratosthenes.html

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A spheroid

© 2007 ESRI Geoinformatik GmbH

In the 16th century the arc measurements restarted > 1525 Francois Fernel > 1635 Richard Norwood > … Based on the results of these arc measurements which deliver different results at different places of the earth: Newton (1643-1727) realized that the earth is a ball which is flattening at the poles (a spheroid = a rotation ellipsoid)

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Today, we know, that due to the gravity that the earth is not even a spheroid, but is even more uneven. The Geoid Have a look the picture of the German Geo Research Centre, where this is exaggerated presentation (in real it’s about +-100m). It’s a “potato”

A geoid

Source: http://www.gfz-potsdam.de/portal/gfz/Public+Relations/M40-Bildarchiv/Bildergalerie_Satelliten/04+Bildergalerie+GRACE/00_Bildergalerie_Kartoffel

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But for the mapping of positions we still use spheroids as model The best representation is the globe

A model of the Earth for mapping

Source: http://de.wikipedia.org/w/index.php?title=Datei:Globus.jpg&filetimestamp=20050904040550


Map projections


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You need a projection to get the Earth to a plane

But how get the Earth on a plane paper?

e.g. Cylindrical projections e.g. Conical projections

Pictures: © 2007 ESRI Geoinformatik GmbH


You will never get everything „right“. You have to choose between > area accurate > angle accurate (conform) > distance accurate (which you can receive only along defined lines,

not for a whole map)

There is no projections with accurate area, angle and distances On a plane map you will always have distortion

Effect of map projections


Think of an orange!

You will never get it to a plane

Picture: © 2007 ESRI Geoinformatik GmbH


Gauß-Krüger Projection and coordinate system

• C.F. Gauß 1777-1855 • J. H. L. Krüger 1857-1923 • Transverse Mercator projection

(cylindrical projections) • Conform projection (direction

accurate) • 100 km wide stripes parallel to the

meridian • Distortion for traverse and

cadastre survey insignificant • < 12,4 cm per km at the border of

the stripes


Universal Transversal Mercator Projection and System (UTM)

• Based on the mathematics algorithms of Gauß

• 200 km wide stripes parallel to the meridian

• < 40 cm per km in the centre of the stripes

• < conform (nearly no horizontal direction deviation)

• Used with the ED50 after the 2. world war in Western Europe from the NATO

• Used with the ETRS89 in Europe


• J.-H. Lambert 1728-1777 • Conic, conform projection • Used in France • For maps with scales 1:500.000

and inferior • 150 – 200 km wide zones parallel

to the central latitude (origin)


These are projections for a local area With only small distortions in an explicit area They were use for printed maps Usually for scale 1:500.000 and inferior Not used for global maps If you use the „old“ local coordinate system to draw the whole world, you get the following results:

Local coordinate systems / map projections


Source for the following screenshots is this world map in WGS84 geographic coordinates


Local German system DHDN Gauß-Krüger 3 stripe


Local European System ETRS89 UTM Zone 32 N


Local France System: Lambert Zone I

Global coordinate systems / map projections


Google has introduced the „Web Mercator Projection“ in the 21th century With Google Maps (Google Earth uses the GCS WGS84) It should be faster (better performance) It was said, it‘s > WGS84 and uses a > Mercator projection

Web Mercator


Google was not the first to think about the „optimal“ map projection for the world ArcGIS knows a lot of map projections for the whole world

Mapping of the world


Mercator Projection (World)

Thought for navigation only Direction accurate Area incorrect (e.g. Greenland)


Plate Carrée (also called equidistant cylindrical and simple cylindrical ) projection

Used to present data in GCS (geographic coordinates) in ArcGIS E.g. WGS84 Used in Google earth Latitude and longitude are directly mapped into y and x Meridians converge toward the poles You can’t measure distances or areas accurately


Web Mercator

Datum WGS84, but take a sphere as model, not a spheroid Mercator projection (but not a real one) Not really conform (= not direction accurate) Not distance accurate Not area accurate Accurate at the equator, less accurate towards the poles


The distortion of projections are often shown with indicatrixs (Tissot’s indicatrix)

Distortion


Web Mercator

ETRS89 Zone 32N Plate Carrée (GCS WGS84)


Map Projections in the ArcGIS Help

Mercator


WGS84 (geographic coordinates) Web Mercator

Famous in the „Web World“ is the use of

Measuring


The Measure tool

Measuring in ArcGIS


Measurement type

Description

Planar Length and areas are calculated based on 2D Cartesian mathematics. The results are „projected“ results, this means they contain all distortions from the map projections.

Geodesic Shortest line between 2 points on the earth's surface on a spheroid (ellipsoid). On a sphere that line is also called “great circle line”.

Loxodrome

Length of the line of constant bearing (or azimuth) between 2 points. Also called rumb line.

Great Elliptic

The line on a spheroid (ellipsoid) defined by the intersection at the surface by a plane that passes through the center of the spheroid and the start and endpoints of a segment

Measurement types of the measure tool

Picture Source: http://mycoordinates.org/improved-algorithms-for-sailing-calculations/


Source http://kartoweb.itc.nl

Great Line and Loxodrome (rumb line)


Measure results ArcGIS Desktop Oslo - Drammen


Map Projection

Planar Geodesic Loxodrome Great Elliptic

ETRS89 UTM Zone 32 N

35134,18 m

35145,22 m

35145,31 m

35145,22 m

Web Mercator 69782,92 m

35145,22 m

35145,31 m

35145,22 m

WGS 84 - 35145,22 m

35145,31 m

35145,22 m

Measure results ArcGIS Desktop Oslo - Drammen


Local coordinate systems are usually designed to be able to measure „planar“ (this is the „projected distances“) in the small area they are thought for (remember: they were used in printed maps) If you want to measure big distances you usually expect the shortest distance between two points: that means the „great circle“. It‘s the measure type „geodesic“ in ArcGIS With Web Mercator you should use the measure type „geodesic“ in ArcGIS The shape length and shape area are calculated „planar“

Measuring in ArcGIS


Measuring in ArcGIS Online


Map Projection

Planar Geodesic Loxodrome Great Elliptic

ETRS89 UTM Zone 32 N

35134,18 m

35145,22 m

35145,31 m

35145,22 m

Web Mercator 69782,92 m

35145,22 m

35145,31 m

35145,22 m

WGS 84 - 35145,22 m 35145,31 m

35145,22 m

ArcGIS Online 35145,1 m

Measuring in ArcGIS Online

• No snapping • Default unit: Meter with 1 decimal after the comma • The Measuring type seems to be „Geodesic“

Area calculation

A planimeter


Measure Tool Only Measure Type: “Planar” No Area Calculation in GCS The results depend on the Coordinate System of the Data Frame

Area calculation in ArcGIS


Area Calculation in ArcGIS, an example


Map projection Result ETRS89 LAEA 1.264,028 km² WGS 84 Not possible (GCS) Web Mercator 4.935.729,365 km² NGO 1948 Zone III (Norway) 1.263,886 km²

Example triangle Oslo – Drammen - Fredrikstad

• LAEA = Lambert Azimuthal Equal Area • You should use an Equal Area Projection appropriate for your area • Or you “stay” in your local coordinate system and it’s defined area • The coordinate system of the data frame is relevant


Area calculation in ArcGIS Online


Map projection Result ETRS89 LAEA 1.264,028 km² WGS 84 Not possible (GCS) Web Mercator 4.935.729,365 km² NGO 1948 Zone III 1.263,886 km² ArcGis Online 1.264,0 km ²

Example triangle Oslo – Drammen - Fredrikstad

• No Snapping • ArcGIS Online seems to use an Equal Area Projection for the

area calculation automatically.

Buffering


2 Buffer tools in ArcGIS

Buffering

Buffer tool in ArcToolbox Buffer Wizard in ArcMap


Till ArcGIS 10.0 you have to distinguish between point and line/area features For points „geodesic“ buffers are created New in ArcGIS 10.1: The Buffer tool now creates true geodesic buffers for line and polygon input data

Buffer tool in ArcToolbox


Buffers look different, but only cause of the projection

Buffer tool in ArcToolbox for point features

Plate Carrée (GCS WGS84)

NGO 1948 Zone III (Transverse Mercator)


Buffer tool in ArcToolbox for line /area features The results are different depending from the projection You can set the projection in the Environment (Output coordinate system)

Buffer tool in ArcToolbox


Buffer tool in ArcToolbox for line /area features (ArcGIS 10.0)

NGO 1948 Zone III (Transverse Mercator)


Web Mercator ETRS89 LAEA

Projection of the Buffer:

Projection for the Display for all: ETRS89 LAEA


For lines/areas the buffer are not “geodesic” until ArcGIS 10.0 You should use appropriate Equal Area Projections until ArcGIS 10.0

Buffer tool in ArcToolbox for line /area features (ArcGIS 10.0)


The behaviour of the Buffer Wizard is dependent of the Settings \Utilities\AdvancedArcMapSettings.exe

Buffer Wizard in ArcMap


Found e.g.: C:\Program Files (x86)\ArcGIS\Desktop10.0\Utilities

AdvancedArcMapSettings.exe


Choose the coordinate system usage for the Buffer Wizard


The result of the default „Feature set optimized coordinate system“ is nearly the same as with the Buffer Tool and an equal area projection

Buffer Wizard in ArcMap

Résumé


Printed maps have a scale and a distinct area. You have a “feeling” for the precision: e.g. you can’t see and measure the cm in a map with the scale 1:500.000 “New” with GIS and Web maps: > Often you can zoom in without limits (and often measure) > Do you know the source and precision of the data you see? > Do you know the map projection and the distortion of this projection? > Do you know the measure type of the measure tool? You can use global projections (as Web Mercator) for visualization, but you must be careful when measuring, geoprocessing,... with these projections Mapping is not easy, our Earth is a potato

Résumé


Thank you!

Hamburg

Hannover Münster

Bonn

Wiesbaden

Leipzig

Zürich

Burgdorf

Nyon

Kranzberg

Uta Griwodz [email protected] con terra – Gesellschaft für Angewandte Informationstechnologie Martin-Luther-King-Weg 24 48155 Muenster Germany Telephone +49 251 747 45 0 www.conterra.de


European Commission Joint Research Centre "Map Projections for Europe". http://www.ec-gis.org


ETRS89 / LAEA Europe EPSG- Code 3035 Single CRS for all Europe. Used for statistical mapping at all scales and other purposes where true area representation is required Lambert Azimuthal Equal Area Projection

ETRS89 LAEA


ETRS89 / LCC Europe EPSG- Code 3034 Single CRS for all Europe. Used for conformal mapping at scales of 1:500,000 and smaller Lambert Conic Conformal (2SP)

ETRS89 LCC

data.aad.gov.au


ETRS89 / TM 26-39 EPSG- Code 3038 - 3051 Zoned CRS covering all Europe Used for conformal mapping at scales larger than 1:500,000 Transverse Mercator

ETRS89 TMz (UTM)

data.aad.gov.au


Peters Projection, Peters World Map


Mercator Web Mercator

Plate Carrée (GCS WGS84) Fuller


Web Mercator

ETRS89 Zone 32N


ETRS89 LAEA


Cylindric Equal Area

planet earth is a potato...different results at different places of the earth: newton (1643-1727)...

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