3 Describing locations, coordinate systems and projections

Linking data to a location

Georeferencing

What sorts of georeferences are used by people?

place names

addresses

What sorts of georeferences are used by computers?

coordinate systems

Requirements for georeferences

• uniqueness

• shared meaning (everyone should interpret it the same way)

• persistent over time

Potential exam question:

1. Give an example of a georeference which is not unique?

2. Give an example of a georeference which is not persistent over time?

1. Let’s meet at the train station (not unique, which train station?)

2. borders of Switzerland, a city

Properties of georeferences

• domain of uniqueness

• may be based on measurement or be relative

• positional uncertainty

Let’s analyze the georeferences in the Icelandic saga!

• What type of georeferences are there?

• uniqueness?

• shared meaning?

• persistent over time?

• domain?

• positional uncertainty?

Let’s analyze the georeferences in the Rebbelib!

• What type of georeferences are there?

• uniqueness?

• shared meaning?

• persistent over time?

• domain?

• positional uncertainty?

Let’s analyze the georeferences in the Yu Ji Tu!

• What type of georeferences are there?

• uniqueness?

• shared meaning?

• persistent over time?

• domain?

• positional uncertainty?

Let’s analyze the georeferences in Predicting and responding to disasters!

• What type of georeferences are there?

• uniqueness of coordinates?

• domain?

• positional uncertainty?

Let’s analyze the georeferences in Choosing routes!

• What type of georeferences are there?

• uniqueness of coordinates?

• domain?

• positional uncertainty?

3 approaches to georeferencing

place names

objects and their relative position to each other

coordinates for positions of discrete objects or continuous fields (reflectance values)

Problems of place names

one place can have more than one name (Flurnamen)

several places can habe the same name

names can change over time

names can have different positional uncertainties (Switzerland vs Rütli, Seelisberg, Switzerland)

What do these problems of place names mean for computers?

These problems can be solved by people but can be difficult for computers, especially rescue services

Problems of addresses and postcodes

different systems in different countries, less formalized

address of a house isn’t always the exact location of the person in MFH or Altbauten

informal settlements are often not captured

Referencing system based on distance, allow to identify locations on a network, historical example: milestones, today: transport networks

Linear reference systems

Potential exam question:

Place names, addresses an distance along e.g. railway tracks can all be used to locate information (as georeferences). Using examples, discuss potential advantages and disadvantages of such approaches to georeferencing

Place names:

(+) Names appear across languages and cultures

(-) not unique

(-) can refer to multiple objects

Adresses:

(+) systematic

(-) different systems in different countries

(-) don’t always specify an exact location

LRS:

(+) easy to map

(-) one-dimensional

(-) only locations along the network

Potential exam question:

Is Bahnhofstrasse 30 a unique georeference? Explain briefly why this is (not) the case?

not unique

lots of streets across Switzerland and other german speaking countries have one street with the same name

What georeference is used for making maps and calculations?

Metric georeferencing

Metric georeferencing:

Geometric property where dist(AC) < dist(AB) + dist(BC)

Triangle inequality

Detail and repeatability of a measurement in metric georeferencing

Spatial precision

How close a measurement is to reality

Accuracy

Precise and accurate

Precise but inaccurate

Imprecise but accurate

Angle measuring distance north or south of equator

with a fixed point relative to earth (north star)

Latitude

Angle measured using time relative to Greenwich

with very accurate clocks

Longitude

How is latitude defined?

Earth be approximated as an ellipsoid at sea level, the flattening of this axis is 1/300 compared to an axis parallel to the equator

How is longitude defined?

We start from the eat axis of rotation. Earths centre of mass lies on this axis and a plane perpendicular to the axis. We divide earth into 360° of longitude (each parallel to axis of rotation). Each degree can be subdivided into 60min and 60s. Prime meridian (0°) runs through Greenwich Observatory

Parameter set describing properties of an ellipsoid

Datum

Global standard ellipsoid for global positioning

WGS84

Properties of WGS84

• Semimajor axis: centre to equator (6378km)

• Flattening: 1 in 298

• 0° longitude 100m east of Greenwich Observatory

Standard code system for datums and projections

originally developed by European Petroleum Survey Group

EPSG codes

Official geographic coordinate system for Switzerland

CH1903+

Why do we need projections?

On a map the world needs to be represented as 2D. To go from ellipsoid 3D to 2D we need to project from spherical coordinates (latitude, longitude) to cartesian coordinates (x, y) -> for this disortion we need a starting point which is a datum of the geographic coordinate system we are starting from (WGS1984 or CH1903+) and a set of equations to transform latitude/longitude into x,y

Projections that maintain the shapes of small features

Conformal projections

Projections that maintain correct surface sizes

Equal area projections

Projection where we wrap a cylinder round the earth, the distortion is the smallest where the cylinder touches the earth

Cylindrical

Projection where we touch the earth with a flat sheet of paper

Planar

Projection where we wrap the earth in a cone

Conic

Simplistic projection mapping long/lat directly to x/y, no equal area

Plate carré

Conformal cylindrical projection with a tangent at the equator

x = λ and y = ln(tan(Φ/2 + π/4)

Mercator

European projection standard, area preserving

Lambert azimuthal equal area

Projection type wrapping a cylinder around poles, military, global remote sensing data, divided into 60 zones, positional uncertainty of 0.04%

Universal Transverse Mercator

What are most countries’ local projections based on?

GPS coordinates

Can you transform between datums and projections?

Yes

Problems when transforming between datums and projections?

GIS reprojects the data on the fly, but all the data should be transformed for calculations

Distortion becomes a problem for maps with large areas

Seal journey projected with WGS84

• Plotting in 2D using WGS -> lot of disortion

• Distance is in degrees -> not meaningful GEO113 – GIS HS2025 Summary gigi 15

• -1° is 111km at equator, 0km at pole

Seal journey projected with Lambert conformal conic

• shapes good

• distances are accurate along parallels and disorted elsewhere

• better for calculating areas than distances

Seal journey projected with equal area projection

• Relative areas good

• Shapes, distances disorted

Potential exam question:

You are working with biologists who are monitoring the position of migrating storks. The biologist wants to measure the size of their territories. The positional data have been collected using geographic coordinates in WGS84. The biologist wants to plot positions and measure areas using a Plate Carrée projection (x=longitude y=latitude).

Explain why this is a dreadful idea

SInce the biologist wants to measure areas globally, the plate carrée will distort the areas. The positions of the storks will also be off, because the plate carrée maps latitude and longitude directly to cartesian coordinates.