Outline: I. Spatial reference systems and projections. II. Geographic

Transcription

Geographic Information System (GIS)
Outline:
I. Spatial reference systems and projections.
II. Geographic Information System (GIS) softwares.
Datum
How to locate a position on Earth ?
- Cartesian coordinates XYZ → relatively inconvenient except in a few cases.
- Geographic reference system → longitude, latitude (+altitude).
Z
- XYZ depend on the origin and axis
directions.
- Lon,Lat depend on the origin, axis
directions + the shape of the ellipsoid
Y → a clear and precise definition is required.
X
To define a geographic reference system or datum:
Or
- Origin (position with respect to the Earth gravity center) and directions of the axes (one
is the pole axis and one crosses the central/origin meridian).
- Fundamental point on Earth surface; azimuth of the North direction; and central
meridian.
+ Ellipsoid shape defined by the semi-major axis and flattening
Datum
For a global reference system: Position of
the origin + definition of the ellipsoid that
best approximates the geoid at global
scale.
For a local reference system:
Position of the fundamental point +
azimuth + definition of the ellipsoid
that best approximates the geoid
near the fundamental point.
Tangent at the fundamental
point
Ellipsoid point
Geoid
Gravity centre
Exemples of Datum
Example of ellipsoid:
- WGS84: used by the GPS system
- IAG-GRS80: used in France and Europe. Very similar to WGS 84 (same semi-major axis
and flattening)
- NAD83: used in North America.
Example of datum:
- Nouvelle triangulation de la France (NTF) : official in France until Dec 2000 ; most IGN
maps are still in this old system based on Clarke 1880 IGN's ellipsoid. The fundamental point
is the Panthéon in Paris.
- Réseau géodésique français (RGF) 1993 : Official in France, based on IAG-GRS80
ellipsoid
- European Datum (ED) 50 : widely used in Europe based on Hayford 1909 ellipsoid. It is
obsolete.
- ETRS89: based on IAG-GRS80. Now official in Europe.
- World Geodetic System (WGS84) : global datum used for GPS, based on WGS84
ellipsoid. The precision is adequate for conventional GPS but is insufficient for geodesic
applications. ITRS datum is the accurate equivalent of WGS84 to use for geodesy.
RGF 1993, ETRS89 and WGS84 can be assumed equivalent for most conventional
applications.
Examples of Datum
Latitudes and longitudes are different in all these systems, differences up to hundreds of meters
between « old » data (e.g. NTF) and the new generation of data (WGS84 and equivalent).
Be carefull when using « old » datum. Detailled information for converting between data:
http://www.crs-geo.eu/
In addition, these systems move respectively to each other due to continent drift. For instance,
ETRS89 uses the same ellipsoid as WGS84 but it is attached to a point in UK while WGS84 is
not attached to any particular point on Earth (it is defined by Earth rotation angular speed). For
a precision better than 1m, differences between ETRS89 and WGS84 may be significant.
Remark: this course is insufficient for geodesic applications.
Conclusion:
Spatial data are/have to be
associated to a well-defined
datum.
Altitudes
Measuring the altitude is a complex subject.
In short, the minimum that you should know:
Attitude can be measured with respect to:
- geoid (equipotential near the mean sea level): Orthometric
Altitude and normal Altitude.
- ellipsoid (altitude given by GPS for instance): Ellipsoid
Altitude
Altitude of geoid with respect to ellipsoid is
up to 140m at global scale.
To work with altitude data, it is necessary to
know:
- the kind of reference surface (ellipsoid or
geoid).
- the characteristics of the particular geoid or
ellipsoid used as reference.
Simplified scheme
→ vertical datum
Schéma simplifié
Map projections
Projections allow to represent the sphere or ellipsoid surface onto a surface that can be directly
a plane or a surface that can be unambiguously unwrapped onto a plane (i.e. cylinder or cone).
Mathematical transformation: (lon,lat) → (x,y)
Northing
y
O
x
Easting
x and y are in meters and defined with respect to the origin of the map.
The interest of a particular projection for a given usage depends upon the mathematical
properties of the projection.
Map projections
Numerous types of projection.
They all causes distortions somewhere.
Criteria to consider when choosing a projection for a given application:
- scale of the map: In general, the coarser the scale, the more significant the
distortions are. However, fine-scale maps are usually used for applications
that require high precision...
- usage of the map: in statistics: preserve surface area, in navigation:
preserve angles (bearing, direction), …
- region of the Earth (e.g. polar or not)
- legal or historical reasons.
- Use the common projection to most of your data to avoid re-projection that
may degrade information (in the case of raster data, see further).
The projections can be classified with respect to the surface used for the
projection.
- cylindrical projections.
- conic projections.
- azimuthal projections (onto a plane).
- unique projections: all the other cases. Some of these projections are not
associated to any surface.
Additional attributes: normal, transverse, oblique
Remark: These classification and attributes are insufficient to fully define a projection (see
further).
Map projections
Important properties:
- equal-area projections (projection équivalente en Francais) locally preserve surface
areas.
- conformal projections (projection conforme en Francais) locally preserve angles and
shapes.
- other projections are called aphylactic.
No projection can be 100% equal-area and conformal.
Another property:
Equidistant: the distance is preserved along some lines. These lines are called “standard
lines”.
Examples of projection types
Examples of projection types:
Azimuthal Equidistant Projection
Gnomonic Projection
Orthographic Projection
Geostationary Projection
Near-Sided Perspective Projection
Mollweide Projection
Robinson Projection
Sinusoidal Projection
Equidistant Cylindrical Projection
Cassini Projection
Mercator Projection
Transverse Mercator Projection
Oblique Mercator Projection
Polyconic Projection
Miller Cylindrical Projection
Gall Stereographic Projection
Lambert Conformal Projection
Lambert Azimuthal Equal Area Projection
Stereographic Projection
Equidistant Conic Projection
Albers Equal Area Projection
Polar Stereographic Projection
Polar Lambert Azimuthal Projection
Polar Azimuthal Equidistant Projection
McBryde-Thomas Flat Polar Quartic
van der Grinten Projection
http://matplotlib.sourceforge.net/basemap/doc/html/
http://www.progonos.com/furuti/MapProj/CartIndex/cartIndex.html
Credits: Basemap site
Conformal: useful in navigation.
Often use for global maps but it does not fairly represent the world. The surface area on the
map of countries near the equator are smaller than at higher latitudes.
Lambert conformal conic. Abbreviation: lcc
Official projection in France (see further)
Tissot's Indicatrice
The most simple projection as: x=longitude, y=latitude
Meridians are standard lines
Equidistant: the shortest path from the centre point toward any point on the map is the straight
line.
Equal-area: useful in statistics because two countries/regions having the same surface area on
Earth are represented with the same surface area on the map. Statistics are simple to
calculated.
Conformal: projection used for the UTM system (see later).
Coordinate reference system
A projection is well-defined by:
- the type/family of projection.
- the parameters (origin meridian, true latitude, primary standard parallel, ...). The lists of
required parameters depends on the type of projection.
E.g:
- polar stereographic projection: Origin latitude, true latitude, origin meridian, ...
- Lambert Conical Conformal: Primary, secondary and origin latitudes, origin meridian, ...
Coordinate reference system (CRS) or spatial reference system (SRS):
- the projection and its parameters.
- the datum.
The CRS is a comprehensive set of data needed to project points or to produce maps.
In GIS softwares, the CRS of any spatial data to be imported must be known.
UTM system
Universal Transverse Mercator:
- a projection type adequate for small-scale areas (fine resolution): Transverse Mercator
- projection parameters depend on the location on Earth and are defined for ~1200 zones.
UTM system
- 20 bands in latitude (entre 84°N – 80°S) and
60 bands in longitude (→ 1200 zones).
- most zones are regular, some exceptions...
Coordinates (x,y) gives the position . “y” is in
meter from the equator. “x” from the central
meridian of the zone.
However, in order to avoid negative numbers,
a “false easting” of 500000m is added to x.
For the points in the Southern hemisphere a
“false northing” of 10000000 m (10000km)
is added.
UTM coordinates are uniquely defined by:
- Zone Number
- The hemisphere (N, S) or the letter of the
zone
- x,y coordinates in meter.
Lambert's projections in France
Since 2000:
In metropolitan France: Lambert 93 ( Lambert Conformal Conic) with the RTF93 datum (close
to WGS84 datum and GPS system).
http://lambert93.ign.fr/
Since 2006:
To improve the accuracy of the Lambert 93
system: 9 zones with specific parameters are
defined (CC42 to CC50).
In practice, the “old” Lambert I, II, III, IV and
Lambert étendue are still used.
Be careful, old Lambert projections use the
NTF datum which is significantly different from
the RTF93 datum and GPS coordinates.
Projections in practice
How does work CRS in GIS ?
Many formats exist to specify a projection, its parameters and the datum.
E.g. information needed to fully defined Lambert 93 projection.
Datum: RGF-93
Projection: Lambert conformal conic.
Units: Meter
First standard parallel: 49°N
Second standard parallel: 44°N
Origin latitude: 46.5°N
Central meridian: 3°E
False easting: 700000m
False northing: 6600000m
Open format:
Well Known Text (Open Geospatial Consortium).
Proj.4
+proj=lcc +lat_1=49 +lat_2=44 +lat_0=46.5 +lon_0=3
+x_0=700000 +y_0=6600000 +ellps=GRS80 +towgs84=0,0,0,0,0,0,0
+units=m +no_defs
GML based on XML
… not so easy to read
EPSG
Previous formats contains all the information required for a specific projection, but
the format are not convenient. The European Petroleum Survey Group manages
a database of widely used projections. Each projection is identified by a unique
number.
e.g. EPSG code of the Lambert 93 is: 2154
The EPSG database is, on Linux machine, in a file called epsg:
# HD1909
<3819> +proj=longlat +ellps=bessel +towgs84=595.48,121.69,515.35,4.115,-2.9383,0.853,-3.408
+no_defs <>
# TWD67
<3821> +proj=longlat +ellps=aust_SA +no_defs <>
# TWD97
<3824> +proj=longlat +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +no_defs <>
# IGRS
<3889> +proj=longlat +ellps=GRS80 +towgs84=0,0,0,0,0,0,0 +no_defs <>
# MGI 1901
<3906> +proj=longlat +ellps=bessel +no_defs <>
# Unknown datum based upon the Airy 1830 ellipsoid
<4001> +proj=longlat +ellps=airy +no_defs <>
# Unknown datum based upon the Airy Modified 1849 ellipsoid
<4002> +proj=longlat +ellps=mod_airy +no_defs <>
# Unknown datum based upon the Australian National Spheroid
<4003> +proj=longlat +ellps=aust_SA +no_defs <>
# Unknown datum based upon the Bessel 1841 ellipsoid
<4004> +proj=longlat +ellps=bessel +no_defs <>
# Unknown datum based upon the Bessel Modified ellipsoid
<4005> +proj=longlat +a=6377492.018 +b=6356173.508712696 +no_defs <>
# Unknown datum based upon the Bessel Namibia ellipsoid
<4006> +proj=longlat +ellps=bess_nam +no_defs <>
# Unknown datum based upon the Clarke 1858 ellipsoid
# Unknown datum based upon the Clarke 1866 ellipsoid
<4008> +proj=longlat +ellps=clrk66 +no_defs <>
# Unknown datum based upon the Clarke 1866 Michigan ellipsoid
# Unknown datum based upon the Clarke 1880 (Benoit) ellipsoid
Search codes on http://spatialreference.org/ and export to various formats like
proj4, WKT, ...
Outline:
I. Spatial Reference systems and projections.
II. Geographic Information System (GIS)
Geographic Information System (GIS)
Definition: software or information system to store, display, manage and analyze
geographic informations (or geospatial data).
This course is about Desktop GIS software.
Examples: ArcGis, MapInfo, QantumGis, ...
GIS are able to deal with geospatial data coded in different “data model”:
- Raster
- Vector
- Triangulated Irregular Network (TIN)
The data model determines the way the data are displayed, stored and analyzed.
Raster
Raster: images or continuous variables on a regular grid.
- Number of rows
- Number of columns
- Data type:
25
* Integer on 1 byte / byte: (0 – 255)
* Integer on 2 bytes / short: (0 – 65536)
* Integer on 4 bytes / int : 0 – 4 billion
* Floating point number on 4 bytes / float32:
7/8 significant numbers
* Floating point number on 8 bytes / float64:
16 significant numbers
- No data value.
Credits: http://linfiniti.com
File size of raster = nb rows x nb columns x size of the data type.
Raster
Remark 1:
Some raster files contain several bands (spectral or multi-temporal images).
Remark 2:
Be aware that two kind of “byte order” may be used depending on the computer they were
produced (Intel-based versus Motorola-based).
http://en.wikipedia.org/wiki/Endianness
Raster
Remark 3:
Example of header file in ENVI format which fully describes an image.
ENVI
description = {
File Imported into ENVI.}
samples = 231
lines = 201
bands = 1
header offset = 0
file type = ENVI Standard
data type = 4
interleave = bsq
sensor type = Unknown
byte order = 0
wavelength units = Unknown
}
Raster
Number of rows, columns, datatype, etc are sufficient to display an image on the screen
but are insufficient for GIS.
Georeference information is needed:
- Coordinate reference system (CRS).
- Pixel size in reality / Resolution.
- Geographic coordinates of at least one point of the image (usually upper left corner)
Using these informations, GIS are able to overlay images having different extent and/or
resolution. However, the images have to be in the same projection.
Raster
Example of file formats for raster:
GeoTIFF, Erdas Imagine, SDTS, ECW, MrSID, JPEG2000, DTED, NITF, ...
With open source softwares, the GeoTIFF open format is recommended:
http://www.gdal.org/formats_list.html
Vector
Why raster data model is not suitable to encode any kind of data ?
Raster data model is inadequate for storing simple geometrical shapes.
Example: Raster image of a map representing watersheds in Ile de France.
What happens when zooming ?
What is the surface area of these watersheds ?
What is the length of the rivers ?
Credits: http://www.iau-idf.fr
Vecteur
Vector data model is designed to store simple geometric shapes.
Example:
A watershed can be defined by a delimited area.
A river can be defined by a line/curve made of several straight segments.
In addition, storing information may be interesting (name of the river, stream flow,
navigability, ...)
Vector
Definitions:
A vector dataset is composed of features.
A feature is a geometrical shape (called “geometry”) and several attributes (also
called “fields”).
A geometry is a set of vertex. Vertex can be connected to each other. Each
vertex is defined by x,y cartesian coordinates (+ z in some cases) in a specified
CRS.
A vector dataset (called vector layer) can be of one of the following types:
- Point: one vertex
- Polyline: a set of connected vertexes. The two extremities are disconnected
- Polygon: a set of connected and closed vertexes. The two extremities are
connected to each other.
These three types cover most of the needs.
Choosing between one of these types depends on the application and scale.
(e.g. cities are points or polygons ? River are lines or polygons ?)
Example of vector data
Earthquakes in 2002 - 2003: POINTS
Attributes: Magnitude, depth of the epicenter.
Rivers: POLYLIGNE
Attributes: Name, Rank (size classification), ...
Note that features in this dataset are small part of the river. This is the choice of the user when
digitalizing. Another option is one feature per river.
Advantages: attributes can be different for each segment (useful for stream flow)
Disadvantages: connections between the features are not explicit. (other more sophisticate
data models exist to deal with this issue).
Fault lines: POLYLINE
Example of vector layer
Geological facies: POLYGON
Orange: Quaternary
Yellow: Volcanic-origin Quaternary
Green: other periods
Blue: seabed.
Remark: other data models store not only the features but also the spatial relationships between
these entities (connectivity, ...). This allows more advanced analysis (e.g. river network, road
network, ...).
Continents: POLYGON
Lakes:
POLYGON
Rivers:
POLYLINE
Zooming on vector layers does not produce blurred images as opposed to raster layers.
However, the intrinsic resolution is always limited and depends on the accuracy of the
digitalization.
E.g: Lemant lake in a global lake database
Vector and attributes
Each vector layer contains a table of attributes.
The table is composed of
- in column: a list of attributes (or fields) chosen by the user during the digitalization or
added after. Example: name, perimeter, surface area, stream flow, ...
- in row: each feature (point, line, …) contained in the layer.
- each cell of the table contains one value.
The data type of the values is defined per attributes:
String (chaine de caractères), integer, floating number, date, ...
Example: Lake attribute table.
Each row corresponds to one polygon of the map.
Tables can be imported in spreadsheets like OpenOffice Calc, Excel, ...
Second example: Earthquake attribute table.
Attributes can be used to control the symbology
Here, the size of the circles is proportional to the magnitude.
The color represents the depth of the Earthquake (blue is deep, green is shallow).
Attributes can be used to control the symbology
Arrows are drawn using 2 attributes: meridional and longitudinal displacement.
More precisely....
- Data associated with features are stored in relational data base (RDB) (Base de données
relationnelle en français).
- Tables are called relations.
- A software to manage RDB is called relational data base management systems (RDBMS).
Examples: MySQL, Postgresql, sqlite, Oracle.
RDB are used in a wide variety of applications beyond GIS (economy/management, web site,
science, ...). Most RDBMS have spatial extensions (or plugins) that allow to store geospatial
information along with other conventional data. Examples: PostGIS, spatialites, Oracle.
To search information in RDB or to manage RDB, a dedicated language exists: Structured
Query Language (SQL).
Operations on vector and raster layers.
GIS are not only tools for creating beautiful and complex maps, but also for
manipulating and analyzing geospatial data.
E.g.
- Arithmetic operations on the attributes.
- Geometrical operations on vector layers.
- Arithmetic and geometrical operations on raster layers.
- Operation between vector and raster layers.
Calculation on the attributes can
be done in a spreadsheet (Excel)
or directly in GIS.
Example:
Join tables (jointure en français):
When two tables (either 1 vector layer+one table, or 2 vector layers) contain one or many
common attributes, they can be joined. This operation is used for adding external data into a
vector layer or to merge data between two tables.
Example: Vector layer with countries + Raw table containing statistics given per country (here
deforestation from FAO). http://gadm.org/world et http://www.fao.org/forestry/fra/fra2005/en/
Attributes
(key) to
join both
tables.
Geometrical operations between vector layers (example shown with 2 layers having 1 polygon
each)
“Logical” operation
Intersection
(Union also exists)
A
B
Difference (A-B)
Symmetrical difference
(=union of A-B and B-A)
Buffer (tampon en français): the buffer is the
polygon(s) whose points are at a given distance
from the features in the vector layer.
Convex hull (Enveloppe convexe en français):
“Minimum” convex polygon around points in a layer.
Example: Where are located earthquakes having magnitude > 4 and considering a distance
of 100km around earthquakes.
We first select the earthquakes respecting a criterion on the attributes.
Create a buffer of ~100km (1° in fact because the data were not projected...don't do that!!).
Earthquakes in 2002-2003 only with buffer. For illustration purpose only.
Spatial join
Attributes are associated from one vector layer with the features in another layer, based on
the spatial juxtaposition of the features on each layer.
A
Example: Layer A contains continents
(polygon). Layer B contains lakes
(polygon) with their area.
→ calculate the total surface area of
lakes in each continent.
B
Spatial join creates a new attribute “SumArea” in the continent layer.
Important: work witj an equal-area projection (what I have not done here...)
- Arithmetic operations between layers.
Some GIS need similar layers (same resolution) other are able to resample the layer with the
coarser resolution.
- More complex but specialized operations exist :
Example: Slope calculation from Digital Elevation Model (Modèle Numérique de Terrain, MNT
en Francais).
Altitude map
Slope map
Operations raster → vecteur:
Example: Contour line calculation (useful for DEM, pressure map, ...)
Dome C
Law Dome
Operation vecteur → raster:
Example: proximity map.
With QGis, two steps are needed: 1) rasterize 2) proximity
Operation combining vector et raster.
Example: Point sampling tool in QGIS → voir TP
Geographic Information System in general
Desktop GIS are only one kind of GIS. Various kind of information system (software or
middleware) are able to deal with geospatial data. Many such systems are related to the
internet.
- Geospatial database: PostGIS, Oracle.
Store geospatial data (vector with attributes) as in GIS, but allows more complex relationships
(not just one table per layer) and allows efficient and multi-user access.
Access to these databases requires a “client” software such as a Desktop GIS.
Database Server:
Vector + other data
User 1
(Client)
ex: QGis
Network
(internet or intranet)
User 2
(Client)
Other software
Geographic Information System in general
- Geocatalog: to search geospatial data
http://geodata.grid.unep.ch/ http://www.eea.europa.eu/data-and-maps
- Specific tools on web sites: Google Map, OpenStreetMap, …
- Online geospatial data. WMS, WFS, …
- Open data movement (http://en.wikipedia.org/wiki/Open_data) ex: Open Data Paris
(http://opendata.paris.fr/)
WMS servers distribute images “ready
to visualize”. Colors, symbology can
not be modified, but the layers to draw
can be chosen… these images are
build on the server from raster ou
vector layers. Access is possible using
an internet navigator (Firefox) or a
Desktop GIS
Examples:
http://atlas.nrcan.gc.ca/site/english/dataservices
http://www.geolittoral.equipement.gouv.fr/
WFS servers distribute vector data. They can be used exactly as vector layers stored in local
files. Symbology, colors, etc can be chosen locally. The advantage is to show real-time
changes of the layers (ex: trajectory of animals, boats, ...).

Outline: I. Spatial reference systems and projections. II. Geographic

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