GEO1002

metadata

data describing other data (when, in what coordinate system, etc.)

main properties of geographic phenomena

• can be named and/or described (what?)

• can be georeferenced (where?)

• have a timestamp or interval (when)

types of geographic phenomena

fields, objects and boundaries

Fields

continuous ←→ discrete

all points in a certain spatial domain have a value

objects

location, shape, size, orientation

have a specific geometry

boundaries

crisp or fuzzy

data values

• nominal

• ordinal

• interval

• ratio

nominal data values

descriptive, providing a name or an identifier

ordinal data values

values can be ordered

interval data values

quantitative values that allow for some simple arithmetic operations like algebraic sum

example: T, pH

ratio data values

continuous numeric, can perform all arithmetic operations, including multiplication and division

example: distance, area, weight

spatial referencing comprises

definitions, physical/geometric concepts, tools

to describe the geometry (and motion) of objects near the earth’s surface

geodesy

discipline that deals with the Earth’s geometric shape, it’s orientation in space, and it’s gravitational field

spatial referencing

• geoid: vertical datum

• ellipsoid: horizontal datum

both approximate the real surface of the Earth

the Geoid

• height reference taken by mareographs (tide gauges), avaraged over long period

• many different local height references exist, based on different mareographs

• virtual datum -levelling lines→ levelling network with benchmarks

the Ellipsoid

• mathematical surface used as reference for horizontal coordinates

• defined by:

  • semi-minor (b) and semi-major (a) axes

  • flattening (f)

  • eccentricity

• both local and global ellipsoids

• triangulation network with monumented points for convenience

approximate Earth radius (sphere)

6365 km

approximate difference between Earth’s semi-minor and semi-major axes

22 km

GNSS satellites distance to Earth’s surface

20 000 km

ITRF

International Terrestrial Reference Frame

(with S: System)

catalogue of precise coordinates of certain points (stations) at a certain time

triangulation network connecting all GNSS (satellite) stations as a 3D polyhedron

WGS84 ellipsoid

• used by GPS/GNSS

• aligned with ITRS: differ by a few centimeters

• coordinates (lat lon and h) can be derived

• !!! h has no physical meaning, we still need the Geoid and it’s orthometric height H

orthometric height, ellipsoidal height, Geoid height

H = orthometric height (geoid → orthometric surface)

h = ellipsoidal height (ellipsoid → orthometric surface)

N = Geoid height (ellipsoid → geoid)

H = h - N

map projection

mathematically described operation (transformation) of how to present the Earth’s curved surface on a flat map

• point(s) of contact: no distortion

• map distortions grow as you move away from the point of contact

Tissot’s indicatrices

equivalent circles that get distorted in different ways depending on their position on the projected surface

map projection used in the Netherlands

EPSG:28992 & EPSG:5709 (NAP height)

shapefiles

• file format for vector data + attributes

• each shapefile contains exclusively one type of geometry

• (consists actually of different files)

capabilities of a GIS

1. data capture and preparation

2. data management (storage and maintenance)

3. data manipulation and analysis

4. data presentation

depending on the specific application, a GIS can be seen as

• a storage system for (spatial) data

• a toolbox

• a technology

• an information source

• a field of science

GNSS

Global Navigation Sattelite System

Secondary data acquisition

• manual digitizing

• automatic digitizing

• semi-automatic digitizing

• input of available digital data

manual digitizing

• coordinate entry via keyboard

• digitizing tablet with cursor

• mouse cursor on computer monitor (heads up)

• (digital) photogrammetry

automatic digitizing

scanner

semi-automatic digitizing

line-following software

spatial data acquisition process

scanning → vectorizing → post-processing (taking away the noise)

web services for geodata

• WMS: web map service

  • merge into a single raster map

• WFS: web feature service

  • vector based, for more comples applications

types of quality checks

• positional accuracy

• attribute accuracy

• temporal accuracy

• lineage (“history of the dataset“)

• completeness

• logical consistency

raster representation advantages

• simple data structure

• simple implementation of overlays

• efficient for image processing

raster representation disadvantages

• less compact

• difficulties in representing topology

• cell boundaries independent of feature boundaries

vector representation advantages

• efficient representation of topology

• adapts well to scale changes

• allows representing networks

• allows asy association with attribute data

vector representation disadvantages

• complex data structure

• overlay more difficult to implement

• inefficient for image processing

• more update intensive

aliasing

variation in the density of pixels → jaggedness and varying line intensity

TIN

Triangulated Irregular Network

• 2.5D models

• no vertical triangles possible

Delaunay triangulation

• for each triangle, no points are allowed inside its circumcircle

• reduces number of thin/skinny triangles

• (dual to Voronoi diagram)

• unique if there are no 4 or more points on the same circle.

RMSE

Root-mean-square error

• frequently used measure of the differences between values predicted by a model and the values observed

• square root of the avarage of squared errors

• sensitive to outliers!
  
  RMSE = sqrt(SUM[ (z_predicted - z_observed)² ] / N)

DEM

digital elevation model

• usually a grid

• most generic term you will find

DTM

digital terrain model

• sometimes class of DEMs

• explicitely only terrain models

• grid or TIN

DSM

digital surface model

• includes also all man-made objects

• grid or TIN

n-DSM

normalised DSM

• difference between DSM and DTM

• focussing on the non-terrain features

slope map

• = gradient

• maximum rate of change in elevation

• magnitude of steepest tilt

• very much linked to the scale of the dataaset

• calculated very differently in TINs and rasters

aspect map

• direction (azimuth) of the steepest tilt is the aspect

• varies from 1 to 360

shaded relief map

• showing how the 3D surface would be illuminated from a point light source

• generally light top left

• generally used to enhance the visualisation of (raster based) DEMs

alphanumeric data

integer, real, Boolean, data, varchar, blob, etc.

maintenance of GIS data

• keeping the data up to date

• making the data accessible and usable to (ideally) as many different users as possible

shapefiles

file format for vector data + attributes

• each shapefile contains exclusively one type of geometry

• consists of different files

• topology is not supported

DBMS

DataBase Management System

• software used to administer the database and to interact with end users, applications and the database itslf

• offers a query language

• takes care of data backup and recovery

• can take care of concurrent usage

query

function that allows to perform CRUD operations on a database

C create

R retrieve

U update

D delete

relational model

• collection of tuples (/records/rows) collected into relations (tables)

• table = records having the same number and type of named fields (/attributes/columns)

attribute

defined by it’s domain (defines which type of data is allowed and it’s interval of validity)

can contain a data value or the NULL value

superkey

a set of attributes within a table whose values can be used to uniquely identify a tuple

candidate key

= minimal superkey / unique key

minimal set of attributes necessary to identify a tuple

primary key

the choice of candidate key
→ remaining candidate key(s) are alternate keys

foreign key

a set of attributes (ideally one) in table B that references a candidate key in table A

referencing table

uses foreign keys to reference referenced tables that contain the primary keys

SQL: *

wildcard = “all columns“

planar partition

no overlaps

structural incompatibility

different ways to store the “same“ data

semantic incompatibility

• the same object is named in different ways in different tables

• different objects are named in the same way in different tables

euclidian space

• linear

• flat

• continuous

• uniform

• coordinate-based

• allows measuring distances and angles

set-based space

• the constituent objects to be modelled = elements (/members)

• collection of elements = sets

• s ∈ S: s is member of S

examples of sets

sets: relations and operations

topology

study of relational properties of form

→ such properties are invariant under topological transformations

→ “rubber-sheet” transformations

topological and non-topological properties

Topological:

• a point is at an end-point of an arc

• a point is on the boundary of an area

• a point is in the interior/exterior of an area

• an arc is simple

• an area is open/closed/simple

• an area is connected

Non-topological:

• distance between two points

• bearing of one point from another point

• length of an arc

• perimeter of an area

G = (V, E)

V: vertices, non empty set (or nodes)

E: edges, unordered pairs of linked vertices

directed <> undirected graphs

degree

number of edges connected to a node

path

sequence of connected edges

cycle

path leading to the origin after traversing at least one edge

connected (graph)

there is a path between any pair of nodes

isomorphic

with the same connectivity relationships

tree

acyclic (only one path per pair of nodes) connected graph

rooted tree

has leafs

planar graph

a graph that can be embedded in the plane such that no edges intersect

Euler’s formula in the plane

if: f - e + v = 1 → the graph is planar

dual G*

• obtained by associating a node in G* with each face in G

• two nodes in G* are connected by an edge if and only if their corrisponding faces in G are adjacent

• a voronoi diagram is the dual G* of the corresponding TIN

network representations

• adjacency matrix

• adjacency list

adjacency matrix

adjacency list

good balance between storage efficiency and computational efficiency

network algorithms

• depth-first

• breadth-first

• Dijkstra’s

• A* (A-star)

Euler 3D

if: f - e + v = 2 → the graph is planar (or 1 if you do not consider outer region face)

0-simplex

1 vertex (“point“)

1-simplex

closed finite line segment

two vertices

2-simplex

set consisting of all the points on the boundary and in the interior of a triangle whose vertices are not collinear

3 vertices

3-simplex

tetrahedron

4 vertices

n-simplex

n-dimensional polytope, convex hull of its n+1 vertices

face of n-simplex

a 0…n-simplex whose vertices form a proper subset of the n+1 vertices of S

faces of n-simplex

n+1 vertices

2^(n+1)-1 faces in total

simplical complex (SC)

a finite set of points, line segments, triangles (and their n-dimensional counterparts) having the following properties:

• every face of a simplex which belongs to the SC is also belonging to the SC

• the non-empty intersection of any two simplexes belonging to the SC is a face belonging itself both to S1 and S2

CW Complex

or Cell Complex

closure-finite, weak (topology)

! non simplical

shape in GIS…

does matter!

GIS = combination of geometrical and topological information

in GIS, topology plays an important role because it…

• describes spatial relationships between neighbouring features

• informs on the validity of a data set

• enables advanced spatial analyses