Transcript The Nature of Geographical Data

The Nature of
Geographical Data
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Copyright, 1998-2015 © Qiming Zhou
GEOG4017. Geographical Information Systems
The Nature of Geographical
Data
 Geographical
phenomena
 Spatial autocorrelation and scale
 Spatial sampling
 Spatial interpolation
 Uncertainty of geographical data
The Nature of Geographical Data
2
Geographical phenomena

Our behaviour in space often reflects past
patterns of behaviour.
 Some geographical phenomena vary smoothly
across space, while others may not.
 The first law of geography: everything is related
to everything else, but near things are more
related than distant things.
 This property is known as spatial
autocorrelation.
The Nature of Geographical Data
3
Spatial autocorrelation and
scale

Spatial autocorrelation:


Temporal autocorrelation:


Measurements on how near and distant things
are interrelated.
The relationship between consecutive events in
time.
Examining spatio-temporal processes:
 explanation in time need only look to the
past, but
 explanation in space must look in all
directions simultaneously.
The Nature of Geographical Data
4
Spatial autocorrelation and
spatial objects

Spatial autocorrelation deal simultaneously
with similarities in the location of spatial
objects.
 It is determined both by similarities in position,
and by similarities in attributes
 Indices are used to measure spatial
autocorrelation of objects.
Moran’s I
 Geary’s C
 Ripley’s K

The Nature of Geographical Data
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Types of spatial objects

Spatial objects are classified according to their
topological dimension, which provides a
measure of the way they fill space.
 Point – dimension 0
 Line – dimension 1
 Area – dimension 2
 Volume – dimension 3
 Time – usually considered to be the fourth
dimension of spatial objects, although GIS is
currently incapable of dealing with it properly.
The Nature of Geographical Data
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Point


A point object has neither length nor breadth nor depth.
May be used to indicate spatial occurrences or events,
and their spatial pattern.
Large scale structure from travel time
tomography of Wenchuan Earthquake
(2008).
On Monday 12 May 2008, an
earthquake of magnitude 7.9 struck
northwestern Sichuan province of
China. Black lines depict the major
fault zones in the region. The focal
mechanism indicates that the main
shock in Wenchuan County involved
thrusting due to compression in NWSE direction. The aftershocks (green
circles) occurred along the Longmen
Shan thrust belt. The background
events (purple dots) are from the EHB
catalog (1964~2007).
Courtesy http://quake.mit.edu/~changli/wenchuan.html
The Nature of Geographical Data
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Line



A line object has length, but not breadth or depth.
Used to represent linear entities that are frequently built
together into networks.
Also used to measure distances between spatial objects.
The Nature of Geographical Data
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Area


An area object has
two dimension,
length and breadth,
but not depth.
Represents
enclose areas of
natural or artificial
objects.
A Forest Plan Map
The Nicola Thompson Fraser Plan
area is situated in the southern
interior, east of the Coast
Mountains and encompassing the
Thompson-Okanagan Plateau,
Canada. The defined forest area
are presented using area objects.
Courtesy thompsonokanagansustainableforestry.ca
The Nature of Geographical Data
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Volume


A volume object have length, breadth and depth.
Used to present natural (e.g. mine bodies and buildings)
or artificial objects.
The Nature of Geographical Data
10
Surface


A surface is a kind of volume object but its depth is
actually the spot height of the surface.
Used to present natural or statistical surface objects.
3m Digital Surface Model
(DSM) of Southern
Sahara, Tunisia, Africa
from Stereo IKONOS
Satellite Image Data
Courtesy Satellite Imaging Corporation
http://www.satimagingcorp.com
The Nature of Geographical Data
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Types of attributes
 Normal
attribute types
 Nominal
 Ordinal
 Interval
 Ratio
 Categories
beyond the normal types
cyclic (0 – 360)
 Average of 1 and 359 = ?
 E.g.
The Nature of Geographical Data
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Positive, negative and zero
spatial autocorrelation
 Positive:
features are similar in location
are also similar in attributes.
 Negative: features that are close
together in space tend to be more
dissimilar in attributes than features that
are further apart.
 Zero: attributes are independent of
location.
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Spatial autocorrelation
A
B
C
D
E
(A) Extreme negative spatial autocorrelation; (B) a dispersed
arrangement; (C) spatial independence; (D) spatial clustering;
and (E) extreme positive spatial autocorrelation.
The Nature of Geographical Data
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The meaning of scale

Level of spatial detail in data
 Geographical extent or scope of a project

e.g. a large-scale project covers a large area.
 A small-scale project covers a small area.

Scale of a map: representative fraction (RF)
 Scale is often integral to the trade off between
the level of spatial resolution and the degree of
attribute detail that can be handled for a given
application.
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Level of resolution
A
B
(A) A coarse-scale representation of attributes in a pattern of
negative spatial autocorrelation. (B) The pattern of spatial
autocorrelation at the coarser scale is replicated at the finer
scale. The overall pattern is said to exhibit the property of
self-similarity.
The Nature of Geographical Data
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Spatial sampling

Self-similar structure is characteristic of natural
as well as social systems.

A rock may resemble the physical form of the
mountain.
 A small group ‘typical’ people’s opinion may
resemble that of the society.

Sampling is therefore the typical way to gain
geographical data.
 Geographical data are only as good as the
sampling scheme used to create them.
The Nature of Geographical Data
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Spatial sampling schema
A
B
C
E
F
G
D
Spatial sample designs: (A) simple random sampling; (B) systematic
sampling; (C) systematic sampling with local random allocation; (D)
systematic sampling with random variation in grid spacing; (E) clustered
sampling; (F) transect sampling; and (G) contour sampling.
The Nature of Geographical Data
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Stratified sampling
Stratified sampling
designs accommodate
the unequal abundance
of different phenomena
on the Earth’s surface.
Hilly, mountainous terrain
Flat, flooding plain
The Nature of Geographical Data
To represent terrain
relief, spot heights of
terrain surface are
sampled. In a hilly,
mountainous terrain,
more sample points are
needed where local
variation likely to be
more heterogeneous. In
a flat, flooding plain, less
observations are
required.
19
Spatial interpolation
 In
sampling, part of reality to hold within
our representation.
 Judgement is required to fill in the gaps
between the observations.
 This requires understanding of the likely
attenuating effect of distance between
samples.
 The function that fills the gaps is known
as interpolation function.
The Nature of Geographical Data
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Distance decay
A
B
wij  bdij
w
C
w
d
wij  exp bdij 
wij  dijb
w
d
d
The attenuating effect of distance: (A) linear distance decay;
(B) negative power distance decay; and (C) negative
exponential distance decay.
The Nature of Geographical Data
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Interpolation processes
 Global
surface fitting
 Trend
 Local
surface
surface fitting
 Distance
reverse weighting functions
 Spline and kriging
The Nature of Geographical Data
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Trend surface
Linear
Quadratic
f  X ,Y   b0  b1 X  b2Y
f  X , Y   b0  b1 X  b2Y 
b3 X 2  b4 XY  b5Y 2
Cubic
Generic form:
f  X ,Y  
r s
b
X
 rs Y
r  s p
The Nature of Geographical Data
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Interpolation
6
5
6
7
6
7
8
5
6
7
Original sample data
Regularly spaced grid
B
measured
E
interpolated
A
measured
D
Elevation
C
n
Z
 Z
k 1
n
Position
k

k 1
k
6.1
5.7
5.3
5.6
7.0
6.5
6.0
5.2
7.6
7.0
6.0
5.7
7.2
7.0
6.2
5.5
k
Completed grid
Location of nearest
sample points
The Nature of Geographical Data
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The creation of isopleth maps
The Nature of Geographical Data
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Choropleth
maps
Upper: Total population – a
spatially extensive variable;
Lower: Population density – a
related but spatially intensive
variable.
The Nature of Geographical Data
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Spatial autocorrelation of objects
The Nature of Geographical Data
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Uncertainty of geographical
data
 The
length of coast line problem
 Uncertainty in the conception of
geographical phenomena
 Further uncertainty in the measurement
and representation of geographical
phenomena
 Further uncertainty in the analysis of
geographical phenomena
The Nature of Geographical Data
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The length of coast line
problem
 How
long is a coast line?
 Indeterminate
 Scale-dependent
The coastline of Maine, at three levels of
recursion: (A) the base curve of the
coastline, (B) approximation using 100-km
steps, (C) 50-km step approximation, and
(D) 25-km step approximation.
(Source: Longley et al. 2016, pp52)
The Nature of Geographical Data
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Coast line of Hong Kong
Coast line of Hong
Kong: The length of
the coastline
increases with the
increasing level of
details and scale. The
precise length of the
coast line is
indeterminate.
The Nature of Geographical Data
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Uncertainty
Real world
U1
U1: Uncertainty in the
conception of geographical
phenomena
Conception
U2: Uncertainty in the
measurements and
representation of
geographical phenomena
U2
Representation
U3: Uncertainty in the
analysis of geographical
phenomena
The Nature of Geographical Data
U3
Analysis
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Uncertainly in geographical
concepts

Conceptions of place: units of analysis


Spatial uncertainty: In many cases there are no
natural unites of geographical analysis.
Conceptions of attributes: vagueness and
ambiguity

Vagueness:


Uncertainty in the position of boundaries and
attributes.
Ambiguity:
Many language terms used to convey geographical
information are inherently ambiguous.
 Ambiguity is introduced when imperfect indicators of
phenomena are used instead of the phenomena
themselves.
 Differences in definitions are a major impediment to
integration of geographical data over wide areas.

The Nature of Geographical Data
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Units of analysis
Unit of analysis is not defined
Unit of analysis is defined
Left: heat map represents where new solar PV (photovoltaics) installations would likely be located based
on current PV capacity and location. (Source: M. Goe, B. Tomaszewski, and G. Gaustad, 2013,
Infrastructure planning for solar technology recycling, Arc User, Winter, 2013, http://www.esri.com/esrinews/arcuser/winter-2013/infrastructure-planning-for-solar-technology-recycling.) Right: County
population map of New York State (Source: www.maps.com).
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Uncertainty in representation
 Representation
and measurement:
difference under field and discrete
object views.
 scale
 Resolution
 Accuracy
and error
 Measurement error: capture, digitisation,
editing errors
 Data integration and sharing
The Nature of Geographical Data
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Discrete
object
and field
The contrast between (Upper)
discrete object and (Lower)
field conceptualizations of an
uncertain coastline.
(Source: Longley et al. 2016,
pp111)
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Uncertainty in analysis
 Spatial
analysis: uncertainty in data lead
to uncertainties in the results of
analysis.
 Aggregation and analysis: in appropriate
inference from aggregate data
The Nature of Geographical Data
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How to live with uncertainty?





It is essential to acknowledge that uncertainty is
inevitable.
Data should never be taken as the truth. Never
trust data that have not been assessed for quality.
It is important to gain some impression of the likely
impacts of uncertain inputs to GIS upon on outputs.
Rely on multiple sources of data whenever possible
in order to facilitate external validation.
Be honest and informative in reporting the results of
geographical information analysis. Recognize that
uncertainty is never likely to be eliminated, but that
it can be managed as part of good scientific
practice.
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Summary






The law of geography states the property of spatial
autocorrelation.
Spatial autocorrelation is the measurements on how
near and distant things are interrelated.
Spatial objects are classified according to their
topological dimension, which provides a measure of the
way they fill space.
Geographical data are only as good as the sampling
scheme used to create them.
Interpolation is the function that fills the gaps in samples.
In all steps of geographical data processing, uncertainty
exists and needs to be properly handled.
The Nature of Geographical Data
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