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Lecture 4. Interpolating environmental datasets. Outline creating surfaces from points interpolation basics interpolation methods common problems. Introduction. Definition: - PowerPoint PPT Presentation
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Lecture 4 GEOG2590 - GIS for Physical Geography
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Lecture 4.Lecture 4.Interpolating Interpolating
environmental datasetsenvironmental datasets•Outline
– creating surfaces from points– interpolation basics– interpolation methods– common problems
Lecture 4 GEOG2590 - GIS for Physical Geography
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IntroductionIntroduction
• Definition:“Spatial interpolation is the procedure of estimating
the values of properties at unsampled sites within an area covered by existing observations.” (Waters, 1989)
• Complex problem– wide range of applications– important in addressing problem of data
availability– quick fix for partial data coverage– interpolation of point data to surface/polygon data– role of filling in the gaps between observations
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Creating surfaces from Creating surfaces from pointspoints
• Waters (1989) provides list of potential uses:– to provide contours for displaying data graphically– to calculate some property of a surface at a given
point– to change the unit of comparison when using
different data models in different layers– to aid in the decision making process both in
physical and human geography and in related disciplines such as mineral prospecting and resource evaluation
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Points Surface
Surfaces from pointsSurfaces from points
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An essential skillAn essential skill
• Environmental data– often collected as discrete observations at
points or along transects– example: soil cores, soil mositure, vegetation
transects, meteorological station data, etc.
• Need to convert discrete data into continuous surface for use in GIS modelling– interpolation
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Interpolation basicsInterpolation basics
• Methods of spatial interpolation:– many different methods available– classification according to:
exact or approximate deterministic or stochastic local or global gradual or abrupt
– examples: thiessen polygons spatial moving overage TINs Kriging
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Data samplingData sampling• Method of sampling is critical
for subsequent interpolation...
Regular Random Transect
Stratified random Cluster Contour
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Question…Question…
• How do you choose a method of interpolation?
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Classification: local or Classification: local or globalglobal
• Global methods:– single mathematical function applied to all
points– tends to produces smooth surfaces
• Local methods:– single mathematical function applied
repeatedly to subsets of the total observed points
– link regional surfaces into composite surface
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Classification: exact or Classification: exact or approximateapproximate
• Exact methods:– honour all data points such that the
resulting surface passes exactly through all data points
– appropriate for use with accurate data
• Approximate methods:– do not honour all data points– more appropriate when there is high
degree of uncertainty about data points
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Classification: gradual Classification: gradual or abruptor abrupt
• Gradual methods:– produce smooth surface between data points– appropriate for interpolating data of low local
variability
• Abrupt methods:– produce surfaces with a stepped appearance– appropriate for interpolating data of high
local variability or data with discontinuities
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Classification: Classification: deterministic or deterministic or
stochasticstochastic• Deterministic methods:
– used when there is sufficient knowledge about the surface being modelled
– allows it to be modelled as a mathematical surface
• Stochastic methods:– used to incorporate random variation in
the interpolated surface
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Question…Question…
• Think of data types that require:– local or global interpolation?– exact or approximate interpolation?– gradual or abrupt interpolation?– deterministic or stochastic
interpolation?
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Interpolation methodsInterpolation methods
• Most GIS packages offer a number of methods
• Typical methods are:– Thiessen polygons– Triangulated Irregular Networks (TINs)– Spatial moving average– Trend Surfaces
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Thiessen PolygonsThiessen Polygons
• Thiessen (Voronoi) polygons:– assume values of unsampled locations
are equal to the value of the nearest sampled point
• Vector-based method– regularly spaced points produces a
regular mesh– irregularly spaced points produces an
network of irregular polygons
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Thiessen polygon Thiessen polygon constructionconstruction
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Example Thiessen polygonExample Thiessen polygon
Source surface with sample points
Thiessen polygons with sample points
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Question…Question…
• What categories does the Thiessen polygon method fall into:– exact or approximate?– deterministic or stochastic?– gradual or abrupt?– local or global?
• What could it be used for?
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TINsTINs
• Another vector-based method often used to create digital terrain models (DTMs)– adjacent data points connected by lines
(vertices) to create a network of irregular trianglescalculate real 3D distance between data
points along vertices using trigonometrycalculate interpolated value along facets
between three vertices
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value a
value b
value c
a
b
c
Interpolated value x
Plan view Isometric view
TIN constructionTIN construction
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Example TINExample TIN
Source surface with sample points
Resulting TIN
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Question…Question…
• What categories does the TIN method fall into:– exact or approximate?– deterministic or stochastic?– gradual or abrupt?– local or global?
• What could it be used for?
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Spatial moving averageSpatial moving average
• Vector and raster method:– most common GIS method– calculates new value of each location
based on range of values associated with neighbouring points
– Neighbourhood determined by a filtersize, shape and character of filter?
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Spatial moving average Spatial moving average (SMA)(SMA)
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Example SMA (circular filter)Example SMA (circular filter)
Source surface with sample points
11x11 circular filter SMA with sample points
21x21 circular filter SMA 41x41 circular filter SMA
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Question…Question…
• What categories does the SMA method fall into:– exact or approximate?– deterministic or stochastic?– gradual or abrupt?– local or global?
• What could it be used for?
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Trend surfacesTrend surfaces
• Uses a polynomial regression to fit a least-squares surface to the data points– normally allows user control over the order of
the polynomial used to fit the surface– as the order of the polynomial is increased,
the surface being fitted becomes progressively more complex
higher order polynomial will not always generate the most accurate surface, it dependent upon the data
the lower the RMS error, the more closely the interpolated surface represents the input points
most common order of polynomials is 1 through 3.
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data point
interpolated point
Fitting a single polynomial Fitting a single polynomial trend surfacetrend surface
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Example trend surfacesExample trend surfaces
Goodness of fit (R2) = 45.42 %
Goodness of fit (R2) = 92.72 %Goodness of fit (R2) = 82.11 %
Linear Quadratic Cubic
Source surface with sample points
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Question…Question…
• What categories does the trend surface method fall into:– exact or approximate?– deterministic or stochastic?– gradual or abrupt?– local or global?
• What could it be used for?
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Common problemsCommon problems
• Input data uncertainty– Too few data points– Limited or clustered spatial coverage– Uncertainty about location and/or
value• Edge effects
– Need data points outside study area– improve interpolation and avoid
distortion at boundaries
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Effects of data uncertaintyEffects of data uncertainty
Original surface
Interpolation based on 10 points
Interpolation based on 100 points
Error mapLow
High
Error map
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Edge effectsEdge effects
Original surface with sample points
Interpolated surface Error map and extract
Low
High
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Question…Question…
• Is it possible to use explanatory variables to improve interpolation, and if so, how?
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ConclusionsConclusions• Interpolation of environmental point data is
important skill• Many methods classified by
– local/global, approximate/exact, gradual/abrupt and deterministic/stochastic
– choice of method is crucial to success
• Error and uncertainty– poor input data– poor choice/implementation of interpolation
method
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PracticalPractical
• Interpolating surfaces from point data • Task: Interpolate a selection of point data
using the most appropriate methods of your choosing
• Data: The following datasets are provided for the Yorkshire area…– 200m resolution DEM (derived from 1:50,000
OS Panorama data)– 25m interval contour data (derived from
1:50,000 OS Panorama data)– metstation data (mean annual rainfall)
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PracticalPractical• Steps:1. Look at the data carefully and choose
appropriate technique(s) for interpolating rainfall– which is most appropriate and why?
2. Interpolate rainfall data using chosen method(s) – have you chosen more than one method and if so why?
3. Display the resulting surface – does it look right, if not why?
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Learning outcomesLearning outcomes
• Familiarisation with range of different interpolation techniques
• Experience at applying interpolation methods in Arc and ArcGRID to environmental datasets
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Next week…Next week…
• Grid-based modelling– linking models to GIS – basics of cartographic modelling– modelling in Arc/Info GRID
• Practical: Land Capability Mapping