lecture 4. interpolating environmental datasets

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


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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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• 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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• 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


Resulting TIN


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• What categories does the TIN method fall into:– exact or approximate?– deterministic or stochastic?– gradual or abrupt?– local or global?



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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)


11x11 circular filter SMA with sample points

21x21 circular filter SMA 41x41 circular filter SMA


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• What categories does the SMA method fall into:– exact or approximate?– deterministic or stochastic?– gradual or abrupt?– local or global?



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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



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• What categories does the trend surface method fall into:– exact or approximate?– deterministic or stochastic?– gradual or abrupt?– local or global?



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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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• 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

lecture 4. interpolating environmental datasets

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