Week 17

GEOG2750 – Earth Observation and GIS of the Physical Environment

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Lecture 14Interpolating environmental

datasets

•Outline– creating surfaces from points– interpolation basics– interpolation methods– common problems

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GEOG2750 – Earth Observation and GIS of the Physical Environment

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Introduction

• 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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GEOG2750 – Earth Observation and GIS of the Physical Environment

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Creating surfaces from points

• 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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GEOG2750 – Earth Observation and GIS of the Physical Environment

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Points Surface

Surfaces from points

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GEOG2750 – Earth Observation and GIS of the Physical Environment

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An 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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GEOG2750 – Earth Observation and GIS of the Physical Environment

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Interpolation 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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GEOG2750 – Earth Observation and GIS of the Physical Environment

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Data sampling

• Method of sampling is critical for subsequent interpolation...

Regular Random Transect

Stratified random Cluster Contour

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GEOG2750 – Earth Observation and GIS of the Physical Environment

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Question…

• How do you choose a method of interpolation?

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GEOG2750 – Earth Observation and GIS of the Physical Environment

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Classification: local or global

• 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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GEOG2750 – Earth Observation and GIS of the Physical Environment

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Classification: exact or approximate

• 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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GEOG2750 – Earth Observation and GIS of the Physical Environment

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Classification: gradual or 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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GEOG2750 – Earth Observation and GIS of the Physical Environment

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Classification: deterministic or stochastic

• 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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GEOG2750 – Earth Observation and GIS of the Physical Environment

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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 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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GEOG2750 – Earth Observation and GIS of the Physical Environment

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Thiessen 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 construction

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Example Thiessen polygon

Source surface with sample points

Thiessen polygons with sample points

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GEOG2750 – Earth Observation and GIS of the Physical Environment

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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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GEOG2750 – Earth Observation and GIS of the Physical Environment

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TINs

• 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 construction

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Example TIN

Source surface with sample points

Resulting TIN

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GEOG2750 – Earth Observation and GIS of the Physical Environment

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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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GEOG2750 – Earth Observation and GIS of the Physical Environment

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Spatial 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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GEOG2750 – Earth Observation and GIS of the Physical Environment

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Spatial moving average (SMA)

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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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GEOG2750 – Earth Observation and GIS of the Physical Environment

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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 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 trend surface

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Example 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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GEOG2750 – Earth Observation and GIS of the Physical Environment

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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 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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GEOG2750 – Earth Observation and GIS of the Physical Environment

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Effects 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 effects

Original surface with sample points

Interpolated surface Error map and extract

Low

High

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Question…

• Is it possible to use explanatory variables to improve interpolation, and if so, how?

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GEOG2750 – Earth Observation and GIS of the Physical Environment

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Conclusions

• 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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Practical

• 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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Practical• 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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GEOG2750 – Earth Observation and GIS of the Physical Environment

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Learning outcomes

• Familiarisation with range of different interpolation techniques

• Experience at applying interpolation methods in Arc and ArcGRID to environmental datasets

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Useful web links

• Another 2 lectures on interpolation– http://www.geog.ubc.ca/courses/klink/gis.notes/ncgia/u

40.html

– http://www.geog.ubc.ca/courses/klink/gis.notes/ncgia/u41.html

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Next week…

• Principles of grid-based modelling– linking models to GIS – basics of cartographic modelling– modelling in ArcGRID

• Practical: Land Capability Mapping