1. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment1 Lecture 14 Interpolating environmental datasets Outline – creating surfaces from points – interpolation basics – interpolation methods – common problems

2. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment2 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

3. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment3 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

4. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment4 PointsSurface Surfaces from points

5. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment5 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

6. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment6 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

7. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment7 Data sampling Method of sampling is critical for subsequent interpolation... RegularRandom Transect Stratified randomCluster Contour

8. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment8 Question… How do you choose a method of interpolation?

9. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment9 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

10. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment10 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

11. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment11 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

12. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment12 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

13. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment13 Question… Think of data types that require: –local or global interpolation? –exact or approximate interpolation? –gradual or abrupt interpolation? –deterministic or stochastic interpolation?

14. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment14 Interpolation methods Most GIS packages offer a number of methods Typical methods are: –Thiessen polygons –Triangulated Irregular Networks (TINs) –Spatial moving average –Trend Surfaces

15. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment15 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

16. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment16 Thiessen polygon construction

17. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment17 Example Thiessen polygon Source surface with sample pointsThiessen polygons with sample points

18. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment18 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?

19. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment19 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 triangles  calculate real 3D distance between data points along vertices using trigonometry  calculate interpolated value along facets between three vertices

20. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment20 value a value b value c a b c Interpolated value x Plan view Isometric view TIN construction

21. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment21 Example TIN Source surface with sample points Resulting TIN

22. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment22 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?

23. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment23 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 filter  size, shape and character of filter?

24. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment24 Spatial moving average (SMA)

25. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment25 Example SMA (circular filter) Source surface with sample points 11x11 circular filter SMA with sample points 21x21 circular filter SMA 41x41 circular filter SMA

26. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment26 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?

27. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment27 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.

28. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment28 data point interpolated point Fitting a single polynomial trend surface

29. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment29 Example trend surfaces Goodness of fit (R2) = 45.42 % Goodness of fit (R2) = 92.72 % Goodness of fit (R2) = 82.11 % Linear QuadraticCubic Source surface with sample points

30. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment30 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?

31. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment31 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

32. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment32 Effects of data uncertainty Original surface Interpolation based on 10 points Interpolation based on 100 points Error map Low High Error map

33. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment33 Edge effects Original surface with sample points Interpolated surface Error map and extract Low High

34. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment34 Question… Is it possible to use explanatory variables to improve interpolation, and if so, how?

35. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment35 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

36. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment36 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)

37. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment37 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?

38. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment38 Learning outcomes Familiarisation with range of different interpolation techniques Experience at applying interpolation methods in Arc and ArcGRID to environmental datasets

39. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment39 Useful web links Another 2 lectures on interpolation –http://www.geog.ubc.ca/courses/klink/gis.notes/ncgia/u 40.htmlhttp://www.geog.ubc.ca/courses/klink/gis.notes/ncgia/u 40.html –http://www.geog.ubc.ca/courses/klink/gis.notes/ncgia/u 41.htmlhttp://www.geog.ubc.ca/courses/klink/gis.notes/ncgia/u 41.html

40. Week 17GEOG2750 – Earth Observation and GIS of the Physical Environment40 Next week… Principles of grid-based modelling –linking models to GIS –basics of cartographic modelling –modelling in ArcGRID Practical: Land Capability Mapping