Lecture 14 Interpolating environmental datasets

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

2. 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 GEOG2750 – Earth Observation and GIS of the Physical Environment

3. 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 GEOG2750 – Earth Observation and GIS of the Physical Environment

4. Surfaces from points Points Surface GEOG2750 – Earth Observation and GIS of the Physical Environment

5. 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 GEOG2750 – Earth Observation and GIS of the Physical Environment

6. 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 GEOG2750 – Earth Observation and GIS of the Physical Environment

7. Data sampling • Method of sampling is critical for subsequent interpolation... Transect Regular Random Contour Stratified random Cluster GEOG2750 – Earth Observation and GIS of the Physical Environment

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

9. 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 GEOG2750 – Earth Observation and GIS of the Physical Environment

10. 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 GEOG2750 – Earth Observation and GIS of the Physical Environment

11. 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 GEOG2750 – Earth Observation and GIS of the Physical Environment

12. 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 GEOG2750 – Earth Observation and GIS of the Physical Environment

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

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

15. 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 GEOG2750 – Earth Observation and GIS of the Physical Environment

16. Thiessen polygon construction GEOG2750 – Earth Observation and GIS of the Physical Environment

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

18. 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? GEOG2750 – Earth Observation and GIS of the Physical Environment

19. 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 GEOG2750 – Earth Observation and GIS of the Physical Environment

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

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

22. 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? GEOG2750 – Earth Observation and GIS of the Physical Environment

23. 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? GEOG2750 – Earth Observation and GIS of the Physical Environment

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

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

26. 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? GEOG2750 – Earth Observation and GIS of the Physical Environment

27. 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. GEOG2750 – Earth Observation and GIS of the Physical Environment

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

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

30. 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? GEOG2750 – Earth Observation and GIS of the Physical Environment

31. 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 GEOG2750 – Earth Observation and GIS of the Physical Environment

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

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

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

35. 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 GEOG2750 – Earth Observation and GIS of the Physical Environment

36. 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) GEOG2750 – Earth Observation and GIS of the Physical Environment

37. Practical • Steps: • Look at the data carefully and choose appropriate technique(s) for interpolating rainfall– which is most appropriate and why? • Interpolate rainfall data using chosen method(s) – have you chosen more than one method and if so why? • Display the resulting surface – does it look right, if not why? GEOG2750 – Earth Observation and GIS of the Physical Environment

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

39. Useful web links • Another 2 lectures on interpolation • http://www.geog.ubc.ca/courses/klink/gis.notes/ncgia/u40.html • http://www.geog.ubc.ca/courses/klink/gis.notes/ncgia/u41.html GEOG2750 – Earth Observation and GIS of the Physical Environment

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