Lecture 4. Interpolating environmental datasets

Lecture 4. Interpolating environmental datasets
Outline creating surfaces from points interpolation basics interpolation methods common problems Lecture 4 GEOG GIS for Physical Geography

GEOG2590 - GIS for Physical Geography
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 Lecture 4 GEOG GIS for Physical Geography

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 Lecture 4 GEOG GIS for Physical Geography

Surfaces from points Points Surface Lecture 4 GEOG GIS for Physical Geography

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 Lecture 4 GEOG GIS for Physical Geography

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 Lecture 4 GEOG GIS for Physical Geography

Data sampling Method of sampling is critical for subsequent interpolation... Transect Regular Random Contour Stratified random Cluster Lecture 4 GEOG GIS for Physical Geography

Question… How do you choose a method of interpolation? Lecture 4 GEOG GIS for Physical Geography

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 Lecture 4 GEOG GIS for Physical Geography

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 Lecture 4 GEOG GIS for Physical Geography

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 Lecture 4 GEOG GIS for Physical Geography

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 Lecture 4 GEOG GIS for Physical Geography

Question… Think of data types that require: local or global interpolation? exact or approximate interpolation? gradual or abrupt interpolation? deterministic or stochastic interpolation? Lecture 4 GEOG GIS for Physical Geography

Interpolation methods
Most GIS packages offer a number of methods Typical methods are: Thiessen polygons Triangulated Irregular Networks (TINs) Spatial moving average Trend Surfaces Lecture 4 GEOG GIS for Physical Geography

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 Lecture 4 GEOG GIS for Physical Geography

Thiessen polygon construction
Lecture 4 GEOG GIS for Physical Geography

Example Thiessen polygon
Source surface with sample points Thiessen polygons with sample points Lecture 4 GEOG GIS for Physical Geography

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? Lecture 4 GEOG GIS for Physical Geography

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 Lecture 4 GEOG GIS for Physical Geography

TIN construction value a value b value c Interpolated value x a b c Isometric view Plan view Lecture 4 GEOG GIS for Physical Geography

Source surface with sample points
Example TIN Source surface with sample points Resulting TIN Lecture 4 GEOG GIS for Physical Geography

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? Lecture 4 GEOG GIS for Physical Geography

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? Lecture 4 GEOG GIS for Physical Geography

Spatial moving average (SMA)
Lecture 4 GEOG GIS for Physical Geography

Example SMA (circular filter)
Source surface with sample points 11x11 circular filter SMA with sample points 21x21 circular filter SMA 41x41 circular filter SMA Lecture 4 GEOG GIS for Physical Geography

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? Lecture 4 GEOG GIS for Physical Geography

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. Lecture 4 GEOG GIS for Physical Geography

Fitting a single polynomial trend surface
interpolated point data point Lecture 4 GEOG GIS for Physical Geography

Example trend surfaces
Source surface with sample points Linear Quadratic Cubic Goodness of fit (R2) = % Goodness of fit (R2) = % Goodness of fit (R2) = % Lecture 4 GEOG GIS for Physical Geography

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? Lecture 4 GEOG GIS for Physical Geography

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 Lecture 4 GEOG GIS for Physical Geography

Effects of data uncertainty
Interpolation based on 100 points Error map Low High Original surface Interpolation based on 10 points Error map Lecture 4 GEOG GIS for Physical Geography

Original surface with sample points
Edge effects Original surface with sample points Interpolated surface Error map and extract Low High Lecture 4 GEOG GIS for Physical Geography

Question… Is it possible to use explanatory variables to improve interpolation, and if so, how? Lecture 4 GEOG GIS for Physical Geography

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 Lecture 4 GEOG GIS for Physical Geography

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) Lecture 4 GEOG GIS for Physical Geography

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? Lecture 4 GEOG GIS for Physical Geography

Learning outcomes Familiarisation with range of different interpolation techniques Experience at applying interpolation methods in Arc and ArcGRID to environmental datasets Lecture 4 GEOG GIS for Physical Geography

Next week… Grid-based modelling linking models to GIS basics of cartographic modelling modelling in Arc/Info GRID Practical: Land Capability Mapping Lecture 4 GEOG GIS for Physical Geography

Lecture 4. Interpolating environmental datasets

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Lecture 4. Interpolating environmental datasets

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