1. L7 - Raster Algorithms L7 – Raster Algorithms NGEN06(TEK230) – Algorithms in Geographical Information Systems

2. L7 - Raster Algorithms Background Store and analyse the geographic information Raster data or Vector data. Raster data have been common in analysis in physical geography. Aerial and satellite images within GIS Continuous surface presentations

3. L7 - Raster Algorithms Aim  The main objective is to familiarize the students with some raster algorithms.  After this lecture the student should be able to write a minor program that treat raster data in one of the areas cost analysis, shaded relief, viewshed and resampling.

4. L7 - Raster Algorithms Content 1.Introduction 2.Local and regional operators 3.Morphological operators 4.Shaded relief 5.Resampling 6.Flow analysis in hydrology

5. L7 - Raster Algorithms Example of raster data and raster analysis 1.Digital maps Cost analysis, location analysis, overlay analysis and generalisation (e.g. by morphological operators) 2.DTMs and DEMs Viewshed analysis, flow analysis, and shaded relief. 3.Images (most often aerial or satellite images) Resampling, image classification and information extraction.

6. L7 - Raster Algorithms Example of raster analysis 1) Morphological operators This is a basic method for digital maps. Several manipulations and analysis of raster maps are based on morphological operators. (shrink and expand)  L9 genralization 2) Shaded relief A shaded layer is created (based on the DEM) for a fictitious sun; this layer is then added to a map to enhance the feeling of topography. 3) Resampling of images To use e.g. an ortophoto in a geographic analysis it must be geocoded. Geocoding - resampling of the image to the new geometry. 4) Flow analysis in hydrology All above are regional operations

7. L7 - Raster Algorithms Vector vs. Raster Distances, area of polygon, point-in-polygon are all fairly simple to perform with raster data. Result is often worse than in the vector case since the resolution of the raster data is not that good Means that the path between two pixels with the lowest total cost (sum of the pixel values for the path) is found. Raster version of Dijkstra’s algorithm can be used. Cost analysis for raster maps Raster data is often used for locational analyses. For example, all buildings that are closed to a lake, close to a road and far from industries are sought.

8. L7 - Raster Algorithms Local and regional operations Kernel filter

9. L7 - Raster Algorithms Morphological operators

10. L7 - Raster Algorithms Shaded relief Enhance the feeling of topography in a map.

11. L7 - Raster Algorithms Shaded relief

12. L7 - Raster Algorithms Computing the shaded relief

13. L7 - Raster Algorithms Approximating the partial derivatives Steepest gradient approach

14. L7 - Raster Algorithms Approximating the partial derivatives Sobel filter

15. L7 - Raster Algorithms Resampling Original grid Transformed grid

16. L7 - Raster Algorithms Resampling method It is important to state what kind of raster data that is used and the application of the resampled data. If the raster data is a digital map (or contain any type of data in nominal or ordinal scale) it is not allowed to do calculations on the raster data values. A recommended resampling method is then nearest neighbour. If the data is an image (which contain continuous data that is in ratio or interval scale ) it is allowed to do calculations on the raster data values

17. L7 - Raster Algorithms Nearest neighbour resampling Original grid Transformed grid

18. L7 - Raster Algorithms Inverse distance resampling

19. L7 - Raster Algorithms Flow analysis in hydrology

20. L7 - Raster Algorithms Drainage Direction – 2 ways Simplified: In a matrix of 9 cells, the water from the centre cell flows to the neighboring cell with the lowest elevation OR, for more realistic algorithms, is distributed proportionally to a number of neighboring cells with lower elevation 7 899 8 7 8 56

21. L7 - Raster Algorithms Surface flow algorithms over digital elevation models for all ß > 0 100 99.8 98.899.8 100.4 99.6100 100.7 Single flow direction algorithm SFD Multiple flow direction algorithm MFD

22. L7 - Raster Algorithms Topographic form

23. L7 - Raster Algorithms A convex surface (flow is split) Multiple flow direction algorithm Form based flow direction algorithm

24. L7 - Raster Algorithms A concave surface – one directional flow Multiple flow direction algorithm Form based flow direction algorithm

25. L7 - Raster Algorithms Break line Flat area Sink Artefacts in real world data

26. Stream Network

27. 00000 0 0 1 0 0 0 0 0 022 2 10 1 0 14 41 19 1 00 0 00 0 0 1 0 0 0 0 0 0 2 22 10 1 0 1 4 14 191 Flow Accumulation Grid. Area draining in to a grid cell

28. 00 0 00 0 0 1 0 0 0 0 0 0 222 10 1 0 1 4 14 191 Flow Accumulation > 10 Cell Threshold 00000 0 0 1 0 0 0 0 0 022 2 1 0 41 1 10 14 19 Stream Network for 10 cell Threshold Drainage Area

29. Watershed Draining to Outlet

30. Estimation of flow accumulation

31. Why we need to create new flow distribution algorithm ?  Problems related to sinks, man made structures and flat areas.  An empirical equation is used to estimate flow distribution in most flow distribution Algorithms.  The flow is distributed to some or all down slope cells, no influence from upslope cells.  Concave verses convex form. for all ß > 0

32. 1 2 3 45 6 7 8 C1 C2 M Triangular form-based multiple flow distribution algorithm (TFM) Area of one triangle =1/8 area of grid cell Triangles has a constant slope

33. 1 2 3 45 6 7 8 C1 C2 M Triangular form-based multiple flow distribution algorithm (TFM)

34. 1 2 3 4 2 3

35. Drainage area estimation on standard surfaces Mathematical estimation TFM D8 ConcaveConvexPlaneSaddle Triangular form-based multiple flow distribution algorithm (TFM)

36. TFM