Raster Data: Digital Elevation Model Catchment Delineation

Transcription

1 Catchment-Analysis with GIS: Raster Data: Digital Elevation Model Catchment Delineation 1

2 Overview Lecture Part 1: Raster Data Short Introduction Part 2: Raster Data Analysis Methods Part 3: DEM Analysis Methods Part 4: DEM Catchment Delineation 2

3 Part 1 Raster Data Short Introduction 3

4 Raster Data What is raster data? geospatial related information are modelled by rectangular cells with homogeneous content all cells do have the same geometry cells are structured in a matrix with specified number of rows and columns 4

5 Raster Data Structure matrix oriented, number of rows and columns fixed raster of cells Geometry, Topology and Thematic Data raster geometry Δx and Δy raster origin x 0 and y 0 row and column index one value per cell -> thematic data 5

6 Raster Data Thematic Data spatial data land use, vegetation type, administrative district spatial physical variables elevation, concentration, temperature image pixel several colour scales and bands satellite images, aerial photos 6

7 Raster Data Data Source - Examples scan of paper based maps and images translation from vector data digital elevation models (remote sensing) orthophotos based on aerial photo satellite images results of numerical simulation models manual thematic maps (e.g. vegetation) 7

8 Raster Data ASCII Format Example Raster 10x10 - ArcGIS ncols 10 nrows 10 xllcorner 500 yllcorner 1000 cellsize 100 nodata_value

9 Example Raster Data Raster 10x10 physical variable (floating point)

10 Example Raster Data Raster 10x10 zonal value (integer)

11 Example Raster Data Raster 10x10: physical variable and zonal values

12 Cell Topology Cell Identification by Indices y-axis: i -> 1, 2, I I = nrows x-axis: j -> 1, 2, J J = ncols c ij cell in row i and column j 1,1 1,2 1,3 1,j 1,J 2,1 2,2 2,3 2,j 2,J i,1 i,2 i,3 i,j I,J I,1 I,2 I,3 I,j I,J 12

13 Cell Topology Cell Neighbourhood to the left : j -> j-1 to the right : j -> j+1 downwards : i -> i+1 upwards : i -> i-1 C i-1,j-1 C i-1,j C i-1,j+1 C i,j-1 C i,j C i,j+1 C i+1,j-1 C i+1,j C i+1,j+1 13

14 Cell Topology Cell Neighbourhood Index Cardinal Relative Bit Code 0,+1 East Right ,+1 SouthEast Down-Right , 0 South Down ,-1 SouthWest Down-Left ,-1 West Left ,-1 NorthWest Up-Left , 0 North Up ,+1 NorthEast Up-Right

15 Cell Geometry Coordinates - Indices basis: cell size Δx and Δy raster origin x 0 and y 0 cell centre of the cell c ij x m = x 0 + (j-1) Δx Δx y m = y 0 + (I-i) Δy Δy cell region x m Δx <= x <= x m Δx y m Δy <= y <= y m Δy 15

16 Cell Geometry Area cell area A = Δx Δy Distance cell distance cell a -> b Manhattan l = i b i a Δy + j b j a Δx Euclidian l = (ib ia) 2 Δy 2 + (j b ja)2δx 2 16

17 Raster Data Data Formats image formats: GIF (Graphics Interchange Format) TIFF (Tagged Image File Format) JPG (Joint Photographic Experts Group) PNG (Portable Network Graphics) GeoTiff: extension of TIFF with georeference several proprietary ASCII formats (e.g. ArcGIS) several proprietary binary formats 17

18 Raster Data Important Properties suitable representation of regular spatial data simple geometry and implicit topology transformation of coordinates are complex, irreversible, and might lead to loss of information scaling: upscaling -> loss of information downscaling -> sketchy, coarse structures simple geometrical operations simple local analysis methods (cell, sub matrix) large amount of date, simple data structure 18

19 Part 2 Raster Data General Analysis Methods 19

20 Analysis Methods Application Regions local -> one cell focal -> neighbourhood of a cell zonal -> group of cells with same value incremental -> sequence of cells global -> whole raster 20

21 Analysis Methods Basic Operations arithmetic (e.g. + - * /, sin cos tan, exp log) logic (e.g. OR, XOR, AND) Operands unary operations on one raster binary operations combination of two (or more) raster 21

22 Analysis Methods Example: Arithmetic Operation x - 10 = application example: elevation offset change of units ( C -> Kelvin, Fahrenheit) 22

23 Analysis Methods Example: arithmetic combination = application examples: elevation groundwater level average income * population density 23

24 Analysis Methods Image Processing Methods image: grey/colour scale <-> raster: variable(s) radiometric transformation thresholding slicing - selection blow and shrink methods -> filling gaps (e.g. dike lines, streets) -> filter for outlier cells filter methods 24

25 Analysis Methods Filter Basis: Convolution k+m l+n general: f kk i=k m j=l n f ii λ ii λ ii weighting factor n,m focal size weighting factor determines the impact of the filter on the raster size of focal region determines the spatial dimension of the effect 25

26 Analysis Methods Filter Methods low pass filter (smoothing) example: λ ii = 1 (mean value) nn reduction of extreme value changes high pass filter (sharpening) inverse to low pass filter k+m l+n f kk fff i=k m j=l n f ii λ ii intensification -> border recognition 26

27 Analysis Methods Filter Methods - Examples: total λ ii = 1 min value max value standard derivation: f kk min(f ii ) f kk maa(fff) f kk 1 k+m j=l n l+n i=k m k+m j=l n l+n i=k m k+m l+n f mm 1 i=k m j=l n ii f 2 27

28 Analysis Methods Derivation Gradient of a Spatial Variable f(x,y): gradient g = g 1 g 2 = backward difference: forward difference: central difference: df dd df dy g 1 = (f ij - f ij-1 ) / Δx g 1 = (f ij+1 - f ij ) / Δx g 1 = (f ij+1 - f ij-1 ) / 2Δx same equations for y direction 28

29 Analysis Methods Integration of a Continuous Variable in a Region: integral I = R f(x, y) dddd integral is replaced by the sum of sub integrals in the relevant cells of the region R sub integral of one cell is replaced by the cell data multiplied by the cell area integral I = R f ii ΔxΔy 29

30 Part 3 Raster Data Analysis Methods DEM 30

31 Analysis Methods DEM Overview Geometric Methods - Examples slope aspect curvature hill shading, pseudo relief viewshed, visibility cut & fill contour, cluster, 31

32 Geometric Analysis Methods Slope (Steigung) gradient: g = g 12 + g 2 2 sssss dddddd = 180 π aaaaaa g g 2 2 sssss percent = 100 g 12 + g 2 2 gradient calculation: central difference (vertical and horizontal) or using all eight neighbours (ArcGIS) 32

33 Geometric Analysis Methods Aspect (Ausrichtung Richtung max. Neigung) calculation: g 2 = ((g + 2h + i) - (a + 2b + c)) / 8 Δx g 1 = ((c + 2f + i) - (a + 2d + g)) / 8 Δy aspect = 180 aaaaaa g 2 π g 1 reference: ESRI 33

34 Geometric Analysis Methods Aspect Example DEM 10x

35 Geometric Analysis Methods Curvature (Krümmung) polynomial approximation f(x,y) = Ax²y² + Bx²y + Cxy² + Dx² + Ey² + Fxy + Gx + Hy + I A = [(Z1 + Z3 + Z7 + Z9) / 4 - (Z2 + Z4 + Z6 + Z8) / 2 + Z5] / L 4 B = [(Z1 + Z3 - Z7 - Z9) /4 - (Z2 - Z8) /2] / L 3 C = [(-Z1 + Z3 - Z7 + Z9) /4 + (Z4 - Z6)] /2] / L 3 D = [(Z4 + Z6) /2 - Z5] / L 2 E = [(Z2 + Z8) /2 - Z5] / L 2 F = (-Z1 + Z3 + Z7 - Z9) / 4L 2 G = (-Z4 + Z6) / 2L H = (Z2 - Z8) / 2L I = Z5 reference: ESRI 35

36 Geometric Analysis Methods Curvature (Krümmung) profile curvature (vertical curvature): k = 2(DD 2 + EE 2 + FFF)/(G 2 + H 2 ) planform curvature (horizontal curvature): k = 2(DD 2 + EE 2 + FFF)/(G 2 + H 2 ) ArcGIS (difference vert. and horiz. curvature): k = 2 D + E application example: flow acceleration: erosion and deposition process reference: ESRI 36

37 Geometric Analysis Methods Hill Shading, Pseudo Relief (Schummerung) hypothetical illumination of a surface based on slope and aspect parameter: azimuth (angular direction of the sun) altitude (angle of the sun above horizon) reference: ESRI 37

38 Geometric Analysis Methods Viewshed, Visibility (Sichtfeld, Sichtbarkeit) viewshed: visibility: 9 parameter: all cells, visible from one position all cells, which have view to a position reference: ESRI 38

39 Geometric Analysis Methods Cut & Fill (Auf- and Abtrag) comparison of two digital elevation models calculation: area and volume reference: ESRI 39

40 Geometric Analysis Methods Cut & Fill (Auf- and Abtrag) example reference: ESRI 40

41 Part 4 Digital Elevation Models Catchment Delineation 41

42 Analysis Methods DEM Overview Application Methods - Examples groundwater Darcy flow, Darcy velocity, particle track, porous puff hydrology watershed, drainage system, flow length solar radiation radiant energy, insolation maps, time based analysis 42

43 Analysis Methods DEM Hydrologic Surface Analysis - Examples flow direction fill sink flow accumulation flow length watershed 43

44 Hydrologic Analysis Overview reference: ESRI 44

45 Hydrologic Analysis Methods Flow Direction (Fließrichtung) D8 model: direction of max. slope slope = difference cell values / distance (L, L) reference: ESRI 45

46 Hydrologic Analysis Methods Fill Sink (Senkenfüllung) fill sinks to remove small imperfections enables continuous river network detection iterative performance reference: ESRI 46

47 Hydrologic Analysis Methods Flow Accumulation (Abflussakkumulation) number of all cells, with flow into the cell reference: ESRI 47

48 Hydrologic Analysis Methods Watershed (Einflußgebiet) based on outlet / pour points parameter: flow direction, pour points reference: ESRI 48

49 Hydrologic Analysis Methods Flow Length (Fließlänge) distance along the flow path to a sink or a outlet directions: upstream downstream distance can be calculated with weights -> e.g. flow resistance 49

50 Raster Data Application Example River Var Catchment reference: GoogleEarth 50

51 Raw Data Digital Elevation Model: 300 m Raster 384 rows 384 columns ca km 2 elevation m 51

52 Raw Data Contour (Isolines) distance: 200 m 52

53 Analysis Methods Slope (Steigung) 0 -> ~45 min/max 53

54 Analysis Methods Aspect (Richtung größte Neigung) 54

55 Analysis Methods Hill Shading (Schummerung) azimuth: 315 altitude: 45 55

56 Analysis Methods Viewshed, Visibility (Sichtfeld, Sichtbarkeit) four points defined viewshed 56

57 Analysis Methods Viewshed, Visibility (Sichtfeld, Sichtbarkeit) four points defined visibility 57

58 Hydrologic Analysis Step 1: Flow Direction 58

59 Hydrologic Analysis Step 2: Sink Check max. 170 m most of them in valleys 1 st Iteration 59

60 Hydrologic Analysis Step 3: Fill Sinks result of iteration: Elevation difference 60

61 Hydrologic Analysis Step 4: Flow Accumulation (Abflußakkumulation) base: flow direction min: 0 max:

62 Hydrologic Analysis Step 4: Flow Accumulation (Abflußakkumulation) alternative visualisation 62

63 Hydrologic Analysis Step 5: Identification of Streams cells with flow accumulation > 50 map algebra: con (accu > 50,1) limit: 50 63

64 Hydrologic Analysis Step 6: Stream Order (Struktur der Wasserläufe) incremental search 64

65 Hydrologic Analysis Step 7: Vectorisation (Stream to Feature) raster > lines 65

66 Hydrologic Analysis Step 8: Flow Length (Ablauflänge) max 118 km 66

67 Hydrologic Analysis Step 9: Watershed (Wassereinzugsgebiete) 6 pour points vector data: points 67

68 Hydrologic Analysis Further Steps: land use rainfall measurements interpolation precipitation 29 April