© GEOSPATIAL ANALYSIS ix
6.2 Surface Geometry ...............................................................................267
6.2.1 Gradient, slope and aspect .............................................................. 267
6.2.1.1 Slope ..................................................................................... 267
6.2.1.2 Aspect.................................................................................... 269
6.2.2 Profiles and curvature .................................................................... 272
6.2.2.1 Profiles and cross-sections............................................................ 272
6.2.2.2 Curvature and morphometric analysis .............................................. 272
6.2.2.3 Profile curvature ....................................................................... 275
6.2.2.4 Plan curvature .......................................................................... 275
6.2.2.5 Tangential curvature .................................................................. 276
6.2.2.6 Longitudinal and cross-sectional curvature........................................ 276
6.2.2.7 Mean, maximum and minimum curvature.......................................... 276
6.2.3 Directional derivatives.................................................................... 276
6.2.4 Paths on surfaces.......................................................................... 277
6.2.5 Surface smoothing......................................................................... 278
6.2.6 Pit filling.................................................................................... 279
6.2.7 Volumetric analysis........................................................................ 280
6.3 Visibility...........................................................................................281
6.3.1 Viewsheds and RF propagation .......................................................... 281
6.3.2 Line of sight ................................................................................ 284
6.3.3 Isovist analysis ............................................................................. 285
6.4 Watersheds and Drainage......................................................................287
6.4.1 Overview of watersheds and drainage ................................................. 287
6.4.2 Drainage modelling........................................................................ 287
6.4.3 D-infinity model............................................................................ 288
6.4.4 Drainage modelling case study .......................................................... 289
6.4.4.1 Flow accumulation..................................................................... 289
6.4.4.2 Stream network construction......................................................... 289
6.4.4.3 Stream basin construction ............................................................ 290
6.5 Gridding, Interpolation and Contouring ....................................................291
6.5.1 Overview of gridding and interpolation................................................ 291
6.5.2 Gridding and interpolation methods.................................................... 292
6.5.2.1 Comparison of sample gridding and interpolation methods..................... 292
6.5.2.2 Contour plots of sample gridding and interpolation methods................... 295
6.5.3 Contouring.................................................................................. 298
6.6 Deterministic Interpolation Methods........................................................300
6.6.1 Inverse distance weighting (IDW) ....................................................... 301
6.6.2 Natural neighbour ......................................................................... 302
6.6.3 Nearest-neighbour......................................................................... 305
6.6.4 Radial basis and spline functions........................................................ 305
6.6.5 Modified Shepard .......................................................................... 306
6.6.6 Triangulation with linear interpolation ................................................ 307
6.6.7 Triangulation with spline-like interpolation........................................... 307
6.6.8 Rectangular or bi-linear interpolation ................................................. 308
6.6.9 Profiling..................................................................................... 308
6.6.10 Polynomial regression..................................................................... 308
6.6.11 Minimum curvature........................................................................ 308
6.6.12 Moving average............................................................................. 309
6.6.13 Local polynomial........................................................................... 309
6.6.14 Topogrid/Topo to raster.................................................................. 309
6.7 Geostatistical Interpolation Methods........................................................311
6.7.1 Core concepts.............................................................................. 311