Digital Terrain Data, Interpolation, Watersheds and Stream ExtractionOverviewRepresenting terrain using dataDigital Elevation ModelsDigital Elevation ModelsDigital Elevation ModelsSpot Elevations – The Starting PointSpot Elevation DensityInterpolating a Raster DEMIssues with IDWThe Interpolation ProblemInterpolation methods for DTAD8 Analysis SequenceNeighborhood OperationsFill SinksSlope and AspectSlope and AspectFlow Direction and AccumulationStream Links, Order, and BasinsProducts of D8 AnalysisWatersheds as an Organizing UnitTopographic Moisture IndexRevised Universal Soil Loss Eqn.Baismans Run CatchmentRUSLE Factors:Slope Length and Steepness Factor (LS)DEM ® LS-factor MappingCover-management Factor (C)LULC Data for Baisman’s RunLULC ® C-factor MappingDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005Digital Terrain Data, Interpolation, Watersheds and Stream ExtractionDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005Overview• Representing terrain using data• Spot elevations – the starting point• Implications of spot elevation density• Interpolating a raster DEM• Using the D8 sequence to extract streams•What products does D8 give us?• How might we use these products?David Tenenbaum – GEOG 070 – UNC-CH Spring 2005Representing terrain using data• We can represent terrain using various sorts of digital elevation models (DEMs). We have briefly looked at each of these representations:– Contours – a vector/arc based model with elevations associated with each contour– Triangulated Irregular Network (TIN) – a model made up of triangular facets– Raster grid – a cell-based model with elevations associated with each cell• From a raster DEM, we can derive how water moves through a landscape (drainage networks) by using of neighborhood analysis operationsDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005Digital Elevation ModelsContoursDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005Digital Elevation ModelsTriangulated Irregular Network (TIN)David Tenenbaum – GEOG 070 – UNC-CH Spring 2005Digital Elevation ModelsRaster GridDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005Spot Elevations – The Starting Point• Where do raster DEMs come from? – We create them from another representationof terrain• Fundamentally, terrain data is collected in the field as a set of spot elevations• Traditionally, survey or photogrammetricmethods are used to collect these• Now we have an alternative source at a higher density – LIDAR (LIght Detection And Ranging)•Why does the density of spot elevations matter?David Tenenbaum – GEOG 070 – UNC-CH Spring 2005Spot Elevation Density•Figure B shows spot elevations collected by photogrammetry•Figure C show spot elevations collected using LIDAR•Higher density of spot elevations supports a raster DEM with smaller cells Æ Produces a more detailed drainage networkDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005Interpolating a Raster DEM• Getting from a set of spot elevations to a gridded raster DEM requires the use of interpolation:• Interpolation creates a continuous fieldrepresentation (like a raster grid) from discrete objects (like spot elevation samples)• We have discussed interpolation briefly, looking at the inverse distance weighting and kriging approaches, but there is much more to learn about interpolation; if interested, have a look at:http://skagit.meas.ncsu.edu/~helena/classwork/topics/honinterp.htmlpoint iknown value zilocation xiweight widistance diunknown value (to be interpolated)location xInverse Distance Weighting (IDW)∑∑=iiiiiwzwz )(xThe estimate is a weighted average21iidw =Weights decline with distanceDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005Issues with IDW•This set of six data points clearly suggests a hill profile (dashed line). But in areas where there is little or no data the interpolator will move towards the overall mean (solid line)•There are other interpolation methodsthat can do better in this situation …David Tenenbaum – GEOG 070 – UNC-CH Spring 2005The Interpolation Problem•If we look at interpolation in a 2-dimensional sense (as shown to the left), what we are trying to do is:•Find a function that passes through (or close to) a set of points•There is no unique solutionto this problem, so we want to pick a function that produces a result that has the properties we want in our surfacehttp://skagit.meas.ncsu.edu/~helena/gmslab/viz/interp1d.htmlDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005Interpolation methods for DTA• Not all interpolation approaches are equally well-suited for creating DEMs for drainage network analysis• Inverse distance weighting (IDW) interpolation is not ideal … the resulting surfaces can have undesirable properties• Tension-spline based methods are better:– These methods fit a polynomial surface to the set of points that tends to vary smoothly and not exhibit the problems that IDW does when there is a lack of input data in a particular locationDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005• Assume we now have a raster DEM and we want to use it find a watershed and drainage network through D8 analysis• We can follow this sequence of analysis steps, each of which involves a neighborhood analysis operation:– Fill Sinks– Slope– Aspect– Flow Direction– Flow Accumulation– StreamLink & StreamOrder– WatershedD8 Analysis SequenceD8 AnalysisDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005•In raster overlay analysis, we compared each cell in a raster layer with another cell in the same position on another layer•In neighborhood operations, we look at a neighborhood of cells around the cell of interest to arrive at a new value:Neighborhood OperationsA 3x3 neighborhoodAn input layerCell ofInterest•Neighborhoods can be of any possible size; we can use a 3x3 neighborhood for any cell except on the edge of the layerDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005Fill Sinks•We need a DEM that does not have any depressions or pits in it for D8 drainage network analysis•The first step is to remove all pits from our DEM using a pit-filling algorithm•This illustrationshows a DEM of Morgan Creek, west of Chapel HillDavid Tenenbaum – GEOG 070 – UNC-CH Spring 2005Slope and Aspect• These are measurements of terrain attributes, usually calculated from a digital elevation model• Slope and aspect are calculated for each cell in the grid, by comparing a cell’s