Environmental Modelling with RASTER DEMs: Hydrologic Features Lecture 4 Environmental Modelling with RASTER DEMs: Hydrologic Features

Delineation of Drainage Boundaries and Networks: DEM (Input) ↓ De-pitting or Depression Filling (Preprocessing) Terrain Analysis (Calculate flow direction, upslope accumulation area, and specific contributing area) ↓ ↓ Watershed Extraction Stream Network Extraction (Extracts watershed boundaries from (Extracts hillslopes and stream a user specified point) network based on user defined thresholds)

Flow Routing Algorithms Flow routing algorithms are used to calculate flow direction and flow accumulation from a DEM. The main differences among routing algorithms lie in: The way that flow direction is calculated, and The way that flow is apportioned to downslope neighbours Flow routing algorithms include: D8 FD8 (Freeman 1991; Quinn et al. 1991) D-infinity (Tarboton 1998)

D8 flow routing algorithm

FD8 flow routing algorithm To solve the problem of flow in only one direction (D8), Quinn et.al (1991) developed an algorithm where the flow direction from any source cell is split proportionally to all lower neighbouring cells The proportion is determined by the slope from the source cell to a lower neighbouring cell relative to the slope from the source cell to the other neighbouring cells

Consider the following example: For the following 3x3 cell window of elevation, there are 4 cells with elevations that are lower than the central ‘8’. Therefore, the flow will be split between those 4 cells. The elevation window. Cells in the elevation window that have elevations that are lower than the center cell. 5 9 8 4 7 5 8 4 7

Storing information on the flow to the four cells is done using a special encoding system. The 8 primary directions are encoded as: The fractional pointer of the center cell is the sum of the primary directions for each of the neighbouring cells at lower elevation than the center cell. NW N NE W E SW S SE 64 128 1 32 2 16 8 4 5 8 4 7

So, in this example, the center cell will have a fractional pointer of: 4+16+32+64=116. The pointer data layer contains pointers with the range: 0-255 (i.e. 1+2+4+16+32+64+128=255). For example, if the pointer code is ’12’, the algorithm ‘knows’ that flow can only occur in the S and SE directions. Similarly, if the fractional pointer code is ‘255’, the algorithm ‘knows’ that flow occurs in all directions. NW N NE W E SW S SE 64 128 1 32 2 16 8 4 5 4 7 8

The flow from any raster cell is split proportionally to all lower neighbouring cells. The amount of flow to a cell is determined by the slope (rise/run) to that cell from the source cell. Recall, for a right-angle triangle, where c is the hypotenuse, and a and b are the other sides, c2=a2+b2: c2 = a2 + b2 b = 1 a = 1

If we assume that the cell size is 25m, then the “run” from the source to each of the 8 neighbouring cells of the window is calculated as follows: 25*1.414 25*1 Slope, which is “rise” over “run”, is calculated as follows: (8-5)/(25*1.414) (8-5)/(25*1) (8-4)/(25*1.414) (8-7)/(25*1.414) 5 4 7 8

The final result: 0.085 0.120 0.113 0.028 5 4 7 8 To determine the fraction of the flow that goes to these lower cells, we normalize the slope values (i.e. we divide by their sum): 0.085/ (0.085+0.120+0.113+0.028) 0.120/ 0.113/ 0.028/

The fractional flows must sum to 1.0: 0.246 0.347 0.326 0.081 5 4 7 8 Notice how there is just as much water going W (value 5) as to SW (value 4) even though the value of the SW cell is lower. This is because the drop to the southwest corner is spread over a longer distance because it is in the diagonal direction, so the slope to the corner cell is reduced. For more details, refer to Quinn et al. (1991).

FD8 SCA PTR 255

D-infinity flow routing algorithm Defines flow direction as the steepest downward slope among the 8 triangular facets 3 2 Facet number 4 1 5 8 6 7 Flow direction measured as counter-clockwise angle from east

Steepest downslope direction If flow direction does not follow one of the cardinal or diagonal directions, it is split between the two downslope cells according to how close the flow angle is to the direct angle to that source cell. The split is ‘inversely proportional’ to the angular distance of the flow direction (i.e. how many degrees away) from the closest cells to this flow direction. Proportion of flow to this cell is 1/(1+2) Steepest downslope direction Proportion of flow to this cell is 2/(1+2) 1 2 3 2 3 2 4 1 4 1 5 8 5 8 6 7 6 7

Consider the following example: NW N NE 40 degrees 3 2 5 degrees 4 1 W E 5 8 6 7 SW S SE The steepest slope is in Facet ‘1’. NE and E cells are the two closest to this direction, with angular distances of 40 and 5 degrees respectively.

For the NE cell, the ‘inversely proportional’ value is VNE =1/40=0.025 NW N NE 40 degrees 3 2 5 degrees 4 1 W E 5 8 6 7 For the NE cell, the ‘inversely proportional’ value is VNE =1/40=0.025 For the E cell, VE=1/5=0.20 Flow is apportioned as follows: flow that goes to the NE cell is PNE=0.025/(0.025+0.20)=0.111 flow that goes to the E cell is PE=0.2/(0.025+0.20)=0.889 therefore, 11% of the flow goes to NE cell and 89% of the flow goes to E cell For more details, refer to Tarboton (1997) SW S SE

Dinf SCA PTR 360

Which flow routing algorithm derives the correct representation? FD8 D-infinity

Use of Topographic Indices in Environmental Models Topography is a major determinant of water erosive agents and transporting mechanisms Topographic attributes can be divided into: -primary attributes -directly calculated from the DTM -secondary attributes -combinations of primary topographic attributes -empirically derived or physically based -used to characterize spatial distribution of hydrological, geomorphological and ecological processes

Use of Topographical Indices in Environmental Models Attribute Significance Altitude Climate, vegetation, soil characteristics Aspect Solar energy, evapotranspiration, flora and fauna distribution and abundance Slope Surface and subsurface flow velocity and runoff rate;geomorphology; soil characteristics (texture, depth, moisture nutrients) Upslope slope Runoff velocity Dispersal slope Rate of soil drainage Upslope area Runoff volume

Use of Topographical Indices in Environmental Models Dispersal Area Rate of soil drainage Specific contributing or catchment area Runoff volume; geomorphology; soil characteristics (texture, depth, moisture, nutrients) Upslope length Flow acceleration; rate of erosion Dispersal length Flow path length Rate of erosion; sediment yield Profile curvature Flow acceleration; erosion/deposition rate; geomorphology Plan curvature Flow convergence/divergence; soil characteristics

Use of Topographic Indices in Environmental Models Secondary (or compound) Attributes: Attribute Significance Wetness Index Index of soil water content Erosion Index (Stream Power) Index of erosive power of overland flow Erosion Index (Sediment Transport) Index of erosion and deposition processes