Drainage networks

The basis for the derivation of many hydrologic parameters is a drainage network, which can manually be digitised into a grid or extracted automatically. The latter is usually the case. You will learn how to do this in the following sections. Local drain directions (i.e. flow directions) in grids are often coded according to the numeric pad on a computer keyboard. A cell discharging southwest would therefore be allocated the value 1, a cell discharging west would be allocated the value 4 and so on.

Local drain directions in a raster can be represented by the numbers on a keyboard.

A map assigning a local drain direction to each grid point is called a local drain direction net or ldd net (Burrough et al. 1998). Various algorithms exist for computing ldd nets, each based on different assumptions on the drainage of water in the terrain.

D8 Algorithm

The D8 algorithm is based on the quite strict assumption, that within a window of 9 cells water always flows in the direction of the steepest slope. I.e. the slope to each of the 8 neighbours of a central source cell has to be computed using the following formula:

where d is the distance and $\Delta z$ is the elevation difference between two grid points. In a raster, where the cell width is 1 we have to distinguish between two cases:

• If we calculate the slope in the direction of north, east, south, or west, the distance d between the grid points is 1.
• If we want to calculate the slope in diagonal directions (northeast, southeast, southwest, northwest), the distance d between the grid points is $\sqrt{2}$.

The local drain direction net - ldd net

We now know how to calculate the local drain direction for a single cell in the center of a window of 9 cells. By moving the window stepwise through the entire map we can assign a local drain direction to every cell and get a "local drain direction net" or "ldd net" at the end.

Local drain direction net (ldd net) for a small DTM. Left: Local drain directions coded as arrows. Right: Local drain directions coded according to the numeric pad on a computer keyboard.