There are eight valid output directions relating to the eight adjacent cells into which flow could travel. This approach is commonly referred to as an eight direction (D8) flow model and follows an approach presented in Jensen and Domingue (1988).
The direction of flow is determined by finding the direction of steepest descent, or maximum drop, from each cell. This is calculated as
maximum drop = change in z-value / distance
The distance is determined between cell centers. Therefore if the cell size is one, the distance between two orthogonal cells is one and the distance between two diagonal cells is 1.414216, the square root of two. If the maximum descent to several cells is the same, the neighborhood is enlarged until the steepest descent is found.
When a direction of steepest descent is found, the output cell is coded with the value representing that direction.
If all neighbors are higher than the processing cell, the processing cell is a sink and has an undefined flow direction. Cells with undefined flow direction can be flagged as sinks using the Sink function. To obtain an accurate representation of flow direction across a surface, the sinks should be filled.