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For example, if cell x flows to the left in the matrix, its flow directionwill be encoded as a 32. Flow direction encoding is done in powersof two so that surround conditions correspond to unique values whenthe powers of two are summed for any unique set of neighbors.There are four possible conditions to consider in determining flowdirection (Table 4). Condition 1 occurs when all eight neighboringcells have elevations higher than center cell. The flow direction willbe encoded as negative for such a cell, indicating an undefined flowdirection. Condition 1 cells are single-cell depressions. They willnot be present after the first step of the depression-filling procedurebut are included in the flow direction procedure for completeness.Condition 2 is the case where the distance-weighted drop from thecenter cell is higher for one cell in the neighborhood over all of theother seven and the flow direction is assigned to this cell. Distanceweighteddrop is calculated by subtracting the neighbor’s value fromthe center cell’s value and dividing by the distance from the centercell, √2 for a corner cell and one for a noncorner cell. Most cells arecondition 2 cells. For condition 3, when two or more cells are equalin having the greatest distance-weighted drop, the flow direction isassigned logically using a table look-up operation. For example, ifthree adjacent cells along one edge of the neighborhood have equaldrops, the center cell is logically chosen and assigned as the flow
direction. If two cells on opposite sides have equal drops, as in Table
4, condition 3, one is arbitrarily chosen. When all cells are equal or
greater in elevation compared to the center cell, as in condition 4,
determining the flow direction is the most time consuming. In this
case, the cell is located in a flat area and the direction to the outflowpoint
is not known. After cells with the first, second, and third
conditions are resolved, the fourth condition cells are resolved in an
iterative process. In each iteration, cells are assigned to flow to a
neighbor if the neighbor has a defined flow direction that does not
point back to the tested cell. In this way, flow direction assignments
iteratively grow into the flat area from the flats’ outflow points until
all cells have flow directions assigned.
The flow direction concept has been employed by both Marks et al.
(1984) and O’ Callaghan and Mark (1984). However, neither
included logic for condition 3 cells or extended the technique beyond
the neighborhood operation to solve for condition 4 cells. When the
flow direction procedure is applied to a depressionless DEM, all cells
will have a definable flow direction value because, by filling
depressions, the DEM is conditioned so that every cell has a flow
path to the data set edge. The flow direction is illustrated
numerically in Table 2c, and visually in Plate 1b.
FLOW ACCUMULATION DATA SET
The third procedure of the conditioning phase makes use of the flow
direction data set to create the flow accumulation data set, where each
cell is assigned a value equal to the number of cells that flow to it
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