Drainage Density Calculator

Drainage density is the summed length of every channel in a basin divided by basin area, giving kilometres of channel per square kilometre. It measures how finely a landscape has been dissected, and it carries a direct hydrological meaning: its reciprocal is the constant of channel maintenance, the basin area required to sustain one kilometre of channel, and half that reciprocal approximates the mean length of overland flow that a raindrop must cross before reaching a channel. Related indices computed alongside it include stream frequency, the number of segments per square kilometre, the infiltration number formed by multiplying density and frequency, the texture ratio of segment count to basin perimeter, and the circularity ratio, four times pi times area divided by the square of perimeter, which equals 1.0 for a perfect circle and falls toward 0.3 for elongated basins. Humid temperate basins commonly fall between 2 and 5, permeable chalk and karst terrain often below 1, and clay badlands can exceed 100. The overriding caveat is that drainage density is not a fixed property of the ground but a property of the map. It depends entirely on what is counted as a channel. Blue lines traced from a topographic sheet at 1:24,000 yield far lower values than a network extracted from a one-metre lidar surface using a small contributing-area threshold, and changing that threshold alone can move the result by a factor of five or more on identical terrain. Comparisons between basins are therefore only meaningful when source scale, extraction algorithm and threshold are held constant, and reported values should always be qualified by the mapping method used.

Drainage density was introduced by Robert E. Horton, an American hydraulic engineer who ran a private hydrological laboratory at Voorheesville, New York. He proposed the measure in a 1932 paper on drainage-basin characteristics and developed it fully in his 1945 paper in the Bulletin of the Geological Society of America on the erosional development of streams and their drainage basins, the same work that set out his laws of stream numbers and lengths and the concept of a belt of no erosion on hillslope crests. Horton's aim was to make basin form a measurable input to runoff prediction rather than a matter of description. Arthur N. Strahler and his students at Columbia University carried the programme forward through the 1950s, revising the stream ordering scheme in 1952 and 1957 and placing the morphometric indices on a statistical footing so that basins could be compared through significance tests. Stanley Schumm's 1956 study of the badlands at Perth Amboy, New Jersey introduced the constant of channel maintenance and documented the extreme densities possible on bare erodible clay. Mark Melton's 1957 work related density to climate through a precipitation-effectiveness index, establishing the link between aridity, vegetation cover and dissection. Interest revived once digital elevation models allowed automatic channel extraction, following the flow-routing algorithm of O'Callaghan and Mark in 1984 and later threshold analyses, which quantified how strongly the reported value depends on the extraction criterion.