Topographic Wetness Index Calculator

The topographic wetness index balances water supplied against water drained away. The numerator, specific catchment area, is upslope contributing area divided by the contour width it crosses, giving units of square meters per meter and representing the flow delivered per unit width of hillslope. The denominator, the tangent of local slope, is the hydraulic gradient driving that water onward under a kinematic assumption that the water table parallels the ground surface. Their ratio has units of length, and the logarithm compresses a strongly right-skewed distribution into the familiar range of roughly 2 to 20. Values under 6 correspond to ridgetops and steep well-drained slopes, 6 to 9 to mid-slope positions, 9 to 12 to convergent footslopes, and above 12 to floodplains and valley bottoms. The modified form divides additionally by soil transmissivity, the product of saturated hydraulic conductivity and soil depth, so that permeable or deep soils are correctly shown as harder to saturate. Several assumptions constrain interpretation. The index is a steady-state construct with no time dimension, so it ranks locations by relative wetness rather than predicting moisture on any given day. It presumes topographic control of flow, which fails where fractured bedrock or deep permeable substrate routes water independently of the surface. Flat cells are a numerical hazard because tangent of slope approaches zero and the index diverges, so a minimum slope must be imposed. Results also depend heavily on the flow routing algorithm, with D8 producing artificial parallel flow lines while D-infinity and multiple-flow-direction methods distribute area more realistically across divergent slopes.

The index emerged from a shift in how hydrologists understood storm runoff. The prevailing view held that runoff arose from rainfall exceeding infiltration capacity across a whole catchment, but field work in forested basins during the 1960s, including the variable source area concept of John Hewlett and Alden Hibbert, showed instead that runoff came from limited saturated areas near channels and hollows that expanded and contracted during a storm. Explaining which parts of a hillslope saturate first required a way to rank locations by their tendency to accumulate water. Mike Kirkby had been developing exactly that at the University of Leeds, and in 1979 Keith Beven and Kirkby published in the Hydrological Sciences Bulletin the variable contributing area model that became TOPMODEL, in which the index ln(a/tan beta) serves as the similarity measure identifying points expected to behave hydrologically alike. The formulation proved unusually portable, migrating out of rainfall-runoff modelling into soil science, ecology, and landslide hazard work as a topographic proxy for soil moisture. Refinements followed in the routing step, with Quinn and colleagues introducing multiple flow direction in 1991 and David Tarboton publishing the D-infinity method in 1997. Beven himself later wrote critically about how far the index had been stretched beyond its assumptions, and Sorensen and coauthors documented in 2006 how much computed values vary with algorithmic choices.