The in(a/tan/β) index: How to calculate it and how to use it within the topmodel framework

Abstract

Topographic indices may be used to attempt to approximate the likely distribution of variable source areas within a catchment. One such index has been applied widely using the distribution function catchment model, TOPMODEL, of Beven and Kirkby (1979). Validation of the spatial predictions of TOPMODEL may be affected by the algorithm used to calculate the model's topographic index. A number of digital terrain analysis (DTA) methods are therefore described for use in calculating the TOPMODEL topographic index, ln(a/tanp) (a = upslope contributing area per unit contour; tan@ = local slope angle). The spatial pattern and statistical distribution of the index is shown to be substantially different for different calculation procedures and differing pixel resolutions. It is shown that an interaction between hillslope contributing area accumulation and the analytical definition of the channel network has a major influence on calculated ln(a/tanp) index patterns. A number of DTA tests were performed to explore this interaction. The tests suggested that an 'optimum' channel initiation threshold (CIT) may be identified for positioning river headwaters in a raster digital terrain model (DTM). This threshold was found to be dependent on DTM grid resolution. Grid resolution is also suggested to have implications for the validation of spatial model predictions, implying that 'optimum' TOPMODEL parameter sets may be unique to the grid scale used in their derivation. Combining existing DTA procedures with an identified CIT, a procedure is described to vary the directional diffusion of contributing area accumulation with distance from the channel network.

Delineation of Valleys and Valley Floors

“…Examples in geomorphology include the topographic wetness index [18,19] and the stream power index [10].…”

Resolution Sensitivity of a Compound Terrain Derivative as Computed from LiDAR-Based Elevation Data

“…Subsequently, the TWI was calculated using ArcGIS [28] and SAGA GIS [29]. The computation included a fill operation and the use of a multiple flow direction algorithm (MFD) according to Quinn et al [30], [31]. This approach was recommended by Beven [2].…”

“…The catchment area per unit contour length was derived from this by applying a division by contour length. Contour lengths were computed l = 0.427 · resolution, where 0.427 is the mean of contour length for diagonal and cardinal neighbours [30], [31]. Gradient was computed by fitting a 2 nd degree polynomial [32].…”

Índices topográficos aplicados à modelagem agrícola e ambiental

“…Os índices topográficos primários (ITP) são calculados diretamente do MNE e representam as características básicas, como, por exemplo, declividade, aspecto e área acumulada; enquanto os índices topográficos secundários (ITS) são calculados por meio da combinação de dois ou mais índices primários e representam características mais complexas, como, por exemplo, umidade do solo ou potencial erosivo (MOORE et al, 1991). Eles são requeridos nos modelos ambientais como informação necessária para inúmeros procedimentos de cálculo, por exemplo, o uso do aspecto para o cálculo do balanço de energia, ou para representar processos de difícil medição, por exemplo, o uso da declividade e área acumulada para determinar as zonas de saturação de água na paisagem (RICHERSON & LUN, 1980;QUINN et al, 1995;2002). Os principais ITPs provenientes do MNE (Tabela 1) utilizados na modelagem matemática de inúmeros processos com aplicação no planejamento agrícola e ambiental são apresentados na tabela 1 (MOORE et al, 1991).…”