POR DEBAJO Y POR ENCIMA DE LA TIERRA

A variety of methods has been used to automatically delineate a stream network from a DEM using characteristics of the local landscape morphology, such as terrain curvature (e.g. Tarboton and Ames, 2001). Most often however, stream networks are delineated by application of a critical support area threshold that defines the minimum contributing area required to initiate a channel (Jenson, 1991; Montgomery and Foufoula-Georgiou, 1993; Verdin and Verdin, 1999; Hutchinson, Stein et al., 2000) (Figure 3.5). The threshold is assumed to represent the level of runoff concentration at which fluvial processes dominate over hillslope processes (O'Callaghan and Mark, 1984). Grid cells with an upstream contributing area greater than the specified threshold are considered to belong to the channel network. The choice of threshold value determines the density of the resulting drainage network; increasing the threshold contributing area leads to an exponential decrease in the channel network extent and the drainage density (Thieken et al., 1999). In practice, threshold values have often been chosen to suit the

3.2 37

Figure 3.5. Delineating a stream network by application of a contributing area threshold . Cells with contributing areas above the designated threshold are considered to belong to the stream network. Contributing areas are computed by accumulating the area of all upstream cells according to the flow direction.

that most closely resembled the streamlines shown on topographic maps (Montgomery and Foufoula-Georgiou, 1993). However, these streamlines reflect subjective cartographic interpretation and generalization and may underestimate the actual channelised flow network (Montgomery and Foufoula-Georgiou, 1993; Gandolfi and Bischetti, 1997; Knighton, 1998; Hansen, 2001).

Tarboton and his colleagues (1991; 1992) proposed quantitative means of identifying

appropriate threshold values, invoking the observed scaling laws of channel networks (constant drop property and power law scaling of slope with area). They suggested the contributing area threshold could be identified from the breakpoint in the log-log plot of link slope against contributing area, assumed to differentiate the change from diffusive hillslope to fluvial channel processes. Montgomery and Foufoula-Georgiou (1993) subsequently pointed out a number of problems with Tarboton et al.’s implementation suggesting an alternative formulation based on local, rather than link (segment) slopes. They also noted that the point of inflexion generated threshold values that implied anomalously large hillslope lengths and that using the point of reversal in the direction of the slope-area relationship was more consistent with theory. The TAUDEM terrain analysis software package (Tarboton, 2004) implements the constant drop scaling procedure. The program identifies the smallest contributing area value that delineates a stream network consistent with the "constant drop law" i.e. a network where the mean stream drop of first order streams is not significantly different from the mean drop of higher order streams. Stream drop is the difference in elevation between the beginning and end

3.2 Delineating a new catchment framework 38 of Strahler streams, where a Strahler stream is an entire set of sequential stream segments of the same stream order.

However, no single threshold value is likely to be appropriate over large areas with

heterogeneous terrain types in which different geomorphic processes dominate (Soille et al., 2003). Applying a uniform contributing area threshold to delineate a stream network may overcome some of the limitations of topographic mapping attributed to cartographic

interpretation, but is not adaptive to the spatial variability in drainage density. Accounting for the role of the local slope in the channel initiation process provides a mechanism for spatially variable drainage density (Tarboton and Ames, 2001). The observed inverse relationship between gradient and catchment area for channel heads (Montgomery and Dietrich, 1989; Montgomery and Foufoula-Georgiou, 1993), yields a slope dependent channelization threshold of the form

aSα _{> C}

where a is specific catchment area and S is slope, α is usually equal to 2 and C is a

proportionality constant that depends on both ground surface (soil properties and vegetation cover) and climate (Montgomery and Foufoula-Georgiou, 1993). This model produces higher drainage densities where slopes are steeper, as observed for natural landscapes, leading Montgomery and Foufoula-Georgiou (1993) to suggest that it is both theoretically and

empirically a more suitable model than the constant contributing area threshold for defining the extent of channel networks, except where bedrock properties control channel head locations. As the value of aSα _{can decrease downstream with declining slope this model is only necessarily}

valid at channel heads (Lindsay 2003).

Again, however, identifying a suitable threshold may be difficult. A uniform threshold will not be appropriate across large areas. Field observations reveal considerable noise in the

relationship between slope and catchment area at channel heads (e.g. Menduni et al., 2002) and it appears that the gradient of this relationship may vary across drainage basins (Kirkby et al., 2003; Moeyersons, 2003). Tarboton and Ames (2001) also report that applying the slope- dependent area threshold produces “feathering” of the drainage network in steeper areas while underestimating the extent of the drainage network in shallower valleys. Montgomery and Foufoula-Georgiou (1993) attribute feathering to the use of an inappropriate value for the proportionality constant C, suggesting the Tarboton and Ames conclusion could be the result of applying a uniform threshold value across a geomorphologically heterogeneous area.

Istanbulluoglu et al. (2002) characterize the observed variability in the channel initiation threshold by treating C as a random variable. Their model derives a spatially variable probability of channel initiation that depends on slope, specific catchment area, and the

3.2 Delineating a new catchment framework 39 model, the channel initiation zone on the slope-area plot varies depending on model input values that characterize climate and landcover variability.

Vogt, Colombo and Bertolo (2003) recognized a broad range of environmental controls on drainage density needed to be considered in order to derive continentally applicable contributing area thresholds. They first identified landscape types delineated according to values of a

drainage density index. The index was derived as a function of environmental factors (climate, vegetation cover, relief, soils and lithology) that were believed to exert a strong control on channel initiation and therefore, the development of the stream network. Type specific

contributing area thresholds were then determined by identifying the breakpoint on plots of the slope-area relationship for each landscape type. Vogt and his colleagues applied the method in Italy yielding threshold values of 3, 10, 50,100 and 700km2 _{respectively for each of the five}

landscape types. While they found the derived patterns of spatial variability of drainage density were reasonable, the threshold values are significantly greater than those reported by other workers, suggesting that they probably underestimated the extent of the true channel network. Wasson (1998), for example, notes that the upstream catchment areas of headwater channels are generally of 1ha or less. Similarly, Montgomery and Foufoula-Georgiou (1993) find

contributing areas of considerably less than 1km2 _{at field mapped channel heads.}

These discrepancies highlight the difficulties that confront automated delineation of channel networks over very large and heterogenous areas. There is a significant mismatch between the scale of the channel initiation processes that these methods seek to model and that of the available information on the controlling factors. Vogt, Colombo and Bertolo (2003), for example, used soil transmissivity classes derived from soil texture information provided on the 1:1,000,000 scale European Soil Map to describe the influence of soil properties on drainage density, but at this scale mapping units include considerable variability in soil parameters (Jamagne et al., 2001). Hillslope lengths, directly correlated with drainage densities are typically in the range of tens to hundreds of metres (T.Dunne unpublished data cited in

Montgomery and Foufoula-Georgiou, 1993; Gallant, 2001), in many instances smaller than the size of an individual grid cell in the 250m resolution DEM used by Vogt et al. in their Italian study. The accuracy of slopes derived from the DEM is a critical limitation on the application of slope-dependent thresholds (Roth, LaBarbera et al., 1996). Derived slopes are particularly sensitive to the DEM resolution. As the grid cell size increases short, steep slopes are

increasingly likely to be missed (Wilson et al., 2000; Gallant, 2001; Clarke and Burnett, 2003). Even high resolution (1m) DEM’s typically underestimate true slopes (Warren et al., 2004). Indeed, Montgomery and Foufoula-Georgiou (1993) concluded that the extent of the channel network could not be directly determined from the drainage area-slope relations extracted from a DEM and that field data were necessary to identify appropriate parameters. Miller (2002) also

3.2 Delineating a new catchment framework 40 reasoned that it was not feasible to accurately locate channel heads from a DEM and therefore the goal should be to select threshold values that reproduce realistic drainage densities.