ANÁLISIS DEL MARKETING MIX

Repeated aerial photography of upland catchments over a period o f 20-30 years (depending on availability) can provide the basis for assessing the differences in the drainage o f low-order stream networks. Some o f the factors which may reflect environmental change are the extension o f first-order streams, and also, the way in which observed changes in stream morphology may be correlated with past hydrological observations and records.

Two sets of aerial photographs, covering the central part o f the Whitendale River catchment, Lancashire County, (Fig. 3.8) spanning a 25-year period, were used as an independent check on cartographic data. The first photoset is black and white, consisting of five photos, obtained in June 1963 at a scale o f 1:10 560. The second set consists of three photos and is part of the most recent aerial survey of the Lancashire County completed in the summer of 1988. It consists o f three colour aerial photographs at a scale of 1:10 000. All aerial photographs have been scanned and converted to .tiff files which is a form of raster map. The colour ranges o f the scanned image are dependent on the hardcopy input and the sensitivity of the scanning device. The images were subsequently imported into the ARC/INFO platform and converted into grid files for further processing. A linear contrast stretch was applied for image contrast enhancement. This is a very common method applied in greyscale images, to remap the actual cell values onto the range of possible grey shades. ARC/INFO offers the opportunity of processing between multiple grids but first they need to be registered before completing any analysis. Each location on the ground must be represented by the same x,y cell address on the different input grids, which means that all images have to be on the same planar coordinate system, because in processing between multiple grids, the cell resolution, like the registration, needs to be the same. Registering data allows it to be viewed

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Fig. 3.9 June 1963 aerial photograph o f the central part o f the W hitendale River catchment

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Fig. 3.10 July 1988 aerial photograph o f the central part o f the W hitendale River catcliment

concurrently with other spatially referenced data. It is a very time-consuming process in terms o f computer resources and also needs a lot o f disc space and a fast CPU.

From a first visual inspection, photograph 1015 from the black and white set (Fig. 3.9) and photograph 030 (Fig. 3.10) from the colour set were selected for an initial pilot analysis, as the ones presenting the most interest in terms o f overall channel network coverage. A basic problem in greyscale images is that it is impossible to use the automatic tracing tool, because the cells that constitute features on the image do not have a homogeneous cell value, although they may appear the same. Automatic raster to vector conversion cannot be applied either, since a greyscale image does not have clear raster lines. Although ARC/INFO permits tracing, it does not allow the saving o f the traced networks as individual files, so stream extraction was finally done by digitising the network.

Figure 3.11 shows the extent o f the network as extracted from the 1963 aerial photo for part o f the Whitendale River and Figure 3.12 shows the same part of the network as seen on the 1988 photo. The two set of aerial photos clearly show profound differences in the network extent for the two dates. A first inspection revealed differences especially in the number of first order streams. The basic Horton ratios have been calculated for the two networks and are shown respectively on Tables 3.3 and 3.4. The number of first order streams has increased by four from 17 to 21 between 1963 and 1988. However, given the fact that defining what constitutes first order streams from aerial photography is a very subjective task, and subject to considerable operator variance, this slight increase seems to have no considerable significance. Likewise, all the relevant morphometric parameters indicative of network configuration were calculated for the two networks: bifurcation ratio Rg and stream length ratio R^. Results again show insignificant variations between the two networks. There is strong indication that the two networks are not fundamentally different when simple geomorphic measures are taken into account. From Tables 3.1 and 3.2, it can be seen that:

Fig. 3.11 Extent of channel network of the 1963 photo (1:10560) Whitendale River

Fig. 3.12 Extent of channel network o f the 1988 photo (1:10000) Whitendale River

i) interpretation of aerial photography is extremely subjective and therefore a rather poor means for obtaining accurate information on the extent o f drainage networks and especially first order streams in an upland environment with a low contrast between vegetation and channels.

ii) there is a dramatic increase in the number of first order streams between successive editions o f OS maps.

iii) there is in general an overall progressive increase in the total length o f all streams from the first order source streams to the trunk fourth order stream, between successive editions of OS maps.

u Nu _Rb ZLu (km) _{L u (km) E L u Rl}

1 17 4.12 7.49 0.44 0.44 2.97

2 5 2.64 0.53 0.97

3 1 2.81 2.81 3.78

Table 3.3 Network parameters from the 1963 aerial photography

u Nu _Rb ELu (km) _{L u (km) E L u Rl}

1 21 4.6 8.65 0.41 0.41 2.9

2 5 2.83 0.56 0.97

3 1 2.51 2.51 3.48

Table 3.4 Network parameters from the 1988 aerial photography

iv) changes in the number and length o f stream channels are accurately mirrored in the adjustment of network measures such as Rg and R^ between the different temporal representations of the same channel network.

As stated earlier, the network width function seems to be an extremely promising avenue for gaining a quantitative understanding o f the dynamics of channel-network evolution (e.g. Wharton, 1994). The drainage networks as viewed at two different instants in time, extracted from the existing two sets o f aerial photography, will be exploited to provide the basis for the subsequent analysis. The 1963 channel network which as stated earlier represents only part o f the total network is 12.94 km long, and the 1988 network is 13.99 km long. The unit distance which is needed for the calculations is derived when the total channel network length is divided by the total number o f links. The unit distance for the 1963 network is 0.39 km and for the 1988 network is 0.32 km. The network width function was calculated and plotted for the 1963 and 1988 networks (Fig. 3.13) as well as for the dimensionless equivalent (Fig. 3.14). All of the graphs indicate the existence of a distinctly bimodal population, the major peaks appearing at roughly one third and two thirds o f the channel network length, which is a very intriguing finding. This preliminary finding clearly shows the existence of a distinct mode of distribution and is therefore worthwhile exploring further, within a bigger and more complete dataset, such as that provided from topographic maps. Moreover these results relate fairly well with the statistical distributions obtained from Parker’s (1977) experimental network analysis.