3 METODOLOGÍA
3.18 DISEÑO DEL PLAN DE MERCADEO
3.18.9 VII EVALUACIÓN DE RESULTADOS
3.1.3.1 The network width function for Parker’s Experiment 1
The number o f links -internal and external- was counted and then used to calculate the unit distance (network length divided by the total number o f links) for each successive Network in Parker’s Experiment 1 (Table 3.1), in order to derive the network width function. All the network width function diagrams share some common characteristics but also exhibit some differences. In order to be able to analyse the network width function diagrams more objectively without the effect of network growth embedded within their structure, and construct a common framework o f reference, they were plotted in their dimensionless form which is obtained if the horizontal x-axis is expressed not as absolute distance but as a dimensionless distance upstream from the outlet to the source. In the same respect
the vertical y-axis shows the percentage unit length o f the total channel network. The graph for Network 1 is weakly bimodal and right skewed with one peak about one third of the distance from the outlet upstream, and the second peak in the headwaters. The one for Network 2 is rather multimodal. The graphs for Networks 3 and 4 are clearly bimodal and left skewed, with one peak near the mid-catchment reaches and the other near the upstream edge. The graph for Network 5 is again rather bimodal, with the peaks located at about one third and two thirds o f the total channel network length (Fig. 3.4). The same can not be said for Network 6, which seems rather multimodal. The diagram for Network 7 is undoubtedly bimodal and left skewed, with the peaks found at about the middle of the network length and near the headwaters. The network width function for Network 8 is rather hard to describe, although the existing peaks are found from the middle o f the catchment and upstream. Bimodality is not very clear for Network 9, which is nevertheless strongly left skewed. Finally the graph for Network 10, is both very strongly bimodal and also left skewed (Fig. 3.5). In summary, during the natural cycle o f network development, after the initial expansion at the available area, growth progresses with further development mainly at the middle reaches, and only baselevel lowering creates increased potential for expansion at the uppermost reaches.
These diagrams allow a true assessment o f the network’s development to be made through time. From this sequence o f diagrams the following findings are highlighted:
a) There is a progressive propagation of network growth from the outlet to the source in the form o f a moving wave which is slowly migrating upstream.
b) There is a marked shift in skewness from the right (upstream reaches) to the left (downstream reaches) o f the graphs through time, again indicating the headward- migrating network evolution.
c) The occurrence o f bimodality indicates the existence o f certain loci of increased activity within the network structure, these being located roughly at 1/2 and 2/3 of the channel length from source to outlet, for Network 6 which represents maximum extension, before baselevel was lowered.
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84 100 10 5 0 20 36 52 68 84 100 10 5 0 20 36 52 68 84 100 10 - 5 - 0 20 36 52 68 84 100 10 5 0 - 20 36 52 68 84 100Fig. 3.4 N etw ork width function o f Parker’s (1977) Experiment 1, times 1-5 from top to bottom. X-axis is dimensionless distance upstream from outlet to source, y- axis is percentage unit length o f total channel network
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84 100 20 36 52 68 84 100 10 5 0 20 36 52 68 84 100 20 36 52 68 84 100 10 5 0 20 36 52 68 84 100Fig. 3.5 N etwork width function o f Parker’s (1977) Experiment 1, tim es 6-10 from top to bottom. X-axis is dimensionless distance upstream from outlet to source, y- axis is percentage unit length o f total channel network
Network Internal Links External Links Unit Distance 1 24 25 0.71 2 36 37 0.75 3 73 74 0.69 4 98 103 0.62 5 109 110 0.67 6 151 163 0.61 7 215 220 0.51 8 272 278 0.53 9 342 348 0.49 10 470 483 0.44
Table 3.1 Morphometric measurements o f Parker’s Experiment 1
Network Internal Links External Links Unit Distance
1 23 24 1.3 2 63 64 1.15 3 80 81 1.15 4 101 102 1 5 113 114 1 6 148 152 0.77 7 115 116 0.95 8 64 65 1.3
d) These two distinct peaks o f the bimodal distribution persist till the end of the experiment, underlining the fact that these two locations on the network maintain the greatest potential for expansion. This contradicts conventional held ideas that only the uppermost upstream reaches of a channel network can undergo extension.
3.1.3.2 The network width function for Parker’s Experiment 2
The same procedure was followed as above in order to calculate the network width function for Experiment 2. Table 3.2 shows the relative network indices used for the calculations o f the network width function. The network width function for Network 1 is highly bimodal, with one peak found at about one third and the other at about two thirds o f the distance upstream from the source. The graphs for Network 2 and 3 do not seem to exhibit any particular type o f distribution, however there is a great concentration o f links near the mid-basin reaches. The graph for Network 4 exhibits a rather weak bimodality, with one peak near the middle o f the catchment and the other close to the source (Figure 3.6). The graphs for Networks 5 through 8 are strongly left skewed (Figure 3.7). In summary, findings from that experimental setup indicate a rather different picture o f network growth compared to Experiment 1. Initial rapid growth, especially elongation o f the channel network at the downstream reaches, shifts very rapidly towards the upstream reaches o f the experimental catchment by stage 3 and this rigorous upstream growth is even more clearly manifested by stage 5. Between stage 5 and stage 8 when the experiment was terminated there is in general a rather slight change in overall network extension between different regions in the network structure.
From this sequence of diagrams the following findings are outlined below:
a) The initial downstream extension rapidly moves towards the upstream reaches of the channel network.
b) There is a very distinctive shift in skewness from the right (downstream reaches) to the left (upstream reaches) of the diagrams, just as in Experiment I.
c) The structure of the network width function diagrams is far simpler compared to Experiment I . Due to the rapid elongation of low-order channels, network drainage
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X i ê •1 20 36 52 68 84 100 10 5 0 20 36 52 68 84 100 20 36 52 68 84 100Fig. 3.^ N etw ork width function o f Parker’s (1977) Experiment 2, times 1-4 from top to bottom. X-axis is dim ensionless distance upstream from outlet to'Source, y- axis is percentage unit length o f total channel network
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Fig. 3.7 Network width function o f Parker’s (1977) Experiment 2, times 5-8 from top to bottom. X-axis is dimensionless distance upstream 'from outlet to source, y- axis is percentage unit length o f total channel network
areas are quickly filled, leading to maximum extension by stage 3, after which abstraction occurred. However, even during abstraction, new first-order streams were initiated at the basin periphery, giving rise to a fairly even distribution of network growth along the network.
An extensive analysis of the network width function variations for two different kinds of experimental networks, produced under different initial conditions, was undertaken. This allowed the compilation o f a comprehensive and detailed database of the mechanics o f network development, for what is recognised as the most comprehensive set of experiments in its kind. It should be underlined that the quality of the output statistics partly relates to the unit distance used for deriving the network measure and because the overall shape of the network width function is not very sensitive to map scale, we can be fairly confident about measured change in the catchment structure. The output of the network width function distribution from Parker’s experiments demonstrated the capacity of this particular morphometric measure in portraying network evolution through time.
Drainage network development on newly exposed surfaces is dependent upon several factors such as underlying geology, soil infiltration capacity, slope etc. This sequence of progressive changes under controlled conditions through time could potentially serve as a reference framework for the comparison with real world networks from the Pennines as these are depicted from OS maps. However, these results should be interpreted with caution as the repeated base-level lowerings have little real bearing on the actual situation in the uplands. It is therefore needed to proceed to examine the degree to which the results from the laboratory derived experimental networks have any bearing with natural networks. It is envisioned that the combination of the network width function with the link concentration function will provide us with a new technique capable o f assessing the current stage of network growth in the English uplands. This method will also enable us to quantify recent adjustments of the channel network due to environmental modifications and could even provide indications as to its near future adjustment to ever-changing climatic conditions.