Having set out the ways in which data can be collected for use in the spatial decision-making exercise, we are in a position to see how the data can be used. Referring back to Figure 1.3 (p.6), it can be seen that raw data is either used as the basis of drawing up various forms of maps, or it can be entered directly into the GIS. This chapter will be concerned with the use of maps as the input to optimizing spatial decisions on aquaculture and inland fisheries. These maps can either be used as they are, or more usefully they can be digitized and can represent the major input to GIS.
Our account about maps needs to be prefaced by a few general cautionary remarks. In performing any task which attempts to utilize and combine a great deal of disparate data in order to produce a series of maps which will be of use in satisfying a single, rather specific, objective - in this case seeking locations for given enterprises in given areas at the present time, or in the near future, then there are bound to be many limitations which must be borne in mind when interpreting the results, e.g.:
Factors relating to scale - the data sources will have varying scales and the optimum scale to be working at will vary from case to case.
Amount of detail - all source material will have been collected showing a different degree of detail, with varying degrees of accuracy and generalizations and having certain simplifying assumptions.
Dating differences - rarely will combinations of data all have the same date and the subjects being dated will “date” at different rates.
Degree of applicability - much data will have been purposefully collected; other sources might be “proxy” data, i.e. the best available.
Availability - all data varies greatly in its cost, its diffusion level (how well it is known) and how easy it is to acquire.
Each country or region will have its own spatial inventory processes, preferences and standards and the interested reader ought to find these out to his or her own satisfaction.
This chapter will comprise of three main sections. Firstly, we will examine the fundamental type of map, a topographic map. From this type virtually all other maps can be successfully produced. The main sub-category of maps produced are thematic maps - these will be looked at both generally and with regard to the main production functions. Finally, what may be called “derived” maps are considered. These represent a type of “proxy” map - one that has been specifically produced for a particular purpose, it usually having been created from a variety of data sources and it is usually only made for a “one-off” situation. It is important to cover this area in some detail because it is the logic behind the construction of the derived maps which will be crucial to the success of GIS, i.e. since the quality of the output gained must principally be related to the quality of the data inputs.
These are general purpose maps whose main function is to portray and identify features of the Earth as faithfully as possible having regard to the imposition set by scale. They are the typical product of most national mapping agencies, and are usually produced in series which consist of all the necessary sheets to cover one region at one scale. Many different scales may be produced and these are typically classified as follows:
| Large scale | 1:1250 to 1:25 000. |
| Medium scale | >1:25 000 to 1:200 000. |
| Small scale | >1:200 000. |
Topographic maps usually form the basis of thematic maps; indeed many thematic maps are simply overlays superimposed on a topographic background. Examples of small-, medium-and large-scale topographic maps are shown in Figure 5.1. All topographic maps have clearly identified keys, scales, direction indicators and a grid/coordinate system, and some series may be produced in colour.
Features shown on topographic maps will vary with scale. On smaller scale maps the main features shown are: rivers, lakes, coastlines, altitude (usually in contours), settlements, transport routes, various political boundaries, sometimes forest or woodland plus certain prominent natural or human features. It is impractical to list all the features shown on larger scale topographic maps, but Figure 5.2 illustrates a typical key to such a map.
Despite the obvious high quality of most topographic maps, there are several problems associated with their use. The rate of topographic mapping coverage varies greatly worldwide. As an example of this Bohme (1988) notes that the rates of mapping by continent at the 1:25 000 scale in 1983 were:
| Africa | 2.4% of land area. |
| N. America | 33.8% |
| S. America | 9.5% |
| Europe | 90.9% |
| U.S.S.R. | 5.0% |
| Asia | 11.0% |
| Australasia | 13.3% |
The accuracy of some of this data might be questionable since Yashchenko (1990) states that the entire U.S.S.R. is now mapped at a 1:25 000 scale. About 80% of the world has been mapped at a 1:250 000 scale, though at this scale the figure is 100% for Europe, U.S.S.R. and Australia. Butler et al (1987) notes that about 42% of the world is mapped at the 1:50 000 scale. This low level of mapping is critical for developmental planning since mapping scales from 1:50 000 to 1:100 000 are optimal for economic planning and general location decisions. Table 5.1, compiled from Parry and Perkins (1987), gives a general indication of smaller scale topographic map availability for West Africa, though it does not indicate the age of maps. Very few recent larger scale topographic maps exist here. Since current rates of mapping or map revision are so low, it is unlikely that the target of complete world coverage at 1:50 000 or 1;100 000 scales will be achieved by the year 2000 as hoped (Bohme, 1988).
Figure 5.1 Examples of Large, Medium and Small Scale Topographic Maps
Figure 5.2 Example of a key to a 1:25 000 Scale Topographic Map
| Map Scale | ||||
|---|---|---|---|---|
| Country | 1:2 000 000 | 1:500 000 | 1:200 000 | 1:100 000 |
| West Africa | X | Xa | ||
| Benin | Xb | X | ||
| Burkina Faso | X | |||
| Gambia | Xc | |||
| Ghana | Xd | Xc | ||
| Guinea | X | |||
| Guinea Bissau | X | |||
| Ivory Coast | Xe | X | X | |
| Liberia | Xf | Xc | ||
| Mali | X | |||
| Nigeria | X | |||
| Nigeria | Xca | X | ||
| Senegal | X | |||
| Sierra Leone | X | Xc | ||
| Togo | X | |||
a = partially mapped
b = 1:600 000
c = 1:250 000
d = 1:1 250 000
e = 1:1 000 000
f = 1:1 350 000
There are other problems related to map revision, accuracy and access. According to Bohme (1988), the revision of dominantly rural area sheets ought to occur at about 20-year intervals-in urban areas even a five-year cycle of revision could be inadequate. Needless to say these targets are rarely met and in many areas currently available sheets may be more than 30 years old. Maling (1989) has detailed the problem of both general standards of topographic mapping accuracy, and the variability in accuracy between different maps and RS image sources. In many parts of the world actual access to larger scale topographic maps is either impossible (for security reasons) or special permission must be sought, e.g. in Thailand, in many “Eastern bloc” countries and in ex-French colonies in West Africa (Parry and Perkins, 1987). A specific problem relating to aquaculture and inland fisheries is that the detail shown on inland water sources is frequently suspect. This relates primarily to water courses which may be intermittent or various water bodies whose spatial extent fluctuates seasonally (Anderson, 1989).
Topographic maps have been used, or could be used, to determine the spatial incidence of the following production functions associated with aquaculture or inland fisheries:
Transport Accessibility. At the medium scale all main and secondary road routes would be shown, and at the 1:25 000 to 1:50 000 scales most access roads are also shown. Rail, shipping, ferry, airport and bridging point data is mostly available if necessary. Kapetsky (1989) reports using 1:190 080 scale topographic maps for identifying roads in Johore, and Kapetsky et al (1987) use a 1:500 000 map to identify transportation networks in Costa Rica. Meaden (1986) used 1:250 000 Ordnance Survey maps to identify spatial variations in the density of the road network in England and Wales, by classes of road (see section 5.4.6).
Market Accessibility. Again the road network can give a clear indication of the relative accessibility of the various market outlets, including the potential for “farm gate” sales. Larger scale topographic maps give an indication of the extent of built-up areas, and the distribution of and density of the settlement pattern shown will give an indication of retail market size.
Relief (Topography). Large- and medium-scale topographic maps have a contour interval usually in the range of 5 to 50 meters. This can give an adequate indication of adverse slopes, i.e. the closeness of contours. Areas of marsh, artificial drainage or excessively flat land can be easily identified. For specific site selection large-scale topographic maps would be essential.
Other spatial variations in production functions which could be identified from topographical maps would be:
Additional to these uses, IFREMER (Institute for the Exploitation of the Sea) have used large-scale topographic maps more generally to survey and list all potential aquaculture sites around the coast of France (Girin, 1989), and Cordell and Nolte (1988b) used medium-scale topographic maps for initial area analysis to determine likely oyster culture sites in southern Alaska.
As maps have become increasingly complex, sub-sets of the original information have been more frequently displayed. These make up special purpose, or distribution or thematic maps. They may be drawn to show an almost limitless variety of selected spatially distributed features and their “…aim is the graphic representation of spatial patterns and relationships, in-so-far as these can be related to geographical space and transformed into cartographic symbols.” (Lehmann and Ogrissek, 1988. p.85).
In order to get proportionality and direction correct, thematic maps are frequently based on topographic maps (or bathymetric charts) and indeed much of the topographic detail and labels may be retained. Additional data for compiling the thematic map may be derived from any of the sources discussed in Chapter 3.
Most thematic maps will be concerned with a single theme, though any individual map may show various sub-categories of that selected theme. In order to purposefully concentrate on any theme, thematic maps may abandon their spatial accuracy - these maps are then called cartograms and they frequently illustrate transport routeways such as airline routes, underground railway networks, etc.
Because of the large range of subjects covered, and the fact that there is an increasing tendency towards computer-generated thematic maps, this type of mapping is growing at a very rapid rate, and their importance to GIS is increasingly being recognized (Bird, 1989). Many thematic maps are available for purchase “off-the-shelf” but by far the greatest number would have been purposely drawn to fulfil specific aims, e.g. for inclusion in a research study, to illustrate a particular area for inclusion in a publication or to help with some form of planning project. There is a rapid growth in the production of Thematic Atlases. These usually cover individual topics (themes) or show a variety of themes related to particular areas or countries.
There has been no universal agreement on a classification of thematic maps, probably because the possibilities and complexities are almost infinite. However, it is realistic to briefly describe those major types which are easily identifiable:
Chorochromatic. These show non-quantitative surface distributions of any feature, i.e. they simply portray the presence or absence of a particular characteristic over a given area (Figure 5.3). Whatever theme they are mapping can be sub-divided into various categories, e.g. as does a soil or geological map. The area under each particular use is either coloured or shaded in, and hence the name “colour patch” map is sometimes used.
Figure 5.3 Chorochromatic Map Showing Land Conservation Areas in S.W. England
Choropleth. These are maps which depict average values per unit of area over some administrative region for which statistics are available, such as density of population or a yield per unit area of land (Figure 5.4). To construct a choropleth map, the figures for each aerial unit must be calculated and, dependent upon the number of classes into which the map is being divided, class boundaries are established. These boundaries are themselves dependent upon the dispersion of the figures to be plotted. Colours or shadings should go from dark (highest density or number) to light (lowest density or number). The value of these maps is greatly dependent upon the number, size and shape of the aerial units, the number of classes chosen and the manner in which quantitative class boundaries are derived.
Figure 5.4 Choropleth Map Showing Changes in Table Trout Production in England and Wales
There are a wide number of variations on the choropleth map - the main ones are:
Dot maps - here the “shading” is carried out by means of placing dots within each aerial unit, so that the number of dots corresponds to the numbers being plotted.
Volumetric symbols - these are drawn such that their area is proportional to the quantity that they represent. The symbols may usefully be sub-divided so as to give additional quantitative information (Figure 5.5).
Figure 5.5 Volumetric Divided Circles Showing the Employment Structure of S.W. England
Located Histograms or bars - these maps are similar to volumetric symbols but the symbols are replaced by sets of quantitative bars or histograms which are appropriately scaled and located.
Isopleth. The bases of these maps are the plotting of values for a particular surface, which are then used as interpolation points for isolines (isopleths) to be drawn (Figure 5.6). Isopleths are thus lines which join all places having an equal value. Common isopleths include contours (showing height), isotherms (temperatures), isobars (air pressure) or isohalines (salinity of the sea), though isopleths can be used for plotting of less usual quantities, e.g. journey times from a particular transport nodal point, cost variations across a surface or economic potential within a large land unit (Figure 5.7).
Point. The previous examples were all maps plotting distributions which are spatially extensive. However, many distributions of both physical and human factors will be punctiformal, i.e. on a map they will appear as points which may show dispersion patterns tending towards an even, random or clustered distribution. Anything which is location specific may be plotted on a point map, although care must be taken since, what might appear as a point on a small scale map, e.g. a town, would appear as being spatially extensive on a large-scale map.
Figure 5.6 The Construction of an Isopleth Map
1. The point-values are located: 2. the critical isopleth of value 70 is interpolated, with the aid of crosses placed between pairs of values at a distance proportional to the value of each; 3. other isopleths are similarly interpolated; 4. a system of density shading is applied for clarity between the isopleths.
Linear. A third form of distribution (after spatially extensive and punctiformal) is linear. Though a number of features show linear distributions, the best known are physical features such as rivers, or human features which are usually associated with communications, e.g. roads, railways, air routes, pipelines, electricity transmission lines, etc. Linear maps can either select one theme and simply show its actual line or routeway, or they can be volumetric by showing lines of movement such that the width of the line is proportional to the volume of goods or traffic using the routes (Figure 5.8).
In sections 2.3, 2.4 and 2.5 we listed over 30 production functions which normally show spatial variability. It would be possible to draw up thematic maps to represent any of these functions, though this would not always be necessary since, as shown in section 5.2, topographic maps can sometimes give sufficient information.
Space precludes an examination of how best thematic maps could be drawn up for each necessary function - instead here we will concentrate on some important requisite considerations and in the next section we will look at worked examples of how some more complex thematic maps might be derived.
Figure 5.7 Economic Potential Isopleths for England and Wales (from Clark, 1966)
Though there might be an optimum or obvious way to draw up a thematic map for any production function, maps could in fact be drawn up in several ways, i.e. the method used would be determined by the way in which the map could best be understood, or the way in which it was going to be used. To exemplify this, consider a map showing “water quantity”. A normal thematic map showing this function would be linear in type, with differentiation of quantity being shown by colour or by differences in the width of stretches of waterway (Figure 5.9). This map would then be easily understood and, given that sufficient information was available on the water quantitative parameters, the map could form the basis of further action.
However, if a map of water quantity was required for integration into some forms of GIS, then it might be desirable to produce a choropleth map showing some measure of water quantity as a complete mapped surface (Figure 5.10). Careful consideration would need to be given as to how the water quantity measurement (or score) was going to be derived for a complete aerial unit.
Figure 5.8 Flowlines Showing Fish Transport Routes in Malawi (from Balarin, 1987)
Figure 5.9 Linear Map Showing Water Quantity Variations
Source: Dept. of Environment, 1978.
Figure 5.10 Choropleth Map Showing Water Quantity Variations in England and Wales
It is also possible to create these complete mapped surfaces for functions having point distributions, e.g. such as “agglomeration”, and for those which are concerned with the availability of particular inputs (which would originate from one or more mapped points perhaps large towns). In these cases, the “score” given to any area would necessarily be calculated as being some function of the distance from another fish farm or from the source of the input, i.e. this might be a time, distance or cost function. As we will show in Chapter 6, this ability to convert all thematic maps to form complete mapped surfaces is extremely convenient for the success of GIS.
Very few of the thematic maps which would be relevant to aquaculture or inland fisheries would be available for purchase or acquisition as “off-the-shelf” products. Those that might include some soil, climatic and water quality maps, plus the topographic maps which form the basis of thematically mapping those functions discussed in section 5.2. Clearly, thematic maps are not generally available because they would rarely be in demand, although many are also not available because the subject (theme) being mapped might undergo frequent changes in its distribution, e.g. “land costs” and “current fishing levels”.
The possibility and ease of drawing up thematic maps would vary greatly from function to function, depending on how much primary and secondary data was readily available, the complexity of the distribution being shown and on the detail in which the map was being drawn. Relatively easy maps to construct would include those showing “agglomeration”, “climatic factors” and “areas designated for other activities”. For these maps the straight-forward plotting of point, choropleth and chorochromatic distributions respectively may be sufficient, and the data, in many cases, would be easy to acquire. Other production functions would be easy to map if only their data were not so difficult to acquire. These include the functions of “relationship between income levels and fish protein costs”, “the social acceptability of aquaculture as a food production practice” and “the prevalence of predators”. The data is difficult to acquire because large-scale and quite detailed surveys would be needed which would not be considered as cost-effective. Finally, as we indicated in section 3.4, for some functions the data for producing maps would simply be unavailable and/or unobtainable, so proxy data might have to be used.
In this section we have deliberately chosen a number of worked examples which give both a wide range of common production function types and a wide range of methods for drawing up the derived thematic maps. Although the examples are all taken from Meaden (1986), and are therefore only concerned with one type of aquaculture in one general location, the methods shown would be applicable in any situation where the necessary data could be obtained, i.e. we are concerned here with the principles, the potential and the methodologies which might be used. Our main aim is to give ideas about “spatial scoring”, to point out some of the many factors which have to be considered, and to underscore the fact that in any operations performed by GISs the user may need to procure or collect a wide variety of mappable data. What thematic mapping is actually done, or is possible, is determined by the use to which it is proposed, the time available, the detail required and the cost-effectiveness of getting the data.
In each example we will indicate the necessary source data, the general methods used and any simplifying assumptions that are inevitably necessary in modelling real world situations. The actual methods of carrying out some of the procedures could be done in several ways - these might be dependent upon the hardware and software available, or other resources, though most of the repetitive calculations shown would clearly best be performed within a GIS. The importance of outlining simplifying assumptions lies both in illustrating how the methodology might limit the accuracy of the final mapped surfaces, and in pointing to the problems and dangers of attempted simplification. In the examples shown, the final thematic maps produced were all choropleth maps based on a 10km × 10km grid cell, and they were all scored on a 0 to 10 scale. The use of “scores” was made since these gave some relative indication of the ability of individual cells to provide for the particular production function, and they were useful because they surmounted the problem of integrating data having different measurement forms. However, it would clearly not be necessary to use this scoring system - the thematic maps could simply be “derived” and left unscored.
A) Sources Used.
A “River Pollution Survey” map covering England and Wales at a scale of 1:250 000 (Dept. of Environment, 1978). As well as showing river water quality by four classes, the map showed the mean water flow volumes of rivers by 10 flow categories (Figure 5.9).
Computer print-out data giving river flow rates for 576 flow gauging stations in England and Wales.
Maps showing the location of these gauging stations.
B) Methods Used.
The fish farmer must be concerned with the total volume of water available, plus the potential accessibility and the flow rate variability of that water. The pollution survey map gives sufficient detail on the first two of these. To show variability of river flow a map was constructed, part of which is shown in Figure 5.11, using data from the 576 flow gauging stations. Variability, for this exercise, equalled the ratio between the 1% exceedence flow rates and the 99% exceedence flow rate of the river. Absolute maximum and minimum flow rates were not used because these rates could be suspect due to difficulties of measuring extreme flows. Also, because the flow rate data had been collected over a considerable time period, then in many cases the monitoring equipment had been improved or the river flow rate had been moderated by various water engineering projects.
Figure 5.11 consists of isopleths which were interpolated from a plot of the 576 variability ratio figures. The map uses six classes which have geometric intervals because of the nature of the frequency distribution shown when the variability ratios were plotted (Figure 2.4). In interpolating the isopleths in Figure 5.11, a knowledge of factors which affect stream flow variability was incorporated.
To achieve a choropleth map showing a “scored” surface, three stages were followed:
For each 10km cell a “relative water volume and accessibility” score was calculated using the formula:
where v = “relative water volume and accessibility” score,
t = total length (in mapped kilometers) of all fresh waterways in the cell, i.e. to tidal limit where relevant,
i....r = each of the 10 categories of river flow range,
w = weightings as per Table 5.2.
As it is impossible to state objectively the proportion of water which might be available from any particular waterway it was assumed that, with increasing waterway size, a decreasing proportion of water would actually be both practically obtainable and potentially available, i.e. equal to the square root of the volume. As well as the total volume of water in any cell, it was essential to include an allowance for river frontage access to water. If no allowance was made then a cell having a short, high water volume stretch of river and long stretches of small volume streams, might seem to offer more potential for fish farming than a cell where the situation was reversed - this would not be the case.
Figure 5.11 Variability of River Water Flow in the North of England
| Flow Range (cumecs) | Relative Volume of Water | Weighting (square root of vol.) |
|---|---|---|
| <0.31 | 1 | 1 |
| 0.31 – <0.62 | 2 | 1.4 |
| 0.62 – <1.25 | 4 | 2.0 |
| 1.25 – <2.50 | 8 | 2.8 |
| 2.50 – <5.00 | 16 | 4.0 |
| 5.00 – <10.00 | 32 | 5.7 |
| 10.00 – <20.00 | 64 | 8.0 |
| 20.00 – <40.00 | 128 | 11.3 |
| 40.00 – <80.00 | 256 | 16.0 |
| 80.00 | 512 | 22.6 |
Using the “variability of water flow” map (Figure 5.11) a “variability score” was calculated for each cell using the formula:
where s = “variability score”,
x = percentage of surface area of the cell in each variability class,
y = weighting as per Table 5.3,
i....n = each class of variability ratio.
| Class | Variability Ratio | Weighting |
|---|---|---|
| 1 | <15 | 10 |
| 2 | >15 – 30 | 8 |
| 3 | >30 – 60 | 6 |
| 4 | >60 – 120 | 4 |
| 5 | >120 – 240 | 2 |
| 6 | >240 | 1 |
A final “score” for each cell was achieved by multiplying the “v” score by the “s” score and then converting the answer to a number between 0 and 10, i.e. by using a probability distribution graph which plotted all possible products (answers) achieved when multiplying together all combinations of integers between zero and 10. Cells receiving a high score would be those having a large volume of water, extensively accessible, and where there was little variation in the river flow range.
C) Simplifying Assumptions.
It was assumed that the “relative water volume and accessibility” factor and the “variability ratio” factor were of equal significance.
It was assumed that the quantity of water potentially available was equal to the square root of the mean water flow rate.
It was difficult to determine the exact length of waterways from the pollution survey map, because the thickness of the flow line tended to obscure smaller mapped bends in the river.
A reservoir might have been built on a waterway since collection of the flow rate data commenced. This would cause the variability ratios to be greatly decreased for all downstream locations. Allowance could be made for this by obtaining data on recent reservoir construction dates.
Some waterways shown on the base map might be intermittent streams and thus be totally unsuited to fish farming.
A) Sources Used.
Computer print-out data giving weekly or fortnightly river water temperature information from 194 harmonized monitoring stations in England and Wales.
“Average Annual Rainfall” maps - Sheet Nos. Met. 0.886 (SB) and Met. 0.886 (NB), published by the Meteorological Office (1977), at a scale of 1:625 000.
“Hydrogeological Map of England and Wales, published by the Institute of Geological Sciences (1977), at a scale of 1:625 000.
Ordnance Survey - Fifth Series sheets covering England and Wales, at a scale of 1:250 000 (e.g. Figure 5.1 (c)).
“River Pollution Survey” maps (Dept. of Environment, 1978) covering England and Wales at a scale of 1:250 000.
The sources listed under Figure 5.13 for obtaining salmonid growth rates at different water temperatures.
B) Methods Used.
Using the above sources a map was constructed, part of which is shown in Figure 5.12, at a scale of 1:625 000, which showed the ability of river water temperatures to meet an optimum water temperature for trout growth of 15C. The stages in its construction were as follows:
Figure 5.12 The Efficiency of River Water Temperatures in Northern England to Provide for Trout Growth
A “best-fit” curve was plotted from a series of curves and points showing salmonid growth rates against water temperatures (Figure 5.13). A best-fit curve was used since the data exhibited slight variations, especially in the amount of one-way linear stretch parallel to the growth axis, i.e. because experimental conditions varied as did species and ages of salmonids being studied. The curve purported to show, for all possible water temperatures, standardized specific growth rates for salmonids (% weight gain per day) and the percentage of maximum growth rate attainable, i.e. the “water temperature growth efficiency” given that the optimum growth rate, occurring at 15°C, represented 100% efficiency. Thus, if the water temperature was at 10°C then trout would only be growing at 78.4% of maximum efficiency, because at 10°C the specific weight gain per day is 1.17% v. 1.5% per day at 15°C. The apex of the curve was deliberately biased towards higher temperatures because it has been shown (Aitken, 1971) that with high fat diets being extensively used, optimum water temperatures could be slightly increased, as could growth rates at any water temperature. Additionally, since the optimum water temperature for growth decreases as the ration decreases (Shelbourn et al, 1973; Elliott, 1975), then it would be realistic to look at a higher figure (for optimum growth) about which to fit a curve, i.e. if the trout are being fed to satiation as is frequent aquacultural practise.
where x = “water temperature growth efficiency” figure (%),
n = number of water temperature readings on the harmonized monitoring station listing
The mean percentage “water temperature growth efficiency” figures were plotted on a base map of England and Wales (Figure 5.12).
Isolines were then plotted on the base map at 5% “water temperature growth efficiency” intervals. In interpolating these isolines due consideration was made for altitude, latitude, run-off, geology and thermal effluents as these factors may have macro-scale influences on prevailing water temperatures. Extra interpolation points were generated in highland areas with the necessary altitudinal water lapse rate data being obtained from known air lapse rates. These temperature reductions were made from the actual mean water temperatures as recorded at monitoring stations having a nearby location, a similar latitude and run-off rate and a known altitude.
For the purposes of the original study, the information shown on the “water temperature efficiency” map was converted to scores, on the 0 to 10 scale, for each 10km cell covering England and Wales, but we need not elaborate here on the method used. Many of the lengthy calculations and the map interpolations could quickly be done using a GIS.
C) Simplifying Assumptions.
It could be argued that the use of annual mean “water temperature growth efficiency” figures upon which to base the isoline map was meaningless since this could disguise large deviations about the mean. However, this was seldom the case - in fact nearly all other climatic data show far greater measurement deviations than water temperatures.
It was assumed that various salmonid species grow at the same rate and exhibit the same growth against water temperature curve. There is some evidence to show that this is approximately correct (Nicholls, 1957).
It was assumed that water temperature lapse rates are equivalent to air temperature lapse rates, are uniform and can be readily assessed from nearby waterways having a similar milieu. This is generally true.
It was assumed that the use of a single weekly or fortnightly water temperature reading, over a five-year period, could form the basis of a reliable “water temperature growth efficiency” score.
Figure 5.13 Best-Fit Curvilinear Regression Line Fitted to Curves or Points Showing Salmonid Growth Rates Against Water Temperatures
+ The vertical axes were reduced by a factor of four because these experiments were conducted on fry who have very rapid specific growth rates. The final results are not affected since it is the shape along the horizontal axis which is important.
A) Sources Used.
“Hydrogeological Map of England and Wales” (1977) at a scale of 1:625 000. This map indicates aquifer flow potential and main characteristics, in 49 sub-categories of geological formation.
“Water Industry - Map 2 - Major Sources of Water Supply”, published by the National Water Council (1980), at a scale of 1:625 000.
Data, obtained by standardized questions put to each Water Authority chief hydrologist, relating to the likelihood of being able to procure access to existing underground water supplies.
B) Methods Used.
Considerations concerning the availability of underground water can be divided into two main types for mapping purposes. The first, for which the hydrological maps could be used in their existing form, was simply the existence of, and available quantities of, aquifer water. The other consideration relates to the likelihood of being able to obtain an abstraction licence to exploit the aquifer.
From the questions put to the chief hydrologists, a map was produced (Figure 5.14) showing the likelihood of being able to procure a licence to abstract underground sources of water. It was only possible to classify the area into three broad divisions, and it is pertinent to note that there are no areas in England and Wales where an abstraction licence could “certainly” be obtained.
To produce a final choropleth map showing the availability of underground water, the following steps were followed:
Each of the 49 sub-categories of geological formation shown on the hydrogeological map was allocated a “supply score” based on the ability of the sub-category to supply underground water (Table 5.4).
| Yield of aquifer (litres per second) | “Supply Score” |
|---|---|
| <10 | 0 |
| >10 – 20 | 1 |
| >20 – 30 | 2 |
| >30 – 40 | 3 |
| >40 – 50 | 4 |
| >50 – 60 | 5 |
| >60 – 70 | 6 |
| >70 – 80 | 7 |
| >80 – 90 | 8 |
| >90 – 100 | 9 |
| >100 | 10 |
Figure 5.14 The Likelihood of Being Able to Procure a Licence to Abstract underground Sources of Water in England and Wales
A transparent overlay, having a 10km square grid at the 1:625 000 scale, was placed over the hydrogeological map and the percentage in each of the aquifer yield classes in each 10km cell was calculated, and the figure obtained for each was multiplied by the “supply score”. This resulted in an aggregate total for each cell in the range of zero to 1 000.
The transparent overlay was then placed over the map showing the likelihood of being able to procure underground water. The aggregate score for each cell obtained in (ii) above was then adjusted to allow for spatial variations in this likelihood of obtaining underground water. Adjustments were as follows:
Suitable adjustments were made for cells which may have been partly in two or more regions.
iv) The adjusted aggregate figures were then divided by 100 and rounded off to the nearest whole number to achieve a final score for each cell in the range of 0 to 10. A high score represented a cell in which aquifers could supply high yields of water and where there was a good chance of obtaining an abstraction licence.
C) Simplifying Assumptions.
The adjustments made in (iii) above were thought to give a reasonable “penalty” to the various areas.
Cognizance could only be taken of the near surface mapped hydrogeological classifications of base rock, i.e. there may be deeper-lying water-bearing sub-strata.
Each of the 10 Water Authority chief hydrologists might have had a different perception of what was meant by, for instance, “a limited chance of” or “a good chance of” obtaining an abstraction licence, i.e. it is very difficult to standardize perceptual questions.
It was only possible to draw estimated boundaries between the three types of abstraction region.
The granting of an abstraction licence may actually depend upon the location of existing boreholes. Allowances could not be made for this since policies vary between and within Authorities and because suitable data on the distribution of boreholes was often non-existent.
The fact of being located near to an existing surface waterway, for the disposal of used water, was not allowed for. This is not a problem over most of England but it might be in some areas.
A) Sources Used
B) Methods Used.
A transparent overlay having a 10km square grid at the 1:250 000 scale, with each 10km cell being further divided into 100 × 4mm square cells (1 km2), was placed in turn over each of the Ordnance Survey sheets.
A count was made of the number of 4mm cells within each mapped 10km cell which contained either of the following:
Where three consecutive contours were not more than 2mm apart. This would indicate areas having at least a 400 feet slope with a gradient of 1 in 4 over some of the 4mm cell.
Where there was evidence of marsh-land, artificial drainage, excessive meandering or “interconnections” (braiding) along river flood plains, i.e. where poor drainage or flooding was likely.
A score for each cell, in the range of 0 to 10, was achieved using the formula:
where 0 = the obtained score,
n = the number of 4mm cells which contained three consecutive contours which were not more than 2mm apart,
m = the number of 4mm cells where poor drainage or flooding was likely.
Answers were rounded to the nearest whole number. Cells receiving high scores would be ones that exhibited no map evidence of large-scale steep slopes or of being situated where flat land on river flood plains was an impediment to drainage and/or liable to flooding. For those kinds of aquaculture where a constant high throughflow of water was not essential, then flat land on flood plains might in fact be advantageous, so any scoring system would need to reflect this.
C) Simplifying Assumptions
Some portions of some of the excluded 4mm cells would undoubtedly be suitable for fish farming.
The scoring method would not account for “rugged” land which had less than a 400 feet elevational range, i.e. the method was designed to eliminate larger scale rugged areas.
Waterways and contour lines may not be very accurately drawn at the 1:250 000 scale. Indeed the Ordnance Survey is unable to state the criteria upon which waterways are included on 1:250 000 sheets and they admit to a degree of “cartographic licence”.
Some flooding could obviously occur in uncounted cells but this would be comparatively rare and impossible to allow for.
A) Sources Used.
“Persons per Square Mile by Ward and Parish - 1971” map, published by Dept. of Environment (1975), at a scale of 1:1 250 000.
“Land Use Capability” map, published by the Soil Survey of England and Wales (1979), at a scale of 1:1 000 000.
“Economic Potential for Great Britain” map, published in Clark (1966).
“Economic Potential for the Enlarged European Community” map, published in Clark et al (1969).
B) Methods Used.
It was shown in section 2.4.5 that land costs are difficult to define in map form because of constant temporal and spatial pricing adjustments. It was also suggested that land costs could best be perceived as being a function of:
Although any one of the three functions individually would not provide a very accurate mapped surface showing likely land costs, by integrating the source maps a reasonable “land cost surface” map could be generated which would give sufficient accuracy to compare the relative costs of land throughout the area. Both the “population density” map and the “land use capability” map could be utilized as they were, but the two “economic potential” maps were combined (by aggregating their economic potential isoline values) to form a “revised economic potential map of England and Wales” (Figure 5.7).
Integration of the three maps to produce a final choropleth map showing land costs was carried out as follows:
Over the population density map a 10km square transparency grid was placed. A “relative population density score” for each cell was established using the formula:
where r = “relative population density score”,
n = number of square mile units within each cell,
w = weighting as per Table 5.5,
g....l = each of the six population density classes on the population map.
| Population Density Class (per square mile) | Weighting |
|---|---|
| <25 | 0.025 |
| >25–50 | 0.05 |
| >50–400 | 0.075 |
| >400–6400 | 0.10 |
| >6400–25000 | 0.125 |
| >25000 | 0.15 |
The weightings in Table 5.5 were designed to give a realistic balance between the likely prices of land in different sized population centers, and such that the range of scores achieved for each cell would be from 0.1 to 6.0.
Over the revised economic potential map (Figure 5.7) a 10km transparent grid was placed, and a score for each cell was established, it being the nearest index of economic potential isoline number (to one decimal place) prevailing at the center of the cell. The range of scores achieved would be from 0.7 to 2.0.
To introduce the land use capability factor each of the land use capability classes shown on the map were given a weighting (Table 5.6). Over the map a 10km transparent grid was placed and the percentage of each class of land, for each cell was established. A “land use capability score” was calculated using the formula:
where u = “land use capability score”,
p = percentage of each class of land,
w = weighting allocated to each class as per Table 5.6,
c....j = each class of land use capability.
| Land Use Capability Class | Weighting |
|---|---|
| Urban land | 4.0 |
| Class 1 | 3.0 |
| " 2 | 2.5 |
| " 3 | 2.0 |
| " 4 | 1.5 |
| " 5 | 1.0 |
| " 6 | 0.5 |
| " 7 | 0 |
The range of scores achieved would be 0.3 to 4.0.
An aggregate total for each cell was achieved by summing the three scores for “relative population density”, “economic potential” and “land use capability”. The theoretical range of aggregate totals was 1.1 to 12.0.
A final score was achieved by subtracting the above aggregate total from 11 and rounding to the nearest whole number. Thus a cell which was seen to have high land values, would be disadvantageous with regard to land costs and it might receive a final score of zero. In many countries the concept of economic land costs might not always apply. In these cases some sort of mapping which incorporated “rights” to land might need to be considered.
C) Simplifying Assumptions.
It was assumed that land costs were a reflection of population density, land use capability and economic potential in the ratio of 3:2:1 respectively, and these ratios were reflected in the maximum contribution which each could make to the final score.
The method of scoring would be unrealistic at the micro-scale, e.g. core areas in city centers would have low populations but high land costs. So for a micro-scale study the methodology would need to be adjusted.
Though the economic potential and population density maps were rather dated, they would still give a significantly accurate basis for scoring since these variables change very slowly at the macro-scale.
A) Sources Used.
B) Methods Used.
Each of the four classes of roads indicated on the “Routemaster” sheets was given a weighting as per Table 5.7.
| Road Class | Weighting |
|---|---|
| Motorways | 3 |
| “A” | 3 |
| “B” | 2 |
| Minor | 1 |
For each 10km grid square a score was achieved using the formula:
where s = score achieved,
l = length of roads in mapped kilometers,
w = weighting as per Table 5.7,
g....j = each Road Class category.
Scores for coastal cells were then calculated using the formula:
where additionally c = score for coastal cell,
p = percentage of the cell occupied by land.
Scores were rounded to the nearest whole number and all cells scoring >9.5 were rounded to 10. Cells receiving a high score were those having a dense network of roads, especially in the Class “A” or motorway category. Figure 5.15 is given as an example of the final map showing “Access to Road Transport”.
Figure 5.15 Example of the map Scored for “Access to Road Transport”
C) Simplifying Assumptions.
Though the weightings given in Table 5.7 do not reflect the volumes of traffic carried by each class of road, road transport accessibility is concerned with a variety of factors, most of which are unrelated to the traffic volume.
Most tracks and farm access roads are excluded from the base maps so the realistic degree of accessibility to potential fish farm sites could not be ascertained. However, as these omissions would be relatively uniform, this problem would have little effect on the results.
The coverage of urban area roads on the base map does not equate with the cover given to rural areas, though this should not detract significantly from the results.
There would not be spatial uniformity in the volume of traffic using a certain class of road in different parts of the country.
It could be argued that considerations should be given to transport accessibility factors such as major road intersections and motorway turn-offs. However, these apparent advantages were not allowed for because of the counter-balancing factors of increased land costs and potential disturbances.
A) Sources Used.
“British Hotels, Restaurants and Catering Association - Guide Book - 1980”, published by the B.H.R. and C.A. (London).
“A.A. - Hotels and Restaurants in Britain (1980)”, published by the Automobile Association (Basingstoke).
“R.A.C. - Guide and Handbook - 1980”, published by the Royal Automobile Club (London).
B) Methods Used.
Since no maps existed showing the location of catering outlets in England and Wales, it was necessary to ascertain their distribution. After corresponding with all known publishers of the relevant guide, it was apparent that the above sources gave a spatially random and comprehensive coverage of catering outlets in England and Wales.
Using the data sources a count was made of the number of separate hotels, guest houses and restaurants listed under each named place in England and Wales (plus the Scottish border area). This figure then represented an assumed number of catering outlets for each settlement.
On a tracing overlay a map was constructed, at a scale of 1:625 000, showing the distribution of these catering outlets by the use of proportional circles. The radius of each circle was calculated using the formula:
where r = radius of the circle (cms),
p = number of catering outlets shown for each settlement.
In the center of each proportional circle the actual number of catering outlets was recorded.
On a transparent overlay three concentric rings were drawn, each consecutively corresponding to 12km, 24km and 36km radii at a 1:625 000 scale. It was thus initially assumed that a trout farmer would be prepared to travel a straight line distance of up to 36kms to serve catering markets.
Placing the central point of the concentric rings over the mid-point of each cell in turn, the number of catering outlets within each of the three market zones was counted. Because the catering markets were represented by proportional circles, thus having spatially varying extensions on the map, a market was counted as being sited in the innermost annulation that its proportional circle appeared in. This method of counting also applied to catering markets whose centers might be beyond the 36km outer circle but whose proportional circle came within the annulations. By utilizing this technique some “gravitational” allowance could be incorporated into the scoring, i.e. it would be worth travelling a little further to serve a larger market, though the extent of this frictional effect of distance is necessarily arbitrary. Figure 5.16 illustrates this methodology.
A weighting was then applied in order to make allowance for the fact that catering markets in the inner zone could be more advantageously served than markets in the outer annulations. Using the formulae:
where x = the average distance needed to travel to serve all randomly distributed catering markets in each zone,
r = radius of each zone,
i....k = each successive outward zone,
the average straight line distances needed to travel to serve each of the three catering market zones, from the central point of each cell, was calculated. The results were 8.49kms, 20.49kms and 32.49kms respectively. These straight line distances were reduced to the ratios of 1, 2.41 and 3.83 respectively. Thus, on average, a trout farmer might need to travel 3.83 times as far to supply catering markets in the outer zone than in the inner zone.
In order to simplify further calculations, and to more approach reality, these ratios were rounded down so as to read 1, 2 and 3 respectively, i.e. transport costs are not linear as a function of distance - they generally decrease proportionally with distance. Using these ratios, catering outlets in the inner circle were given a weighting of 3, outlets in the middle zone 2 and outlets in the outer zone were left unweighted as 1.
The number of catering outlets counted in each of the three market zones was multiplied by the three respective weightings and then the three figures were totalled.
Figure 5.16 Methodology Used to Establish Scores for Distance from Catering markets
Scoring for the cell indicated would be:
| Weighting | Total | |
|---|---|---|
| Catering outlets in inner zone = | 12 × 3 = | 36 |
| Catering outlets in middle zone = | 75 × 2 = | 150 |
| Catering outlets in outer zone = | 82 × 1 = | 82 |
| Total for cell = | 268 | |
Note that the coastal cell having 15 catering outlets is centred some 2kms beyond the outer (36kms) concentric circle but it still counted for ‘objective scoring’, i.e. suggesting that a trout farmer would be prepared to travel 38 straight line kilometres to serve that settlement.
A final score was then allocated to each cell using Table 5.8. A cell receiving a high score was one where many hotels and restaurants were in close proximity to, or within the “gravity field” of, the center of that cell.
A similar methodology to this could be used for supplying fish to any market sector. Calculations would be easier for supplying wholesale markets, i.e. since there are fewer of them.
| Aggregate Weighted Total of Catering Outlets | Allocated Score |
|---|---|
| <150 | 0 |
| >150– 300 | 1 |
| >300– 450 | 2 |
| >450– 600 | 3 |
| >600– 750 | 4 |
| >750– 900 | 5 |
| >900– 1050 | 6 |
| >1050– 1200 | 7 |
| >1200– 1350 | 8 |
| >1350– 1500 | 9 |
| >1500 | 10 |
C) Simplifying Assumptions.
It was assumed that each catering outlet was selling the same volume of trout. Although this is unrealistic it would have little effect on the score since there is no evidence of trout being unacceptable by region.
It was impossible to verify that there was no regional bias in the choice of catering outlets listed in the data sources used.
Some restaurants would be serving a foreign cuisine and thus be unlikely to sell trout, and some restaurants or hotels might be part of a large chain who practice centralized buying.
Many suburban areas might be under-represented in the restaurant guides, though in practice these are likely to be areas where trout sales would be minimal.
Catering outlets were all considered to be centrally sited in each specific settlement. In practice this is unrealistic although the true dispersion of these outlets would rarely affect the score allocated.
