Solution 1

Solution 2

At step 10 it is difficult to decide between [DD + FF] or [Al + DD] as the shortest link. The alternatives are subtly different. Both are correct. Your submitted figures should resemble one or other of these. Small errors of a few mms are perfectly OK, but if your work differs wildly from both of these two routes, there is probably something wrong.

2.a My view is that it is best to end the grouping process at Step 13, prior to the large jump in link length required by Step 14. Step 13 gives a three-group classification, which has two major advantages: 1) it is parsimonious (i.e. it uses just a few groups, and so makes it easy to handle); and 2) it is contiguous (i.e. the groups form coherent spatial regions). However, few students bothered to explain in full the significance of the break in slope: prior to Step 13, link length rises gradually, so the links made join places/groups with fairly similar climate; after Step 13 is made, the large jump in link length necessary to make further groups implies we are now forced to join groups with dissimilar climates. Such dissimilar groupings make little practical sense.

Lots of students made a bad mistake by choosing a classification which breaks the rules of the grouping procedure. If you wish to accept group X, then you must also accept groups formed previously which contain places with more similar climates. Once formed, groups cannot be broken up. Perhaps the most common error of this type was to map Group NN (Dumfries, Paisley, Baltasound and Stornoway), but to break up Group MM (everything else except St Mawgan), despite the fact that this group forms at the previous step, and so is a 'better' (i.e. more similar) group (see Solution 1). This may fit your preconceived ideas as to what the climate of the British Isles is like, but it defeats the purpose of using a fixed set of rules. This is exactly the kind of error based on preconceptions the grouping process is designed to avoid. Other students simply ignored the grouping procedure and linkage tree information altogether when choosing their classification and map.

Any student handing in work with a mismatch between their classification/map, and their grouping diagrams was given a maximum mark of 12, regardless of the quality of their other answers (on the grounds that they ignored and/or failed to comprehend the fundamental technique on which the exercise centres). Mark scheme.


2.b This will depend on the answer above - students who go for a small number of groups leave themselves less work to do. Anything sensible is OK. Nick's divisions (3-group solution):
A. South-west. Highly maritime, warm and wet.
B. East - relatively 'continental' - cool and damp.
C North-west - cold and wet.

Some students chose to use the labels 'tropical' and 'polar' to describe climate groups. This is not strictly appropriate. Tropical and polar describe the source regions of major air masses, but air temperatures fall/rise respectively as air masses move north/south. Britain is nowhere consistently warm or cold enough to qualify as tropical or polar climate (with the possible exception of the high mountain tops); it is temperate. Similarly, I would prefer to see the use of the adjective 'continental' qualified in some way: East Anglia may be continental by UK standards, but compared to say the interior of Siberia it is not.

2.c See my example. To a certain extent, the boundaries are arbitrary, if an intelligent guess, although they are unlikely to take the form of straight lines, and must pass between places, not through the black dots. You should use your skill and judgement to extrapolate boundaries, and fill in the gaps; no 'white' areas not allocated to any groups should be left. However, given the absence of data for the Republic of Ireland, it is correct to exclude this area from classification and mapping. Every place must be in a group, even if it makes a group on its own, and groups must not overlap or nest inside each other. Your map must conform to your chosen classification which must in turn conform to the grouping rules/linkage tree. Credit for anything reasonable, and suitably annotated. Despite being asked to include one, many students omitted a title! (-1 mark in this case).

3.a Most answers to question 3 were certainly along the right lines, although a large number omitted to mention the importance of depressions. Marks dropped here usually as a result of description, but no explanation, and/or a level of technical content better suited to standard-grade than University study. 'Buzzwords' we looked for: Maritime. Humid, temperate western margin-type climate, generally warm for latitude, if damp. Generally equable. Reflects pervasive flux onshore of heat and moisture. Much of heat released to atmosphere from ocean - North Atlantic Drift - bonus marks to anyone who mentions this in the context of the Atlantic Conveyor and the thermohaline circulation. Climate reflects this heat and moisture transferred to atmosphere - in path of surface depression tracks; frequent cyclogenesis reflects upper westerlies, Rossby Waves and activity of Jet Stream.

A perceptive student might mention that, within the context of this practical, the general climate of the British Isles is described by the co-ordinates of the final (i.e. single) grouping - ~9.2 degrees C and ~1000 mm rainfall; other students calculated the mean T and rf of the original data sets, which gives a slightly different answer, but still got credit.

b. Main contrasts can be summarised as a south-to-north temperature gradient, and a west-to-east rainfall gradient. Temperature: because of latitude which affects intensity of solar radiation receipts (mean T used, so not clear if seasonal effects - e.g. short daylight hours in Lerwick in winter - are balanced by reverse in summer. Should be in theory, but other factors - e.g. seasonal variations in cloud cover - could intervene). Cold Polar or Arctic air masses are more likely to influence the north, warm Tropical air masses are likely to influence the south - although the interaction of air masses (to give depressions) has just as much an influence on climate as does the balance between individual air masses. [Note: the temperature data given are corrected for altitude (and you are told this in the caption to Table 2!), although no site in the data set is sufficiently high up for its altitude to make a significant difference to climate. However, answers which argue that the classification ignores variations in T and rf experienced in highland areas are right.]

Rainfall: Proximity to west coast - onshore advection of heat, plus scavenging of moisture. Rainshadow effect particularly pronounced where mountains intervene e.g. Durham, Leuchars, Craibstone. Summer - depression tracks pushed north, south more likely to come under influence of blocking anticyclone - extension of sub-tropical high pressure.

4. Obvious point - close relationship between the two - shift in space = shift in climate. Places close together have similar climates, far apart, dissimilar climates. Evident in classification which produces contiguous (spatially-connected) climate regions. However, the correlation is good, but not that good. So spatial distance is not a brilliant predictor of climate distance on the whole. What this means in effect, is that, say 100 km in one direction will not necessarily produce a similar change in climate to 100 km in a different direction. What this illustrates is that climate GRADIENTS are different in different parts of the British Isles. Generally, I assume that the W-E gradient is sharper than the N-S gradient, particularly where relief influences rainfall. Climate gradients seem to be especially sharp in Scotland, as your maps should illustrate. One of the most telling e.g.s is the difference between Paisley and Leuchars: point (109, 64). These are third-equal closest in spatial distance (109 km) but 64 mm apart in climate distance, and are not grouped until the final step. Most of this difference is accounted for by the sharp fall in rainfall as you head east across Scotland (i.e. rainshadow). Conversely, point (335, 11) represents Anglesey and Everton: pretty similar climates, despite being a long way apart (335 km). The difference in longitude (W-E) is smaller than the difference in latitude (N-S) here, supporting the concept of a relatively gentle N-S climate gradient - maritime influences carry heat north, producing relatively high temperatures for the latitude, especially in the west.

5. Most students correctly identified the main problems: a) it's slow, because it proceeds one step at a time; and b) it gets cumbersome/messy with large data sets, whether using graphical or mathematical methods. However, possible solutions to speed up/clarify the process were, on the whole, rather vague. We didn't understand what many students meant by their answers: a distinct example or sketch would have helped in many cases! Nevertheless, a large number of answers included the idea that it would help to group more than two points at each stage. A lot of answers suggested things like "group the four closest points" at each stage, but did not tell us how the "four closest points" were to be defined. To me, this suggests a lot more measuring to be done to find the 'four closest' combination, even if it cuts down the number of points left far more quickly.

The process can be speeded up by forcing all individuals to link up to their nearest neighbour at the first step, which rapidly reduces the number of groups. Doing this here would reduce the data to 6 groups at the first step. This is explained in Johnston, if anyone actually bothers to go and read it. The cost of this is that it can lose important information by forcing outliers to make groups early, when in theory, it is possible for one individual to form a perfectly acceptable group. E.g. using a hierarchical procedure St Mawgan only submits at step 14 here, whereas a non-hierarchical procedure would throw St Mawgan , Aldergrove, Anglesey, Manchester and Everton together at step 1. This is shown in the scatterplot attached.

Some common misconceptions when answering this question included:

a) Using more points will make it more difficult because it will increase the variability of the data set. This is not necessarily so, at least in this case. Given the large spread of data, adding more points would most likely fall within the range already defined. More variability is good: it stretches the distances, and makes measurements easier; it is the likelihood of more points clustered closely together (i.e. more data, but little or no increase in overall variability) which would make things more difficult.

b) Make it easier by splitting the data up first. This introduces a logical inconsistency: you are required to divide the data into groups so you can then divide the data into groups! What criteria would you use to split the initial data up? If you don't use an established procedure, what confidence do you have in these preliminary groups?

c) Use an a priori stopping rule, so you don't have to take the procedure so far. Two points here. Firstly, more data points does not necessarily mean that you will not finish with a small number of satisfactory groups, likely to be revealed only in retrospect. Secondly, it is the early stages which are the clumsiest to negotiate, not the later stages once the data has been reduced. An a priori stopping rule will not get rid of the difficult first few steps. It is the grouping rules which are best modified, not the stopping rule.

6.a A wide range of responses possible here. Credit for anything reasonable. Some ideas. Mean T and total rf are generally accepted as reasonable summaries of climate, and seem to work well here. In its most simple sense, global warming is defined in terms of a secular rise in overall temperatures. However, some kind of time series data are required to assess such a potential trend, whereas the data given here relate to a single slice of time (means for 1961-1990). Perceptive students did note that there is increasing interest in the wider climatic changes covered by the catch-all phrase 'global warming': e.g. seasonal contrasts in weather, changes to the intensity of rainfall, etc. Simple mean data offer little insight in this respect. Changing spatial as well as temporal patterns of climate are important, so a map-based approach to prediction and assessment of the impact of global warming is entirely appropriate.

6.b Hard! In effect this questions asks how could you add a third axis so you can add a third variable. The catch here is that the graphical procedure can only be used on a standard graph with perpendicular axes for two variables. This limits its use. Although it is possible to draw a 3-D graph, the distance between points cannot be measured from this because it is flat. However, it is possible to calculate the distance between points using the extension of Pythagoras' Theorem to 3-D (or indeed 4-D, or 5-D...): i.e. distance = Ö (x² + y² + z²), with x = difference in x axis variable, etc.. Clearly this would be time-consuming, but it would be feasible to do by hand for small data sets, and a suitable spreadsheet could be set up to speed up the calculations for larger data sets.

There is a problem with using Pythagoras Theorem with raw data. Imagine two places, A with T = 5 degrees C, rf = 500 mm, and B with T = 10 degrees C, rf = 1,000 mm. If we use Pythagoras to calculate the distance between the two (ignoring the units) we get:
distance = Ö [(10 - 5)² + (1,000 - 500)²] = Ö (25 + 250,000) = 500.025.
Notice what happens: because rainfall values are typically ~100x temperature values, the raw calculation gives much more weight to the distance attributable to the difference in rainfall (whereas I set up the scatterplot to equalise weights given to each variable). If using calculations it is necessary to standardise the data in some way to get rid of this effect. (At this level students might be expected to notice the problem; but would not necessarily be expected to propose a suitable solution, however.)

A second acceptable answer would be to use a triangular plot which consists of three axes arranged as an equilateral triangle. This could be used to identify similar data pairs as you did in the main exercise, but again there is a problem here with the data. Triangular plots work only if the data on the three axes sum to say 1.0 or 100: i.e. if data can be partitioned between three categories as fractions of a whole. So (100, 0, 0), (80%, 10%, 10%) and (0.45, 0.35, 0.20) can all be plotted on a triangular plot, but none of (100, 100, 100), (70%, 50%, 20%) or (0, 0, 0) can! Some kind of data transformation would be necessary to make the data suitable for a triangular plot - I'm not sure what it would be but I think it could be done. However, as with the idea of Pythagoras above, I was more interested in students getting the idea than for them to give me the fine details of the problems involved.

< 9 Desperate!

9-11 Reasonable attempt at Qu. 1-3, but sloppy completion of Figs. and vague/incorrect written work..

12-14 Adequate completion of Figs, sound classification of climate and reasonable discussion of underlying causes. Struggles with Qu. 4, 5 and 6.

15-17 Sound performance on 1-3, plus a reasonable stab at 4-6.

18-20 Sound performance on 1-3, with use of climate buzzwords. Gets notion of variable climate gradients on 4, and provides thoughtful response with evidence of insight into technique on 5 and 6.