Two Farms, One Watershed: Reading the Scale of a Map
A regional planning office has two maps of the same 240 km² agricultural watershed. Map A is a small-scale map covering the whole watershed on one page; Map B is a large-scale map showing only the northern 40 km² at high detail. A planner marks the same 6 km irrigation canal on both maps and measures it: on Map A the canal is 1.5 cm long, on Map B it is 9 cm long. The office also has a table of census tracts whose boundaries follow the canal but do not match farm parcel boundaries. A colleague argues the canal 'looks the same' on both maps and therefore the two maps must use the same scale.
1. Determine the representative fraction of each map and explain why the colleague's reasoning confuses map scale with something else.
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Map A: 1.5 cm represents 6 km = 600,000 cm, so 1 cm = 400,000 cm → 1:400,000 (small scale, large area per cm).
Map B: 9 cm represents 6 km = 600,000 cm, so 1 cm = 66,667 cm → 1:66,667 (large scale, more detail).
The colleague has confused scale with apparent size on the page. The canal is drawn bigger on Map B precisely because Map B is more detailed and covers less ground per centimeter - the opposite of 'same scale.' The correct habit is to read the representative fraction, not the visual length.
2. The census tracts and farm parcels form two different sets of boundaries over the same land. Explain what this illustrates about geographic scale and why it matters for a policy that allocates irrigation water by census tract.
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The land is the same, but the units of analysis differ: census tracts are administrative/political constructs; farm parcels are land-use/operational units. This is the modifiable areal unit problem (MAUP) - the boundaries you choose change the pattern you see and the conclusions you draw.
Allocating water by census tract means water is assigned to a population-based container, not to the actual irrigators. A tract may contain several farms of very different sizes, or one large farm split across two tracts. The result: some farms are over- or under-served purely because of where the boundary was drawn, not because of need. The planner should either use parcel-level data or explicitly state that tract-level allocation is a proxy with known boundary bias.
3. The office must decide whether to publish the watershed map at 1:400,000 or 1:66,667 for a public meeting where farmers will locate their own fields. Recommend one and justify using scale concepts.
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Recommend 1:66,667 for the field-location task, or a two-map solution: a small-scale overview (1:400,000) for context plus a large-scale detail sheet for field identification.
Reasoning: locating your own field requires enough detail that parcel edges, roads, and the canal are distinguishable - that is a large-scale job. At 1:400,000, 1 cm = 4 km, so individual fields collapse into a few millimeters and cannot be reliably identified. However, 1:66,667 only covers the northern 40 km², so it cannot orient a farmer to the whole watershed. The defensible answer names the trade-off: detail vs. coverage - no single scale serves both, so match scale to the task and supplement rather than substitute.