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Overlay finds where layers coincide: intersections, unions and erases give areas, and a share divides the overlap by the chosen whole.
Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.
By the end of this lesson you will be able to choose an overlay operation, compute the areas it produces, and report shares with the right denominator.
You know a GIS stores the world as layers that share a coordinate system, and you can measure area from raster cells. This lesson combines layers: laying one over another to find where they coincide, and turning the result into areas and percentages.
| Term | What it means |
|---|---|
| Overlay | Combining two or more layers to find how their features coincide. |
| Intersection | The area covered by both layers. |
| Union | The area covered by either layer. |
| Erase | The first layer with the area of the second removed. |
| Dissolve | Merging neighboring shapes that share a value into one. |
| Suitability analysis | Overlaying several criteria to find places that meet them all. |
Overlay combines layers to answer questions that neither answers alone.
Another way: picture
Picture two colored transparent sheets, one shaded where land is zoned for housing and one where it floods. Stack them against a window. Where the colors mix is the intersection; everywhere with any color is the union; the housing color alone is the erase. A GIS does this with coordinates instead of light.
Another way: steps
An attribute join uses a key shared by tables. A spatial join uses a location rule such as a point lying inside a polygon. Neither is identical to an intersection, which derives overlapping geometry. In a fictional shelter study, first join opening hours to shelter points by a unique shelter ID. Check duplicate keys and unmatched shelters before selecting those open at the time of the study. Joining by row order can silently attach the wrong hours. Missing hours mean unknown availability, not closed or open by default.
A buffer creates a proximity zone around geometry. An intersection retains common space; a union retains both polygon extents and their attributes. Dissolving removes internal boundaries between features grouped by an attribute. Record the rule for points exactly on a boundary so shared edges do not produce accidental double counts. Overlay can establish that conditions coincide, but that coincidence does not identify a causal mechanism.
Suppose shelters S and T have verified IDs and opening hours. S is open in the evening and T is closed. A residential block lies 400 m from S across a canal, but the permitted bridge makes the shortest walk 1200 m. First select S using the joined hours. Next represent paths as connected edges and junctions as nodes; attach walking times, direction restrictions and closures. Solve the least-cost route or service area for the permitted network. A line crossing another line on a drawing is not necessarily a connected junction, as a footbridge and a road beneath it illustrate. Finally intersect the service area with residential polygons. This answers where modeled accessibility overlaps residences. Counting everyone in a partly intersected block as served requires an additional population-allocation assumption. A simple buffer remains useful as an initial proximity screen, provided the report does not call it a travel-time boundary.
An intersection answers "where are both true?" Which homes are in the flood zone? Which farms lie over the aquifer? Which schools are within a heat island?
The result is a new layer containing only the shared area, carrying the attributes of both inputs, so each piece knows its zoning and its flood risk.
A union answers "where is either true?" All land under any hazard, for instance. Because the overlap belongs to both layers, adding their areas counts it twice, so the union is $A + B - \text{overlap}$.
An erase answers "where is the first true but not the second?" Housing land outside the flood zone is the housing layer with the flood zone erased: $A - \text{overlap}$.
A share depends on the whole you divide by. If $10$ of a park's $40$ square kilometers flood, a quarter of the park floods, $25$ percent. If the flood zone covers $50$ square kilometers, the park holds a fifth of it, $20$ percent.
Both are correct; they answer different questions. State which whole you mean.
| Layer or result | Area (km²) |
|---|---|
| Residential zoning | 30 |
| Flood zone | 12 |
| Intersection | 4 |
| Union | 38 |
| Residential outside flood zone | 26 |
The three pieces, $26$ residential only, $4$ both, and $8$ flood zone only, add to the union of $38$.
Rasters overlay cell by cell. If one raster marks slopes under ten percent with a one and another marks land outside the floodplain with a one, multiplying them gives one only where both are true.
Counting those cells and multiplying by the cell area measures the suitable land, just as in the last lesson.
Choosing a site for a landfill, school or wind farm means meeting many criteria at once: flat enough, away from homes, near a road, outside wetlands. Each criterion becomes a layer, and overlay finds where all are met.
The answer depends on the thresholds chosen. Moving a buffer from one kilometer to two can remove most of the candidate land.
To estimate how many people an overlap affects, multiply its area by the population density of the neighborhood it covers. $4$ square kilometers at $1500$ people per square kilometer is about $6000$ people.
This assumes people are spread evenly, which is rarely true; finer layers, such as census blocks or building footprints, improve the estimate.
Checking an answer. An intersection is never larger than either layer. A union is never smaller than either. A share of a whole cannot pass a hundred percent.
Subtracting the overlap once in a union is allowed because it was added twice, once with each layer. Subtracting the overlap in an erase is allowed because the overlap is exactly the part of the first layer inside the second.
Dividing by the whole is allowed because a percent compares a part to its whole.
Overlaying pollution sources with neighborhoods has shown, again and again, that hazards cluster near low-income communities and communities of color. The Environmental Protection Agency's EJScreen tool, released in 2015, overlaid environmental and demographic layers for the whole country so anyone could see it.
The same method can hide as much as it shows: large polygons average away local hot spots, the issue raised in the choropleth lesson.
When two layers trace the same boundary separately, such as a county line digitized once for a parcel layer and once for a flood layer, the lines rarely match exactly. Overlaying them creates slivers: long, thin polygons that belong to neither layer's intent.
Slivers add tiny false areas to every result and can make a count of affected parcels too high. GIS software removes them by snapping lines that fall within a small tolerance, say a meter, to one another, or by dropping polygons below a minimum width. The tolerance is a choice: too small leaves slivers, too large merges real features, so it is recorded with the analysis.
The cleanest fix is upstream: build layers from a shared boundary file, such as the Census Bureau's county lines, so the edges match from the start. Shared boundaries are one reason agencies publish official base layers that everyone else is encouraged to build on.
The most common slip is dividing the whole by the part, which gives a figure over a hundred percent. Another is adding areas for a union without removing the overlap.
A third is using the whole zone's area when only the overlap matters. A fourth is overlaying layers in different datums, so that the overlap itself is wrong.
Overlay turns separate facts into combined ones, and most planning questions need that. The next lesson adds distance: buffers find everything within a set distance of a feature, and are often overlaid in turn.
In his 1969 book Design with Nature, the landscape architect Ian McHarg showed how to choose a highway route by overlaying transparent maps of values: shaded darker where land was steep, flood-prone, historic, wooded or costly. Where the stacked sheets let the most light through, the road did the least harm.
He applied it to a proposed parkway on Staten Island in New York, arguing that a route drawn by overlay would protect wetlands and forests that a route drawn only for cost would destroy. His method spread through planning schools across the country.
Computers soon replaced the transparent sheets, but the logic of modern GIS suitability analysis is still McHarg's: turn each concern into a layer, and let overlay show where they agree.
FEMA publishes its flood hazard maps as a national GIS layer. Cities, insurers and researchers overlay it with parcel and building layers to count how many homes lie in the zone where flood insurance is required for federally backed mortgages.
Those counts shape budgets and politics. A city that learns that a fifth of its homes lie in the flood zone may buy out the most flooded blocks, raise roads, or change its zoning so new homes are built elsewhere.
The answer depends on the layers. Research groups that overlay newer flood models, which include heavy rainfall and small streams, often find millions more properties at risk than the official maps show, which is why overlay results always need their sources named.
It is easy to divide the two numbers in whichever order comes to mind and report the result as a percent. But a share of a park is the overlap over the park; turning it over gives a figure larger than a hundred percent, which cannot be a share.
A related slip is adding two layers' areas for a union, counting their overlap twice. Subtract it once, and the union can never exceed the two areas added together.
A $40$ square kilometer park has $10$ in the flood zone. Name the whole.
$\text{the park}$
The question is about the park.
Divide the overlap by the park.
$10 \div 40 = 0.25$
A fraction.
Convert to a percent.
$25\%$
Times a hundred.
Name the inverted slip.
$40 \div 10 = 400\%$
Whole over part.
Zoning covers $30$, the flood zone $12$, and they overlap on $4$ square kilometers. Add the two.
$30 + 12 = 42$
The overlap counted twice.
Subtract the overlap once.
$42 - 4 = 38$
The union.
Find residential land outside the zone.
$30 - 4 = 26$
The erase.
Find flood zone outside residential land.
$12 - 4 = 8$
The other erase.
Check the parts add to the union.
$26 + 4 + 8 = 38$
Three pieces.
A county has $20$ square kilometers zoned for housing, with $5$ flooded, $4$ wetland, and $2$ both. Add the hazards.
$5 + 4 = 9$
Both counted twice.
Subtract the overlap.
$9 - 2 = 7$
Under either hazard.
Erase the hazards.
$20 - 7 = 13$
Buildable land.
Name the double-subtraction slip.
$20 - 5 - 4 = 11$
The overlap removed twice.
Find the share buildable.
$13 \div 20 = 65\%$
Of the zoned land.
Say what the planner does next.
$\text{overlay roads and sewers}$
More criteria.
Divide the farmland by the refuge.
$10 \div 50 = 0.2$
Part over whole.
Convert to a percent.
$20\%$
Times a hundred.
Find the rest.
A park covers $50$ square kilometers. Overlaying the flood zone layer shows $20$ square kilometers of the park inside the zone. What percent of the park is in the flood zone?
Complete the worked solution: a proposed wildlife refuge covers $120$ square kilometers, and an intersection with the farmland layer shows $30$ square kilometers of it are farmed. Find the area not farmed, the percent farmed, and the percent not farmed.
Find the area not farmed.
$\text{refuge} - \text{farmland} =$ a
An erase.
Find the percent farmed.
$\text{farmland} \div \text{refuge} \times \text{a hundred} =$ p
A share of the refuge.
Find the percent not farmed.
$\text{a hundred} - \text{percent farmed} =$ q
The rest.
Say who cares about the answer.
$\text{the farmers and the agency}$
Land would change use.
Match each overlay operation to what it produces from two layers.
| only the area covered by both layers | all the area covered by either layer | the first layer with the second cut out of it | adjacent shapes with the same value merged into one | |
|---|---|---|---|---|
| intersection | ||||
| union | ||||
| erase | ||||
| dissolve |
A town's residential zoning covers $30$ square kilometers and its flood zone $12$ square kilometers; they overlap on $4$ square kilometers. Fill in the area in both, the area in either, and the residential area outside the flood zone.
| area | |
|---|---|
| in both (km²) | |
| in either (km²) | |
| residential outside the flood zone (km²) |
Two layers cover areas that add to $65$ square kilometers. Write the area of their union as a function of their overlap $x$.
Answer:
A flood zone covers $20$ square kilometers. It overlaps a neighborhood on $5$ square kilometers, and the neighborhood has $2000$ people per square kilometer. About how many people live in the overlap?
Answer: people
A county planner has $15$ square kilometers of land zoned for housing. Inside it, $4$ square kilometers lie in the FEMA flood zone and $3$ are wetland, and $1$ square kilometers are both. How much land is left that is neither flooded nor wetland?
Answer: unit: m2 / km2
A fictional town has 4 candidate cooling centers, opening hours keyed by center ID, residential polygons, a river and a walking network with one usable bridge. The question asks which residential areas intersect a center's 15-minute walk service area. Which operation chain answers it?
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
Two layers cover areas that add to $36$ square kilometers. Write the area of their union as a function of their overlap $x$.
Answer:
You can reason with overlay. Explain why a union of two layers is smaller than their areas added together.
26. Your turn: a refuge of $50$ square kilometers contains $10$ of farmland. What percent is farmland?, step 3
$80\%$
Not farmed.