SME
Geographic Information Systems (GIS) · Problem type
Weighted-overlay suitability score
Use this for “A solar-farm overlay weighs slope 0.5, distance to power lines 0.3 and land cover 0.2. A cell scores 4, 2 and 5. How suitable is it?”
Chart
Layer 1, w₁ × s₁: 2
Layer 2, w₂ × s₂: 0.6
Layer 3, w₃ × s₃: 1
This is an example. Type your own values to start a new problem.
S
=
w₁
×
s₁
+
w₂
×
s₂
+
w₃
×
s₃
Formulas
w₁
+
w₂
+
w₃
=
1
0.5 + 0.3 + 0.2 = 1
S
=
w₁
×
s₁
+
w₂
×
s₂
+
w₃
×
s₃
3.6 = 0.5 × 4 + 0.3 × 2 + 0.2 × 5
Assumptions
•
Each layer is first reclassed to one shared scale, here 1 to 5, with 5 the most suitable.
•
The weights share 1 among the layers, so the suitability stays on the same 1–5 scale.
•
A low score on one layer can be made up by the others: no layer rules a cell out.
Step-by-step
WE KNOW
w₁ = 0.5, w₂ = 0.3, s₁ = 4, s₂ = 2, s₃ = 5
FIND
layer 3 weight (w₃), suitability (S)
Step 1 · Find layer 3 weight (w₃)
Use w₁ + w₂ + w₃ = 1
The weights share 1, so the last layer takes what the other two leave.
w₃
=
1
−
w₁
−
w₂
w₃
=
1
−
0.5
−
0.3
w₃
=
0.2
Step 2 · Find suitability (S)
Use S = w₁ × s₁ + w₂ × s₂ + w₃ × s₃
Each layer’s score counts for its weight’s share; their sum is the cell’s suitability.
S
=
0.5
×
4
+
0.3
×
2
+
0.2
×
5
0.5 × 4 = 2
0.3 × 2 = 0.6
0.2 × 5 = 1
2 + 0.6 + 1 = 3.6
S
=
3.6
Check
Put the numbers back in. Both sides should match.
0.5 + 0.3 + 0.2 = 1 ✓
3.6 = 0.5 × 4 + 0.3 × 2 + 0.2 × 5 ✓
Topic check
See what you know: 5 questions on this topic
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