Search and rescue

Why this matters

A 1 × 0.6 km riverside forest is too large to search every square metre in the time available. The team must decide where to search first, how densely, and, after searching without success, whether to search the same place again or move on. The search theory long used by coast guards and rescue services gives answers as numbers that can be explained, instead of decisions by feel.

Search patterns

The IAMSAR Manual (IMO and ICAO, 2025 edition) and AMSA’s search and rescue manual describe the common search patterns.

• Parallel track covers a wide area evenly when the location is uncertain
• Expanding square starts at the most likely point and spirals outward, suited to a fairly well-known last position
• Sector passes over a centre point from several directions, suited to a small area around a well-known point
• Creeping line flies across a long axis and creeps along it, suited to searching along a route such as a riverbank

Coverage and probability of detection

The US Coast Guard’s The Theory of Search, based on Koopman’s work, defines the effective sweep width ($W$) as a width reflecting the sensor’s ability to detect a target under given conditions; it is not the image width. Coverage is $C=WL/A$; for parallel tracks with spacing $S$, $C=W/S$, and for random search POD = 1 − e^(−C).

import math

AREA_M2, SWEEP_W, SPEED = 1000 * 600, 20.0, 5.0
for spacing in (40, 20, 10):
    coverage = SWEEP_W / spacing
    pod = 1 - math.exp(-coverage)
    track_km = AREA_M2 / spacing / 1000
    print(f"spacing {spacing:>2} m: C {coverage:.1f}, POD {pod:.0%}, "
          f"{track_km:.0f} km of track, {track_km * 1000 / SPEED / 60:.0f} min")

spacing 40 m: C 0.5, POD 39%, 15 km of track, 50 min
spacing 20 m: C 1.0, POD 63%, 30 km of track, 100 min
spacing 10 m: C 2.0, POD 86%, 60 km of track, 200 min

POS and updating POC

POC (probability of containment) is the probability that the missing person is in an area, judged from the last known position, behaviour and terrain. POS = POC × POD is the probability that this search finds them. After searching an area without success, that area’s POC is reduced by the factor $(1-\text{POD})$, as in the Coast Guard document, and after normalising in the Bayesian way (Kratzke, Stone and Frost, 2010) the POC of the other areas rises.

import math

poc = {"A": 0.5, "B": 0.3, "C": 0.2}
pod_a = 1 - math.exp(-1.0)
print(f"POS of searching A: {poc['A'] * pod_a:.3f}")

not_found = 1 - poc["A"] * pod_a
updated = {k: (v * (1 - pod_a) if k == "A" else v) / not_found for k, v in poc.items()}
for k in poc:
    print(f"area {k}: POC {poc[k]:.2f} -> {updated[k]:.3f}")
print("search next:", max(updated, key=updated.get))
print(f"searching A twice at C=1 gives cumulative POD {1 - (1 - pod_a) ** 2:.0%}")

POS of searching A: 0.316
area A: POC 0.50 -> 0.269
area B: POC 0.30 -> 0.439
area C: POC 0.20 -> 0.292
search next: B
searching A twice at C=1 gives cumulative POD 86%

Reading images in search work

The knowledge unit on search and rescue warns that a bright spot in a thermal image is not always a person; it may be a sun-warmed rock, hot equipment or an animal. FLIR explains that thermal cameras cannot see through walls, only surface temperatures; glass reflects infrared like a mirror, though thermal cameras can see through smoke. Therefore not finding someone in an image does not mean nobody is there, especially under trees or roofs. Reports of suspected sightings must include the image ID, time, location with its uncertainty and the reason, and go to a reviewer; victims’ locations are never published on public channels.

Module lab

Common mistakes

Summary

• Choose a search pattern by how certain the last position is and the shape of the area
• C = W/S and POD = 1 − e^(−C); denser searching raises POD by less and less
• POS = POC × POD; after an unsuccessful search that area’s POC falls and the others rise
• Not seen does not mean not there; thermal cameras cannot see through walls

Check your understanding

1. W = 30 m and track spacing 30 m. What is POD?
2. POC 0.4 and POD 0.6. What is POS?
3. An area is searched twice with POD 0.5 each time. What is the cumulative POD?
4. Why does B’s POC rise after A is searched without success?
5. Can a thermal camera see a person behind a wall?