where
N
= the number, or fraction, of critical separations, and constant spacings are assumed. These POD values are applicable to any terrain and conditions and agree with Wartes' published field data for moderately dense underbrush (Table2.11),
which is widely accepted, giving greater credibility to the theory.2.4.3.1 Purposeful Wandering
Perkins and Roberts
[137]
emphasize the ease and practicalities of the critical separation approach, along with its increased effectiveness. An effectiveness which has shown by experience to be further increased by purposeful wandering, where the "searcher wanders about as he moves through the terrain rather than attempt to maintain a constant spacing" ,[137,
page9].
The searcher stops regularly to look around, particularly in difficult terrain and to search possible places of concealment. As Perk ins[137,
page24]
states:"searching is a positive activity; it entails much more than just walking for wards along an imaginary line - a searcher must move around within his strip
of ground to look in likely hiding places and to gain good vantage points, and must stop at frequent intervals to look back."
Field observations by Perkins and Roberts indicate that employing this tactic with ex perienced searchers increases the POD when using critical separation from a theoretical
50%
to approximately75-80%.
This measures to some extent the effect and importance of purposeful wandering.Another method which is assigned the name of purposeful wandering is a method which was adapted in Germany during the Second World War. In this instance purposeful wandering involved sending additional people into the search area to wander through the area following their gut instincts and known information on the lost person
[81].
2 . 5 Success o f a Search Operation
The Probability of Success (POS) of a search in a region i, z. e. the probability of
the detection of the subject in region i, is found by the multiplication of POA and POD values.
POSi
= P(subject in region i and detected) =POAi
xPODi
POS is used as a predictive measure of how effective one choice of search resource and search technique will be in comparison to another. As POS values for each search region are independent, they can be summed to give a total POS measure for a given phase in the SAR operation. POS is a useful planning tool in determining the overall search strategy. However, as it depends upon POA values which are subjective; "any notion of obtaining 'an exact solution' is unreasonable" ,
[136,
page51].
Cumulative POS (POScum), measuring the likelihood of detection based on all search ing on the operation up until the current time, can be calculated by three methods
[150]:
1.
POScum = �fll regionsPOAi
xPODcum,i
where
PODcum,i
represents thePODcum
value for search region i2.
POScum = �fll searchesPOSi
3.
POScum =1
-�fll regionsPOAi
The first method uses the initial POA values assigned to the search regions. The method is not recommended as the assumptions underlying the formula are not usually valid in reality
[150]
(those assumptions are that the only influence on the subject's location probability distribution are the actual searches) . Both the second and the third method of calculation are valid under any search situation provided that the POA values2.6. Location Probability Distribution Update 35
of each search region are adjusted to account for non-detection on the completion of each search. The methods also assume that POA values are not normalized when updated after each search.
The calculation of the POScum can be used to monitor whether or not search effort is being allocated to the correct area. A high value, indicating a continued lack of success, could indicate that the wrong region is being searched
[150]
and that the current scenario being followed is incorrect[62].
However, Stone[153]
cautions that the definition of 'high' is subjective. POScum can also be used as one decision factor when search suspension is under consideration.2 . 6 Location Probability Distribution Update
"Most searches take place sequentially, or over a long enough period of time, so that the search planner can receive feedback from the search and adjust his plan accordingly" ,
[153,
page227].
The subject location probability distribution, and hence POA values, can be updated to account for all of the information gained during searching up to a given point in time. If a region is searched without subject detection then the probability that the subject is in another region may be increased, taking into consideration the level at which the region was searched, i. e., the possibility that the subject may have been missed. As more regions are searched the current POA value of previously searched regions may be high enough to warrant those regions being re-searched. These probability calculations can be time consuming (although much less so with advances in computing power) , but Syrotuck[159]
emphasizes their utility as an aid to monitoring the progress of the operation and the likely position of the subject.The subject's prior probability distribution is replaced by a posteriori probability distribution by a Bayesian update of the POA values. Bayes' theorem for mutually exclusive events
Bl, B2, ... , Bk,
of which one must occur, is given on page150
of[55]
as:which is equivalent to:
If we describe the event
Bi
as the event that the subject is located in region i , we can see that theBi
events for i =1, 2
... or k, for k regions, are indeed mutually exclusive;the subject cannot be located in more than one region at any given time. If the ROW region is included, say as event
Bk,
then it is also true that one of theBi
events must occur. Hence, it is valid to apply Bayes' theorem to calculate the probabilityP(BiIA),
namely the probability that the subject is located in region i, given that region i has been searched and the subject was not detected. This is equivalent to finding the updated POA value for region i, PO Ai ·
Decomposing the right hand side of the equation we can see that the probabilities can be individually expressed as:
P(A) the probability that region i was searched without detection, which is equivalent to the probability that the subject is in region i and was missed or that the subject is not in region i
= POAi .
(1 - PODi) + (1 - POAi)
P(Bd the probability that the subject is located in region i
= POAi
P(AIBd the probability that region i was searched without detection given that
the subject is located in region i
Therefore,
= ( 1 -PODi) OA* _
POAi · - P . -
This equation can be simplified to:
POA! = POAi · t
1 -
POAiPODi(1 -
PODdTo ensure that all subject location probabilities sum to one at any time the POA values of the other search regions can be normalized. For such a region j the updated P�A value is then:
POA* = POAj J .
(1
- P�Ai')1 -
POAiSubstituting the simplified expression for PO Ai into this equation yields:
* POAj
POAj =
1 -
POAiPODiClark
[19]
refers to the term (l-POAiPODd as the probability of "non-success" as this is equivalent to(1
- POSi).However, Cooper
[30]
states that the most effective and undisputed way to adjustPOA values upon the receipt of substantial new information is to obtain a new consensus, this approach being "superior and simpler to alternative methods of either subjectively or mathematically adjusting P OA in similar situations."
2 . 7 Search Measurements
Hill
[88]
states that "using resources efficiently means getting the most coverage from the resource for the number of man hours expended, and, ultimately, finding the lost person2.7. Search Measurements 3 7
sooner rather that later."
A number of quantitative measurements exist to monitor the effectiveness of the search operation. These are largely contained in the classical search theory literature
[100, 150]
and consist of the following.Effective search or sweep rate is calculated as:
Effective Search Rate = W x searchspeed
The area effectively swept is then defined as:
Area Effectively Swept = Effective Search Rate x t
where t represents the time spent in the search region.
Search effort, Z, is defined in search theory as the area which can be effectively swept
[150]
and is calculated as:Z = W x L
where L represents the distance travelled by the sensor in the search area. Or, alterna tively, it may be defined as:
Z = W x V x T
where V is the search speed and T the hours spent in the search area. This definition of effort is different to the searcher-hour definition commonly used by the land SAR community.
The coverage, C,12 of a search area is determined as a ratio of the search effort and the size of the search area.
c = Z A
For straight, equally spaced, parallel sweep searches, the coverage can equivalently be defined as:
c = W
S
where
S
denotes the track spacing. Where k equivalent search resources are searching simultaneously in one area, C is calculated as[65]:
c = Z x k A
Overall search effectiveness is measured by the cumulative POS and search efficiency is measured by the rate of POS growth over the search operation
[62].
1 2 Also referred to
2 .7 . 1 Searcher Utilization
Perkins [137J gives three parameters by which to measure searcher utilization for ground searchers conducting a visual sweep search: POD value; the number of searchers; and the width of the search corridor (given in standardized units of critical separation) . He places these in the following formula,
utilization = (corridor width x POD) / number of searchers,
where the search corridor is the total width covered by the searchers spaced in a line, from end searcher to end searcher, and also includes the outer distance searched by the end searchers. The corridor width is calculated as (M - 1)N + 1 critical separations if
N > 1 or as 2N + 1 if N
�
1 , where M represents the number of searchers and N equals the spacing in critical separations.Perkins investigates differing values for the search parameters, finding that spacing searchers at critical separation gives the best searcher utilization for larger search teams. Perk ins claims that, theoretically, critical separation between searchers results in the best utilization of searchers, as the entire area between any two searchers is covered and no area is covered by more than one searcher. Any other search spacing "will result in either a lower POD or a lower utilization" , [137, page 23J. Particularly, the use of a wider spacing will produce no gains but higher priority areas may require a closer spacing to increase the POD. However, Frost [62J cautions against jumping to the conclusion "that the overlapping of detection profiles from adjacent searcher tracks is to be avoided under all circumstances . . . with realistic detection profiles, some overlap is often required to achieve a practical approximation to the optimal search plan."
Perkins also identifies an effect on searcher utilization for smaller teams which he terms the 'end man effect '. This effect identifies that the search terrain covered at either edge of the team's search corridor by the outside searchers, as a proportion of the entire corridor, is larger for smaller teams. In this instance the searcher utilization is a maxi mum when searchers are spaced at 0.7 critical separations.
These concepts, predictive statistics and search measures comprise the fundamentals of effective search management. We now review how these concepts are currently in corporated in the procedures followed by land SAR managers, examining the decisions required in initiating a SAR response, allocating search resources and executing specific search techniques.
C H A P T E R 3