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Tuesday, 9 December 2014

Should we in Sweden be surprised when we learn that there are foreign submarines in the Stockholm archipelago? Hardly!

On the Swedish politician's statements it sounds like the foreign submarine in Swedish waters (October 2014) was a one-time event. However, given the characteristics of the archipelago, it is very unlikely that this was and is a rare event.

Analyses of submarine operations have a relative long scientific tradition of successfully using quantitative methods. This started during the Second World War where especially UK drafted a very competent group of scientists with the ambition to win the Submarine War in the Atlantic. Under the concept of operations research UK developed methods to analyse submarine movements and behaviour in order to figure out how best to attack them (see, for example, the U-boats in the Bay of Biscay, an essay in Operations Analysis of McCue and Methods of Operations Research Morse and Kimball). This was the start of a successful civil and military research field.
Obviously, when analysing this type of event there are many uncertainties, but there are also some things we know with certainty, for example, about the Stockholm archipelago. If we use what we know about the archipelago, but also are honest about what we do not know with certainty, one can assess the likelihood of actually discovering a foreign ongoing submarine operation. Things we do not know exactly are for example, the duration of the submarine operation, how often the submarine have to surface and the probability for the Armed Forces finding clear evidence if they are searching thoroughly. Here I assume that a submarine operation is one to four days, the submarine is surfacing two to four times a day and that the Armed Forces probability to confirm the presens of a submarine is somewhere between 20 and 70 percent (given a foreign submarine in the archipelago). From the Armed Forces own reports we also know that two independent observations from civilians were required before the operation began.

Given the assumptions above and some probability calculations the probability to confirm a performed hostile operation is about 7 per thousand, but this figure is, as a result of uncertainties, not easy to determine exactly. We can say, however, given the assumed uncertainties, that the probability, with a 95 percent probability, is between 3 per thousand and 16 per cent (informed readers now understand that I'm not a frequentist, but rather a Bayesian). Not minding the exact values, it still can be concluded that it is very difficult, and therefore rare, to succeed in confirming an ongoing underwater operation. Therefore, it is even more unlikely to confirm an operation in more sparsely populated archipelagos or at sea.
Was this incident a one-time event, given the way the world looks today, or a common phenomenon that Sweden so far only discovered once? I don’t know. Also, how to comment on it depends on what we mean by a “one-time event” and how we define "today". We know that submarines have been in Swedish waters before, but it was during the Cold War and both Sweden’s ability to detect submarines and the security situation was different then. Therefore, we look at three different cases:
Assumptions A: The frequency of foreign operations as well as Sweden’s ability to detect these operations have been reasonably constant over the past ten years.
=>  The probability that this was a one-time event calculates to between 1 and 6 per thousand

Assumption B: Conditions, such as the crisis in Ukraine, has influenced the situation so that we only can assume that the conditions have remained constant over the past year.
=> The probability that this was a one-time event calculates to less than 0.6 per thousand.

Assumption C: The situation continues like it is now and after totally 20 similar years only Sweden till has only one confirmed foreign operation.
=> The probability that this was a one-time event calculates to between 3 per thousand and 1.2 per cent.
My conclusion from the probabilities above is that this was not a one-time event, but I can be wrong!

Allowing the archipelago of the Swedish capitol to be so unguarded so that it is virtually impossible to detect an ongoing operation is as if we wouldn’t notice foreign military airplanes until they are landing at the Arlanda airport (just outside Stockholm).
There is only one way to change this equation and increase the likelihood of detection. It is by constantly having (much) more presence at sea and more sensors in the water (as fixed installations and on ships, submarines and helicopters) while also having greater capacity to more closely examining suspicious observations. If Sweden focuses on this, the likelihood to confirm foreign operations can be increased. However, to reach a level where Sweden with high reliability can meet submarine operations in Swedish waters takes substantial efforts.

Given what we know today, the only surprise is that Sweden actually managed to confirm the submarine visit, it is a great achievement for the Armed Forces. The submarine in itself is not surprising and a single event like this should not alter our perception of the outside world. Estimates of how common unwelcome visits are must (as before) instead based on what the visitors have to gain in relation to what they have to lose (gain vs risk). Today, there is no shortage of theories about what the purpose may be and, as shown above, the probability of detection is low (i.e. there are many plausible gains and low risk). However, the consequence of a discovery can be very serious (if Sweden will use weapons if needed). If visiting submarine sailors are going here about once a year, it is about as dangerous as working on a fishing vessel. This, even though there is a small probability that a visit could result in death.
There are a lot more dangerous things that people do just for fun.

-        This was most probably not a one-time event.
-        The risks for a foreign submarine operating in Swedish waters are low.
-        The military purpose of a submarine operation in Swedish waters doesn’t need to be substantial. As a result of the low risks the purpose can be no more than crew training.