10.1 Introduction

Possibly the most unfortunate legacy of the Battle of the Atlantic is the great number of wrecks lying in coastal and marine waters that still contain oil, unexploded ordnance, and other pollution or safety hazards. This has become an increasingly pressing issue in recent years, as these wrecks are now entering their eighth decade underwater and many are experiencing significant structural degradation due to natural corrosion and anthropogenic causes. While some of these potentially polluting wrecks have been located and steps taken to mitigate their pollution risk, many more remain missing, particularly those which sank in deep water (NOAA, 2013a, b; Symons et al., 2014; Hoyt et al., 2021; Brennan, Chap. 1, this volume).

This chapter discusses a potential method for locating these missing wrecks, using as a case study the oil tanker William Rockefeller. Rockefeller was a twin-screw, steel-hulled oil tanker, owned and operated by the Standard Oil Company of New Jersey. It was 554 feet long with a 75-foot beam and a gross tonnage of 14,054 tons. Its cargo capacity was 22,390 deadweight tons, or approximately 146,745 barrels of oil, carried in eight tanks amidships divided by 13 oil-tight bulkheads. When launched in 1921, Rockefeller and its sibling ship John D. Archbold were the largest oil tankers in the world. Rockefeller operated in the Gulf and Pacific oil trades for most of its career, though with the advent of World War II it began taking on cargo from international ports (Newport News Shipping and Dry Dock Company, 1920:9–20; Standard Oil, 1946:320–321).

On 28 June 1942, Rockefeller was sailing past Cape Hatteras en route from Aruba to New York with a cargo of heavy fuel oil when it was ambushed by the German submarine U-701. A single torpedo caught Rockefeller amidships, breaching one of its storage tanks, spraying oil across the deck, and setting the ship on fire. After its crew abandoned ship, Rockefeller was left to drift with the currents and wind before finally going down sometime later. There are several versions of Rockefeller’s sinking; contemporary accounts indicate that it either sank on its own or after U-701 hit it with a second torpedo almost 12 h after the attack, while some secondary sources record a claim that it was sunk the following morning by the Coast Guard as a hazard to navigation (Fig. 10.1) (Degen, 1942; Standard Oil, 1946:321–323; Hoyt et al., 2021:7–278).

Fig. 10.1
A 3 D map of the ocean with Pamlico Sound. It marks Captain Stewart sinking location, Supplemental Statement Sinking Coordinates, attack location, sinking location, and attack location from north to south, respectively.

Attack locations and possible sinking locations derived from various sources on Rockefeller’s loss. From bottom to top: the point at which Rockefeller’s known course diverged from prescribed convoy routes; attack location as given by uboat.net; attack location as given in the Office of the Chief of Naval Operations’ (OCNO) supplemental statement to the summary of events given by Rockefeller’s crew; sinking location as given by uboat.net; attack location as given by Rockefeller’s master William Stewart; sinking location based on OCNO’s coordinates, given a sinking time just before midnight of 29 June; sinking location based on Captain Stewart’s account, given the above sinking time; sinking location based on OCNO’s statement given an approximate sinking time in the early morning of 29 June; sinking location based on Captain Stewart’s account, given the ship sinking on the morning of 29 June. (OCNO, 1942b, c; uboat.net 2021; map drawn by the author)

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When it went down, Rockefeller was carrying 136,647 barrels (5,739,174 gallons or 21,725,136 liters) of heavy fuel oil, excluding its bunkered fuel. Some of this oil was spilled or burned off by U-701’s torpedoes, but it is probable that a significant amount remains in the wreck (OCNO, 1942a, c; Standard Oil, 1946:321; NOAA, 2013b:13). Because of this, it is one of the 87 wrecks listed in the RULET database given the potential it poses for severe pollution of the Eastern seaboard. Since the wreck has not yet been located and its condition is unknown, NOAA’s risk assessment screening package has recommended conducting surveys of opportunity to locate the vessel, determine its condition, and judge whether it is an imminent hazard (NOAA, 2013b:16–22, 38–39; Symons et al., 2014).

Since Rockefeller sank after drifting for at least 11 h, possibly more, and the only claimed eyewitness to its sinking did not give coordinates for its last resting place in his narrative of events, establishing a search area for the wreck has proven problematic (see Fig. 10.2). Some estimates have suggested that a search would encompass up to 750 square nautical miles (NOAA, 2011, 2013b:6). As this area would require significant outlay of time and effort to fully cover, this chapter discusses a means by which this potential search box may be shrunk to a more manageable size using Bayesian search theory, a method that has been tested and proven in multiple maritime searches. If successful in locating Rockefeller, this methodology may be useful in the creation of search models for other potentially polluting shipwrecks lost under similar circumstances.

10.2 Why Bayesian Search?

A shipwreck is typically a high-stress event involving imminent risk to life and limb, with accompanying repercussions for the thought processes, emotions, and memories of those involved (Gibbs, 2002:72–76). Even if someone thinks to record a sinking ship’s last coordinates in the heat of the moment, it is very possible that these coordinates will be mistaken, or later misremembered. One has only to look at the records of past wreck search expeditions to see this problem in action: numbers are transposed, latitudes and longitudes are scrambled, and in some cases the coordinates given are simply wrong. Possibly the most notorious example of this phenomenon is that of the RMS Titanic. As the famed liner was sinking, wireless operators Harold Bride and Jack Phillips repeatedly transmitted distress signals containing what they believed to be an accurate position for the stricken ship. Subsequent search expeditions took this position data at face value and based their efforts on it, only to come away empty-handed. It was not until Dr. Robert Ballard reevaluated the problem, concluded that the positional data must be in error, and expanded the search area that Titanic was relocated in 1985, 13 nautical miles from the position given by Bride and Phillips (Ballard, 1987:23, 26, 66, 83).

The problem for the archaeologist or historian is how to sift through these disparate or sparse sets of information in such a way as to maximise their chances of completing a successful search. Then comes the second issue, which is equally important: selecting a theoretical framework/model into which this data can be fed to generate a search plan. All this is done with an eye toward optimising the search parameters so as to produce the highest chance of success with the least expenditure of money, time, and effort. Dr. Lawrence Stone refers to this as the basic problem of optimal search (Stone, 1975:32). There have been a variety of methods proposed for the solution of this problem, but Bayesian search theory offers a method that accounts for all possible scenarios while still allowing researchers and archaeologists to focus their efforts on a smaller, high-priority search area. It has been successfully employed in multiple maritime search efforts, including the recovery of an H-bomb lost off the coast of Spain in 1966 and locating the wrecks of USS Scorpion, SS Central America, and Air France Flight 447 (Richardson & Stone, 1971:141–144; Stone, 1992:42–53; Sontag et al., 1998:58–60, 104–106; Craven, 2001:167–170, 173–174, 213; Frost & Stone, 2001:3–4; Stone, 2011:21, 23; Stone et al., 2014:72–80).

Bayesian search theory is based on the statistical models of eighteenth-century English statistician and philosopher Thomas Bayes (Bayes & Price, 1763). Put simply, Bayesian statistics operate on a definition of probability wherein ‘probability’ expresses a degree of belief in the occurrence of a given event. This belief may be based on prior knowledge of the event, whether derived from personal experience or historical records, or it may be based on one’s own theories or beliefs about said event. The probabilities are expressed as part of an equation which is used for a given purpose, in this case searching for a lost shipwreck.

Bayesian theory as applied to maritime search is a relatively straightforward concept. The researcher must form as many reasonable hypotheses as possible about what may have happened to their target object, based either on hard data or their own beliefs. These hypotheses are used to generate a probability density function for the object’s location, which calculates the probability of a random variable (in this case, the location of a submerged object) falling within a particular range of values (Stone, 2011:23).

After this, a second function is constructed which expresses the likelihood that the target object will be found at a given location, if it is really in that location. This information is used to generate a probability map, which gives the probability of finding the target object in a given location for all possible locations within the projected search area. After this, a search grid and path is devised that covers the entire area from highest to lowest areas of probability. During the search, the probabilities must be continually revised according to the findings. For example, if the object is believed to have fragmented before sinking, and fragments are not found in the areas where they are most likely to be according to the map, then the fragmentation hypothesis becomes less probable and should be revised or discarded accordingly (Stone, 2011:23–24).

As new data is gathered, it is fed into the model to update the probabilities contained therein. The model, of course, is only as good as the data that is used to make it, so someone who employs Bayesian search theory must be sure that they are collecting and using data that is as accurate as possible. Given the problems mentioned at the beginning of this section, this is not always an easy task. Such proved to be the case when applying the principles of Bayesian search to the problem of finding William Rockefeller.

10.3 Searching for Rockefeller

In the case of William Rockefeller, there existed several eyewitness accounts of the attack on the tanker, including its master William Stewart and Kapitänleutnant Horst Degen, the captain of U-701, who was captured and interrogated after his submarine was sunk in the vicinity of Cape Hatteras on 7 July 1942. These accounts form the basis of most of the research done on the tanker’s loss; while they are in general agreement as to Rockefeller’s last hours afloat, there were some discrepancies that had to be accounted for. Most of these discrepancies could be put down to the stress of the sinkings and the unreliability of human memory, though there were indications of deliberate obfuscation or selective recall, especially when comparing the initial accounts of the attack to those set down years or decades later (Degen, 1942; OCNO, 1942a, c; Standard Oil, 1946; Offley, 2014). The accounts were used to construct a series of scenarios for Rockefeller’s loss, with the aim of covering all the possibilities as to the tanker’s fate. They may be summarised as follows:

  • Scenario 1: Rockefeller sinking on its own after drifting and burning for just over 11 h. This is based on the reports of the US Navy and Coast Guard.

  • Scenario 2: Rockefeller being sunk by a second torpedo from U-701, after ~12 h adrift. This is based on the interrogation of KptLt Degen and his unpublished postwar account.

  • Scenario 3: Rockefeller being scuttled by Coast Guard aircraft on the morning of 29 June. This is based on the accounts of several secondary sources which record a Coast Guard report to this effect.

As is obvious, the scenarios cannot all be correct, so what weight is to be given to each of them? This is a task requiring subjective probability analysis; in plain language, this analysis involves a person looking at all the information they have gathered and deciding what they believe to be the most reliable. This is a part of the Bayesian method that is meant to quantify the otherwise unquantifiable human factors of intuition, gut feelings, and hunches. This is not to say that the process is unscientific, for it requires the person or persons conducting the analysis to carefully study the available data and evidence when making their decisions, but it contains an element of uncertainty since it is based on subjective opinions (Stone, 1992:45–46; Sontag et al., 1998:59, 104–105; Craven, 2001:167–168). In this case, the author decided that Scenario 2 was the most likely, since it tracked closely with what is generally accepted about Rockefeller’s last hours and Degen provided a persuasive account of his claimed second attack on the submarine (USONI, 1942; Offley, 2014). Scenario 1 overlaps in most particulars with Scenario 2; it may even be the case that Degen’s second attack on Rockefeller was seen and processed as the tanker sinking on its own. These two scenarios were therefore weighted as being equally likely. The third scenario is not well-supported by the primary sources and appears mainly in secondary sources; it was therefore rated as the least likely of the three.

With the scenarios devised and weighted, a probability map was created using ArcGIS and SAROPS, a software package developed for the US Coast Guard that employs Bayesian mathematics and Markov chain Monte Carlo simulations to generate probability maps for maritime search-and-rescue efforts (United States Coast Guard, 2008; Kratzke et al., 2010:1–2).

Monte Carlo simulations are used to calculate the results of a scenario with numerous variables, expressing the outcome as a probability distribution showing the range of possible outcomes according to the likelihood of their occurrence. However, a standard Monte Carlo simulation is not suitable for more complex problems, since it relies on the assumption that the values for which it calculates results are independent of each other and may be drawn independently. The solution to this problem is to use a Markov chain, which calculates each successive variable based on the value of the last variable generated, creating a stochastic chain that allows for greater flexibility in generating the final probability density (Brownlee, 2019).

SAROPS uses Markov chain Monte Carlo simulations to generate a probability density function by sequentially generating random variables based on the data that is fed into the program. For a typical SAR scenario, this data is acquired in real time, which enables the production of highly accurate maps (Roylance, 2007:4D). In this case the simulation had to rely on historical data, which added a greater degree of uncertainty to the outcome. The two main variables were the currents and wind speed prevailing during the attack; a combination of interpretations and contemporary data had to be employed to reconstruct them.

The attack occurred within the Gulf Stream, meaning that Rockefeller’s drift after being abandoned would have been influenced by this relatively strong and predictable current. Its precise speed on 28 June 1942 is not known, but the Coast Guard casualty report for Rockefeller indicates the ship was drifting at 1.5 kt when abandoned (USCG, 1944b). Data obtained from a 1942 Coast and Geodetic Survey publication indicated that the Gulf Stream was then known to flow strongly northeastward during the summer months, peaking in strength during July. The monthly average of the Gulf Stream in June as measured by the Diamond Shoals lightship from 1919 to 1928 was 0.66 kt (Haight, 1942:24–25, 52). It is therefore probable that the Stream was pushing Rockefeller northeast at low speed. Similar examples of Gulf-influenced drift can be seen in the cases of the merchant ship Papoose and U-701. Papoose was torpedoed approximately 15 miles southwest of Cape Lookout, North Carolina, and drifted north with the Stream for 2 days before sinking off Oregon Inlet, and the survivors of U-701 were carried northeast with the current for 49 h before being recovered by the Coast Guard (USCG, 1944a; USONI, 1942:1; Hickam, 1989:278–282; NOAA, 2022).

Wind speed is another variable for which assumptions and estimates had to be made, though in this case more solid data was available. Rockefeller was being escorted by a Coast Guard cutter that logged weather data at 4-h intervals, noting general conditions, barometric pressure, cloud cover, visibility, and wind speed. At noon, 16 min before Rockefeller was attacked, the cutter logged the following weather data: barometric pressure 3001, winds from the southwest at Beaufort Force 1 (1–3 mph/1–3 kt), blue skies with scattered cumulonimbus clouds, visibility 7 miles (USCG, 1942:2). Given that Rockefeller was drifting at about 1.5 kt when it was abandoned, it may be presumed that the wind was very light at this time, possibly not more than 1 kt, therefore both wind and current would have been exerting force against the tanker’s hull.

These estimates were added to a data package which also included events, times, Rockefeller’s speed (known or estimated), Rockefeller’s position, general weather conditions, and compass bearings. The package was then sent to the Coast Guard to be input into SAROPS. Senior Chief Petty Officer Ian Brown, an experienced SAROPS technician, was given the task of creating the SAROPS model. He consulted with oceanographer Dr. Cristina Forbes, who helped him format the data for SAROPS, calculated possible wind and current speeds, and proposed that he create three different scenarios based on possible weather conditions at the time. After this consultation, Chief Brown fed the resulting data into the SAROPS simulator. He explained to the author that the maximum vessel length that could be input into the program was 300 feet, since the program is tailored toward searching for lost individuals and small craft, not large vessels. As Rockefeller was 554 ft. in length, this meant that he had to split the simulated vessel into two parts and recombine the results later. He also input the estimated current, wind, and drift speeds from the historical data and his consultations with Dr. Forbes. All times in the program were recorded in Greenwich Mean Time (GMT) and were then adjusted into Eastern War Time (EWT) (Ian Brown 2022, pers. comm.).

To account for the uncertainty of wind speeds, Chief Brown ran multiple iterations of the scenario. For the first iteration, he used a wind speed of 0.87 kt and a current speed of 0.66 kt until time index 1700 GMT (1300 EWT), representing the likely point at which Rockefeller would have been in the middle of the Gulf Stream and experiencing its full strength, which he calculated at 1.5 kt. For the second iteration of the scenario, he used a wind speed of 1.74 kt and the same current estimates as in the first iteration, with Rockefeller entering the middle of the Gulf Stream at time index 1700 GMT/1300 EWT. For the third iteration, he again used the same current estimates and a wind speed of 2.6 kt. Each of these iterations produced a probability density cloud illustrating potential sinking locations for Rockefeller as based on the estimates fed into the program. For each stage of the scenarios, he placed a ring around the density cloud to indicate the general size of the area of potential drift, given in square nautical miles (Ian Brown 2022, pers. comm.).

These density clouds were added to an ArcGIS map containing the sinking locations from the historical records and a drift analysis created by the author to produce a final probability density map (see Fig. 10.2). A search grid was imposed over the area of highest density with cells measuring 16 square nautical miles each; this grid covers a total of 384 square nautical miles. The potential search area has thus been almost halved from NOAA’s original estimate of 750 nautical miles. If sectioned into a grid of 4 by 4 nm segments, this gives 24 cells in which to search within this box (see Fig. 10.3). The question that follows is how to further prioritise the search area to maximise the chances of success. According to Bayesian methods, the factors that must be considered here are the following: the prior distribution of information, the subjective probabilities of the occurrence of given events, and posterior distribution of data obtained from previous search efforts (Stone, 2011; Stone et al., 2014; Rossmo et al., 2019).

Fig. 10.2
A combined density cloud containing data points from the author's G I S work. The density of the data points is the highest centrally. It decreases moving outwards. The respective data points are labeled.

Combined density cloud containing data points from the author’s GIS work and the SAROPS simulations. (Map created by the author and Senior Chief Ian Brown)

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Fig. 10.3
A 4 by 6 grid of sinking locations. Scenario 2.3 is at the top, rightwards, with scenario 3.2, 2.1, and supplemental statement sinking coordinates at the bottom, leftwards.

Calculated sinking locations with priority search grid overlaid. (Map drawn by the author)

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When speaking of maritime search, the prior distribution consists of any data collected prior to the current operation. As an example, we may consider the prior distribution of the 2011 search for Air France Flight 447’s black box, which was conducted by Dr. Lawrence Stone using Bayesian methods. In that case, the prior distribution consisted of the last GPS ping received from Flight 447 before its disappearance, the estimated distance the plane might have traveled from its last known position based on the cessation of signal data, and the recovery locations of debris and victims from the wreck, which was used to plot a reverse-drift scenario to estimate the crash location (Stone et al., 2014:72–75).

In the context of the search for Rockefeller, the prior distribution consists of the historical and spatial data assembled regarding Rockefeller’s loss and the maps and models created from this data. The balance of the data suggests strongly that Rockefeller drifted slowly northeastward after being abandoned, probably not more than 17 nm and almost certainly no more than 25 nm. There is some margin of error here; Rockefeller’s given drift speed of 1.5 kt is only an approximation based on the Coast Guard casualty report, and it is possible that the winds may have shifted, pushing it in another direction. This factor was accounted for in the Coast Guard’s SAROPS probability maps, which posited three different wind speeds and applied different current speeds as well throughout the scenario.

The next factor to be considered is the probability of events occurring. This is a subjective, not objective factor, since in this case the probability is based on what the person conducting the study knows or believes to be true. As stated previously, this study has accepted KptLt Degen’s account of sinking Rockefeller as the most probable scenario with allowance for the fact that the tanker may also have sunk on its own around the same time, as stated in Scenario 1. The third scenario, in which Rockefeller was scuttled by the Coast Guard, is regarded as less probable and has been weighted accordingly. Each scenario was given a percentage, all of which added to 100: Scenario 1 = 45%, Scenario 2 = 45%, Scenario 3 = 10%. If a search is undertaken, these probability percentages can be fed into the basic Bayesian probability equation, which runs as follows:

$$ P\left(A|B\right){=}_{P(B)}^{P\left(B|A\right)P\ (A)} $$

  • where P (A|B) is the conditional probability of event A given event B;

  • P (B|A) is the conditional probability of event B given event A;

  • P(A) is the probability of Event A;

  • P(B) is the probability of Event B (Rossmo et al., 2019:45).

In this case, there are three events to solve for, those being the scenarios described previously. Event A may be given as Scenario 1 (Rockefeller sinking on its own), Event B as Scenario 2 (Degen sinking Rockefeller with a second attack), and Event C as Scenario 3 (Rockefeller being scuttled by the Coast Guard). Some of these equations are zero-sum games. Degen’s account and the scuttling scenario cannot both be true, thus the conditional probability of Event B given Event C would be zero, and vice versa. The only way to know for sure is to go and look. When a search operation is launched, this equation and its derivatives may be used to update the probabilities according to the search finds, with the results fed into the predictive model in ArcGIS to create an updated search map.

The posterior distribution of information is assembled from all data acquired during previous search efforts. In the case of AF Flight 447, the posterior distribution included various unsuccessful searches for the plane’s wreckage in 2009 and 2010, which Dr. Stone and his colleagues factored into their probability maps (Stone et al., 2014:75–79). In the context of this study, there is no posterior distribution to consider, as there have been no searches conducted for Rockefeller’s remains. It may be the case, of course, that this study’s conclusions are in error and a search based on them fails to locate Rockefeller’s wreck. In this case, a posterior distribution can be created from the data obtained in this search and used to refine the search area for the next expedition.

In the context of the initial search for Rockefeller’s wreck, the areas of greatest coordinate density are the four cells in the center of the grid and the two cells at its lower left edge. Focusing the search on these cells further reduces the priority search area from 384 square nautical miles to 96 sq. nm. Searching these grid cells is therefore the logical place to begin. Should the ship not be found in these areas, the remainder of the grid can be covered in descending level of priority, either in the same expedition or a follow-up search.

10.4 Conclusion

This chapter has presented a method for locating lost potentially polluting shipwrecks in American waters, using Bayesian search theory and computer modeling to calculate the potential drift of an abandoned ship prior to its sinking. The initial results have produced a more manageable search box that can be further subdivided into smaller search areas based on the time and resources available. Furthermore, these search areas can be easily covered by existing underwater search technologies such as side-scan sonar and autonomous underwater vehicles. Should this method prove successful in locating the wreck of William Rockefeller, it can be repeated for other missing potentially polluting wrecks, provided sufficient data is available.