Saturday, January 2, 2010

Using Bayesian Analysis to find a lost nuclear weapon

Ten years ago I picked this book up at an airport bookstore, Blind Man's Bluff: The Untold Story of American Submarine Espionage, by Sherry Sontag and Christopher Drew. Some thinking I've been doing recently related to a project reminded me of this example of Bayesian Analysis described in the book:

[In January, 1966] A B-52 bomber had collided with an air tanker during a refueling operation 30,000 feet in the air off the coast of Palomares, Spain, losing its atomic payload. Three of the four bombs were recovered almost immediately. But a fourth was lost and had presumably fallen to the bottom of the Mediterranean.


[Naval intelligence officer John P.] Craven called in a group of mathematicians and set them to work constructing a map of the sea bottom outside Palomeres.


Once the map was completed, Craven asked a group of submarine and salvage experts to place Las Vegas-style bets on the probability of each of the different scenarios that might describe the bomb's loss being considered by the search team in Spain. Each scenario left the weapon in a different location.

Then, each possible location was run through a formula that was based on the odds created by the betting round. The locations were then replotted, yards or miles away from where logic and acoustic science alone would place them.


[Craven] was relying on Bayes' theorem


Craven applied that doctrine to the search. The bomb had been hitched to two parachutes. He took bets on whether both had opened, or one, or none. He went through the same exercise over each possible detail of the crash. His team of mathematicians wrote out possible endings to the crash story and took bets on which they believed most. After the betting rounds were over, they used the odds they created to assign probability quotients to several possible locations. Then they mapped those probabilities and came up with the most probably site and several other possible ones.

Without ever having gone to sea, the team now believed they knew where the bomb was [...] in a deep ravine [far from where the first three bombs were recovered].

Long story short, a deep sea submersible found the bomb in that ravine, right where the calculations plotted it would be.


Anonymous said...

Hey Dave, did you know about the missing H-bomb that still rests somewhere off the coast of Savanah, Georgia?

The Case of the Missing H-Bomb: The Pentagon Has Lost the Mother of All Weapons

By Jeffrey St. Clair, CounterPunch. Posted May 16, 2009.

60 years have passed since a damaged jet dropped a hydrogen bomb near Savanah, Ga. -- and the Pentagon still can't find it.

Things go missing. It's to be expected. Even at the Pentagon. Last October, the Pentagon's inspector general reported that the military's accountants had misplaced a destroyer, several tanks and armored personnel carriers, hundreds of machine guns, rounds of ammo, grenade launchers and some surface-to-air missiles. In all, nearly $8 billion in weapons were AWOL.

Those anomalies are bad enough. But what's truly chilling is the fact that the Pentagon has lost track of the mother of all weapons, a hydrogen bomb. The thermonuclear weapon, designed to incinerate Moscow, has been sitting somewhere off the coast of Savannah, Georgia for the past 40 years. The Air Force has gone to greater lengths to conceal the mishap than to locate the bomb and secure it.

On the night of February 5, 1958 a B-47 Stratojet bomber carrying a hydrogen bomb on a night training flight off the Georgia coast collided with an F-86 Saberjet fighter at 36,000 feet. The collision destroyed the fighter and severely damaged a wing of the bomber, leaving one of its engines partially dislodged. The bomber's pilot, Maj. Howard Richardson, was instructed to jettison the H-bomb before attempting a landing. Richardson dropped the bomb into the shallow waters of Warsaw Sound, near the mouth of the Savannah River, a few miles from the city of Tybee Island, where he believed the bomb would be swiftly recovered.

The Pentagon recorded the incident in a top secret memo to the chairman of the Atomic Energy Commission. The memo has been partially declassified: "A B-47 aircraft with a [word redacted] nuclear weapon aboard was damaged in a collision with an F-86 aircraft near Sylvania, Georgia, on February 5, 1958. The B-47 aircraft attempted three times unsuccessfully to land with the weapon. The weapon was then jettisoned visually over water off the mouth of the Savannah River. No detonation was observed."

Soon search and rescue teams were sent to the site. Warsaw Sound was mysteriously cordoned off by Air Force troops. For six weeks, the Air Force looked for the bomb without success. Underwater divers scoured the depths, troops tromped through nearby salt marshes, and a blimp hovered over the area attempting to spot a hole or crater in the beach or swamp. Then just a month later, the search was abruptly halted. The Air Force sent its forces to Florence, South Carolina, where another H-bomb had been accidentally dropped by a B-47. The bomb's 200 pounds of TNT exploded on impact, sending radioactive debris across the landscape. The explosion caused extensive property damage and several injuries on the ground. Fortunately, the nuke itself didn't detonate.

The search teams never returned to Tybee Island, and the affair of the missing H-bomb was discreetly covered up. The end of the search was noted in a partially declassified memo from the Pentagon to the AEC, in which the Air Force politely requested a new H-bomb to replace the one it had lost. "The search for this weapon was discontinued on 4-16-58 and the weapon is considered irretrievably lost. It is requested that one [phrase redacted] weapon be made available for release to the DOD as a replacement."

See link for full article:

Anonymous said...


DaveinHackensack said...

That story sounds vaguely familiar, anon, but thanks for reminding me of it here.