How Big and Small Numbers Influence Science Communication Part 1: Understanding Fuel Spill Volumes

This weekend I got a tweet from a friend who wanted everyone on her twitter list to be deeply concerned about the remaining oil from the BP oil spill in the Gulf of Mexico (more on that later). In reading the tweet and the cited news report it struck me that one of the major roadblocks in the comprehension of science, to the non-scientist, is the recognition that we, as a species, have a hard time understanding really big and really small numbers. This lack of a feel for big and small numbers often causes us to struggle badly to understand relative risks. Since this idea relates a lot to my previous posts on Fukushima radiation I thought I would write a bit more on the topic today.

As the parent of small children, I am amazed at how their young and inexperienced minds handle complex concepts like time and numbers. For my youngest daughter, time consists of today, yesterday and a nebulous time unit called "a week". In her mind anything that happened outside of her little perspective of understandable time happened either "last week" or will happen "next week". So her visit to the Halloween store (where she was terrified by a jumping spider display) still only happened "last week". My son, as he was growing, went from that perspective to relating to time via an understanding of sleeps. Since he was a napper we had small sleeps (afternoon naps) and big sleeps (overnight) and upon waking up an event tomorrow afternoon was two little sleeps and one big sleep away. Over most of human evolution the concept of time was almost that simple. Add in the seasons and that is how our pre-historical ancestors operated. Similarly, mathematics is at best 50,000 years old and formalized numbering systems didn't come into play until as little as 5,000 years ago. We, as mammals, thus evolved in a world where there were, one, two, three...a fist-full...more than a fist-full etc... This has left us not well-equipped to deal with numbers that are really big or really small.

Most everyone I know has a pretty reasonable grip on numbers up to the thousands. Thereafter it starts getting nebulous and by the millions/billions we end up working by analogy. On a regular basis I hear people describe volume based on an "Olympic-sized swimming pool" (OSP). The OSP, like many analogies, is actually a pretty poor one. The reason for this is that very few people have actually seen a true OSP. We are used to our local community pool (likely a 25 m pool) with shallow and deep ends and a diving area. An OSP, on the other hand, is 50 m long by 25 m wide and only 2 m deep ref. That gives it a volume of 2500 meters cubed or a liquid volume of 2.5 million liters. That is about 660,000 gals (U.S) and in oil terms that comes out to approximately 15,725 bbl.

Similarly, when dealing with very small numbers we often get stumped. We are good at 1 hundredths (pennies) but have a hard time instinctively going much smaller. In my work on contaminated sites we work in the parts per million and parts per billion range with our instrumentation able to "see" to the parts per trillion range. But what does that mean? Going back to our OSP model a part per billion would be about a drop of water in an OSP. My old supervisor while explaining the precision of his new mass spectrometer would point out that one part per trillion represented a single grain of sand on the entire length of Willow's Beach (a long, local beach in Victoria).

So how does this all relate to the BP oil spill? Well according to the tweeted story in Salon, researchers at Florida State University identified some 6 to 10 million gallons of oil buried in the sediment at the bottom of the Gulf, covering a 9,300 square mile area southeast of the Mississippi Delta. From an outside perspective 6 million gallons sounds pretty huge. But to put it into perspective the Gulf of Mexico has a volume of 2,434,000 cubic kilometers of water (6.43 x 10¹⁷ or 643 quadrillion gallons) ref. So the remaining oil these scientists attribute to the BP oil spill represent about 10 one-trillionths of the volume in the Gulf (or 10 grains of sand on Willow's Beach). The second version sounds a lot less menacing than the first but both represent the same value. To add further complexity, what the story did not mention is that there are more than 600 different seeps (areas where oil oozes from rocks) underlying the Gulf of Mexico. These oil seeps act like underwater springs for oil and release between 560,000 and 1.4 million barrels of oil annually (according to the National Research Council ref or ref). Going back to our conversions, 1 million barrels is approximately 42 million gallons of oil. So it is not unexpected that the researchers found oil in the sediment in the Gulf since the natural geology is spewing 42 million gallons of oil a year into the Gulf. Certainly the BP oil spill was a local disaster, but on a regional scale it now represents only one of many sources of petroleum hydrocarbons in the Gulf sediments.

In a similar vein, last year there was concern about a "Russian tanker full of fuel" (which was subsequently re-labelled a "fuel-laden cargo ship" (ref)) that was going to run aground off Haida Gwai after it lost power during a winter storm. What caused all the confusion to the press and public at the time was the volume of fuel carried by the cargo ship. It was reported to carry about 500 metric tonnes of bunker oil and 50 metric tonnes of diesel (ref). Using densities of 0.90 and 0.83, respectively, that would represent about 555,000 liters of fuel oil and 60,000 liters of diesel. To reporters this sounded like an awful lot of fuel and so for the first few days the ship was mistakenly reported as a tanker even though many older cargo ships carry similar volumes of fuel (older cargo ships are fuel hogs). A failure by the reporters to understand big numbers resulted in them getting confused and subsequently confusing their readers. This confusion continues as every time a ship has an incident it is called "fuel-laden" but when a car has an accident we never read about "a fuel-laden automobile" having an accident at 4th and Columbia? To further put this number into perspective, the BC Government West Coast Spill Response Study (ref) estimates that cargo ships operating along the coast transport approximately 42 billion liters of bunker fuel in their fuel tanks. This is more than the 38 billion liters a year that is shipped to the Puget Sound refineries in US oil tankers. This second number puts a lie to the belief that there is some form of "West Coast tanker ban". That ban is on the Canadian side of the ledger only, and doesn't affect our American cousins.

From a risk perspective, we have been trained to fear oil tankers even though they are highly regulated and have strict maintenance/piloting/tugboat requirements. Meanwhile, we are essentially oblivious to all those container ships travelling without tugs through our "narrow and dangerous" straits. Even more frightening are all those barges being towed along the coast. Few people ask how coastal BC communities get their fuel supplies? Well most are supplied by barges towed to their destinations by tugs. According to the spill response study 48 billion liters a year of fuels are transported by barge in coastal BC. Much of this material is considered "non-persistent" as it represents refined fuels that do not last as long in the environment once spilled. Lack of persistence, does not, however, mean risk-free. That lack of persistence must be tempered by the fact that these barges operate in inshore waters close to shore, so spills are more likely to migrate to land and cause damage to marine and coastal ecosystems. For volume comparisons, the biggest barges can carry 8 to 21 million liters of fuel. Going back to our OSP analogy, that represents between 3 and 8 OSPs of fuel per barge. The scary part is that the study had to use estimates, because unlike oil tankers, the barges do not even have to be fully reported.

Looking back at all these big numbers I have thrown around, a lot of people might become pretty panicky. After all, according to the Dogwood Initiative, we are only one "Exxon Valdez" away from Vancouver becoming a desolate hellscape. Of course that scenario conveniently ignores the fact that technology has advanced tremendously since the time of the Exxon Valdez and it also ignores the fact Vancouver Port regulations would not allow a tanker to traverse below the Lion's Gate Bridge without a local pilot and accompanied by emergency tugs. I, on the other hand, am reassured by the numbers. Considering how much traffic we have had moving for how long it is a testament to our current system that we have not had a major spill, to date. I do not deny that we can do more but I also recognize that these really big sounding numbers aren't nearly as scary as some would have us believe. Moreover, by re-framing the numbers (improving our analogies) we can do a better job of giving non-scientists a reasonable understanding of the relative risks of moving this material.

So having taken a brief look at how big numbers can confound and frighten, my next post will look at how very little numbers (and our difficulty in making estimates at low concentrations) are also used to scare us. But that is, as they say, the work of another day.