In my post yesterday, Don’t Shoot Down USA 193, I voiced my “suspicion … that the expected risk to the ISS crew will be surprisingly competitive with the expected risk to persons on the ground” from the falling satellite.

My friend, the geographer Tim Gulden, did the math and it turns out my suspicion seems quite plausible.

Overall, Tim finds the chance that the debris will fall in an area with a population density of one or more persons per 1/4 hectare — about the size of the contamination zone — to be no more than one-half of one percent. That’s about 5 chances in 1,000. The probability that the debris will come down in an area with 3 or more persons per quarter hectare is about 2 chances in 1,000.

———— Original Message ————
Subject: Risk from Hydrazine onboard USA 193
Date: Mon, 18 Feb 2008 12:06:58 -0500
From: Tim Gulden
To: Nancy Gallagher, Jeffrey Lewis

I have done some really simple calculations of the risk of the hydrazine tank onboard USA193 actually landing in a densely enough populated area that people might be exposed. These calculations are based on the LandScan 2005 data set (developed by Oak Ridge National Labs): http://www.ornl.gov/sci/landscan/

The method here is to choose a threshold of population density and then see what percentage of the earths surface under the satellites orbit (between 58.5 degrees north and 58.5 degrees south) has a population density that high or higher.

The “contamination zone” for the hydrazine tank is stated as having a radius of about 27 meters — that is very nearly 1/4 of a hectare (which is an area 100 meters square).

The simplest thing to look at, then, is the percentage of the area under the orbit that has a density of 4 people per hectare or more. That corresponds to a very low density suburban type environment (one family every 100 meters on average). Approximately one half of one percent of the area under the orbit has this density or higher. That means that there are about five chances in 1000 that the tank lands in an area with this kind of density.

If we step the density up to a real urban density of 100 people per hectare, that is to say 25 people per contamination zone, this probability drops to about 0.02% or two chances in 10,000.

At 12 people per hectare, or 3 people per contamination zone, the probability is about 2 in 1000 — a risk of similar magnitude to the 1 in 1000 risk that NASA suggested for a debris strike from the interception hitting the International Space Station (and presumably killing its three crew members).

I am assuming that people stay where they live. The actual behavior of people toward this fallen object will matter a great deal more than it does with most falling debris. If people are inclined to move toward the tank, and stay near it, they could be killed even if it lands half a kilometer away. If, on the other hand, people are inclined to leave the area with the toxic smelling gas (apparently ammonia-like), then the people would not likely be killed even if they lived near enough to be exposed.

Another important caveat here is that these data are fine-grained, but not quite as fine-grained as would be ideal. The LandScan grid cells are 30 arc seconds square. At the equator, that translates to about 0.85 square kilometers. At the northern and southern extremes of the orbit it is about half a square kilometer. There are 100 hectares in a square kilometer and about 400 potential contamination zones in a kilometer. There are 100 hectares in a square kilometer and about 400 potential contamination zones in a kilometer. My calculations assume that people are evenly distributed within each cell — when in fact they are likely to be clustered. This would tend to drive the probability of hitting an occupied contamination zone downward. To the extent that low-density areas are typified by villages and extended family households, this could be really significant. I am guessing that clustering within cells could drive the probability of exposure down by a factor of 5 or more.

Of course, the error bars on both calculations are very large. The ISS estimate is extrapolated from Griffin’s comments about a NASA analysis that we cannot see for ourselves. Moreover, Tim did not model the probability that the tank remains intact — merely where it was likely to come down.

I continue to maintain that the Bush Administration should make public the real calculations of the risk. NASA published such estimates, by the way, for the Compton Gamma Ray Observatory — placing the probability that someone would be killed in an uncontrolled deorbit at 1 in 1,000. (Thanks to Yousaf Butt at the Union of Concerned Scientists for pointing this out.)

The unnecessary secrecy will feed the perception that Administration officials are being less than truthful about the President’s motivation for the intercept.