One of the most misunderstood insights into the riddle of MH370 is how the plane’s final path can be derived from Inmarsat BTO data alone.
Recall that the data, which was generated after someone on board caused the Satellite Data Unit (SDU) to re-logon to the Inmarsat Satellite 3F-1 over the Indian Ocean at 18:25, comes in two flavors. The first, the Burst Timing Offset (BTO) data, reveals how far the plane is from the satellite at a given time. This can be mathematically converted into a set of “ping rings” along which the plane must have been at a given time. The BTO data is very well understood and fairly precise, providing an accuracy of within 10 km.
The second, the Burst Frequency Offset (BFO) data, is more more complicated and much fuzzier than the BTO data; its inherent uncertainties are equivalent to a position error of hundreds of miles. It doesn’t have a single physical correlate but is related to how fast a plane is going, what direction it is headed, and where it is located.
For a time after MH370 disappeared, searchers hoped that they could combine these two data sets to identify the area where the plane issued its final ping. After months of work, however, they determined that this would be impossible. The BFO data is just too vague. However, along with the bad news came some good: it turned out that by the clever use of statistics they could figure out where the plane went using the BTO data alone. The methodology developed by Australia’s Defense Science and Technology Group (DSTG) and explained in an ATSB report entitled “MH370 – Definition of Underwater Search Areas” released last December.
Many independent researchers do not understand the technique and believe that it is invalid. For instance, reader DennisW recently opined that “The ISAT data cannot, by itself, be used to determine a flight path. One has to invoke additional constraints to derive a terminus.” But I believe that the DSTG position is correct, and that one does not need to invoke arbitrary additional assumptions in order to calculate the plane’s track. I’ll explain why.
First, some basics. Imagine that you have two ping rings, one created an hour after the other. For the sake of simplicity, let’s say the rings are concentric, with the later ring’s radius 300 nautical miles bigger than the earlier one’s. Let’s further assume that the plane crossed some arbitrary point on the innermost ring. If that’s all we know, then the plane could have taken any of an infinite number of routes from the first to the second. It could have travelled radially directly outward at 300 knots. Or, if traveling straight at 400 knots, it could have turned left or right at an angle. Or, it could have traveled faster than 300 knots on any number of meandering paths. So, the fact of the matter is that this simple understanding of the plane’s situation indicates that it could have traveled by wide number of paths and speeds to a wide range of points on the second arc.
However, there are some pecularities of commercial aviation that narrow the possibilities considerably. The most important is that planes can only travel in straight lines. They can turn, but in between turns they will fly straight. Knowing this vastly reduces the number of paths that MH370 could have taken between 19:41 and 0:11. It could not of simply meandered around the sky; it must have followed a path of one, two, three, four, or more straight segments.
Through the marvels of modern computing, researchers can generate a huge number of random routes and test them to see which fit the observed data. It turns out that if the plane flew straight in a single segment, the only routes that match the data are those that are fast, around the speed that commercial jets normally fly, and end up over the current search area. If you assume that the flight involved two straight segments, it turns out the ones that fit best are those in which the two segments are nearly in a straight line and are also fast and wind up over the current search area.
If you suppose that the flight after 19:41 involved a larger number of segments, your computer’s random generation process will be able to come up with valid routes that are neither straight nor fast, and do not end up in the current search area. But to come up with such routes, the computer will have to generate many, many others that do not fit. So it is extremely unlikely that by random chance the plane would have happened to travel a slow, curving route that just happened to “look like” a straight, fast route.
“Well,” you might object, “presumably whoever was in control didn’t fly randomly, they had a plan, so modeling by random paths isn’t appropriate.” But a plan of unknown characteristics is equivalent for our purposes to a random one. After all, there is no imaginable reason for someone to fly a plane over empty ocean in the dark at a slower-than-usual rate, making slight turns every hour or so. (Before you say that they might have done it to throw searchers off their trail after the fact, bear in mind that whoever took the plane would have had no way to know that Inmarsat had started logging BTO values a few months before, let alone imagine that they would be able to conduct this kind of analysis.)
When DSTG ran the math, they came up with a probability distribution along the arc that looks like the image at top.
Worth noting that the peak of the curve, and the lion’s share of the area under it, lie in the southern half of the search box, but it also has tails that extend past the box in either direction.
When the search of the seabed began, many expected that the plane would be found in short order. When it wasn’t, the burning question then became: how far out from the 7th arc should we search? A one-dimensional question had now become a two-dimensional one. Based on past loss-of-control accidents and flight simulations, the ATSB decided that an out-of-fuel 777 with no pilot would enter a spiral dive and impact the surface within 20 nautical miles. Mapping the two probability distributions (i.e., where the plane crossed the 7th arc, and where/how far it flew after that) yielded the following probability distribution:
I believe that we have to take the image above with a grain of salt, as I don’t think it is really possible for a plane to fly more than 40 km by itself. It’s generally agreed that the only way the plane could have plausbily gone further than that is if the pilot was conscious and actively holding the plane steady in a glide, in which case it might have gone as far as 100 nm.
A few months before the ATSB publlshed this analysis, a further set of information about the impact point of MH370 became availalble: the plane’s right-hand flaperon washed up on Réunion Island. Reverse-drift analysis was performed by several independent groups to determine where the flaperon might have started its journey. The German institute GEOMAR came up with the following results:
As you can see, the probability distribution hardly overlaps at all with the probability distribution derived from the BTO data; it only touches at the northeastern corner of the search box. Drift analysis performed by other groups reached a similar conclusion. Using a branch of mathematics called Bayesian analysis, it’s possible to take two probability distributions and merge them into a single one. I’m not a mathematician myself, but intuitively one would surmise that given both the BTO and the drift-model data sets, the new peak probability are should lie somewhere between the northern end of the current search box and Broken Ridge.
The ATSB report disagreed, arguing that the drift analysis
… made no meaningful changes to the ATSB search area due to the relative weighting of the significance of the drift analysis in comparison with the analysis based on the satellite data. While this debris find is consistent with the current search area it does not provide sufficient information to refine it.
What this means is that the ATSB considers the BTO data and its analysis “hard” and the reverse-drift analysis “soft,” because the random motion of ocean currents introduces a large amount of uncertainty. However, the reported also noted that “if additional debris is identified it will be included in the analysis to provide further information on the location of source areas.” Indeed, after the report came out other pieces of debris were found, and drift modeling of these pieces be used to refine the search area. Indeed, after I published last week’s guest post by MPat, reader Ge Rijn pointed out:
Over those 20 years in MPat’s model only 7 out of 177 buoys landed in Australia. Those 7 all passed the search box under 36S… [this] points clearly to the trend the more south you go under ~36S the more likely it becomes buoys (debris) will land on Australia and the more north you go above 36S the less likely it becomes buoys~(debris) will land on Australia. This is also because the more south you go under ~36 the currents tend to go further east and the more north you go around 36S the currents tend to bend stronger to the north avoiding Australia. And this is exacly what the facts about found debris shows us till now.
Note that 36 degrees south is just shy of the northern end of the current search area; as Ge Rijn observes, historical drift data suggests that if the plane had crashed south of this latitude, debris should have been found in Australia, which it obviously hasn’t.
The size and species mix of barnacles growing on ocean debris could provide clues as to which waters it floated through; oxygen isotope analysis can provide information about the temperature of the waters that it floated through. As far as I know, no such analyses have been conducted. For a long while now, the ATSB’s weekly update reports have included the phrase “In the absence of credible new information that leads to the identification of a specific location of the aircraft, Governments have agreed that there will be no further expansion of the search area.” The fact is, though, that further information is available, and it could be used to determine which of the two possible explanations is more likely: that the plane passed over the current search area and was held in a glide, or crossed the seventh arc further (but not too much further) to the northeast.