Long tails wagging geological dogs…

Last fall, Boulder Colorado and environs experienced a rather dramatic event, experiencing 9 inches of rain in 24 hours (the monthly record prior to this event was only 9.6″).  The usual analysis of how often we might expect such tremendous rainfall suggests an event like this should occur in a given year with a probability below one in a thousand (thus this might be termed a thousand-year rain).  There are questions out there about just exactly how you derive such probabilities (unless you observe a thousand years of weather, you are extrapolating from a smaller subset of observations and to do that, you have to assume some kind of probability distribution). Basically, when you plot the probability of an event versus the magnitude of the event, you get some big lump (or lumps) where most things happen and these trail off into long, thin “tails”.  So, for instance, the rainfall record from Boulder is shown below; you can’t even see much beyond 1″.


BoulderRainfall(If you are wondering, Boulder has had 344 days with 1″ or more of precipitation out of the 38404 days where records were kept, or just under 1% of the time.  2″ or more has occurred only 49 times, 3″ or more 12 times.  Note that these include snowfalls–three of the 12 3″+ events were associated with heavy snowfall as were 9 of the 49 2″+ events).

Set aside for the moment the statistical issues and consider the geological impact of the weather on those 38,404 days. Most of the time, there was nearly nothing: some sand grains moved down the creeks where there was water flowing and not much else.  When we start getting over about a quarter of an inch in a day (2818/38404 or about 7.3% of the time) we might start seeing some slope wash of material downhill, some overland transport of fine material in ephemeral channels (depending on how fast the rain fell).  Real mass movement of material probably needs somewhat more rain.  

The 2013 flood moved a huge amount of material; it might well be one of the very few historical events to have produced a noticeable deposit downstream.

Now shift to a geologic perspective.  If you saw a sedimentary sequence laid down by a river, what events would you be seeing?  Would you see the annual rise and fall of the river as snow melted or the wet season occurred? If you were looking at overbank muds, maybe.  Usually what you see are beds deposited in more exceptional events: a river channel deposit might be a meter thick.  The Ogallala Group is typically a bit over 100′ thick in Colorado and might have been deposited over 7  million years or more.  If you happened upon an outcrop just of river channels, you might only see 40 or so channels from the 7 million years of the history of deposition; each might be nearly 200,000 years apart in creation and could conceivably record events from just a few days.  Channel deposits are likely outcomes from major changes in river geometry, which are most common in flood events; would this record then be informing us of the 200,000-year floods and nothing more?  When we go to look at these deposits, we are not seeing the usual state of affairs but an exceptional moment.  While this isn’t 19th century catastrophism, it isn’t entirely uniformitarianism either.

Now some geologic environments will preserve the usual passage of events.  Deep water sediments and perenial lake bottom sediments generally include the slow ongoing accumulation of material as well as any exceptional events; sediment doesn’t tend to bypass these locations.  River deltas might, as a whole, be the same though unconformities in individual channels could be frustrating. But these are often not the rocks we are investigating associated with tectonics (creation of mountain belts).

Take two kinds of measurements that have been applied recently to tectonic issues.  One is an estimate of the grade of a paleoriver, one is a means of determining paleotemperature of the surface.

A means of estimating the grade of a braided river is to determine the depth of the channel and the size of the largest cobbles being moved (see McMillan et al., Geology, 2002 for an application).  The idea is that you need a certain shear stress on the bottom of the channel to move cobbles of a certain size, and that stress is related to the velocity of the water which is related to the grade and water depth. Underestimate the water depth and you overestimate the slope. Although a major caveat on this approach is that you need a braided stream without cohesive banks, consider what event we might be looking at.  Why did these deposits get buried?  Was it the front end of a major flood, when high waters carry everything in their path? Do we know the water depth?  Or was it just a channel that was cutoff by “normal” migration of the stream and the infill is just backwater deposits into an abandoned channel? You kind of wonder how much of the assumptions made in interpreting such beds are informed by the more extreme occurrences that we rarely see but that must be geologically common.

The second measurement looks at the isotopic composition of carbonate ions in limestones and similar deposits to determine the paleotemperature when the carbonate was created (see Huntington et al, Tectonics, 2010 for an application in the western U.S.).  This technique gets applied to soil carbonates, carbonates in ephemeral lakes as well as limestones deposited within perennial lakes. One big discussion in the community on this approach has been whether these carbonates are being created seasonally, but what if they are also produced during exceptional events? Would, for instance, a major drought produce a deposit of carbonate in a perennial lake? Might solid carbonates be created in exceptionally dry (or maybe exceptionally wet) years? Would this bias the record?  It certainly seems possible.  

If these techniques face biases because of the rather upside-down way that geology tends to preserve exceptional events while discarding common ones, can we correct for that?  One would hope so, but then you need to know something more about that distribution on the tail of rainfall that we started with.  We could just wait and keep collecting more data, but as we are changing the earth’s climate, this tail of the distribution might well be changing on us. We can (and should) try and use the climatic history of the past several thousand years, where we at least have some decent proxies (tree rings, ice records), but what controls the behavior of the tails of the distribution?  Would an ice-free world (as in the Cretaceous) tend to have much fewer extreme events?

The study of long-tailed distributions are often couched as study of extreme events, but in geology we arguably are seeing more of these tails than the “typical” parts of the distribution. In some ways, geologists are already expert in the study of extreme events because these form the bulk of the material available to study.


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