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46 comments on Links to tutorial material on Hubbert Linearization

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WebHubbleTelescope on July 8, 2006 - 12:06am Permalink | Subthread | Parent | Comments top
What I don't understand is why we don't try to plot these curves (rate vs cumulative) instead of (rate/cumulative vs cumulative).  If you do it the first way, then you can see the "upside down" symmetric parabola fairly clearly, IF it is a logistic curve. Howver, since the data rarely shows the symmetry, I guess that's why the linearization technique is favored.  The weirdness at the start is then swept under the rug.

Plotted the first way, the majority of the curves look like this:

You can see the general shape of the upside-down parabola but since it is not symmetric, it can't be the logistic curve.

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Stuart Staniford on July 8, 2006 - 3:00am Permalink | Subthread | Parent | Comments top
Not a bad idea, Web. Here's the US curve done that way:

Makes a nice parabola and actually this looks much better than the linearization (since it's not blowing up the misfit in the tails with a 1/Q factor). The predicted URR is within error bars of what the linearization says. I only fooled around a tiny bit, but it seems that it does ok at robust prediction too:

(BTW, as a process/communication issue I would prefer that you not accuse others of acting in bad faith ("swept under the rug"), without good evidence. It's more polite to assume that the other people simply see things differently, which is usually the case, certainly around here.)

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Khebab on July 8, 2006 - 10:00am Permalink | Subthread | Parent | Comments top
Nice results, this representation seems to have good asymptotic properties.
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WebHubbleTelescope on July 8, 2006 - 5:50pm Permalink | Subthread | Parent | Comments top
I don't think so. The fit with more recent data pushes the asymmetric peak to the left giving longer tails to the right.  This will continue to happen as you get more and more data. The properties of temporal causality makes it so.

I guess I am more into the understanding rather than the predictive properties.  I just don't get how this stuff works out without any kind of forcing function included.  I am categorizing this set of formulations under the heading "Immaculate Conception Hubbert Peak Analyses".  Without a forcing function, I might as well look into causes of Spontaneous Human Combustion.

A thought experiment for us to engage in. Say from now out, time=T, the quantity of discoveries followed as:
 K/(C + (time-T))

In this case, we would still have the peak centered at the same point but the URR will blow up to infinity.  Until this is discussed by someone other than me, I can say that it is "swept under the rug", which is a mildly-offensive euphemism for "ignored".  And for all I know someone has discussed this, but I don't know about it.

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Stuart Staniford on July 8, 2006 - 6:49pm Permalink | Subthread | Parent | Comments top
You might want to spend some time contemplating whether there's likely to be any relationship between the frequency with which you insult other people, and the amount of effort they are likely to put into thinking about your ideas.
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WebHubbleTelescope on July 9, 2006 - 11:48am Permalink | Subthread | Parent | Comments top
I usually try to limit my insults to ideas, which last time I looked are inanimate objects and pretty immune to such things as feelings.

Oops, maybe that was an insult as well.  I will try to stifle myself, and just consider anything outside the bounds of decent behavior as my attempts at snark (people such as Michael Lynch, George W. Bush, and Michael Crichton excluded).

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Stuart Staniford on July 8, 2006 - 6:59pm Permalink | Subthread | Parent | Comments top
The second graph corresponds to a prediction in 1976. After another 30 years of evidence, it's moved by about 10%. In my book, that makes it a pretty useful prediction method (for this case - as I've discussed elsewhere I think there are a lot of caveats elsewhere). There are very few ways to predict anything in the far future that won't have moved a lot more than 10% after 30 years. A-priori, I would only have expected the logistic to be a very rough approximation to something like oil production and it still surprises me that it does as well as it does.

I agree, as I've said repeatedly, that we lack a theoretical understanding of why the US production curve is so Gaussian and that's unsatisfactory. However, I view that as an interesting challenge that we should try to solve rather than a reason to dismiss the fact that it has been so up to now (modulo some noise).

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Stuart Staniford on July 8, 2006 - 7:05pm Permalink | Subthread | Parent | Comments top
I should also point out that the shift is pretty much due to Alaska coming on line as a late chunk of discover - the lower 48 prediction would be significantly better I imagine (as Wes and Khebab showed for linearization a while back).
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Don Sailorman on July 8, 2006 - 7:35pm Permalink | Subthread | Parent | Comments top
Do you know why economics textbooks usually show supply and demand curves at straight lines? They did not used to be (say prior to about 1954) shown as such but instead were often shown as rectangular hyperbolas (i.e. price elasticity of exactly one). Well, you hardly ever have a price elasticity of demand or supply of exactly one; it happens, but rarely.

It was George Stigler (I think) in his first edition (late 1940s I believe) who pointed out for the first time that BECAUSE we economists do not know the empirical shape of most supply and demand curves that we should draw them as straight lines TO EMPHASIZE THAT THEY ARE ARBITRARY AND DO NOT REFER TO THE REAL WORLD. Unfortunately, after Stigler, relatively few authors make his point, thus needlessly confusing generations of miserable and bewildered and hostile students.

HOWEVER, I shout;-)
     For a small change in price for a well-behaved supply or demand function a straight line is often a pretty darn good approximation to the real world.

It is almost never a decent approximation for a large (say more than 20%) change in price.

When I taught economics I explained these nuts and bolts, and guess what: Almost half my students got a fairly good understanding of supply and demand. In the typical introductory and even intermdiate microeconomics classes at U.C., Berkeley, my guess is that fewer than ten percent grasped the most basic fundamentals of supply and demand.

Now elementary need not be hard at all. No! The problem is that most teachers of lower division classes do not give a darn about teaching and could care less that 90% of the students are ignorant of fundamentals.

Grump.

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WebHubbleTelescope on July 9, 2006 - 12:01pm Permalink | Subthread | Parent | Comments top
Don Sailorman,
The linearization talked about here concerns a technique to turn a highly non-linear function into a straight line. It has nothing to do with small perturbations affecting linearity to the first order, as a Taylor series approximation does.

That property I do believe in but that does not influence my disagreement with the original premise of using a logistic curve or gaussian curve formulation to describe the stochastic behavior.

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Don Sailorman on July 9, 2006 - 7:56pm Permalink | Subthread | Parent | Comments top
I understand what you are saying; no analogy is perfect. However, IMO my main point is valid and does apply apply.

I think (but do not know) that Stuart agrees with my line of reasoning; he has expressed it himself in somewhat different words--just a few days ago.

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WebHubbleTelescope on July 9, 2006 - 11:55am Permalink | Subthread | Parent | Comments top
But for the US, didn't we hit the peak around 1970?  So we already knew the fit would work and the subsequent 30 years that have passed haven't really added much insight to the peak position.  More to the point is how the depletion tails will work out. This I think is a work in progress and something that has yet to be verified due to issues such as reserve growth and future discoveries.  And the discovery profile is something that is not included in any of these immaculate conception models.
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westexas on July 9, 2006 - 1:58pm Permalink | Subthread | Parent | Comments top
"But for the US, didn't we hit the peak around 1970?  So we already knew the fit would work and the subsequent 30 years that have passed haven't really added much insight to the peak position"

The key point is that Hubbert, in 1956, accurately predicted the Lower 48 peak.  

What Khebab and I attempted to address was how good the HL model was at predicting post-peak cumulative production, using only Lower 48 production data through 1970.  The answer was that actual cumulative Lower 48 production was 99% of what the HL model predicted that it would be.  

Assuming that Deffeyes is right that we are past the peak of conventional crude + condensate production, the HL model should therefore offer us a very accurate prediction for post-peak world production.

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