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46 comments on Links to tutorial material on Hubbert Linearization

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Stuart Staniford on July 7, 2006 - 3:01pm Permalink | Subthread | Parent | Comments top
The situation actually seems to be more interesting than you might think.  I explored the US case here, and while it's true that the US production curve is better fit across the full history by a Gaussian than a logistic, Hubbert linearization is the most robust predictor, and is the only one to give very reliable results before the peak.  Quality of model fit and quality of prediction are often very different things.
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IFeelFree on July 7, 2006 - 3:31pm Permalink | Subthread | Parent | Comments top
You've looked at this issue more than I had realized. I was commenting more on the use of the HL technique to approximate a Gaussian curve. From that limited mathematical perspective, it's not a particularly good approximation.

The problem is that:

(1) The data has noise.

(2) The correct model may not be a Gaussian.

In the U.S. case, HL may have given better early predictions of the peak than the Gaussian, but that might not be true of world data. I suppose the best we can do is to try different fitting methods and get a "rough estimate" of world peak oil production. The estimate should improve over time. As you point out in your discussion, error bars and sensitivity analysis are important.

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TrueKaiser on July 7, 2006 - 3:44pm Permalink | Subthread | Parent | Comments top
correct me if i am wrong but when ever someone says 'the data has noise'
the noise is almost always data that doesn't fit the person's pre-determined opinion from what i have seen.
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IFeelFree on July 7, 2006 - 3:58pm Permalink | Subthread | Parent | Comments top
No. Noise has particular characteristics that are independent of the model. Noise is random. There is no reasonable model that could account for the small, short-term fluctuations in the data that we call noise. However, a bad model simply doesn't fit the data very well. An example is the HL technique in the very early part of the oil production history. A straight line doesn't fit that part of the curve, and it's not because of noise.
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westexas on July 7, 2006 - 4:26pm Permalink | Subthread | Parent | Comments top
The best way that I could think of to test the post-peak validity of the HL technique was the excercise that Khebab did with the Lower 48 data.  Post-1970 cumulative Lower 48 production, through 2004, was 99% of what the HL model predicted that it would be--using only 1970 and earlier production data to generate a predicted production profile.  

The same exercise for Russia showed that post-1984 cumulative Russian production was 95% of what the HL model predicted, using only production data through 1984 to generate the predicted production profile.

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IFeelFree on July 7, 2006 - 5:03pm Permalink | Subthread | Parent | Comments top
One problem with this is that the person fitting the data using the HL technique makes a (subjective) choice about where to start the linear fit. To quote Stuart Staniford, "Long experience has taught us that the linearization generally does a bad job in the early part of the history...". Therefore, its possible, after the fact, to choose a starting point for the fit that gives good ageement with the known post-peak data.
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westexas on July 8, 2006 - 11:20am Permalink | Subthread | Parent | Comments top
 "Therefore, its possible, after the fact, to choose a starting point for the fit that gives good ageement with the known post-peak data."

I proposed the Lower 48/Russian experiment to Khebab, and he chose all of the technical parameters.  If you have read any of his posts, you can tell that Khebab is an objective scientist. IMO, he is a genius.

In any case, Khebab had zero preconceived expectataions of how the results would turn out.  When you look at the actual 1970 and earlier Lower 48 data and actual 1984 and earlier Russian data, they both show very strong HL patterns.

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westexas on July 8, 2006 - 5:55pm Permalink | Subthread | Parent | Comments top
The following link will take you to several Energy Bulletin articles:  http://www.energybulletin.net/news.php?author=jeffrey+brown&keywords=&cat=0&action=searc h

"M. King Hubbert's Lower 48 Prediction Revisited" has the HL modeling of the Lower 48.

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Don Sailorman on July 8, 2006 - 1:51pm Permalink | Subthread | Parent | Comments top
Approximations are often more useful than precision.

For example, back when I was a teenager I used to grind and polish astronomical mirrors (for Newtonian and Hershel-style off-axis) reflecting telescopes. The goal was to get to the Raleigh Limit--one-eighth of a wavelength of sodium light, and the figure desired was a parablola.

Guess what: for a 4 1/4 diameter F-20 mirror I figured it to a SPHERE which is well within the Raleigh limit for a parabola, even when using the off-axis style to avoid the diffraction from a Newtonian diagonal and its support.

Even at F-12 or thereabouts for a Newtonian style, a sphere is within the Raleigh Limit for a little mirror, such as 6".

BTW, for observing planets, most nights the atmosphere is too turbulent to get much if any benefit from a telescope over 6" or 8"     And on many nights a 60 mm lens on a good refractor actually shows better images than you get from a big scope because of the nature of atmospheric turbulence, which is (to put it mildly) complex.

Anyway, what matters and costs the most in amateur scopes is usually the stability of the mounting rather than the quality of the lenses and mirrors.

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