Hubbert Linearization

I discovered the dirty little secret behind Hubbert Linearization. The conventional wisdom basically states that plotting dU/dt/U versus U, where U refers to cumulative oil extracted, you can extrapolate a negatively sloped line that intercepts the axis at ultimately recoverable resources. Most analysts use the logistic curve or Verhulst equation to "prove" this limiting behavior. Whereas, in practice, any peak will do.

First take dU/dt, which gives the production rate. When plotted, this will give a Hubbert-like peak somewhere in its lifetime. Any somewhat symmetric peak when Taylor-series expanded about its center point looks like this -- an upside-down parabola:

dU/dt = A (1 - k2(t - t0)2)

And then, any cumulative production increase looks like this near the peak -- a linear trend upward:

U = a (1 + b/a(t - t0))

Then make the substitution for time shifted around t0, T = t - t0, and you get this relationship:

dU/dt/U ~ (1+kT)(1-kT)/(1+b/aT)

The two positively increasing terms in the numerator and denominator more or less cancel, and you get

dU/dt/U ~ C (1-kT)

Which basically gives the famed Hubbert linearization term. Unfortunately, it doesn't give one any insight other than proof that you can linearize an upside-down parabola. Big little deal. We need way more insight than this to make headway in our understanding of depletion. (cue in the Oil Shock Model).

Peak Oil and TOD commenter Khebab also had an interesting point a while ago concerning residual analysis from Hubbert Linearization. As I got reamed for not doing this recently, it pays to read what Khebab said (which I agree with, if you substitute U for Q in the following derivation):

I'm skeptical about the use of this method to present production data because the relative error doesn't seem to be distributed uniformly. The relative error in the log domain of the vertical ordinates according to the logistic model is the following:

D(ln(aP/Q)) = Dk/k - DQ/Q x Q / (1 - Q)

where D stands for the greek symbol Delta, Dk/k and DQ/Q are the relative errors on k and Q which can be presumed constant. The error behaves has following:

• Production start Q -> 0:

  D(ln(aP/Q)) = Dk/k



• Production Q -> 1 (total URR has been extracted):

  D(ln(aP/Q)) = -infinity

Because we are in log domain, D(ln(aP/Q)) = -infinity means that deviation around the asymptotic line will tend toward zero!

That's why, we observe these wild deviations around the line when production is starting whereas it seems to converge nicely when Q tend toward 1. This behavior can be misleading for an observer because it seems to reinforce that there is some inexorable mechanism at work pushing the production data around the line.

I checked the math on this, and it really gets you thinking about what data visualization expert Tufte says about graphing data in a biased fashion. That convergence on a continuously shrinking error acts like a laser beam and gives people the impression of an excellent fit that may have dubious value at best.

Which explains my reluctance to do error analysis when the competition has issues of their own.

BioWeasels

Monbiot wrote a Guardian story on what we all suspected: "Worse Than Fossil Fuel":

The last time I drew attention to the hazards of making diesel fuel from vegetable oils, I received as much abuse as I have ever been sent by the supporters of the Iraq war. The biodiesel missionaries, I discovered, are as vociferous in their denial as the executives of Exxon. I am now prepared to admit that my previous column was wrong. But they're not going to like it. I was wrong because I underestimated the fuel's destructive impact.

Before I go any further, I should make it clear that turning used chip fat into motor fuel is a good thing. The people slithering around all day in vats of filth are performing a service to society. But there is enough waste cooking oil in the UK to meet one 380th of our demand for road transport fuel(2). Beyond that, the trouble begins.

[...]

It is prepared to sacrifice the South East Asian rainforests in order to be seen to do something, and to allow motorists to feel better about themselves.

All this illustrates the futility of the technofixes now being pursued in Montreal. Trying to meet a rising demand for fuel is madness, wherever the fuel might come from. The hard decisions have been avoided, and another portion of the biosphere is going up in smoke.

Proving once again how much you have to work to get unstuck between a rock and a hard place.

In regards to a HuffingtonPost entitled "The Plan to Steal Iraq's Oil", Charlie Cray describes how other human weasels show their true designs on raiding the hen house. PSA's used to refer to Public Service Announcements; short spots made on radio and television stations to provide balance to those people unable to get their voices heard. The acronym now means nothing more than deal making on a bait-and-switch level. How nice, PSA, a Production Sharing Agreement. We will all share. Yea, sure.

Theory vs Experiment

Working out theories about oil depletion through non-traditional channels such as a blog has some interesting side effects. I basically sit here and pontificate about stuff that I don't work on as part of my day job. This apparently gets some people upset, even though they pontificate about the same things I do and presumably don't do this as their day job either (actually I shouldn't pretend to know what they do).

So I have finally got someone beyond the tipping point:

I've explained to you about 10 times what you need to do to establish that you have a better model. You never do it - you just complain that people still choose to use the best predictive model we have right now If you had the first bit of sense, you'd realize that Hubbert was a first-rate scientist, and name-calling him takes away from your credibility rather than his.

Which prompted me to reply with this:

What is wrong? I have a theory. Theorists don't always have to defend their position. That's what experimentalists are around for. It's a classic position in the scientific world. Theorists don't mind getting attacked for their ideas. And that's not to say I am any first rate theorist, just that I know how the game is played.

No use getting worked up over this.

Hubbert never used any mathematical model; as far as I can tell he did his computations graphically. And why would I name call Hubbert anything? I think I dissed "Hubbert Linearization" because it is based on that ridiculous Logistic curve. It doesn't have any basis in reality.

I remember clearly the rallying cry my co-researchers and I would sing out when faced with challenging circumstances, man-made or not, "Nature's fighting us. We must be on the right track!"

In reality, I play the part of either Punch or Judy in a hand puppet dramatization of the world's oil predicament. Puppets sitting around theorizing versus neocons experimenting with their own puppets in toeholds of power, I actually feel part of some absurd War on Brains.

As Milfington would say, "whatever".

Wait, disaster happens

Part-time NO resident Harry Shearer on his Le Show radio program yesterday said that the tide has turned (so to speak) and the Katrina flood has transformed from a natural disaster into becoming the largest man-made disaster of all time. He reiterated this assertion on his Eat the Press blog at the Huffington Post.

Try this Google search on for size: "largest civil engineering disaster".

Robert Bea, a University of California, Berkeley professor who led a National Science Foundation investigation of the levee failures, said the mistakes made by the engineers on the project were hard to accept because the project was so "straightforward."

"It's hard to understand, because it seemed so simple, and because the failure has become so large," Bea said.

"This is the largest civil engineering disaster in the history of the United States. Nothing has come close to the $300 billion in damages and half-million people out of their homes and the lives lost," he said. "Nothing this big has ever happened before in civil engineering."

Esso: Morph This!

Apparently, the British and other members of the international reality-based community do not think highly of Bush for his oil industry connections. I do computer visualizations for a living, and despise Macromedia Flash for its prorietary, non-open format, but this stuff keeps me grinning.

Even before global peak oil has recently become a media reality, Greenpeace and other organizations had built up quite an awareness campaign to ostensibly alert the world to the dangers of global warming. They have unwittingly given the oil depletion crowd lots of reusable snarkware components for the coming roller-coaster.

This one has BushCo relevance as well. Off-topic, but the same animator adapted a short video based on a dream diary of Air America Radio's Marc Maron. Unfortunately, we only have two more weeks of the Morning Sedition radio program to go before it officially gets axed.

I'm just glad thoughtful,
funny people are on the
radio while I sit at my
computer day after day.

Modes de Transport

If I want to travel from point A to point B without the aid of a powertrain, I usually mull through a few options depending on the weather and terrain. I don't claim my list complete, but short of including draft animals, no one would claim that we have an abundance of human-powered alternatives to choose from. As you will see, not all these provide a practical means of commuting, unless, as you will notice, the proverbial hell freezes over.

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Mountain Bike:
The old reliable that operates decently under just about any climactic conditions. I bought this one custom-made in 1984 and still use it after it remained in cold storage with a frozen seat-post for several years. This one has a shorter wheel-base than my other mountain bike which gives it a squirrelly feel and a more upright ride. Notice the snow on the tires. At one point long ago, I tried an experiment and I covered the tire treads with an array of short machine screws to gain better traction on ice. Unfortunately, I chose screws a wee bit too long and I made it a few yards before the tires deflated with dozens of puncture marks. Duh. Lesson: You may fall on ice. Deal with it.

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Road Bike:
I will pass on the mountain bike without hesitation if I have good road biking conditions. The choice really comes down to efficiency; I will break less of a sweat on a road bike any day. The day-to-day trade-off remains dealing with tire flats. Keep the tires inflated to avoid pinch flats and don't skimp on quality tires and tubes. Pictured: a Bridgestone RB-2 purchased for $99.

I don't think I would ever use a recumbent bicycle; I would much rather loom over a car driver than sit at the same elevation as road-kill. Never mind the differences in mass, road bikers and bike messengers will become the Alpha males of the city streets once all the SUV's disappear. Height always wins.

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Hypno Skates:
Hypno makes inline roller blades with a detachable chassis. I would recommend these for any relatively smooth pavement without a lot of steep downhills. I have a long history with in-line skates, having purchased the original RollerBlades not long after local hockey playing brothers first brought these to market in the early 1980's. I can remember naively skating around university hallways on RollerBlades before the big crackdown - "NO SKATES ALLOWED!". The Hypno Skates bring back some of that freedom. As for advice, resist the temptation to use the heel brakes; practice until you get good at doing slalom/pivot stops.

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Cross-Country Skis:
No lie: I have actually commuted on cross-country skies, about 7 miles each way. I started with classical skis, but have used skate skis almost exclusively the last dozen or so years. For skate skis, you need specific snow crust conditions to get the best efficiency and mobility. Basically you have to wait for a thick blanket of snow, followed by a partial meltdown, and topped off by a hard freeze. If you have this and happen to live on a large connected maze of lakes or safely frozen rivers, consider yourself lucky. Unlike England, we can't count on right-of-way pasture lands to navigate. And, conversely, England can't count on snow. Rats, Utopia does not exist. One other possibility, you can follow rural snowmobile trails or use partially plowed roads. Unfortunately, these will become your "rock skis" after this point. Lastly, consider a move to Norway.

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Hypno Skates (ice):
Kind of bizarre, but I have ice skating attachments for my Hypno skate boots. Occasionally one can find a considerate lakeshore homeowner who will Zamboni a skating lane around the perimeter of a lake. Many people from warmer climates don't realize this, but the number of transportation routes increases in the winter. Commuters that had to make quite a detour to cross a river during the warmer months get to use an ice crossing for a few months in the winter. A narrow window of opportunity (and safety) to say the least.

Clap Ice Skates: These speed skates use cross-country ski bindings and boots. A European idea, I bought these from REI a few years ago; I don't think they caught on but they do work amazingly well. As a word of advice, unless you live on a series of canals ala Amsterdam, don't depend on the consistency of lake ice; prepare to take a number of "headers". In the last few years, we haven't had as much snow, so I have gotten used to unexpectedly flying through the air hat first.

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Kayak:
This narrowly beats a canoe if you happen to have a commute that follows a slow-moving creek or river or a long lake. Kind of a rare occurrence, I know, but what the heck.

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Finally, I can't forget to mention the backup strategies: walk, jog, or run. Advice: Start by crawling, and you will soon get the hang of it, usually by the age of two.

Monkeys flying out of butt quiet time

Bombshell from the assmissile:

"With oil prices declining rapidly since September, prospects for current and future economic growth appear excellent."

Excellent? Not.

Assmissile and his bud ShortTrunk have become the Wayne and Garth of the right-wing set -- always guaranteed for post-pubescent overexuberence and unbridled optimism.

Next time the Ponzi gang at Powerlien should dispense with the formalities and just interject "party time!" over and over.