World Forecast Update

I applied the discovery model of quadratic growth with negative feedback to the world oil shock model in the clickable chart below:
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This model reduces to three input parameters:

1. The acceleration term for quadratic discovery growth = c
2. The feedback term for discovery growth damping = a
3. Parameter to the shock model for each of the lag terms: fallow, construction, maturation, and extraction. I set each of these to the same value of 12.5 years (i.e. a stochastic rate of 0.08/year). So you can see the phases progress in increasingly darker shades as the lags accumulate.

I kept the same starting point for discoveries of 1859 as the USA model, but slightly reduced the feedback term and more than doubled the acceleration term to account for a greater worldwide interest in finding oil; in other words, a greater population presents a higher acceleration of human resources devoted to discovery. However, the world feedback term should not change too much from the USA model as it presents the same damping of enthusiasm as discoveries top off.

This formulation presents a slightly different tact than previous attempts with estimated backdated discoveries, as the model has become completely analytic (though I still solve it numerically) with the only adjustable parameters provided by the physically based and potentially measurable rate terms. I really believe that each of these input terms have significance beyond that of the typical Hubbert heuristics -- definitely not of the inscrutable Logistic model variety.

After the solution of the differential equations, the result gives P(t), the yearly world-wide production of oil assuming an initially finite resource and impending collapse.

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I post this as I listen to author Dilip Hiro discuss his latest book ("Blood of the Earth: The Battle for the World's Vanishing Oil Resources") on Laura Flanders' Air America radio show (here). I really could not follow too much of what he said because of a hyper-speedy Indian accent (somewhere in there I heard a mention of "Hubert's (sic) curve"), so I suppose I shouldn't feel bad if I lose somebody due to too much math in my own posts, ha ha. Must ... try ... to ... concentrate. Apparently Chomsky likes the book.