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:
This model reduces to three input parameters:
- The acceleration term for quadratic discovery growth = c
- The feedback term for discovery growth damping = a
- 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.
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.
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.