Evaluation of the logit/probit transform method to modeling historical resource production and forecasting compared to conventional Hubbert modeling

This paper compares modeling of historical resource production and forecasting of future production trends using the logit/probit transform advocated by Rutledge (2011) with conventional Hubbert curve fitting, using global coal production as a case study. The conventional Hubbert/Gaussian method fits a curve to historical production data whereas a logit/probit transform uses a linear fit to a subset of transformed production data. Within the errors and limitations inherent in this type of statistical modeling, these methods provide comparable results. That is, despite that apparent goodness-of-fit achievable using the logit/probit methodology, neither approach provides a significant advantage over the other in either explaining the observed data or in making future projections. For mature production regions, those that have already substantially passed peak production, results obtained by either method are stable, and estimates of ultimately recoverable resources obtained by either method are comparable. In contrast, for immature regions, estimates of ultimately recoverable resources generated by either of these alternative methods are unstable and thus, need to be used with caution. Although the logit/probit transform generates high quality-of-fit correspondence with historical production data, this approach provides no new information compared to conventional Gaussian or Hubbert-type models and may have the effect of masking the noise and/or instability in the data and the derived fits. Therefore, production forecasts for immature or marginally mature production systems based on either method need to be regarded with caution.