September 16, 2009 | General

Legal Limits Of Math

BioCycle September 2009, Vol. 50, No. 9, p. 53
Biomass Energy Outlook
Mark Jenner

AS a professional biomass economist, I make my living on a frontier for which little high quality data exists. In fact, all the terabytes of economic data in existence have limited relevance to the emerging carbon-centric bioeconomy. So how does one plan for a future when there isn’t any realistic data on new industries? Via normative economics, a branch of economics based on subjective judgments rather than historical data, where new realities are “constructed” to answer questions about potential opportunities and challenges. These analyses can be illuminating, but at the end of the day are all hypothetical.
And this is a very disturbing aspect of the emerging suite of biomass climate policies. We are writing laws based on best available fiction. If this does not scare you, it should.
It is very easy to click a spreadsheet button and create a stunning trend line on a graph of 6 data points. There is no statistical significance to 6 numbers, so even though the spreadsheet chart may show a trend, statistically, it does not exist. Creating a computer generated number does not authenticate its value.
When complex systems of equations known as mathematical models are fed poor quality data, numbers will still be generated. These numbers may look useful, but like the trend line above, they are hollow. In most cases, process and lifecycle models are used with great integrity within their designed capacity. These “what if” models provide great understanding and value. The value begins to unravel, however, as the results from one model are transferred, or chained, to another unrelated model. Bruce Dale, Michigan State U., has noted that this can create a propagation of errors.
This violation of mathematical principles is further distorted by giving it the force of law. The regulatory agencies are trying to write rules that the Congressional lawmakers have created. The agencies enlist respected institutions to generate different kinds of answers that are required to fulfill Congressional obligations, and then integrate the independent results into their long-range forecasts. Combining results from vastly different process models is not allowed mathematically. In this case, generating an estimated number is not better than having no number at all. Adding insult to injury, these imaginary facts are becoming the foundation for new laws.
At a recent national conference on the methodologies underlying the U.S. EPA’s revised Renewable Fuel Standard, the EPA outlined steps they took to develop its proposed rule. Various institutions were asked to provide numbers as I have just described. Most of the presentations that followed described the narrow limitations in which the models were accurate. There is a nagging sense that agencies are more motivated to serve the lawmakers than adhere to the principles of mathematics.

The worst violation here is that laws are being written on a fictitious future. There are three areas that violate the fundamentals of math: data quality issues, model bias issues, and the influence of time on biomass and climate models.
The data quality issues are manageable within each process model or lifecycle analysis. It is only when multiple mathematical models are chained together that the output quality rapidly deteriorates. Process models and lifecycle analyses are built on the best available data. Data is costly to collect. Statistically significant laboratory data is easier to collect than statistically significant field data.
Technically, statistics only apply within the context of the data used to establish them. Sometimes model coefficients, based on laboratory data, are stretched to represent field conditions in the models. These add some risk of error, but within each model the risks are limited. When multiple models are used, the risk of error is magnified with each model involved and also by using values beyond the limits of the original statistical boundaries.
In economics the word “bias” simply means that an analysis is not objective. If a process model is constructed to measure emissions it will look and behave differently than one that measures energy production. Different forms of carbon create specific model characteristics. These analytical characteristics include emissions, energy, food, nitrogen, phosphorus, water, water quality, solid waste, wood products, paper products, plastics and on and on.
An unintentional bias is created by linking unrelated models together. No bias exists if the models are used independently. But when the models are chained together an external bias is created and passed through the model chain. Three models linked together, like food production, carbon emissions and energy, transfer biased results from one kind of model to another. The emissions model is dependent on the output of the food model, and the energy calculations are dependent on the output of the emissions model. By the end of the model chain, the restrictions carried through are so narrow, little can be accomplished.
As we progress on this policy frontier of biomass production/emissions reduction the methodologies continue to evolve. The Intergovernmental Panel on Climate Change (IPCC) has changed the global warming potential of methane from 21 to 23 to 25 times the radiative forcing as carbon dioxide in 1996, 2001 and 2007, respectively. While emissions adjustments are updated religiously, advances in technical efficiency are rarely included. Using more efficient appliances and fuel-efficient vehicles rarely show up in the emissions math. Consequently, when energy use is reduced to 1990 levels using advanced efficient technologies, our emissions will not return to 1990 levels.
The current biomass-climate policy process is mathematically flawed. We are pretty much making up numbers for legal standards. This is a serious moral dilemma: to get the rules written, or get them right.

Mark Jenner, PhD, operates Biomass Rules, LLC and has over 25 years of biomass utilization expertise. Burning Bio News, the Biomass Rules newsletter, is available at

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