Embracing Monte Carlo Simulations

Oct. 28, 2024, 11:02 a.m. • By Adam Forster

A New Chapter in Emission Uncertainty Calculations

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In our continuous pursuit of precision, we're excited to announce the implementation of Monte Carlo simulations in our uncertainty calculations for emissions data. This advancement marks a significant step forward in how we model and interpret uncertainty, ultimately providing you with more accurate and insightful information.

A Journey from Categories to Individual Emissions

Historically, we've utilised the pedigree matrix approach to assess data quality and estimate uncertainty at the overall emissions category level. The pedigree matrix, a method for assigning quantitive uncertainties from qualitative measures to carbon emissions calculations, has been instrumental in assigning uncertainty scores based on factors like data reliability, completeness, and methodological consistency.

Under this framework, we operated under the assumption that emissions categories were uncorrelated. This allowed us to combine uncertainties using the Taylor series expansion - a mathematical method well-suited for independent variables. It provided reasonable estimates and served us well when our focus was on broader categories.

However, as the landscape of emissions reporting evolves, so do the needs of our clients. The demand for more granular, detailed uncertainty estimates at the individual emission source level has grown. This shift necessitated a re-evaluation of our existing methods.

The Challenge of Correlated Emissions

Calculating uncertainties for individual emissions introduced a new layer of complexity: correlation between emission sources. Unlike broader categories, individual emissions often share common data sources, estimation methods, or influencing factors, leading to inherent correlations.

These correlations pose a significant challenge. The Taylor series expansion relies on the assumption of independence between variables. When variables are correlated, this assumption no longer holds true, and the Taylor series can produce inaccurate results. We recognised that continuing to use this method would not meet our standards for precision and could potentially misinform your decision-making processes.

Understanding Log-Normal Distributions and the Pedigree Matrix

To address the complexities of individual emissions uncertainties, it’s essential to understand why emissions data are best modelled using log-normal distributions.

Firstly what is a log normal vs a normal distribution. A normal distribution is a classic bell (gaussian) curve as seen below. In contract, a log normal distribution is a distribution in which the log of the variable is normally distributed. Taking the log converts multiplicative operations into additive ones and, as I will go on to explain, this is an important property in emissions calculations.

So, why do we use log normal distributions. Here’s a simplified explanation:

  1. Emissions Are Always Positive: Emission quantities can’t be negative—you can’t emit a negative amount of CO2. A log-normal distribution, unlike a normal distribution, only includes positive values, making it a natural fit for modelling emissions.

  2. Multiplicative Uncertainties: Uncertainties in emissions data often scale with the size of the emission. For example, a measurement might have a ±20% uncertainty regardless of whether the emission is large or small. This multiplicative nature aligns with log-normal distributions, which handle scaling effects.

  3. Skewed Data: Emissions data tend to have a long tail of higher values—think of a few large factories emitting much more than smaller sources. A log-normal distribution is skewed to accommodate this pattern, accurately reflecting the reality that while most emissions might be moderate, there are possibilities for significantly higher values.

  4. Combination of Multiple Factors: Emissions are usually calculated by multiplying several positive numbers, like activity data and emission factors. When you multiply several positive variables together, the resulting distribution leans towards being log-normal.

  5. Incorporating Data Quality: Our pedigree matrix assesses various aspects of data quality and assigns uncertainty factors accordingly. These factors often affect the data in a multiplicative way. Using a log-normal distribution ensures we capture the combined effect of these uncertainties appropriately.

By continuing to use the pedigree matrix within this new framework, we ensure that each emission source’s unique characteristics and data quality assessments inform the uncertainty calculations.

Introducing Monte Carlo Simulations

Given the challenges posed by correlations and the nature of emissions data, we’ve adopted Monte Carlo simulations—a robust statistical technique ideal for handling complex, correlated variables.

What Are Monte Carlo Simulations?

A Monte Carlo simulation uses random sampling and statistical modelling to estimate mathematical functions and mimic the operation of complex systems. Think of it like running thousands of "what-if" scenarios to see all the possible outcomes.

Why Monte Carlo for Emissions?

Monte Carlo simulations are particularly well-suited for our needs because they:

  • Handle Complex Distributions: They can accurately simulate log-normal distributions and their sums, which is crucial given the nature of emissions data.
  • Incorporate Individual Uncertainties: They allow us to model each emission source based on its unique uncertainty profile derived from the pedigree matrix.
  • Account for Correlations: They can include correlations between emissions, ensuring that the combined uncertainty reflects real-world interdependencies.

By running a large number of simulations, we generate a distribution of possible total emissions. This provides a comprehensive picture of potential variability and uncertainty, going beyond a single-point estimate. Below is an animation of just such an estimate.

As you can see, the sum of total emissions is significantly lower than the statistical average of the resultant distribution. This is critical to understand when reporting emissions. Simply summing the emissions calculated is not enough as it does not account for the significant uncertainty in emissions calculated and indeed, systematically under reports the expected value.

Benefits to You

Enhanced Accuracy and Confidence

With this new approach, you receive uncertainty estimates that are not only more precise but also more representative of the complexities inherent in emissions data. This means you can have greater confidence in the numbers informing your strategies and compliance efforts.

Better Risk Management

Understanding the full spectrum of potential outcomes allows for more effective risk assessment. Whether you’re planning reductions, investing in mitigation technologies, or reporting to stakeholders, having detailed uncertainty information supports more informed decisions.

Staying Ahead with Innovation

By embracing advanced statistical methods, we’re ensuring that you benefit from the latest developments in emissions analysis. This proactive approach keeps you ahead of regulatory changes and industry standards, positioning you as a leader in environmental responsibility.

Looking Forward

We’re thrilled about the possibilities this advancement opens up. Our commitment is to provide you with the best tools and insights, and adopting Monte Carlo simulations is a testament to that promise.

If you have questions about how this new method affects your emissions reporting or would like to delve deeper into the technical aspects, we’re here to help. Together, we can navigate the complexities of emissions uncertainty and chart a course toward a more sustainable future.

At C Free, we’re dedicated to continuous improvement and innovation in environmental analysis. Stay tuned for more updates as we continue to enhance our services to meet your evolving needs.

Note: We understand that statistical concepts like log-normal distributions and Monte Carlo simulations can be complex. Our team is always available to explain these methods in more detail and discuss how they apply to your specific context. Don’t hesitate to reach out for a conversation - we’re here to make emissions data understandable and actionable for you.

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