Why Intelligent Colouring Matters in Simulation Decomposition

Sometimes, it’s not about what you simulate — it’s about how you show it.
Simulation Decomposition (SimDec) transforms Monte Carlo data into visual insights, revealing how combinations of inputs shape a model’s outputs. But the clarity of those insights depends on one deceptively simple design choice: colour.

In their article “The Importance of Intelligent Colouring for Simulation Decomposition in Environmental Analysis” (Journal of Environmental Informatics Letters, 2023), A. Alam, M. Kozlova, L. T. Leifsson, and J. S. Yeomans demonstrate how intelligent colouring, based on global sensitivity indices, makes SimDec visualizations both interpretable and scientifically rigorous.

🔗 Read the paper: https://doi.org/10.3808/jeil.202300118

The Problem: Colour Is Not Just Decoration

Monte Carlo simulation results are typically shown as single-colour histograms — but that hides interactions between inputs.
SimDec solves this by partitioning output distributions according to input states (e.g. “low,” “medium,” “high”) and colouring each scenario.

However, as the authors show, many studies have used ad hoc or random colouring schemes that:

• obscure which variable drives the pattern,
• mix unrelated hues that confuse perception,
• and make it impossible to interpret scenario legends correctly.

The consequence? Important relationships remain hidden — even when the math is right.

What Is Intelligent Colouring?

Intelligent colouring uses the most influential variable, determined through sensitivity indices (such as Sobol’ or Shapley values), as the anchor for colour assignment.

Here’s how it works (see Figure 1, page 3):

1. Rank inputs by sensitivity.
2. Assign each state of the most influential variable a distinct base colour.
3. Use gradations (light-to-dark shades) of those base colours to encode secondary variables.
4. Keep less influential factors in matching tones to preserve visual consistency.
5. Display the decomposed output as a stacked histogram — with colour continuity showing how each combination of inputs shapes the outcome.

This way, human perception follows the logic of the model.
Blue might represent low battery capacity, green medium, yellow high — and lighter or darker tones within those show secondary effects.

A Simple Model, A Powerful Lesson

The paper uses a mathematical model (y = x₁ + x₂x₃²) from Liu et al. (2022) to illustrate the difference.

When coloured randomly (see Figure 2), the SimDec histogram correctly computes results but fails to reveal structure — it’s just a rainbow of confusion.

When coloured intelligently (see Figure 5), patterns emerge:

• Low, medium, and high states form clean left-to-right blocks.
• Interactions between x₂ and x₃ become visible as clear colour gradients.
• The dominant influence of x₃ is unmistakable — just as sensitivity indices predicted.

This clarity allows researchers to see how inputs interact and when their effects intensify or fade.

Best Practices for SimDec Visuals

To make SimDec results accurate and readable, the paper recommends:
✅ Start decomposition with the most influential variable (based on sensitivity indices).
✅ Use distinct primary colours for the top-ranked variable’s states.
✅ Apply consistent gradients for secondary factors.
✅ Remove non-influential variables (“variable pruning”) to avoid visual noise.

When applied correctly, intelligent colouring turns a complex histogram into a decision-ready visual analytic — clear enough for policymakers, not just modellers.

Why It Matters for Environmental Modelling

In environmental systems, uncertainty isn’t just numerical — it’s visual and interpretive.
From energy transitions to water systems, intelligent colouring helps experts communicate model dynamics clearly, identify nonlinear effects, and reveal hidden feedbacks.

As the authors conclude:

“Many analytical discoveries cannot be accomplished without appropriate colour scheme visualizations.”

Reference:

Alam, A., Kozlova, M., Leifsson, L. T., & Yeomans, J. S. (2023). The Importance of Intelligent Colouring for Simulation Decomposition in Environmental Analysis. Journal of Environmental Informatics Letters, 10(2), 63–73.
https://doi.org/10.3808/jeil.202300118

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