Taylor Diagram in Python | Matplotlib Guide with Examples

Learn what a Taylor Diagram is and how to create one using Python's Matplotlib. This beginner-friendly guide explains standard deviation, correlation, and variability with clear examples.

🎯 What is a Taylor Diagram?

A Taylor Diagram helps you visually compare how similar multiple models or simulations are to a reference dataset (usually real-world observations). It’s widely used in science and engineering.

🔍 3 Key Statistics it Shows

It packs three pieces of info into one graph:

📈 Reading the Diagram

• The black dot is the reference point (usually the observed data).
• Each model is a dot somewhere on the diagram.
• The closer a model’s dot is to the black dot, the better it performed.

For example:

• Model A has high correlation and standard deviation close to the observation → It’s very good!
• Model C has a lower correlation and too much variability → Not so good.

🧠 Why this is powerful

Instead of looking at many charts or numbers, a Taylor diagram shows everything at once:

• Which model matches the trend?
• Which one has the right spread?
• Which one is overall closest to the truth?

🛠️ Terms in plain language:

• Standard Deviation: How “bouncy” the data is. Big std = wild swings.
• Correlation: If the model zigzags just like the real data — even if it’s too high or too low.
• RMSE: How far off the model is overall (lower is better).

• Model dots: Show how each model performs.

• Arrows:

  • Point to higher correlation (model follows the shape of real data better).
  • Indicate increasing variability (standard deviation).
  • Remind you: closer to the black dot (Observation) means better performance.

correlation and variability work together to give a complete picture of model performance — especially in Taylor diagrams.

Correlation vs Standard Deviation

🎯 1. Correlation → Pattern Similarity

• Measures how well the model captures the shape or trend of the observed data.
• Value ranges from –1 (opposite) to +1 (perfect match).

✅ High correlation → model follows ups and downs of the observed data ❌ Low correlation → model doesn’t match the timing or direction

📊 2. Standard Deviation (Variability) → Amplitude of Fluctuations

• Measures how much values spread out from the mean.
• In Taylor diagrams: radial distance from origin = model variability.

✅ Close to observation SD → model captures correct magnitude of fluctuations ❌ Too low/high SD → model is too flat or too exaggerated

🔗 Together in a Taylor Diagram:

Each model is represented by a point with:

• Angle = correlation with observations
• Radius = model’s standard deviation
• Reference point = observed data (ideal model)

✅ Good Model:

• High correlation (close to 1 → angle near zero)
• Correct variability (distance from origin ≈ observed SD)

❌ Examples of Problematic Models:

📍 Interpretation:

• Black Dot: Observation (reference) – shows the correct variability.
• Model A (Red): High correlation, but low variability → too smooth.
• Model B (Green): High correlation, high variability → too jumpy.
• Model C (Blue): Low correlation, correct variability → wrong pattern, right spread.
• Model D (Magenta): Low correlation, low variability → misses both pattern and magnitude.

This shows why you need to evaluate both:

• The correlation (angular position)
• The standard deviation (radial distance)

📌 Summary:

📘 Related Topics

• Understanding Variability in Taylor Diagram | Python Matplotlib Tutorial – Explore the concept of variability in a Taylor Diagram using Python and Matplotlib. Learn how variability helps interpret model performance with practical visualization examples. 👉 Learn more