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To create a Taylor diagram in Python for comparing five models against observations, you can use the skill_metrics or taylorDiagram implementations from various libraries. Here’s a step-by-step using Matplotlib and SkillMetrics, which is commonly used in the geoscience community.

✅ What You Need

Observed data: The reference dataset.
Model outputs: Five different model outputs to compare.
Python libraries: numpy, matplotlib, and optionally, skill_metrics.

🔧 Step-by-Step Code (Without External Library)

Below is a custom implementation using only matplotlib.

import matplotlib.pyplot as plt
import numpy as np

# Example data
obs = np.array([3.0, 3.5, 4.0, 4.5, 5.0])  # observed values

models = {
    'Model A': np.array([2.8, 3.4, 4.2, 4.7, 4.9]),
    'Model B': np.array([3.2, 3.6, 4.1, 4.4, 5.1]),
    'Model C': np.array([2.9, 3.2, 4.0, 4.3, 4.8]),
    'Model D': np.array([3.0, 3.7, 3.9, 4.6, 5.0]),
    'Model E': np.array([3.1, 3.5, 4.3, 4.5, 5.2]),
}

# Compute statistics
def compute_stats(model, obs):
    std_model = np.std(model)
    std_obs = np.std(obs)
    corr_coeff = np.corrcoef(model, obs)[0, 1]
    return std_model, corr_coeff

# Setup Taylor diagram
fig = plt.figure(figsize=(8, 6))
ax = fig.add_subplot(111, polar=True)
ax.set_theta_direction(-1)
ax.set_theta_offset(np.pi / 2)

# Reference STD
std_ref = np.std(obs)
ax.plot([0], [std_ref], 'ko', label='Observation')

# Grid and labels
rs = np.linspace(0, 1.5 * std_ref, 100)
ts = np.arccos(np.linspace(0, 1, 100))
for r in rs[::20]:
    ax.plot(ts, np.full_like(ts, r), color='gray', alpha=0.3)

# Plot each model
colors = ['r', 'g', 'b', 'm', 'c']
for i, (name, model_data) in enumerate(models.items()):
    std_model, corr = compute_stats(model_data, obs)
    theta = np.arccos(corr)
    ax.plot(theta, std_model, 'o', label=name, color=colors[i])

ax.set_title('Taylor Diagram')
ax.set_rlim(0, 1.5 * std_ref)
ax.set_rlabel_position(135)
ax.legend(loc='upper right', bbox_to_anchor=(1.3, 1.1))
plt.tight_layout()
plt.show()

Taylor Diagram in Python Using Pandas and Matplotlib | Model Comparison Example

import pandas as pd
import matplotlib.pyplot as plt
import numpy as np

df = pd.read_excel("test_data.xlsx")

# Separate observed and model data
obs = df['Observed']
models = df.drop(columns='Observed')

# Compute statistics
def compute_stats(model, obs):
    std_model = np.std(model)
    corr_coeff = np.corrcoef(model, obs)[0, 1]
    return std_model, corr_coeff

# Setup Taylor diagram
fig = plt.figure(figsize=(8, 6))
ax = fig.add_subplot(111, polar=True)
ax.set_theta_direction(-1)
ax.set_theta_offset(np.pi / 2)

# Reference STD
std_ref = np.std(obs)
ax.plot([0], [std_ref], 'ko', label='Observation')

# Grid and labels
rs = np.linspace(0, 1.5 * std_ref, 100)
ts = np.arccos(np.linspace(0, 1, 100))
for r in rs[::20]:
    ax.plot(ts, np.full_like(ts, r), color='gray', alpha=0.3)

# Plot each model
colors = ['r', 'g', 'b', 'm', 'c']
for i, column in enumerate(models.columns):
    model_data = models[column].values
    std_model, corr = compute_stats(model_data, obs)
    theta = np.arccos(corr)
    ax.plot(theta, std_model, 'o', label=column, color=colors[i % len(colors)])

ax.set_title('Model 1 - Test',pad=30)
ax.set_rlim(0, 1.5 * std_ref)
ax.set_rlabel_position(135)
ax.legend(loc='upper right', bbox_to_anchor=(1.3, 1.1))
plt.tight_layout()
plt.show()

Code Explanation 📒

🔹 1. Import Required Libraries

import pandas as pd
import matplotlib.pyplot as plt
import numpy as np

pandas: for reading and handling tabular data from Excel.
matplotlib.pyplot: for creating the polar plot (Taylor diagram).
numpy: for numerical operations like standard deviation and correlation.

🔹 2. Read Excel File

df = pd.read_excel("test_data.xlsx")

Loads the Excel file test_data.xlsx into a DataFrame named df.

🔹 3. Separate Observed and Model Data

obs = df['Observed']
models = df.drop(columns='Observed')

obs: the column containing the observed/reference data.
models: all other columns, each assumed to be output from a different model.

🔹 4. Define a Function to Compute Statistics

def compute_stats(model, obs):
    std_model = np.std(model)
    corr_coeff = np.corrcoef(model, obs)[0, 1]
    return std_model, corr_coeff

Calculates:
- std_model: standard deviation of the model’s predictions.
- corr_coeff: correlation coefficient between the model and observations.

🔹 5. Set Up the Taylor Diagram Plot

fig = plt.figure(figsize=(8, 6))
ax = fig.add_subplot(111, polar=True)

Creates an 8×6 inch figure.
Adds a polar subplot (used for Taylor diagrams).

🔹 6. Adjust Polar Orientation

ax.set_theta_direction(-1)
ax.set_theta_offset(np.pi / 2)

set_theta_direction(-1): clockwise direction.
set_theta_offset(np.pi / 2): sets 0° (correlation = 1) to the top of the plot.

🔹 7. Plot the Observed Reference Point

std_ref = np.std(obs)
ax.plot([0], [std_ref], 'ko', label='Observation')

Calculates the standard deviation of the observed data.
Plots it as a black circle at angle 0 (correlation = 1) and radius = std_ref.

🔹 8. Draw Grid Circles (Optional Background)

rs = np.linspace(0, 1.5 * std_ref, 100)
ts = np.arccos(np.linspace(0, 1, 100))
for r in rs[::20]:
    ax.plot(ts, np.full_like(ts, r), color='gray', alpha=0.3)

Draws concentric circular lines to guide comparison of standard deviations.
rs: radial distances.
ts: angular values converted from correlation.

🔹 9. Plot Each Model’s Statistics

colors = ['r', 'g', 'b', 'm', 'c']

Predefined colors for different models.

for i, column in enumerate(models.columns):
    model_data = models[column].values
    std_model, corr = compute_stats(model_data, obs)
    theta = np.arccos(corr)
    ax.plot(theta, std_model, 'o', label=column, color=colors[i % len(colors)])

Loops through each model column:
- Gets model values.
- Calculates standard deviation and correlation.
- Converts correlation to polar angle (theta).
- Plots each model’s point on the diagram with a unique color and label.

🔹 10. Final Plot Customization

ax.set_title('Model 1 - Test', pad=30)

Adds title to the plot and increases vertical spacing using pad.

ax.set_rlim(0, 1.5 * std_ref)

Sets radial (standard deviation) axis limit.

ax.set_rlabel_position(135)

Places the radial axis labels (STD values) at 135°.

ax.legend(loc='upper right', bbox_to_anchor=(1.3, 1.1))

Adds a legend outside the plot for model names.

plt.tight_layout()
plt.show()

Ensures layout is neat and displays the plot.

Example: Taylor Diagram of Model Predictions — Quarter Circle View with Correlation Labels

📌 Summary:

This code reads observed and model data from Excel and uses a Taylor diagram to compare models based on:

Standard deviation (radial distance),
Correlation (angle),
And distance from reference (related to RMSE, visually).

📌 Taylor Diagram Shows:

Radial distance: Standard deviation
Angle: Correlation coefficient
Distance from reference point: Root mean square error (implicitly)

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. 👉 Learn more
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