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Climate Science Simulation Summary

Here’s a sample dataset generated using two core climate science formulas:

1. Equilibrium Temperature (T)

Calculated using:

\[ T = \left( \frac{S (1 - \alpha)}{4 \sigma} \right)^{1/4} \]

With typical values, Earth’s equilibrium temperature is approximately 254.6 K (without atmospheric greenhouse effects).

2. Radiative Forcing (ΔF)

Increases with higher CO₂ levels:

\[ \Delta F = 5.35 \cdot \ln\left(\frac{C}{C_0}\right) \]

Where \( C_0 = 280 \, \text{ppm} \) (pre-industrial) and \( C \) varies from 280 to 1000 ppm.

Python Code

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

# Constants
sigma = 5.67e-8  # Stefan-Boltzmann constant (W/m^2K^4)
S = 1361         # Solar constant (W/m^2)
alpha = 0.3      # Earth's average albedo
C0 = 280         # Pre-industrial CO₂ concentration (ppm)

# Temperature formula: T = ((S(1 - α)) / (4σ))^(1/4)
T_eq = ((S * (1 - alpha)) / (4 * sigma)) ** 0.25

# CO₂ concentration range
C_values = np.linspace(280, 1000, 100)
delta_F = 5.35 * np.log(C_values / C0)

# DataFrame
df = pd.DataFrame({
    "CO2 Concentration (ppm)": C_values,
    "Radiative Forcing ΔF (W/m²)": delta_F,
    "Equilibrium Temperature T (K)": [T_eq] * len(C_values)
})

# Plotting
plt.figure(figsize=(8, 5))
plt.plot(C_values, delta_F, color='green')
plt.title('Radiative Forcing vs CO₂ Concentration')
plt.xlabel('CO₂ Concentration (ppm)')
plt.ylabel('Radiative Forcing ΔF (W/m²)')
plt.grid(True)
plt.tight_layout()
plt.show()

df.head()

Sample Data

CO₂ (ppm)	ΔF (W/m²)	T (K)
280.0	0.00	254.58
287.3	0.14	254.58
294.5	0.27	254.58
301.8	0.40	254.58
309.1	0.53	254.58

Simulate further scenarios with temperature changes.

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