ENSO power spectrum periodogram generated by ChatGPT

enso_periodogram_modify.py

import numpy as np
import matplotlib.pyplot as plt
from scipy.signal import periodogram, windows

# Parameters
years = 500
dt = 1 / 365.25  # daily resolution
t = np.arange(0, years, dt)
fs = 1 / dt  # sampling frequency in cycles per year

# Sharp annual impulse (high-order sine)
N = 80  # sharpness of annual impulse
annual_impulse = np.sin(np.pi * t) ** N

# Lunar tidal cycles in days
lunar_periods_days = {
    'Draconic Month': 27.2122,
    'Tropical Month': 27.3216,
    'Anomalistic Month': 27.5546,
    'Synodic Month': 29.5306,
    'Lunar Perigee (Mm)': 27.5546,
    'Lunar Apogee (Mf)': 13.6608,
    'Lunar Nodal (18.6 years)': 6798.4
}

# Convert to frequencies in cycles/year
lunar_frequencies = {name: 365.25 / days for name, days in lunar_periods_days.items()}

# Simulate combined tidal signal (sum of sinusoids)
tidal_signal = np.zeros_like(t)
for freq in lunar_frequencies.values():
    tidal_signal += np.sin(2 * np.pi * freq * t)*freq  ### only added *freq to simulate a derivative

# Combined forcing: annual impulse modulating lunar tides
modulated_signal = annual_impulse * tidal_signal

# Compute spectrum
window = windows.hann(len(modulated_signal))
frequencies, power = periodogram(modulated_signal, fs=fs, window=window, scaling='spectrum')

# Plot spectrum
plt.figure(figsize=(12, 6))
plt.semilogy(frequencies, power, label='Synthetic ENSO-like Signal')
plt.axvline(0.5, color='gray', linestyle='--', label='0.5 cycles/year')
for name, freq in lunar_frequencies.items():
    if freq < 2:  # Show only long-period components
        plt.axvline(freq, linestyle=':', label=name)

plt.xlim(0, 2)
plt.xlabel('Frequency (cycles/year)')
plt.ylabel('Spectral Power')
plt.title('Spectrum of Annual-Impulse Modulated Lunar Tidal Signal')
plt.legend(loc='upper right', fontsize='small')
plt.grid(True)
plt.tight_layout()
plt.show()

run.sh

### shell command
python .\enso_periodogram_modify.py

NINO4 spectrum

see above peaks at
0.052 (18.6 lunar nodal) -- star symbol
0.258 (lunar anom Mm or Mf) -- open square
0.367 (lunar trop) -- small open circles
0.426 (lunar drac) -- large open circles

NINO34

Another view showing more detail with possible biennial (2) and quad (4) modulations and the mirror folding about 0.5

How do you generate the plots above?

"How do you generate the plots above?"

Some are created by ChatGPT, run the script generated in a Python session and it will plot as shown.

Some of the other plots are customized, those with extra annotations and labeling. Not sure what you are asking as apart from that, it is either plotting straight data or model results.