Entropy-based measures for time series analysis with NumPy and Xarray.

📌 Note:
If you use xentropy in your published work, please cite:

Stuecker, M. F., Zhao, S., Timmermann, A., Ghosh, R., Semmler, T., Lee, S.-S., Moon, J.-Y., Jin, F.-F., Jung, T. (2025). Global climate mode resonance due to rapidly intensifying El Niño–Southern Oscillation. Nature Communications. https://doi.org/10.1038/s41467-025-64619-0

Implements commonly used entropy metrics for time series analysis:

• Sample Entropy (SampEn, Richman and Moorman 2000)
• Approximate Entropy (ApEn, Pincus 1991)
• Cross-ApEn / Cross-SampEn (Costa et al. 2002)
• Multiscale Entropy (MSE) (Costa et al. 2002)

You can install xentropy in the following way:

pip install git+https://github.com/senclimate/xentropy.git

import xarray as xr
import numpy as np
from xentropy import xentropy

# create sample data
time = np.arange(1000)
data = np.sin(0.1 * time) + 0.1*np.random.randn(1000)
da = xr.DataArray(data, dims=["time"])

xe = xentropy(dim='time')
SampEn = xe.SampEn(da)
print(SampEn.values)

• ENSO reguliarity (SampEn) in observation, AWI-CM3 and CMIP6 models (Fig. 2 in Stuecker et al. 2025), an detailed example for observation is available in examples/enso_regularity.ipynb

• Pincus, S. M. (1991). Approximate entropy as a measure of system complexity. PNAS, 88(6), 2297–2301.
• Richman, J. S., & Moorman, J. R. (2000). Physiological time-series analysis using approximate entropy and sample entropy. AJP, 278(6), H2039–H2049.
• Costa, M., Goldberger, A. L., & Peng, C. K. (2002). Multiscale entropy analysis of complex physiologic time series. PRL, 89(6), 068102.
• Pincus, S. M., & Singer, B. H. (1996). Randomness and degrees of irregularity. PNAS, 93(5), 2083–2088.