This work stands apart from its neighbors, which focus on exoplanet observations and atmospheric phenomena, as its subject is Earth's climate dynamics. The Asian monsoon is one of the most powerful oscillatory climate systems, yet its internal variability on intraseasonal timescales remains poorly understood. Existing geophysical hydrodynamic models are largely Hamiltonian, and it has previously been shown that Hamiltonian distributed chaos governs the behavior of the AAO, AO, NAO, and PNA indices. It is therefore natural to expect similar dynamics for monsoon indices.
The analysis used daily values of the ISMI, WNPMI, AUSMI, Niño 3, and Niño 4 indices for the period from 1948 to 2015 (for the Niño indices, from 1981 to 2018). Intraseasonal variability was isolated by subtracting a 121-day moving average, which removes interannual and annual components. Power spectra were computed using the maximum entropy method, which is optimal for chaotic time series. The resulting spectra were compared with the theoretical stretched exponential form E(f) ∝ exp[-(f/f₀)^β] for β = 3/4 and β = 1/2.
For ISMI, the spectrum corresponds to β = 3/4 with a characteristic time scale T₀ = 1/f₀ ≈ 32 days. For WNPMI, AUSMI, Niño 3, and Niño 4, the spectra correspond to β = 1/2 with characteristic times T₀ ≈ 171, 143, 280, and 196 days, respectively. The difference in β values between ISMI and WNPMI reflects differences in their geographical location and energy sources. The similarity of the WNPMI, AUSMI, and ENSO index spectra indicates a dynamical connection, with AUSMI apparently belonging to the extended ENSO system on intraseasonal timescales.
This work differs from its archive neighbors in applying the concept of Hamiltonian distributed chaos to climate indices, whereas neighboring works focus on astrophysical objects and other atmospheric phenomena. The obtained β = 3/4 and β = 1/2 values are analytical predictions for Hamiltonian systems, confirming the Hamiltonian nature of monsoon dynamics. This allows a unified description of various climate oscillations within a single theoretical framework.
The topic could develop toward applying Hamiltonian distributed chaos to other climate indices and to climate model outputs. It may be possible to investigate the relationship between the β parameter and physical characteristics of the system, such as basin geometry or convection intensity. Also promising is the study of transitions between regimes with different β under changing external conditions.
The results could be useful for improving prediction of monsoon activity and ENSO on intraseasonal timescales, as well as for validating climate models.
The next step could be analysis of reanalysis data and climate model outputs to test the reproducibility of the spectral characteristics and their relationship to model parameters.
Connection to unresolved problems in climatology: understanding the sources of intraseasonal monsoon variability, the mechanisms of monsoon-ENSO interaction, and the predictability of these phenomena on timescales from weeks to months.
The characteristic time for ISMI (32 days) is close to the lunar month period, although no direct connection is implied. For WNPMI, the characteristic time (171 days) is almost one and a half times longer than for AUSMI (143 days), reflecting the different inertia of the circulation systems.