A hybrid dynamical-stochastic model of maximum temperature time series of Imphal, Northeast India incorporating nonlinear feedback and noise diagnostics

Climate variability is a complex phenomenon resulting from numerous interacting components of a climate system across a wide range of temporal and spatial scales. Although significant advances have been made in understanding global climate variability, there are relatively less studies on regional climate modeling, particularly in developing countries. In this work, we propose a framework of data driven hybrid dynamical stochastic modeling to investigate the variability of maximum temperature recorded for the capital city of Imphal in the state of Manipur, located in the Northeast India. In light of increasing concerns over global warming, studying maximum temperature variability over varying time scales is an important area of research. Analysis using publicly available climate data over the course of 73 years, our approach yields key insights into the temperature dynamics, such as a positive increase in temperature in the region during the period investigated. Our hybrid model, combining spectral analysis and Fourier decomposition methods with stochastic noise terms and nonlinear feedback mechanisms, is found to effectively reproduce the observed dynamics of maximum temperature variability with high accuracy. Our results are validated by robust statistical and qualitative tests. We further derive Langevin and Fokker-Planck equations for the maximum temperature dynamics, offering the theoretical ground and analytical interpretation of the model that links the temperature dynamics with underlying physical principles.

💡 Research Summary

The paper presents a data‑driven hybrid dynamical‑stochastic framework for modeling the variability of daily maximum temperature (Tmax) in Imphal, the capital of Manipur, India, using a 73‑year record (1951‑2024). After retrieving the data from the Indian Meteorological Department via the open‑source IMDlib library, the authors clean the series by discarding physically implausible values (<0 °C or >50 °C) and reconstruct missing observations with a Kalman filter, which simultaneously estimates the system state and observation noise.

The core of the methodology is a three‑component decomposition of the temperature signal: (i) a deterministic backbone Λ(t) obtained through Singular Spectrum Analysis (SSA) followed by Fast Fourier Transform (FFT); (ii) a nonlinear feedback term F(t) that captures temperature‑dependent memory effects; and (iii) a stochastic noise term ζ(t) whose statistical properties are diagnosed in detail.

SSA is performed after selecting an optimal window length based on the power spectral density (PSD) estimated with Welch’s method. The trajectory matrix is built via a Hankel transform and decomposed by singular value decomposition (SVD). Components with singular values above 1 % of the maximum are classified as signal, while the remainder is treated as noise. The dominant (trend) and secondary (sub‑annual oscillations) components are retained as the deterministic part. FFT is then applied to these components, and only the most energetic frequencies are kept, yielding a truncated Fourier series that reproduces the mean and variance of the original series.

Two forms of nonlinear feedback are investigated. The first is a cubic delayed feedback, (F(t)=\varepsilon_{1}