[Paper Review] On the predictability of Rainfall in Kerala- An application of ABF Neural Network

Ninan Sajeeth Philip, K Babu Joseph|ArXiv.org|Feb 18, 2001

Complex Systems and Time Series Analysis4 citations

TL;DR

This study applies an Adaptive Basis Function Neural Network (ABFNN) to 87 years of rainfall data from Trivandrum, Kerala, to assess long-term predictability. Despite nonlinear fluctuations and chaotic influences, the ABFNN successfully models rainfall trends with low error (RMS ~0.09), showing minimal residual power in spectral analysis, indicating stable long-term patterns with negligible deviation from historical behavior.

ABSTRACT

Rainfall in Kerala State, the southern part of Indian Peninsula in particular is caused by the two monsoons and the two cyclones every year. In general, climate and rainfall are highly nonlinear phenomena in nature giving rise to what is known as the `butterfly effect'. We however attempt to train an ABF neural network on the time series rainfall data and show for the first time that in spite of the fluctuations resulting from the nonlinearity in the system, the trends in the rainfall pattern in this corner of the globe have remained unaffected over the past 87 years from 1893 to 1980. We also successfully filter out the chaotic part of the system and illustrate that its effects are marginal over long term predictions.

Motivation & Objective

• To evaluate the long-term predictability of rainfall in Kerala, a monsoon- and cyclone-influenced region in southern India.
• To determine whether nonlinear and chaotic influences significantly disrupt historical rainfall patterns over time.
• To assess the effectiveness of Adaptive Basis Function Neural Networks (ABFNN) in modeling complex, nonstationary rainfall time series compared to traditional Fourier analysis.
• To quantify model error using spectral analysis of residual power spectra between predicted and actual rainfall.

Proposed method

• An Adaptive Basis Function Neural Network (ABFNN) is trained on 40 years (1893–1933) of monthly rainfall data from Trivandrum, Kerala.
• The network uses a learning algorithm that adapts basis functions to better fit the nonlinear dynamics of rainfall, improving performance over standard backpropagation.
• After training, the network predicts rainfall for the remaining 47 years (1934–1980) as an independent test set.
• Model performance is evaluated using root mean square error (RMSE) and spectral analysis of predicted vs. actual time series.
• Fourier Power Spectra (FPS) of actual and predicted sequences are compared, and the residual FPS (difference) is analyzed to detect systematic model errors or new trends.
• Residual power distribution across frequency bands is used to assess the significance of deviations, with low power indicating minimal chaotic or structural perturbations.

Experimental results

Research questions

• RQ1 Can an ABFNN effectively model and predict long-term rainfall patterns in Kerala despite inherent nonlinearity and chaotic influences?
• RQ2 To what extent do environmental perturbations such as ENSO or solar activity cause significant deviations in the predicted rainfall compared to historical data?
• RQ3 Does the residual power in the Fourier Power Spectra of predicted vs. actual rainfall indicate systematic model failure or new climatic trends?
• RQ4 How does the ABFNN’s predictive performance compare to traditional Fourier analysis in capturing nonstationary rainfall dynamics?
• RQ5 Is the observed deviation in rainfall predictions primarily due to model limitations or external chaotic forcing?

Key findings

• The ABFNN achieved a root mean square error (RMSE) of approximately 0.09 on the independent test dataset (1934–1980), indicating strong predictive accuracy.
• The residual Fourier Power Spectrum (FPS) of the predicted vs. actual rainfall showed minimal power across all frequency bands, indicating negligible systematic error or major structural deviation.
• Residual power was primarily distributed as low-amplitude, random fluctuations across the spectrum, resembling white noise, suggesting that chaotic perturbations have marginal long-term impact.
• The network successfully filtered out chaotic components, with only minor spikes in the difference diagram corresponding to known events such as delayed monsoons or ENSO-related anomalies.
• The residual FPS for the test period showed lower power than the training period, indicating the model generalized well and did not overfit to historical patterns.
• The ABFNN outperformed standard Fourier analysis by capturing nonstationary dynamics, as Fourier analysis assumes stationarity and fails to represent the true time-varying behavior of rainfall systems.