Noise Persistence in a Cyclostationary Linear Inverse Model Framework and Its Impact on ENSO Evolution and Prediction Skills

Abstract Linear inverse models (LIMs) are widely used empirical methods for studying ENSO. While conventional LIMs have proven effective in understanding, reproducing, and forecasting climate variability, they are often limited by assumptions of stationarity or memoryless white-noise random forcing. This study introduces a new LIM variant called CS-Colored-LIM, which extends the cyclostationary (CS) white-noise-forced LIM by modeling random forcing with Ornstein–Uhlenbeck colored noise. Applying LIMs to global climate indices, the results show that the cyclostationary framework reproduces the observed winter peak in ENSO variability and enables LIMs to quantitatively explain the spring predictability barrier in terms of first-order dynamics and stochastic forcing. Meanwhile, the colored-noise representation effectively captures the temporal structure of stochastic forcing, which plays a sustained and nonnegligible role in ENSO evolution. As a result, CS-Colored-LIM outperforms existing LIM variants by improving short-term forecast skill via seasonality and enhancing long-range forecast skill through noise persistence, achieving performance comparable to machine learning and nonlinear approaches. These findings underscore the dual importance of seasonal modulation and persistent stochastic forcing in ENSO modeling and establish CS-Colored-LIM as a simple yet powerful approach for data-driven, extended-range ENSO prediction.