Nonlinear extensions of linear inverse models under memoryless or persistent random forcing

This study extends the linear inverse modeling (LIM) framework to nonlinear settings by presenting White-nLIM and Colored-nLIM, statistics-based empirical methods that construct approximate stochastic systems incorporating quadratic deterministic dynamics with either memoryless Gaussian white noise or persistent Ornstein-Uhlenbeck colored noise. Beyond the evident improvements over linear models, Colored-nLIM offers a robust approach to parameter estimation and statistical modeling under persistent stochastic forcing. Together with White-nLIM, these methods provide a systematic framework to assess the role of noise persistence in inverse modeling. Applications to the Lorenz 63 system and a simplified El Niño-Southern Oscillation model demonstrate their potential to capture chaotic behavior and climate variability.