CRO: Community Recharge Oscillator#
What is CRO?#
The recharge oscillator (RO) model is one of the leading theories for the El Niño–Southern Oscillation (ENSO) [Jin, 1997, Jin et al., 2020, Vialard et al., 2025]. While the literature contains many RO variants and implementations, CRO is an open-source Python and Matlab package for solving the RO equations, fitting parameters to observational or model data, and applying the model in teaching and research [Kim et al., 2026].
Installation instructions.
Quickstart of CRO
CRO equations and parameters
CRO solver
CRO fitting
CRO applications
The essential API.
Key Features#
Solver: Numerical and analytical solvers for the RO equations.
Fitting: Parameter estimation from observations, reanalysis, or climate model data.
Applications: Simulations, sensitivity experiments, and analysis of ENSO dynamics.
Citation#
Please cite [Kim et al., 2026] if you use this package in your research.
Warning
This package is still in its early stage and under active development, and its API could be changed frequently.
Note
CRO focuses on the core features and flexibility of the Recharge Oscillator (RO) framework. It provides multiple fitting methods and supports varying degrees of seasonality in individual parameters.
In contrast, the eXtended nonlinear Recharge Oscillator (XRO) XRO (senclimate/XRO) extends the basic RO formulation by including interactions between ENSO and other climate modes, thereby providing enhanced predictive capabilities [Zhao et al., 2024].
Both models share the same theoretical RO foundation and belong to the same RO family.
References#
Jin, F.-F. (1997). An equatorial ocean recharge paradigm for ENSO. Part I: conceptual model. J. Atmos. Sci., 54, 811–829. doi:10.1175/1520-0469(1997)054<0811:aeorpf>2.0.co;2
Jin, F.-F., Chen, H.-C., Zhao, S., Hayashi, M., Karamperidou, C., Stuecker, M. F., … Geng, L. (2020). McPhaden, M. J., Santoso, A., & Cai, W. (Eds.). Simple ENSO Models. El Niño Southern Oscillation in a Changing Climate (pp. 119–151). American Geophysical Union (AGU).
Kim, S.-K., Zhao, S., & et al. (2026). Community Recharge Oscillator (CRO) v1.0: an open-source Python and MATLAB package for solving, parameter fitting, and practical applications of the ENSO recharge oscillator. In preparation.
Vialard, J., Jin, F.-F., McPhaden, M. J., Fedorov, A., Cai, W., An, S.-I., … Thual, S. (2025). The El Niño Southern Oscillation (ENSO) Recharge Oscillator Conceptual Model: Achievements and Future Prospects. Reviews of Geophysics, 63(1), e2024RG000843. doi:10.1029/2024RG000843
Zhao, S., Jin, F.-F., Stuecker, M. F., Thompson, P. R., Kug, J.-S., McPhaden, M. J., … Cai, W. (2024). Explainable El Niño predictability from climate mode interactions. Nature, 630(8018), 891–898. doi:10.1038/s41586-024-07534-6