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., 2025].

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.

Warning

This package is still in its early stage and under active development, and its API could be changed frequently.


Installation

Installation instructions.

Installation
Model

CRO equations and parameters

Model
Solver

CRO solver

Solver
Fitting

CRO fitting

Fitting
Application

CRO applications

Application
API

The essential API.

API Reference

Relationship with XRO#

The eXtended nonlinear Recharge Oscillator XRO (senclimate/XRO) was developed to study interactions between ENSO and other climate modes, providing advanced predictive capabilities [Zhao et al., 2024].

CRO, in contrast, focuses on the core features and flexibility of the RO framework. It offers multiple fitting methods and supports varying degrees of seasonality in individual parameters.

Both models share the same theoretical RO foundation and belong to the same RO family.

References#

[Jin, 1997]

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 et al., 2020]

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 et al., 2025]

Kim, S.-K., Zhao, S., & et al. (2025). 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 et al., 2025]

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 et al., 2024]

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