@article{fdi:010092108,
  title = {{A} physics-informed auto-learning framework for developing stochastic conceptual models for {ENSO} diversity},
  author = {{Z}hang, {Y}. {L}. and {C}hen, {N}. and {V}ialard, {J}{\'e}r{\^o}me and {F}ang, {X}. {H}.},
  editor = {},
  language = {{ENG}},
  abstract = {{U}nderstanding {E}l {N}iño-{S}outhern {O}scillation ({ENSO}) dynamics has tremendously improved over the past few decades. {T}he {ENSO} diversity in spatial pattern, peak intensity, and temporal evolution is, however, still poorly represented in conceptual {ENSO} models. {I}n this paper, a physics-informed auto-learning framework is applied to derive {ENSO} stochastic conceptual models with varying degrees of freedom. {T}he framework is computationally efficient and easy to apply. {O}nce the state vector of the target model is set, causal inference is exploited to build the right-hand side of the equations based on a mathematical function library. {F}undamentally different from standard nonlinear regression, the auto-learning framework provides a parsimonious model by retaining only terms that improve the dynamical consistency with observations. {I}t can also identify crucial latent variables and provide physical explanations. {T}his methodology successfully reconstructs the equations of a realistic six- dimensional reference {ENSO} model based on the recharge oscillator theory from its data. {A} hierarchy of lower-dimensional models is derived, and their representation of {ENSO} (including its diversity) is systematically assessed. {T}he minimum model that represents {ENSO} diversity is four-dimensional, with three interannual variables describing the western {P}acific thermocline depth, the eastern and central {P}acific sea surface temperatures ({SST}s), and one intraseasonal variable for westerly wind events. {W}ithout the intraseasonal variable, the resulting three-dimensional model underestimates extreme events and is too regular. {A} limited number of weak nonlinearities in the model are essential in reproducing the observed extreme {E}l {N}iño events and the observed nonlinear relationship between eastern and western {P}acific {SST}s.},
  keywords = {{E}l {N}ino ; {ENSO} ; {W}ind stress ; {O}cean models ; {S}tochastic models ; {M}achine learning},
  booktitle = {},
  journal = {{J}ournal of {C}limate},
  volume = {37},
  numero = {23},
  pages = {6323--6347},
  ISSN = {0894-8755},
  year = {2024},
  DOI = {10.1175/jcli-d-24-0092.1},
  URL = {https://www.documentation.ird.fr/hor/fdi:010092108},
}