Table 2 Selected studies that obtain climate insights related to four of the key challenges identified in the paper by applying nonlinear dynamical approaches to observations, conceptual models and global circulation and Earth system models

Chekroun et al.¹⁰⁶

Pullback attractor

Stochastically forced Lorenz model, Low-dimensional, nonlinear stochastic model of ENSO

Exploring the system’s dynamics and statistics

Shi et al.¹⁰⁷

Convergent cross mapping

Observations

Detecting drought propagation

Wang et al.¹⁰⁸

Convergent cross mapping

Observations, Reanalysis

Effect of soil moisture on precipitation

Ramesh and Cane, 2019⁶³

Attractor reconstruction

General circulation model

Predictability of tropical Pacific decadal variability

Krishnamurthy, 2019 and references therein³⁸

Phase space reconstruction

Observations

Nonlinear climate forecasting of Indian monsoon

Sahastrabuddhe and Ghosh, 2021⁵⁸

Nonlinear local Lyapunov exponent

Observations

Limits of predictability of SSTs

Drótos et al. ⁴⁰

Snapshot attractor

Forced Lorenz-84 model

Change detection of mid-winter westerly windspeeds

Charo et al.⁷⁰ Charo et al.⁷¹

Branched manifold analysis through homologies

Stochastically forced Lorenz model

Detection of tipping points

Boers et al. 2022 and references therein⁶⁶

Bifurcation

Paleoclimate data

Detection of tipping points

Shukla et al.⁷⁶ Seo et al.⁷⁵

Relative entropy

Subset of CMIP3 models, Subset of CMIP5 models

Climate model evaluation

Sane et al.⁸⁰

Shannon entropy, mutual information

GFDL-ESM2M (Ocean component) LE

Internal vs forced variability

Pierini et al.¹⁰⁹

Pullback attractor

Low order quasi-geostrophic double-gyre ocean model

Climate change in the presence of natural variability