Stéphane Vannitsem

The Liang–Kleeman Information Flow (LKIF) framework has been increasingly used to identify causality in Earth–system dynamics in recent years. Yet, uncertainties remain regarding how the causal graph changes when mediators and confounders (conditioners) are introduced, i.e., divergence between the bivariate and conditioned forms. A controlled synthetic experiment shows that LKIF preserves correct causal directions under hidden confounding, while differences between bivariate and multivariate estimates still occur. We characterize these differences using time-varying LKIF and introduce several quantifiers, including Conditioner Dominance Index, Moderation Gain, Conditioning Pressure, and Convergence Rate, to evaluate the contributions of conditioners. This is illustrated in an application to soil moisture (SM) and vapor pressure deficit (VPD) couplings with vegetation (leaf area index (LAI) and gross primary productivity (GPP)) in humid forest regions of Southeast China and the Amazon Basin, using satellite-derived and reanalysis data over 1981–2018. We find that the influence of SM on LAI remains consistently stable and shows little sensitivity to the selected conditioners, whereas its influence on GPP and that of VPD on vegetation exhibit substantial divergence between bivariate and multivariate estimates. This divergence peaks under compound dry–hot conditions, with VPD and temperature emerging as dominant conditioners. These results demonstrate that bivariate and multivariate LKIF can yield markedly different conclusions across time and space, especially under compound environmental stress. More importantly, even for the same variables in a causal graph, the same conditioners can affect the temporal evolution of the causal relationships very differently at different locations. This highlights how stationary assumptions may oversimplify causal structure by masking relevant temporal transitions, particularly under compound environmental stress.

The atmospheric tropical belt is believed to be more predictable than the extratropics. This question is revisited here by exploring the emergence of chaos in reduced-order model versions of the vorticity equation under the weak temperature gradient hypothesis, which provides a good description of the large-scale tropical atmosphere. The analysis reveals that under fairly realistic divergence forcing amplitudes, chaos may emerge, sometimes with Lyapunov time scales of less than a day. This result contrasts with the idea of a predictable tropical atmosphere, and opens important questions on the effective origin of predictability in the Tropics.

The atmospheric tropical belt is believed to be more predictable than the extratropics. This question is revisited here by exploring the emergence of chaos in reduced-order model versions of the vorticity equation under the weak temperature gradient hypothesis, which provides a good description of the large-scale tropical atmosphere. The analysis reveals that under fairly realistic divergence forcing amplitudes, chaos may emerge, sometimes with Lyapunov time scales of less than a day. This result contrasts with the idea of a predictable tropical atmosphere, and opens important questions on the effective origin of predictability in the Tropics.

The atmospheric tropical belt is believed to be more predictable than the extratropics. This question is revisited here by exploring the emergence of chaos in reduced-order model versions of the vorticity equation under the weak temperature gradient hypothesis, which provides a good description of the large-scale tropical atmosphere. The analysis reveals that under fairly realistic divergence forcing amplitudes, chaos may emerge, sometimes with Lyapunov time scales of less than a day. This result contrasts with the idea of a predictable tropical atmosphere, and opens important questions on the effective origin of predictability in the Tropics.

The atmospheric tropical belt is believed to be more predictable than the extratropics. This question is revisited here by exploring the emergence of chaos in reduced-order model versions of the vorticity equation under the weak temperature gradient hypothesis, which provides a good description of the large-scale tropical atmosphere. The analysis reveals that under fairly realistic divergence forcing amplitudes, chaos may emerge, sometimes with Lyapunov time scales of less than a day. This result contrasts with the idea of a predictable tropical atmosphere, and opens important questions on the effective origin of predictability in the Tropics.

The atmospheric tropical belt is believed to be more predictable than the extratropics. This question is revisited here by exploring the emergence of chaos in reduced-order model versions of the vorticity equation under the weak temperature gradient hypothesis, which provides a good description of the large-scale tropical atmosphere. The analysis reveals that under fairly realistic divergence forcing amplitudes, chaos may emerge, sometimes with Lyapunov time scales of less than a day. This result contrasts with the idea of a predictable tropical atmosphere, and opens important questions on the effective origin of predictability in the Tropics.

The atmospheric tropical belt is believed to be more predictable than the extratropics. This question is revisited here by exploring the emergence of chaos in reduced-order model versions of the vorticity equation under the weak temperature gradient hypothesis, which provides a good description of the large-scale tropical atmosphere. The analysis reveals that under fairly realistic divergence forcing amplitudes, chaos may emerge, sometimes with Lyapunov time scales of less than a day. This result contrasts with the idea of a predictable tropical atmosphere, and opens important questions on the effective origin of predictability in the Tropics.

The predictability of the generative AI-based nowcasting model LDCast is evaluated over Belgium, together with the pysteps implementation of the nowcasting algorithm STEPS. Neither STEPS nor LDCast were fine-tuned for the Belgian region, so both models are evaluated under conditions in which they will most likely be used in practice at national weather offices. STEPS and LDCast are slightly underdispersive, but the ensemble spread provides an estimation of the error at almost all scales. Both models adapt the properties of their ensembles to the type of event, either convective or stratiform. The spatial scores of the STEPS and LDCast ensembles are compared with those of surrogate ensembles, revealing that both STEPS and LDCast have very little ability to spatially localise the error of the ensemble mean. This suggests that the content of STEPS and LDCast ensembles is informative in terms of statistics, but not in terms of dynamics.

The atmospheric tropical belt is believed to be more predictable than the extratropics. This question is revisited here by exploring the emergence of chaos in reduced-order model versions of the vorticity equation under the weak temperature gradient hypothesis, which provides a good description of the large-scale tropical atmosphere. The analysis reveals that under fairly realistic divergence forcing amplitudes, chaos may emerge, sometimes with Lyapunov time scales of less than a day. This result contrasts with the idea of a predictable tropical atmosphere, and opens important questions on the effective origin of predictability in the Tropics.

Baroclinic instability is a fundamental mechanism driving atmospheric dynamics. In this work, we revisit Pedlosky’s two-layer model for finite amplitude baroclinic waves—a seminal framework for studying the unstable growth of finite perturbations—leveraging modern nonlinear techniques and computational resources. We show that the geophysical state of the baroclinic wave exhibits a rich diversity of dynamical regimes governed by the level of dissipation induced by Ekman boundary layers. In the inviscid limit, we demonstrate that the model is integrable. Upon increasing dissipation, the system undergoes a complex sequence of bifurcations. On the one hand, deterministic chaos, identified by means of the Lyapunov exponents, provides a genuine mechanism for destabilization of the wave. On the other hand, in regimes where the wave equilibrates, dependence on the initial condition is crucial, eventually leading to the coexistence of multiple attractors. We study the governing equations of the model and their truncation to a finite-dimensional system of ordinary differential equations, together with the minimal low-order truncated system, which is structurally equivalent to the Lorenz model. Its bifurcation diagram elucidates the transition of the wave amplitude from stable equilibration to periodic oscillations—terminating in homoclinic orbits—and, ultimately, deterministic chaos through a period-doubling route. We finally comment on the robustness of these features for higher-dimensional models.