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Weather forecasts are typically given in the form of forecast ensembles obtained from multiple runs of numerical weather prediction models with varying initial conditions and physics parameterizations. Such ensemble predictions tend to be…

A new approach to data-driven discovery of Koopman eigenfunctions without a pre-defined set of basis functions is proposed. The approach is based on a reference trajectory, for which the Koopman mode amplitudes are first identified, and the…

While proper orthogonal decomposition (POD)-based surrogates are widely explored for hydrodynamic applications, the use of Koopman autoencoders for real-world coastal-ocean modelling remains relatively limited. This paper introduces a…

Weather and climate forecasts are inherently uncertain due to chaotic dynamics, imperfect initial conditions, and incomplete representation of the underlying physical processes. Operational ensemble forecasts aim to represent these…

Ensemble Kalman methods are widely used for state estimation in the geophysical sciences. Their success stems from the fact that they take an underlying (possibly noisy) dynamical system as a black box to provide a systematic,…

Deep learning is revolutionizing weather forecasting, with new data-driven models achieving accuracy on par with operational physical models for medium-term predictions. However, these models often lack interpretability, making their…

In many scenarios, it is necessary to monitor a complex system via a time-series of observations and determine when anomalous exogenous events have occurred so that relevant actions can be taken. Determining whether current observations are…

Prediction models that capture and use the structure of state-space dynamics can be very effective. In practice, however, one rarely has access to full information about that structure, and accurate reconstruction of the dynamics from…

Accumulated precipitation forecasts are of high socioeconomic importance for agriculturally dominated societies in northern tropical Africa. In this study, we analyze the performance of nine operational global ensemble prediction systems…

The controllability of advection-diffusion systems, subject to uncertain initial values and emission rates, is estimated, given sparse and error affected observations of prognostic state variables. In predictive geophysical model systems,…

We present an ensemble prediction system using a Deep Learning Weather Prediction (DLWP) model that recursively predicts key atmospheric variables with six-hour time resolution. This model uses convolutional neural networks (CNNs) on a…

The eigenspectrum of the Koopman operator enables the decomposition of nonlinear dynamics into a sum of nonlinear functions of the state space with purely exponential and sinusoidal time dependence. For a limited number of dynamical…

Accurate medium-range precipitation forecasting is crucial for hydrometeorological risk management and disaster mitigation, yet remains challenging for current numerical weather prediction (NWP) systems. Traditional ensemble systems such as…

Most operational climate services providers base their seasonal predictions on initialised general circulation models (GCMs) or statistical techniques that fit past observations. GCMs require substantial computational resources, which…

Accurate prediction of extreme weather events remains a major challenge for artificial intelligence-based weather prediction systems. While deterministic models such as FuXi, GraphCast, and SFNO have achieved competitive forecast skill…

Natural climate variability, captured through multiple initial condition ensembles, may be comparable to the variability caused by knowledge gaps in future emissions trajectories and in the physical science basis, especially at…

Predictability estimates of ensemble prediction systems are uncertain due to limited numbers of past forecasts and observations. To account for such uncertainty, this paper proposes a Bayesian inferential framework that provides a simple…

Time series forecasting plays a vital role across scientific, industrial, and environmental domains, especially when dealing with high-dimensional and nonlinear systems. While Transformer-based models have recently achieved state-of-the-art…

Data-driven emulation of nonlinear dynamics is challenging due to long-range skill decay that often produces physically unrealistic outputs. Recent advances in generative modeling aim to address these issues by providing uncertainty…

Extracting the latent underlying structures of complex nonlinear local and nonlocal flows is essential for their analysis and modeling. In this work, we attempt to provide a consistent framework through Koopman theory and its related…