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Artificial ensemble inflation is a common technique in ensemble data assimilation, whereby the ensemble covariance is periodically increased in order to prevent deviation of the ensemble from the observations and possible ensemble collapse.…

Ensemble forecasting is a technique devised to palliate sensitivity to initial conditions in nonlinear dynamical systems. The basic idea to avoid this sensitivity is to run the model many times under several slightly-different initial…

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…

Complex Earth System Models are widely utilised to make conditional statements about the future climate under some assumptions about changes in future atmospheric greenhouse gas concentrations; these statements are often referred to as…

In data assimilation, an ensemble provides a way to propagate the probability density of a system described by a nonlinear prediction model. Although a large ensemble size is required for statistical accuracy, the ensemble size is typically…

The predictive advantage of combining several different predictive models is widely accepted. Particularly in time series forecasting problems, this combination is often dynamic to cope with potential non-stationary sources of variation…

Quantifying forecast uncertainty is a key aspect of state-of-the-art numerical weather prediction and data assimilation systems. Ensemble-based data assimilation systems incorporate state-dependent uncertainty quantification based on…

Dynamical weather and climate prediction models underpin many studies of the Earth system and hold the promise of being able to make robust projections of future climate change based on physical laws. However, simulations from these models…

Quantifying uncertainty in weather forecasts is critical, especially for predicting extreme weather events. This is typically accomplished with ensemble prediction systems, which consist of many perturbed numerical weather simulations, or…

Improvement of time series forecasting accuracy through combining multiple models is an important as well as a dynamic area of research. As a result, various forecasts combination methods have been developed in literature. However, most of…

Accurate time series forecasting is critical for a wide range of problems with temporal data. Ensemble modeling is a well-established technique for leveraging multiple predictive models to increase accuracy and robustness, as the…

Recently, deep learning has emerged as a promising tool for statistical downscaling, the set of methods for generating high-resolution climate fields from coarse low-resolution variables. Nevertheless, their ability to generalize to climate…

Multi-model ensembles provide a pragmatic approach to the representation of model uncertainty in climate prediction. However, such representations are inherently ad hoc, and, as shown, probability distributions of climate variables based on…

Ensemble forecasting of nonlinear systems involves the use of a model to run forward a discrete ensemble (or set) of initial states. Data assimilation techniques tend to focus on estimating the true state of the system, even though model…

Ensemble forecasting is, so far, the most successful approach to produce relevant forecasts with an estimation of their uncertainty. The main limitations of ensemble forecasting are the high computational cost and the difficulty to capture…

One essential component of operational space weather forecasting is the prediction of solar flares. With a multitude of flare forecasting methods now available online it is still unclear which of these methods performs best, and none are…

Delay embedding---a method for reconstructing dynamical systems by delay coordinates---is widely used to forecast nonlinear time series as a model-free approach. When multivariate time series are observed, several existing frameworks can be…

Ensembling is a powerful technique for improving the accuracy of machine learning models, with methods like stacking achieving strong results in tabular tasks. In time series forecasting, however, ensemble methods remain underutilized, with…

Ensemble weather forecasts enable a measure of uncertainty to be attached to each forecast, by computing the ensemble's spread. However, generating an ensemble with a good spread-error relationship is far from trivial, and a wide range of…

Weather forecasting has seen a shift in methods from numerical simulations to data-driven systems. While initial research in the area focused on deterministic forecasting, recent works have used diffusion models to produce skillful ensemble…