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This paper extends the subjects dicussed in the Data Analysis and Dynamical Systems courses by looking at the subject of modelling data. This task is nontrivial as the underlying process could be non-linear. In the paper some common…
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…
This work proposes an innovative approach using machine learning to predict extreme events in time series of chaotic dynamical systems. The research focuses on the time series of the H\'enon map, a two-dimensional model known for its…
We present a new chaotic system of three coupled ordinary differential equations, limited to quadratic nonlinear terms. A wide variety of dynamical regimes are reported. For some parameters, chaotic reversals of the amplitudes are produced…
In this brief report we discuss how continuous changes on the physical parameters that determine the weather conditions may lead to long term climate variability. This variability of the weather patterns are a response to continuous random…
Although it is now understood that chaos in complex classical systems is the foundation of thermodynamic behavior, the detailed relations between the microscopic properties of the chaotic dynamics and the macroscopic thermodynamic…
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…
This paper deals with the question of whether uncertainty regarding model structure, especially in climate modeling, exhibits a kind of "chaos." Do small changes in model structure, in other words, lead to large variations in ensemble…
Global warming leads to the increase in frequency and intensity of climate extremes that cause tremendous loss of lives and property. Accurate long-range climate prediction allows more time for preparation and disaster risk management for…
Predictability horizon properties of chaotic dynamical systems can be related to their spectral properties. It is shown, using this relationship, that the spectral properties of the leading large-scale climate daily indices indicate a…
Spatiotemporal chaotic systems are difficult to characterize in a model-free manner because of their high dimensionality, strong nonlinearity, and sensitivity to initial conditions. Coupled map lattices, as a representative class of…
Representing and quantifying uncertainty in physical parameterisations is a central challenge in weather and climate modelling, and approaches are often developed separately for different timescales. Here, we introduce a unified framework…
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…
Numerical climate models are used to project future climate change due to both anthropogenic and natural causes. Differences between projections from different climate models are a major source of uncertainty about future climate. Emergent…
An extremely challenging problem of significant interest is to predict catastrophes in advance of their occurrences. We present a general approach to predicting catastrophes in nonlinear dynamical systems under the assumption that the…
We present results for long term and intermediate term prediction algorithms applied to a simple mechanical model of a fault. We use long term prediction methods based, for example, on the distribution of repeat times between large events…
Some issues which are relevant for the recent state in climate modeling have been considered. A detailed overview of literature related to this subject is given. The concept in modeling of climate, as a complex system, seen through Godel's…
Complex numerical weather prediction models incorporate a variety of physical processes, each described by multiple alternative physical schemes with specific parameters. The selection of the physical schemes and the choice of the…
Over the last few decades, climate scientists have devoted much effort to the development of large numerical models of the atmosphere and the ocean. While there is no question that such models provide important and useful information on…
The forecasting of high-dimensional, spatiotemporal nonlinear systems has made tremendous progress with the advent of model-free machine learning techniques. However, in real systems it is not always possible to have all the information…