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The stability of classical semi-implicit scheme, and some more advanced iterative schemes recently proposed for Numerical Weather Prediction (NWP) purpose is examined. In all these schemes, the solution of the centred-implicit non-linear…
In this article, we review the interdisciplinary techniques (borrowed from physics, mathematics, statistics, machine-learning, etc.) and methodological framework that we have used to understand climate systems, which serve as examples of…
Using in a simple way the theory of non linear dynamical systems, we show that increasing climatic instabilities may be a qualitative warning sign for the occurrence of a nearby bifurcation, yielding a discontinuous and sudden climate…
Correctly forecasting the timing and location of changes in winter precipitation type could help decision makers mitigate the worst impacts of winter storms. Multiple precipitation type algorithms have been developed from both physical and…
Remote sensing observations of the Earth's surface are frequently stymied by clouds, water vapour, and aerosols in our atmosphere. These degrade or preclude the measurementof quantities critical to scientific and, hence, societal…
A wide body of work has applied the concept of critical slowing down to estimate the stability of different Earth system components. Most of them -- such as global vegetation -- are inherently non-stationary, for example due to strong…
A promising approach to improve climate-model simulations is to replace traditional subgrid parameterizations based on simplified physical models by machine learning algorithms that are data-driven. However, neural networks (NNs) often lead…
We use the Global Historical Climatology Network--daily database to calculate trends in sea-level atmospheric pressures, their variance and the variance of their day-to-day differences in nine regions of the world. Changes in pressure…
We construct a network from climate records of different geographical sites in the North Atlantic. A link between two sites represents the cross-correlations between the records of each site. We find that within the different phases of the…
To answer the questions of whether global warming is accelerating and when the 1.5{\deg}C Paris Agreement target will be exceeded, the global mean surface temperature from 1880 to 2025 is first examined using a purely graphical approach and…
Extreme sea level estimates are fundamental for mitigating against coastal flooding as they provide insight for defence engineering. As the global climate changes, rising sea levels combined with increases in storm intensity and frequency…
We revisit a recent claim that the Earth's climate system is characterized by sensitive dependence to parameters; in particular, that the system exhibits an asymmetric, large-amplitude response to normally distributed feedback forcing. Such…
With a changing climate, the frequency and intensity of extreme weather events are likely to increase, posing a threat to infrastructure systems' resilience. The response of infrastructure systems to localised failures depends on whether…
Reliable dynamic sea level forecasts are hindered by numerous sources of uncertainty on daily-to-seasonal timescales (1-180 days) due to atmospheric boundary conditions and internal ocean variability. Studies have demonstrated that certain…
The path toward realizing the potential of seasonal forecasting and its socioeconomic benefits depends heavily on improving general circulation model based dynamical forecasting systems. To improve dynamical seasonal forecast, it is crucial…
Using observational data and an elementary rigorous statistical fact it is easily shown that the distribution of Earth's climate is non-stationary. Examination of records of hundreds of local Industrial Era temperature histories in the…
Universal role of the nonlinear one-third subharmonic resonance mechanism in generation of the strong fluctuations in such complex natural dynamical systems as global climate and global solar activity is discussed using wavelet regression…
El Ni\~no-Southern Oscillation (ENSO) exhibits significant impacts on the frequency of extreme weather events and its socio-economic implications prevail on a global scale. However, a fundamental gap still exists in understanding the…
Using optimal detection techniques with climate model simulations, most of the observed increase of near surface temperatures over the second half of the twentieth century is attributed to anthropogenic influences. However, the partitioning…
In recent years extensive studies on the Earth's climate system have been carried out by means of advanced complex network statistics. The great majority of these studies, however, have been focusing on investigating correlation structures…