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El Ni\~{n}o is a typical example of a coupled atmosphere--ocean phenomenon, but it is unclear whether it can be described quantitatively by a correlation between relevant climate events. To provide clarity on this issue, we developed a…
Global weather patterns and regimes are heavily influenced by the dominant modes of Pacific sea surface temperature (SST) variability, including the El Ni\~no-Southern Oscillation (ENSO), Tropical Pacific Decadal Variability (TPDV), North…
The perturbation theory of operator semigroups is used to derive response formulas for a variety of combinations of acting forcings and reference background dynamics. In the case of background stochastic dynamics, we decompose the response…
Equilibrium climate sensitivity (ECS) is a key predictor of climate change. However, it is not very well constrained, either by climate models or by observational data. The reasons for this include strong internal variability and forcing on…
Global climate change, extreme climate events, earthquakes and their accompanying natural disasters pose significant risks to humanity. Yet due to the nonlinear feedbacks, strategic interactions and complex structure of the Earth system,…
We study the dynamics of the El Nino phenomenon using the mathematical model of delayed-action oscillator (DAO). Topics such as the influence of the annual cycle, global warming, stochastic influences due to weather conditions and even…
In recent years, the application of machine learning approaches to time-series forecasting of climate dynamical phenomena has become increasingly active. It is known that applying a band-pass filter to a time-series data is a key to…
We consider dynamical systems evolving near an equilibrium statistical state where the interest is in modelling long term behavior that is consistent with thermodynamic constraints. We adjust the distribution using an entropy-optimizing…
Climate response metrics are used to quantify the Earth's climate response to anthropogenic changes of atmospheric CO2. Equilibrium Climate Sensitivity (ECS) is one such metric that measures the equilibrium response to CO2 doubling.…
Annual North Atlantic tropical cyclone (TC) counts are frequently modeled as a Poisson process with a state-dependent rate. We provide a lower bound on the forecasting error of this class of models. Remarkably we find that this bound is…
Projections of storm surge return levels are a basic requirement for effective management of coastal risks. A common approach to estimate hazards posed by extreme sea levels is to use a statistical model, which may use a time series of a…
El Ni\~no episodes are part of the El Ni\~no-Southern Oscillation (ENSO), which is the strongest driver of interannual climate variability, and can trigger extreme weather events and disasters in various parts of the globe. Previously we…
Rare events arising in nonlinear atmospheric dynamics remain hard to predict and attribute. We address the problem of forecasting rare events in a prototypical example, Sudden Stratospheric Warmings (SSWs). Approximately once every other…
Due to the rapidly changing climate, the frequency and severity of extreme weather is expected to increase over the coming decades. As fully-resolved climate simulations remain computationally intractable, policy makers must rely on…
We investigate a low-dimensional slow-fast model to understand the dynamical origin of El Ni\~no-Southern Oscillation. A close inspection of the system dynamics using several bifurcation plots reveals that a sudden large expansion of the…
Statistical modeling of physical laws connects experiments with mathematical descriptions of natural phenomena. The modeling is based on the probability density of measured variables expressed by experimental data via a kernel estimator. As…
El Ni\~no-Southern Oscillation global (ENSO) imprint on sea surface temperature comes in many guises. To identify its tropical fingerprints and impacts on the rest of the climate system, we propose a global approach based on archetypal…
We consider the inference problem for parameters in stochastic differential equation models from discrete time observations (e.g. experimental or simulation data). Specifically, we study the case where one does not have access to…
An estimate of the net direction of climate interactions in different geographical regions is made by constructing a directed climate network from a regular latitude-longitude grid of nodes, using a directionality index (DI) based on…
Accurate estimates of historical changes in sea surface temperatures (SSTs) and their uncertainties are important for documenting and understanding historical changes in climate. A source of uncertainty that has not previously been…