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The traditional dynamical phase transition refers to the appearance of singularities in an observable with respect to a control parameter for a late-time state or singularities in the rate function of the Loschmidt echo with respect to…
We investigate the changing nature of the frequency, magnitude and spatial extent of extreme temperatures in Ireland from 1931 to 2022. We develop an extreme value model that captures spatial and temporal non-stationarity in extreme daily…
The frequency and magnitude of weather extreme events have increased significantly during the past few years in response to anthropogenic climate change. However, global statistical characteristics and underlying physical mechanisms are…
The North Atlantic Oscillation (NAO) obtained using instrumental and documentary proxy predictors from Eurasia is found to be characterized by a quasi 60-year dominant oscillation since 1650. This pattern emerges clearly once the NAO record…
Quantitative estimates of the contributions of the anthropogenic forcing, characterized by changes in the radiative forcing of atmospheric greenhouse gases (CO2, in particular), and solar activity variations to the trends of the global…
Earth's temperature variability can be partitioned into internal and externally-forced components. Yet, underlying mechanisms and their relative contributions remain insufficiently understood, especially on decadal to centennial timescales.…
Astronomical (or Milankovi\'c) forcing of the Earth system is key to understanding rhythmic climate change on time scales >~ 10 kyr. Paleoceanographic and paleoclimatological applications concerned with past astronomical forcing rely on…
Global deep-learning weather prediction models have recently been shown to produce forecasts that rival those from physics-based models run at operational centers. It is unclear whether these models have encoded atmospheric dynamics, or…
In this chapter we review stochastic modelling methods in climate science. First we provide a conceptual framework for stochastic modelling of deterministic dynamical systems based on the Mori-Zwanzig formalism. The Mori-Zwanzig equations…
The computational cost of dynamical downscaling limits ensemble sizes in regional downscaling efforts. We present a newly developed generative-AI approach to greatly expand the scope of such downscaling, enabling fine-scale future changes…
The El Ni\~no phenomenon, synonymously El Ni\~no-Southern Oscillation (ENSO), is an anomalous climatic oscillation in the Equatorial Pacific that occurs once every 3-8 years. It affects the earth's climate on a global scale. Whether it is a…
We develop a unified statistical framework for attributing heatwaves as spatio-temporal phenomena under climate change. We quantify the impact of anthropogenic forcing on the probability and persistence of heatwaves not captured by standard…
We theoretically study long-term trends in the statistics of record-breaking daily temperatures and validate these predictions using Monte Carlo simulations and data from the city of Philadelphia, for which 126 years of daily temperature…
Understanding the interactions between the El Nino-Southern Oscillation (ENSO) and the Madden-Julian Oscillation (MJO) is essential to studying climate variabilities and predicting extreme weather events. Here, we develop a stochastic…
Statistical methods are required to evaluate and quantify the uncertainty in environmental processes, such as land and sea surface temperature, in a changing climate. Typically, annual harmonics are used to characterize the variation in the…
Vital parts of the climate system, such as the West Antarctic Ice Sheet, are at risk even within the aspired aims of the Paris Agreement to limit global temperature rise to 1.5 -- 2{\deg}C. These so-called natural tipping elements are…
Entanglement fluctuations associated with Schr\"{o}dinger evolution of wavefunctions offer a unique perspective on various fundamental issues ranging from quantum thermalization to state preparation in quantum devices. Very recently, a…
The climate change attribution problem is addressed using empirical decomposition. Cycles in solar motion and activity of 60 and 20 years were used to develop an empirical model of Earth temperature variations. The model was fit to the…
There is an ongoing debate in the literature about whether the present global warming is increasing local and global temperature variability. The central methodological issues of this debate relate to the proper treatment of normalised…
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…