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Normalization and scaling are fundamental preprocessing steps in time series modeling, yet their role in Transformer-based models remains underexplored from a theoretical perspective. In this work, we present the first formal analysis of…

The global mean surface temperature is widely studied to monitor climate change. A current debate centers around whether there has been a recent (post-1970s) surge/acceleration in the warming rate. This paper addresses whether an…

Climate models are essential to understand and project climate change, yet long-standing biases and uncertainties in their projections remain. This is largely associated with the representation of subgrid-scale processes, particularly…

The Earth has warmed in the last century with the most rapid warming occurring near the surface in the arctic. This enhanced surface warming in the Arctic is partly because the extra heat is trapped in a thin layer of air near the surface…

Periodically forced turbulence is used as a test case to evaluate the predictions of two-equation and multiple-scale turbulence models in unsteady flows. The limitations of the two-equation model are shown to originate in the basic…

We develop a three-timescale framework for modelling climate change and introduce a space-heterogeneous one-dimensional energy balance model. This model, addressing temperature fluctuations from rising carbon dioxide levels and the…

Global warming arises from 'temperature forcing', a net imbalance between energy fluxes entering and leaving the climate system and arising within it. Humanity introduces temperature forcing through greenhouse gas emissions, agriculture,…

Although transient convection is ubiquitous in natural and manmade phenomena, few research works attempted to make a compact model for it, altogether, others attempted a compact model that contradicts problem physics. The correct modelling…

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…

Arctic sea ice plays an important role in the global climate. Sea ice models governed by physical equations have been used to simulate the state of the ice including characteristics such as ice thickness, concentration, and motion. More…

Pattern formation often occurs in confined systems, yet how boundaries shape patterning dynamics is unclear. We develop techniques to analyze confinement effects in nonlocal advection-diffusion equations, which generically capture the…

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…

In this paper we discuss and address the challenges of predicting extreme atmospheric events like intense rainfall, hail, and strong winds. These events can cause significant damage and have become more frequent due to climate change.…

Evidence of past climate variations are stored in ice and indicate glacial-interglacial cycles characterized by three dominant time periods of 20kyr, 40kyr, and 100kyr. We study the scaling properties of temperature proxy records of four…

The response of the climate system to increased greenhouse gases and other radiative perturbations is governed by a combination of fast and slow feedbacks. Slow feedbacks are typically activated in response to changes in ocean temperatures…

Typical deep learning approaches to modeling high-dimensional data often result in complex models that do not easily reveal a new understanding of the data. Research in the deep learning field is very actively pursuing new methods to…

The CMIP3 multi-model ensemble spread most likely underestimates the real model uncertainty in future climate predictions because of the similarity, and shared defects, of the models in the ensemble. To generate an appropriate level of…

Climate change is a non-uniform phenomenon. This paper proposes a new quantitative methodology to characterize, measure, and test the existence of climate change heterogeneity. It consists of three steps. First, we introduce a new testable…

Using a time series model to mimic an observed time series has a long history. However, with regard to this objective, conventional estimation methods for discrete-time dynamical models are frequently found to be wanting. In fact, they are…

Stochastic methods are a crucial area in contemporary climate research and are increasingly being used in comprehensive weather and climate prediction models as well as reduced order climate models. Stochastic methods are used as…