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One of the key choices for numerical models of geophysical fluids is how parametrisations of physical processes interact with the numerical methods that handle the resolved flow, known in the atmospheric community as the dynamical core. As…

Numerical Analysis · Mathematics 2026-05-05 Nell Hartney , Thomas M. Bendall , Jemma Shipton

Climate simulations, at all grid resolutions, rely on approximations that encapsulate the forcing due to unresolved processes on resolved variables, known as parameterizations. Parameterizations often lead to inaccuracies in climate models,…

The moist shallow water equations offer a promising route for advancing understanding of the coupling of physical parametrisations and dynamics in numerical atmospheric models, an issue known as 'physics-dynamics coupling'. Without moist…

Numerical Analysis · Mathematics 2025-05-15 Nell Hartney , Thomas M. Bendall , Jemma Shipton

This article discussesl a few of the problems that arise in geophysical fluid dynamics and climate that are associated with the presence of moisture in the air, its condensation and release of latent heat. Our main focus is Earth's…

Atmospheric and Oceanic Physics · Physics 2020-06-14 Geoffrey K. Vallis

Urban areas are a high-stake target of climate change mitigation and adaptation measures. To understand, predict and improve the energy performance of cities, the scientific community develops numerical models that describe how they…

Physicists face major challenges in modelling multi-scale phenomena that are observed in geophysical flows (e.g. in the Earth's oceans and atmosphere, or liquid planetary cores). In particular, complexities arise because geophysical fluids…

Design, control, and estimation for dynamic systems require accurate and analytically tractable models. However, modern engineered systems contain components that are described with heterogeneous modeling paradigms, as well as subsystems…

Systems and Control · Electrical Eng. & Systems 2026-04-21 Leeroy Makusha , Preston Abadie , Donald J. Docimo

In this article, we address both recent advances and open questions in some mathematical and computational issues in geophysical fluid dynamics (GFD) and climate dynamics. The main focus is on 1) the primitive equations (PEs) models and…

Mathematical Physics · Physics 2009-03-12 Jianping Li , Shouhong Wang

The near-surface environment is often too complex to enable inference of hydrological and environmental variables using one geophysical data type alone. Joint inversion and coupled inverse modeling involving numerical flow- and transport…

Geophysics · Physics 2017-01-09 N. Linde , J. Doetsch

The last decade has seen the success of stochastic parameterizations in short-term, medium-range and seasonal forecasts: operational weather centers now routinely use stochastic parameterization schemes to better represent model inadequacy…

Cosmological models can be studied effectively using dynamical systems techniques. Starting from Brown's formulation of the variational principle for relativistic fluids, we introduce new types of couplings involving a perfect fluid, a…

General Relativity and Quantum Cosmology · Physics 2024-09-13 Christian G. Boehmer , Antonio d'Alfonso del Sordo

The interactions between climate and the environment are highly complex. Due to this complexity, process-based models are often preferred to estimate the net magnitude and directionality of interactions in the Earth System. However, these…

Atmospheric and Oceanic Physics · Physics 2015-09-30 Erik Casagrande , Brigitte Mueller , Diego Miralles , Dara Entekhabi , Annalisa Molini

The understanding and prediction of large wildland fire events around the world is a growing interdisciplinary research area advanced rapidly by development and use of computational models. Recent models bidirectionally couple computational…

Atmospheric and Oceanic Physics · Physics 2020-07-06 J. L. Coen , W. Schroeder , S. Conway , L. Tarnay

Modern weather and climate models share a common heritage, and often even components, however they are used in different ways to answer fundamentally different questions. As such, attempts to emulate them using machine learning should…

Atmospheric and Oceanic Physics · Physics 2022-03-21 Duncan Watson-Parris

Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…

chao-dyn · Physics 2016-08-31 A. J. Roberts

Modeling galaxy formation in a cosmological context presents one of the greatest challenges in astrophysics today, due to the vast range of scales and numerous physical processes involved. Here we review the current status of models that…

Astrophysics of Galaxies · Physics 2015-09-23 Rachel S. Somerville , Romeel Davé

Coupling constitutes a foundational mechanism in the Earth system, regulating the interconnected physical, chemical, and biological processes that link its spheres. This review examines how emerging artificial intelligence (AI) methods…

Atmospheric and Oceanic Physics · Physics 2026-04-07 Maria Kaselimi , Anna Belehaki

The main components of an atmospheric model for numerical weather prediction are the dynamical core, which describes the resolved flow, and the physical parametrisations, which capture the effects of unresolved processes. Additionally,…

Numerical Analysis · Mathematics 2023-10-03 Alex Brown , Thomas M. Bendall , Ian Boutle , Thomas Melvin , Ben Shipway

Climate science is the multidisciplinary field that studies the Earth's climate and its evolution. At the very core of climate science are indispensable climate models that predict future climate scenarios, inform policy decisions, and…

Systems and Control · Electrical Eng. & Systems 2025-11-03 Salma M. Elsherif , Ahmad F. Taha

In groundwater hydrology, geophysical imaging holds considerable promise for improving parameter estimation, due to the generally high resolution and spatial coverage of geophysical data. However, inversion of geophysical data alone cannot…

Geophysics · Physics 2017-01-06 T. Lochbühler , J. Doetsch , R. Brauchler , N. Linde
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