The Mathematics of Models for Climatology and Environment

This book is the culmination of the NATO Advanced Study Institute on The Mathematics of Models for Climatology and Environment which was held at Puerto de la Cruz ,Tenerife, Spain during 11-21 January 1995. One of the main goals of the ASI was to establish a bridge between mathematical modellers on the one hand and physical oceanographers and climatologists on the other. The book is divided into fourth parts containing a total of 16 chapters: Parts I, II and III are devoted to general models and Part IV to models related to some local problems. Most of the mathematical models here considered involve systems of nonlinear partial differential equations. The mathemat ical treatment cover a large list of subjects: existence and uniqueness for well-possed problems, large time behaviour, stability, bifurcation,diagrams of equilibria, conditions for the occurrence of interfaces or free boundaries, numerical algorithms and its implementation, controllability of the problems, etc. I thank Jacques- Louis Lions and Cornelius Johannes van Duijn for their guidance and collaboration as co-directors of the AS!. I also thank J.F.Padial and G. Diaz for their help in the planning and conduct of the ASI as well as in the preparation of this book.

Texte du rabat

This book presents a coherent survey of modelling in climatology and the environment and the mathematical treatment of those problems. It is divided into 4 parts containing a total of 16 chapters. Parts I, II and III are devoted to general models and Part IV to models related to some local problems. Most of the mathematical models considered here involve systems of nonlinear partial differential equations. The mathematical treatment covers a large range of subjects: existence and uniqueness of well-posed problems, long time behaviour, stability, bifurcation, diagrams of equilibria, conditions for the occurrence of interfaces or free boundaries, numerical algorithms and their implementation, controllability of the problems etc.

Contenu
I. General Models.- Mathematical Modelling and Optimal Control Methods in Water Pollution.- Some Mathematical Problems Associated with the Development and Use of Marine Models.- Modeling Surface Processes in Climate System Models.- Analysis of Some Oceanography Physics Problems by the Galerkin's Method.- Inertial Manifolds and Slow Manifolds.- II. General Models: Energy Balance Models.- On the Mathematical Treatment of Energy Balance Climate Models.- S-Shapedness for Energy Balance Climate Models of Sellers-Type.- Small Ice Caps in Climate Models.- III. General Models: Some Problems in Glaciology.- Glaciers and Ice Sheets.- Some Free Boundary Problems in Theoretical Glaciology.- IV. Local Problems.- A Multi-Layer Shallow-Water Model. Applications to the Strait of Gibraltar and the Alboran Sea.- Interannual Variability Simulated in the Tropical Pacific.- Climate, Mathematics, and the Canary Islands.- Heat Gain in the Eastern North Atlantic Subtropical Gyre.- One Back-Trajectories Model in Describing a Flow Climatology in Canary Islands.- Mesoscale in the Western Mediterranean: Interaction with the Large Scale Circulation and Impact on Vertical Transport of Biogeo chemical Tracers.