Mathematical Paradigms of Climate Science

1. Front Matter

   Pages i-x

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2. Core Climate Issues

   1. Front Matter

      Pages 1-1

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   2. A Mathematical Perspective on Microbial Processes in Earth’s Biogeochemical Cycles

      • Christof Meile, Chris Jones

      Pages 3-14

   3. Turbulence, Horizontal Convection, and the Ocean’s Meridional Overturning Circulation

      • Francesco Paparella

      Pages 15-32

3. Mathematical Techniques

   1. Front Matter

      Pages 33-33

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   2. Source Reconstruction by Partial Measurements for a Class of Hyperbolic Systems in Cascade

      • Fatiha Alabau-Boussouira, Piermarco Cannarsa, Masahiro Yamamoto

      Pages 35-50

   3. Remarks on Stochastic Navier-Stokes Equations

      • Franco Flandoli

      Pages 51-65

   4. Remarks on Long Time Versus Steady State Optimal Control

      • Alessio Porretta, Enrique Zuazua

      Pages 67-89

4. Paleoclimate

   1. Front Matter

      Pages 91-91

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   2. Effects of Additive Noise on the Stability of Glacial Cycles

      • Takahito Mitsui, Michel Crucifix

      Pages 93-113

   3. On the Calibration of Lévy Driven Time Series with Coupling Distances and an Application in Paleoclimate

      • Jan Gairing, Michael Högele, Tetiana Kosenkova, Alexei Kulik

      Pages 115-136

5. Data Assimilation

   1. Front Matter

      Pages 137-137

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   2. Data Assimilation for Geophysical Fluids: The Diffusive Back and Forth Nudging

      • Didier Auroux, Jacques Blum, Giovanni Ruggiero

      Pages 139-174

   3. Deterministic Treatment of Model Error in Geophysical Data Assimilation

      • Alberto Carrassi, Stéphane Vannitsem

      Pages 175-213

   4. Decreasing Flow Uncertainty in Bayesian Inverse Problems Through Lagrangian Drifter Control

      • Damon McDougall, Chris K. R. T. Jones

      Pages 215-228

This book, featuring a truly interdisciplinary approach, provides an overview of cutting-edge mathematical theories and techniques that promise to play a central role in climate science. It brings together some of the most interesting overview lectures given by the invited speakers at an important workshop held in Rome in 2013 as a part of MPE2013 (“Mathematics of Planet Earth 2013”). The aim of the workshop was to foster the interaction between climate scientists and mathematicians active in various fields linked to climate sciences, such as dynamical systems, partial differential equations, control theory, stochastic systems, and numerical analysis. Mathematics and statistics already play a central role in this area. Likewise, computer science must have a say in the efforts to simulate the Earth’s environment on the unprecedented scale of petabytes. In the context of such complexity, new mathematical tools are needed to organize and simplify the approach. The growing importance of data assimilation techniques for climate modeling is amply illustrated in this volume, which also identifies important future challenges.

• Climate change
• Data assimilation
• Optimal control
• Earth system processes
• Numerical simuations

• Dipartimento di Matematica, Università degli Studi di Padova, Padova, Italy

  Fabio Ancona

• Dipartimento di Matematica, Università di Roma - Tor Vergata, Roma, Italy

  Piermarco Cannarsa

• Department of Mathematics, University of North Carolina, Chapel Hill, USA

  Christopher Jones

• Scienze Agrarie, Forestali e Alimentari, Università degli Studi di Torino, Torino, Italy

  Alessandro Portaluri

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