NAW publication on Mathematics and Planet Earth

Daan Crommelin (CWI) and Henk Schuttelaars (TU Delft) were guest editors of a special issue of Nieuw Archief voor Wiskunde (NAW) on Mathematics and Planet Earth that was recently published. Daan Crommelin also wrote a blog post for the Daily Blog of the 'Mathematics of Planet Earth 2013' (MPE) website on this special publication. A summary follows below.

Publication date: 09-10-2013

Daan Crommelin (CWI) and Henk Schuttelaars (TU Delft) were guest editors of a special issue of Nieuw Archief voor Wiskunde (NAW) on Mathematics and Planet Earth that was recently published.

Daan Crommelin also wrote a blog post for the Daily Blog of the 'Mathematics of Planet Earth 2013' (MPE) website on this special publication. A summary follows below.

Summary: MPE-themed Issue of 'Nieuw Archief voor Wiskunde'

What is a wave attractor? How can we 'see' below the Earth’s surface while staying above ground? And what does desertification have to do with balloons?

These and other topics are discussed in the September 2013 issue of the Nieuw Archief voor Wiskunde (NAW or 'New Archive for Mathematics'), the quarterly journal of the Royal Mathematical Society (KWG) in the Netherlands. NAW is aimed at a broad audience: anyone professionally involved in mathematics, whether as an an academic or industrial researcher, student, teacher, journalist or decision maker.

The MPE-themed issue of NAW starts with an article on extreme-value statistics for deterministic dynamical systems. This topic is relevant for the study of meteorological extremes, as many atmosphere models can be regarded as (highly complex) dynamical systems. In the next article the most important current data assimilation methods are discussed. Among atmosphere and ocean scientists, data assimilation is the technique for systematically combining models and observations. It is an important aspect, for example, of operational weather prediction. Internal waves are waves below the surface of a lake or ocean. They are caused by density stratification and rotation of the Earth and behave very differently from free surface waves. At the bottom of the sea, another interesting type of pattern formation can occur. Morphodynamics, the formation and evolution of patterns such as sand banks and beach cusps by sediment transport in shallow seas, is also discussed.

Another article brings us from the bottom to the surface of the ocean, describing the motion of the ocean surface. This formulation makes it very suitable for modeling and simulation of free surface waves, for example wave focusing, the occurrence of freak waves, and the prediction of waves from radar observations. Dynamics of phytoplankton patterns in the ocean is yet another topic. Mathematical models used to describe phytoplankton dynamics can display very complex behavior, including phytoplankton blooms and spatio-temporal chaos.

El Niño is a natural climate variability pattern primarily taking place in the tropical Pacific Ocean. The hierarchy of models for understanding the physics of this phenomenon is decribed. The predictability of El Niño events is still limited to about 6–9 months due to inherent nonlinear processes. Under slowly changing environmental conditions (for example, average rainfall), healthy ecosystems can suddenly collapse to a desert state. Such catastrophic changes can be studied using specific conceptual models. The vegetation patterns in these models can destabilize one by one, until the desert state remains as the only stable pattern. Models for porous media flow with multiple fluids (for example, water and oil) are also discussed. Such models are important for studying techniques such as geological storage of CO2 and water driven oil recovery.

Lightning and other types of electric discharges in the atmosphere (such as elves, sprites, and jets) are difficult to measure and to investigate experimentally. Because of their destructive power and their contribution to greenhouse gases (production of NOx, leading to ozone), numerical simulation is an important tool for studying atmospheric discharges. Christoph Koehn, Margreet Nool and Ute Ebert from CWI in Amsterdam explain how they simulate discharges.The final article of the NAW MPE theme issue is concerned with seismic inversion. To study subsurface structure, waves are generated with acoustic sources at the Earth (or sea) surface. The reflection of these waves by subsurface layers are measured with special microphones at the surface.

The articles (in Dutch) become freely available online one year after publication.

Source: Daan Crommelin (CWI) on http://mpe2013.org/2013/09/17/special-issue-of-nieuw-archief-voor-wiskunde/