Past Mathematical Geoscience Seminar

Rising sea levels are frequently cited as one of the most pressing societal consequences of climate change. In order to understand the present day change in sea level we need to place it in the context of historical changes. The primary source of information on sea level change over the past 100-150 years is tide gauges. However, these tide gauges are a globally sparse set of point measurements located largely at the coast. "Global mean sea level" calculated from these tide gauges is therefore biased and is also more variable than than global mean sea level calculated from the past 19 years of satellite altimtery measurements.

The work presented here explores the use of simple statistical approaches which make use of reanalysis wind stress datasets and heat content reconstructions to model the sea level records. It is shown that these simple models have skill in reproducing variability at decadal time-scales. The results suggest that there are active regions of wind stress and heat content in the ocean which affect regional variability in sea level records that point to the atmospheric and oceanic processes which drive the variability. Acceleration seen in the longest continous sea level record at Brest is shown to be partially attributable to changes in wind stress over the past 140 years.

A new approach for data-based stochastic parametrisation of unresolved scales and processes in numerical weather and climate prediction models is introduced. The subgrid-scale model is conditional on the state of the resolved scales, consisting of a collection of local models. A clustering algorithm in the space of the resolved variables is combined with statistical modelling of the impact of the unresolved variables. The clusters and the parameters of the associated subgrid models are estimated simultaneously from data. The method is tested and explored in the framework of the Lorenz '96 model using discrete Markov processes as local statistical models. Performance of the scheme is investigated for long-term simulations as well as ensemble prediction. The present method clearly outperforms simple parametrisation schemes and compares favourably with another recently proposed subgrid scheme also based on conditional Markov chains.

Studies of the ocean circulation and climate have come to be dominated by the results of complex numerical models encompassing hundreds of thousands of lines of computer code and whose physics may be more difficult to penetrate than the real system. Some insight into the large-scale ocean circulation can perhaps be gained by taking a step back and considering the gross time scales governing oceanic changes. These can derived from a wide variety of simple considerations such as energy flux rates, signal velocities, tracer equilibrium times, and others. At any given time, observed changes are likely a summation of shifts taking place over all of these time scales.

The presence and flow of fluid inside a crack within a solid causes deformation of the solid which in turn influences the flow of the fluid.

This coupled fluid-solid problem will be discussed in the context of dyke propagation and hydrofracture. The background material will be discussed in detail and some applications to specific geometries presented.

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