Mathematical Geoscience Seminar
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Fri, 04/05/2012 14:30 |
Prof. Peter Jan van Leeuwen (University of Reading) |
Mathematical Geoscience Seminar  |
DH 3rd floor SR |
| Data assimilation in highly nonlinear and high dimensional systems is a hard problem. We do have efficient data-assimilation methods for high-dimensional weakly nonlinear systems, exploited in e.g. numerical weather forecasting. And we have good methods for low-dimensional (<5) nonlinear systems. The combination is more difficult, however. Recently our data-assimilation group managed to generate efficient particle filters that seem to scale almost perfectly with the dimension of the system, that is the number of particles (model runs) needed is independent of the system dimension. This will be demonstrated on the barotropic vorticity equations in the chaotic regime, exploring different observation strategies. The main question now is why these methods are so efficient. The performance seems to be independent of traditional measures of stability, such as the number of positive Lyaponov exponents or decorrelation times of the dynamics. Our latest progress in this area will be discussed, bringing in elements of extreme value statistics and the stability of the combined model/observation system. | |||
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Fri, 18/05/2012 14:30 |
Dr. Hilmar Gudmundsson (British Antarctic Survey, Cambridge) |
Mathematical Geoscience Seminar |
DH 3rd floor SR |
| Inverse methods are frequently used in geosciences to estimate model parameters from indirect measurements. A common inverse problem encountered when modelling the flow of large ice masses such as the Greenland and the Antarctic ice sheets is the determination of basal conditions from surface data. I will present an overview over some of the inverse methods currently used to tackle this problem and in particular discuss the use of Bayesian inverse methods in this context. Examples of the use of adjoint methods for large-scale optimisation problems that arise, for example, in flow modelling of West-Antarctica will be given. | |||
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Fri, 01/06/2012 14:30 |
Dr Jari Fowkes (University of Edinburgh) |
Mathematical Geoscience Seminar |
DH 3rd floor SR |
| This talk will consist of two parts. In the first part we will present a motivating application from oil reservoir simulation, namely finding the location and trajectory of an oil producing well which maximises oil production. We will show how such a problem can be tackled through the use of radial basis function (RBF) approximation (also known as Kriging or Gaussian process regression) and a branch and bound global optimization algorithm. In the second part of the talk we will show how one can improve the branch and bound algorithm through the use of Lipschitz continuity of the RBF approximation. This leads to an entirely new global optimization algorithm for twice differentiable functions with Lipschitz continuous Hessian. The algorithm makes use of recent cubic regularisation techniques from local optimization to obtain the necessary bounds within the branch and bound algorithm. | |||
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Fri, 15/06/2012 14:30 |
Dr Henry Winstanley (University of Limerick) |
Mathematical Geoscience Seminar |
DH 3rd floor SR |
| Respiration is a redox reaction in which oxidation of a substrate (often organic) is coupled to the reduction of a terminal electron acceptor (TEA) such as oxygen. Iron oxides in various mineral forms are abundant in sediments and sedimentary rocks, and many subsurface microbes have the ability to respire using Fe(III) as the TEA in anoxic conditions. This process is environmentally important in the degradation of organic substrates and in the redox-cycling of iron. But low mineral solubility limits the bioavailability of Fe(III), which microbes access primarily through reductive dissolution. For aqueous nutrients, expressions for microbial growth and nutrient uptake rates are standardly based on Monod kinetics. We address the question of what equivalent description is appropriate when solid phase Fe(III) is the electron acceptor. | |||
