Mathematical Geoscience Seminar
|
Fri, 27/01/2012 14:30 |
Dr. Amos S. Lawless (University of Reading) |
Mathematical Geoscience Seminar  |
DH 3rd floor SR |
| Data assimilation aims to correct a forecast of a physical system, such as the atmosphere or ocean, using observations of that system, in order to provide a best estimate of the current system state. Since it is not possible to observe the whole state it is important to know how errors in different variables of the forecast are related to each other, so that all fields may be corrected consistently. In the first part of this talk we consider how we may impose constraints between different physical variables in data assimilation. We examine how we can use our knowledge of atmospheric physics to pose the assimilation problem in variables that are assumed to be uncorrelated. Using a shallow-water model we demonstrate that this is best achieved by using potential vorticity rather than vorticity to capture the balanced part of the flow. The second part of the talk will consider a further transformation of variables to represent spatial correlations. We show how the accuracy and efficiency with which we can solve the transformed assimilation problem (as measured by the condition number) is affected by the observation distribution and accuracy and by the assumed correlation lengthscales. Theoretical results will be illustrated using the Met Office variational data assimilation scheme. | |||
|
Fri, 10/02/2012 14:30 |
Dr. James Maddison (AOPP University of Oxford) |
Mathematical Geoscience Seminar |
DH 3rd floor SR |
| Ocean climate models are unlikely routinely to have sufficient resolution to resolve the turbulent ocean eddy field. The need for the development of improved mesoscale eddy parameterisation schemes therefore remains an important task. The current dominant mesoscale eddy closure is the Gent and McWilliams scheme, which enforces the down-gradient mixing of buoyancy. While motivated by the action of baroclinic instability on the mean flow, this closure neglects the horizontal fluxes of horizontal momentum. The down-gradient mixing of potential vorticity is frequently discussed as an alternative parameterisation paradigm. However, such a scheme, without careful treatment, violates fundamental conservation principles, and in particular violates conservation of momentum. A new parameterisation framework is presented which preserves conservation of momentum by construction, and further allows for conservation of energy. The framework has one dimensional parameter, the total eddy energy, and five dimensionless and bounded geometric parameters. The popular Gent and McWilliams scheme exists as a limiting case of this framework. Hence the new framework enables for the extension of the Gent and McWilliams scheme, in a manner consistent with key physical conservations. | |||
|
Fri, 24/02/2012 14:30 |
Dr. Adrian Jenkins (British Antarctic Survey, Cambridge) |
Mathematical Geoscience Seminar |
DH 3rd floor SR |
| The part of the West Antarctic Ice Sheet that drains into the Amundsen Sea is currently thinning at such a rate that it contributes nearly 10 percent of the observed rise in global mean sea level. Acceleration of the outlet glaciers means that the sea level contribution has grown over the past decades, while the likely future contribution remains a key unknown. The synchronous response of several independent glaciers, coupled with the observation that thinning is most rapid at their downstream ends, where the ice goes afloat, hints at an oceanic driver. The general assumption is that the changes are a response to an increase in submarine melting of the floating ice shelves that has been driven in turn by an increase in the transport of ocean heat towards the ice sheet. Understanding the causes of these changes and their relationship with climate variability is imperative if we are to make quantitative estimates of sea level into the future. Observations made since the mid‐1990s on the Amundsen Sea continental shelf have revealed that the seabed troughs carved by previous glacial advances guide seawater around 3‐4°C above the freezing point from the deep ocean to the ice sheet margin, fuelling rapid melting of the floating ice. This talk summarises the results of several pieces of work that investigate the chain of processes linking large‐scale atmospheric processes with ocean circulation over the continental shelf and beneath the floating ice shelves and the eventual transfer of heat to the ice. While our understanding of the processes is far from complete, the pieces of the jigsaw that have been put into place give us insight into the potential causes of variability in ice shelf melting, and allow us to at least formulate some key questions that still need to be answered in order to make reliable projections of future ice sheet evolution in West Antarctica. | |||
|
Fri, 09/03/2012 14:30 |
Prof. Leonard A. Smith (London School of Economics and Pembroke College) |
Mathematical Geoscience Seminar |
DH 3rd floor SR |
| Probability does not exist. At least no more so than "mass" "spin" or "charm" exist. Yet probability forecasts are common, and there are fine reasons for deprecating point forecasts, as they require an unscientific certainty in exactly what the future holds. What roles do our physical understanding and laws of physics play in the construction of probability forecasts to support of decision making and science-based policy? Will probability forecasting more likely accelerate or retard the advancement of our scientific understanding? Model-based probability forecasts can vary significantly with alterations in the method of data assimilation, ensemble formation, ensemble interpretation, and forecast evaluation, not to mention questions of model structure, parameter selection and the available forecast-outcome archive. The role of each of these aspects of forecasting, in the context of interpreting the forecast as a real-world probability, is considered and contrasted in the cases of weather forecasting, climate forecasting, and economic forecasting. The notion of what makes a probability forecast "good" will be discussed, including the goals of "sharpness given calibration" and "value". For a probability forecast to be decision-relevant as such, it must be reasonably interpreted as a basis for rational action through the reflection of the probability of the outcomes forecast. This rather obvious sounding requirement proves to be the source of major discomfort as the distinct roles of uncertainty (imprecision) and error (structural mathematical "misspecification") are clarified. Probabilistic forecasts can be of value to decision makers even when it is irrational to interpret them as probability forecasts. A similar statement, of course, can be said for point forecasts, or for spin. In this context we explore the question: do decision-relevant probability forecasts exist? | |||
