Colm Clancy

On the use of exponential time integration methods in atmospheric models

Exponential integration methods offer a highly accurate approach to the time integration of large systems of differential equations. In recent years, they have attracted increased attention in a number of diverse fields due to advances in their computational efficiency. This has been as a result of the use of Krylov subspace methods for the approximation of the matrix exponentials which typically arise. In this work, we investigate the potential of exponential integration methods for use in atmospheric models. Two schemes are implemented in a shallow water model and tested against reference explicit and semi-implicit methods. In a number of experiments with standard test cases, the exponential methods are found to yield very accurate solutions with time-steps far longer than even the semi-implicit method allows. The relative efficiency of the exponential integrators, which depends mainly on the choice of the specific algorithm used for the calculation of the matrix exponent, is also discussed. The future work aimed at further improvements of the proposed methodology is outlined.

A class of semi-implicit predictor-corrector schemes for the time integration of atmospheric models

In this paper a class of semi-implicit predictor-corrector time integration schemes is proposed. Linear stability analysis is used to identify promising methods and these are applied to the nonlinear system of the shallow water equations on an icosahedral grid. The model used is a testbed for the future development of a more complete atmospheric model. Experiments with standard test cases from the literature show that the investigated time integration schemes produce stable results with relatively long time-steps while maintaining a sufficient level of accuracy. These facts suggest that the analysed methods could be useful for the construction of a more complex model based on the Euler equations.

Local Analysis of Wave Fields Produced From Hindcasted Rogue Wave Sea States

Global-scale wave climate models, such as WAVEWATCH III, are widely used in oceanography to hindcast the sea state that occurred in a particular geographic area at a particular time. These models are applied in rogue-wave science for characterizing the sea states associated with observations of rogue waves (e.g., the well known “Draupner” [1] or “Andrea” [2] waves). While spectral models are generally successful in providing realistic representations of the sea state and are able to handle a large number of physical factors, they are also based on a very coarse grained representation of the wave field and therefore unsuitable for a detailed resolution of the wave field and refined wave-height statistics.On the other hand, local wave models based on first-principle fluid dynamics equations (such as the Higher Order Spectral Method) are able to represent wave fields in detail, but in general they are hard to interface with the full complexity of real-world sea conditions. This paper displays our efforts in coupling these two types of models in order to enhance our understanding of past extreme events and provide scope for rogue wave risk evaluation. In particular, high resolution numerical simulations of a wave field similar to the “Andrea” wave one are performed, allowing for accurate analysis of the event.Copyright

SPATIAL VARIABILITY OF EXTREME SEA STATES ON THE IRISH WEST COAST

Recent studies have revealed a long history of large waves around Ireland, which can be attributed to persistent strong winds in this area. At the same time, due to the consistently high levels of wave energy, the West Coast of Ireland has attracted a lot of interest as a prospective site for deployment of wave energy converters (WECs) farms. The design of such devices, and in fact of any offshore installation, depends crucially on the knowledge of extreme sea states they will experience during their deployment time.With this in mind, an Extreme Value Analysis incorporating seasonality and accounting for long-term trends was performed, based on a 29 year hindcast for Ireland. The hindcast was performed using the WAVEWATCH III wave model in a 3 nested grid setup, with the largest grid covering the North Atlantic basin and the finest resolution grid (10km) focusing on Ireland. The model was forced with ERA-Interim 10m winds from the European Centre for Medium Range Weather Forecasts. The wave model was validated by comparison to buoy data from the Irish Marine Data Buoy Network.The analysis was performed on the entire fine resolution grid. This affords a characterisation of the spatial variability in extremes both along the coast and with depth gradients. This is of interest in many marine applications, and in particular WEC design and deployment. Indeed, in the nearshore, wave energy levels can be similar to those found in the offshore. This, in conjunction with the diminished risk of extreme sea states, makes nearshore areas attractive for future ocean energy sites.Copyright