Now showing 1 - 10 of 14
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Pedro Nunes and the Retrogression of the Sun

2018, Lynch, Peter

In northern latitudes we are used to the Sun rising in the East, following a smooth and even course through the southern sky and setting in the West. The idea that the compass bearing of the Sun might reverse seems fanciful. But that was precisely what Portuguese mathematician Pedro Nunes showed in 1537. Nunes made an amazing prediction: in certain circumstances, the shadow cast by the gnomon of a sun dial moves backwards.

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Reducing errors of wind speed forecasts by an optimal combination of post-processing methods

2011-09-13, Sweeney, Conor, Lynch, Peter, Nolan, Paul

Seven adaptive approaches to post-processing wind speed forecasts are discussed and compared. 48-hour forecasts are run at horizontal resolutions of 7 km and 3 km for a domain centred over Ireland. Forecast wind speeds over a two year period are compared to observed wind speeds at seven synoptic stations around Ireland and skill scores calculated. Two automatic methods for combining forecast streams are applied. The forecasts produced by the combined methods give bias and root mean squared errors that are better than the numerical weather prediction forecasts at all station locations. One of the combined forecast methods results in skill scores that are equal to or better than all of its component forecast streams. This method is straightforward to apply and should prove beneficial in operational wind forecasting.

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Adaptive post-processing of short-term wind forecasts for energy applications

2011-04, Sweeney, Conor, Lynch, Peter

We present a new method of reducing the error in predicted wind speed, thus enabling better management of wind energy facilities. A numerical weather prediction model, COSMO, was used to produce 48 h forecast data every day in 2008 at horizontal resolutions of 10 and 3 km. A new adaptive statistical method was applied to the model output to improve the forecast skill. The method applied corrective weights to a set of forecasts generated using several post-processing methods. The weights were calculated based on the recent skill of the different forecasts. The resulting forecast data were compared with observed data, and skill scores were calculated to allow comparison between different post-processing methods. The total root mean square error performance of the composite forecast is superior to that of any of the individual methods.

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On resonant Rossby-Haurwitz triads

2009-05, Lynch, Peter

The dynamics of non-divergent flow on a rotating sphere are described by the conservation of absolute vorticity. The analytical study of the non-linear barotropic vorticity equation is greatly facilitated by the expansion of the solution in spherical harmonics and truncation at low order. The normal modes are the well-known Rossby–Haurwitz (RH) waves, which represent the natural oscillations of the system. Triads of RH waves, which satisfy conditions for resonance, are of critical importance for the distribution of energy in the atmosphere. We show how non-linear interactions of resonant RH triads may result in dynamic instability of large-scale components. We also demonstrate a mathematical equivalence between the equations for an orographically forced triad and a simple mechanical system, the forced-damped swinging spring. This equivalence yields insight concerning the bounded response to a constant forcing in the absence of damping. An examination of triad interactions in atmospheric reanalysis data would be of great interest.

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Precession and recession of the rock'n'roller

2009-09-30, Lynch, Peter, Bustamante, Miguel

We study the dynamics of a spherical rigid body that rocks and rolls on a plane under the effect of gravity. The distribution of mass is non-uniform and the centre of mass does not coincide with the geometric centre. The symmetric case, with moments of inertia I1 = I2 < I3, is integrable and themotion is completely regular. Three known conservation laws are the total energy E, Jellett’s quantity QJ and Routh’s quantity QR. When the inertial symmetry I1 = I2 is broken, even slightly, the character of the solutions is profoundly changed and new types of motion become possible. We derive the equations governing the general motion and present analytical and numerical evidence of the recession, or reversal of precession, that has been observed in physical experiments. We present an analysis of recession in terms of critical lines dividing the (QR,QJ ) plane into four dynamically disjoint zones. We prove that recession implies the lack of conservation of Jellett’s and Routh’s quantities, by identifying individual reversals as crossings of the orbit (QR(t ),QJ (t)) through the critical lines. Consequently, a method is found to produce a large number of initial conditions so that the system will exhibit recession.

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Stokes's Fundamental Contributions to Fluid Dynamics

2019-06-27, Lynch, Peter

George Gabriel Stokes was one of the giants of hydrodynamics in the nineteenth century. He made fundamental mathematical contributions to fluid dynamics that had profound practical consequences. The basic equations formulated by him, the Navier-Stokes equations, are capable of describing fluid flows over a vast range of magnitudes. They play a central role in numerical weather prediction, in the simulation of blood flow in the body and in countless other important applications. In this chapter we put the primary focus on the two most important areas of Stokes’s work on fluid dynamics, the derivation of the Navier-Stokes equations and the theory of finite amplitude oscillatory water waves. Stokes became an undergraduate at Cambridge in 1837. He was coached by the ‘Senior Wrangler-maker’, William Hopkins and, in 1841, Stokes was Senior Wrangler and first Smith’s Prizeman. It was following a suggestion of Hopkins that Stokes took up the study of hydrodynamics, which was at that time a neglected area of study in Cambridge. Stokes was to make profound contributions to hydrodynamics, his most important being the rigorous establishment of the mathematical equations for fluid motions, and the theoretical explanation of a wide range of phenomena relating to wave motions in water.

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Weather and climate forecasting : chronicle of a revolution

2010-06, Lynch, Peter

Remarkable advances in weather forecasts during the past half-century have brought great benefits to humanity. Accurate forecasts save many lives, and early warnings mitigate the worst effects of extreme weather events, when they are available. Detailed, accurate forecasts are of huge economic value, with numerous studies showing that the benefits of forecasts outweigh the costs many times over. Advances in climate modeling over the past fifty years have also been outstanding. General circulation models have been developed and applied to examine the factors causing changes in our climate, and their likely timing and severity.

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Improving the Laplace transform integration method

2015-11-03, Lynch, Peter, Clancy, Colm

We consider the Laplace transform filtering integration scheme applied to the shallow water equations, and demonstrate how it can be formulated as a finite difference scheme in the time domain. In addition, we investigate a more accurate treatment of the non linear terms. The advantages of the resulting algorithms are demonstrated by means of numerical integrations.

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Initialization

2010-08, Lynch, Peter, Huang, Xiang-Yu

The spectrum of atmospheric motions is vast, encompassing phenomena having periods ranging from seconds to millennia. The motions of interest to the forecaster typically have time-scales of a day or longer, but the mathematical models used for numerical prediction describe a broader span of dynamical features than those of direct concern. For many purposes these higher frequency components can be regarded as noise contaminating the motions of meteorological interest. The elimination of this noise is achieved by adjustment of the initial fields, a process called initialization.

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Laplace transform integration of the shallow-water equations. Part 2: Lagrangian formulation and orographic resonance

2011-04, Clancy, Colm, Lynch, Peter

In this paper we combine the Laplace transform (LT) scheme with a semi- Lagrangian advection scheme, and implement it in a shallow water model. It is compared to a reference model using the semi-implicit (SI) scheme, with both Eulerian and Lagrangian advection. We show that the LT scheme is accurate and computationally competitive with these reference schemes. We also show, both analytically and numerically, that the LT scheme is free from the problem of orographic resonance that is found with semi-implicit schemes.