Now showing 1 - 10 of 14
  • Publication
    From Richardson to early numerical weather prediction
    (Cambridge University Press, 2010-12)
    The development of computer models for numerical simulation of the atmosphere and oceans is one of the great scientific triumphs of the past fifty years. These models have added enormously to our understanding of the complex processes in the atmosphere and oceans. The consequences for humankind of ongoing climate change will be far-reaching. Earth system models are the best means we have of predicting the future of our climate. The basic ideas of numerical forecasting and climate modeling were developed about a century ago, long before the first electronic computer was constructed. However, advances on several fronts were necessary before numerical prediction could be put into practice. A fuller understanding of atmospheric dynamics allowed the development of simplified systems of equations; regular observations of the free atmosphere provided the initial conditions; stable finite difference schemes were developed; and powerful electronic computers provided a practical means of carrying out the calculations required to predict the changes in the weather. In this chapter, we trace the history of computer forecasting from Richardson’s prodigious manual computation, through the ENIAC (Electronic Numerical Integrator and Computer) integrations to the early days of operational numerical weather prediction and climate modeling. The useful range of deterministic prediction is increasing by about one day each decade. We set the scene for the story of the remarkable progress in weather forecasting and in climate modeling over the past fifty years, which will be treated in subsequent chapters.
      288
  • Publication
    Pedro Nunes and the Retrogression of the Sun
    (Irish Mathematical Society, 2018)
    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.
      89
  • Publication
    Weather and climate forecasting : chronicle of a revolution
    (World Meteorological Organization, 2010-06)
    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.
      114
  • Publication
    Adaptive post-processing of short-term wind forecasts for energy applications
    (Wiley, 2011-04) ;
    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.
      613Scopus© Citations 13
  • Publication
    The Fractal Boundary of the Power Tower Function
    (Associacao Ludus, 2017-08-23)
    We consider the function called the power tower function, defined by iterated exponentiation (or tetration) of the complex variable z. For real values x, it converges on the interval exp(−e)
      155
  • Publication
    The two-child paradox : dichotomy and ambiguity
    (Irish Mathematical Society, 2011-07)
    Given that one of the children in a two-child family is a boy, what are the chances that the other is also a boy. The intuitive answer is 50 : 50. More careful investigation leads us to a 1-in-3 chance. We investigate circumstances under which these answers are correct. The imposition of further conditions yields some very surprising results.
      243
  • Publication
    Stokes's Fundamental Contributions to Fluid Dynamics
    (Oxford University Press, 2019-06-27)
    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.
      203
  • Publication
    Improving the Laplace transform integration method
    (Wiley, 2015-11-03) ;
    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.
      240Scopus© Citations 2
  • Publication
    Reducing errors of wind speed forecasts by an optimal combination of post-processing methods
    (Wiley-Blackwell, 2011-09-13) ; ;
    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.
      832Scopus© Citations 51
  • Publication
    Initialization
    (Springer, 2010-08) ;
    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.
      129Scopus© Citations 15