Search

The local instabilities of a nonlinear dynamical system can be characterized by the leading singular vectors of its linearized operator. The leading singular vectors are perturbations with the greatest linear growth and are therefore key in assessing the system's predictability. In this paper, the analysis of singular vectors for the predictability of weather and climate and ensemble forecasting is discussed. An overview of the role of singular vectors in informing about the error growth rate in numerical models of the atmosphere is given. This is followed by their use in the initialization of ensemble weather forecasts. Singular vectors for the ocean and coupled ocean-atmosphere system in order to understand the predictability of climate phenomena such as ENSO and meridional overturning circulation are reviewed and their potential use to initialize seasonal and decadal forecasts is considered. As stochastic parameterizations are being implemented, some speculations are made about the future of singular vectors for the predictability of weather and climate for theoretical applications and at the operational level. [ABSTRACT FROM AUTHOR]

Historical evidence is reviewed to show that what Ed Lorenz meant by the iconic phrase ‘the butterfly effect’ is not at all captured by the notion of sensitive dependence on initial conditions in low-order chaos. Rather, as presented in his 1969 Tellus paper, Lorenz intended the phrase to describe the existence of an absolute finite-time predicability barrier in certain multi-scale fluid systems, implying a breakdown of continuous dependence on initial conditions for large enough forecast lead times. To distinguish from ‘mere’ sensitive dependence, the effect discussed in Lorenz's Tellus paper is referred to as ‘the real butterfly effect’. Theoretical evidence for such a predictability barrier in a fluid described by the three-dimensional Navier–Stokes equations is discussed. Whilst it is still an open question whether the Navier–Stokes equation has this property, evidence from both idealized atmospheric simulators and analysis of operational weather forecasts suggests that the real butterfly effect exists in an asymptotic sense, i.e. for initial-time atmospheric perturbations that are small in scale and amplitude compared with (weather) scales of interest, but still large in scale and amplitude compared with variability in the viscous subrange. Despite this, the real butterfly effect is an intermittent phenomenon in the atmosphere, and its presence can be signalled a priori, and hence mitigated, by ensemble forecast methods. [ABSTRACT FROM AUTHOR]