Martin Ehrendorfer

TL;DR: The theoretical justification for the use of SVs in ensemble prediction systems is investigated and it is shown that, in a tangent-linear framework, SVs represent the most efficient means for predicting the forecast error covariance matrix.

TL;DR: In this paper, the spectrum of finite-time most unstable structures, referred to as singular vectors (SVs), is computed for a regional, mesoscale primitive-equation model.

TL;DR: The Liouville Equation (Liouville equation) as discussed by the authors provides a framework for the consistent and comprehensive treatment of the uncertainty inherent in meteorological forecasts, in which the conservation of the phase-space integral of the number density of realizations of a dynamical system originating at the same time instant from different initial conditions, in a way completely analogous to the continuity equation for mass in fluid mechanics.

TL;DR: The Liouville equation represents the consistent and comprehensive framework for the treatment of the uncertainty inherent in meteorological forecasts as discussed by the authors, which avoids problems that are inherent to commonly used methods for predicting forecast skill, such as the need for higher-moment closure within stochastic-dynamic prediction, or the generation of large ensemble sizes within ensemble forecasting.

TL;DR: In this paper, the evaluation of forecasts encompasses the processes of assessing both forecast quality and forecast value, and these processes necessarily play key roles in any effort to improve forecasting performance or to enhance the usefulness of forecasts.