Recent work has shown that the full (nonlinear) growth of perturbations in atmospheric ensemble forecasts can depart significantly from tangent linear growth after relatively short time periods (2-days). This may have significant implications for applications in which tangent linear perturbation growth is assumed, as in, for example, the use of adjoint-based techniques for targeted observing applications.

In this study we examine the energetics of the tangent linear and nonlinear growth of singular vector perturbations scaled to have initial amplitudes consistent with estimates of analysis uncertainty. The potential and kinetic contributions to perturbation energy are examined as a function of wave number and altitude. Preliminary results indicate that the nonlinear perturbations have more energy on the smallest scales and less energy on synoptic scales than the tangent linear perturbations after two days. Application of the relative nonlinearity index of Gilmour et al. (2001) indicates that nonlinearities are less significant when considering relatively smooth fields, such as geopotential height, than when considering fields that have more small-scale structure. Other results also indicate that the tangent linear-nonlinear differences are larger when considering kinetic energy as compared to potential energy. The impact of the inclusion of moisture in the tangent linear calculations will also be examined. Implications for ensemble generation and targeted observing will be discussed.