Optimal perturbation time evolution and sensitivity of ensemble prediction to perturbation amplitude

Certain characteristics of the perturbations which grow most rapidly over a finite time interval in a primitiveequation atmospheric model are discussed. They are the singular vectors of a linear approximation of the European Centre for Medium‐Range Weather Forecasts primitive‐equation model. They are computed using the adjoint technique at horizontal spectral truncation T21 with 19 vertical levels. Linear combinations of singular vectors, named optimal perturbations, can be used in ensemble prediction to generate the initial conditions of perturbed integrations. Firstly, having specified the initial amplitude to be comparable with the amplitude of analysis‐error estimates, the nonlinear time evolution of optimal perturbations when added to the control initial conditions are studied. In particular, estimates are made of the time limit, TNL, after which nonlinear processes cannot be neglected. Considering optimal perturbations generated using singular vectors with maximum growth over a 36‐hour time interval, and characterized by amplitudes comparable with analysis‐error estimates, two different methods estimate TNL ≈︁ 2‐2.5 days. Secondly, the sensitivity of ensemble predictions to the optimal perturbation amplitude is analysed. This sensitivity study suggests that an increase of the root‐mean‐square amplitude of the initial perturbation can give a more realistic ensemble spread. Lastly, an estimate of the possible impact of the reduction of the amplitude of analysis errors on the skill of numerical weather prediction is deduced from the comparison of ensemble experiments run with T21 initial perturbations characterized by different amplitudes. Results indicate that a reduction of the root‐mean‐square amplitude of the analysis error by a factor √2 may lead to an improvement of medium‐range predictability up to 1 day, and that a reduction by a factor 2√2 may reduce the errors of the 7‐day forecast to values shown, at present, at forecast‐day 5.