Abstract
The (linear) time evolution of singular vectors computed with a primitive equation model following a 36-h evolving trajectory is analyzed at horizontal triangular spectral truncations T21, T42, and T63.
First, for each resolution, the impact of horizontal diffusion on the singular vectors characteristics (amplification factors, total energy spectra) is analyzed. Forecast error and singular vectors computed with different horizontal diffusion damping times are compared to assess whether, at each resolution, forecast error projection onto the first 10 most unstable singular vectors is maximized for specific values. Results suggest that better projections are obtained with horizontal diffusion damping times on the smallest scale (on divergence) of 3 h at T42 and T63 resolution, and of 12 h at T21.
Then amplification factors, geographical locations, total energy vertical distributions, and spectra of T21, T42, and T63 singular vectors computed, respectively, with 12-, 3-, and 3-h damping time on the smallest scale are analyzed. The ratio among the singular vector amplification factors at T21:T42:T63 resolution is shown to be approximately 1:1.5:2.5. The geographical location and the total energy vertical distribution of T21, T42, and T63 singular vectors are quite similar. By contrast, total energy spectra differ substantially. Forecast error projection onto singular vectors is shown to be slightly larger if higher-resolution singular vectors are used. It is argued that the impact of horizontal resolution on the forecast error projection is marginal because of the lack of physical processes in the forward and adjoint tangent model versions. Moreover, the fact that forecast error projections onto the leading 10 singular vectors are rather small could be seen as an indication that more singular vectors are needed to capture the growing components of forecast error.
Finally, singular vectors and forecast errors are compared to quantify the relevance of the singular vectors of day d to capture the growing features of the error of the forecast started on day d. Results indicate that forecast error projection onto the leading 10 singular vectors decreases if singular vectors of a wrong date are used.
Corresponding author address: Dr. Roberto Buizza, European Centre for Medium-Range Weather Forecasts, Shinfield Park, Reading, Berkshire RG2 9AX, United Kingdom.
Email: ner@ecmwf.int
