Tim Palmer

Abstract:

Operational forecasting is hampered both by the rapid divergence of nearby initial conditions and by error in the underlying model. Interest in chaos has fuelled much work on the first of these two issues; this paper focuses on the second. A new approach to quantifying state-dependent model error, the local model drift, is derived and deployed both in examples and in operational numerical weather prediction models. A simple law is derived to relate model error to likely shadowing performance (how long the model can stay close to the observations). Imperfect model experiments are used to contrast the performance of truncated models relative to a high resolution run, and the operational model relative to the analysis. In both cases the component of forecast error due to state-dependent model error tends to grow as the square-root of forecast time, and provides a major source of error out to three days. These initial results suggest that model error plays a major role and calls for further research in quantifying both the local model drift and expected shadowing times.

Abstract:

With the introduction of diabatic processes in the forward and adjoint tangent models of the European Centre for Medium-Range Weather Forecasts's model, it is possible to determine singular vectors (SVs) for situations where diabatic physics may be important in producing perturbation growth. In this paper, the linear physical parametrizations are used to compute SVs for the tropical region, or subsets thereof, with an optimization time of 48 h. Perturbation growth is measured in terms of the so-called total energy norm, augmented with a term for specific humidity. Difficulties that may arise in computing tropical SVs, such as associated with spurious upper-tropospheric perturbation growth, are described. Also, the impact on the SV structure by including a specific-humidity term in the defining norm is discussed. Using a term for specific humidity based on background-error statistics in the norm at initial time yields SVs with a more realistic specific-humidity vertical profile. SVs are determined in various configurations for two tropical cyclones. Results show that targeting in the vicinity of the cyclone is required to obtain SVs associated with the cyclone dynamics. The dominant targeted SVs for tropical cyclones show resemblance to fast-growing structures found for idealized vortices.