Slow-start procedures were developed decades ago in order to provide a smoother evolution in numerical simulations performed with three-time-level integration schemes. The advantages of a slow start versus a conventional forward start should increase as the time step increases. With the advent of centered semi-Lagrangian semi-implicit schemes, we now have accurate numerical weather prediction models that can use much larger time steps than before, and the impact of the start-up procedure becomes more important. This paper examines the advantages of a slow-start procedure in the context of such models.
The impacts on Rossby and gravity waves are analyzed, and some of the advantages are illustrated through tests with an idealized solution. This is a Haurwitz-type solution that has been modified to satisfy the divergence equation rather than just the balance equation as in the Phillips solution. Experiments are performed with shallow-water models initialized with real data in order to assess under what conditions the quantitative impact of the start-up is significant. It is found that inserting a single start-up at the beginning of an integration does not appear to have a significant impact on medium-range forecasts, although a slow start is important in order to retain the benefit of a careful initialization procedure when the models are subsequently run with large time steps permitted by semi-Lagrangian semi-implicit algorithms. When a start-up is made every 6 h, as in an analysis cycle, the forward start introduces a significant error when the time step is large, but this error decreases rapidly as the time step is reduced. For all the time stops examined, the slow start is very effective in controlling the error due to the computational modes introduced by the start-up. Tests are also performed with an operational baroclinic model that uses a time step of 30 min, and it is found that, with this time step, even repeated start-ups with a conventional forward start do not generate significant computational modes.