The stream function and the velocity potential can be easily computed by solving the Poisson equations in a unique way for the global domain. Because of the var- ious assumptions for handling the boundary conditions, the solution is not unique when a limited domain is concerned. Therefore, it is very important to reduce or eliminate the effects caused by the uncertain boundary condition. In this paper, an iterative and ad- justing method based on the Endlich iteration method is presented to compute the stream function and the velocity potential in limited domains. This method does not need an explicitly specifying boundary condition when used to obtain the effective solution, and it is proved to be successful in decomposing and reconstructing the horizontal wind field with very small errors. The convergence of the method depends on the relative value for the distances of grids in two different directions and the value of the adjusting factor. It is shown that applying the method in Arakawa grids and irregular domains can obtain the accurate vorticity and divergence and accurately decompose and reconstruct the original wind field. Hence, the iterative and adjusting method is accurate and reliable.
The Advanced Regional Eta-coordinate Model （AREM） is used to explore the predictability of a heavy rainfall event along the Meiyu front in China during 3-4 July 2003. Based on the sensitivity of precipitation prediction to initial data sources and initial uncertainties in different variables, the evolution of error growth and the associated mechanism are described and discussed in detail in this paper. The results indicate that the smaller-amplitude initial error presents a faster growth rate and its growth is characterized by a transition from localized growth to widespread expansion error. Such modality of the error growth is closely related to the evolvement of the precipitation episode, and consequently remarkable forecast divergence is found near the rainband, indicating that the rainfall area is a sensitive region for error growth. The initial error in the rainband contributes significantly to the forecast divergence, and its amplification and propagation are largely determined by the initial moisture distribution. The moisture condition also affects the error growth on smaller scales and the subsequent upscale error cascade. In addition, the error growth defined by an energy norm reveals that large error energy collocates well with the strong latent heating, implying that the occurrence of precipitation and error growth share the same energy source-the latent heat. This may impose an intrinsic predictability limit on the prediction of heavy precipitation.
The numerical solution of Boussinesq equations is worked out as an initial-value problem to study the effect of the instabilities of flow on the initial error growth and mesoscale predictability. The development of weather systems depends on different dynamic instability mechanisms according to the spatial scales of the system and the development of mesoscale systems is determined by symmetric instability. Since symmetric instability dominates among the three types of dynamic instability, it makes the prediction of the associated mesoscale systems more sensitive to initial uncertainties. This indicates that the stronger instability leads to faster initial error growth and thus limits the mesoscale predictability. Besides dynamic instability, the impact of thermodynamic instability is also explored. The evolvement of convective instability manifests as dramatic variation in small spatial scale and short temporal scale, and furthermore, it exhibits the upscale growth. Since these features determine the initial error growth, the mesoscale systems arising from convective instability are less predictable and the upscale error growth limits the predictability of larger scales. The latent heating is responsible for changing the stability of flow and subsequently influencing the error growth and the predictability.
A fine heavy rain forecast plays an important role in the accurate flood forecast, the urban rainstorm watedogging and the secondary hydrological disaster preventions. To improve the heavy rain forecast skills, a hybrid Breeding Growing Mode （BGM）- three-dimensional variational （3DVAR） Data Assimilation （DA） scheme is designed on running the Advanced Research WRF （ARW WRF） model using the Advanced Microwave Sounder Unit A （AMSU-A） satellite radiance data. Results show that： the BGM ense- mble prediction method can provide an effective background field and a flow dependent background error covariance for the BGM- 3DVAR scheme. The BGM-3DVAR scheme adds some effective mesoscale information with similar scales as the heavy rain clu- sters to the initial field in the heavy rain area, which improves the heavy rain forecast significantly, while the 3DVAR scheme adds information with relatively larger scales than the heavy rain clusters to the initial field outside of the heavy rain area, which does not help the heavy rain forecast improvement. Sensitive experiments demonstrate that the flow dependent background error covariance and the ensemble mean background field are both the key factors for adding effective mesoscale information to the heavy rain area, and they are both essential for improving the heavy rain forecasts.
