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In this study, a multi-time-scale four-dimensional variational data assimilation (MTS-4DVar) scheme is developed and applied to the assimilation of radar observations. The MTS-4DVar employs multitime windows with various time lengths in the framework of incremental 4DVar in the Weather Research and Forecasting Data Assimilation (WRFDA). The objective of MTS-4DVar is to enable the 4DVar data assimilation system to extract multiscale information from radar observations, and the algorithm of MTS-4DVar is first discussed in detail. Using a heavy rainfall case, it is shown that the nonlinearity growth of reflectivity is faster than that of radial velocity, suggesting that the time window for assimilating reflectivity in the incremental 4DVar should be shorter than that of radial velocity. A series of single observation tests and observing system simulation experiments (OSSEs) are then presented to examine the physical characteristics and performance of MTS-4DVar. These experiments demonstrate that the MTS-4DVar is capable of combining the larger-scale information from a longer time window and the local-scale features from a shorter time window. With the OSSEs it is shown that the value of the cost function is reduced properly in the minimization of the MTS-4DVar with a combination of longer and shorter time windows. By assimilating the radar radial velocity alone, we found that the MTS-4DVar reduces the analysis and forecast errors and improves the precipitation forecasts in comparison with the normal incremental 4DVar. Additional assimilation of reflectivity further improved the precipitation forecasts, and the results show that the radar reflectivity can also be well assimilated by using MTS-4DVar.

A Multi-Time-Scale Four-Dimensional Variational Data Assimilation Scheme and Its Application to Simulated Radial Velocity and Reflectivity Data