**5. Discussion**

By carrying out a comparative analysis on the output results of different assimilation frequencies, it can be proved that by reducing the length of the assimilation window, the rainfall forecasting can be closer to the observations and can better present storm center. The hourly data assimilation frequency in the WRF-3DVAR allows for the addition of useful information and results in improved performance of the rainfall forecasting. However, misestimates may be caused when applying high assimilation frequency.

First, the quality of the output analysis depends on the error in the model initialization when inaccurate boundary field and background information is inputted into the assimilation system. As is widely understood, accurate initial condition is crucial to data assimilation and prediction of numerical weather prediction (NWP) system. Data assimilation system can combine all useful information about atmospheric conditions in the given time window, and obtain estimated value of the valid atmospheric conditions in given analysis time. Where, information used for model calculations is sourced from the observations, background, previous estimate of the atmospheric state, as well as their specific inherent errors. Compared with other error sources (e.g., physical parameterization, boundary conditions, and predicting dynamics), the relative importance of prediction errors caused by initial condition errors depend on many factors, including resolution, domain, data density, orography as well as the forecast product of interest [55]. The assimilation data of the WRF-3DVAR system is dedicated to providing initial conditions and further improving the WRF predictions, and then applied to creating forecasting of regional climates in the future, which is excitingly possible.

Especially, the radar data as one of the assimilation data sources, which represent the small-scale and rapid evolution in the boundary layer, are often unsatisfactory, especially in the events of extreme rainfall intensity. This is because the rainfall estimate of radar is not directly measured, but is indirectly obtained by the measured radar reflectivity. The measurement of radar reflectivity and the conversion process from reflectivity to intensity are affected by many error sources. In order to improve the accuracy of the radar data used

for initial conditions of mode, it can be adjusted according to the rain gauge measurements. In this way, it can combine the advantages of the precise measurement of rainfall by the rain gauge at the point and the better performance of the radar in the spatial distribution, and overcome the disadvantages of the rainfall deviation caused by the uncertainty of the radar in the rain measurement. Studies are being conducted to find the optimal technique for radar observations to improve the initial state of the model.

Second, the error in the actual numerical prediction system may be highly non-linear, although the variational method includes linearized dynamic and physical processes, which limits the practicability of variational data assimilation in highly non-linear regions (such as convective scale or tropical region). Therefore, it is necessary to develop a more objective method, such as a method based on ensemble prediction for estimating the uncertainty of a flow-related prediction background [5]. Nevertheless, despite these limitations, this study provides a prototype for short-term practical prediction of a local convective weather system. It is hoped that these research topics can be discussed in the future research and application of the 3DVAR system.

Furthermore, it is shown that the WRF model can reasonably predict a low-intensity and long-lasting rainfall event. However, the result from this study indicates that this model often leaves out rare small-scale and short-term rainfall prediction events or underestimates the precipitation intensity, because small-scale interference is filtered when large-scale analysis keeps a better balance [15]. The main reason for this is that convection is a smallscale phenomenon, and false estimates may be caused if the increment in diffusion spreads too far. This is exactly what should be improved in the predictions, by applying different model parameterization technology [56] or data assimilation technology for instance [3].

For mesoscale catchments, the spatial distribution of rainfall is also important due to its significant impact on the flood volume, flood peak, and time to peak [28]. In addition, approaches to improve the spatial accuracy of precipitation predictions after data assimilation are also worth exploring. It is necessary to analyze more storm events in different survey regions in order to find more general radar data assimilation criteria and thus facilitate numerical prediction.
