**4. Results**

#### *4.1. Effect of Data Assimilation on Temporal Rainfall Distributions*

As illustrated by Figure 3, it shows the results of different assimilation frequencies. The first guess file generated from the previous run will provide the initial conditions for the next run. "DA\_1h\_1km" and "DA\_1h\_3km" are assimilated data with an interval of 1 h, and "DA\_6h\_3km" is 6 h. The forecasted accumulative rainfall is calculated from the average value of rainfall at each grid point in the study area. When the area of the grid within the watershed boundary accounts for more than 50% of the grid area, the rainfall value of the grid point participates in the calculation of the rainfall accumulations. As for the observations, the observed accumulative rainfall is calculated by averaging rain gauge observations using the Thiessen polygon method.

When the different assimilation frequencies are chosen in the model, the curve structure in the rainfall forecasting is significantly altered ("DA\_1h\_3km" and "DA\_6h\_3km"). The evolution of "DA\_1h\_3km" and "DA\_6h\_3km" in WRF-3DAVR system shows similar patterns with higher differences in the rainfall peak. The improvement of assimilation frequency led to a significant increase in precipitation. In WRF-3DVAR system, the operation with high assimilation frequency will produce incremental adjustment, which makes the prediction closer to the observation. In addition, through evaluating the outputs from different domain resolution on rainfall prediction, the improvement of WRF-3DVAR system domain output resolution is less obvious on the accumulative rainfall ("DA\_1h\_1km" and "DA\_1h\_3km"). In other words, the data assimilation of the outer domain has a positive effect on the output of the inner domain, but the improvement is not obvious. This may be due to the fact that no data is assimilated on the 1 km horizontal resolution domain. The larger the volume of assimilation data import to model, the longer time it will take to forecast the rainstorm. However, rainstorm forecasting has a high requirement for effectiveness for a given period of time, so in practical application it is beneficial to obtain the effective information of rainfall as soon as possible. In order to balance the

accuracy and timeliness of rainstorm forecasting, data assimilation is not carried out in the innermost domain.

**Figure 3.** Rainfall accumulation of rain gauge and four data assimilation schemes for Event I, II, III, IV.

#### *4.2. Effect of Data Assimilation on Spatial Rainfall Distributions*

The spatial distributions of predicted precipitation with and without assimilation are shown in Figure 4. It is not difficult to see that after the data assimilation, the spatial temporal distribution of rainfall forecast has been improved in varying degrees compared with without assimilation. "DA\_1h\_1km", "DA\_1h\_3km", and "DA\_6h\_3km" performed much better as rainfall forecasts, respectively, than "NA\_1km" in spatial distributions. The results show that the WRF-3DAVR system can obtain the major rain band located around the east and south border of the study area while the same rain band is disorganized in the WRF model. That is, the improvements to certain extents in spatial distributions after data assimilation.

Figure 4 shows spatial distributions of the 24 h accumulative rainfall for the four storm events in the Fuping and Zijingguan catchment. It can be intuitively seen from the spatial variations in Event II-IV that the rainfall forecast after data assimilation is significantly larger in numerical value than before assimilation. The storm centers of events were captured relatively well by WRF-3DAVR; however, some parts of the catchments with high rainfall accumulations were missed by WRF-3DAVR, such as the northern rainband of Event III and the western rainband of Event IV. By analyzing the evenness of storm events, the temporal and spatial distribution of Event I is more even, Event II is uneven in time, and Event III-IV is uneven in space and time. The results show that the rainfall with even spatial distribution has the best predicted results on the spatial scale, while the rainfall with uneven spatial distribution has the worst predicted results on the spatial scale. WRF-3DAVR is easier to accurately simulate or forecast rainfall with more uniform spatial distribution, while WRF-3DAVR is more difficult to accurately forecast rainfall area with uneven spatial distribution. It can also be obtained from the index analysis of each rainfall forecast result in Table 8. In addition, whether the rainfall is evenly distributed on the time scale has a certain influence on the forecast results of rainfall on the spatial scale but does not play a decisive role. From "DA\_1h\_1km" and "DA\_1h\_3km", simply increasing the resolution of domain has no significant improvement in the spatial dimension of the rainfall simulations, this is probably because the innermost domain does not assimilate data. Furtherly, Table 8 in Section 4.3 provides the root mean square error (*RMSE*), mean bias error (*MBE*), critical success index (*CSI*), and *CSI*/*RMSE* of 24 h rainfall accumulation values using WRF and the different WRF-3DAVR schemes.

(4) Event IV

**Figure 4.** Spatial rainfall distributions of gauge observations and forecasts from four data assimilation schemes for Event I, II, III, IV, from left to right: (**a**) observation; (**b**) NA\_1km; (**c**) DA\_1h\_1km; (**d**) DA\_1h\_3km; (**e**) DA\_6h\_3km.

#### *4.3. Evaluation on the Storm Process Improvements*

The evaluation scores for the four 24-h rainstorm forecasts from 1 and 6 h time intervals with and without assimilation are shown in Table 8. In evaluations in the spatial

scale, the model forecasts are interpolated to the rain gauge locations for comparisons with the observations. Firstly, compared with "NA\_1km", the rainfall forecasts at different assimilation schemes are improved significantly. For example, *RMSE* of "NA\_1km" without assimilation in Event I on the temporal dimension was 2.3393, while the highest *RMSE* with data assimilation is 2.1320 (DA\_6h\_3km) and the lowest *RMSE* is 1.7816 (DA\_1h\_1km). Possibly it is because Event I has a relatively even distribution in both time and space (0.3975 for spatial *Cv* and 0.6011 for temporal *Cv*), and data assimilation has no large improvement on the rainfall forecasting with even spatial-temporal distribution. Similarly, on the spatial dimension, *RMSE* of the assimilated schemes is better than that without assimilation. In the spatial dimension, for example, *RMSE* of "NA\_1km" in Event III is 2.8849, which is no assimilation, while the worst *RMSE* with data assimilation in Event III is 1.4068 (DA\_6h\_3km). Therefore, the good performance for selected typical precipitation events shown by the cycling data assimilation gradually improves not only temporal but also spatial variability.

Secondly, the performance of the 1 h assimilation time interval with respect to its 6 h counterpart with data assimilation is examined. It is shown (Table 8) that experiment hourly assimilation time interval has lower *RMSE* than its 6-hourly counterpart in most events in both the temporal and spatial dimension, indicating the potential for a better forecast. Event I, Event III, and Event IV show positive effect in rapid update assimilation, and much precipitation rises in WRF-3DAVR compared to low assimilation frequency ("DA\_1h\_3km" and "DA\_6h\_3km"). In the case of Event IV in the spatial dimension, for example, a decrease in *RMSE* from 12.6979 after 6 h assimilation time interval to 8.7782 occurred after hourly assimilation frequency; a similar trend was noted during Event I and Event III. In the meantime, hourly assimilation frequency has a lower MBE than 6-hourly assimilation time interval for most events. This might be the result that the regional approach with higher-resolution observations and closing to actual atmospheric boundary conditions may improve the assimilation effect and help offset temporal and spatial information lost by WRF. For the study area with small-scale, the assimilation time interval of 6 h is too long, and the model background field is not corrected in time. As time goes on, the observation error of radar is constantly amplified in the model background field, which reduces the effect of rainfall forecast.

However, WRF-3DAVR and high assimilation frequency are mixed. In Event II, experiment hourly cycled configuration had slightly lower scores than those of the 6-hourly counterpart in the both time dimension and spatial distribution for Event II. Although the low assimilation frequency appears to be slightly better than the high assimilation frequency for Event II, this does not seem to pose a threat to the hourly assimilation frequency. But it also reflects the disadvantages of spreading too much radar information to places where the radar data are not available.

In addition, the influence of data assimilation of outer domain on the output of inner domain is discussed, and the precipitation outputs of 3 and 1 km domain are compared. The results show that although the data assimilation of outside domain has a positive impact on the output of the inside domain, inside domain generated very small helpful increments, especially in the time scale.

All the schemes show different amounts of false precipitation in study areas from *CSI*. The high *CSI* are Event I and II, indicating that the model basically captures the occurrence time and rainstorm area of Event I and II, the low *CSI* are Event III and IV, and the lowest is Event III, indicating that the simulation results of these rainfall fields are poor in terms of time and space. In order to further evaluate the forecasting results of WRF-3DAVR system for each rainfall type on the temporal scale, *CSI/RMSE* was taken as a comprehensive index to evaluate the forecasting results. In the temporal dimension, the forecasting results of Event I and Event II are the best, with the value range of four schemes of *CSI/RMSE* being 0.2412 to 0.4538, while the forecasting results of Event III and Event IV are the worst, value range of four schemes of *CSI/RMSE* being 0.0345 to 0.0948. In the spatial distribution, the same law is presented, that is, WRF-3DAVR system is easier to accurately simulate

or forecast rainfall with more uniform time distribution, but more difficult to simulate or forecast rainfall with short duration and concentrated rainfall. Combined with the calculation of the spatiotemporal variation coefficient (*Cv*) of precipitation events, it shows that Event II–IV are more uneven in time and space than Event I. In Event III, for example, the temporal *Cv* value of 2.3925 and the spatial *Cv* value of 0.7400 are much higher than those of Event I (0.6011 and 0.3975). This may explain the increased bias in assimilation, since the improved effectiveness of the rainfall forecast after assimilation is determined by the amount of effective information contained in the data. It is easier for radar reflectivity and GTS data to capture data during periods of rainfall that is homogeneously distributed in space and time.

**Table 8.** Temporal and spatial values of the four assessment indices for Event I, II, III, IV with four schemes.


Assimilation of all possible data with high assimilation frequency may not be the most effective method in precipitation forecasting. Especially, the influence of assimilation frequency on rainfall forecast is rather small in Event II; the precipitation forecasts with 1 h cycle do not have much difference from those with 6 h cycle. That may indicate the impact of false rainfall forecasting fields is enlarged because of the inaccurate radar observed data. One may wonder whether the results of assimilation have anything to do with the quality of the assimilated data, such as radar data. To answer that question, the ability of Doppler radar to retrieve precipitation is plotted (Figure 5). In each single subfigure, the black bars and yellow solid curve indicate measure rainfall and accumulative rainfall from rain gauge, respectively. Green bars and pink curve indicate rainfall and accumulative rainfall from radar observed reflectivity inverse calculation. The left y-axis is the cumulative rainfall value, corresponding to the curve, and the y-axis on the right is the value of hourly rainfall, which corresponds to the bar graph.

As can be seen from Figure 5, the radar precipitation estimation of Event I was closer to the observation accumulation curve, and at the same time, assimilation effect of Event I was also the best in all events. In addition, there was substantial rainfall growth during the first nine hours of the rainfall after the radar data assimilation for Event III, and the accumulated rainfall increased abruptly. Additionally, we found that the radar measures rainfall from the 1st hour to the 9th hour as much larger than the observed rainfall (Figure 5), as revealed in many previous studies [54]. Therefore, in our storm events selected, the accuracy of radar reflectivity is of primary importance in improving the quality of precipitation forecast within the time range of forecasting [5].

When WRF-3DVAR technology is applied, a matter of effective radar data assimilation could be tackled by using shorter assimilation time interval to achieve greater information assimilation. Although the assimilated radar data can help WRF model to forecast

precipitation effectively, it increases the conflict between radar data and domain. In the process of data assimilation, the validity of assimilated data should be judged as far as possible in advance, which can not only improve the prediction accuracy of WRF model, but also improve the assimilation efficiency. There are many factors affecting assimilation, and radar data may be only a part of them, and more factors need to be further explored, such as the resolution of GFS data, nested boundary conditions, the dynamic structure of the model, numerical discretization, etc.

**Figure 5.** Observations and radar measurements of 24 h rainfall accumulations for Event I, II, III, IV.
