3.1. Sensitivity Analysis Results
Using the QMC sampling method, 250 parameter sample sets were taken from the 25 parameter ranges listed in Table S1
. The corresponding WRF simulation errors (i.e., RMSE) were also obtained by comparison with the default simulation results. As a pair of input variables, the 250 parameter samples and the corresponding WRF simulation errors were entered into the MARS sensitivity analysis method, and the parameter sensitivity scores were finally obtained.
shows the normalized sensitivity scores for the 25 parameters. The x
-axis represents the 25 parameters, and the y
-axis represents parameter sensitivity scores for the different regions. Three common sensitivity parameters were found for the precipitation simulations: P5, P6, and P7. In addition, P4 and P23 were sensitive for precipitation simulations in the d02B domain. Finally, five parameters (P4, P5, P6, P7, and P23) were ranked as sensitive parameters for precipitation simulations. For 10-m wind, two common sensitive parameters, P3 and P4, were found. In addition, P6 and P23 were sensitive in the d02A and d02B domains respectively. Overall, four parameters (P3, P4, P6, and P23) were sensitive for the 10-m wind simulations.
To validate the reasonability of the screened sensitive parameters, the responses of model performances to six screened sensitive parameters and four cloud microphysics parameters (i.e., ice_stokes_fac
, and peaut
) which were thought to be insensitive using MARS method were compared. The results are shown in Figure 3
. Each parameter range was equally divided into 10 bins, and the red curve represented an average of the simulation errors at each bin. The first and second lines represented the responses of precipitation simulation errors to the screened precipitation sensitivity parameters (pd
, and pfac
corresponding to P5, P6, P7, and P23 respectively in Figure 2
) and cloud microphysics parameters respectively. The responses of 10-m wind simulation errors to 10-m wind sensitivity parameters (znt_zf
, and pfac
corresponding to P3, P4, P6, and P23 respectively in Figure 2
) and cloud microphysics parameters were represented in the third and fourth lines of Figure 3
respectively. It is noteworthy that the simulation error was RMSE of WRF simulations with between-default and perturbed parameters.
showed that the perturbation for the sensitive parameters of precipitation and 10-m wind brought more significant model outputs changes than that for the insensitive parameters (cloud microphysics parameters). Compared with sensitive parameters, the variances of the precipitation and 10-m wind simulation errors caused by cloud microphysics parameter perturbation were basically a straight line. Therefore, the cloud microphysics scheme parameters should be insensitive and the variances of their values had no significant influence on the precipitation and 10-m wind simulations. It demonstrated that the parametric sensitivity conclusion (shown in Figure 2
) drawn by ASMO method were reasonable. Finally, the six sensitive parameters were quantified and are listed in Table 2
3.2. Parameter Optimization Results
shows the optimization speed for the total NRMSE of the precipitation and 10-m wind simulations using the ASMO method. The minimum error was about 0.92 in 100 simulations of the initial parameter samples obtained by the QMC sampling method. This meant that the precipitation and 10-m wind simulations were improved on average by 8% compared with the WRF default simulations. Next, the total NRMSE was further reduced to 0.898 by 78 adaptive sampling runs. After this, an additional 30 runs (equal to five times the dimensionality of the parameters) did not change the previous minimum NRMSE. Therefore, the convergence criterion of the optimization was met, and the optimal parameters had finally been found. In a word, the ASMO method improved the precipitation and 10-m wind simulations by 10.2% on average using only 178 model runs. This demonstrated that the ASMO optimization method was highly efficient.
To illustrate the optimization results, comparisons of WRF simulations with default and optimal parameters for 6-hourly precipitation and 10-m wind were conducted. The results are shown in Figure 5
. Overall, the simulations for the 6-hourly precipitation and 10-m wind were improved by 6.83% and 13.64% respectively. This demonstrated that the improvement for wind was larger than that for precipitation. For six single events, all precipitation simulations were improved to an extent varying from 0.26% for event (2) to 11.88% for event (6), and four of six 10-m wind simulations were improved to an extent varying from 10.43% for event (4) to 35.04% for event (2). Note also that some event simulations for 10-m wind showed negative improvements (e.g., events (3) and (6)). This is related to the optimization objective function, which focuses on the accumulated simulation errors for all six events rather than on each one. However, note that the negative improvements mainly occurred in events with lower simulation errors. In addition, the larger simulation errors for 10-m wind and precipitation occurred in the d02A and d02B regions respectively. The larger the error, the more significant the improvement was.
Besides comparisons for single-typhoon simulations, WRF typhoon simulations with default and optimal parameters were compared for different lead times. The results are shown in Figure 6
. Figure 6
a shows that the optimal parameters improved the WRF precipitation simulations at 6-hourly lead time by amounts ranging from 0.07% to 25.20%. Similarly, Figure 6
b shows that the optimal parameters improved the 10-m wind simulations at 6-hourly lead time except for the 30th hour (−3.55% improvement), and other positive improvements ranged from 1.54% to 41.22%, which were generally greater than the improvement rate of precipitation simulations at each lead time. In addition, it seemed that the improvement rate had an increasing tendency for both precipitation and 10-m wind simulations as lead time increases.
It was noted in Figure 6
b that the difference between 10-m wind default simulation and observation was low (less than 8 m s−1
), so the smaller reduction for RMSE by the optimal simulation would demonstrate a larger percentage improvement. To avoid misleading results, it was suggested that the error value and its relative improvement percentage should be combined to accurately evaluate the model performance improvement.
Comparisons of the spatial distribution of 3-day precipitation simulations using the WRF model with default and optimal parameters were also conducted, and the results are shown in Figure 7
. The first column represents the spatial distribution of observed daily precipitation for six typhoons in the d02A and d02B regions. It showed that strong precipitation occurred mainly in the northeastern parts of Hainan and Fujian Provinces and the coastal areas of Fujian Province. The second and third columns represent the differences between observations and WRF simulations with default and optimal parameters respectively. By comparing Figure 7
b with Figure 7
c, it is found that the large positive deviation (marked in red and yellow in Figure 7
b) for default precipitation simulations in the d02A region was significantly reduced by the optimal precipitation simulations. A similar situation can also be observed in the d02B region by comparing Figure 7
e with Figure 7
f. In addition, the improvement was significant for simulation of strong precipitation. For instance, large precipitation amounts (over 60 mm day−1
) occurred in the northeastern part of Hainan Province in the d02A region, where deviations were lower for the optimization simulation than for the default simulation. For the d02B region, a similar situation occurred north of the border between Fujian and Jiangxi Provinces.
Comparisons of 10-m wind evolution simulations for each single event were also conducted, and the results are shown in Figure 8
. Noted that the 10-m wind was an abbreviation of typhoon central 10-m maximum wind speed (referred in introduction section), so it represented a specific grid point value near typhoon center. The location of 10-m wind in Figure 8
was constantly shifting as the typhoon center moved. Overall, compared with the default simulations, the optimal simulations were closer to observations for most of the lead times. The most significant improvements occurred in events (1) and (2), and therefore the average improvement of the optimal simulations in the d02A region including events (1), (2), and (3) was higher than in the d02B region including events (4), (5), and (6), a result that is consistent with the conclusions shown in Figure 5
. The optimal simulations decreased the default simulation values to approximate the observations in event (1), while increased the default simulation values close to observations in event (2). Therefore, the parameter optimization method is different from statistical deviation correction, which provides an overall upward or downward shift for the default simulation results to approximate observations. Hence, the parameter optimization method seemed to be more reasonable than the deviation correction method. In addition, there was some indication that the improvement was more significant as the lead time increased.
The results in Figure 8
seemed that default and optimal experiments were almost identical except event (2), which was mainly caused by the definition of the objective function. According to formula (2), the optimization method was more inclined to improve the total simulation error rather than the error of a single event, so more improvement was achieved with events with larger simulation errors. It was apparent that the event (2), with the largest simulation errors, had the most significant improvement. In addition, the optimal simulations did not deviate from the default simulations too far or even improved them for other events with relatively low simulation errors. Therefore, the optimal parameter was reasonable. Future multi-objective parameter optimization could balance the improvement percentage of all individual events.
3.3. Atmospheric Structure Analysis
Two representative events (events (2) and (5)) were selected to analyze the differences between WRF simulations with default and optimal parameters on high-altitude variables such as 500-hPa geopotential height, 500-hPa wind, and precipitable water.
shows the simulated fields of 500-hPa geopotential height and wind at lead times of 24 h, 48 h, and 72 h using the WRF model with default and optimal parameters compared with ERA-interim observations for event (2). The first line represents the observations. The second and third lines represent the simulated field at 500 hPa using the WRF model with default and optimal parameters respectively. The red lines marked with 588 dagpm represented the scope of the subtropical high. By comparing the location of 588 dagpm lines, it was found that when the optimal simulation was used, the southern scope line of the subtropical high moved slightly toward the observation at 24 h; however, the whole scope of the subtropical high significantly moved northeast closer to the observation at 48 h and 72 h. Overall, the simulation of the scope of the subtropical high (marked by the red line) showed improvement, especially for 48 h and 72 h lead times. When the scope of the subtropical high moved east, the flow on the west side of the subtropical high varied from north to northwest, making the typhoon center move slightly south, closer to observations (Figure 9
b,e,h). Accordingly, the simulation of typhoon central wind speed was strengthened (see Figure 9
d,g, or Figure 9
e,h), which is consistent with the results in Figure 8
The same comparisons were also conducted for event (5) and the results are shown in Figure 10
. As the conclusion of Figure 9
, the simulation for the scope of the subtropical high for event (5) showed improvement, especially for lead times of 48 h and 72 h. The difference was that the optimization expanded the scope of the subtropical high in event (5) and shrank the scope in event (2). The improved simulation at 48 h caused the flow on the east and west sides of the subtropical high to shift from northwest to north, which was close to the observed flow. In the same way, the improvement of the subtropical high simulation at 72 h caused the flow on the east and west sides of the subtropical high to shift from northwest to northeast, which was close to the observed flow.
The precipitable water is the total amount of water vapor in a vertical column with unit cross-sectional area. It is an important indicator of precipitation. Figure 11
and Figure 12
show a comparison of the results of precipitable water simulations with default and optimal parameters for event (2) and event (5) respectively. To better demonstrate the improvement in the precipitable water simulation by the WRF model with optimal parameters, the areas with high water-vapor content were shaded. The shaded areas in Figure 11
and Figure 12
represent values higher than 65 kg m−2
and 70 kg m−2
respectively. As shown in Figure 11
and Figure 12
, the optimal simulations reduced the shaded area of the default simulations to be closer to observations, especially for the area around the typhoon center.
3.4. Validation Analysis of WRF Optimal Parameters
It is necessary to address the question of whether the optimal parameters will still work on WRF simulations of new typhoon events. Therefore, six new typhoon events from 2016 and 2017 were simulated to verify whether the WRF optimal parameters were still reasonable. The new events were different from the previous optimization events from 2013 to 2015. Other than the simulation events, the validation experiment used the same configuration as the previous optimization experiment, including simulation area, WRF model configuration, and forcing data source. In addition, the six new validation events were equally divided into two d02 domains. The uniform simulation period was three days. Detailed descriptions of the observed typhoon tracks and durations are presented in Figure 13
and Table 3
Comparisons of precipitation (10-m wind) simulations for the six new typhoon events (I)–(VI) using the WRF model with default and optimal parameters were conducted, and the results are shown in Figure 14
. Compared with the default WRF simulations, the WRF model with the optimal parameters improved the simulations of 6-hourly precipitation and 10-m wind by 4.78% and 8.54% respectively. It is apparent that the optimal parameters not only improved the typhoon simulations of precipitation and 10-m wind for the optimization period from 2013 to 2015, but also for the validation period from 2016 and 2017. Similarly, the improvement rate for wind simulation was higher than for precipitation simulation. These conclusions on the comparison of precipitation simulations with validation events are consistent with those for previous optimization events, which in turn confirms that the optimal parameters obtained by the ASMO method are robust.
Overall, the optimal simulations reduced the positive deviation of the default simulations for the spatial distribution of precipitation, and the improvement was significant for the simulation of strong precipitation (Figures not shown). Comparative analyses were also performed for the 10-m wind simulations in each validation event. Figure 15
shows the corresponding results. Generally, compared with the default simulations, the optimization simulations were closer to observations for most lead times. Among these, the most significant improvements occurred in events (II) and (V). Note also the slightly negative improvements for events (I) and (III), with lower errors between the default simulations and observations. This happened because the objective function for optimization was the total accumulated error for the simulations of all six events, and therefore some event simulations with lower errors might have been slightly sacrificed. However, the optimal parameters overall improved the 10-m wind simulations by the default WRF model, as shown in Figure 14
b. It was also found that the improvement of the optimal simulations for 10-m wind was more significant after 24 h, implying that the effect of parameter optimization may be highlighted when the effect of initialization has weakened.
3.5. Parametric Comparison and Physical Interpretation
The default and optimal parameters were normalized based on the parameter ranges listed in Table 2
. The normalized results of the default and optimal parameters are shown in Figure 16
. The variations for all the optimal parameters are inconsistent. For the parameters znt_zf
(scaling related to surface roughness), karman
(von Kármán constant), and pe
(scaling related to entrainment mass flux rate), their optimal values decreased compared with their default values. However, the opposite situation occurred for the parameters pd
(scaling related to downdraft mass flux rate), ph
(starting height of downdraft above updraft source layer, and pfac
(profile shape exponent of the momentum diffusivity coefficient).
To further demonstrate the relation between model outputs and the sensitive parameters, the analyses on how the variances of the sensitive parameters affect the model performances were also conducted. Based on observations and the previous 178 model simulations from optimization experiment, the response of three variables (i.e., precipitation, 10-m wind, and track) to six sensitive parameters were obtained, and the results are shown in Figure 17
. Here, the range of each parameter was equally divided into 10 bins, and the red curves represented an average of the simulation errors at each bin. The simulation error with default parameters was marked as a red cross. The first and second lines demonstrated the variances of the precipitation and 10-m wind simulation errors as parameter value increased respectively. The variances of the track simulation errors were represented in the third lines.
For znt_zf parameter, the default value was close to the optimal value for the precipitation and 10-m wind simulations, but it was still be found that slightly decreasing the default value would improve the precipitation and 10-m wind simulations. The znt_zf was insensitive to track simulation, and therefore it was difficult to improve the track simulation by adjusting znt_zf value. For karman parameter, the default value in the precipitation and 10-m wind simulations was significantly higher than the optimal value, and an apparent upward trend existed between them. Therefore, decreasing the default value of karman could improve the WRF simulations on precipitation and 10-m wind. Like znt_zf, karman was insensitive to track simulation. For pd parameter, the default value was lower than the optimal value for the simulations of precipitation, 10-m wind, and track. Therefore, increasing the default value would improve the respective default simulations.
For pe parameter, the default value was larger than the optimal value for three variables, and the significant upward trend existed between the input parameter and model output errors, so the simulations for three variables could be improved by decreasing the default value. For ph parameter, there was an obvious downward trend for the 10-m wind and track simulation errors as the parameter value increased; however, a slightly upward trend existed for precipitation simulation errors. Therefore, increasing the default value would improve the 10-m wind and track simulations, and the opposite situation occurred in precipitation simulation. For pfac parameter, the default value was lower than the optimal value for three variables, and the downward trend existed between the input parameter and model output errors. Therefore, increasing the default value will improve three variable simulations.
Previous analyses have found (e.g., Figure 7
and Figure 8
) that overall, the default simulations overestimated (underestimated) the amount of precipitation (10-m wind), whereas the optimal simulations partially rectified the overestimation (underestimation). This can be interpreted using the physical meanings of the parameter perturbations. Lower values of znt_zf
mean that a decreased roughness length exists in the surface layer, and therefore the simulated wind speed will be increased. The 10-m wind simulation is only sensitive to znt_zf
parameter (i.e., P3), and therefore the optimal znt_zf
values work mainly on wind simulations. A lower karman
value can reduce the momentum exchange coefficient (drag coefficient) at the near-surface layer, and therefore the upper 10-m wind speed increases. For precipitation simulation, a smaller karman
value meant a smaller enthalpy exchange coefficient at the near-surface level, which caused less water vapor to rise into the atmosphere, leading to less precipitation.
, and ph
are the parameters from the cumulus convection scheme, and therefore it is reasonable that precipitation is sensitive to them, as shown in Figure 2
. A larger downdraft mass flux rate (larger pd
) leads to more condensed water evaporation and further to less precipitation. A higher downdraft-flux starting height (larger ph
) will bring more downdraft flow, leading to more condensed water evaporation and less precipitation. A lower entrainment rate (smaller pe
) will reduce the mixed amount of the updraft from cold environmental air, leading to less condensed water production and therefore less precipitation. With lower pe
, less cold air is involved in the updraft, prompting further development of convection. Correspondingly, the wind speed is increased.
has a positive effect on the momentum diffusion intensity of turbulent eddies in the planetary boundary layer. When pfac
increases, the vertical momentum and heat diffusion intensity are strengthened, inducing higher wind speed. However, the increase in heat diffusion intensity makes more water vapor from the ground transfer upward, leading to more precipitation. It is noteworthy that the increase of pfac
parameter improved the low bias of 10-m wind simulation, but had a negative improvement to precipitation simulation. However, the total objective error combined precipitation and 10-m wind evaluations was finally reduced as shown in Figure 4
. It can be inferred that the 10-m wind adjustment is more discriminating in terms of pfac
parameters than precipitation, and pfac
has an antagonistic effect on precipitation simulation compared with pd