Rainfall Simulations of Typhoon Morakot with Controlled Translation Speed Based on EnKF Data Assimilation

Typhoon Morakot produced record-breaking accumulated rainfall over southern Taiwan in August 2009. The combination of several factors resulted in this extreme weather event: the steep terrain in Taiwan, the prevailing south-westerly flow in the monsoon trough, Typhoon Goni over the northern South China Sea, and the slow translation speed of Morakot itself over Taiwan. In this study, the influence of the translation speed is particularly emphasized. Based on the EnKF data assimilation, an innovative method is applied to perform ensemble simulations with several designated translation speeds of Morakot using the WRF model. Thus the influence of the translation speed on the amount of accumulated rainfall over Taiwan can be quantitatively evaluated. In the control simulation with observed translation speed, the maximum amount and geographic pattern of accumulated rainfall during the landfall period of Morakot are generally consistent with the observations, though the detailed overall distributions of accumulated rainfall is mostly underestimated, resulting in the low bias of the frequency distribution of the accumulated rainfall. In a simulation with nearly-doubled translation speed of Morakot, the maximum accumulated rainfall is decreased by 33% than that in the control simulation, while the rainfall distribution over Taiwan remains similar. In addition, the 28 ensemble members can further provide additional information in terms of their spread and other statistics. The results from ensemble members reveal the usefulness of ensemble simulations for the quantitative precipitation forecast.


Introduction
Tropical cyclone (TC) is one of the most devastating weather systems, and one of the most important severe weather events in Taiwan. The rainfall associated with TCs is an important component of water resources in Taiwan. Taking year 2009 as an example, cold front systems in spring, Mei-Yu systems, and afternoon thunderstorms during that summer did not bring enough rainfall to Taiwan. As a result, the government and the residents of Taiwan started to restrain water usage because of low water storage levels around Taiwan. Nevertheless, abundant rainfall came unexpectedly with Typhoon Morakot on 6 to 9 August. It not only filled up all water reservoirs in three days but also led to severe mudslides and flooding, resulting in more than 700 casualties and enormous economic damage. To mitigate this damage, improving TC forecasts, including not only the tracks, but also the rainfall amount and distribution, is one of the most urgent and challenging tasks regarding TC research and forecasting in Taiwan.
The most important characteristic of Morakot is its astoundingly heavy precipitation.
Heavy rainfall over southern Taiwan usually occurred in an environment with prevailing moisture-rich south-westerly flow, in which mesoscale disturbances are embedded (Chen and Chen 2003). The steep terrain also plays a key role in substantially increasing the total rainfall amounts over Taiwan (Wu and Kuo 1999;Wu 2001;Wu et al. 2002). There have been a series of papers aiming to address the scientific and forecasting issues related to Morakot after the event. Based on a synoptic analysis and various types of observation data including satellite and radar images, the torrential rainfall in the south-western Taiwan in three consecutive days was found to be closely related to huge continuouslydeveloping convective rainbands over the Taiwan Strait, which can be partly attributed to the convergence of northerly wind associated with TC outer circulation and the southwesterly monsoon flow Jou et al. 2010;Wang et al. 2010). From a broader perspective, Hong et al. (2010) showed that Morakot was embedded in a monsoon circulation of different time scales which provided a favorable environment.
The record-breaking rainfall was the result primarily from the typhoon vortex and the submonthly large-scale cyclonic disturbance. The influence of the quasi-biweekly-scale gyre and low-frequency monsoon flows on the slow movement and asymmetric precipitation of Morakot was also emphasized in observational ) and modeling   On the other hand, high-resolution simulation using mesoscale models, such as the fifth-generation Pennsylvania State University-National Center for Atmospheric Research Mesoscale Model (MM5) and Weather Research and Forecasting (WRF) model, can further improve our understanding of the mechanism of this heavy rainfall event. The rainfall pattern over Taiwan can be reasonably simulated in these models, provided that the model and terrain resolution is sufficient and the TC track in the model doesn't excessively deviate from the observation (Wu et al. 2002(Wu et al. , 2010aGe et al. 2010;Zhang et al. 2010;Tao et al. 2011;Hendricks et al. 2011). Better model forecasts on the track and intensity of Morakot can be obtained with appropriate implementation of various TC initialization schemes (Nguyen and Chen 2011;Huang et al. 2011). The roles of the terrain and other typhoon, Goni, have been discussed in these studies. The peak value of the accumulated rainfall will decrease significantly and the rainfall pattern will shift eastward if a reduced terrain height over the island of Taiwan is used in the model (Ge et al. 2010;Huang et al. 2011). Typhoon Goni, circling around the northern South China Sea during the same period as Morakot, also played an important role in enhancing the wind speed of the southwesterly flow as well as elevating the moisture content in such flow. Therefore, the heavy rainfall in southern Taiwan was further enhanced (Huang et al. 2011;Nguyen and Chen 2011;Jou et al. 2010).
The slow translation speed of Morakot is also a critical factor leading to the significant accumulated rainfall. The slower a TC moves, the longer it influences Taiwan.
As a result, the duration of rainfall lasts longer, and the total accumulated precipitation amounts to a higher level. Lin et al. (2001) pointed out that the slow movement of a convective system is a common ingredient contributing to heavy orographic rainfall.
Morakot is a case in point and highlights the importance of translation speed of a landfalling TC. However, the lack of ability to control TC motion in numerical model hinders us from examining this factor more quantitatively with numerical simulations.
At this point, directly assimilating the tracks of a hurricane-like vortex into the model based on the ensemble Kalman Filter (EnKF; Evensen 1994Evensen , 2003) is a possible method to address this issue. This method has been tested and examined using a 2dimentional barotropic model (Chen and Snyder 2007) and a full-physics high-resolution mesoscale model (i.e., WRF model; Torn and Hakim 2009;Wu et al. 2010b). Based on the framework used by Wu et al. (2010b), we design a series of numerical experiments with different TC translation speeds to quantitatively assess its impact on the accumulated rainfall amount associated with Morakot. The innovative method to control TC motion in the mesoscale model is the focus of this short article, and the advantages of ensemble forecast for quantitative precipitation forecast (QPF) are also discussed in this study.
The lifecycle of Typhoon Morakot and its influence on Taiwan are briefly reviewed in section 2. Section 3 describes the methodology and experimental design. Section 4 shows the results of ensemble simulation and the rainfall characteristics in terms of two different TC translation speeds. Section 5 presents several concluding remarks.

Overview of Typhoon Morakot
In early August 2009, the monsoon trough over the western North Pacific was relatively active. Typhoon Morakot, the dominating feature in this monsoon trough, formed to the east of Taiwan at 0000 UTC 03 August. It then headed steadily westward and made landfall at the central east coast of Taiwan at 1600 UTC 07 August, with a maintained intensity around category 1 to 2. At the same time, another weaker typhoon, Goni, formed at 1200 UTC 03 August, circled cyclonically over the Hainan Island region.
There seems to be a Fujiwhara effect (Lander and Holland, 1993;Wu et al. 2003) between these two typhoons. Goni eventually weakened mostly due to the intense environmental vertical shear over the northern South China Sea. In such a period, Morakot and Goni, associated with a third tropical depression (the predecessor vortex of Typhoon Etau), composed a broader monsoon gyre (Lander 1994) with a zonal span of more than 4000 km (Fig. 1).
After Morakot made landfall in Taiwan, its translation speed decreased significantly from more than 20 km h -1 to around 10 km h -1 . This fact resulted in a prolonged influence time in Taiwan, and the heavy rainfall thus lasted for more than 4 days. Figure   2 shows the observed 4-day (0000 UTC 06 August -0000 UTC 10 August) accumulated rainfall from the rain gauge network. The heavy rainfall covered most of the mountain area and south-western plain of Taiwan, and amounted to a maximum value of around 3000 mm during these four days on the south-western slope of the Central Mountain Range (CMR) of Taiwan. In the most intense rainfall period selected in this study (1200 UTC 07 August -1800 UTC 08 August), Morakot produced a maximum accumulated rainfall of 1609 mm at Wei Liao Shan station within 30 hours (Fig. 6d).

Methodology a. Model settings and EnKF data assimilation system
The ensemble Kalman filter (EnKF) first proposed by Evensen (1994) is a powerful and efficient method to optimally estimate model state from the background and observations with the flow-dependent background error statistics. In recent years, it has been extensively adopted in atmospheric numerical models for the use of research in various topics (Snyder and Zhang 2003;Torn and Hakim 2009;Zhang et al. 2009) and of operational weather prediction systems (Szunyogh et al. 2008;Whitaker et al. 2008;Torn and Hakim 2008). In addition, it has been shown that the performance of EnKF is generally better than the 3-dimensional variational (3D-VAR) data assimilation scheme and is comparable to the 4-dimensional variation (4D-VAR) method (Anderson et al. 2009). Wu et al. (2010b) used the ensemble square root filter (EnSRF; Whitaker and Hamill 2002) to assimilate TC center position, storm motion vector, and axisymmetric surface wind profile directly into the model, by constructing these three newly proposed observation operators for TCs. They employed this method to initialize a high-resolution inner-core structure of Typhoon Fung-wong (2008). In addition, a cycling run has been performed to obtain a reasonable analysis field of Typhoon Sinlaku (2008) spanning the whole eyewall replacement cycle . The same WRF-based EnKF data assimilation system is used in this study. Detailed discussions of this method are presented in Wu et al. (2010b). localization is set at 800 km also based on previous tests (Wu et al. 2010b). The assimilation of axisymmetric surface wind profile is suspended at 1200 UTC 07 August when its circulation is very close to the Taiwan terrain, because the interaction between Morakot and the Taiwan terrain should result in a highly-asymmetric surface wind structure and the surface friction also reduces the 10-m surface wind considerably in the model. This situation does not meet the original idea of designing this special TC observational parameter. While the conventional observation data could be included in the assimilation to improve the analysis of environmental field and lead to better TC simulations ), they are not assimilated into the model in this study. As stated above, the 3-day simulation from 0000 UTC 06 August to 0000 UTC 09 August is regarded as the control (CTRL) experiment.

b. Controlled TC track based on EnKF
In addition to the CTRL experiment, to quantitatively evaluate the impact on accumulated rainfall associated with the translation speed of Morakot, other experiments, FAST and SLOW, are initiated at 1200 UTC 07 August with hypothetical faster and slower tracks, respectively. The track of FAST is artificially constructed by skipping every two center position data after 1200 UTC 07 August, i.e., the center position at 1800 UTC 07 August is replaced by that originally at 0000 UTC 08 August, and the center position at 0000 UTC 08 August is replaced by that originally at 1200 UTC 08 August, and so on. On the other hand, the track of SLOW is constructed by assigning the delayed time to each center position data so that the translation speed is halved after 1200 UTC 07 August. Then, the hypothetical fast-moving or slow-moving tracks are assimilated into the model based on the aforementioned technique in order to force the simulated Morakot move with doubled or halved speed than that of observation. In the following sections of this study, only the results from CTRL and FAST (not SLOW) experiments will be analyzed and compared because the TC translation speed in SLOW is unrealistic slow while that in FAST is, in contrast, falling within the common value of landfalling TCs in Taiwan.

a. The resulting tracks of each experiment
As shown in Fig UTC 07 August is about twice as fast as the observation (Fig. 4), which is consistent with the original purpose of the EnKF data assimilation. Note that through the rapid update cycle of TC center and motion vector assimilation, the evolution of those analyses or short-term (1 hour) model forecasts does not only come from the model dynamics, but also the artificial modification introduced in each analysis step. As a result, the Morakot simulation can move much faster than the observation.

b. Comparison of accumulated rainfalls
The accumulated rainfall amounts in the hourly update-cycle simulations are computed with the summation of the rainfall amounts in each 1-hour forecast. To more precisely compare the results between each experiment with different TC translation speeds, all the following comparisons of their accumulated rainfall are made based on the time intervals in which the simulated TCs pass through the similar section of track, namely, the whole landfall period in addition to roughly 100-km passage over the ocean at the beginning and end (Fig. 4). The corresponding times are 1200 UTC 07 August to 1800 UTC 08 August (30 hours; enhanced thick long dashed line segment in Fig. 4) in CTRL, 1200 UTC 07 August to 0600 UTC 08 August (18 hours; enhanced thick short dashed line segment in Fig. 4) in FAST, and 1200 UTC 07 August to 0000 UTC 10 August (60 hours; not shown) in SLOW, respectively. Note that although the selected periods are different in order to match up the movements of TCs, the lack of the latter 12h interval in FAST has no significant influence on the accumulated rainfall amount (figure not shown). It is because the Morakot simulation in FAST has moved far away from the island of Taiwan and has made landfall in China (Fig. 4). The sequential 6hourly-averaged translation speeds of Morakot within the periods for comparison are listed in Table 1. The averaged translation speed during this period of JTWC, CTRL, FAST, and SLOW are 8.7, 12.0, 18.6, and 6.2 km h -1 , respectively.
The simulated rainfall amounts in D3 with 3.33-km resolution (ensemble mean) are shown in Fig. 6. Compared with the observation from the rain gauge network in Taiwan ( Fig. 6d) (Ge et al. 2010;Zhang et al. 2010;Lin et al. 2010;Nguyen and Chen 2011;Huang et al. 2011;Tao et al. 2011) also showed that these mesoscale models have the ability to produce extreme rainfall amounts comparable to the observation. However, it is found that coverage of the low-to medium-rainfall area in the simulation is narrower than the observation, especially in the south-western plain and central-northern mountain area in Taiwan. The extreme rainfall is thus restricted to the north-south elongated area located at the southern CMR and slightly southward to where it was observed. This rainfall characteristic can also be found in some independent studies using the WRF model with similar experimental settings and resolution Tao et al. 2011;Huang et al. 2011  Although the rainfall pattern remains the same in FAST, the maximum value only reaches 1207 mm within the corresponding period (Table 1), reflecting the influence of accumulated rainfall brought about by the translation speed of Morakot. The difference in accumulated rainfall amount between these two experiments (CTRL minus FAST) is also shown in Fig. 6e. Clearly, different translation speeds of TCs lead to a significant difference in the accumulated rainfall over Taiwan. In all, a 55% increase (from 12.0 to 18.6 km h -1 ) of the translation speed of Typhoon Morakot leads to a 33% reduction (from 1800 to 1207 mm) in the maximum accumulated rainfall over Taiwan. In addition, the accumulated rainfall in SLOW can further verify the important role of translation speed of TCs in the extreme rainfall event. The maximum accumulated rainfall amount reaches 2259 mm when the simulated TC passes Taiwan at a fairly slow pace (Fig. 6c). It is worth pointing out that in addition to the increasing maximum rainfall amount, the lowto medium-rainfall area is notably broadened in SLOW, especially around the two secondary local maxima in the central-western (Ali Shan) and north-western (Hsueh Shan) mountain areas. The overall rainfall pattern turns out to be more similar to the observation though the translation speed of simulated TC in SLOW is less than the observed. This result is likely attributed to the enhanced accumulated effect due to the longer influence time of Morakot over Taiwan. Meanwhile, it is worth noting that the model physics used in this study is able to depict the rainfall mechanism and reproduce the precipitation pattern although the total rainfall amount may not be in accord with the observation.

c. Ensemble spread in rainfall simulations
The value of the ensemble is not limited to performing the EnKF data assimilation, but it also provides additional information of the spread and other statistics over the ensemble members. The ensemble tracks and ensemble rainfall distributions in CTRL and FAST are shown in Fig. 7 to Fig. 9. As mentioned in Section 3, only D1 and D2 are used during the ensemble integration and data assimilation because of the limitation in computational resources. Therefore, these figures here are plotted using the finest available domain, D2, with 10-km resolution. It is found that the ensemble TC tracks in both CTRL (Fig. 7a) and FAST (Fig. 7b) keep a certain spread during the landfall period.
In some members, the Morakot simulation passes the northern-most tip of Taiwan, while it crosses the main part of CMR in some other members. This dataset provides a unique opportunity to explore the rainfall characteristics with respect to the deviation of TC tracks. The accumulated rainfalls from 1200 UTC 07 August to 1800 UTC 08 August of all ensemble members in CTRL are plotted in Fig. 8. The ensemble member displays some diverse rainfall patterns and amounts. Generally speaking, all members are able to simulate heavy rainfall on the windward side of the southern CMR. Nevertheless, the maximum value of the rainfall ranges from 456 (member # 28) to 1081 (member # 20) mm in spite of minor differences in TC tracks (Fig. 7a). The result of variant rainfall amounts is consistent with Zhang et al. (2010), although they obtained more diverse rainfall patterns as a result of the much larger spread of TC tracks in their free-run ensemble forecasts without data assimilation. This fact highlights the uncertainty and difficulty regarding the QPF of TCs, while implying the potential of the probabilistic forecasts. Note that the reduction of the maximum rainfall here compared with Fig. 6 is mainly due to the coarser resolution of D2. This issue will be discussed in the next subsection. Moreover, even with the coarser 10-km grids, the investigation of rainfall patterns would still be helpful, and some members exhibit a pattern close to that which was observed (e.g., member #3, #13, #19). Regarding the FAST experiment ( Fig. 9), the overall characteristics remain the same, while the maximum rainfall amounts are less than those in CTRL, ranging from 315 (member # 28) to 865 (member # 15) mm.

d. Rainfall distribution with respect to Taiwan terrain and model resolution
The cumulative frequency of the total rainfall in D3 based on the data points over the island of Taiwan is calculated and shown in Fig. 10, as well as that for the rain gauge observation. It is clear that the area of medium rainfall in observation is much broader than those areas in both CTRL and FAST simulations as mentioned in the previous subsection. Also, rainfall distribution in FAST is more scattered with smaller accumulated amount than that in CTRL, especially at the high-rainfall end. For example, the area with a rainfall amount higher than 500 mm in FAST is nearly half the size of that in CTRL. In addition, it is interesting that in SLOW the cumulative frequency is closest to the observation, though there are obviously overestimated accumulative frequencies at both low-and high-rainfall ends. It is consistent with what we found in Fig. 6 where the rainfall pattern in SLOW is much broader than those in CTRL and FAST. Again, this fact highlights the critical role of TC translation speed in the extreme rainfall event.
Furthermore, rainfall distribution with respect to the Taiwan terrain is also presented.
All data points over the island are categorized based on their terrain height. The average accumulated rainfall of each 500-m height interval in each domain of each experiment is shown in Fig. 11. For the results from D3 with 3.33-km resolution (solid lines in Fig. 11), the rainfall amount increases with the increase of terrain height from 0 to 1500 meters, and then it is saturated over the high mountain area with about 300-mm average rainfall in CTRL and 220-mm average rainfall in FAST. This distribution is consistent with the results from independent simulations in Tao et al. (2011), which also concluded that most of the surface rainfall occurs over terrain above 1500 meters.
Meanwhile, a significant reduction of the average rainfall is found when the results from D2 are discussed (dashed lines in Fig. 11). This reduction is mainly attributed to the insufficient resolution of model variables, especially the terrain height, which cannot properly resolve the precipitation process associated with the topography-enhanced vertical motion (Wu et al. 2002). As shown in Figs. 12a, b, the insufficient resolution in D2 leads to a poor representation of the Taiwan terrain. It also fails to exhibit the elevations of the two main peaks of the island of Taiwan, which are exactly 3886 and 3952 meters at their maximum elevation in northern and southern Taiwan, respectively.
Also, it is interesting that the terrain height dependency of accumulated rainfall in 10-kmresolution domains is much different from that in 3.33-km-resolution domains. The average rainfall amount in areas with a lower terrain height is surprisingly larger than that in high mountain areas. A careful examination of the spatial distribution of accumulated rainfall in each domain (Figs. 6a, b; Fig. 8; Fig. 9) indicates that the rainfall amount in D2 is not only less than that in D3, but its pattern also diverts slightly to the southwest of that in D3, further toward the south-western plain of Taiwan and the Taiwan Strait. An additional experiment called CTRL_lowT is conducted to highlight the importance of terrain resolution. All settings in CTRL_lowT are the same as those in CTRL, except the model terrain of its D3, in which the terrain resolution is degraded to the same resolution as D2 (10 km), while the other model variables maintain the fine resolution of 3.33 km.
The overall terrain height dependency of accumulated rainfall in D3 of CTRL_lowT (dotted line in Fig. 11) is rather similar to that of D2 in CTRL (dashed line with square marks in Fig. 11), except that the increasing trend with terrain below 1000 meters is much closer to that in the 3.33-km-resolution domain (D3) of CTRL (solid line with triangle marks in Fig. 11). In addition, the comparison between the results from CTRL and CTRL_lowT is also made by directly subtracting the accumulated rainfall amount in CTRL_lowT from that in CTRL (Fig. 12c). The geographic shift in rainfall patterns can be clearly observed in Fig. 12c as the simulation with finer terrain resolution (CTRL) tends to produce more rainfall toward the mountain region than that with coarser terrain resolution. The increment can be up to 600 mm in some particular areas. In all, the terrain resolution can affect not only the accumulated rainfall amount associated with TCs, but also the rainfall distribution with respect to the terrain. The result from CTRL_lowT further emphasizes the importance of terrain resolution in numerical models to better simulate the topography-enhanced heavy precipitation as described in Wu et al. (2002).

Concluding Remarks
Typhoon Thus the center position and motion vector taken from these three tracks are directly assimilated into WRF model in the CTRL, FAST and SLOW experiments, respectively.
The accumulated rainfall pattern during the landfall period of Morakot in CTRL generally matches the observations, with a maximum rainfall amount of 1800 mm located in the windward sloping areas in southern Taiwan, although the coverage of the low-to medium-rainfall area in the simulation is narrower than the observation. Regarding the FAST experiment, the 55% increase of the translation speed of simulated Morakot than that in CTRL leads to a 33% reduction in the maximum accumulated rainfall within the similar rainfall patterns over Taiwan. In contrast, the accumulated rainfall amount increases remarkably in SLOW with a rather slow translation speed of the simulated TC.
This simple study demonstrates the capability of the EnKF assimilation to examine some sensitivities related to TC movements by controlling TC translation speed directly.
On the basis of the ensemble data assimilation scheme, the 28 ensemble members         UTC 07 August to 1800 UTC 08 August in CTRL. Figure 9. Same as in Fig. 8, but for the FAST experiment from 1200 UTC 07 August to 0600 UTC 08 August.         . Same as in Fig. 8, but for the FAST experiment from 1200 UTC 07 August to 0600 UTC 08 August % mm Figure 10. The cumulative frequency of the total rainfall from 1200 UTC 07 August to 1800 UTC 08 August in CTRL (square marks), from 1200 UTC 07 August to 0600 UTC 08 August in FAST (triangle marks), and from 1200 UTC 07 August to 0000 UTC 10 August in SLOW (diamond marks) based on the data points over the island of Taiwan in domain 3. The observed cumulative frequency calculated from rain gauge observations in the same time interval as CTRL is also shown with dashed line and circle marks.