1. Introduction
Taiwan is a relatively small subtropical island (400 km long and 150 km wide) and has regions extending above 3000 m [Central Mountain Range (CMR)] within a distance of 50 km (Fig. 1). Typhoons are considered the most critical of all natural disasters that occur in Taiwan even if no landfall occurs. In the past two decades, Taiwan endured an annual average of 3.7 typhoons. These storms, which are associated with heavy rainfall and strong winds, cause serious agricultural damage and the loss of human lives (Wu and Kuo 1999). In particular, the continuous torrential rainfall associated with typhoons often causes flooding, landslides, and debris flows, leading to substantial damage in Taiwan (Lee et al. 1997, 2006). For example, 2855 mm of rainfall was measured over a 4-day period during Typhoon Morakot (2009), which triggered massive mudslides and severe flooding, resulting in 619 deaths and 76 missing persons (Wu and Yang 2011). Thus, it is extremely important to have reliable quantitative precipitation forecast (QPF) products for the prevention and mitigation of typhoon-related disasters in Taiwan.
The terrain of Taiwan (m; shaded) with the rain gauge station locations (dots).
Citation: Weather and Forecasting 30, 1; 10.1175/WAF-D-14-00037.1
However, accurate predictions of typhoon precipitation in Taiwan are challenging, primarily because of the island’s high mountain range. Significant mesoscale variations caused by orographic effects (Wang 1992)—including track deflection (Chang 1982; Yeh and Elsberry 1993a,b; Lin et al. 1999, 2002; Jian and Wu 2008); secondary low development (Chang 1982; Chan 1984); intensity changes; and mesoscale changes in pressure, wind, and precipitation (Chang et al. 1993; Chu et al. 1977; Kuo and Wang 1997; Wu et al. 2002)—are common, contributing to the challenge of providing accurate typhoon QPFs in Taiwan. Recently, QPF accuracy from numerical models has progressed as a result of improvements in data assimilation (e.g., Huang et al. 2005; Hsiao et al. 2009, 2010), model physical parameterization, and model resolution (Wu et al. 2002, 2009; Huang et al. 2011; Tao et al. 2011). However, substantial typhoon QPF improvements are necessary because of the unavoidable uncertainty in the track forecast. If a model is able to provide an acceptable track prediction for a particular case, the model QPF provides valuable forecast guidance. If the model track error is larger, the model QPFs are less valuable.
A statistical approach based on the close relation between the observed rainfall and typhoon position [e.g., Yeh (2002) and the typhoon rainfall climatology model described by Lee et al. (2006)] provides an important reference for operational typhoon rainfall forecasts at the Central Weather Bureau (CWB) in Taiwan. The basic consideration of the typhoon rainfall climatology model is that typhoon rainfall is highly correlated with the typhoon position in Taiwan. Therefore, for a given forecasted typhoon position, the typhoon QPFs can be obtained from the climatology of the historical typhoon position and the associated rainfall observations. This close relation between the typhoon position and rainfall implies that the terrain lifting of the typhoon circulation plays a major role in determining the rainfall amount associated with the typhoon, resulting in a phase-lock effect between the typhoon rainfall pattern and the terrain. For example, Wu et al. (2002) found that the CMR played an important role in modifying the rainfall distribution during Typhoon Herb (1996). Lin et al. (2002) showed that the rainfall from Typhoon Bilis (2000) that occurred near mountainous topography was primarily controlled by orographic forcing rather than typhoon rainbands. Moreover, Chien and Kuo (2011) found that the rainfall amount in Taiwan was nearly proportional to the reciprocal of the typhoon translation speed rather than the typhoon intensity.
In general, the typhoon rainfall climatology model is able to provide reasonable estimates of both the pattern and quantity of rainfall. However, a climatology model can only provide a statistical mean rainfall estimate. Therefore, rainfall forecasts for specific cases, such as systems with active or stationary typhoon rainbands, and the rainfall amount associated with a weakening or smaller system are difficult to produce with a climatology model. In particular, climatology models are deficient for cases with strong atmospheric circulations, such as the torrential rainfall caused by the enhanced northeasterly monsoon during Typhoon Babs (1998) (Wu et al. 2009) and the abundant water vapor supplied by the southwesterly monsoon flow during Typhoon Morakot (2009) (Chien and Kuo 2011). Finally, limited historical cases restrict the applicability of climatology models as a result of a lack of sample sizes.
Recently, an ensemble prediction system (EPS) was applied to study typhoon rainfall events over the Taiwan area. Zhang et al. (2010) demonstrated that a high-resolution, convection-permitting, mesoscale ensemble prediction system could produce valuable probability forecast information. Fang et al. (2011) found that significant variability existed in the storm track, timing, landfall location, and storm intensity of typhoons, which subsequently increased the rainfall variability. Their analysis also showed that Taiwan’s topography substantially increased the variability of rainfall prediction. Xie and Zhang (2012) found that a good rainfall forecast foremost requires a good track forecast. The dependence of the accuracy of the quantitative precipitation forecast on the track forecast is clearly evident from the high correlation between the normalized precipitation error and the storm’s center position error among different ensemble members averaged from forecasts before and after landfall time. Hsiao et al. (2013) demonstrated that the coupled ensemble–hydrometeorological method was able to provide accurate rainfall forecasts, useful probability information, and runoff forecasts over mountainous watersheds during Typhoon Nanmadol (2011). The success of their rainfall and runoff forecasts is due to the accurate track forecasts. Overall, the high-resolution EPS has the ability to capture the variability and accuracy of the typhoon rainfall forecasts. However, how to best handle the track forecast uncertainty in an EPS plays a key role in developing the ensemble QPFs.
In the present paper, we incorporate the concept of the typhoon rainfall climatology model. Nevertheless, the model QPFs from an EPS are used instead of the historical rainfall observations. The so-called ensemble typhoon QPF (ETQPF) model is described in section 2. Descriptions of the experimental design and case study are provided in sections 3 and 4. Finally, a summary and concluding discussion are presented in section 5.
2. The ensemble typhoon QPF model
The ETQPF model is based on the concept of the climatology model, but using the QPFs from an ensemble prediction system instead of the historical rainfall observations. Climatology models are successful because of the close relationship between typhoon rainfall and position. However, it is difficult to develop accurate typhoon QPFs for outlier cases and cases with strong environmental interactions. Moreover, the QPFs from deterministic models with high-resolution often provide reasonable results if the track forecast errors are handled properly (Wu et al. 2002; Xie and Zhang 2012). In particular, models can effectively represent the effects of the Taiwan terrain on the evolution of the typhoon structure, and the interaction between the environment and typhoon circulation. However, the greatest weakness of model QPFs stems from the uncertainty of the track forecast.
In this paper, the ETQPF model simply incorporates the concept of the climatology model. Nevertheless, the model QPFs from an EPS are used instead of the historical rainfall observations. As shown in Fig. 2, the 3-h predicted typhoon locations from the EPS span a wide range. Each predicted typhoon location is associated with a 3-h accumulated model QPF. For a given typhoon track (e.g., the official or consensus track forecast), the cases along the track within a certain radius can be screened out (Fig. 2). By averaging over the selected cases, obtaining the QPF estimate (i.e., the ETQPF rainfall) along the given track is straightforward.
The predicted typhoon location distribution (black dots) in 3-h intervals from the EPS. Each predicted typhoon location is associated with a 3-h accumulated model QPF; an example is shown in the top-right corner. The red line and black circle are the given typhoon track with 3-h intervals and a radius of 30 km centered at each typhoon position, respectively.
Citation: Weather and Forecasting 30, 1; 10.1175/WAF-D-14-00037.1
As shown in Fig. 2, the ETQPF model requires enough ensemble spread in the predicted typhoons to cover the given typhoon track. Without this spread, the ETQPF model will not work. Moreover, because of the phase-lock effect, the typhoon QPFs over Taiwan are sensitive to the typhoon location, but not the model initial and validation times. Therefore, “real time” predictions are not critical. Instead, by including the ensemble QPFs from lag predictions and coordinating with the communities or other institutions (which is generally difficult to accomplish and still meet the operational deadline), the ensemble spread is improved. Moreover, this work helps promote the ETQPF model for operational typhoon rainfall forecasts.
Furthermore, certain criteria can be applied to further screen the selected cases. These criteria could include, for example, the screen radius, typhoon propagation speed, typhoon size or strength, vertical wind shear, forecast hour, and the particular model. Following the screening procedure, the ensemble cases can be further selected according to speculations about the future or subjective expectations. Therefore, more ensembles are expected to further increase the value of the ETQPF model.
3. Cases and experimental design
a. Typhoon cases
Six typhoons (as listed in Table 2, described in greater detail below) were used to evaluate the ETQPF model performance. Typhoons Fanapi (2010) and Megi (2010) were adopted for the detailed analysis. The general ETQPF rainfall forecast performance was demonstrated by the other four typhoons in 2013, Soulik, Trami, Usagi, and Fitow.
Typhoon Fanapi moved westward and made landfall south of Hualien at approximately 0040 UTC 19 September 2010, exiting Taiwan near Tainan at 2300 UTC on the same day (Fig. 3a). Before landfall, Fanapi reached a maximum intensity (with regard to sea level pressure) of approximately 940 hPa. Figure 3b shows the 24-h accumulated rainfall from 1800 UTC 18 September to 1800 UTC 19 September. The figure also shows that the rainfall over the eastern CMR was primarily due to the terrain lifting effect during landfall. The rainfall distribution over the southwestern plain of Taiwan was attributed to the nearly stationary east–west-oriented convective line (Fig. 4a). The convective cells were further enhanced by the high terrain in southern Taiwan, resulting in torrential rainfall up to 1127 mm (24 h)−1 over the mountainous regions. In addition, the radar reflectivity shows that the convection was suppressed over the northern part of the typhoon because of the blocking by the CMR and the dry air intrusion (21°C dewpoint temperature at Penghu station) from the northerly wind component over the Taiwan Strait (Fig. 4b). These phenomena caused low rainfall over northwestern Taiwan after landfall.
(a) Best track of Typhoon Fanapi (2010) issued by the CWB at 6-h intervals. Purple, blue, green, and red indicate the estimated max wind speed ranges <17.2, 17.2–32.6, 32.7–50.9, and >51.0 m s−1, respectively. The black circle indicates the typhoon position during the rainfall accumulation period in (b). (b) The observed 24-h accumulated rainfall (mm; from 1800 UTC 18 Sep to 1800 UTC 19 Sep 2010) during the passage of Typhoon Fanapi.
Citation: Weather and Forecasting 30, 1; 10.1175/WAF-D-14-00037.1
(a) The CWB composite radar reflectivity (dBZ; color shading) for Typhoon Fanapi at 0800 UTC 19 Sep 2010. (b) The surface streamline (dashed line), surface wind speed (m s−1; solid line), and station plot at 0800 UTC 19 Sep 2010. The Penghu station is denoted by the star symbol.
Citation: Weather and Forecasting 30, 1; 10.1175/WAF-D-14-00037.1
Unlike Fanapi, Typhoon Megi (Fig. 5a) moved westward along the southern edge of a subtropical ridge and reached a maximum intensity (with regard to the sea level pressure) of 895 hPa before making landfall in the Philippines at 0000 UTC 18 October 2010. After passing the Philippines, Megi weakened and turned northward into the South China Sea. However, even though Megi remained over the South China Sea and far from Taiwan (up to hundreds of kilometers), the outer circulation of Typhoon Megi from 20 to 21 October strengthened the northeasterly monsoon and produced a maximum 24-h accumulated rainfall in northeastern Taiwan of 928.8 mm between 1200 UTC 20 October and 1200 UTC 21 October 2010 (Fig. 5b). This distant rainfall was primarily caused by terrain blocking and lifting effects, which were enhanced by the northeasterly monsoon over northeastern Taiwan. This rainfall distribution pattern is typical when the northeasterly monsoon interacts with wintertime tropical cyclones over the South China Sea (Cheung et al. 2008; Wu et al. 2009).
(a) As in Fig. 3a, but for Typhoon Megi (2010). (b) The 24-h accumulated rainfall (mm) from 1200 UTC 20 Oct to 1200 UTC 21 Oct 2010.
Citation: Weather and Forecasting 30, 1; 10.1175/WAF-D-14-00037.1
b. The ensemble prediction system and observations
Two ensemble prediction systems based on the Weather Research and Forecasting (WRF) Model (Skamarock et al. 2008) from the CWB and the Taiwan Typhoon and Flood Research Institute (TTFRI) were used to provide the ensemble QPFs in this study. Both ensemble prediction systems have the same model configuration with three-nested domains with 45-km (222 × 128), 15-km (184 × 196), and 5-km (151 × 181) horizontal resolutions (Fig. 6) and 45 levels in the vertical. The convection-permitting innermost domain covers Taiwan and the surrounding ocean region, resolving the terrain effects on the evolution of the typhoon precipitation system.
The CWB and TTFRI EPS domains.
Citation: Weather and Forecasting 30, 1; 10.1175/WAF-D-14-00037.1
The operational CWB EPS (Li and Hong 2011, 2014) was run four times (0000, 0006, 0012, and 0018 UTC) per day. There were 20 members per run with perturbations to the initial conditions, boundary conditions, and model physics. The system was initially perturbed from the National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS) analysis by adding analysis uncertainties based on random perturbations that have a Gaussian distribution with zero mean and unit standard deviation in the control variable space of the WRF three-dimensional variational data assimilation (3DVAR; Barker 2005). The control variables in WRF 3DVAR are streamfunction, unbalanced velocity potential, unbalanced temperature, pseudo–relative humidity, and unbalanced surface pressure. The lateral boundary perturbations were obtained from NCEP ensemble GFS forecasts. The EPS further applied a six-model physics suite in the forecast model to enhance the forecast uncertainty. The six-model physics suite included a combination of planetary boundary layer, cumulus, and microphysical parameterization schemes (Table 1). Details and references for all physical schemes are presented in Skamarock et al. (2008).
The six-model physics suite used in the CWB EPS.
In 2010, the TTFRI conducted an ensemble forecast experiment for typhoon quantitative precipitation forecasts (Hsiao et al. 2013) with the same domain configuration as the CWB EPS. The TTFRI EPS was run four times (0000, 0006, 0012, and 0018 UTC) per day and was composed of 18 members, including the WRF and the Fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5). The initial conditions in the TTFRI EPS were perturbed using different data-assimilation strategies (cold-start and partial-cycle runs), two statistical background error covariances (CV3 and CV5 in WRF 3DVAR), and the outer-loop procedure in WRF 3DVAR (Hsiao et al. 2012, 2013). The cold-start run was initialized by the NCEP GFS analysis. The partial-cycle run included a cold-start run 12 h prior to the analysis time and a subsequent data-assimilation cycle every 6 h. To better represent the typhoon inner-core structure, dynamically consistent bogus data were created near an observed typhoon in 3DVAR. The bogus data at 19 pressure levels between 1000 and 200 hPa, including sea level pressure, wind, temperature, and relative humidity, were derived from an idealized vortex at the observed typhoon location (Hsiao et al. 2010). Depending upon the size of the typhoon, 29–37 bogus data points were used and treated as observational data and assimilated into the WRF 3DVAR analysis. To consider model physics uncertainty, different cumulus, microphysics, and boundary layer schemes were applied to different ensemble members (Hsiao et al. 2013).
In the present study, the ensemble runs were collected for 3 days before the major rainfall events, including the predictions initiated from 1200 UTC 15 September to 0000 UTC 20 September 2010 for Fanapi and from 1200 UTC 17 October to 1200 UTC 21 October 2010 for Megi. Only the rainfall predictions from the 5-km mesh were used. The so-called ensemble case was defined as the forecast output every 3 h with forecast lengths of between 9 and 72 h for all ensemble members, which are indicated with black dots in Fig. 2. To abandon the 0–9-h forecast is to avoid the model precipitation spinup issues in the first few hours of the forecast. Because of the limited domain coverage and complicated inner-core structure of the 5-km mesh, the typhoon position in the 5-km mesh was defined by the minimum sea level pressure center in the 15-km mesh. The predicted typhoon position, translation speed, and 3-h accumulated rainfall were derived for each ensemble case and used in the ETQPF model. All the time stamps, including the model initial time and forecast length, associated with the ensemble cases were not used in the ETQPF model. Criteria were applied to screen out ensemble cases, including a 30-km screening radius and ±5 km h−1 translation speed, along the given typhoon track. The cases that passed the screening were referred to as pick-out cases. The criteria used above are based on our experience. The number of the pick-out cases is too few as the criteria are too strict. In this study, the ETQPF rainfall was determined by the rainfall forecast averaged over the pick-out cases in the ETQPF model.
Hourly rain gauge observations were provided by the Automatic Rainfall and Meteorological Telemetry System (ARMTS; operated by the CWB) network. A total of 464 stations (distributed as in Fig. 1) were used and projected onto the model grid using the successive Cressman interpolation method (Cressman 1959) to produce the rainfall plots and QPF verifications.
c. The QPF verification
The 2 × 2 contingency table includes four categories that are defined relative to a specific rain threshold: both observed and forecasted A, forecast but not observed B, observed but not forecasted C, and neither observed nor forecasted D. A perfect prediction should produce only A and D, which yields Bias = 1. The bias score is a way to determine whether the model precipitation, averaged over many cases, is overpredicted (Bias > 1) or underpredicted (Bias < 1) for the given threshold. The bias score cannot ensure forecast accuracy. The equitable threat score is similar to the threat score except that it corrects for the expected number of chance hits E.
4. Results
a. Typhoon Fanapi
1) Examination of the ETQPF rainfall and sensitivity test
An experiment was conducted during the Fanapi landfall period (from 2100 UTC 18 September to 1800 UTC 19 September 2010) to evaluate the ETQPF model performance. This experiment was designed using the best track to exclude rainfall forecast errors that arose from track errors. By using the forecast track in the model, additional errors were introduced into the ETQPF rainfall forecast as a result of the track error. This error source is not discussed here.
A total of 23 ensemble cases (Fig. 7) were screened out as Fanapi was located east of Taiwan at 0000 UTC 19 September 2010. As shown in Fig. 7, the 3-h accumulated model QPFs from eyewall convection and precipitation system over mountainous areas toward the typhoon center exhibited a small spread. The spread was represented by the standard deviation (Fig. 8), which exhibited larger values over the ocean and the northeastern and southern mountainous areas. Without the screen-out procedure, the standard deviation in the ensemble cases selected based on the same initial time (according to the given typhoon position) will be substantially larger than is shown in Fig. 8 because of the track forecast spread in the EPS [not shown here; Zhang et al. (2010); Fang et al. (2011)].
The 3-h accumulated rainfall (mm) of the 23 pick-out cases screened using a 30-km radius and translation speed within ±5 km h−1 along the best track at 0000 UTC 19 Sep 2010. The bottom-right corner shows the typhoon position of the 23 pick-out cases at 30-km radius along the best track.
Citation: Weather and Forecasting 30, 1; 10.1175/WAF-D-14-00037.1
The 3-h accumulated model QPF std dev (mm) from the 23 ensemble cases shown in Fig. 7.
Citation: Weather and Forecasting 30, 1; 10.1175/WAF-D-14-00037.1
Figure 9a shows the averaged 3-h accumulated rainfall over the 23 pick-out cases at 0000 UTC 19 September 2010 shown in Fig. 7 and the 3-h accumulated ETQPF rainfall, demonstrating a very close agreement with the observations (Fig. 9b). In particular, the ETQPF rainfall performed very well in both the location and total amount of precipitation in northeastern Taiwan, which was due to the terrain lifting effect before landfall. For rainfall over the southern mountainous area, the precipitation pattern was also captured. However, the peak value was not well resolved because the ETQPF model shifted the precipitation southward.
(a) The 3-h accumulated ETQPF rainfall (mm) averaged over the 23 ensemble cases shown in Fig. 7 at 0000 UTC 19 Sep 2010. (b) As in (a), but for the observed precipitation. The accumulated rainfall is valid from 2100 UTC 18 Sep to 0000 UTC 19 Sep 2010.
Citation: Weather and Forecasting 30, 1; 10.1175/WAF-D-14-00037.1
Figure 10 shows the 20 pick-out cases as Fanapi passed over Taiwan at 0900 UTC 19 September 2010, demonstrating that most pick-out cases (especially those highlighted with the boldface line) exhibited similar rainfall structure to the observations (Figs. 4 and 11b). Specifically, the stationary convective system in southern Taiwan, the terrain lifting–enhanced rainfall over the eastern coastal area, and the small rainfall amounts over northwestern Taiwan were well represented. As shown in Figs. 7 and 10, the model was able to represent the phase-lock effect and produced a reasonable typhoon QPF over the complex terrain.
As in Fig. 7, but for the pick-out cases screened along the best track at 0900 UTC 19 Sep 2010. The members with similar rainfall structure to the observations (Fig. 4) are highlighted with the boldface boxes.
Citation: Weather and Forecasting 30, 1; 10.1175/WAF-D-14-00037.1
(a) The 3-h accumulated ETQPF rainfall (mm) averaged over the 20 ensemble cases shown in Fig. 10 at 0900 UTC 19 Sep 2010. (b) As in (a), but for the observed precipitation. (c) As in (a), but for the screened radius increased to 50 km. (d) As in (a), but for values without translation speed screening. The accumulated rainfall is valid from 0600 to 0900 UTC 19 Sep 2010.
Citation: Weather and Forecasting 30, 1; 10.1175/WAF-D-14-00037.1
Compared with the observations, the 3-h accumulated ETQPF rainfall pattern (Fig. 11a) performed well, especially for the narrow precipitation line caused by a stationary rainband. However, because the phase-lock effect over the plain area was weaker than over the mountains, more degrees of freedom for convection occurred over the plains, especially near the stationary rainband. This additional freedom enhances the smoothing effect of averaging over the pick-out cases and results in an underprediction of the maximum ETQPF rainfall.
Figure 11a also illustrates that the ensemble mean overpredicted the rainfall over the eastern coastal area, that is, along the upwind side of the steep mountain (Fig. 1). This pattern was more noticeable in certain individual ensemble cases (Fig. 10). Because all ensemble cases shown in Fig. 10 had similar typhoon positions, such a bias was most likely due to model error, which tended to overpredict the rainfall on the upwind side of the steep mountain range, and not due to the track forecast error.
It has long been known that excessive precipitation occurs over regions with steep and high mountains in atmospheric models (Hong 2003). Many factors can result in such a bias, for example, 1) a poorly resolved horizontal moisture flux in the terrain-following coordinates, 2) excessively strong upslope winds in the boundary layer on the resolvable scales that are generated by excessive daytime heating in the boundary layer along the mountain slopes, 3) not enough friction to slow down the upslope winds, 4) the conditions for cumulus convection being too easily satisfied on mountaintops, and 5) the absence of blocked flow drag (Chao 2012). Subgrid mixing and numerical filtering are also crucial for cloud formation, especially over terrain (Takemi and Rotunno 2003). Most importantly, microphysical parameterization also plays an important role in rainfall bias (Tao et al. 2011).
Two experiments were conducted to further examine the sensitivity of the screen-out criteria. First, the screened radius was extended from 30 to 50 km (Fig. 11c), and, second, the translation speed screening step was skipped (Fig. 11d). The number of pick-out cases required to composite the ETQPF rainfall was increased from 20 (Fig. 11a) to 33 (Fig. 11c) and then 26 (Fig. 11d) by applying the looser criteria. The increased pick-out cases will inevitably increase the ensemble variability and subsequently enhance the smoothing effect caused by taking the average. In the end, these differences result in smoother ETQPF rainfall patterns over southwestern Taiwan (Figs. 11c,d). Therefore, it is critical to apply suitable criteria to screen out the ensemble cases in the ETQPF model. It appears that the ETQPF model performance improves when stricter criteria are applied to guarantee that the pick-out cases are similar to the observations.
Figure 12a shows the 24-h accumulated ETQPF rainfall from 1800 UTC 18 September to 1800 UTC 19 September. The predicted rainfall pattern corresponded qualitatively well to the observations (Fig. 3b). Moreover, decreased rainfall over northwestern Taiwan, terrain lifting–enhanced rainfall over eastern Taiwan during the landfall period, and heavy rainfall over southwestern Taiwan due to the stationary precipitation system were represented in the ETQPF rainfall. Quantitatively, the ETQPF rainfall error (Fig. 12b) suggests that the ETQPF model overpredicted the rainfall across the eastern coastal area and underpredicted the rainfall over the southwestern plain area. The underprediction was primarily due to the offset of the ensemble average, which resulted from a reduced phase-lock effect over the plain area. Moreover, the overprediction over the eastern coastal area might be related to the model bias, which tended to produce excessive rainfall on the upwind side of the steep mountain area.
(a) The 24-h accumulated ETQPF rainfall (mm; from 1800 UTC 18 Sep to 1800 UTC 19 Sep 2010) and (b) ETQPF rainfall forecast error (mm) against the rain gauge observations shown in Fig. 3b. (c) As in (a), but for the ensemble mean of all CWB and TTFRI ensemble predictions initiated at 1800 UTC 18 Sep 2010. (d) As in (a), but for the climatology model.
Citation: Weather and Forecasting 30, 1; 10.1175/WAF-D-14-00037.1
Figure 12c shows the ensemble mean of the 24-h accumulated rainfall from all ensemble predictions initiated at 1800 UTC 18 September 2010, representing the most common ensemble product following Zhang et al. (2010) and Fang et al. (2011). Figure 12c shows a relatively smooth rainfall distribution with no east–west-oriented heavy rainfall pattern over southwestern Taiwan. The maximum 24-h accumulated rainfall was 787 mm, which was less than the ETQPF (837 mm) and observed (1127 mm) rainfall. The smooth rainfall pattern was caused by the ensemble averaging over a larger ensemble spread in the track forecast. Figure 12d shows the 24-h accumulated QPFs based on the best track from the climatology model (Lee et al. 2006), demonstrating that the climatology model only predicts rainfall over southwestern and northeastern Taiwan. However, the rainfall amount was substantially underpredicted.
2) Verification
The mean error and correlation coefficient of the 3-h accumulated ETQPF rainfall forecast relative to the observations in Taiwan are presented in Fig. 13. The correlation coefficient between the 3-h ETQPF rainfall and observations ranged from 0.6 to 0.8. All the correlation coefficients are statistical significance at the 0.0001 level. The maximum correlation coefficient was 0.82 for the 24-h accumulated ETQPF rainfall. Just before landfall (i.e., 0000 UTC 19 September), the maximum correlation coefficient was 0.79, and the mean error (0.1 mm) was lowest. This finding suggests that the strong phase-lock effect before landfall resulted in the improved ETQPF model performance. However, the lowest correlation coefficient and underprediction at 0300 UTC 19 September occurred during the landfall period, which resulted from the complex evolution of the precipitation system because the typhoon was over a high mountain range. After Fanapi passed over Taiwan at 0600 UTC 19 September, the correlation coefficient gradually increased and ETQPF rainfall tended to be slightly overpredicted.
Mean error (mm; blue line) and correlation coefficient (red line) calculated over Taiwan for the 3-h accumulated ETQPF rainfall during Fanapi from 2100 UTC 18 Sep to 1800 UTC 19 Sep 2010.
Citation: Weather and Forecasting 30, 1; 10.1175/WAF-D-14-00037.1
The distribution of the 24-h accumulated rainfall thresholds was designed to be approximately a factor of 8 larger than the 3-h accumulated rainfall in Bias and ET score. A total of eight 3-h and one 24-h ETQPF rainfall forecasts were collected to calculate the skill score. The bias scores for the 3- and 24-h accumulated ETQPF rainfall (Fig. 14) ranged from 1 to 1.5 for thresholds lower than 75 mm (3 h)−1 and 500 mm (24 h)−1, decreasing gradually to less than 1 for higher rainfall thresholds. This finding suggests that the ETQPF rainfall slightly overpredicted the occurrence of precipitation for most thresholds. The maximum ET score for the 24-h accumulated ETQPF rainfall was 0.75 for a 100-mm threshold, decreasing gradually for higher thresholds. The decrease of the ET score at a higher threshold is consistent with the overprediction of the heavy rainfall over the eastern coastal area, as shown in Fig. 12a. For the 3-h accumulated ETQPF rainfall, the ET score was greater than 0.3 for light to moderate precipitation thresholds (<75 mm). For the Typhoon Fanapi case, the ETQPF model, which was qualitatively compared and quantitatively verified, provided a reasonable typhoon rainfall forecast. Moreover, the ETQPF model may be valuable for real-time operational applications.
Bias and ETS of the ETQPF rainfall forecast as a function of rain threshold (upper x axis gives 24- and lower x axis gives 3-h accumulated rainfall) for Typhoon Fanapi from 1800 UTC 18 Sep to 1800 UTC 19 Sep 2010. The red and blue lines are the scores for the 3- and 24-h accumulated ETQPF rainfall, respectively. The solid lines are for the ETS, and the dashed lines are for the bias scores.
Citation: Weather and Forecasting 30, 1; 10.1175/WAF-D-14-00037.1
b. Typhoon Megi
As discussed above, the heavy rainfall mechanism over Taiwan for Typhoon Megi was different than for Typhoon Fanapi. The distant rainfall was concentrated over northeastern Taiwan while Megi was located over the South China Sea. The heavy rainfall was due to terrain blocking and lifting effects from the enhanced northeasterly monsoon flow caused by the outer circulation of Megi. To accurately predict this distant rainfall event required a close temporal and spatial correlation between the typhoon outer circulation and the northeasterly monsoon system. It is very difficult to provide an accurate QPF from the typhoon rainfall climatology model.
The 24-h accumulated ETQPF rainfall based on the best track during Megi (1200 UTC 20 October–1200 UTC 21 October 2010; Fig. 15a) shows that the rainfall pattern qualitatively matched the observations (Fig. 5b) very well. The concentrated ETQPF rainfall over northeastern Taiwan demonstrated that the ensemble prediction system was able to represent the distant rainfall mechanism in Megi. However, the magnitude and specific location of the ETQPF rainfall deviated from the observations. The maximum rainfall was 781.9 mm (24 h)−1, which was less than the observations [928.8 mm (24 h)−1]. The reason for the underprediction was partially due to the offset of the extremes in the averaging procedure. Moreover, the ETQPF rainfall over northeastern Taiwan shifted more inland. This shift resulted in the ETQPF rainfall forecast error, which appeared as a dipole pattern (Fig. 15b) with a maximum value greater than ±400 mm (24 h)−1. This error may have been due to insufficient model resolution, making the model unable to resolve the abrupt topographic gradients in northeastern Taiwan.
(a),(b) As in Figs. 12a,b, but for Typhoon Megi. The 24-h accumulated rainfall (mm) is valid from 1200 UTC 20 Oct to 1200 UTC 21 Oct 2010. (c) As in (a), but for the ensemble mean of all CWB and TTFRI ensemble predictions initiated at 1200 UTC 20 Oct 2010. (d) As in (a), but for the climatology model.
Citation: Weather and Forecasting 30, 1; 10.1175/WAF-D-14-00037.1
Figure 15c shows the ensemble mean of the 24-h accumulated rainfall from the CWB and TTFRI ensemble predictions initiated at 1200 UTC 20 October 2010, demonstrating that the ensemble mean also predicted the concentrated rainfall over northeastern Taiwan. However, the maximum 24-h accumulated rainfall was 631 mm, which was less than the ETQPF (781.9 mm) and observed (928.8 mm) rainfall. The climatology model (Fig. 15d) also failed to predict the concentrated rainfall pattern over northeastern Taiwan.
Similar to Fanapi, the bias score for Megi (Fig. 16) shows that the ETQPF model slightly overpredicted the 3- and 24-h accumulated rainfall for most thresholds. For thresholds of 100 mm (3 h)−1 and 600 mm (24 h)−1, the bias score rapidly decreased to less than 0.6. The ET score for Megi was not as good as for Typhoon Fanapi, ranging from 0.2 to 0.5. In general, the ET score is expected to be better for longer accumulation periods. In Megi, the 24-h accumulated ETQPF rainfall ET scores were only slightly better than the 3-h accumulated ETQPF rainfall ET scores. This result implies that the error source was dominated by the location shift throughout the forecast period (Fig. 15b).
As in Fig. 14, but for Typhoon Megi from 1200 UTC 20 Oct to 1200 UTC 21 Oct 2010.
Citation: Weather and Forecasting 30, 1; 10.1175/WAF-D-14-00037.1
Considering the forecast track issued by the CWB in 12-h intervals from 1200 UTC 19 October to 0000 UTC 21 October, the ETQPF model performance for Typhoon Megi is shown in Fig. 17. The figure shows that the forecast track errors decreased as Megi approached Taiwan. The 12-h accumulated ETQPF rainfall predictions valid from 0000 to 1200 UTC 21 October were determined based on the forecast track. Figure 17 shows that the 12-h accumulated ETQPF rainfall was closer to the observations as the track error was reduced, which subsequently decreased the mean error and mean absolute error (Fig. 18). Figures 17 and 18 also indicate that the track error dominates the typhoon QPF error. Therefore, better track forecasts will lead to better ETQPF rainfall forecasts. In addition, the ETQPF model is able to provide the typhoon QPF “scenario” based on different tracks. Figure 19 shows the 24-h accumulated ETQPF rainfall according to the different typhoon track forecasts for Megi, demonstrating that the ETQPF rainfall (Fig. 19d) was concentrated over northeastern Taiwan and the track forecast (Fig. 19a) was far from the island. As the track moved closer to Taiwan (Figs. 19b,c), the rainfall distribution shifted farther toward the eastern coast (Figs. 19e,f). This analysis can provide different QPF scenarios as a result of the track forecast uncertainty; the analysis is valuable for risk assessment and decision making for disaster prevention and reduction.
(a),(d),(g),(j) CWB official track forecasts (black) and best tracks (red) issued from 1200 UTC 19 Oct to 0000 UTC 21 Oct in 12-h intervals. (b),(e),(h),(k) The 12-h accumulated ETQPF rainfall (mm) valid from 0000 to 1200 UTC 21 Oct based on the CWB official track forecasts shown in (a),(d),(g),(j), respectively. (c),(f),(i),(l) Forecast errors (mm) from (b),(e),(h),(k), respectively; negative (positive) values indicate under- (over-) predictions. (m) Observed rainfall (mm) valid from 0000 to 1200 UTC 21 Oct. (n) The 12-h accumulated ETQPF rainfall (mm) based on the best track valid from 0000 to 1200 UTC 21 Oct. (o) The forecast error (mm) of (n).
Citation: Weather and Forecasting 30, 1; 10.1175/WAF-D-14-00037.1
Average ETQPF rainfall forecast error (mm) and absolute forecast error over Taiwan from Figs. 17c,f,i,l,o.
Citation: Weather and Forecasting 30, 1; 10.1175/WAF-D-14-00037.1
(d)–(f) The 24-h accumulated ETQPF rainfall (mm) according to (a)–(c) the different typhoon track forecasts. The accumulated rainfall is valid from 0000 UTC 22 Oct to 0000 UTC 23 Oct 2010.
Citation: Weather and Forecasting 30, 1; 10.1175/WAF-D-14-00037.1
c. ETQPF performance for typhoons during 2013
To further examine the general model performance, the ETQPF model was applied to estimate the QPFs for typhoons affecting Taiwan during 2013, including Typhoons Soulik, Trami, Usagi, and Fitow as listed in Table 2. The ensemble members were from the EPS operated by the CWB and TTFRI. Figure 20 shows the 72-h accumulated ETQPF rainfall estimated according to the best-track forecast. The 72-h duration approximately expressed the period during which the typhoons affected Taiwan. Figure 20 shows that the 72-h accumulated ETQPF rainfall forecasts are generally reliable and very comparable to the observations, especially for rainfall patterns. The mean errors (pattern correlations) are 38.1 mm (0.89), 41.6 mm (0.8), −5.29 mm (0.86), and 6.01 mm (0.9) for Typhoons Soulik, Trami, Usagi, and Fitow, respectively. However, the errors for the location and the magnitude of the rainfall maximum were exhibited in these cases. For example, the southern maximum in Soulik and the northeastern maximum in Usagi were underestimated in the ETQPF forecasts. Again, the ETQPF model also overpredicted the rainfall maximum across the eastern coastal area. Overall, the rainfall pattern has been roughly represented by the climatology model; however, it appears to underpredict the rainfall amount for all four of the typhoons.
List of the typhoon cases and forecast periods for the ETQPF rainfall.
The 72-h accumulated rainfall (mm) for (a),(d),(g),(j) observations; (b),(e),(h),(k) ETQPF forecasts; and (c),(f),(i),(l) the climatology model for Typhoons Soulik, Trami, Usagi, and Fitow. The forecast period is listed in Table 2.
Citation: Weather and Forecasting 30, 1; 10.1175/WAF-D-14-00037.1
5. Summary and discussion
In this study, a so-called ensemble typhoon QPF (ETQPF) model was developed, which utilizes particular components of the climatology model and the ensemble QPF. The ETQPF model simply adopts the concepts of the climatology model. Nevertheless, the ensemble QPF is used instead of the historical rainfall observations.
Two typhoon cases [i.e., Fanapi (2010) and Megi (2010)] were studied to evaluate the ETQPF model performance. Both typhoons produced torrential rainfall over Taiwan. However, the heavy rainfall mechanisms were completely different. Fanapi made landfall along the eastern coast and produced up to 1127 mm (24 h)−1 of rain over southwestern Taiwan because of a nearly stationary convective line. Moreover, Megi remained over the South China Sea. As a result, distant rainfall occurred with a maximum of 928.8 mm (24 h)−1 over northeastern Taiwan, primarily caused by terrain blocking and lifting effects from the enhanced northeasterly monsoon.
The Fanapi rainfall patterns of the pick-out ensemble cases according to the best track were similar to the observations, implying that the ensemble QPFs represented the phase-lock effect because the model typhoon location was close to the observations. The average rainfall for the pick-out cases (i.e., the ETQPF rainfall) matched the observations well, including the stationary convective system in southern Taiwan, terrain lifting–enhanced rainfall over the eastern coastal area, and low rainfall amounts over northwestern Taiwan. Quantitatively, the ETQPF rainfall was overpredicted across the eastern coastal area and underpredicted across the southwestern plain area.
The highest correlation coefficient was 0.79, which occurred just before landfall. The strong phase-lock effect appears to have resulted in the improved ETQPF performance before landfall. However, the lowest correlation coefficient and underprediction occurred during the landfall period, which was related to the complexity of the evolution of the precipitation system while the typhoon was located over a high mountain range.
The bias score shows that the ETQPF rainfall systematically slightly overpredicted precipitation for most thresholds. The maximum ET score for the 24-h accumulated ETQPF rainfall was 0.75 for the 100-mm threshold, gradually decreasing as the threshold increased. For the 3-h accumulated ETQPF rainfall, the ET score was greater than 0.3 for light to moderate precipitation thresholds (<75 mm).
In Megi, the concentrated ETQPF rainfall over northeastern Taiwan matched the observations very well. However, similar to Fanapi, the ETQPF model underpredicted the maximum rainfall over northeastern Taiwan. Moreover, the ETQPF rainfall over northeastern Taiwan shifted farther inland. This shift resulted in ETQPF rainfall forecast errors that appeared as a dipole pattern throughout the analysis period and in the comparable ET scores for the 3- and 24-h accumulated ETQPF rainfall.
Several distinguishing characteristics of the ETQPF model can be summarized:
Due to the phase-lock effect, “real time” predictions are not critical for the ETQPF model. Therefore, by including the ensemble QPFs from lag predictions and coordinating with the communities or other institutions, the ensemble spread can be improved. This finding is helpful for promoting ETQPF model applications in operational typhoon rainfall forecasts.
As the number of pick-out cases increased, more meaningful statistical products (e.g., the standard deviation and the probabilistic QPFs) could be determined by the ETQPF model because the statistical significance increased. Therefore, the ETQPF model is more valuable when more ensembles are considered.
In general, the performance of the official forecast track or consensus track from the multimodel ensemble is better than that of a single model. Consequently, the ETQPF model based on the official/consensus track forecast is expected to improve typhoon QPFs as a result of reduced track error.
In this study, several ETQPF model deficiencies were also explored. The average over the pick-out cases offsets the extremes and reduces the maximum ETQPF rainfall. The resulting underprediction is especially noticeable in weak phase-locked rainfall systems, such as convective rainbands. Furthermore, the ETQPF rainfall error is related to the systematic bias of the forecast model. For example, we found that the model tended to overpredict rainfall over steep mountainous areas. The shift in the maximum ETQPF rainfall in Megi was suggested to be associated with the coarser model terrain resolution. Therefore, improving model bias is an important issue for enhancing the ETQPF model performance.
Overall, the ETQPF model, which was qualitatively compared and quantitatively verified, produced a reasonable typhoon rainfall forecast. Our findings suggest that the ETQPF model performance will improve with stricter screening criteria that ensure that the pick-out cases are similar to the observations. Therefore, the increased numbers of ensembles are required to apply stricter criteria.
A comparison among the ETQPF, the ensemble mean, and the climatology model for Fanapi and Megi shows that the ETQPF model performs better than the other two algorithms. Moreover, the general ETQPF model performance for typhoons affecting Taiwan has been demonstrated to have valuable real-time operational applications. Traditionally, the “best” typhoon QPF is estimated from a deterministic model; this approach is aggressive and seeks to achieve the greatest accuracy. However, the ETQPF model differs from the traditional thinking. We demonstrated that the ETQPF rainfall is trustworthy based on the best-track forecast. Moreover, by applying a range of forecast tracks, the ETQPF model provides different typhoon QPF “scenarios” according to the given track. These scenarios, which are based on the typhoon track uncertainty, are also the most trustworthy because of the ETQPF model confidence. This approach is relatively conservative, providing typhoon QPF uncertainty to the model users. The ETQPF model then is able to aggressively provide valuable information for risk assessment and decision making for the prevention and reduction of damage caused by natural disasters.
Acknowledgments
The computer resources for the ensemble prediction were supported by the Central Weather Bureau of Taiwan and the Taiwan Typhoon and Flood Research Institute. The authors thank Dr. Delia Yen-Chu Chen, Yiru Chen, and Mrs. Hsin-I Ku for their help in providing the QPFs from the ensemble mean and climatology model. We also thank the CWB Typhoon Database for providing the surface analysis in Fig. 4b. Particular thanks are given to the anonymous reviewers who substantially improved the manuscript. This work was partially supported through the National Science Council of Taiwan under Grant NSC99-2625-M-052-006-MY3.
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