In this study, the performance of a new ensemble quantitative precipitation forecast (QPF) system for Taiwan, with a cloud-resolving grid spacing of 2.5 km, a large domain of 1860 km × 1360 km, and an extended range of 8 days, is evaluated for six typhoons during 2012–13. Obtaining the probability (ensemble) information through a time-lagged approach, this system combines the strengths of high resolution (for QPF) and longer lead time (for hazard preparation) in an innovative way. For the six typhoons, in addition to short ranges (≤3 days), the system produced a decent QPF at a longest range up to days 8, 4, 6, 3, 6, and 7, providing greatly extended lead times, especially for slow-moving storms that pose higher threats. Moreover, since forecast uncertainty (reflected in the spread) is reduced with lead time, this system can provide a wide range of rainfall scenarios across Taiwan with longer lead times, each highly realistic for the associated track, allowing for advanced preparation for worst-case scenarios. Then, as the typhoon approaches and the predicted tracks converge, the government agencies can make adjustments toward the scenario of increasing likelihood. This strategy fits well with the conventional wisdom of “hoping for the best, but preparing for the worst” when facing natural hazards. Overall, the system presented herein compares favorably in usefulness to a typical 24-member ensemble (5-km grid size, 750 km × 900 km, 3-day forecasts) currently in operation using similar computational resources. Requiring about 1500 cores to execute four 8-day runs per day, it is not only powerful but also affordable and feasible.
a. Background of research
Quantitative precipitation forecasts (QPFs), especially those for heavy to extreme rainfalls due to their hazardous nature, are among the most challenging tasks in modern numerical weather prediction (NWP) and are under heavy demands around the world (e.g., Fritsch et al. 1998; Golding 2000; Fritsch and Carbone 2004; Cuo et al. 2011). They are particularly important in Taiwan, where heavy rainfalls brought on by tropical cyclones (TCs; mainly during July–October) and during the mei-yu season (May–June) are responsible for the majority of its weather hazards (e.g., Cheung et al. 2008; Su et al. 2012; Chang et al. 2013). Over the past two decades, linked to the needs for probability information and to quantify forecast uncertainty (foremost in tracks), an ensemble approach utilizing multiple members simultaneously, sometimes a large group of members, has been adopted as the primary method for producing QPFs (e.g., Epstein 1969; Leith 1974; Toth and Kalnay 1993; Du et al. 1997; Molteni et al. 1996; Kalnay 2003). This is also the case in Taiwan, as both the Central Weather Bureau (CWB) and the Taiwan Typhoon and Flood Research Institute (TTFRI) use multimember ensembles (e.g., Hsiao et al. 2013; Hong et al. 2015).
As the computer technology advances and increasingly higher resolutions can be used for QPFs in NWP, convective clouds that produce the intense rainfall (as opposed to stratiform clouds) can no longer be treated as “subgrid scale” processes in most, if not all, regional models (e.g., Frank 1983; Molinari and Dudek 1992; Arakawa 2004). In other words, convection must be “resolved” by the model grid and treated explicitly (e.g., Done et al. 2004; Kong et al. 2006). From a scientific point of view, the immediate logical question is what is the grid size Δx necessary to adequately resolve the basic structure, such as updrafts and downdrafts, of deep convective clouds? Many earlier studies suggest the answer to be around 2 km (e.g., Rotunno et al. 1988; Roebber et al. 2002; Kong et al. 2006), as six to eight grid points are needed in each direction for typical deep cumuli about 10–15 km in diameter (e.g., Bluestein 1992, section 1.1.2). While obviously smaller Δx values are required to resolve finer details of convection (e.g., Klemp and Wilhelmson 1978; Bryan et al. 2003; Petch 2006; Wang and Huang 2009), models with Δx ≤ 3 km can be termed cloud resolving and those with Δx ≈ 4–5 km are usually referred to as convection permitting instead (e.g., Weisman et al. 1997; Walser et al. 2004; Roberts and Lean 2008; Clark et al. 2009; Zhang et al. 2010). Simulation works on some heavy-rainfall events in Taiwan have shown that cloud-resolving models (CRMs) can properly capture their evolution and magnitude (e.g., Wang et al. 2005, 2009, 2011, 2013a, 2014; Yang et al. 2011), including the devastating case of Typhoon (TY) Morakot in 2009 (e.g., Tao et al. 2011; Wang et al. 2012, 2013b; Huang et al. 2014).
When used in forecasting, CRMs also often show promising results, such as in Adlerman and Droegemeier (2002), Xue et al. (2003), Done et al. (2004), Liu et al. (2006), Kong et al. (2006), Weisman et al. (2008), Clark et al. (2009), and Schwartz (2014). These efforts, however, are mostly limited to individual events or fixed campaign periods. Since 2008, the Cloud-Resolving Storm Simulator (CReSS; Tsuboki and Sakakibara 2002, 2007) has been used for typhoon forecasts in Taiwan, and routine operations (3-day forecasts every 6 h) throughout the entire year, with a Δx of 2.5 km, have been achieved since 2010. Recently, Wang (2015, hereafter referred to as W15) evaluated 24-h QPFs by this model for all 15 TCs during 2010–12 and demonstrated its superior performance. For the periods with the most rainfall and highest hazard potential (roughly the top 5% of the sample), the 0–24-h (day 1) QPFs generated by CReSS have mean threat scores (TSs; to be detailed in section 2c) of 0.67, 0.58, 0.51, and 0.32 at thresholds of 50, 130, 200, and 350 mm; the 24–48-h (day 2) QPFs yield mean TSs of 0.73, 0.57, 0.42, and 0.17; and the 48–72-h (day 3) QPFs yield mean TSs of 0.57, 0.37, 0.33, and 0.22, respectively. For the biggest event in Morakot, the scores (from real-time forecasts) are even higher, and those of day-2 QPFs reach 0.87, 0.69, 0.50, and 0.38 at heavy to extreme thresholds of 200, 350, 500, and 1000 mm, respectively [see also Wang (2014)]. While this particular forecast for Morakot [experiment F7A in Wang et al. (2013b)] produced peak 48-h total rainfall (7–8 August) very close to the observation (about 2200 mm), other models at the time struggled to reach 1400 mm in their 3- or 4-day totals (e.g., Wu et al. 2010; Hendricks et al. 2011). Thus, the evidence points strongly toward model configuration and resolution for improved QPFs, as attested to by W15. The study of W15 also demonstrates the strong basic property of “the more rain, the higher the score” in categorical statistics, and it is a misperception that the models (CRMs in particular) have little ability to predict extreme rainfalls.
As shown above, the 2.5-km CReSS can provide high quality QPFs for large, hazardous events not only on days 1 and 2, but also often on day 3 (48–72 h), at the longest range in those forecasts (e.g., Figs. 2, 3, 7, and 9 in W15). As a rule of thumb in all forecasts, one tries to make a decent forecast as early as possible. Thus, we seek to find out whether a high quality QPF is attainable at ranges longer than 3 days, and if so, how frequently can it be achieved? These questions provide a basic incentive for us to carry out the present study. Nevertheless, our motivation and the study objectives within a larger context of forecast strategy for hazard preparation and reduction will be elaborated upon further below.
b. Motivation and objectives of study
Produced by a single model, the CReSS forecasts discussed above are deterministic forecasts that can better resolve convection and topography and produce more realistic intensity and evolution of high-impact weather such as TCs, but are generally regarded as having no helpful information in terms of probability. Ensemble forecasts, on the other hand, with the computational resources divided among their members, can measure confidence in forecasts and quantify uncertainty, better cover possible event scenarios through spread, but typically underpredict heavy rainfall as a result of their lower resolution. Although the two approaches are complementary to each other (Roebber et al. 2004), in reality, however, compromises are often made with a fixed (and often limited) amount of computational resources (e.g., Clark et al. 2009), and the ensemble approach has been adopted as mentioned.
Based on and modified from Nakazawa (2010), Table 1 (top) lists five major items for typhoons provided by regional low-resolution ensemble forecasts versus high-resolution (cloud resolving) deterministic forecasts and their general quality: rainfall, track, intensity, striking probability, and lead time. At this time, our discussion focuses only on the first two columns in Table 1. As a benchmark, the low-resolution ensemble approach is deemed to yield results of average (or fair) quality in all five items for its usefulness in hazard preparation. Compared to it, the deterministic forecasts, as discussed above (e.g., W15), provide improved QPFs that are judged to be very good (close to the highest quality that can be expected, given the limitations in predictability and the current technology). High-resolution deterministic forecasts also give good quality (better than average) in terms of track and intensity, but are poor (below average) in lead time with no probability information. It is clear that the high quality QPFs, which are the most needed in Taiwan, can only be provided by CRMs, and thus we seek possible ways to improve the two major drawbacks of this approach: lead time and probability.
One straightforward solution to tackling the issue of lead time and to satisfy our curiosity, as mentioned earlier, is to increase the forecast range. Once the range is extended, as shown in Fig. 1, the probability information can be obtained from different runs through a time-lagged approach. While such a method was applied only to short-range QPFs previously (e.g., Yuan et al. 2008; Trilaksono et al. 2012; Chang et al. 2012), it is clear that the longer the range, the more the available members there will be (at a fixed forecast frequency; cf. Fig. 1), so we performed 8-day forecasts into the medium range since 2012 using an enlarged domain (to be detailed later). Thus, as objectives of this study, we evaluate the performance of the 8-day forecasts/QPFs by the 2.5-km CReSS, using all five TCs to hit Taiwan (for which the CWB issued warnings) in 2012 and the most hazardous TC in 2013 (Kong-Rey). In the process, the two questions posed at the end of section 1a are also resolved.
2. Forecast experiment and evaluation of results
a. The CReSS model
The CReSS model is a CRM employing a nonhydrostatic and compressible equation set and a terrain-following vertical coordinate based on height (Tsuboki and Sakakibara 2002, 2007). Having a single domain (without nesting), the model (version 2.3) and basic configuration are the same as those in W15. In CReSS, clouds are treated only explicitly using a bulk cold-rain microphysical scheme with a total of six species (vapor, cloud water, cloud ice, rain, snow, and graupel). Parameterized subgrid-scale processes include turbulent mixing in the planetary boundary layer, radiation, and surface momentum and energy fluxes. The CReSS model is open to the research community upon request, and its further details can be found online (http://www.rain.hyarc.nagoya-u.ac.jp/~tsuboki/cress_html/index_cress_jpn.html).
b. The forecast experiment
Since 1 May 2012, one 8-day forecast is performed each day at 0000 UTC, with a high-resolution domain (Δx = 2.5 km) of 1860 km × 1360 km (x × y) in size and 40 levels (Fig. 2a, Table 2). The domain is designed for typhoons, such that most TCs that approach Taiwan from the east or southeast can enter the fine grid as early as possible. Once finished, the results are posted online (http://cressfcst.es.ntnu.edu.tw/). For routine plots that are not shown in the discussion, they can be found here for verification.
The National Centers for Environmental Prediction (NCEP) Global Forecast System (GFS) analyses and forecasts (Kalnay et al. 1990; Kleist et al. 2009), available on a 1° × 1° latitude–longitude grid at 26 levels, are used as initial and boundary conditions (IC/BCs) of the CReSS forecasts. At the lower boundary, terrain data on a (1/120)° grid and the NCEP-analyzed sea surface temperatures (1° × 1°) are provided (Table 2). For the daily forecasts presented in sections 3 and 4a, all results were produced in real time. To further highlight TY Kong-Rey (2013) in section 4b, four runs a day were utilized and the additional ones (at 0600, 1200, and 1800 UTC) were produced recently but also in forecast mode. Thus, the procedure is identical to that in real time.
In comparison to the traditional approach in terms of cost and effect (in resources and forecast products), we select the TTFRI QPF ensemble, which has roughly 24 members, running every 6 h and each for 78 h [basically 3-day forecasts, cf. Fig. 1a; Hsiao et al. (2013)]. This system uses mainly the Weather Research and Forecasting (WRF) Model (Skamarock et al. 2005) with a triply nested grid (Δx = 45, 15, and 5 km), and the fine mesh is 750 km × 900 km (Fig. 2a). The same basic strategy and domain configuration are also used by the CWB (Hong et al. 2015). It is worth noting that one 8-day forecast uses about 5–6 times the computational resources of each TTFRI WRF member, after scaling for job size and computer speed.
c. Evaluation of model results and QPFs
To examine the quality of the CReSS forecasts in various aspects, the following data are employed. The best-track data from the CWB and the Joint Typhoon Warning Center (JTWC) are used for the basic information of typhoons. Weather maps and NCEP Final Analysis data (1° × 1°) are used for synoptic discussion. To verify their quality, especially in storm rainfall structures, the forecasts are compared with snapshots provided by the Tropical Rainfall Measuring Mission (TRMM) Precipitation Radar (PR) and TRMM Mapping Imager (TMI) from the Naval Research Laboratory (NRL), at instants when such observations are available.
To verify QPFs, hourly rainfall data from more than 400 automated rain gauges over Taiwan (Hsu 1998) are used (Fig. 2b), and accumulated rainfall distributions are computed and visually compared with model predictions. In additional to subjective verification, objective verification based on the 2 × 2 contingency table (i.e., categorical measure) is also used and the TS is calculated for 24-h QPFs (days 1–8), across a threshold range up to 750 mm. Evaluated at the rain gauge sites (by interpolating forecast results onto these sites) with equal weights (e.g., Wang 2014), the TS (Schaefer 1990; Wilks 1995) at a given threshold is defined as TS = H/(H + M + FA), where H, M, and FA are the counts of the hits (observed and predicted), misses (observed but not predicted), and false alarms (predicted but not observed), respectively, among all verification points N. Thus, TS has a value between 0 and 1, and the higher the better. While direct visual comparison is provided for all forecasts discussed later, other measures such as the probability of detection [POD = H/(H + M)], false alarm rate [FAR = FA/(H + FA)], and bias score [BS = (H + FA)/(H + M); e.g., Wilks (1995)] will also be given on occasion for additional information.
3. Results of forecast experiment
a. Overall results for all typhoons
In this section, the overall results from our daily time-lagged forecasts for all five typhoons in 2012 and Kong-Rey (2013) are first presented, with emphasis on the quality and high realm of rainfall prediction and the longer lead time. The overall advantages and benefits of the time-lagged approach are stressed and possible limitations at times are also pointed out. When necessary, synoptic conditions in individual cases are given to discuss the rainfall scenario and the reasons why the QPF was successful or otherwise. Later in section 4, the case of Kong-Rey is further highlighted to demonstrate the results from the forecasts executed four times a day, with emphasis on effectiveness, feasibility, and probability information. For easy reference, Table 3 lists and groups the panels in Figs. 3–11 for each of the TC cases.
The tracks produced by the daily time-lagged 2.5-km CReSS and the TTFRI WRF ensemble (from 15-km mesh; Fig. 2a) are shown in Fig. 3 for all six typhoons included in this study. Produced and released by the TTFRI, the WRF plots selected here are the earliest available for each case, except for Saola (the second release, 6 h after the first one) and Tembin (to be further discussed). Ostensibly, the two track forecasts are roughly comparable for most typhoons, except Talim and Doksuri, where the CReSS tracks are considerably fewer in number (Figs. 3a–d). Not all the time-lagged tracks were available at the time of the TTFRI forecasts, and for the most part only those up to the one marked were (Fig. 3, triangle in the legend). However, one should keep in mind that the former, producing at most one track per day, utilized only about a quarter of the computational resources compared to the latter. In five of the six cases, the time-lagged tracks show advantages in being much farther into the future (Saola, Tembin, and Kong-Rey), having earlier availability at longer lead times (all except Talim), and/or having a larger spread of tracks (most evident in Kong-Rey; Figs. 3k,l). The tendency of a larger spread through the time-lagged approach is directly linked to the longer forecast range and will be further discussed. Overall, the significantly longer tracks (and thus potential lead time for preparation), which are most clear in slow-moving TCs such as Saola, Tembin, and Jelawat (Figs. 3e–j), are a desirable feature of the 8-day forecasts.
To focus our discussion on QPFs, we identify the highest mean daily rainfall from each typhoon and examine all daily forecasts by CReSS for that day at different ranges (i.e., from different initial times), as QPFs for other days are less important (W15). Only for the two most hazardous TYs of Saola and Kong-Rey are 2 and 3 days selected for verification because of their large event magnitude and long duration of heavy rainfall. Thus, the observed and predicted daily (0000–2400 UTC) rainfall amounts over Taiwan for the most rainy day(s) of each typhoon in 2012 (Figs. 4a–f) are shown in Fig. 4, with QPFs from the longest to shortest range (from day 8 to 1) plotted from left to right. Similarly, the rainfall forecasts for and observations on 29–31 August 2013 during Kong-Rey are presented in Fig. 5. The TS values of all the above 24-h QPFs at thresholds from 0.05 to 750 mm are shown in Fig. 6, and those with TS ≥ 0.2 at 50, 100, 200, and 350 mm are marked in Figs. 4 and 5 by thick boxes in black, red, blue, and green, respectively. Typically, the value of TS = 0.2 can indicate some level of skill in QPFs at that threshold (e.g., Chien et al. 2006).
The most striking feature in Fig. 4 is that high quality QPFs over Taiwan were produced not only within 3 days for all TCs in 2012 (as in W15), but also at longer ranges except for Tembin, including on day 8 for 20 June (Talim), on day 4 for 28 June (Doksuri), on day 4 for 1 August and day 6 for 2 August (Saola), and on day 6 again for 28 September (Jelawat). Among a total of 30 QPFs at ranges of 4–8 days shown in Fig. 4, 15 and 9 of the runs (50% and 30%) have TSs reaching 0.2 at 50 and 100 mm, respectively. For target dates with observed peak rainfall of at least 200 mm (so that TS > 0 is possible, Doksuri excluded), 6 out of 25 forecasts (24%) at ranges beyond 3 days have TS ≥ 0.2 at that threshold (Fig. 4). The most impressive forecasts are perhaps those on day 8 targeted for 20 June in Talim (TS = 0.22 at 200 mm; Fig. 6a), on day 6 for 2 August in Saola (TS = 0.50 at 350 mm; Fig. 6d), and on day 6 for 28 September in Jelawat (TS = 0.50 at 200 mm; Fig. 6f). For Kong-Rey (2013) where heavy rainfall occurred on three successive days over 29–31 August, high quality QPFs were made as early as on days 7, 4, and 5 (Fig. 5), with the TSs hitting 0.28 and 0.26 at 200 mm and 0.40 at 100 mm, respectively (Figs. 6g–i). Thus, for the nine dates in Figs. 4 and 5, the 2.5-km CReSS on average produced a decent QPF on day 5.2, significantly earlier than what is attainable by the TTFRI ensemble (≤3 days). Overall, the model failed to do so for just one typhoon in Tembin.
The quality of the QPFs from a given run is linked to how closely the predicted rainfall scenario resembles the reality, and this depends primarily on two factors. The first is the evolution of the TC that can be reflected by track errors, as revealed by the better forecasts in Figs. 3–5 (more often at shorter ranges). The second factor lies in the model’s capability to simulate actual rainfall (i.e., in its resolution as reviewed in section 1). The rainfall structures observed by TRMM PR/TMI at selected times with an optimal view of the storm in proximity to Taiwan (from NRL) are shown in Fig. 7 for Talim, Doksuri, and Saola; Fig. 8 for Tembin and Jelawat; and Fig. 9 for Kong-Rey. In these figures, the forecasts made at an earlier time are chosen and compared directly with the satellite images. One can see that each of the rainfall patterns of the TCs, often unique in its own way, was forecast beforehand with high verisimilitude at various ranges within days 1–5 (Figs. 7–9). For example, the characteristics of a small TC in Tembin and much larger ones in Saola and Jelawat (Figs. 7 and 8), and the asymmetric structure in Talim, Doksuri (Figs. 7a–d), Tembin after it crossed Taiwan (Figs. 8c,d), and Kong-Rey (Fig. 9) were all captured with high realm, so were the locations of major rainbands and regions of intense (or weak) rainfall within the storm in Saola (Figs. 7e,f) and Jelawat (Figs. 8e,f). Well-predicted features also include the frontal rainband to the northeast of Taiwan during Talim (Figs. 7a,b), the distant rainband of Doksuri east of Taiwan (Figs. 7c,d), and the heavy rain over southwestern Taiwan near 2100 UTC 28 August during Kong-Rey (Figs. 9e,f). It is such highly realistic forecasts, due to the model’s ability to resolve convection and the topography of Taiwan (cf. Fig. 2b), that yield the quality in the QPFs (when the evolution is captured reasonably well). However, since larger track errors are inevitable at times, especially at longer ranges (cf. Fig. 3), the QPFs by some other forecasts are not ideal in their accuracy (Figs. 4 and 5). Therefore, it is important to view each QPF as an approximated (and yet realistic) rainfall scenario in Taiwan if that particular evolution (and track) takes place.
b. Individual typhoon cases in 2012
Now, we examine deeper each of the TCs and discuss why some of the QPFs, especially at longer ranges beyond 3 days, were successful while others were not. For Talim and Tembin (and later for Kong-Rey), some attention is directed toward their interaction with the southwesterly monsoon and a more complicated situation for rainfall. The discussion of Saola and Jelawat is partially focused on their hazard effects, while that on Doksuri will be brief.
The first typhoon to strike Taiwan in 2012 was Talim, a tropical storm that developed over the northern South China Sea (SCS) and approached from the southwest (Figs. 3a,b). Historically, only about 16% of TCs in Taiwan come from this direction (Shieh et al. 1998). After lingering near 19°N, 113°E for about 2 days, Talim started to accelerate toward the northeast around 1200 UTC 18 June and then passed by northwestern Taiwan rapidly (near 40 km h−1) on 20 June (Fig. 10a). Because of its quick approach and the design of the domain (to better accommodate TCs from the east; cf. Fig. 2a), relatively few tracks were available in Fig. 3b as noted earlier. However, high quality QPFs for 20 June were made for several days in a row from 13 to 16 June, especially the earliest on day 8 (Figs. 4a and 6a). Consequently, we investigate the reason for this impressive result. At 1200 UTC 18 June when Talim started to move northeastward, it was accompanied by a southwesterly flow surge (at 850 hPa; Fig. 10a), which was at least partly induced by another much stronger TC, Guchol (near 25°N, 129°E, category 4 before 0600 UTC 18 June), that traveled northward. Therefore, Talim’s movement was in response to the monsoon surge, and its rainfall pattern was asymmetric, as captured in the model (Fig. 7b; t = 26 h). In the forecast made on 13 June, Talim had diminished before it reached Taiwan and yet heavy rainfall over large areas was still caused by the strong monsoonal flow with Talim’s remnant embedded (not shown), yielding TS = 0.22, POD = 0.74, and FAR = 0.76 at 200 mm. Similar situations also occurred with monsoon rainfall alone in other daily forecasts made prior to 17 June (as no track was identified; cf. Fig. 3b). Therefore, even though Talim had diminished to a remnant in these earlier forecasts, the QPFs provided up to 8 days in advance were nonetheless still very informative and valuable, since the monsoon surge that constituted an important part of the total rainfall was captured. At shorter ranges, as is often the case, the QPFs become better again, especially on day 1 with TS = 0.38 (FAR = 0.0) at 350 mm, a threshold not much lower than the peak amount of 415 mm (Figs. 4 and 6a).
The second typhoon, Tropical Storm Doksuri, occurred roughly 1 week after Talim in late June. Around the time when the first TTFRI track forecast was released, four tracks from the daily CReSS were available (Figs. 3c,d), one fewer than expected as the run on 27 June was not executed because of data issues. This tropical storm moved west-northwestward through the Luzon Channel at about 24 km h−1, missing the southern tip of Taiwan by about 200 km, and was loose in structure with nearby rainfall mostly in the western and northwestern quadrants (Figs. 7c,d). As a result, the rainfall over Taiwan was limited and mostly to the southeast, while a decent QPF (at the earliest) was produced on 24 June for day 4 (Figs. 4b, 6b).
The third typhoon, Saola, posed a much greater threat to Taiwan than either Talim or Doksuri, as it was large and more intense (Figs. 7e,f), and most of all, it moved very slowly at only about 10 km h−1 inside a low pressure zone (synoptic map not shown) upon its approach (Figs. 3e,f). While the daily CReSS forecasts produced much longer tracks starting about 3 days earlier than the TTFRI ensemble for this category-1 TC, the earlier ones tended to predict a track more toward the east and the later ones increasingly close to Taiwan (Fig. 3f). Such a greater uncertainty yielded a larger spread in tracks and, consequently, a variety of rainfall scenarios for 1–2 August (Figs. 4c,d). As a result of this gradual shift in tracks, the worst-case scenario occurred. On both days, peak rainfall of at least ~900 mm was received, first over northern and then central Taiwan, and Saola became the most hazardous TC in 2012 (with seven deaths; W15). While Fig. 7f shows the high realm of the storm in the forecast made on 30 July (with considerable wobbling of its center), decent QPFs were produced on 29 July for 1 August (day 4) and, most impressively, on 28 July for 2 August (day 6, Fig. 4; TS = 0.5, POD = 0.6, FAR = 0.27, and BS = 0.82 at 350 mm). In the run on 29 July (Fig. 3f, navy blue) the track error at 0000 UTC 1 August was about 170 km to the east (TC near 22.7°N, 125.2°E; t = 72 h). In the forecast 1 day earlier (green), the track error at 0000 UTC 2 August was larger and about 240 km (TC near 24.0°N, 124.2°E; t = 120 h), partly because of the sudden westward turn of the actual storm off Taiwan’s coast, but a slow translation speed was predicted. Thus, with typical track errors at their range, the model was able to produce realistic QPFs early for Saola (given its relatively large size and wide rainfall area to the west and southwest; cf. Figs. 7e,f) and extend the lead time to 5–6 days (Figs. 4 and 6c,d; see also W15). Such results are very encouraging.
The next TC, Tembin, initially moved northward after its formation east of Luzon but suddenly turned westward toward Taiwan at 1200 UTC 21 August (Fig. 3h, black). After it penetrated southern Taiwan into the Taiwan Strait, it first stalled over the northern SCS, then turned back to accelerate northeastward and almost make a second landfall (Fig. 3h). In Fig. 3g, the TTFRI ensemble released on 23 August was chosen in order to cover its early prediction on this rare track reversal, which took place under the influence of another large and intense typhoon, Bolaven (category 4 during 24–26 August) that induced a southwesterly monsoon (Fig. 10b). The Fujiwhara effect (Fujiwhara 1921; Kuo et al. 2000; Prieto et al. 2003) between the two TCs might have played some role as well. The TTFRI forecast at 0000 UTC 23 August had the majority of storms turning back prematurely, but the track reversal was predicted quite well (and much longer into the future) by CReSS (Figs. 3g,h), which also captured nicely Tembin’s size and structural characteristics at different stages (Figs. 8a–d). The first westward turn and subsequent landfall (near 2200 UTC 23 August) were predicted by CReSS on both 20 and 21 August (Fig. 3h, red and green; t = 94 and 70 h), but the timing was a little early (by ~14 and 8 h) and the turn was not sharp enough, causing the landfall point to shift north by about 190 km, which is a comparatively large distance for this small storm. As a result of the track errors in both direction and speed, the predicted rainfall occurred mainly on 23 August over the northeastern quadrant of Taiwan with comparable amounts (not shown), and the QPFs for 24 August were dissimilar to the observations (Fig. 4e). Starting from 22 August, the QPFs on days 1–3 were much improved (also Fig. 6e). Nonetheless, the rainfall predictions made on 20–21 August, with the correct event magnitude, could still provide useful information to experienced forecasters.
The last TC in 2012 was Jelawat, a large and robust category-3 typhoon. Since it moved quite slowly (13–15 km h−1) upon approach (cf. Figs. 8e,f), its proximity to Taiwan and landfall possibility were of great concern. As seen in Fig. 3j, starting almost 1 week earlier (on 20 September), all but one of the tracks from CReSS were available (roughly) at the time of the first TTFRI release (Fig. 3i). Thus, the time-lagged ensemble provided advanced warning for this typhoon. While the overall track errors were small for their range, the CReSS predictions fell into two categories: more westward tracks and landfall (or nearly so, including those made on 20–22 and 24 September), and recurving tracks that missed Taiwan (all other forecasts). Consequently, the QPFs for 28 September (Fig. 4f) were either 1) a great amount of rain over much of eastern Taiwan (on days 8, 7, and 5) or 2) concentrated rainfall in northeastern Taiwan only (on all other days). The former group provided the worst-case scenario for Jelawat with a longer lead time. Fortunately, the latter case associated with recurving tracks occurred. Some of the track errors in the second group were very small; for instance, the one in Fig. 8f (made on 23 September) was only 110 km at t = 119 h (cf. Fig. 3j, cyan). Under such conditions with more steady steering flow, the QPFs were highly consistent and accurate (Fig. 4), and those on days 6, 4, 2, and 1 all yielded TSs of 0.50 at 200 mm, which is remarkably high for a threshold so close to the peak value of 216 mm (Fig. 6f). In three of these four forecasts, the POD is 0.5 and the FAR is 0.0 at 200 mm. While an impressive QPF was first made on day 6, the shifting forecast results with time also give the forecasters a good sense about which scenario is more and more likely to occur, as is also evident in Saola and some other cases. This is clearly another useful and desirable feature of such a time-lagged ensemble.
4. The highlighted case of Kong-Rey
a. Forecasts by the daily ensemble
In section 3, the capability and usefulness of highly realistic QPFs at extended lead time are demonstrated, especially for slow-moving TCs such as Saola and Jelawat. As is also exemplified by the Jelawat case, if the TC vortex is directly responsible for the rain, the QPFs by such a CRM are often very accurate when track errors are small. Moreover, in situations when the rainfall is produced not solely by the TC, a decent QPF can be obtained without a good track, or even without a track at all, if the atmospheric evolution is reasonably well predicted, such as for Talim. Often with significant monsoon interaction, these more complicated situations present higher challenges in forecasts than do more straightforward events, and thus we seek such a hazardous TC for further highlights. Typhoon Kong-Rey (2013) fits this profile and thus is chosen. Below, forecasts for Kong-Rey by the daily ensemble (section 4a) and the ensemble running four times a day (section 4b) are presented and discussed.
Kong-Rey was a tropical storm moving northward off the eastern coast of Taiwan (Fig. 3l, black). At the time of the first TTFRI release (after 0000 UTC 27 August; Fig. 3k), five long tracks were already available with a large spread, indicating a higher uncertainty in the earlier predictions with longer lead time (Fig. 3l). Unlike Saola and Jelawat, Kong-Rey was very loose and weak with evident rainfall asymmetry (Fig. 9). However, a moisture-laden southwesterly monsoon surge over the SCS took place as Kong-Rey passed by Taiwan (Fig. 10c), and heavy rainfall occurred on three days in a row over 29–31 August during and in the wake of the storm (also Fig. 5). Because of torrential rains, flash floods occurred in many cities over the plains in central and southern Taiwan with six deaths (source: CWB), making Kong-Rey the most deadly and hazardous TC in 2013. The heavy rainfall of this event, especially over the plains, was not well predicted and the disproportionally large damages by a weak storm caught many by surprise. Hence, it is selected as our highlight case. In the past, a few typhoons with similar tracks also led to extreme rainfall from their interaction with the monsoon after departure, such as Mindulle in 2004 and Kalmaegi in 2008 (Chien et al. 2008; Chang et al. 2013; Yu and Cheng 2014).
As mentioned, decent QPFs were made on days 7, 4, and 5 for 29, 30, and 31 August, respectively (Fig. 5). In Fig. 3l, the earliest forecast (on 23 August; Fig. 3l, red) predicted Kong-Rey to move off the western coast instead, and had the TC near 24.2°N, 120.2°E at 1200 UTC 28 August with a track error of about 300 km (t = 132 h). However, the rainfall scenario from this weak, asymmetric storm with the monsoon surge (Figs. 9 and 10c) was not too different from reality, allowing a high quality QPF for 29 August at such a long lead time (TS = 0.28, POD = 0.31, and FAR = 0.26 at 200 mm; cf. Fig. 6g). Subsequent daily forecasts on 24–26 August had the tracks too far east, degrading the accuracy of the QPFs (Figs. 3l and 5) even with a realistic TC structure (Figs. 9a–d). Afterward on 27 August, the model track improved in direction but the speed was too fast (Fig. 3l, magenta) such that the track error grew from about 120 km at t = 36 h, and yet the monsoon rainfall on 30 and 31 August was captured (days 4 and 5; Fig. 5). Apparently, the track error became less important during the later stages of this event, since the monsoon rather than the TC was responsible for the rain. With overall reduced errors, decent QPFs for all three days could be produced since 28 August as expected, with most TS ≥ 0.2 at 100 mm and some at 200 mm (for peak amounts of 315–426 mm; Figs. 5 and 6g–i). Thus, in Kong-Rey we again see that the rainfall scenarios related to TCs in Taiwan can be quite sophisticated as a result of the influences of the monsoon and steep terrain, and it does not necessarily take a robust typhoon to lead to extreme rainfall. These types of delicate events are more difficult to predict well in advance, and we stress that the high resolution of CRMs, with their improved overall ability to simulate topographic effects as well as convection and moist processes and thus their interaction with the environment, is particularly crucial to achieve this goal, compared to those events caused by simpler situations.
b. Forecasts by the ensemble every 6 h
While high quality QPFs are attainable at a lead time of nearly 1 week even for a forecast challenge in Kong-Rey (2013), we have up to now only examined the daily forecasts by the 2.5-km CReSS at about a quarter of the computational expense of the TTFRI 3-day ensemble. So, additional runs in forecast mode every 6 h (cf. Fig. 1b), as described in section 2b, were performed for Kong-Rey to further highlight the full capabilities of the time-lagged ensemble at comparable expense, with emphasis on its effectiveness, feasibility, and probability information.
With four 8-day forecasts per day, the tracks are quadrupled in number (Fig. 11) from those in Fig. 3l with even a slightly larger spread. The number of lagged members for QPFs at a range of at least 3 days is 21, comparable to the TTFRI system. With more tracks, their shifting in time appears more gradual and 11 (out of 12 runs) are already available by 25 August (Fig. 11a), two full days before the first TTFRI release (cf. Fig. 3k). While the latter did not cover the actual track, the CReSS tracks already yielded a much wider maximum spread at this time, with earlier ones more toward the left and subsequent ones on 24 August more toward the right compared to the best track (Fig. 11a). Any track outside such a spread would have a much reduced impact on Taiwan. In Figs. 11b and 11c, the tracks produced during 25–26 and 27–28 August are shown, respectively, and they gradually swing back and close in on the observed track. Again, associated with a decrease in forecast uncertainty, the reduction in spread at shorter range gives indications about which scenario has increased likelihood. Furthermore, the initial large spread provides a wide spectrum of possible rainfall scenarios from this event for Taiwan at longer lead time, and this is highly useful for hazard preparation and will be further elaborated upon. In Fig. 11d, all 27 tracks produced through 28 August (available by 0000 UTC 29 August) are plotted, and the time-lagged ensemble clearly provides much better information compared to Fig. 3k (note that the seven tracks after 0000 UTC 27 August are also included in Fig. 11d; cf. Table 3).
Because of the long duration of this event, the 48-h accumulated rainfall over 29–30 August is selected for discussion (Fig. 12). A total of 25 time-lagged runs, executed between 0000 UTC 23 August and 0000 UTC 29 August, can cover the target period, which is very comparable in number to the multimember ensemble. In the latter approach (3-day forecasts), the earliest predictions available to cover the same 48-h period would be on 28 August (cf. Fig. 1). In contrast, a new member is added every 6 h beginning 1 week earlier through the time-lagged approach, and more importantly, each provides a highly realistic rainfall scenario associated with that particular track. A brief inspection of Fig. 12 suggests that at least 18 members (72%) predict heavy rainfall over the plains in central or southern Taiwan, or both, and most of the rest were made during 0000 UTC 24 August and 0600 UTC 25 August when the tracks deviate too far east (Figs. 11a,b). In a few members, the scenarios are even slightly worse than actuality (Fig. 12).
The probability distributions derived from the 25 time-lagged members are shown in Figs. 13a–d for 48-h thresholds at 100, 200, 350, and 500 mm, respectively. Over the southern mountains (cf. Fig. 2b), there is more than a 20% chance of receiving 500 mm of rain. Over parts of the central and southern plains, up to about 65%, 35%, 20%, and 10% of the members reach the four thresholds, respectively (Figs. 13a–d). While early warning of heavy-rainfall potential is indicated by the members prior to 0000 UTC 26 August (Figs. 13e–h), the significant increase in probabilities over the plains from the members afterward, by some 15%–30% (~10% at 500 mm; Figs. 13i–l), confirms the danger that lies ahead even though Kong-Rey is merely a weak storm. Thus, not only available, the probability information through the time-lagged method from deterministic CRMs is highly useful, as shown in both sections 3 and 4. After Morakot in 2009, both Zhang et al. (2010) and Fang et al. (2011) studied its predictability using convective-permitting WRF ensembles (Δx = 4 and 4.5 km) with 60 and 32 members, respectively, but the resources needed for two 4-day forecasts per day are estimated to be about 25 and 7 times of the TTFRI WRF ensemble system. Such heavy demands in computing power are obviously not yet easily feasible at many operational centers.
Thus, because of its long range, our time-lagged strategy is very effective in providing a fuller spectrum of possible scenarios in QPFs at extended lead times, so that the disaster mitigation agencies can start their preparations early, first for the worst-case scenario and then making adjustments later as the situation evolves. Such a mindset fits the conventional wisdom of “hope for the best, but prepare for the worst” very well, and we believe it is a prudent strategy when confronted with the hazard potential of a typhoon.
5. Discussion and concluding remarks
By adopting the time-lagged method to obtain probability (ensemble) information, the forecast strategy in this study becomes highly cost effective compared to a typical 24-member ensemble using similar computational resources, as shown in Table 1 (bottom). The resolution is doubled from Δx = 5 to 2.5 km to become cloud resolving, the fine domain size is enlarged from 750 km × 900 km to 1860 km × 1360 km (by 3.75 times), and the forecast range is extended from 3 to 8 days, all at the same time (Table 1; cf. Fig. 2a). Such a dramatic improvement in model configuration is achievable because now each forecast (completed within 6 h) is made using the full resources rather than a small fraction of them divided among the members. Thus, in an innovative way, our system combines the strengths of high resolution for QPF and longer lead time for hazard preparation together, and its performance is evaluated for all five typhoons in 2012 and an additional highlight case of Kong-Rey (2013).
For all six typhoons evaluated, the daily ensemble from the 2.5-km CReSS produced high quality QPFs at ranges within 3 days, as expected. More importantly, such decent QPFs were also made at the longest range, up to days 8, 4, 6, 3, 6, and 7 beforehand, respectively, for each of the six typhoons (Figs. 4–6), providing much extended lead time, especially for slow-moving TCs that pose higher threats. The large domain and extended range allow the TC to enter the fine mesh as early as possible, thereby realizing the chance for a decent QPF to be made at longer lead time when the atmospheric evolution (with the TC embedded) is reasonably well captured (Figs. 7–10, sections 3 and 4). Even if the track errors are relatively large, the scenario (including rainfall) is still realistic and useful as one of the possibilities (Figs. 3–6 and Figs. 11– 13). After all, at early stages when the TC is still far away from Taiwan, there is no guarantee that any given scenario will happen. This is the nature of making any forecast for the future, and the reason why the ensemble approach is adopted in the first place. Therefore, at longer ranges, the forecasts should not be expected to be correct (as most of them will likely turn out to be wrong), but the information generated can be used to our advantage for earlier and more effective hazard preparation.
Linked to the nonlinearity of the atmosphere (Lorenz 1963), it is well known that the spread tends to grow with time in ensemble forecasts because of the increase in uncertainty with range. However, when time-lagged outputs are used, this trend reverses in order and the forecast uncertainty is initially larger and gradually reduces (Figs. 3 and 11). Thus, at a medium range out to 8 days, our system can exhibit large spread and provide a wide spectrum of rainfall scenarios at longer lead times (say, ≥4–5 days), each highly realistic for its track, for advanced preparation for the worst case. For hazard preparation, such a worst-case scenario is always necessitated by government agencies at the earliest time possible, and the time-lagged ensemble is well suited to deliver it. In addition, the common issue of inadequate spread in a short-range ensemble (e.g., Roebber et al. 2004; Eckel and Mass 2005) is easily solved. As the typhoon approaches and the predicted tracks converge in association with a reduced uncertainty, the disaster mitigation agencies can make adjustments toward the scenario with growing likelihood. As demonstrated, this property makes our strategy highly useful for hazard preparation, and fits well the conventional wisdom to “hope for the best, but prepare for the worst.” The choice of forecast range, hence, not only dictates the number of time-lagged members available (cf. Fig. 1b), but also affects the degree of maximum spread in the tracks (and thus QPFs). As evaluated herein, 8 days appear to be a good choice at the present time.
Finally, we return to Table 1 (top) and grade the overall performance of the 2.5-km CReSS time-lagged ensemble system (four 8-day forecasts per day) at expenses similar to the 3-day multimember ensemble. The quality of the QPFs, as in the short-range deterministic models (e.g., W15), is very good (Figs. 4–9 and 12), while the intensity remains in the “good” category. With a range of 192 h, the tracks are much longer and comparable in number to the multimember ensemble (Figs. 3 and 11), and the potential lead time is dramatically improved (Figs. 4–6 and 12). Thus, qualities in both track and lead time are now very good. With larger spread early on, the system can produce a wide range of possible scenarios that almost certainly cover the real one (cf. Fig. 11) and can provide highly useful information at longer ranges (≥4–5 days). The estimates in probability are therefore also good or even very good at times with the evolving information (Figs. 12 and 13). Thus, by combining high resolution with long range, the time-lagged approach is clearly an improvement on the traditional method in all five major items in need (Table 1). As shown in Fig. 1, the QPFs for any day (or fixed period) come from all the cores running for roughly 1 week, versus less than 6 h in the multimember system. Our 8-day time-lagged ensemble, running four times a day, needs roughly 1500 cores, which is clearly already feasible and affordable by virtually every operational center.
Because of the great advantages found when using CRMs with a large domain and long forecast range through time-lagged ensembles, as demonstrated herein, forecast centers that demand high quality QPFs should consider adopting such a system, particularly for regions prone to rainfall hazards. When affordable, a small number of different CRMs (or the same CRM with different physical combinations), each using such a time-lagged approach, is also recommended for better coverage of scenarios, as this approach would be very powerful in providing realistic QPFs for hazard preparation and emergency action.
The authors are thankful for the constructive comments from the two reviewers that helped improve the manuscript. CCW wishes to thank his colleague, Prof. Greg Shellnutt, for proofreading the manuscript, and assistants Y.-W. Wang, T.-R. Wang, and K.-Y. Chen for their help on this study. The 8-day forecasts were run on the Advanced Large-scale Parallel Supercluster (ALPS) of the National Center for High-performance Computing (NCHC), and this computational resource is appreciated. Original plots of Fig. 2a and WRF tracks in Fig. 3 were provided by the TTFRI, and the TRMM PR/TMI observations in Figs. 7–9 are from NRL. This study is supported by the Ministry of Science and Technology of Taiwan under Grants MOST-103-2625-M-003-001-MY2 and MOST-103-2119-M-003-001-MY2.