Abstract

To quantify the effects of long-term climate change on typhoon rainfall near Taiwan, cloud-resolving simulations of Typhoon (TY) Sinlaku and TY Jangmi, both in September 2008, are performed and compared with sensitivity tests where these same typhoons are placed in the climate background of 1950–69, which is slightly cooler and drier compared to the modern climate of 1990–2009 computed using NCEP–NCAR reanalysis data.

Using this strategy, largely consistent responses are found in the model although only two cases are studied. In control experiments, both modern-day typhoons yield more rainfall than their counterpart in the sensitivity test using past climate, by about 5%–6% at 200–500 km from the center for Sinlaku and roughly 4%–7% within 300 km of Jangmi, throughout much of the periods simulated. In both cases, the frequency of more-intense rainfall (20 to >50 mm h−1) also increases by about 5%–25% and the increase tends to be larger toward higher rain rates. Results from the water budget analysis, again quite consistent between the two cases, indicate that the increased rainfall from the typhoons in the modern climate is attributable to both a moister environment (by 2.5%–4%) as well as, on average, a more active secondary circulation of the storm. Thus, a changing climate may already have had a discernible impact on TC rainfall near Taiwan. While an overall increase in TC rainfall of roughly 5% may not seem large, it is certainly not insignificant considering that the long-term trend observed in the past 40–50 yr, whatever the causes might be, may continue for many decades in the foreseeable future.

1. Research background and motivation

When facing disastrous, extreme, or record-breaking weather events like tropical cyclones (TCs) and heavy rainfall, it is generally very difficult to assess the influences of anthropogenic forcing (related to “global warming”) or long-term climate change (including natural forcing and internal variability as well) since the dynamical forcing in these rare, high-impact events is typically much larger than the climate forcing and favorable factors across a wide range of scales often come together in synergy to produce them. Thus, while an increase in the severity of extreme weather events is consistent with the expected effects of climate change, it is generally difficult to attribute any single event to the warming or climate change (e.g., Solomon et al. 2007; Stott et al. 2010; Min et al. 2011; Pall et al. 2011).

Obviously, the likely changes in tropical cyclones and other types of extreme weather events in the future are of major concern under the global warming scenario. One common approach to tackle such questions is to perform long-term simulations with global or regional climate models and compare event statistics in the present and future climates (e.g., Meehl and Tebaldi 2004; Knutson et al. 2007, 2008; Zhao et al. 2009; Murakami et al. 2012; Sillmann et al. 2013). One issue of this approach is the reliability of such models in reproducing the observed characteristics of extreme weather events with rather coarse resolution (typically more than tens of kilometers), raising the need for further dynamical or dynamical–statistical downscaling (e.g., Stott et al. 2010; Knutson et al. 2013; Emanuel 2013). Also, because of the high degree of natural variability involved among the two groups of different events (one in present and the other in future climate) as well as the uncertainties in the projection of future climate, especially at regional scale, a large number of samples is often needed to establish the statistical significance and potentially the confidence for a thorough assessment (e.g., Stott et al. 2004; Karl et al. 2008; Pall et al. 2011 ,Alexander and Tebaldi 2011; Fischer et al. 2013).

Instead of assessing the possible changes in typhoons in the future, which involves reliability and much higher uncertainties as mentioned above, in this study we attempt to address the following issue quantitatively: How much rain, in terms of percentages, from the most rainy typhoon cases near Taiwan in modern days can be attributed to the effects of long-term climate change (whether due to anthropogenic impact or natural variability) that we have already seen? To do this, we select specific modern-day typhoons near Taiwan and perform highly realistic simulations of their life cycle using a cloud-resolving model (i.e., control runs, one for each typhoon). Then, we place these same typhoons in a climate background representing conditions from about 40 yr ago, constructed by subtracting the long-term trend from gridded analyses during the case period, and run sensitivity tests and make direct comparison with the control simulations. Here, because the long-term trend is computed using reanalysis data based on observations, the uncertainties involved with climate projection are not present (although the ultimate causes of the climate change over the period remain debatable). Also, two cloud-resolving, high-resolution runs of the same typhoon (with identical synoptic evolution) are compared with the only difference in their mean climate state, and much of the uncertainties from natural variability among events and inadequate model resolution are eliminated. Thus, quantitative assessments are allowed for individual events from a small number of model experiments through sensitivity tests, as has long been practiced to address the roles or isolate the impacts of various factors (e.g., Gall 1976; Kuo et al. 1991; Stein and Alpert 1993; Braun and Tao 2000; Wang et al. 2005, 2012, 2013a). Typically, systematic responses in the model and the underlying physics are examined in these tests without strict statistical inference. To our knowledge, such a strategy has not been adopted to access the impacts of climate change on high-impact weather systems before, and thus this paper, using a small number of cases at first, also serves to establish the concept of this methodology. Herein, we report our results on two landfall typhoons in Taiwan: Typhoon (TY) Sinlaku (2008) and TY Jangmi (2008). Both TCs exhibited a typical track to approach from the southeast, and they are ranked as the 3rd and 10th most rainy typhoon in Taiwan over the past 50 yr (Chang et al. 2013). Our primary goal is to quantify the change in TC rainfall itself, and the secondary objective is to examine the rainfall change over Taiwan. Further details on the methodology and results are given below.

2. Methodology and experiments

To compute the long-term trend of climate change for the global atmosphere, a dataset extending back into the past for as long as possible is preferred. Therefore, for this purpose we adopt the National Centers for Environmental Prediction (NCEP)–National Center for Atmospheric Research (NCAR) monthly-mean global gridded reanalysis (2.5° × 2.5°; Kalnay et al. 1996), as in Chu et al. (2012). These reanalysis data are used to compute the mean climate states for two 20-yr periods, 1950–69 and 1990–2009, and subsequently their differences for all major variables at all pressure levels and the surface. For sea surface temperature (SST), the 1° × 1° Hadley Centre Sea Ice and Sea Surface Temperature (HadISST) data (Rayner et al. 2003) for the same periods are employed. Using 20-yr averages, signals from variations up to decadal time scale are largely removed, and these differences (called the delta values or “Δ” for short) represent the long-term climate trend during the past half century or so under a mixture of both natural and anthropogenic forcings. Although some multidecadal variability (e.g., Pacific decadal oscillation; Trenberth 1990; Biondi et al. 2001) or climate regime shifts (Lo and Hsu 2008) may still be present in the Δ values, it is widely accepted that anthropogenic influence on global-mean temperature became relatively more detectable in recent decades, especially since the 1990s (e.g., Solomon et al. 2007).

Our results of the mean state in modern climate of 1990–2009 and the Δ values from 1950–69 to 1990–2009 (latter minus former) over the western North Pacific (WNP) are shown in Figs. 1 and 2, respectively. Compared to the mean state (Fig. 1), the long-term changes since 1950–69 near Taiwan are quite small as expected and include slight increases in northwesterly wind components at low levels (1000–700 hPa) and in westerly wind components in the middle troposphere (600–400 hPa), both by about 0.5 m s−1 (Figs. 2a,b) and in general agreement with Chu et al. (2012). There is also a warming and moistening trend of roughly 0.5 K and 0.1–0.4 g kg−1 at low levels, as well as an increase in SST by about 0.6–1.5 K near Taiwan (Figs. 2c,d). Further aloft, weak warming (≤0.3 K) exists at 200–300 hPa and mild cooling of about 0.5 K also appears at 100 hPa near Taiwan (not shown), in rough agreement with Vecchi et al. (2013) and Emanuel et al. (2013). More precisely, the above changes correspond to a weakening in easterly to southeasterly mean flow by about 0.5 m s−1, an increase in moisture by about 1.5%, and a warming by about 0.6 K below 500 hPa and by 0.68 K in SST (averaged over 14°–32°N, 114°–135°E), and we can anticipate that modern-day typhoons might move slightly slower if it is to approach Taiwan from the southeast and produce more rain because of a wetter environment.

Fig. 1.

The 1990–2009 long-term mean states of geopotential height (gpm; contours) and horizontal winds (m s−1, vectors, reference vector at bottom) at (a) 850 and (b) 500 hPa, (c) temperature (K; contours, every 2 K) and specific humidity (g kg−1; color) at 1000–700 hPa, and (d) SST (K) over the WNP. Intervals of geopotential height contours are 10 and 20 gpm in (a),(b), and the thick dotted lines depict ridge axes. The model domains used for the two typhoons are also plotted in (d).

Fig. 1.

The 1990–2009 long-term mean states of geopotential height (gpm; contours) and horizontal winds (m s−1, vectors, reference vector at bottom) at (a) 850 and (b) 500 hPa, (c) temperature (K; contours, every 2 K) and specific humidity (g kg−1; color) at 1000–700 hPa, and (d) SST (K) over the WNP. Intervals of geopotential height contours are 10 and 20 gpm in (a),(b), and the thick dotted lines depict ridge axes. The model domains used for the two typhoons are also plotted in (d).

Fig. 2.

The long-term trend (Δ values) between two 20-yr averaged mean states of 1950–69 and 1990–2009 (latter minus former) of geopotential height (gpm; contours every 3 gpm) and horizontal winds (m s−1; vectors; reference vector at bottom) averaged over (a) 1000–700 hPa and (b) 600–400 hPa, (c) temperature (K; contours every 0.2 K; dashed for negative values) and specific humidity (g kg−1; color) averaged through 1000–700 hPa, and (d) SST (K) over the WNP. Note that the color scales are not linear in (c),(d).

Fig. 2.

The long-term trend (Δ values) between two 20-yr averaged mean states of 1950–69 and 1990–2009 (latter minus former) of geopotential height (gpm; contours every 3 gpm) and horizontal winds (m s−1; vectors; reference vector at bottom) averaged over (a) 1000–700 hPa and (b) 600–400 hPa, (c) temperature (K; contours every 0.2 K; dashed for negative values) and specific humidity (g kg−1; color) averaged through 1000–700 hPa, and (d) SST (K) over the WNP. Note that the color scales are not linear in (c),(d).

The Cloud-Resolving Storm Simulator (CReSS) of Nagoya University, Japan (Tsuboki and Sakakibara 2007) is used for the high-resolution numerical experiments at a grid size of 3 km with a dimension (x, y, z) of 720 × 720 × 50 and model top at 25 km, so the model domain is 2160 km × 2160 km for both cases (cf. Fig. 1d). The vertical grid of CReSS is stretched and the spacing (Δz) increases gradually from 100 m at the bottom to 632.45 m above 12 km, while the mean Δz is 500 m. The same physical options as those used in Wang et al. (2012) are employed. For the control experiments, the European Centre for Medium-Range Weather Forecasts (ECMWF) Year of Tropical Convection (YOTC) analyses (0.25° × 0.25°, every 6 h; Waliser and Moncrieff 2007) are used as the initial conditions (ICs) and boundary conditions (BCs), and the monthly-mean 1° × 1° HadISST and real topography (at a resolution of about 1 km × 1 km) are provided at the lower boundary. Aimed to reproduce the events at high realm, the control runs are named S1 for Sinlaku (2008) and J1 for Jangmi (2008). For S1, the integration starts at 1200 UTC 8 September and ends at 0000 UTC 18 September 2008, for a total of 9.5 days (228 h), while J1 (2008) covers the period from 1200 UTC 26 September to 0000 UTC 1 October 2008 (for 4.5 days or 108 h). Occurring in the same month, the best tracks of the two TCs from the U.S. Joint Typhoon Warning Center (JTWC) are plotted in Fig. 3, and the two storms both approached from the southeast and recurved near northern Taiwan. Besides best-track data, the simulation results are also verified against satellite observations such as the Tropical Rainfall Measuring Mission (TRMM) and the rainfall over Taiwan from a dense network of about 400 automated rain gauges operated by the Central Weather Bureau (CWB; Hsu 1998; for details see, e.g., Fig. 2 of Wang et al. 2013b). Previous studies on various aspects of these two typhoons can be found in Kuo et al. (2012), Wu et al. (2012), Leroux et al. (2013), and Sanger et al. (2014), among others.

Fig. 3.

The JTWC best tracks (blue) and model TC tracks (a) in S1 (dark green) and S2 (red) for TY Sinlaku and (b) in J1 (dark green) and J2 (red) for TY Jangmi. For best tracks, navy (light) blue indicates the time period during (before/after) model experiments. All tracks give locations of TC center every 6 h with symbols plotted every 12 h at 0000 and 1200 UTC. Selected dates (in September 2008) are also labeled for locations at 0000 UTC.

Fig. 3.

The JTWC best tracks (blue) and model TC tracks (a) in S1 (dark green) and S2 (red) for TY Sinlaku and (b) in J1 (dark green) and J2 (red) for TY Jangmi. For best tracks, navy (light) blue indicates the time period during (before/after) model experiments. All tracks give locations of TC center every 6 h with symbols plotted every 12 h at 0000 and 1200 UTC. Selected dates (in September 2008) are also labeled for locations at 0000 UTC.

In the sensitivity test for each of the two typhoons (named S2 and J2, respectively), all model configurations are identical to the control run except that the long-term climate change (i.e., the Δ values) is subtracted from the IC/BCs, including both the YOTC and HadISST analyses. Here, bilinear interpolation is applied to obtain Δ values on the ECMWF grid (0.25°) from the coarser reanalysis data (2.5°). Using the above method, we essentially place the two typhoons in the climate background in the 1950–60s with the same synoptic forcing and evolution in the sensitivity tests, compare their differences to the control (modern day) experiments, and investigate the underlying physical reasons. Of course, issues related to possible changes in typhoon frequency or active regions over time (e.g., Bender et al. 2010) cannot be addressed here, and the feedbacks from the ocean are also neglected. In this study we focus exclusively on rainfall changes, since typhoon hazards are mostly induced by the heavy rainfall in Taiwan (e.g., Cheung et al. 2008; Su et al. 2012; Chang et al. 2013; Wang et al. 2013b) and in many other regions experiencing TCs around the world.

3. Model results of Typhoon Sinlaku (2008)

In the S1 control run, the simulated track of Sinlaku matches well with the JTWC best track, except for the last day (Fig. 3a). In intensity, the model TC in S1 is considerably stronger than the YOTC analysis in both its minimum sea level pressure (SLP) and maximum surface wind before landfall (Fig. 4). While the estimated intensity in the best tracks by different operational centers (e.g., JTWC and CWB) varies to some extent, the model TC appears to intensify less rapidly than the best tracks before 11 September. On the other hand, the model agrees better in SLP with the C-130 in situ observations (Wu et al. 2012), and the agreement with best tracks also improves since 12 September when the peak intensity is reached in S1 with a minimum SLP of 938 hPa and a maximum wind of 46 m s−1 (Fig. 4a).

Fig. 4.

Time series of (a) minimum SLP (hPa) and (b) maximum surface (10 m) wind speed (m s−1) from the JTWC and CWB best-track data, YOTC analysis, and model experiments of S1 and S2 (see legend) over the simulation period in September 2008 for TY Sinlaku. Black dots in (a) mark the minimum SLP from C-130 observations, adapted from Fig. 4 of Wu et al. (2012).

Fig. 4.

Time series of (a) minimum SLP (hPa) and (b) maximum surface (10 m) wind speed (m s−1) from the JTWC and CWB best-track data, YOTC analysis, and model experiments of S1 and S2 (see legend) over the simulation period in September 2008 for TY Sinlaku. Black dots in (a) mark the minimum SLP from C-130 observations, adapted from Fig. 4 of Wu et al. (2012).

Figure 5 shows TRMM satellite observations at selected times with better coverage of Sinlaku among all available images (from the Naval Research Laboratory) and can be compared directly with model results in S1 within 2 h in Fig. 6. It is confirmed that the model reproduces the TC rainfall structure well during 9–14 September in S1, except perhaps that the eye size is slightly too large (Figs. 5 and 6). Indeed, on 10 and 13 September, when Sinlaku’s eye appeared smaller (about 25–40 km in radius; Figs. 5b,e), the radius of maximum wind (RMW) in S1 also reduces but still remains at about 50 km (Fig. 7a). Thus, even though the CReSS model can successfully simulate the rainfall structure and processes resembling the eyewall contraction and replacement cycle (e.g., Willoughby et al. 1982; Houze et al. 2007; Kuo et al. 2009; Rozoff et al. 2012) at 3-km grid spacing (Figs. 6 and 7a), the inner core intensity is not fully captured, for which purpose TC bogus and/or intensive data assimilation may be required (e.g., Wu et al. 2012; Leroux et al. 2013; Sun et al. 2013). Nonetheless, the 5-day total accumulated rainfall during 11–15 September over Taiwan compares favorably with the rain gauge measurements (Figs. 8a,b). Thus, the life cycle of Sinlaku is reproduced in close agreement with the observations using the CReSS model at high resolution, except perhaps for its inner core intensity before landfall. Since the rainfall simulation in S1 is highly realistic (Figs. 5, 6, and 8a,b), a model sensitivity test can be used for our purpose to examine the changes in TC rainfall in the environment of past climate.

Fig. 5.

(a) TRMM Precipitation Radar (PR) or TRMM Microwave Imager (TMI) rain rates (inch h−1; color; scales at bottom) overlaid on the geostationary Multifunctional Transport Satellite (MTSAT) infrared cloud imagery (at closest time) of TY Sinlaku at (a) 0425 UTC 9 Sep, (b) 0330 UTC 10 Sep, (c) 0315 UTC 12 Sep, (d) 1947 UTC 12 Sep, (e) 0220 UTC 13 Sep, and (f) 0124 UTC 14 Sep 2008. All panels are from the Naval Research Laboratory.

Fig. 5.

(a) TRMM Precipitation Radar (PR) or TRMM Microwave Imager (TMI) rain rates (inch h−1; color; scales at bottom) overlaid on the geostationary Multifunctional Transport Satellite (MTSAT) infrared cloud imagery (at closest time) of TY Sinlaku at (a) 0425 UTC 9 Sep, (b) 0330 UTC 10 Sep, (c) 0315 UTC 12 Sep, (d) 1947 UTC 12 Sep, (e) 0220 UTC 13 Sep, and (f) 0124 UTC 14 Sep 2008. All panels are from the Naval Research Laboratory.

Fig. 6.

Model-simulated rain rates (inch h−1; color; scales at bottom) and horizontal winds (m s−1; full barb = 10 m s−1) at the height of 100 m in S1 run at (a) 0500 UTC 9 Sep, (b) 0300 UTC 10 Sep, (c) 0500 UTC 12 Sep, (d) 2100 UTC 12 Sep, (e) 0200 UTC 13 Sep, and (f) 0100 UTC 14 Sep 2008.

Fig. 6.

Model-simulated rain rates (inch h−1; color; scales at bottom) and horizontal winds (m s−1; full barb = 10 m s−1) at the height of 100 m in S1 run at (a) 0500 UTC 9 Sep, (b) 0300 UTC 10 Sep, (c) 0500 UTC 12 Sep, (d) 2100 UTC 12 Sep, (e) 0200 UTC 13 Sep, and (f) 0100 UTC 14 Sep 2008.

Fig. 7.

Evolution of azimuthally averaged wind speed (m s−1) at a height of 870 m (fourth model output level) with respect to radius from TC center in (a) S1 and (b) S2 and (c) their difference (S1 minus S2) for TY Sinlaku. The thick dashed lines in depict the radius of maximum wind.

Fig. 7.

Evolution of azimuthally averaged wind speed (m s−1) at a height of 870 m (fourth model output level) with respect to radius from TC center in (a) S1 and (b) S2 and (c) their difference (S1 minus S2) for TY Sinlaku. The thick dashed lines in depict the radius of maximum wind.

Fig. 8.

(a) Observed and (b),(c) model-simulated total 5-day rainfall (mm) over Taiwan in (b) S1 and (c) S2 and (d) the difference between the two runs (S1 minus S2) over the period of 0000 UTC 11 Sep–0000 UTC 16 Sep 2008 for TY Sinlaku. (e)–(h) As in (a)–(d), but for (e) observed and (f),(g) model-simulated 3-day rainfall in (f) J1 and (g) J2 and (h) the difference (J1 minus J2) over 0000 UTC 27 Sep–0000 UTC 30 Sep 2008 for TY Jangmi. Color scales for the total rainfall are plotted next to (c),(g), and terrain elevations at 1 and 2.5 km are also plotted (gray contours) in (d),(h).

Fig. 8.

(a) Observed and (b),(c) model-simulated total 5-day rainfall (mm) over Taiwan in (b) S1 and (c) S2 and (d) the difference between the two runs (S1 minus S2) over the period of 0000 UTC 11 Sep–0000 UTC 16 Sep 2008 for TY Sinlaku. (e)–(h) As in (a)–(d), but for (e) observed and (f),(g) model-simulated 3-day rainfall in (f) J1 and (g) J2 and (h) the difference (J1 minus J2) over 0000 UTC 27 Sep–0000 UTC 30 Sep 2008 for TY Jangmi. Color scales for the total rainfall are plotted next to (c),(g), and terrain elevations at 1 and 2.5 km are also plotted (gray contours) in (d),(h).

In the sensitivity test (S2) where the Δ values are removed from the IC/BCs, only small differences in typhoon track and intensity are produced as expected (Figs. 3 and 4). The variations in azimuthally averaged wind speed, also relatively small, mainly reflect the differences in the evolution of the inner core (Figs. 7a–c). However, our focus here is in the changes in rainfall. While the averaged hourly rainfall associated with the TC in S1 (control run) typically decreases with increasing radius from 200 to 500 km (i.e., larger circle size for averaging), it varies substantially with time as expected (Fig. 9a). This is especially true for the difference of S1 minus S2 in Fig. 9b, where positive and negative spikes of short duration (down to about 2–3 h) frequently appear. Thus, the results need to be averaged through time for easy comparison, as summarized in Table 1. For Sinlaku, a higher total rainfall amount associated with the TC, by roughly 5%–6% at 200–500 km from the storm center occurs over 10–16 September in S1 compared to S2 (Table 1, top), consistent with Fig. 9b where the total areas above zero surpass those below, since the present-day atmosphere has slightly more moisture (by about 1.5%) and the SST is a little higher (by roughly 0.68 K near Taiwan, as mentioned; cf. Fig. 2). Here and in all later instances, the relative changes (in %) are computed as (S1 − S2)/S1 for Sinlaku [and (J1 − J2)/J1 for Jangmi], since the modern-day case is our benchmark for comparison.

Fig. 9.

(a) Time series of model-mean hourly rainfall (mm) inside radii of 200, 300, 400, and 500 km (see legend) from TC center in S1 and (b) its difference from S2 (S1 minus S2). The zero value in (b) is marked by the horizontal dashed line.

Fig. 9.

(a) Time series of model-mean hourly rainfall (mm) inside radii of 200, 300, 400, and 500 km (see legend) from TC center in S1 and (b) its difference from S2 (S1 minus S2). The zero value in (b) is marked by the horizontal dashed line.

Table 1.

(top) Model areal-mean daily rainfall (mm) (left) inside different radii of 200–500 km from the TC center for the period of 10–16 Sep and (right) inside the radius (r) of 500 km for each date and the entire 7-day period in S1 and S2, their difference (S1 − S2), and the difference in percent change [%; (S1 − S2)/S1] for Sinlaku (2008). (bottom) As in (top), but for daily rainfall inside different radii for the period of 27–30 Sep and inside the radius of 300 km in J1 and J2 and their differences for Jangmi (2008).

(top) Model areal-mean daily rainfall (mm) (left) inside different radii of 200–500 km from the TC center for the period of 10–16 Sep and (right) inside the radius (r) of 500 km for each date and the entire 7-day period in S1 and S2, their difference (S1 − S2), and the difference in percent change [%; (S1 − S2)/S1] for Sinlaku (2008). (bottom) As in (top), but for daily rainfall inside different radii for the period of 27–30 Sep and inside the radius of 300 km in J1 and J2 and their differences for Jangmi (2008).
(top) Model areal-mean daily rainfall (mm) (left) inside different radii of 200–500 km from the TC center for the period of 10–16 Sep and (right) inside the radius (r) of 500 km for each date and the entire 7-day period in S1 and S2, their difference (S1 − S2), and the difference in percent change [%; (S1 − S2)/S1] for Sinlaku (2008). (bottom) As in (top), but for daily rainfall inside different radii for the period of 27–30 Sep and inside the radius of 300 km in J1 and J2 and their differences for Jangmi (2008).

The similar track and the close resemblance of the TCs in S1 and S2 noted earlier indicate that the synoptic evolution remains almost the same and a more significant bifurcation does not occur between the two runs under the constraints of the IC/BCs with perhaps a suitable domain size (of not being too large). This lack of bifurcation during the integration is consistent with our experiment design and helps to attribute any systematic changes in rainfall, when smaller-scale variations are smoothed out through averaging, to the differences in the background at larger scale: that is, the long-term trend in our study.

Except for the total rainfall amount associated with the TC, there is also an increase in the frequency of more-intense rainfall in S1 for the modern typhoon (Fig. 10a), by roughly 5%–25% over the intensity range of ≥20 mm h−1, especially for the period during and after landfall (detailed figures not shown). At higher rain rates (e.g., ≥40 mm h−1), the overall frequency increase tends to be larger (Fig. 10a). Over Taiwan, the total rainfall brought by Sinlaku during 11–15 September in S2 is very comparable to that in S1 (Figs. 8b,c) and the details are better revealed by their difference in Fig. 8d. While this difference exhibits considerable spatial variation, overall the rainfall in S1 is slightly more than S2, mainly over the northern half of the island (Fig. 8d). An exception exists over the interior of central–southern Taiwan and mainly on 14 September, as the TC in S2 travels more slowly across northern Taiwan and upon departure (cf. Fig. 3a) and its circulation, with an RMW of about 150 km (cf. Fig. 7b), is forced to override the terrain there (Fig. 8d). During 13–15 September, when the most rain was received over the island, on average there is also more rainfall over Taiwan in S1 compared to S2, by about 2.2% (details not shown). Thus, although the rainfall in Taiwan are roughly consistent with a higher overall amount associated with the TC in modern climate, it is more sensitive to small variations in track because of the steep and complex terrain of the island.

Fig. 10.

(a) The percent change (%; of S1 − S2 relative to S1; bars; scale on left) and the sample size in S1 (red curve; scale on right) as functions of rain rate (mm h−1) inside a radius of 500 km from the TC center during the period of 0000 UTC 9 Sep–0000 UTC 18 Sep 2008 for Sinlaku. (b) As in (a), but showing the percent change of J1 − J2 relative to J1 and the sample size in J1 inside 300 km during 0000 UTC 27 Sep–0000 UTC 30 Sep 2008 for Jangmi. The sample size is the number of grid points within the circle and the period considered from all model outputs at 1-h intervals.

Fig. 10.

(a) The percent change (%; of S1 − S2 relative to S1; bars; scale on left) and the sample size in S1 (red curve; scale on right) as functions of rain rate (mm h−1) inside a radius of 500 km from the TC center during the period of 0000 UTC 9 Sep–0000 UTC 18 Sep 2008 for Sinlaku. (b) As in (a), but showing the percent change of J1 − J2 relative to J1 and the sample size in J1 inside 300 km during 0000 UTC 27 Sep–0000 UTC 30 Sep 2008 for Jangmi. The sample size is the number of grid points within the circle and the period considered from all model outputs at 1-h intervals.

To further investigate the source of the increased rainfall associated with TY Sinlaku (2008) near Taiwan in the modern-day climate, a water budget analysis for a cylindrical volume using different radii is performed. Here, we adopt the budget equation of Trenberth and Guillemot (1995), which, after substituting by using ρυ = (where ρ is air density, ρυ is vapor density, and q is specific humidity), partitioning the water substance into vapor and hydrometeors, and rearranging, can be written (in z coordinates) as

 
formula

where P is precipitation, E is evaporation, wυ and wh are the total vapor and hydrometeor contents in the column, ρh is hydrometeor density (same as ρυ but for condensates), is horizontal wind vector, and R is the residual term. Thus, for a fixed volume of air column, Eq. (1) states that the convergence of vapor flux (CVF), convergence of hydrometeor flux (CHF), and evaporation (from the lower boundary) are the source of water, which either falls out as precipitation or stays inside to moisten the air. In the tendency term (TDC), the water contents wυ (i.e., precipitable water) and wh (suspending condensates) are defined as

 
formula

while CVF can be further divided into the convergence (CONV) and advection (ADV) of vapor by winds, such that

 
formula

In practice, all terms in Eqs. (1)(3) are computed for the air column (from the surface to model top) at each grid point except for R, and then averaged inside different radii of 200–500 km from the TC center. Since model outputs at every hour give the accumulated values of P and E over the past 1-h period, all tendency and vertical-integral terms are evaluated at full hours and then averaged to obtain the values over each 1-h period. Finally, R is computed as the difference between the two sides of Eq. (1).

The results of the water budget calculation for TY Sinlaku (2008), averaged within a radius of 500 km and over 9 days from 0000 UTC 9 September to 0000 UTC 18 September, are summarized in Table 2 (top). To evaluate the contribution from the changes in CONV in Eq. (3), the total precipitable water [PW5.5; cf. Eq. (2)] and integrated horizontal convergence from sea level to z1 = 5.5 km (IHC5.5) are computed as

 
formula
 
formula

and their values and percent changes are also given in Table 2. In S1, the mean TC rainfall is 1.388 kg h−1 m−2 (or mm h−1) and mainly comes from the CVF across the lateral boundary of the imaginary cylinder (1.172 mm h−1 or 84.4%), while evaporation from the underlying surface (mostly ocean) contributes 13.1%. The TDC, CHF, and R terms are all very small and their sum only accounts for the remaining 2.5% of P. This is why they are combined together in Eqs. (1) and (2) and not broken down. In CVF, the main contributor is the CONV, while ADV has a small negative effect since the low-level inflow of TCs typically brings in less moist air with lower equivalent potential temperature (θe) from the surroundings (e.g., Hawkins and Imbembo 1976; Liu et al. 1997; Wallace and Hobbs 2006, section 8.4.1).

Table 2.

Results of water budget analysis for a cylindrical volume from the surface to model top (top) inside a radius of 500 km averaged from 0000 UTC 9 Sep to 0000 UTC 18 Sep for Sinlaku (2008) and (bottom) inside a radius of 300 km averaged from 0000 UTC 27 Sep to 0000 UTC 30 Sep for Jangmi (2008). Terms include precipitation (P), tendency of total water contents, convergence of vapor flux, convergence of hydrometeor flux, evaporation (E), and residual (R), while CVF is further partitioned into convergence and advection of vapor by winds. All units are in kg h−1 m−2 (or mm h−1), except for PW5.5 (in mm) and IHC5.5 (in 10−2 m s−1) in CONV [see Eqs. (3)(5)]. The changes of S1 − S2 (or J1 − J2) in PW5.5 and IHC5.5 are expressed in percent (%).

Results of water budget analysis for a cylindrical volume from the surface to model top (top) inside a radius of 500 km averaged from 0000 UTC 9 Sep to 0000 UTC 18 Sep for Sinlaku (2008) and (bottom) inside a radius of 300 km averaged from 0000 UTC 27 Sep to 0000 UTC 30 Sep for Jangmi (2008). Terms include precipitation (P), tendency of total water contents, convergence of vapor flux, convergence of hydrometeor flux, evaporation (E), and residual (R), while CVF is further partitioned into convergence and advection of vapor by winds. All units are in kg h−1 m−2 (or mm h−1), except for PW5.5 (in mm) and IHC5.5 (in 10−2 m s−1) in CONV [see Eqs. (3)–(5)]. The changes of S1 − S2 (or J1 − J2) in PW5.5 and IHC5.5 are expressed in percent (%).
Results of water budget analysis for a cylindrical volume from the surface to model top (top) inside a radius of 500 km averaged from 0000 UTC 9 Sep to 0000 UTC 18 Sep for Sinlaku (2008) and (bottom) inside a radius of 300 km averaged from 0000 UTC 27 Sep to 0000 UTC 30 Sep for Jangmi (2008). Terms include precipitation (P), tendency of total water contents, convergence of vapor flux, convergence of hydrometeor flux, evaporation (E), and residual (R), while CVF is further partitioned into convergence and advection of vapor by winds. All units are in kg h−1 m−2 (or mm h−1), except for PW5.5 (in mm) and IHC5.5 (in 10−2 m s−1) in CONV [see Eqs. (3)–(5)]. The changes of S1 − S2 (or J1 − J2) in PW5.5 and IHC5.5 are expressed in percent (%).

When the differences between S1 and S2 are examined, the heavier areal-mean rainfall in S1 (within 500 km, by 0.078 mm h−1) is again from enhanced CVF, by 0.084 mm h−1, as local evaporation from the ocean increases only marginally. The increase in CVF is due to a greater enhancement in CONV (by 0.153 mm h−1) that offsets the stronger negative effect from ADV (by −0.069 mm h−1). The larger CONV is in turn attributed to both a more moist background (by 2.5%) as well as a stronger low-level wind convergence (by 8.95%). These results in Table 2 (top) indicate a more active transverse circulation associated with the present-day Sinlaku in S1, when its environment has become slightly warmer and wetter and thus more water vapor is available for latent heat release. In Fig. 11a, it is confirmed that the outward-tilted eyewall, low-level inflow, and upper-level outflow are all captured nicely in S1, with a mean RWM of about 65 km prior to landfall (cf. Fig. 7a). While the ascent at the eyewall and descent inside the eye are also stronger in S1 compared to S2, the strengthening in low-level inflow and outflow aloft (with rising motion) is quite evident near 200 km and farther out (Fig. 11b) and contributes to the higher percent increase in rainfall at radii of 200–500 km (Table 1).

Fig. 11.

The azimuthally averaged radius–height profiles of (a) vertical velocity (w; m s−1; colors), tangential wind [Vt; m s−1; contours every 2 m s−1: positive (negative) (dashed) for cyclonic (anticyclonic) motion], and radial wind (Vr) and w (m s−1; vectors; reference vector at lower left; w multiplied by 15 for proper aspect ratio) averaged through the period from 1200 UTC 9 to 1800 UTC 13 Sep 2008 (24–126 h) within 600 km from TC center in S1 and (b) the differences of S1 − S2 (every 0.2 m s−1 for Vt and as indicated by color scale for w and reference vector for Vr) in the same period for TY Sinlaku.

Fig. 11.

The azimuthally averaged radius–height profiles of (a) vertical velocity (w; m s−1; colors), tangential wind [Vt; m s−1; contours every 2 m s−1: positive (negative) (dashed) for cyclonic (anticyclonic) motion], and radial wind (Vr) and w (m s−1; vectors; reference vector at lower left; w multiplied by 15 for proper aspect ratio) averaged through the period from 1200 UTC 9 to 1800 UTC 13 Sep 2008 (24–126 h) within 600 km from TC center in S1 and (b) the differences of S1 − S2 (every 0.2 m s−1 for Vt and as indicated by color scale for w and reference vector for Vr) in the same period for TY Sinlaku.

4. Model results of Typhoon Jangmi (2008)

For Jangmi (2008), whose path was similar to Sinlaku but with a faster translation speed, the simulated track in J1 is also close to the JTWC best track, but the TC makes landfall across central Taiwan, slightly to the south than what was observed (Fig. 3b). As in Sinlaku case (cf. Fig. 4), the model shows deficit in TC intensity before landfall near 1200 UTC 28 September (Fig. 12; cf. Fig. 3b), although the storm is already stronger than that in the YOTC analyses by about 20 hPa and 10 m s−1. Thus, the model typhoon apparently cannot intensify rapidly enough to overcome the deficit from the initial fields, and the small inner eye (with a radius about 30 km) is not well captured (Fig. 13), as a plot similar to Fig. 7a but for J1 also indicates an RMW decreasing from about 150 km since 27 September to 65 km upon landfall (not shown). Such a deficiency is often seen in model simulations without intensive data assimilation or TC bogus (e.g., Liu et al. 1997; Leroux et al. 2013), also for this particular typhoon (Wang et al. 2014). Apart from the inner core, however, the overall life cycle of Jangmi, including the rainfall structure, is reproduced reasonably well in J1 (Figs. 3b, 12, and 13). Because of the small track error and the size of the eye being too large (not compact enough), the accumulated rainfall in J1 is underpredicted in central Taiwan but still agrees reasonably well with the rain gauge data in northern and southern Taiwan (Figs. 8e,f). Since our focus is in rainfall and its change in J2, the J1 simulation is judged to be of reasonable quality for the next step.

Fig. 12.

As in Fig. 4, but from the JTWC and CWB best-track data, YOTC analysis, and model experiments of J1 and J2 for TY Jangmi.

Fig. 12.

As in Fig. 4, but from the JTWC and CWB best-track data, YOTC analysis, and model experiments of J1 and J2 for TY Jangmi.

Fig. 13.

(a)–(c) As in Fig. 5, but for TY Jangmi at (a) 1954 UTC 26 Sep, (b) 1857 UTC 27 Sep, and (c) 0801 UTC 28 Sep 2008 (from Naval Research Laboratory). (d)–(f) As in Fig. 6, but in J1 run at (d) 2000 UTC 26 Sep, (e) 1900 UTC 27 Sep, and (f) 0800 UTC 28 Sep 2008.

Fig. 13.

(a)–(c) As in Fig. 5, but for TY Jangmi at (a) 1954 UTC 26 Sep, (b) 1857 UTC 27 Sep, and (c) 0801 UTC 28 Sep 2008 (from Naval Research Laboratory). (d)–(f) As in Fig. 6, but in J1 run at (d) 2000 UTC 26 Sep, (e) 1900 UTC 27 Sep, and (f) 0800 UTC 28 Sep 2008.

When Jangmi is placed in the past climate, again only small differences in track are produced and a more evident bifurcation in the evolution of the TC does not occur (Figs. 3b and 4b). Consistent with weaker westerly wind components (i.e., stronger easterly ones) at low to middle levels in the past climate (cf. Figs. 2a,b), the TC in J2 follows a path slightly to the west, particularly near Taiwan, and travels longer over the northern Taiwan Strait after landfall (Fig. 3b). Over the 4-day period (27–30 September) when Jangmi is near Taiwan, again a higher total rainfall is produced in J1 than J2, by about 4%–7% inside a radius of 300 km (Table 1, bottom), while the difference in percent becomes smaller farther out from the TC center (1.5%–2%). In terms of absolute values, both TCs reach maximum increase at 300 km (by 3.8 mm for S1 − S2 and 4.4 mm for J1 − J2). Similar to Sinlaku, the positive differences of J1 − J2 are also quite consistent through the period, except for 30 September, when the storm already weakens and moves away from Taiwan (cf. Figs. 3b and 12). Also, the frequency of more-intense rain is again higher in J1 than J2, by about 5%–25% over the range of 20–50 mm h−1, while the weakest rainfall (<3 mm h−1) tends to reduce in frequency (Fig. 10b). However, the total rainfall over Taiwan during 28–29 September in J1 is less than in J2, by 6.3%, most likely linked to an overall track slightly more to the west in J2 (cf. Fig. 3b), in agreement with Fig. 2 and Su et al. (2012).

The reason for the apparent inconsistency noted above—that is, more rain is associated with the TC within 300 km from its center but less rain is received in Taiwan over 28–29 September in J1, as compared to J2—is further examined. While the 3-day total rainfall over Taiwan are not very different between J1 and J2 (Figs. 8f,g), their difference of J1 − J2 (Fig. 8h) has a pattern quite similar to that of S1 − S2 for Sinlaku, with generally more rain in northern but less rain in southern Taiwan (cf. Fig. 8d). In addition, the eastern Taiwan also receives significantly less rain in J1, most evident on 28 September (Fig. 14a), and this is the main reason for the less overall 2-day rainfall of 28–29 September. The more rainfall over eastern Taiwan (mainly north of 23.5°N) on 28 September in J2 is linked to a track slightly to the southwest prior to landfall, by about 30–40 km, which allows the stronger part of the TC circulation to impinge on the higher topography to produce rainfall (Fig. 14a; cf. Fig. 8h). In J1, the track is slightly to the north on 28 September, and significantly more rain is produced just offshore of much of Taiwan. On 29 September, when the TC gradually moves away, there is more rain over Taiwan in J1 than J2 (Fig. 14b) but not enough to overcome the preceding deficit. Thus, the rainfall received over Taiwan, due to its steep terrain, is very sensitive to small TC track differences, even though more overall rainfall is associated with the TC in modern climate (Fig. 14 and Table 1, bottom).

Fig. 14.

As in Fig. 8h, but for the rainfall differences between J1 and J2 (J1 minus J2) on (a) 28 and (b) 29 Sep 2008 for TY Jangmi. The detailed tracks in J1 (dark green) and J2 (purple) are also plotted, with locations of TC center marked every 3 h (dots) and enlarged every 12 h as labeled.

Fig. 14.

As in Fig. 8h, but for the rainfall differences between J1 and J2 (J1 minus J2) on (a) 28 and (b) 29 Sep 2008 for TY Jangmi. The detailed tracks in J1 (dark green) and J2 (purple) are also plotted, with locations of TC center marked every 3 h (dots) and enlarged every 12 h as labeled.

The same water budget analysis is also carried out for TY Jangmi, and the results over 27–29 September using a radius of 300 km are shown in Table 2 (bottom). Since a smaller circle is used, most terms in J1 are larger in magnitude (e.g., P = 2.842 mm h−1) compared to the Sinlaku case. The increase in rainfall in J1 versus J2 (by 0.125 mm h−1) is again primarily from CVF (0.103 mm h−1), which in turn comes from a considerably stronger CONV (by 0.22 mm h−1) to offset the increased negative effect from ADV (by −0.118 mm h−1). Also, both the precipitable water and vertically integrated convergence below 5.5 km are larger in J1 than J2 to account for the increase in CONV, but the percent change in the former (3.92%) is more than that in the latter (1.52%) for TY Jangmi. In Fig. 15a, the axisymmetrical structure of the tangential wind and transverse circulation associated with the TC in J1, averaged over 27–30 September (including periods during and after landfall), is shown. Compared to J2, its stronger ascent is mainly located at 150–325 km and not at 325–500 km (Fig. 15b), also consistent with the result in Table 1. Thus, while more overall rainfall in modern climate is obtained for both TC cases, more significant increase occurs near the eyewall and also at other radii ranges farther out that are linked to detailed TC structure and can vary to some extent among the cases.

Fig. 15.

As in Fig. 11, but for the azimuthally averaged radius–height profiles of (a) w, Vt, and Vr averaged through the period from 0000 UTC 27 Sep to 0000 UTC 1 Oct 2008 (12–108 h) in J1 and (b) the differences of J1 − J2 in the same period for TY Jangmi.

Fig. 15.

As in Fig. 11, but for the azimuthally averaged radius–height profiles of (a) w, Vt, and Vr averaged through the period from 0000 UTC 27 Sep to 0000 UTC 1 Oct 2008 (12–108 h) in J1 and (b) the differences of J1 − J2 in the same period for TY Jangmi.

5. Discussion and conclusions

a. Statistical test on overall rainfall change

Although the Δ values are small and our main interest of the study is to quantify their effects on the rainfall of the two TCs, some statistical test on the significance of our results is perhaps worthwhile. As our major finding is an overall increase of TC rainfall in S1/J1 versus S2/J2 (by roughly 4%–7%), the appropriate test is the one-tail t test for paired samples (e.g., Barber 1988; section 9.2). Here, we test whether the mean daily rainfall within 500 and 300 km from the TC center over 10–16 and 27–30 September has changed. With a null hypothesis that the mean of daily rainfall in S1/J1 does not increase (i.e., the difference remains at 0 mm), the hypothesis is rejected at the confidence level of 0.995 (0.990) for rainfall inside a radius of 500 (300) km, as shown in Table 3. When the values of percent change in daily rainfall are used instead, the results are also similar (t = 3.452 and 2.594, respectively). Thus, the t-test result suggests that it is highly confident that a systematic increase in overall rainfall does occur under modern-day climate in our experiments and not arise from random processes in the model. More importantly, however, is that the changes in total rainfall are attributable to the background difference in sensitivity tests (provided that evident bifurcations do not occur) and a consistent underlying physical mechanism is also identified and presented to explain the reason in this study.

Table 3.

The data of daily rainfall changes (mm), averaged inside the radius of 500 and 300 km from the TC center, over 10–16 Sep and 27–30 Sep 2008 used for the upper-tail t test for paired samples (sample size n = 11) and their mean, standard deviation (SD), and t values. The null hypothesis is that the mean has not increased (i.e., the mean change remains at 0 mm), and it is rejected when t exceeds the criterion at the specified confidence level with 10 (or n − 1) degrees of freedom (e.g., Barber 1988). The rainfall changes inside 500 km for Sinlaku and 300 km for Jangmi are the same as those in Table 1.

The data of daily rainfall changes (mm), averaged inside the radius of 500 and 300 km from the TC center, over 10–16 Sep and 27–30 Sep 2008 used for the upper-tail t test for paired samples (sample size n = 11) and their mean, standard deviation (SD), and t values. The null hypothesis is that the mean has not increased (i.e., the mean change remains at 0 mm), and it is rejected when t exceeds the criterion at the specified confidence level with 10 (or n − 1) degrees of freedom (e.g., Barber 1988). The rainfall changes inside 500 km for Sinlaku and 300 km for Jangmi are the same as those in Table 1.
The data of daily rainfall changes (mm), averaged inside the radius of 500 and 300 km from the TC center, over 10–16 Sep and 27–30 Sep 2008 used for the upper-tail t test for paired samples (sample size n = 11) and their mean, standard deviation (SD), and t values. The null hypothesis is that the mean has not increased (i.e., the mean change remains at 0 mm), and it is rejected when t exceeds the criterion at the specified confidence level with 10 (or n − 1) degrees of freedom (e.g., Barber 1988). The rainfall changes inside 500 km for Sinlaku and 300 km for Jangmi are the same as those in Table 1.

b. Conclusions and summary

To quantitatively assess the effects of long-term climate change on typhoon rainfall near Taiwan, we perform cloud-resolving simulation of TY Sinlaku (2008) and TY Jangmi (2008) and test their sensitivity when these same cases are placed in the climate background in the 1950s–60s, which contained changes in mean flow by about 0.5 m s−1, slightly less moisture (by about 1.5%) and was slightly cooler in both the atmosphere (by ~0.6 K below 500 hPa) and ocean surface (by ~0.7 K). Although these changes are small (compared to e.g., short-term fluctuations or diurnal or seasonal cycle) and the same TCs in the paired experiments are highly similar, the approach of sensitivity test allows for a meaningful and quantitative assessment on the impacts of the observed long-term trend, produced under a mixture of both natural and anthropogenic forcings, in the past 40–50 yr on TC rainfall. Thus, the present paper also serves as a concept paper to establish such a methodology, and a small number of cases are used first. Our primary goal is to quantify the change in rainfall of these two TCs in response to the observed climate change and investigate on its reasons, and the secondary objective is to examine the rainfall change over Taiwan.

Even though only two cases are studied, the effects found are largely consistent (i.e., the responses of the TCs in the model are systematic) and tested as statistically significant (at a confidence level of ≥0.99). In control experiments (S1/J1), both modern-day typhoons yield more rainfall than their counterpart in past climate (S2/J2), by up to about 5%–6% at 200–500 km from the TC center for Sinlaku and roughly 4%–7% within 300 km of Jangmi, throughout much of their life cycle near Taiwan. The frequency of more-intense rainfall (20 to ≥50 mm h−1) also increases, by roughly 5%–25% in both cases, and the increase tends to be larger toward higher rain rates. These results are in general agreement with many previous studies (e.g., Karl and Knight 1998; Trenberth et al. 2003; Fujibe et al. 2005; Allan and Soden 2008; Knutson et al. 2010) and also the recent works of Villarini et al. (2014) and Scoccimarro et al. (2014) that consider many TCs. Because of the steep topography, the accumulated rainfall over Taiwan itself brought by the TCs is prone to the influence of small track changes. For the particular track type studied, our results indicate slightly more rainfall in Sinlaku but less in Jangmi in modern climate, even though both present-day TCs produce overall more rain near the island.

To investigate the source of TC rainfall increase in modern climate, a water budget analysis is carried out and the results, also consistent between the two cases, indicate that the increased rainfall is attributable to both a wetter environment (by 2.5%–4%) and a more active secondary circulation (i.e., low-level convergence, by 1.5%–9%) of the typhoon during the case period. These two factors combine to offset the increased negative effect from moisture advection (by the inflow) and lead to enhanced convergence of water vapor flux associated with the TC in the modern climate. A stronger transverse circulation also agrees well with a more significant increase in higher rain rates, which tend to occur at smaller radii near the inner core, and a slight decrease in weak rainfall that becomes more frequent at larger radii toward the outer edge. Thus, a changing climate may already have had a discernible impact on TC rainfall near Taiwan.

While the above increase in TC rainfall of roughly 5% from our results may not seem large, in our opinion it is certainly not insignificant either, considering that the long-term trend used here represents the change of climate in only 40 yr (from 1950–69 to 1990–2009). If the warming due to anthropogenic forcing constitutes a significant portion of this change as generally believed, a similar trend may continue or even amplify for many decades to come according to some projected scenarios by the Intergovernmental Panel on Climate Change (IPCC). To more fully understand the change of TC rainfall and its variability, especially over Taiwan, additional studies of other cases and track types throughout the typhoon season are currently underway. Furthermore, using a similar strategy, refined estimates of relative contribution from various forcings (of anthropogenic and natural origin) in the past and future model projections at multidecadal, century, or longer time scales are also possible and recommended for future studies.

Acknowledgments

The authors thank the editor, Dr. Kevin Walsh, and anonymous reviewers for their valuable comments and suggestions that lead to improvements in the presentation and clarity of this paper. Miss Y.-W. Wang and S.-Y. Huang helped produce some of the figures and the U.S. Naval Research Laboratory is also acknowledged for providing Figs. 5 and 13a–c. This study is jointly supported by the Ministry of Science and Technology of Taiwan under Grants NSC-102-2119-M-003-003, NSC-100-2119-M-003-005-MY5, and MOST-103-2119-M-003-001-MY2.

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