66 JOURNAL OF CLIMATE VOLUME 28

Quantifying the Effects of Long-Term Climate Change on Rainfall Using a Cloud-Resolving Model: Examples of Two Landfall Typhoons in

CHUNG-CHIEH WANG,BO-XUN LIN,CHENG-TA CHEN, AND SHIH-HOW LO Department of Earth Sciences, National Taiwan Normal University, , Taiwan

(Manuscript received 9 January 2014, in final form 11 September 2014)

ABSTRACT

To quantify the effects of long-term climate change on typhoon rainfall near Taiwan, cloud-resolving sim- ulations 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 2 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 change (e.g., Solomon et al. 2007; Stott et al. 2010; Min et al. 2011; Pall et al. 2011). When facing disastrous, extreme, or record-breaking Obviously, the likely changes in tropical cyclones and weather events like tropical cyclones (TCs) and heavy other types of extreme weather events in the future are rainfall, it is generally very difficult to assess the influences of major concern under the global warming scenario. One of anthropogenic forcing (related to ‘‘global warming’’) or common approach to tackle such questions is to perform long-term climate change (including natural forcing and long-term simulations with global or regional climate internal variability as well) since the dynamical forcing models and compare event statistics in the present and in these rare, high-impact events is typically much larger future climates (e.g., Meehl and Tebaldi 2004; Knutson than the climate forcing and favorable factors across et al. 2007, 2008; Zhao et al. 2009; Murakami et al. 2012; a wide range of scales often come together in synergy to produce them. Thus, while an increase in the severity of Sillmann et al. 2013). One issue of this approach is the extreme weather events is consistent with the expected reliability of such models in reproducing the observed effects of climate change, it is generally difficult to at- characteristics of extreme weather events with rather tribute any single event to the warming or climate 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 de- Denotes Open Access content. gree 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 pro- Corresponding author address: Prof. Chung-Chieh Wang, jection of future climate, especially at regional scale, Department of Earth Sciences, National Taiwan Normal University, No. 88, Sec. 4, Ting-Chou Rd., Taipei 11677, Taiwan. a large number of samples is often needed to establish the E-mail: [email protected] statistical significance and potentially the confidence for

DOI: 10.1175/JCLI-D-14-00044.1

Ó 2015 American Meteorological Society Unauthenticated | Downloaded 10/07/21 09:22 AM UTC 1JANUARY 2015 W A N G E T A L . 67 a thorough assessment (e.g., Stott et al. 2004; Karl et al. 2. Methodology and experiments 2008; Pall et al. 2011 Alexander and Tebaldi 2011; Fischer et al. 2013). To compute the long-term trend of climate change for Instead of assessing the possible changes in typhoons the global atmosphere, a dataset extending back into the in the future, which involves reliability and much higher past for as long as possible is preferred. Therefore, for this uncertainties as mentioned above, in this study we at- purpose we adopt the National Centers for Environmen- tempt to address the following issue quantitatively: How tal Prediction (NCEP)–National Center for Atmospheric much rain, in terms of percentages, from the most rainy Research (NCAR) monthly-mean global gridded re- typhoon cases near Taiwan in modern days can be at- analysis (2.5832.58; Kalnay et al. 1996), as in Chu et al. tributed to the effects of long-term climate change (2012). These reanalysis data are used to compute the (whether due to anthropogenic impact or natural vari- mean climate states for two 20-yr periods, 1950–69 and ability) that we have already seen? To do this, we select 1990–2009, and subsequently their differences for all specific modern-day typhoons near Taiwan and perform major variables at all pressure levels and the surface. For highly realistic simulations of their life cycle using a sea surface temperature (SST), the 18318 Hadley Centre cloud-resolving model (i.e., control runs, one for each Sea Ice and Sea Surface Temperature (HadISST) data typhoon). Then, we place these same typhoons in a cli- (Rayner et al. 2003) for the same periods are employed. mate background representing conditions from about Using 20-yr averages, signals from variations up to de- 40 yr ago, constructed by subtracting the long-term trend cadal time scale are largely removed, and these differ- from gridded analyses during the case period, and run ences (called the delta values or ‘‘D’’ for short) represent sensitivity tests and make direct comparison with the the long-term climate trend during the past half century control simulations. Here, because the long-term trend or so under a mixture of both natural and anthropogenic is computed using reanalysis data based on observations, forcings. Although some multidecadal variability (e.g., the uncertainties involved with climate projection are Pacific decadal oscillation; Trenberth 1990; Biondi et al. not present (although the ultimate causes of the climate 2001) or climate regime shifts (Lo and Hsu 2008) may still change over the period remain debatable). Also, two be present in the D values, it is widely accepted that an- cloud-resolving, high-resolution runs of the same ty- thropogenic influence on global-mean temperature be- phoon (with identical synoptic evolution) are compared came relatively more detectable in recent decades, with the only difference in their mean climate state, and especially since the 1990s (e.g., Solomon et al. 2007). much of the uncertainties from natural variability among Our results of the mean state in modern climate of events and inadequate model resolution are eliminated. 1990–2009 and the D values from 1950–69 to 1990–2009 Thus, quantitative assessments are allowed for indivi- (latter minus former) over the western North Pacific dual events from a small number of model experiments (WNP) are shown in Figs. 1 and 2, respectively. Com- through sensitivity tests, as has long been practiced to pared to the mean state (Fig. 1), the long-term changes address the roles or isolate the impacts of various factors since 1950–69 near Taiwan are quite small as expected (e.g., Gall 1976; Kuo et al. 1991; Stein and Alpert 1993; and include slight increases in northwesterly wind com- Braun and Tao 2000; Wang et al. 2005, 2012, 2013a). ponents at low levels (1000–700 hPa) and in westerly wind Typically, systematic responses in the model and the components in the middle troposphere (600–400 hPa), 2 underlying physics are examined in these tests without both by about 0.5 m s 1 (Figs. 2a,b) and in general strict statistical inference. To our knowledge, such a agreement with Chu et al. (2012).Thereisalso strategy has not been adopted to access the impacts of a warming and moistening trend of roughly 0.5 K and 2 climate change on high-impact weather systems before, 0.1–0.4 g kg 1 at low levels, as well as an increase in and thus this paper, using a small number of cases at first, SST by about 0.6–1.5 K near Taiwan (Figs. 2c,d). also serves to establish the concept of this methodol- Further aloft, weak warming (#0.3 K) exists at 200– ogy. Herein, we report our results on two landfall ty- 300 hPa and mild cooling of about 0.5 K also appears phoons in Taiwan: Typhoon (TY) Sinlaku (2008) and at 100 hPa near Taiwan (not shown), in rough agreement TY Jangmi (2008). Both TCs exhibited a typical track with Vecchi et al. (2013) and Emanuel et al. (2013).More to approach from the southeast, and they are ranked as precisely, the above changes correspond to a weaken- the 3rd and 10th most rainy typhoon in Taiwan over the ing in easterly to southeasterly mean flow by about 2 past 50 yr (Chang et al. 2013). Our primary goal is to 0.5 m s 1, an increase in moisture by about 1.5%, and a quantify the change in TC rainfall itself, and the sec- warming by about 0.6 K below 500 hPa and by 0.68 K in ondary objective is to examine the rainfall change over SST (averaged over 148–328N, 1148–1358E), and we can Taiwan. Further details on the methodology and results anticipate that modern-day typhoons might move are given below. slightly slower if it is to approach Taiwan from the

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21 FIG. 1. The 1990–2009 long-term mean states of geopotential height (gpm; contours) and horizontal winds (m s , vectors, reference 2 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). southeast and produce more rain because of a wetter (BCs), and the monthly-mean 18318 HadISST and real environment. topography (at a resolution of about 1 km 3 1 km) are The Cloud-Resolving Storm Simulator (CReSS) of provided at the lower boundary. Aimed to reproduce Nagoya University, (Tsuboki and Sakakibara 2007) the events at high realm, the control runs are named S1 is used for the high-resolution numerical experiments at a for Sinlaku (2008) and J1 for Jangmi (2008). For S1, the grid size of 3 km with a dimension (x, y, z)of7203 720 3 50 integration starts at 1200 UTC 8 September and ends at and model top at 25 km, so the model domain is 0000 UTC 18 September 2008, for a total of 9.5 days 2160 km 3 2160 km for both cases (cf. Fig. 1d). The (228 h), while J1 (2008) covers the period from 1200 UTC vertical grid of CReSS is stretched and the spacing (Dz) 26 September to 0000 UTC 1 October 2008 (for 4.5 days increases gradually from 100 m at the bottom to 632.45 m or 108 h). Occurring in the same month, the best tracks of above 12 km, while the mean Dz is 500 m. The same the two TCs from the U.S. Joint Typhoon Warning Center physical options as those used in Wang et al. (2012) are (JTWC) are plotted in Fig. 3, and the two storms both employed. For the control experiments, the European approached from the southeast and recurved near Centre for Medium-Range Weather Forecasts (ECMWF) northern Taiwan. Besides best-track data, the simula- Year of Tropical Convection (YOTC) analyses (0.2583 tion results are also verified against satellite observa- 0.258, every 6 h; Waliser and Moncrieff 2007) are used as tions such as the Tropical Rainfall Measuring Mission the initial conditions (ICs) and boundary conditions (TRMM) and the rainfall over Taiwan from a dense

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FIG. 2. The long-term trend (D values) between two 20-yr averaged mean states of 1950–69 and 1990–2009 (latter minus former) of 2 geopotential height (gpm; contours every 3 gpm) and horizontal winds (m s 1; vectors; reference vector at bottom) averaged over 2 (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). network of about 400 automated rain gauges operated in the sensitivity tests, compare their differences to the by the Central Weather Bureau (CWB; Hsu 1998; for control (modern day) experiments, and investigate the details see, e.g., Fig. 2 of Wang et al. 2013b). Previous underlying physical reasons. Of course, issues related to studies on various aspects of these two typhoons can be possible changes in typhoon frequency or active regions found in Kuo et al. (2012), Wu et al. (2012), Leroux et al. over time (e.g., Bender et al. 2010) cannot be addressed (2013), and Sanger et al. (2014), among others. here, and the feedbacks from the ocean are also neglected. In the sensitivity test for each of the two typhoons In this study we focus exclusively on rainfall changes, since (named S2 and J2, respectively), all model configurations typhoon hazards are mostly induced by the heavy rainfall are identical to the control run except that the long-term in Taiwan (e.g., Cheung et al. 2008; Su et al. 2012; Chang climate change (i.e., the D values) is subtracted from the et al. 2013; Wang et al. 2013b) and in many other regions IC/BCs, including both the YOTC and HadISST analy- experiencing TCs around the world. ses. Here, bilinear interpolation is applied to obtain D values on the ECMWF grid (0.258) from the coarser re- 3. Model results of (2008) analysis data (2.58). Using the above method, we essen- tially place the two typhoons in the climate background in In the S1 control run, the simulated track of Sinlaku the 1950–60s with the same synoptic forcing and evolution matches well with the JTWC best track, except for the

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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. last day (Fig. 3a). In intensity, the model TC in S1 is Kuo et al. 2009; Rozoff et al. 2012) at 3-km grid spacing considerably stronger than the YOTC analysis in both (Figs. 6 and 7a), the inner core intensity is not fully its minimum sea level pressure (SLP) and maximum captured, for which purpose TC bogus and/or intensive surface wind before landfall (Fig. 4). While the esti- data assimilation may be required (e.g., Wu et al. 2012; mated intensity in the best tracks by different opera- Leroux et al. 2013; Sun et al. 2013). Nonetheless, the tional centers (e.g., JTWC and CWB) varies to some 5-day total accumulated rainfall during 11–15 Septem- extent, the model TC appears to intensify less rapidly ber over Taiwan compares favorably with the rain gauge than the best tracks before 11 September. On the other measurements (Figs. 8a,b). Thus, the life cycle of Sinlaku hand, the model agrees better in SLP with the C-130 in is reproduced in close agreement with the observations situ observations (Wu et al. 2012), and the agreement using the CReSS model at high resolution, except per- with best tracks also improves since 12 September when haps for its inner core intensity before landfall. Since the the peak intensity is reached in S1 with a minimum SLP rainfall simulation in S1 is highly realistic (Figs. 5, 6,and 2 of 938 hPa and a maximum wind of 46 m s 1 (Fig. 4a). 8a,b), a model sensitivity test can be used for our purpose Figure 5 shows TRMM satellite observations at se- to examine the changes in TC rainfall in the environment lected times with better coverage of Sinlaku among all of past climate. available images (from the Naval Research Laboratory) In the sensitivity test (S2) where the D values are and can be compared directly with model results in S1 removed from the IC/BCs, only small differences in within 2 h in Fig. 6. It is confirmed that the model re- typhoon track and intensity are produced as expected produces the TC rainfall structure well during 9–14 (Figs. 3 and 4). The variations in azimuthally averaged September in S1, except perhaps that the size is wind speed, also relatively small, mainly reflect the slightly too large (Figs. 5 and 6). Indeed, on 10 and 13 differences in the evolution of the inner core (Figs. 7a–c). September, when Sinlaku’s eye appeared smaller (about However, our focus here is in the changes in rainfall. 25–40 km in radius; Figs. 5b,e), the radius of maximum While the averaged hourly rainfall associated with the wind (RMW) in S1 also reduces but still remains at about TC in S1 (control run) typically decreases with in- 50 km (Fig. 7a). Thus, even though the CReSS model can creasing radius from 200 to 500 km (i.e., larger circle size successfully simulate the rainfall structure and processes for averaging), it varies substantially with time as ex- resembling the eyewall contraction and replacement pected (Fig. 9a). This is especially true for the difference cycle (e.g., Willoughby et al. 1982; Houze et al. 2007; of S1 minus S2 in Fig. 9b, where positive and negative

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FIG. 4. Time series of (a) minimum SLP (hPa) and (b) maximum surface (10 m) wind speed 2 (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). spikes of short duration (down to about 2–3 h) frequently differences in the background at larger scale: that is, the appear. Thus, the results need to be averaged through long-term trend in our study. time for easy comparison, as summarized in Table 1. For Except for the total rainfall amount associated with Sinlaku, a higher total rainfall amount associated with the TC, there is also an increase in the frequency of the TC, by roughly 5%–6% at 200–500 km from the more-intense rainfall in S1 for the modern typhoon storm center occurs over 10–16 September in S1 com- (Fig. 10a), by roughly 5%–25% over the intensity range 2 pared to S2 (Table 1, top), consistent with Fig. 9b where of $20 mm h 1, especially for the period during and the total areas above zero surpass those below, since the after landfall (detailed figures not shown). At higher 2 present-day atmosphere has slightly more moisture (by rain rates (e.g., $40 mm h 1), the overall frequency in- about 1.5%) and the SST is a little higher (by roughly crease tends to be larger (Fig. 10a). Over Taiwan, the 0.68 K near Taiwan, as mentioned; cf. Fig. 2). Here and total rainfall brought by Sinlaku during 11–15 Septem- in all later instances, the relative changes (in %) are ber in S2 is very comparable to that in S1 (Figs. 8b,c) and computed as (S1 2 S2)/S1 for Sinlaku [and (J1 2 J2)/J1 for the details are better revealed by their difference in Jangmi], since the modern-day case is our benchmark for Fig. 8d. While this difference exhibits considerable comparison. spatial variation, overall the rainfall in S1 is slightly The similar track and the close resemblance of the more than S2, mainly over the northern half of the island TCs in S1 and S2 noted earlier indicate that the synoptic (Fig. 8d). An exception exists over the interior of central– evolution remains almost the same and a more signifi- southern Taiwan and mainly on 14 September, as the TC cant bifurcation does not occur between the two runs in S2 travels more slowly across northern Taiwan and under the constraints of the IC/BCs with perhaps upon departure (cf. Fig. 3a) and its circulation, with an a suitable domain size (of not being too large). This lack RMW of about 150 km (cf. Fig. 7b), is forced to override of bifurcation during the integration is consistent with the terrain there (Fig. 8d). During 13–15 September, our experiment design and helps to attribute any sys- when the most rain was received over the island, on tematic changes in rainfall, when smaller-scale varia- average there is also more rainfall over Taiwan in S1 tions are smoothed out through averaging, to the compared to S2, by about 2.2% (details not shown).

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21 FIG. 5. (a) TRMM Radar (PR) or TRMM Microwave Imager (TMI) rain rates (inch h ; 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.

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21 21 FIG. 6. Model-simulated rain rates (inch h ; color; scales at bottom) and horizontal winds (m s ; full barb 5 2 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.

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21 FIG. 7. Evolution of azimuthally averaged wind speed (m s ) 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 maxi- mum wind.

Thus, although the rainfall in Taiwan are roughly con- ð › ‘ sistent with a higher overall amount associated with the P 1 w 1 w 52 $ Á r dz › ( y h) ( yV) TC in modern climate, it is more sensitive to small var- t 0 TDC CVF iations in track because of the steep and complex terrain ð‘ 2 $ Á r 1 1 of the island. ( hV) dz E R, (1) 0 To further investigate the source of the increased CHF rainfall associated with TY Sinlaku (2008) near Taiwan in the modern-day climate, a water budget analysis for where P is precipitation, E is evaporation, wy and wh are a cylindrical volume using different radii is performed. the total vapor and hydrometeor contents in the column,

Here, we adopt the budget equation of Trenberth and rh is hydrometeor density (same as ry but for conden- Guillemot (1995), which, after substituting by using ry 5 qr sates), V is horizontal wind vector, and R is the residual (where r is air density, ry is vapor density, and q is term. Thus, for a fixed volume of air column, Eq. (1) specific humidity), partitioning the water substance into states that the convergence of vapor flux (CVF), con- vapor and hydrometeors, and rearranging, can be writ- vergence of hydrometeor flux (CHF), and evaporation ten (in z coordinates) as (from the lower boundary) are the source of water,

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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). which either falls out as precipitation or stays inside to grid point except for R, and then averaged inside dif- moisten the air. In the tendency term (TDC), the water ferent radii of 200–500 km from the TC center. Since contents wy (i.e., precipitable water) and wh (suspending model outputs at every hour give the accumulated condensates) are defined as values of P and E over the past 1-h period, all tendency and vertical-integral terms are evaluated at full hours ð‘ ð‘ ð‘ 1 5 r 1 r 5 r 1 r and then averaged to obtain the values over each 1-h wy wh y dz h dz ( y h) dz, (2) 0 0 0 period. Finally, R is computed as the difference between the two sides of Eq. (1). while CVF can be further divided into the convergence The results of the water budget calculation for TY (CONV) and advection (ADV) of vapor by winds, such Sinlaku (2008), averaged within a radius of 500 km and that over 9 days from 0000 UTC 9 September to 0000 UTC 18 September, are summarized in Table 2 (top). To eval- ð‘ ð‘ ð‘ uate the contribution from the changes in CONV in Eq. 2 $ Á (ryV) dz 52 ry($ Á V) dz 2 V Á $ry dz . 0 0 0 (3), the total precipitable water [PW5.5; cf. Eq. (2)] and CVF CONV ADV integrated horizontal convergence from sea level to z1 5 (3) 5.5 km (IHC5.5) are computed as ð z In practice, all terms in Eqs. (1)–(3) are computed for 5 1 r PW5:5 y dz, and (4) the air column (from the surface to model top) at each 0

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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. ð z1 together in Eqs. (1) and (2) and not broken down. In 52 $ Á IHC5:5 ( V) dz, (5) CVF, the main contributor is the CONV, while ADV has 0 a small negative effect since the low-level inflow of TCs and their values and percent changes are also given in typically brings in less moist air with lower equivalent 21 22 Table 2. In S1, the mean TC rainfall is 1.388 kg h m potential temperature (ue) from the surroundings (e.g., 2 (or mm h 1) and mainly comes from the CVF across the Hawkins and Imbembo 1976; Liuetal.1997; Wallace and 2 lateral boundary of the imaginary cylinder (1.172 mm h 1 Hobbs 2006, section 8.4.1). or 84.4%), while evaporation from the underlying surface When the differences between S1 and S2 are exam- (mostly ocean) contributes 13.1%. The TDC, CHF, and R ined, the heavier areal-mean rainfall in S1 (within 2 terms are all very small and their sum only accounts for 500 km, by 0.078 mm h 1) is again from enhanced CVF, 2 the remaining 2.5% of P. This is why they are combined by 0.084 mm h 1, as local evaporation from the ocean

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 2 S2), and the difference in percent change [%; (S1 2 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).

Radius (km) Individual date/entire 7-day period (r 5 500 km) Sinlaku 200 300 400 500 10 11 12 13 14 15 16 10–16 S1 102.5 71.5 50.7 37.4 52.7 48.8 43.3 33.0 29.8 29.9 24.5 37.4 S2 101.1 67.7 47.6 35.0 48.9 43.4 43.3 31.7 27.4 29.2 21.3 35.0 S1 2 S2 1.4 3.8 3.1 2.4 3.8 5.4 0.0 1.3 2.2 0.7 3.2 2.4 Percent change 1.4 5.3 6.1 6.4 7.1 11.1 0.1 3.8 8.1 2.3 13.2 6.4 Radius (km) Individual date/entire 4-day period (r 5 300 km) Jangmi 200 300 400 500 27 28 29 30 27–30 J1 76.9 63.7 53.4 46.0 117.3 75.1 41.2 21.4 63.7 J2 73.5 59.3 52.4 45.2 106.9 72.0 35.6 22.8 59.3 J1 2 J2 3.4 4.4 1.0 0.8 10.4 3.1 5.6 21.4 4.4 Percent change 4.4 6.9 2.0 1.6 8.9 4.2 13.6 26.7 6.9

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FIG. 10. (a) The percent change (%; of S1 2 S2 relative to S1; bars; scale on left) and the 2 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 2 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. increases only marginally. The increase in CVF is due and contributes to the higher percent increase in rainfall 2 to a greater enhancement in CONV (by 0.153 mm h 1) at radii of 200–500 km (Table 1). that offsets the stronger negative effect from ADV (by 2 20.069 mm h 1). The larger CONV is in turn attributed 4. Model results of Typhoon Jangmi (2008) to both a more moist background (by 2.5%) as well as a stronger low-level wind convergence (by 8.95%). For Jangmi (2008), whose path was similar to Sinlaku These results in Table 2 (top) indicate a more active but with a faster translation speed, the simulated track in transverse circulation associated with the present-day J1 is also close to the JTWC best track, but the TC makes Sinlaku in S1, when its environment has become slightly landfall across central Taiwan, slightly to the south than warmer and wetter and thus more water vapor is avail- what was observed (Fig. 3b). As in Sinlaku case (cf. able for latent heat release. In Fig. 11a, it is confirmed Fig. 4), the model shows deficit in TC intensity before that the outward-tilted eyewall, low-level inflow, and landfall near 1200 UTC 28 September (Fig. 12; cf. upper-level outflow are all captured nicely in S1, with a Fig. 3b), although the storm is already stronger than that 2 mean RWM of about 65 km prior to landfall (cf. Fig. 7a). in the YOTC analyses by about 20 hPa and 10 m s 1. While the ascent at the eyewall and descent inside the eye Thus, the model typhoon apparently cannot intensify are also stronger in S1 compared to S2, the strengthening rapidly enough to overcome the deficit from the initial in low-level inflow and outflow aloft (with rising motion) fields, and the small inner eye (with a radius about is quite evident near 200 km and farther out (Fig. 11b) 30 km) is not well captured (Fig. 13), as a plot similar to

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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 21 22 21 22 21 vapor by winds. All units are in kg h m (or mm h ), except for PW5.5 (in mm) and IHC5.5 (in 10 ms ) in CONV [see Eqs. (3)–(5)]. The changes of S1 2 S2 (or J1 2 J2) in PW5.5 and IHC5.5 are expressed in percent (%).

CVF CONV

Expt P TDC Total Total PW5.5 IHC5.5 ADV CHF ER S1 1.388 20.022 1.172 1.357 54.07 2.75 20.185 20.010 0.182 0.023 S2 1.310 20.018 1.088 1.204 52.72 2.50 20.116 20.008 0.177 0.035 S1 2 S2 0.078 20.004 0.084 0.153 2.50% 8.95% 20.069 20.002 0.005 20.012 J1 2.842 20.180 2.224 3.036 55.16 5.99 20.812 20.008 0.344 20.103 J2 2.717 20.165 2.121 2.816 53.00 5.90 20.694 20.014 0.301 20.144 J1 2 J2 0.125 20.015 0.103 0.220 3.92% 1.52% 20.118 0.006 0.043 0.041

2 Fig. 7a but for J1 also indicates an RMW decreasing 5%–25% over the range of 20–50 mm h 1, while the 2 from about 150 km since 27 September to 65 km upon weakest rainfall (,3mmh 1) tends to reduce in fre- landfall (not shown). Such a deficiency is often seen in quency (Fig. 10b). However, the total rainfall over Tai- model simulations without intensive data assimilation or wan during 28–29 September in J1 is less than in J2, by TC bogus (e.g., Liu et al. 1997; Leroux et al. 2013), also 6.3%, most likely linked to an overall track slightly more for this particular typhoon (Wang et al. 2014). Apart to the west in J2 (cf. Fig. 3b), in agreement with Fig. 2 and from the inner core, however, the overall life cycle of Su et al. (2012). Jangmi, including the rainfall structure, is reproduced The reason for the apparent inconsistency noted reasonably well in J1 (Figs. 3b, 12, and 13). Because of above—that is, more rain is associated with the TC the small track error and the size of the eye being too within 300 km from its center but less rain is received in large (not compact enough), the accumulated rainfall in Taiwan over 28–29 September in J1, as compared to J1 is underpredicted in central Taiwan but still agrees J2—is further examined. While the 3-day total rainfall reasonably well with the rain gauge data in northern and over Taiwan are not very different between J1 and J2 southern Taiwan (Figs. 8e,f). Since our focus is in rainfall (Figs. 8f,g), their difference of J1 2 J2 (Fig. 8h) has a and its change in J2, the J1 simulation is judged to be of pattern quite similar to that of S1 2 S2 for Sinlaku, with reasonable quality for the next step. generally more rain in northern but less rain in southern When Jangmi is placed in the past climate, again only Taiwan (cf. Fig. 8d). In addition, the eastern Taiwan also small differences in track are produced and a more ev- receives significantly less rain in J1, most evident on 28 ident bifurcation in the evolution of the TC does not September (Fig. 14a), and this is the main reason for the occur (Figs. 3b and 4b). Consistent with weaker westerly less overall 2-day rainfall of 28–29 September. The more wind components (i.e., stronger easterly ones) at low to rainfall over eastern Taiwan (mainly north of 23.58N) on middle levels in the past climate (cf. Figs. 2a,b), the TC 28 September in J2 is linked to a track slightly to the in J2 follows a path slightly to the west, particularly near southwest prior to landfall, by about 30–40 km, which Taiwan, and travels longer over the northern Taiwan allows the stronger part of the TC circulation to impinge Strait after landfall (Fig. 3b). Over the 4-day period (27– on the higher topography to produce rainfall (Fig. 14a; 30 September) when Jangmi is near Taiwan, again cf. Fig. 8h). In J1, the track is slightly to the north on 28 a higher total rainfall is produced in J1 than J2, by about September, and significantly more rain is produced just 4%–7% inside a radius of 300 km (Table 1, bottom), offshore of much of Taiwan. On 29 September, when the while the difference in percent becomes smaller farther TC gradually moves away, there is more rain over Tai- out from the TC center (1.5%–2%). In terms of absolute wan in J1 than J2 (Fig. 14b) but not enough to overcome values, both TCs reach maximum increase at 300 km (by the preceding deficit. Thus, the rainfall received over 3.8 mm for S1 2 S2 and 4.4 mm for J1 2 J2). Similar to Taiwan, due to its steep terrain, is very sensitive to small Sinlaku, the positive differences of J1 2 J2 are also quite TC track differences, even though more overall rainfall consistent through the period, except for 30 September, is associated with the TC in modern climate (Fig. 14 and when the storm already weakens and moves away from Table 1, bottom). Taiwan (cf. Figs. 3b and 12). Also, the frequency of The same water budget analysis is also carried out more-intense rain is again higher in J1 than J2, by about for TY Jangmi, and the results over 27–29 September

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21 FIG. 11. The azimuthally averaged radius–height profiles of (a) vertical velocity (w;ms ; 21 21 colors), tangential wind [Vt;ms ; contours every 2 m s : positive (negative) (dashed) for 21 cyclonic (anticyclonic) motion], and radial wind (Vr)andw (m s ; 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 21 of S1 2 S2 (every 0.2 m s for Vt and as indicated by color scale for w and reference vector for Vr) in the same period for TY Sinlaku.

2 using a radius of 300 km are shown in Table 2 (bottom). J2 (by 0.125 mm h 1) is again primarily from CVF 2 Since a smaller circle is used, most terms in J1 are (0.103 mm h 1), which in turn comes from a considerably 2 2 larger in magnitude (e.g., P 5 2.842 mm h 1)compared stronger CONV (by 0.22 mm h 1) to offset the increased 2 to the Sinlaku case. The increase in rainfall in J1 versus negative effect from ADV (by 20.118 mm h 1). Also,

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.

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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.

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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. both the precipitable water and vertically integrated con- mean of daily rainfall in S1/J1 does not increase (i.e., the vergence below 5.5 km are larger in J1 than J2 to account difference remains at 0 mm), the hypothesis is rejected for the increase in CONV, but the percent change in the at the confidence level of 0.995 (0.990) for rainfall inside former (3.92%) is more than that in the latter (1.52%) for a radius of 500 (300) km, as shown in Table 3. When the TY Jangmi. In Fig. 15a, the axisymmetrical structure values of percent change in daily rainfall are used in- of the tangential wind and transverse circulation asso- stead, the results are also similar (t 5 3.452 and 2.594, ciated with the TC in J1, averaged over 27–30 September respectively). Thus, the t-test result suggests that it is (including periods during and after landfall), is shown. highly confident that a systematic increase in overall Compared to J2, its stronger ascent is mainly located at rainfall does occur under modern-day climate in our 150–325 km and not at 325–500 km (Fig. 15b), also con- experiments and not arise from random processes in the sistentwiththeresultinTable 1. Thus, while more overall model. More importantly, however, is that the changes rainfall in modern climate is obtained for both TC cases, in total rainfall are attributable to the background dif- more significant increase occurs near the eyewall and also ference in sensitivity tests (provided that evident bi- at other radii ranges farther out that are linked to detailed furcations do not occur) and a consistent underlying TC structure and can vary to some extent among the cases. physical mechanism is also identified and presented to explain the reason in this study. b. Conclusions and summary 5. Discussion and conclusions To quantitatively assess the effects of long-term cli- a. Statistical test on overall rainfall change mate change on typhoon rainfall near Taiwan, we per- Although the D values are small and our main interest form cloud-resolving simulation of TY Sinlaku (2008) of the study is to quantify their effects on the rainfall of and TY Jangmi (2008) and test their sensitivity when the two TCs, some statistical test on the significance of these same cases are placed in the climate background in our results is perhaps worthwhile. As our major finding the 1950s–60s, which contained changes in mean flow by 2 is an overall increase of TC rainfall in S1/J1 versus S2/J2 about 0.5 m s 1, slightly less moisture (by about 1.5%) (by roughly 4%–7%), the appropriate test is the one-tail and was slightly cooler in both the atmosphere (by t test for paired samples (e.g., Barber 1988; section 9.2). ;0.6 K below 500 hPa) and ocean surface (by ;0.7 K). Here, we test whether the mean daily rainfall within 500 Although these changes are small (compared to e.g., and 300 km from the TC center over 10–16 and 27–30 short-term fluctuations or diurnal or seasonal cycle) and September has changed. With a null hypothesis that the the same TCs in the paired experiments are highly

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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 2 J2 in the same period for TY Jangmi. similar, the approach of sensitivity test allows for a increase tends to be larger toward higher rain rates. These meaningful and quantitative assessment on the impacts of results are in general agreement with many previous the observed long-term trend, produced under a mixture studies (e.g., Karl and Knight 1998; Trenberth et al. 2003; of both natural and anthropogenic forcings, in the past Fujibe et al. 2005; Allan and Soden 2008; Knutson et al. 40–50 yr on TC rainfall. Thus, the present paper also 2010) and also the recent works of Villarini et al. (2014) serves as a concept paper to establish such a methodol- and Scoccimarro et al. (2014) that consider many TCs. ogy, and a small number of cases are used first. Our pri- Because of the steep topography, the accumulated rainfall mary goal is to quantify the change in rainfall of these two over Taiwan itself brought by the TCs is prone to the in- TCs in response to the observed climate change and in- fluence of small track changes. For the particular track vestigate on its reasons, and the secondary objective is to type studied, our results indicate slightly more rainfall in examine the rainfall change over Taiwan. Sinlaku but less in Jangmi in modern climate, even though Even though only two cases are studied, the effects both present-day TCs produce overall more rain near the found are largely consistent (i.e., the responses of the TCs island. in the model are systematic) and tested as statistically To investigate the source of TC rainfall increase in significant (at a confidence level of $0.99). In control ex- modern climate, a water budget analysis is carried out periments (S1/J1), both modern-day typhoons yield more and the results, also consistent between the two cases, rainfall than their counterpart in past climate (S2/J2), by indicate that the increased rainfall is attributable to both up to about 5%–6% at 200–500 km from the TC center for a wetter environment (by 2.5%–4%) and a more active Sinlaku and roughly 4%–7% within 300 km of Jangmi, secondary circulation (i.e., low-level convergence, by throughout much of their life cycle near Taiwan. The 1.5%–9%) of the typhoon during the case period. These 2 frequency of more-intense rainfall (20 to $50 mm h 1) two factors combine to offset the increased negative also increases, by roughly 5%–25% in both cases, and the effect from moisture advection (by the inflow) and lead

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TABLE 3. The data of daily rainfall changes (mm), averaged in- Acknowledgments. The authors thank the editor, side the radius of 500 and 300 km from the TC center, over 10–16 Dr. Kevin Walsh, and anonymous reviewers for their Sep and 27–30 Sep 2008 used for the upper-tail t test for paired valuable comments and suggestions that lead to im- samples (sample size n 5 11) and their mean, standard deviation (SD), and t values. The null hypothesis is that the mean has not provements in the presentation and clarity of this paper. increased (i.e., the mean change remains at 0 mm), and it is rejected Miss Y.-W. Wang and S.-Y. Huang helped produce some when t exceeds the criterion at the specified confidence level with of the figures and the U.S. Naval Research Laboratory is 10 (or n 2 1) degrees of freedom (e.g., Barber 1988). The rainfall also acknowledged for providing Figs. 5 and 13a–c. 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