Variations in extreme wave events near a South Pacific Island under global warming: case study of Tropical Cyclone Tomas

The intensification of tropical cyclones (TCs) and wind-induced ocean waves is expected to be amplified under global warming conditions. In 2010, strong TC Tomas approached the Fiji Islands and caused severe damage. Here, an ensemble simulation technique is combined with a pseudo-global warming (PGW) method to investigate future variations in TCs and wind-induced ocean waves. Ensemble PGW simulations were implemented using the weather research and forecasting (WRF) model with five different future projections. Hindcast and PGW simulations showed similar tracks of Tomas. In four PGW simulations, the central pressures of the simulated TCs decreased. Enhanced near-surface wind was recognized in three PGW simulations around the Fiji main island (Viti Levu). In the other two future simulations, the surface wind speed was weaker than the one in the present climate because of the slight eastward shift in the track and delayed development of the TC. WaveWatchIII (WW3) was applied for offshore wave simulations forced by the wind field obtained by WRF simulation results. In three future simulations, a clear increase in the maximum significant wave height (Hs) was found on the southeastern coast of Viti Levu. One future simulation yielded almost the same offshore wave characteristics as those under the present climate. In another future simulation, the ensemble mean Hs was as high as that in the present climate, but extremely large Hs values were found in several ensemble members. Future simulations using multiple global climate model (GCM) projections showed possible variations in TCs and wind-induced ocean waves which is useful for the risk assessment of various hazards.


Introduction
Ocean surface waves are generated by local surface wind; thus, wave characteristics are highly affected by variations in atmospheric conditions caused by climate change. In the region of tropical cyclones (TCs), typhoons, and hurricanes, extreme ocean waves cause disaster in coastal areas. A large number of studies have reported an increasing number of the most intense cyclones under future global conditions (Knutson et al. 2010;Marciano et al. 2015;Kanada et al. 2017a;Nayak and Takemi 2019, etc.). Projections of the future ocean wave induced by strong storms (TCs, typhoons, and hurricanes) are crucial for assessing the impact of climate change on coastal regions and the development of appropriate adaptation strategies. Several studies have focused on future variations in cyclone-induced ocean waves and storm surges. Tasnim et al. (2015) performed hindcast and future simulations of TC Nargis. The predicted future cyclone was stronger than that in the present climate. Moreover, the predicted surge in the future TC was approximately 3 m higher than that in the hindcast. Nakamura et al. (2016) conducted numerical weather simulations and storm surge simulation of super typhoon Haiyan under the current and global warming climates. The simulation results indicated that typhoon intensity and storm surge will be larger in the future. Appendini et al. (2017) derived information of TCs from reanalysis data and future projections of global climate models (GCMs) and investigated future variations in wave climates. They found increasing significant wave height in certain areas. Timmermans et al. (2017) investigated future variations in global wind-induced wave climate and showed further increases in extreme wave height in TC regions. However, there was large variation in wave heights; detail assessments for specific region are indispensable. Patricola and Wehner (2018) investigated anthropogenic influence on extreme TCs. They implemented high-resolution numerical simulations of TCs under the current, pre-industrial, and future climate conditions and found that the intensification of future TCs is larger than the change in TCs from the preindustrial to the current climate.
For future climate assessment, the output of GCMs are used; however, these model predictions do not include ocean waves, and some analysis or numerical simulation is needed to interpret the effects of any projected change in the climate on ocean waves. Moreover, a high spatial resolution is desirable in such projections to assess detailed impacts of changes in the wave climate for specific coastal areas. Statistical projection is one major approach to produce a wave climate projection. There are also numerous estimations of the future wave climate from numerical wave models. Laugel et al. (2014) compared finer resolution wave climates estimated based on either statistical or dynamical downscaling methods. This study found that the results based on the dynamical method showed better predictive skills of the observed wave climates, and the difference in the computed wave climates between the dynamical and statistical methods was more significant under more severe conditions of global warming. The same study also highlighted that statistical methods have disadvantages in the estimation of the tails of the wave probability distributions or extreme cases. Martinez-Asensio et al. (2016) also compared the results of statistical and dynamical downscaling for the North Atlantic wave climate and found that a statistical model based on wind speed yielded results similar to the dynamical downscaling results. The statistical model using climate indices, sea level pressure, and/or pressure gradient, however, did not reproduce the long-term trend found in the dynamical downscaling results. In addition, statistical downscaling methods neglect swell effects (Mori et al. 2013). Therefore, dynamical methods could be more appropriate for estimating the possible impact of climate change under more severe conditions. Hemer et al. (2013) showed that the direct use of GCM output to force a wave model can cause biases in the wave climate or the overestimation of wave generation in broad regions of the southern Pacific Ocean due to swells. Subsequent work by Hemer and Trenham (2016) showed poorer skill in wave simulation or larger negative biases in the wave height when the GCMs output from the Coupled Model Intercomparison Project Phase 5 (CMIP5; Taylor et al. 2012) was directly used to force a wave model. To prevent the above-referenced bias effects of the GCMs, a pseudo global warming (PGW) method has been proven to be useful (Sato et al. 2007). In early PGW method, atmospheric conditions were generated by considering variations of thermodynamic and momentum conditions under increasing atmospheric temperature (Schär et al. 1996). In the recent PGW method, future anomalies generated from the GCM output are added to the reanalysis data. Then, new future conditions (or PGW conditions) are produced. The PGW conditions are very similar to the reanalysis data used as initial and boundary conditions for reproductive simulations. However, they contain largescale differences in future climatological conditions. Simulations forced by the PGW conditions can be compared with simulations forced by the reanalysis data, which are expected to be more accurate than the results obtained from the direct use of the GCM outputs. To evaluate possible future variations in extreme weather events, the PGW method was applied to actual past extremes (Hill and Lackmann 2011;Lackmann 2015;Meredith et al. 2015;Taniguchi and Sho 2015).
The South Pacific is one of the major ocean basins where TCs occur. Most tropical islands are affected by the passage of violent storms. At the same time, Fiji is located along the southern border of the South Pacific convergence zone and is exposed to seasonal trade winds that greatly influence the wave climate. In March 2010, TC Tomas hit the northern and eastern areas of Fiji as a Category 4 TC on the Saffir-Simpson scale. Tomas brought destructive winds and heavy rains. In Fiji, two lives were lost, 649 houses were destroyed, and 1387 houses were damaged. The Fiji National Disaster Management Office estimated that the total damage was almost $43.6 million USD. Regarding TC behaviors in the South Pacific, decreasing frequency is reported (Walsh et al. 2012;Bell et al. 2019;Walsh et al. 2015;Zhang and Wang 2017;Yoshida et al. 2017). Walsh et al. (2015) showed insignificant variations in frequency of intense TCs under the global warming condition. Zhang and Wang (2017) found that decreasing tendency is more significant for weak TC in the South Pacific. On the other hand, results in Yoshida et al. (2017) indicates decreasing frequency of category 4 or 5 TCs. These results indicate uncertainty in future variations of TC in the South Pacific.
In this study, numerical weather simulations with the PGW method are implemented for TC Tomas. An ensemble simulation technique (i.e., the lagged-simulated perturbation (LSP) method) developed by Taniguchi (2018) is combined with the PGW simulations to consider uncertainties in the forcing data of the simulations. Then, wave simulations are determined with wind data Taniguchi and Tajima Progress in Earth and Planetary Science (2020)

Methods/Experimental
Data This study uses the National Centers for Environmental Prediction (NCEP) FNL (Final) Operational Global Analysis (NCEP FNL) for the initial and boundary conditions of the hindcast weather simulation of TC Tomas and the base state of the PGW conditions. NCEP FNL provides data with a spatial resolution of 1°× 1°at a time interval of 6 h. The FNL product is generated on a sixhourly basis by the global data assimilation system (GDAS) at NCEP from 1999 to a near-current date. Observational data from the Global Telecommunications System (GTS) and other sources are used in GDAS. The FNL is made with the same model used in the Global Forecast System (GFS), although it is prepared approximately 1 h after the GFS is initialized. Thus, more observational data are accounted for in the analysis. The analyses are available at the surface, 31 pressure levels from 1000 millibars to 1 millibar, and other specific layers as the tropopause, cloud bottom level, cloud top level, and several other levels. The parameters include surface pressure, sea level pressure, geopotential height, temperature, sea surface temperature (SST), soil values, ice cover, relative humidity, u-and v-winds, vertical motion, vorticity, and ozone (NCEP 2018). The present simulation used SSTs from the National Oceanic and Atmospheric Administration (NOAA) Optimum Interpolation 1/4 Degree Daily SST (NOAA OI SST) analysis data (Reynolds et al. 2007) as a lower boundary condition for the numerical weather simulations. The NOAA OI SST is a dataset that combines different types of observation (satellites, ships, and buoys). In situ data from ships and buoys are used for the largescale adjustment of satellite biases. The product uses SSTs from the advanced very high resolution radiometer (AVHRR) and Advanced Microwave Scanning Radiometer on the Earth Observing System (AMSR-E). The spatial resolution of the product is 0.25°× 0.25°, which is higher than that of the NCEP FNL reanalysis product.
The PGW conditions consist of the NCEP FNL data and future climate projections from five different GCMs that were developed for CMIP5 (Taylor et al. 2012). In CMIP5, several scenarios of atmospheric greenhouse gas concentrations (i.e., representative concentration pathways; RCPs) were applied to generate future projections under different climate conditions. In this study, future projections based on the RCP8.5 scenario were used for preparation of the PGW conditions. In the RCP8.5 scenario, the radiative forcing of the Earth in the year 2100 is 8.5 W/m 2 greater than the preindustrial level. Based on the evaluation of climate models in CMIP5 report (Flato et al. 2013), reproducibility of SST was investigated for 20 available GCM projections, and five GCMs, which exhibited the better reproducibility of SST than the others, were selected to prepare PGW conditions. The five GCMs used in this study are listed in Table 1.

Numerical weather simulation
The weather research and forecasting (WRF) model version 3.5.1 (Skamarock et al. 2008) was used for the numerical weather simulations. As shown in Fig. 1, twoway, two-level nesting was adopted in this study. The spatial resolutions of the simulations were 30 km and 6 km for the parent (D01) and child (D02) domains, respectively. The number of vertical layers was set to 35 in both domains. The atmospheric pressure at the top boundary of the domain was set to 20 hPa. Various parameterizations are available for each physical process. The parameterization settings in this study are shown in Table 2.
In this study, extreme weather events in a specific area (e.g., around the main island of Fiji, Viti Levu) were investigated by applying the ensemble simulation technique (LSP method described later) to obtain several simulation results. To compare the variations in the characteristics of typhoons and ocean waves in a specific region under different climate conditions, the results of the ensemble simulations must have similar meteorological spatial distributions. Therefore, for D01, a spectral nudging method was applied for atmospheric temperature, zonal wind, meridional wind, and geopotential height every 6 h above a height of 6-7 km.

Wave simulations
The third-generation spectral wave model WaveWatch-III (WW3; Tolman 2009) was used for the wave simulation in this study. A two-domain nesting system was applied to the simulation. The parent domain covered the sea area around the Fiji Islands and their surroundings, while the child domain covered the sea area around the main island (Viti Levu) of Fiji ( Fig. 1). The spatial resolutions were 0.1°and 0.033°for the parent and child domains, respectively. In the simulations, the wave spectrum at every computational grid point was discretized to a component of 24 wave directions and 25 wave frequencies from 0.04118 to 0.44617 Hz, with a logarithmic increment of f(n + 1) = 1.1f(n), where f(n) represents the nth frequency. The settings used for WW3 are summarized in Table 3. Applicability of WW3 for the Central and South Pacific regions was investigated by Durrant et al. (2014). They showed that significant wave height simulated by WW3 agreed well with the buoy observation around Fiji. Their results support confidence of finer resolution WW3 simulation which resolves the required coastal variability.

PGW method
Following Sato et al. (2007), the PGW conditions were generated from NCEP FNL and future climatological anomalies using the five GCM projections. As in Sato et al. (2007), future climatological anomalies were calculated as the difference of 10-year monthly mean climate conditions between the future and present. Twenty-year mean climate conditions are often applied in climatological studies; however, 10-year mean conditions were used to include impacts of climate change under advanced global warming conditions. The future 10-year monthly mean climate conditions were calculated from 2091 to 2100 under the RCP8.5 scenario. The present conditions were calculated for 1991-2000 in the historical runs by each GCM. These anomalies were added to the 6-h atmospheric conditions from NCEP FNL. Then, a set of PGW conditions were obtained for wind, atmospheric temperature, geopotential height, and surface pressure. For relative humidity, the original values in NCEP FNL were used in the PGW conditions, and specific humidity under PGW was calculated from the relative humidity and modified atmospheric temperature in  Planetary boundary layer scheme Bougeault-Lacarrère scheme (Bougeault and Lacarrèr 1989) Longwave and shortwave radiation Rapid radiative transfer model (Iacono et al. 2008)  the future climate. In the PGW conditions, the ranges and patterns of the temporal variations (e.g., diurnal, seasonal, and interannual variations) of the variables were the same as the reanalysis data and future variations were not included. Even with such a limitation, the PGW method can be easily applied and is useful to investigate the effects and impacts of global warming on the climatological mean conditions. The SSTs for the PGW conditions were generated by adding the SST anomalies obtained from the future and present climates in each GCM to the NOAA OI SST dataset. Using the corresponding number of each GCM in Table 1, the ensemble experiments with the PGW conditions are termed PGW-1, PGW-2, PGW-3, and so on, and the ensemble hindcast is called CTL. Figures 2 and 3 show composite of atmospheric temperature and geopotential height at 850 and 500 hPa layers for the hindcast and 5 PGW conditions. These atmospheric conditions are parts of initial condition by WRF simulations. There are considerable differences in the atmospheric temperature at 850 and 500 hPa (T850 and T500, respectively) among 5 PGW conditions, but all results show higher T850 and T500 than in the initial condition for the hindcast. In warmer atmospheric condition, saturation specific humidity of atmosphere also increases and more precipitation is expected. Increasing precipitation could cause more latent heat release in TC, and it would sustain TC intensity. Geopotential height at 850 and 500 hPa are also higher in PGW conditions, but atmospheric structure (or horizontal patterns of geopotential height) is similar for the hindcast and PGW conditions. Figure 4 is spatial distribution of SST at the initial time of the hindcast and 5 PGW simulations. There are significant increases in SST for PGW conditions, and it could provide more heat and moisture flux from the ocean to the atmosphere in PGW conditions. Then, there is high likelihood of intensification of TC. On the other hand, surface heat flux and moisture fluxes are determined by relative difference between the surface and atmosphere, and warmer SST does not always provide large heat and moisture from the ocean.

Ensemble simulation
A new, simple ensemble simulation method (i.e., the LSP method) developed by Taniguchi (2018) was used in this study. The LSP method is based on the lagged average forecasting (LAF) method (Hoffman and Kalnay 1983). The LAF method makes multiple simulations that start at different initial times. In the LSP method, ensemble simulations are conducted in three steps. First, three simulations starting at different initial times are implemented to obtain three base state vectors (X 1 , X 2 , and X 3 ) at an appropriate interruption time. Second, two difference vectors (ΔX 2 and ΔX 3 ) are calculated as the difference between X 2 and X 1 and between X 3 and X 1 , respectively. Third, new state vectors (X n ) are prepared from a single base state (X 1 ) and the two difference vectors (ΔX 2 and ΔX 3 ) using the following equation: where α and β represent the scale factors for ΔX 2 and ΔX 3 , respectively. Then, the ensemble simulations are conducted from the interruption time with the new state vectors. The initial and interruption times are shown in Table 4. In the new state vectors, atmospheric temperature, zonal and meridional wind components, specific humidity, atmospheric pressure, and SST are updated via the LSP method. The same scale factors (α and β) are applied for all variables. The LSP method is only applied to the initial conditions. The boundary conditions are the same for all ensemble members. The LAF method requires unnecessarily large lags to generate many ensemble members. Furthermore, the LAF method should yield large differences in accuracy depending on the length of the simulations. As shown in Table 4, three simulations have different initial time, but others are started from the same initial time. Therefore, the aforementioned weaknesses of the LAF method are eliminated in the LSP method. The scale factors used in this study are given in Table 5, and 19 members are produced for each ensemble simulation (one present and five future climate simulations).

Results and discussion
Hindcast of TC Tomas and ocean waves Figure 5a shows the track of TC Tomas based on the best track data from the Joint Typhoon Warning Center (JTWC) and the tracks of the hindcast ensemble from WRF. TC Tomas moved from the north to south. In the early stage (i.e., north of 20°S), simulated tracks and the best track agree well with each other. On the other hand, south of 20°S, the simulated tracks are slightly moved from the best track in the eastward direction. However, the track of TC Tomas is reproduced well in the WRF simulations because of the effect of the spectral nudging. Figure 5b shows the temporal variations in the central pressure of TC Tomas. The central pressure of the best track data reaches a minimum central pressure of 937 hPa, whereas the ensemble mean central pressures of the present simulation yields a minimum pressure of 949.8 hPa, and the lowest minimum central pressure of the 19 ensemble members is 932.9 hPa. These results indicate that several ensemble members duplicate strong TCs that are as intense as actual TC Tomas (or the JTWC result). Although the time profile of the simulated central pressure appears to be delayed for approximately 1 day compared with that of the best track data, the simulated profile reasonably captures the decreasing slope and minimum central pressure of the best track data. Several studies have shown delayed intensification of simulated TCs (Oku et al. 2010;Takayabu et al. 2015;Nasuno et al. 2016;Kanada et al. 2017b; Nayak and Takemi 2019). Takayabu et al. (2015) indicated the effect of initial and boundary conditions on TC simulations. Nayak and Takemi (2019) also highlighted the role of initial and boundary conditions in delayed TC development. Moreover, Nasuno et al. (2016) showed that small latent heating differences over the ocean can delay the development of TCs. Kanada et al. (2017b) indicated that sea surface cooling can suppress the delayed evolution of the simulated TCs. However, it is not the main scope of this study to improve the boundary condition (SSTs) and surface physics schemes. Therefore, the future simulations were conducted based on the results shown in Fig. 5. Figure 6 shows the spatial distribution of the simulated and observed surface wind speeds around Fiji. The observed wind speed was obtained from Advanced Microwave Scanning Radiometer for EOS (AMSR-E) onboard the Earth observation satellite Aqua (Shibata 2006). To compare the overall structure of TC Tomas, the WRF simulation results are extracted from the parent domain. At 14 UTC on 15 March 2010, the peaks of the sea surface wind speeds based on the AMSR-E and WRF simulations are located in nearly the same place, and the peak wind speeds obtained from the AMSR-E and WRF simulations are comparable, although the area of relatively strong wind is wider in the WRF simulation than in the AMSR-E-based observations. At 02 UTC on 16 March, the WRF simulation result shows a larger wind speed near the center of TC Tomas and a wider area of relatively high wind speed compared to the AMSR-E-  Using the WRF simulation results to force the model, wave simulations are implemented by WW3. Figure 7 shows the spatial distribution of the ensemble mean maximum wind speed in CTL. A strong wind greater than 45 m/s is recognized southeast of the main island of Fiji (Viti Levu). The spatial distribution of the ensemble mean maximum significant wave height (H s ) in CTL shows significantly high waves in the area of strong wind (Fig. 8a). The maximum H s in the target domain is from 15.2 to 18.9 m southeast of Viti Levu. Figure 8b shows the temporal variation in H s around the offshore region of Suva ( Barstow and Haug (1994), the observation value of the ocean waves induced by TCs around Fiji is recorded. In December 1992, TC Joni passed through the western region of Fiji, and the maximum 1 (10) minute mean wind speeds were 56.9 (45.8) m/s. In the case of TC Joni, the maximum Hs southwest of Kadavu Island (located south of Viti Levu, see Fig. 1b) was 7.2 m. In the case of TC Tomas, the maximum 1min and 10-min means of the wind speed were 59.2 m/s and 51.4 m/s, respectively. The stronger wind from TC Tomas could cause a larger H s than that from TC Joni, which is consistent with the present results based on the WW3 computations.
Variations in TC Tomas and ocean waves in the future Figure 9 compares the TC tracks of CTL and the five PGW ensemble simulations. The tracks of PGW-2, PGW-3, PGW-4, and PGW-5 match well with the best track. While the simulated TC track of PGW-1 slightly shifts eastward south of 17.5°S, the simulated TC track agrees reasonably well with the best track data. All five PGW ensemble simulations give tracks that are approximately similar to that of TC Tomas in CTL. The temporal variations in central pressure of the simulated TC are shown in Fig. 10. In PGW-1 and PGW-5, the ensemble mean minimum central pressure (P min ) is lower than that in the CTL. The minimum values of central pressure among the 19 ensemble members in PGW-1 and PGW-5 are also lower than those in CTL. These results indicate the apparent intensification of the TC in PGW-1 and PGW-5. The ensemble mean minimum central pressure is slightly lower in PGW-2 and PGW-4 than that in CTL, and the minimum values are no smaller than those in CTL. The minimum value of the ensemble mean time series in PGW-3 is nearly equal to that of the CTL. The ensemble spread, indicated by shading in Fig. 10, shows that the most intense ensemble member in PGW-3 is also comparable to CTL. Difference of T500 and T850 (or T500-T850) averaged over the region of 178E-178W, 14S-22S is shown in Table 6. In PGW-2 and 3, the difference of the two layers is smaller than the other simulations. Difference of T850 and SST (or T850-SST) for the same region is also smaller in PGW-2 and 3 (Table 6). These results indicate more stable atmospheric stratification and smaller upward heat flux in PGW-2 and PGW-3. As shown in Figs. 2 and 3, atmospheric temperature and SST are higher in all PGW conditions, and intensification of TC is expected in PGW simulations. But more stable and smaller heat flux could prevent TC intensification. Figure 11 shows the difference in the ensemble mean maximum wind speed between CTL and the five PGW ensemble simulations. While the TC was intensified in  PGW-1 (Fig. 10), the ensemble mean wind speed in PGW-1 is smaller than that in CTL southeast of Viti Levu (Fig. 11b). This feature may be caused by an eastward shift in the TC track in PGW-1 (Fig. 11b). In another intensified TC simulation (PGW-5), the wind speed becomes larger in the wider area of domain 2. PGW-2 and PGW-4 show similar variations in the central pressure, but the spatial distributions of the wind speed are quite different. In PGW-4, significant increases in the maximum wind speed are recognized, and a weakened wind is found in limited areas. On the other hand, the ensemble mean maximum wind speed becomes weaker than that in the CTL in a wide area in PGW-2. The minimum peak in the central pressure in PGW-2 occurs later than that in CTL (Fig. 10c), and an increased wind speed is found near the southern boundary of domain 2. These results indicate that the development of the TC delays PGW-2 and that the wind speed is weaker around Fiji. The other four PGW simulations show almost the same timing of the minimum peak in the ensemble mean central pressure as CTL. In PGW-3, an enhanced wind is found around Viti Levu, and a weakened wind occurs east of these areas, which can be caused by a slight westward shift in the track in PGW-3 (Fig. 11d). Variations in the ensemble mean maximum H s (H s max ) in the PGW simulations are shown in Fig. 12. Generally, increasing and decreasing H s max correspond to variations in wind speed, as shown in Fig. 11. In PGW-3, PGW-4, and PGW-5, significant increase in H s max (larger than 0.8 m) is found over the southeastern coast of Viti Levu. In PGW-1, the eastward shift in the TC track results in a significant increase in H s max over the southeast edge of domain 2 and a decrease southeast of Viti Levu. In PGW-2 because of the decreased wind speed shown in Fig. 11, H s max is smaller than that in CTL. As discussed in the previous subsection, such a decreasing H s max in domain 2 may be because of the slower development of the TC in PGW-2. Figure 13 shows the temporal variation in H s around the offshore region of Suva (178.47°E,18.20°S) in the CTL and five PGW simulations. The ensemble mean Hs Results are average for 178E-178W, 14S-22S Fig. 11 Spatial distribution of the ensemble mean maximum wind speed. a CTL results (same as Fig. 4). b-f Difference in the ensemble mean maximum wind speed between the CTL and each PGW ensemble simulation. The unit of color bar is m/s in PGW-1 shows faster enhancement than that in CTL, but the maximum value in PGW-1 is the same as that in CTL. At the same time, the ensemble spread (indicated by shading) is also the same as that of the CTL. In PGW-2, the peak of the ensemble mean H s is the same as that of the CTL. However, the maximum peak in H s in the PGW-2 ensemble is more than 1 m larger than that in the CTL. In PGW-3, PGW-4, and PGW-5, the peak of the ensemble mean H s is clearly larger than that in the CTL. Even in the minimum case, the peak of H s is larger than that in the CTL in these three PGW simulations. Figure 14 shows histograms and the probability density curves of the maximum significant wave height (H s_max ) around Suva in the CTL and five PGW simulations. Here, the probability densities were calculated based on the assumption of a normal distribution. The CTL results show a peak at approximately 8.5 m, and the range Fig. 12 Spatial distribution of the ensemble mean maximum significant wave height. a CTL results (same as Fig. 5a). b-f Difference in the ensemble mean maximum significant wave height between the CTL and each PGW ensemble simulation. The unit of the color bar is m. of H s_max is from 7.5 to 9.5 m. PGW-1 shows similar results to the CTL. In PGW-2, the probability density peak of H s_max is the same as that in the CTL, but the H s_max spread is much wider than that in other ensemble simulations. This result indicates that in some global warming conditions, the average of the extremes is the same as the present climate, but a significantly severe case can occur under particular conditions. In PGW-3, PGW-4, and PGW-5, frequency peaks are found at a significantly larger H s_max than those in the CTL. The results of these three PGW ensemble simulations indicate that, when a TC similar to Tomas occurs in a future climate, it will make much larger ocean waves, which could cause severe disasters. Especially in PGW-3 and PGW-4, the histogram and probability density curves hardly overlap with those of the CTL, and H s_max around Suva reaches an unexpected scale in the present climate with high probability. A summary of the CTL and PGW ensemble simulations is shown in Table 7. PGW-4 and PGW-5 indicate an intensified TC and larger H s near the offshore region of Suva in a future climate. The results of PGW-1 and PGW-2 also show a somewhat enhanced TC, but H s near the offshore region of Suva is comparable to that of the CTL. On the other hand, the intensity of the TC in PGW-3 is similar to that in the CTL, but H s is quite larger than that in the CTL. Significantly high ocean waves and larger storm surges are expected in PGW-4 and PGW-5. PGW-1 and PGW-2 show a high possibility of a larger storm surge, but ocean waves are as high as those in the present climate. In PGW-3, the scale of the storm surge is expected to be the same as that in the CTL, but higher ocean waves are expected in the future climate.
In Table 7, standard deviations and medians are also shown for the minimum central pressure (P min ), maximum wind speed (U max ), and maximum H s in the offshore region of Suva (H s_max ). In many PGW simulations, the standard deviations are smaller than those in the CTL for P min , U max , and H s_max . Some PGW simulations show larger standard deviations, but they are comparable to those of the CTL. At the same time, the medians for these three variables are almost the same as the ensemble mean values. Thus, the future intensification of TCs and higher ocean waves are not caused by rare extreme events, but they exist with high probability when they do occur.  The results in Table 7 indicate various types of hazards under global warming. For sufficient risk assessment near coastal areas, various mixed hazards and their possibilities have to be evaluated based on ensemble simulations using multiple GCM outputs.

Conclusions
Based on TC Tomas in 2010, ensemble PGW simulations were implemented to investigate future variations in the characteristics of TCs and induced ocean waves around Fiji. Five GCM projections were used to produce PGW conditions for future simulations. The ensemble mean minimum central pressures of TCs in four PGW simulations are smaller than those in the hindcast (CTL). In three of the five future simulations, the tracks and development of the TC are similar to those of the CTL. In these PGW simulations, a significant increase in the maximum significant wave height was recognized southeast of the Fiji main island (Viti Levu). In the case of an eastward shift in the track in PGW-1, the significant wave height was smaller than that of the CTL around Viti Levu, but higher in the more eastern regions. In PGW-2, the delayed development of the TC caused a lower significant wave height around Fiji but a higher wave height in the southern region. In PGW simulations whose maximum significant wave height is larger than the hindcast (or PGW-3, 4, and 5), the probability density of the maximum significant wave height in the offshore region of Suva (i.e., the southern part of Viti Levu) showed that when a TC similar to Tomas occurs in future climate, there will be significantly larger ocean waves, which are not expected under the present climate. Two PGW simulations showed very different probability density curves from those of the CTL, which indicates the high probability of a significant wave height dominating the maximum in the present climate. At the same time, in PGW-2, where the ensemble mean maximum wave heights are similar to those in the CTL, a wider variability was found. This result indicates that variability of ocean waves would be larger and extremely high ocean waves would be more likely to occur under the condition of global warming. In this study, future variation of TC frequency is not considered. For assessment of effects of future variations in TC and ocean waves, it is necessary to combine frequency of TC occurrence and changes in characteristics of extreme events.
Five PGW simulations showed different types of characteristics of TCs and ocean waves in a future climate: large ocean waves and lower surface pressure (which cause large storm surge), large ocean waves with moderate pressure, and moderate ocean waves with lower surface pressure. These results indicate the importance of using future projections from multiple GCMs to make an adequate evaluation of risk assessments and possible hazards. For a more comprehensive assessment, more GCM projections and other global warming scenarios should be applied for various TC events. By focusing on a specific area or place, a small difference in the TC track might significantly affect the results of the wave simulations or the evaluation of hazards induced by TCs. Shimura et al. (2015) suggested the importance of TC track shifts. In addition to various patterns of TC characteristics using multiple GCM projections, considering a number of TC tracks is crucial for risk assessment. At the same time, there are limitations in numerical weather simulations. First, as stated in the methodology, same lateral boundary conditions were applied for all ensemble members based on the LSP method. Second, the spectral nudging was applied to obtain similar TC tracks among the hindcast and PGW simulations. These limitations may make ensemble spread smaller and reduce the degree of freedom in TC simulations. To increase the number of TC samples and reduce the effect of these limitations, application of stochastic technique may be useful. In this study, possible future variations of TC characteristics and induced ocean waves were investigated through the case study of TC Tomas. For more comprehensive understanding of impacts of global warming on extreme TCs and ocean waves, it is indispensable to increase the number of similar numerical simulations of various TC events. In WRF simulations, physical processes in the ocean and upwelling water along TC are not fully resolved. It may cause overestimation of SST and intensity of TCs. Simulations by atmosphere-ocean coupled model is also important to consider more detailed processes of TC development and to enhance the accuracy in estimation of global warming impacts. At the same time, a technique to translate the results from numerous ensemble simulations and probability information has to be established for designing measures for mitigation and adaptation.