Quantification and attribution of ocean cooling induced by the passages of typhoons Faxai (2019) and Hagibis (2019) over the same region using a high‐resolution ocean model and cooling parameters

This study quantitatively evaluated the typhoon‐induced sea surface temperature (SST) cooling caused by typhoons Faxai (2019) and Hagibis (2019) using a high‐resolution ocean model and the cooling parameter (Co). Faxai and Hagibis both passed over the ocean south of the eastern part of the Japanese main island, but the associated average SST decreases differed. Faxai produced a decrease of less than 2°C, whereas Hagibis produced a decrease of more than 2°C. The average Co value was 1.6 for Faxai and 3.6 for Hagibis, indicating that SST was more easily cooled by Hagibis than by Faxai, consistent with the observations. The impact of ocean conditions on the typhoon‐induced SST cooling by Hagibis was 2.6 times larger than the impact by Faxai, indicating that the ocean before Hagibis passes is less hard to cool ocean than Faxai. In short, it is important for ocean cooling not only ocean conditions but also typhoon characteristics because in fact, Hagibis cooled the ocean more than Faxai. In addition, the impact of Hagibis's characteristics on the typhoon‐induced SST cooling was 4.8 times larger than the impact of Faxai's characteristics. Thus, SST was more likely to cool by typhoon characteristics in the case of Hagibis. In particular, among Hagibis's characteristics, typhoon size in the horizontal direction had the most efficient effect on SST cooling. Although Co does not consider the effects of the advection of ocean water, we suggest that Co is a practical indicator for estimating SST cooling caused by a typhoon and comparing factors of typhoon‐induced SST cooling in multiple cases.


| INTRODUCTION
Typhoon Faxai (2019) occurred in early September 2019 and made landfall over the Kanto District, Japan. In early October, a month later, Typhoon Hagibis (2019) approached Japan along a track similar to Faxai's track, crossing the same ocean region around the southeastern Japanese Archipelago (Figure 1). According to the best track data of the Regional Specialised Meteorological Centres Tokyo-Typhoon Centre, Japan, the maximum wind speed (Vm) of Faxai reached 43.7 mÁs À1 and the Vm of Hagibis was 54.0 mÁs À1 . The horizontal size of Faxai, that is, the radius of sustained wind of 15 mÁs À1 (R15), was 330 km and that of Hagibis was 750 km. Faxai had an average speed of movement over the ocean south of the eastern Japanese main island of 8.1 mÁs À1 , similar to that of Hagibis (6.8 mÁs À1 ). Therefore, Hagibis was stronger and larger than Faxai, and the two typhoons had similar tracks and speeds over the ocean.
High-resolution satellite observations from Himawari-8 showed that sea surface temperature (SST) decreased with the passage of both typhoons (Figure 1a,c). Typhoon-induced SST cooling is caused by the effects of the strong winds associated with typhoons (Ginis, 1995;Price, 1981). A typhoon develops more efficiently over the ocean at higher SST as a result of ocean heat flux and water vapour inflow (e.g., Emanuel, 1986), but typhoon-induced SST cooling can directly suppress typhoon intensity via oceanic feedback (e.g., Wada, 2007;Wada et al., 2010). Therefore, it is important to understand typhoon-induced SST cooling to predict typhoon intensity, that is, maximum wind speed.
SST cools as seawater is mixed by strong typhoon winds, which is a one-dimensional response, and a threedimensional response also occurs due to the influence of currents in the ocean surface layer or upwelling (Price, 1981;Suzuki et al., 2011;Yablonsky & Ginis, 2009). Quantitatively, rainfall contributes less to SST cooling than other factors (Yu & Subrahmanyam, 2017). In addition, the magnitude of typhoon-induced SST cooling is related not only to the ocean conditions beneath a typhoon but also to the characteristics of the typhoon, such as Vm, horizontal size, and speed of movement. The impacts of ocean conditions on typhoon intensity are indicated by the ocean heat content (OHC) and the tropical cyclone heat potential (TCHP) (Leipper & Volgenau, 1972). These indicators represent ocean conditions but do not consider the magnitude of the impact on SST cooling of typhoon characteristics.
The cooling parameter (Co) is a non-dimensional number that theoretically indicates the magnitude of SST cooling during the passage of a typhoon, as proposed by Miyamoto et al. (2017). We used Co because it reflects not only ocean conditions but also typhoon characteristics. Co allows for a quantitative assessment of the relationship between ocean conditions and typhoon characteristics.
In this study, we utilise Co in a high-resolution ocean model for targeted analysis of typhoons Faxai and Hagibis, as Miyamoto et al. (2017) did not report an application of Co to real typhoons or ocean data in detail. The purpose of this study was to evaluate typhoon-induced SST cooling quantitatively, separating the impacts of typhoon characteristics from the impacts of ocean conditions using Co. The rest of the paper is organised as follows: Section 2 briefly describes the ocean model and the equations of Co; F I G U R E 1 Differences in SST over the 4-day periods of (a, b) 6-10 September 2019 during the passage of Typhoon Faxai and (c, d) 8-12 October 2019 during the passage of Typhoon Hagibis. (a, c) SST according to Himawari-8 and 6-hourly typhoon centre locations derived from the best track. (b, d) SST simulated based on the ocean model and hourly typhoon centres from the MSM. Grey areas indicate a lack of satellite data. Section 3 validates the SST cooling caused by Faxai and Hagibis using Co; and Section 4 summarises the main findings of the study and future study.

| METHODS
This study used a submesoscale-permitting ocean general circulation model to investigate the distribution of seawater temperature at fine resolution according to the impacts of moving typhoons. The model, named ICTKSMW, is based on MRI.COM ver. 4.7 (Tsujino et al., 2017) and covers the Pacific side of Eastern Japan (26. 00-37.99 N, 135.32-142.54 E). The horizontal resolution is 1/60 . It has 35 vertical layers (0.25-5825.00 m). Other settings are basically the same as those in Tanaka et al. (2018). The bulk equation is Large and Yeager (2004), (Large & Yeager, 2009). The mixed layer model follows Noh and Kim (1999). The tidal forcing of the eight main constituents (M2, S2, N2, K2, K1, O1, P1, and Q1) was considered through the tidal model of Sakamoto et al. (2013). The lateral boundary conditions for physical variables were derived from the daily analysis of the western North Pacific by the Japan Meteorological Agency (Usui et al., 2006), and those for tidal sea surface height and barotropic velocity were from NAO.99Jb (Matsumoto et al., 2000).
The model was driven by the hourly wind vectors, u and v, at 10-m height; sea level pressure; atmospheric temperature and specific humidity at 1.5-m height; downward shortwave radiation; precipitation rate from the mesoscale model (MSM; Japan Meteorological Agency 2013); and 3-hourly downward longwave radiation from the Japanese 55-year Reanalysis Project (JRA55; Kobayashi et al. 2015). The numerical calculation was performed from 00 UTC on April 1, 2019 to 00 UTC on November 1, 2019. The seawater temperature from ICTKSMW was interpolated vertically at 1-m intervals to calculate Co. Miyamoto et al. (2017) proposed Co as a nondimensional indicator for evaluating the typhooninduced SST cooling effect caused by ocean mixing, to improve the accuracy of the maximum potential intensity framework developed by Emanuel (1986). Co is estimated from the ratio of typhoon characteristics and ocean conditions as follows: where F ms0 (kgÁm À1 Ás À2 ) is the surface momentum flux, λ (m) is the length scale of the vortex, vt (mÁs À1 ) is the speed of movement, α (K À1 ) is the thermal expansion coefficient, ρ (kgÁm À3 ) is water density, g (mÁs À2 )is gravitational acceleration, h 0 (m) is the mixed layer depth (MLD), and Γ (KÁm À1 ) is the temperature lapse rate below the mixed layer. Note that MLD is defined only by ocean temperature. ρ a (kg m À3 ) is air density and C d is the surface exchange coefficient for momentum.
Co includes the following parameters for typhoon characteristics: R15 (nm), the radius of maximum wind (m) (RMW) (Equations 1 and 2), Vm (mÁs À1 ), and vt (mÁs À1 ). R15 and RMW are included in λ, which represents the size of the typhoon, and λ is effective for the square. For the typhoon characters in this study, R15, RMW, and Vm at 1-h intervals were detected from the MSM hourly data, instead of the best-track data with lower temporal resolution. Using the 10-m height winds in MSM, the centre of the typhoon, R15, and RMW were detected by the maximum axisymmetric mean tangential wind.
The ocean conditions considered in Co include h 0 and Γ. The ocean conditions for Co were standardised at 24 h before the time of each typhoon's passage. MLD works to the fourth power. The ocean conditions were derived from the ocean model results averaged over a 2 Â 2 box relative to the typhoon centre at each time point. Co was calculated for all 25 hourly positions of both typhoons from latitude 29 N to 34 N every 1 h. The Co of Faxai was estimated for 12 UTC September 7 to 12 UTC September 8, 2019, whereas the Co of Hagibis was estimated from 06 UTC October 11 to 06 UTC October 12, 2019. Note that Co values greater than 10 were excluded because the speed of movement was slow in such cases (<3 mÁs À1 ).
The magnitude of SST cooling (ΔSST) was defined as the difference in SST from the reference time to the time of passage [0] (e.g., the time of passage [0] is 14 UTC September 7 for Faxai and 06 UTC October for Hagibis at 29 N) as well as to 3, 6, 9, 12, 24, 36 h after passage, and 4 days before and after passage. Except for the assessment at 4 days, the reference time is 24 h before the typhoon's closest approach to each location. This study used several time intervals for ΔSST because long-and short-term intervals are affected differently by typhoon impacts and the recovery of ocean conditions.
3 | RESULTS Figure 1 shows ΔSST for the 4 days around the passages of Faxai and Hagibis derived from satellite observations, and the outputs of the ocean model. ΔSST was negative; that is, SST decreased during the passage of the typhoon along the track, as cooling can be caused by the strong winds associated with typhoons. The negative ΔSST values distributed around the tracks of Faxai and Hagibis were generally in good agreement with the numerical results. Most of the SST decreases <2 C were associated with the passage of Faxai, while SST decreases >2 C accounted for about 40% of the total, including about 10% exceeding 3 C, and occurred in the negative ΔSST region during the passage of Hagibis. The numerical results demonstrate that SST decreases more due to cooling during the passage of Hagibis than Faxai. Asymmetry in the distribution of the SST decrease appeared along the path of the typhoon according to both the satellite observations and numerical results, as noted by Price (1981). Figure 2 shows vertical-latitudinal cross-sections at 29 N of ocean temperature changes based on the numeric results. The variations of ocean temperature at 0, 6, 12, and 24 h after the passages of Faxai and Hagibis are shown for the specific latitude of 29 N relative to the reference times of 14 UTC on September 6 for Faxai and 06 UTC on October 10 for Hagibis. Faxai cooled the shallow ocean layers above the 50 m depth over a horizontal width of <2 , while Hagibis cooled the ocean at depths below 50 m across an area wider than 2 . Hagibis produced a region showing an SST decrease of 2 C during its passage, which was broader than the equivalent region for Faxai and had local decreases >3 C. These results suggest that Hagibis cooled the ocean more widely and deeply than Faxai. Local ocean cooling started at the time of passage for both typhoons, proceeded further after 6 h, and then diminished at 12 h after the passage of Faxai, while the region associated with Hagibis showed a longer period of more extensive cooling. At 24 h after the passage, there was a slight recovery of ocean temperature in the case of Faxai.
The daily averages and standard deviations of ΔSST, Co, and the typhoon characteristic and ocean condition statistics around Faxai and Hagibis are listed in Tables 1 and 2. The average Co values for Faxai and Hagibis were 1.6 and 3.6, respectively. Co for Hagibis was about twice that of Faxai, indicating that SST cooled more easily with the passage Hagibis than Faxai, consistent with the observations and results of the ocean model. Figure 3 shows the distribution of the effect of ocean conditions on Co estimated from the ocean model data at an interval of 0.5 when both typhoons were located at 26.5-34.0 N. Most of the ocean conditions were less than 5 for Faxai and greater than 5 for Hagibis. The ocean conditions were high (greater than 15) during the passage of Hagibis in the area north of 31 N. In this case, the Kuroshio Current followed a different path (not shown), explaining the difference observed around 33 N. The average ocean condition values were 4.5 during Faxai and 11.5 during Hagibis when the ocean before their passages is compared in ocean stability (Tables 1 and 2). A higher this value indicates that the ocean is more stable and less tends to mix and cool. As a result, oceanic condition values were approximately 2.6 times greater for Hagibis (11.5) than Faxai (4.5), indicating that the ocean before Hagibis passes is less hard to cool ocean than Faxai when only the ocean before the typhoon passages is compared. On average, MLD was about 10 m deeper during Hagibis (46.7 m) than Faxai (36.2 m). Meanwhile, the lapse rates under the mixed layer were 0.07 KÁm À1 for Hagibis and 0.06 KÁm À1 for Faxai. This finding indicates that the ocean was more difficult to cool before the passage of Hagibis compared to Faxai due to the significant impact of MLD. However, Hagibis actually cooled the ocean more than Faxai shown in Figure 2, suggesting that typhoon characteristics are important for ocean cooling.
The average impact of typhoon characteristics was 4.8 times larger for Hagibis (31.5) compared to Faxai (6.5). Among the typhoon characteristics listed in Tables 1 and 2, Hagibis had a three-times larger R15 (421.6 km vs. 150.2 km) and two-times larger RMW (59.6 km vs. 35.0 km) than Faxai. The 24-h average Vm was almost equal between Faxai (36.7 mÁs À1 ) and Hagibis (33.2 mÁs À1 ), even though Hagibis had a larger life-time maximum Vm value (54.0 mÁs À1 ) than Faxai (43.7 mÁs À1 ), as seen in the best track data of the Japan Meteorological Agency. The average speed of movement of Faxai (8.1 mÁs À1 ) was comparable to that of Hagibis (6.8 mÁs À1 ). Thus, in terms of the impact of typhoon characteristics, T A B L E 1 Average and standard deviation of Co, Co separated by typhoon characteristics and ocean conditions, R15, RMW, maximum wind, speed of movement, MLD, and Γ for Typhoon Faxai. the Hagibis had more potential to cool the ocean than Faxai, attributable mainly to its larger size. Figure 4 shows the relationships between Co and ΔSST for Faxai and Hagibis. Larger Co values are explained by the greater ΔSST values. The correlation coefficients are listed in Table 3; the correlation coefficients are from 24 h before passage to the time of passage (0) and to 3,6,9,12,24, and 36 h after passage. The correlation coefficients were 0.3-0.7 for Faxai and 0.7 for Hagibis. Therefore, Co is a practical indicator of SST cooling. Additionally, the increase rates of Faxai and Hagibis were similar (both within 0.11-0.16, as shown in Figure 4). The correlation coefficients between Co and ΔSST decreased with time for Faxai but remained almost constant for Hagibis (Table 3). This result is consistent with the ocean temperature changes (Figure 2). The correlation for Faxai was 0.68 at the time of passage, which worsened after 6 h, decreased to 0.40 F I G U R E 4 Correlation between hourly Co and ΔSST. The periods are from 12 UTC September 7-12 UTC September 8 for Typhoon Faxai (red) and from 06 UTC October 11 to 06 UTC October 12 for Typhoon Hagibis (blue). SST cooling was determined from 24 h before passage to the time of passage (ΔSST_0) and to 6 h (ΔSST_6), 12 h (ΔSST_12), and 24 h (ΔSST_24) after passage. after 12 h, and subsequently remained relatively constant (Table 3).

| CONCLUSION
This study quantitatively evaluated the factors of typhoon-induced SST cooling caused by typhoons Faxai and Hagibis. The average observed ΔSST differed substantially between the two typhoons. From the highresolution ocean model results, the average Co was 1.6 for Faxai and 3.6 for Hagibis. The Co can separately estimate the impacts of ocean conditions and typhoon characteristics, such as Vm, the size in the horizontal direction, and the speed of movement. The impact of ocean conditions on the typhoon-induced SST cooling by Hagibis was 2.6 times larger than the impact by Faxai; that is, SST is hard to cool in the case of the ocean before Hagibis passes. In short, it is important for ocean cooling not only ocean conditions but also typhoon characteristics because in fact, Hagibis cooled the ocean more than Faxai. In addition, the impact of Hagibis's characteristics on the typhoon-induced SST cooling was 4.8 times larger than the impact of Faxai's characteristics. Thus, SST was more likely to cool by typhoon characteristics in the case of Hagibis. Among Hagibis's characteristics, typhoon size had the greatest impact on ocean cooling. From the above, as indicated by the Co values, Hagibis cooled the ocean well due to the large impact of the typhoon, even though the ocean was less easily cooled than in the case of Faxai. The difference in ocean cooling between typhoons Faxai and Hagibis was clarified through the use of Co. Although typhoon-induced SST cooling is mainly related to ocean conditions, such as OHC and TCHP, or to ocean structures such as MLD. Typhoon characteristics are also important factors in the ocean cooling associated with typhoon passage and can be assessed using Co. Therefore, we suggest that Co is a practical indicator for estimating the magnitude of SST cooling caused by strong typhoon winds, and comparing factors of typhooninduced SST cooling in multiple cases even though it does not include the effects of ocean water advection. Future studies should apply Co to other cases to gain a better understanding of this parameter and clarify the domain within which the ocean is affected by typhoons.
In our future study, we will do a composite analysis of typhoon-induced SST cooling the dependence of typhoon characteristics and ocean conditions involved in physical processes including typhoons passed over the ocean around Japan region from April to October in 2019 to provide important findings to typhoon-ocean interactions.