Corresponding author: A. Wada, Meteorological Research Institute, Japan Meteorological Agency, 1-1 Nagamine, Tsukuba, Ibaraki 305-0052, Japan. (email@example.com)
 We investigated whether the maximum intensity of tropical cyclones (TC) in the North Pacific Ocean depends on sea surface temperature (SST) and tropical cyclone heat potential (TCHP). The study used reanalysis data sets for both the oceans and atmosphere: daily, 10-day, and monthly oceanic data sets; six-hour and monthly atmospheric data sets; and a daily satellite SST data set, for the July-to-October season from 2002 to 2005. For each TC, we summed TCHP from the time of genesis to the time of first reaching a minimum central pressure (MCP), to obtain an accumulated TCHP. In a linear regression analysis, the relationship between maximum TC intensity and accumulated TCHP differed between the eastern and western Pacific: high values of accumulated TCHP were needed before a TC attained a certain MCP in the western Pacific. In addition, the background convective available potential energy (CAPE) value was nearly four times larger in the western Pacific than in the eastern Pacific. The static stability was also 6.5% lower, the inertial stability 29.7% higher, and the size of tropical cyclones 38.2% larger in the western Pacific than in the eastern Pacific. The result indicated a deeper Rossby penetration depth and stronger TC in the western Pacific. Finally, we validated the TCHP values derived from three oceanic reanalysis data sets by using Argo profiling float observations. We found that use of only the daily data can reproduce the cooling effect of a passage of a TC, which caused a decrease in the TCHP values.
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 Accurate prediction of tropical cyclones (TC) is indispensable to mitigate the disastrous impacts of TCs. However, our current understanding of the mechanisms of TC intensification has not been sufficient to improve the predictions of TCs, particularly their intensity [Wang and Wu, 2004]. An essential condition for TC intensification is a high sea surface temperature (SST). Miller  and Holland  concluded that the SST and the height of the convective equilibrium level controlled the maximum potential intensity (MPI) of a TC. Emanuel  assumed that a TC can be regarded as an open cycle, irreversible heat engine [Bister and Emanuel, 2002] and proposed a different theory for MPI than that of Miller and Holland (but it too was governed by SST). Some authors derived MPI from empirical formulas that depended on SST [DeMaria and Kaplan, 1994; Whitney and Hobgood, 1997], although SST alone was inadequate to predict TC intensity [Evans, 1993]. Kossin and Camargo  considered MPI calculated along cyclone tracks in the context of secular hurricane trends and concluded that there was no tacit expectation that hurricanes became stronger based solely on MPI theory.
 Recent studies reported that not only SST but also vertical profiles of water temperature and salinity in the ocean affected TC intensity and intensification. TCs tend to intensify when they pass over the western Pacific warm pool [Wang and Zhou, 2008; Wada and Chan, 2008], the southern eddy zone in the western North Pacific [Lin et al., 2005; Wada and Usui, 2007], and warm-core eddies in the North Atlantic [Shay, 2009]. Gray  emphasized the need for warm oceans to a depth to provide the necessary heat to support the hurricane against its tendency to cool the ocean by upwelling and turbulent mixing. We previously applied the concept of tropical cyclone heat potential (TCHP) [Leipper and Volgenau, 1972] to investigate the relationship between TC intensity and upper ocean heat content [Wada and Usui, 2007; Wada, 2009; Wada and Usui, 2010]. TCHP is a measure of the ocean heat content from the surface down to the depth of the 26°C isotherm (hereafter, Z26). According to Wada and Usui , TCHP was highly correlated with the central pressure of Typhoons Chaba and Songda in 2004 at their decaying phase. Wada  argued that mesovortices and merger of vortices play a crucial role in intensifying TCs, and that TCs intensify less once an annular ring of potential vorticity completely forms in their mature phase. Holland  and Simpson et al.  noted the importance of mesovortices in the early stages of TC development, too. In addition, Holland  pointed out the importance of the structure of the western Atlantic atmospheric flow in enhancing wave accumulation and vortex merger.
Rozoff et al.  reported that an initial vortex breaks down into discrete mesovortices earlier in the life of a TC when the growth rate is small. They also reported that the mesovortices continue to intensify after they are formed. The number of mesovortices diminishes as discrete mesovortices merge and the vorticity is vigorously mixed within a vortex [Wada, 2009]. Finally a single vortex temporarily forms. During intensification, the vortex causes sea surface cooling, which delays the merger of discrete mesovortices [Wada, 2009] by damping the eddy flux of relative angular momentum in the low- to mid-troposphere.
 While the mesovortices are merging, increasing sea-to-air fluxes of sensible and latent heat trigger moist convection around the mesovortices. Diabatic heating by condensation in moist convection is an important way to develop a warm core in the upper troposphere at the center of a vortex, and it strengthens the secondary circulation in the radial-vertical plane. At the same time that a vortex intensifies, the SST underneath a vortex decreases due to strong wind stress curl [Price, 1981]. The amount of a decrease in SST is affected by the thermal structure in the ocean as well as by the intensity of a vortex and its translation speed [Price, 1981; Wada, 2002]. These processes of vortex's intensification and sea surface cooling lead to the idea that continuous sea-to-air fluxes of sensible and latent heat, including the variations in the upper-ocean heat content, are indirectly related to the positive air temperature anomaly at the center of a vortex, namely warm-core anomaly of a TC. Therefore, we propose that the warm core anomaly is related to the summation of the upper-ocean heat content (hereafter, theaccumulated TCHP or ATCHP). The correlation between TC intensity and ATCHP has not been investigated so far for the eastern Pacific or other areas. This raises the question as to whether ATCHP uniquely predicts the maximum intensity of a TC, for all areas of the world ocean, as the MPI theory of Miller  and Holland  does.
 The ATCHP is calculated from the TCHP existing just beneath a TC before the TC attains the maximum intensity, and from the duration of the TC. Not only does passage of a TC change the TCHP value, but TCHP also varies on seasonal to interannual time scales in the North Pacific [Wada and Chan, 2008]. In particular, the El Niño-Southern Oscillation (ENSO) is closely related to TC activity in both the eastern Pacific [Gray and Sheaffer, 1991; Frank and Young, 2007] and western Pacific [Wang and Chan, 2002; Camargo and Sobel, 2005]. For example, specific track types related to ENSO [Camargo et al., 2007] and a southeastward shift of the TC genesis region [Chia and Ropelewski, 2002] cause longer duration of a TC, and thus a larger ATCHP value [Wada and Chan, 2008]. Not only the long duration of a TC but also a deeper pool of warm water (as measured by a larger value of Z26) increase a ATCHP value along the track of a TC. Even the seasonal to interannual variations in Z26 may possibly affect TC activity [Wada and Chan, 2008].
 The purpose of this study is to clarify the relationships of SST and TCHP to the maximum intensity of TCs in the North Pacific. We used daily, 10-day, and monthly oceanic reanalysis data sets, monthly and six-hour atmospheric reanalysis data sets, and a daily, microwave-based, satellite SST data set; the study period was from July to October in the four years 2002 to 2005. We also investigate atmospheric influences on these relationships. For example,Merrill reported that certain upper-tropospheric flows are associated with intensifying or non-intensifying TCs.Chan  reported that dynamic factors like vertical shear are much more important than thermodynamic ones for explaining variations of intensity of TCs on climatic time scales. Considering the dynamic factors, DeMaria  studied how vertical shear affects TC intensity change, and suggested that the Rossby penetration depth influences the effectiveness of an adiabatic process that acted to reduce the vertical tilt of the vortex. The Rossby penetration depth depends on the horizontal scale of the vortex, the inertial stability, and the static stability. Thus, many consider that atmospheric and oceanic environments affect TCs in important ways. However, the relationships between atmospheric and oceanic thermal environments and maximum TC intensities and rates of intensification have not been clarified so far.
 The TCHP data are calculated by a numerical modeling system [Shay et al., 2000; Wada and Usui, 2007]. The model enables us to produce various oceanic reanalysis data sets with various space and time resolutions (Table 1). Therefore, the quality of these oceanic reanalysis data sets should be checked using in situ observations from two viewpoints: the relationship between ATCHP and maximum TC intensity, and the ocean's response to a TC (although our oceanic assimilation system actually assimilated the in situ observations). This study provides evidence that the oceanic reanalysis data help to unravel the interactions between TCs and the ocean.
Table 1. Ocean Reanalysis Data Sets Used in the Present Study
 This paper consists of five sections. Section 2 documents the data and methodology of this study. Section 3 presents the results on the relationship of maximum TC intensity to ATCHP and to atmospheric environments in both the eastern and western Pacific, and validates oceanic reanalysis data sets used in this study against in situ observations. A discussion of some results follows in section 4. Section 5 presents the conclusions with some remarks.
2. Data and Methodology
 The period of investigation was the four-month season from July to October in four years from 2002 to 2005. The domain was the North Pacific Ocean wherever the depth exceeds 200 m. A dividing line between the eastern and western Pacific is 180° of longitude (Figure 1).
2.1. TC Best Track Data
 We used the International Best track Archive for Climate Stewardship (IBtRACS) data set [Knapp et al., 2010]. TC intensity is defined by both the maximum wind speed (MWS) and MCP, which are based on the World Meteorological Organization's (WMO) official definition of intensity. The WMO standard for estimating the mean wind uses a 10 min average. Therefore, the average duration of the MWS is 10 min in both the eastern and western Pacific.
 During the investigation period, there were 67 TCs in the western North Pacific, and 47 in the eastern North Pacific (Table 2). The positions where TCs attain their MCP are widely distributed in the western Pacific; a few TCs attain their MCP even north of 30°N (Figure 1a). In the North Pacific, the number of TCs is largest in August and smallest in October (Figure 1b). The seasonal variation of TC frequency in the eastern Pacific is similar to that in the western Pacific. However, the positions where TCs attain their MCP are concentrated in a narrower area in the eastern Pacific (Figure 1a).
Table 2. Numbers of TCs in the Sample, and Mean Values and Standard Deviations of Four Quantities: Their Duration, Their Maximum Wind Speed (MWS), Their Minimum Central Pressure (MCP), and the Radius Where the Mean Wind Speed was 34 kt
Number of TC
MWS (m s−1)
Radius of 34 kt Wind Speed (km)
2.0 ± 1.4
61.9 ± 29.2
980.2 ± 25.5
191.5 ± 109.9
3.5 ± 2.2
70.2 ± 27.5
959.5 ± 28.4
255.4 ± 96.2
2.2. Argo Floats
 The Argo project is an international effort to collect high-quality temperature and salinity profiles in the upper ocean, to a depth of 2000 m. The data come from battery-powered autonomous floats that mostly drift at constant depth, where they are stabilized at a constant pressure level by being less compressible than seawater. Typically, at 10 day intervals, the floats pump fluid into an external bladder and rise to the surface over about 6 h while measuring temperature and salinity. On surfacing, satellites read the position of the floats, and receive the transmitted data [Gould et al., 2004].
 The Argo profiling float data archived in the World Ocean Database 2009 (WOD09) (obtained from http://www.nodc.noaa.gov/OC5/WOD09/pr_wod09.html) were used in this study. Only data having a quality flag labeled with QC = 1 were used for calculating TCHP and Z26. Argo data were selected if the Argo float was positioned within a 1.5° square box collocated with the TC center at the time of passage, and data were used from two days before passage of a TC to three days after passage. In order to analyze the variation in TCHP during passage of a TC, this period was further divided into three TC sub-periods: “Pre-TC” was from two days before passage of a TC until the day of the passage, “Passing-TC” included the day of passage of a TC, and “Post-TC” was from one day after passage of a TC to three days after passage. The ocean's response to a TC differs in these three periods. Passage of a TC hardly affects the upper ocean in the Pre-TC period. In the Passing-TC period, vertical turbulent mixing dominates beneath a TC, while Ekman upwelling and inertial pumping induced by nearly inertial currents occur in the Post-TC period [Price, 1981]. When a TC moves slowly, Ekman pumping is dominant beneath a TC, while inertial pumping occurs when the translation speed of a TC exceeds 3 m s−1 [Wada et al., 2009a].
 Water temperature and salinity profiles obtained from Argo profiling floats were extrapolated from the subsurface (a depth of nearly 5 m) to a depth of 200 m by using the method of Akima . Because there is no surface observation by Argo profiling floats, temperature and salinity from the surface to a depth of 5 m were assumed to be the same as at 5 m depth.
2.3. Satellite Sea-Surface Temperature
 We use a daily Microwave, Optimally Interpolated (OI) sea-surface temperature (SST) data set (MW OI SST) from 2002 to 2005 to investigate the relationship between maximum TC intensity and accumulated sea-surface heat content (ASSHC). Here ASSHC is the analog to ATCHP and is calculated by integration of the ocean heat content at the sea surface at six-hour intervals from the genesis time of a TC to the time it first reaches MCP. The MW OI SST (obtained from the site:http://www.ssmi.com/) includes two satellite SST data sets derived from two instruments: the Tropical Rainfall Measuring Mission (TRMM)/TRMM Microwave Imager (TMI), and the Aqua/Advanced Microwave Scanning Radiometer for Earth observing system (AMSR-E) satellite radiometers. The MW OI SST data set covers the global ocean with a horizontal resolution of 0.25°. It should be noted thatWada and Usui used accumulated SST instead of ASSHC. However, accumulated SST is a rather non-physical quantity, while ASSHC may be analog to heating degree days. Therefore, we use ASSHC instead of accumulated SST in this study.
2.4. Oceanic Reanalysis Data
 The three oceanic reanalysis data sets used in this study were calculated by the Meteorological Research Institute multivariate ocean variational estimation (MOVE) system [Usui et al., 2006]. The data sets are as follows: the ‘Global’ data set is a monthly mean oceanic reanalysis data set, the ‘Pacific10’ a 10-day mean data set, and the ‘Pacific1’ a daily mean data set.Table 1 specifies each data set. The SST observation provided to the MOVE system was obtained from the gridded Centennial in situ Observation Based Estimates of variability of SST (COBESST) and marine meteorological variables SST data set [Ishii et al., 2005], for producing the Global data set, and from the Merged satellite and in situ data Global Daily Sea Surface Temperatures in the global ocean (MGDSST) data set [Kurihara et al., 2006], for producing the Pacific10 and Pacific1 data sets. The along-track satellite sea-surface height data are assimilated in Pacific10 and Pacific1 in the MOVE system [Usui et al., 2006]. Water temperature and salinity profiles were interpolated from the uppermost layer to a depth of 200 m at 1 m intervals from oceanic reanalysis data according to the method of Akima . The interpolation method was the same as that in section 2.2. In order to validate the data sets using Argo profiling float data, we extracted vertical temperature and salinity profiles from the three data sets at the times and locations of each Argo profiling float.
2.5. Atmospheric Reanalysis Data
 This study used three atmospheric reanalysis data sets in producing the three oceanic reanalysis data sets (Table 1), respectively: the National Center for Environmental Prediction - National Center for Atmospheric Research (NCEP-NCAR) reanalysis I (NCEP R-1) [Kalnay et al., 1996] for producing the Global data set; NCEP and the Department of Energy Atmospheric Intercomparison Project reanalysis (NCEP R-2) [Kanamitsu et al., 2002] for producing the Pacific1 data set; and the Japanese 25-year Reanalysis (JRA-25) [Onogi et al., 2007] and a subsequent reanalysis data set since 2005 (conventionally known as JCDAS) for producing the Pacific10 data set. In addition, we used monthly (at both 40 height levels and 23 pressure levels in the vertical) and six-hour (at 23 pressure levels) JRA-25 and JCDAS data for investigating atmospheric influences on the maximum intensity of TCs. Hereafter, JRA-25 and JCDAS are referred to simply as JRA-25. We used horizontal winds for calculating a vertical shear (Vs), and air temperature (Ta), specific humidity (qv) and geopotential height (z) for calculating saturation moist static energy (S), static stability (N), and convective available potential energy (CAPE), as explained in the next section.
2.6. Atmospheric and Oceanic Factors
 The following are the atmospheric dynamical and thermodynamical factors calculated with the six-hour and monthly JRA-25 reanalysis data sets. Vertical shear is first defined as
where Vi is the horizontal wind speed vector at the i-th level andzi the geopotential height at the i-th level.Equation (1)indicates that vertical shear is an absolute value of the difference of wind speed vector from a certain level to the reference level (close to the level of the 850 hPa surface: which is the third pressure level in the six-hour and monthly JRA-25 data sets, and the seventh height level in the monthly JRA-25 data set), per unit meter of the height difference.
 Saturation moist static energy is defined as
where cp is the specific heat at constant pressure, Ta the air temperature, g the gravitational acceleration, Lv the constant for latent heat of vaporization of water, and qv the specific humidity of saturated air at temperature Ta.
 Static stability (N) is calculated by
where θ is the potential temperature, and is the average of θ within a square box of 6.25°centered at the grid point in this study.
 Convective available potential energy (CAPE) is calculated by
where p0 is the atmospheric sea level pressure, pLNB the atmospheric pressure at the level of neutral buoyancy, and αp0 the specific volume at sea level. Now αe is the specific volume of the atmospheric environment at pressure pand is derived from the average within a square box of 6.25°collocated at the grid point corresponding to the TC center. CAPE calculated using monthly JRA-25 data values is called the background CAPE in this study. Background CAPE is regarded as environmental CAPE, whereas CAPE calculated from six-hourly JRA-25 data includes CAPE caused by the TC itself. It should be noted that CAPE calculated in this way differs from the model CAPE ofPersing and Montgomery . According to them, environmental CAPE appears nowhere in Emanuel's MPI formulation [Emanuel, 1995; Bister and Emanuel, 2002], while it is a factor in Miller's MPI model [Miller, 1958], and to a lesser extent, in Holland's MPI model [Holland, 1997], because of the complete calculation of the surface pressure deviation [Persing and Montgomery, 2005]. Strictly speaking, background CAPE is different from environmental CAPE in that environmental CAPE explicitly excludes moisture added to the air by the TC.
 Inertial stability is approximately defined as
where f is the Coriolis parameter. This definition does not include the effect of the cyclonic circulation always present in a TC.
 According to DeMaria , the Rossby penetration depth (D) in the atmosphere as described in the introduction is
where LR is the horizontal scale of a TC. In this study, a mean radius of 34 kt wind speed is used as LR.
where Q is TCHP (J cm−2), Ti water temperature in °C at the i-th level, Δzi a layer thickness of water at the i-th layer, andρi density of water at the i-th level. ATCHP is defined as the integration of TCHP from the genesis of the tropical cyclone to the time of first reaching MCP [Wada and Usui, 2007]:
where Tg is the genesis time. Now T is the time that a TC first reaches MCP. ASSHC is calculated using the following formula:
where QASSHC is ASSHC (J cm−2), Ts satellite SST in °C and ρsdensity of sea-surface water for satellite SST. The unit of both ATCHP and ASSHC is denoted precisely as J cm−2 day.
 We investigated the number of TCs in our sample, their duration, peak wind speed MWS, MCP, and mean radius of 34 kt wind speed (see section 2.1) in the eastern and western Pacific (sample means and variations in Table 2). The sample mean values of MWS and MCP in the western Pacific (70.2 m s−1 and 959.5 hPa) indicated that TCs in the western Pacific were stronger than those in the eastern Pacific (61.9 m s−1 and 980.2 hPa) at least in those four years. There was a significant difference in mean MCP (20 hPa) and mean duration (1.5 days) between the eastern and western Pacific at the 99.9% significance level (based on the t-test), although the mean MWS was not significantly different. TCs in the western Pacific were also larger (300 km) than those in the eastern Pacific (200 km). The difference in the radius was significant at the 99% significant level, based on thet-test. There was greater uncertainty in the values of MWS and mean radius of 34 kt wind speed in the eastern Pacific than in the western Pacific.
3.1. Relationship of ATCHP to Maximum TC Intensity
 Previous studies [Lin et al., 2008, 2009; Wada and Usui, 2007, 2010; Wada, 2010] reported that TCHP is closely related to the intensity of a TC and its intensification. Because of the scientific interests described in the introduction, this study investigated the relationships of ASSHC and ATCHP to maximum TC intensity using the satellite SST data set and the three oceanic reanalysis data sets (Table 1), respectively. Hereafter, we use the parameters below, which were determined uniquely for each TC.
 1. Attainable TC intensity is defined as the sea level pressure and surface wind speed (at a height of 10 m) when a TC first attains its MCP and MWS, when data are recorded every six hours along the best track.
 2. The duration is defined as the period from the genesis to the time of first reaching MCP of a TC, and is determined from the best-track data recorded every six hours. The phases of tropical depression and extratropical cyclone (even in the process of TC intensification) are not included in this definition of duration.
 3. ATCHP and ASSHC are defined as the accumulation of six-hourly TCHP and sea-surface heat content, respectively, averaged within a 1.5° square box centered at the current TC center.
 First, we investigated the relationship between MCP and ASSHC in the eastern and western North Pacific. This correlation was significant at the 99.9% level, based on the t-test. MCP decreased as ASSHC increased (Figure 2a); the slope of the linear regression was −0.37 hPa/kJ cm−2 day in the eastern Pacific, and −0.27 hPa/kJ cm−2 day in the western Pacific. The slope was steeper in the eastern Pacific. However, the difference of MCP was only 4.5 hPa per 45 kJ cm−2 day of ASSHC, which occurs when a TC passes over warm waters with a SST of approximately 30°C over 1.5 days (six measurement times). Considering the difference in durations between the eastern (2 days) and western Pacific (3.5 days) (Table 2), there was little difference in the MCP-ASSHC relationship between the eastern and western Pacific.
 Next, we investigated the relationships between ATCHP and MCP, all calculated from the Global, Pacific10, and Pacific1 data sets (Table 1). The correlations denoted in Figures 2b–2d were significant at the 99.9% level, based on the t-test. Unlike the relationship between MCP and ASST, the slopes of the regression lines clearly differed between the eastern Pacific (−0.07 hPa/kJ cm−2 day) and western Pacific (−0.02 hPa/kJ cm−2 day) (Figures 2b–2d). The result implies that the relationship of ATCHP to MCP does not depend on the spatial resolution (whether 0.5° or 1.0°) or the temporal resolution (whether day or month) of an oceanic reanalysis data set. It even suggests that we can estimate the MPI, derived from ATCHP, to some extent by using just monthly mean oceanic data having a horizontal resolution of only 1°.
 The relationships between MWS and ASSHC or ATCHP (Figure 3) possessed the same characteristics as those between MCP and ASSHC or ATCHP (Figure 2). The regression lines for ASSHC had slopes of +0.45 m s−1/kJ cm−2 day in the eastern Pacific and +0.26 m s−1/kJ cm−2 day in the western Pacific, while the lines for ATCHP were +0.08 to 0.09 m s−1/kJ cm−2 day in the eastern Pacific and +0.02 m s−1/kJ cm−2 day in the western Pacific. The above results suggest that there is a direct relationship between MWS and MCP. However, this relationship clearly differed (Figure 4) between the eastern and western Pacific. The distinct curves on Figure 4 indicate that for a given peak wind speed (100 m s−1, say), the minimum pressure tended to be deeper in the western Pacific than in the eastern Pacific. The ocean environment may influence the maximum TC intensity differently in these two areas.
3.2. Atmospheric Environments
 The above results suggest that TCs in the western Pacific need much more ATCHP to attain their MCP than those in the eastern Pacific do, although TCs are more intense in the western Pacific than in the eastern Pacific (Table 2). The western Pacific may be regarded as a “thermodynamically low efficiency” region for attaining maximum TC intensity. When we used ASSHC to measure oceanic energy, we never obtained this low efficiency (Figures 2a and 3a). So a difference in Z26 between the eastern and western Pacific may explain the low efficiency, in addition to the difference in duration. Now, we recall that atmospheric dynamic factors are responsible for intense TCs [Chan, 2009]. Holland and Merrill reported that the maximum TC intensity depends on interactions with the environment, and that some properties of the atmospheric or oceanic environment are necessary conditions, while others are merely sufficient conditions for intensifying the storm. Conditions in the oceanic environment, including SST (or sea-surface heat content), TCHP, and Z26, are considered to be necessary conditions for TC genesis [Gray, 1979]. Atmospheric environmental influences such as wind shear, inertial stability, and static stability are considered to be sufficient conditions not only for genesis of a TC but also for reaching maximum intensity. A critical issue that needs to be addressed is the relationship of ATCHP to these atmospheric sufficient conditions in the North Pacific, and the relationship of ATCHP and the atmospheric environments to maximum TC intensity.
 We investigated mean profiles of environmental vertical shear, saturation moist static energy, and static stability in the eastern and western Pacific (Figure 5), using monthly JRA-25 atmospheric reanalysis data [Onogi et al., 2007] with 40 vertical height levels. The analysis only performed when a TC first attained a MCP. We have linked these profiles with values of background CAPE.
 Mean vertical shear in the western Pacific was small below the height of the 850-hPa surface in the lower troposphere (Figure 5a, left). However, it grew large in the middle-to-upper troposphere. In the profiles of saturation moist static energy (Figure 5b), this energy was higher in the western Pacific than in the eastern Pacific, below a height of 4000 m. In the eastern Pacific, static stability was high near a height of 1500 m, corresponding to the 850-hPa surface (Figure 5c); and it was higher than in the western Pacific. In the eastern Pacific, the value of mean inertial stability was 4.8 × 10−5 (s−1), smaller than in the western Pacific (6.3 × 10−5 s−1). Such a difference is reasonable, given the distribution of TC tracks (Figure 1).
 Mean background CAPE (and its standard deviation) was 130.3 ± 165.8 J kg−1 in the western Pacific and 35.4 ± 120.4 J kg−1in the eastern Pacific; these were calculated from a monthly JRA-25 data set with 40 height levels. Even though the standard deviations are very high relative to the mean values, the mean values themselves are significant at the 99% level, based on thet-test. When a monthly JRA-25 data set with 23 pressure levels in the vertical was used, mean background CAPE was reduced to 82.0 ± 113.2 J kg−1 in the western Pacific, and 8.7 ± 14.0 J kg−1in the eastern Pacific. This result suggests that background CAPE was usually high in the western Pacific even though the value depends on the vertical coordinate system and the number of vertical levels of an atmospheric reanalysis data set. Mean CAPE derived from a six-hourly data set was 155.9 ± 194.3 J kg−1 in the western Pacific and 62.8 ± 73.3 J kg−1in the eastern Pacific. Since CAPE derived from this six-hourly data set explicitly included data from a TC, we can roughly estimate the CAPE due to the TC by finding the difference in mean CAPE between the monthly and six-hourly data sets (with 23 pressure levels). The difference was 73.9 J kg−1 in the western Pacific, and 54.1 J kg−1 in the eastern Pacific. These are reasonable values for the TC intensities shown in Table 2. If our assumptions are correct, calculating the difference in CAPE should eliminate the mean environmental CAPE, and leave a residual CAPE that is caused by the TC itself. This is analogous to Emanuel's MPI theory.
 Air parcels leaving a region of constant forcing are physically able to move horizontally or vertically in an axisymmetric coordinate system, depending on their inertial and static stabilities [Holland and Merrill, 1984]. In the western Pacific, high inertial stability plays a role in restricting the inward extent of the secondary circulation of a TC, according to these authors. They reported that the inward extent of the secondary circulation response would also be further limited if moist processes were included in a conditionally unstable atmosphere. In contrast, low inertial stability leads to a longer horizontal circulation and high positive static stability resists vertical motion. Large vertical shear is not considered favorable for intensification of TCs, according to Merrill . However, there is a different perspective, that intense TCs tend to be less sensitive to vertical shear [DeMaria, 1996]. This study agrees to the fact that mean TC intensity was strong in the western Pacific where vertical shear was relatively large in the mid-to-upper troposphere. Here, we investigate the effect of static and inertial stabilities on TCs, using the Rossby penetration depth as described insection 2.6, in order to obtain an indirect indication of the depth of Ekman pumping.
 The atmospheric penetration depth D in equation (6) is much deeper in the western Pacific (where it is 81.2 m) than in the eastern Pacific (where it is 40.3 m), because I and LR (Table 2) are much larger in the western than the eastern Pacific. In fact, I was 29.7% larger and LR 38.2% larger in the western Pacific. In addition, at a height of 1500 m, N was 6.5% lower in the western Pacific than the eastern Pacific (Figure 5c). As a result, the western Pacific Ocean tends to experience deep atmospheric Ekman pumping, which enhances adiabatic processes and thus creates stronger TCs. High ATCHP and background CAPE in the western Pacific are important in sustaining the deep penetration depth through low static stability in the lower troposphere, which is irrelevant to the Emanuel's MPI theory. In other words, the “thermodynamically low efficiency” of the western Pacific region derives in part from the low static stability in the lower troposphere, which results from the high ATCHP and background CAPE in this region. In the western Pacific, it is easy for a TC to intensify, owing to the low static stability in the lower troposphere and high inertial stability, which restrict the inward extent. In the eastern Pacific, however, it is hard for a TC to intensify because of the region's low inertial stability, which results in small inward transport of angular momentum, and also because of relatively high static stability in the lower troposphere, which suppresses vertical motion.
 Therefore, the thermodynamically low efficiency for maximum TC intensity is not directly related to CAPE produced by an individual TC itself, but can be attributed to the sustenance of high background CAPE and its influence on maximum TC intensity through low static stability in the western Pacific. A small effect of background CAPE on maximum TC intensity is consistent with studies of Camp and Montgomery  and Persing and Montgomery , who showed that the effect of environmental CAPE may be discarded in deriving MPI. However, our study indicates that background CAPE can affect maximum TC intensity even though its effect is smaller than that of inertial stability (I), and that of the size of a tropical cyclone (given by LR).
3.3. Validation of TCHP and Z26
 As described in previous sections, atmospheric and oceanic environments clearly differ between the eastern and western Pacific. High ATCHP is indirectly related to high background CAPE and low static stability in the lower troposphere, which together result in a deep Rossby penetration depth and thus strong TCs in the western Pacific. However, we have not yet checked the quality of ATCHP data derived from the oceanic reanalysis data sets. The MOVE system used in this study actually assimilates the Argo profiling float (hereafter Argo) data by the three-dimensional variational method. However, the impact of Argo data on the quality of the oceanic reanalysis data in the vicinity of a TC has never been investigated. It is important to evaluate the quality of ATCHP data in order to be sure that the difference between the eastern and western Pacific is real, in terms of the dependence of maximum TC intensity on ATCHP. This section validates the western Pacific TCHP and Z26 fields derived from three oceanic reanalysis data sets, against Argo data archived in WOD09. Because the number of Argo data points (71) in the eastern Pacific was much less than that the number (669) in the western Pacific,section 3.3.2 only covers validation in the western North Pacific. For validation of the vertical profiles of temperature and salinity in the Global, Pacific10, and Pacific1 data sets (Table 1); see auxiliary material.
3.3.1. Mean TCHP and Z26
 The mean TCHP and Z26 values with their standard deviations were calculated using Argo data and the three oceanic reanalysis data sets from the eastern Pacific, from 2 days before the passage of a TC to 3 days after the passage (Table 3). Mean values of TCHP ranged from 42.0 to 49.0 kJ cm−2, and mean Z26 from 33.8 to 38.7 m. Considering that the vertical resolution of oceanic reanalysis data sets as described in section 2.4 is poor, the error of nearly 5 m in Z26 is acceptable.
Table 3. Mean Tropical Cyclone Heat Potential (TCHP) and the Depth of 26°C Isotherm (Z26) in the Study Period in the Eastern Pacific
TCHP (kJ cm−2)
46.4 ± 34.6
38.9 ± 15.3
49.0 ± 27.6
37.2 ± 15.0
42.0 ± 22.6
35.7 ± 9.9
45.5 ± 29.7
33.8 ± 11.6
 In the western Pacific, mean TCHP values ranged from 149.1 to 169.1 kJ cm−2, and Z26 from 70.8 to 78.6 m (Table 4). The error of 7.7 m in Z26 was greater than it was in the eastern Pacific. On the whole, the three oceanic reanalysis data sets reproduced reasonably vertical profiles of water temperature and salinity observed by Argo (see auxiliary material), as well as mean TCHP and Z26 derived from Argo data. Thus, the relation of ATCHP to maximum TC intensity, and the difference in this relation between the eastern and western Pacific are robust. Because the dependence of maximum TC intensity on ATCHP is independent of the space and time resolutions of the oceanic reanalysis data sets, the result implies that climatological Z26 has a crucial role in the relationship between maximum TC intensity and ATCHP.
Table 4. Same as Table 3 Except in the Western Pacific
TCHP (kJ cm−2)
159.3 ± 91.7
77.4 ± 32.4
169.1 ± 89.1
78.6 ± 27.6
149.1 ± 81.3
70.8 ± 29.0
157.8 ± 85.2
73.6 ± 31.9
3.3.2. The Variations in TCHP by Passage of a TC
 In this section, we statistically examine the oceanic response to passage of a TC using Argo data by putting the data into three TC periods (Table 5): “Pre-TC,” “Passing-TC,” and “Post-TC” as defined insection 2.2. There were 247 samples in Pre-TC, 98 in Passing-TC, and 324 in Post-TC.
Table 5. Same as Table 3Except That Means and Standard Deviations are Calculated Only Within the Three Periods (Pre-TC, Passing-TC, and Post-TC) Defined inSection 2.2a
TCHP (kJ cm−2)
Pre-TC (n = 247)
Passing-TC (n = 98)
Post-TC (n = 324)
Pre-TC (n = 247)
Passing-TC (n = 98)
Post-TC (n = 324)
Here n indicates the number of Argo data samples.
152.9 ± 96.3
167.3 ± 107.1
143.2 ± 82.0
71.8 ± 33.8
82.2 ± 36.3
80.2 ± 29.4
159.6 ± 96.6
167.5 ± 95.1
176.8 ± 77.7
74.4 ± 29.5
78.0 ± 30.2
81.9 ± 24.5
138.0 ± 84.9
141.5 ± 102.2
157.2 ± 74.0
66.6 ± 29.1
70.5 ± 31.2
74.1 ± 27.7
155.1 ± 90.8
164.3 ± 103.3
157.1 ± 74.2
71.0 ± 33.7
76.0 ± 35.3
74.7 ± 29.3
 First, we investigated the differences in mean TCHP and Z26 values between Pre-TC, Passing-TC, and Post-TC periods calculated for the Argo data and for the three oceanic reanalysis data sets (Table 5). The greatest range of Z26 was 12.5 m in Passing-TC, which is not a negligible value when one considers the vertical resolution in the Global data set (section 2.4). TCHP and Z26 values increased in the Post-TC phase in the Global and Pacific10 data sets, but decreased in the Argo and Pacific1 data sets. This result suggests that the Global and Pacific10 data sets do not reproduce the decreases in TCHP and Z26 in the Post-PC period, seen in the Argo data.
 Next we explore mean TCHP and Z26 values in the Passing-TC period in the western Pacific because their variations differed in different locations relative to the TC center. There were only a few Argo data when the forward speed of a TC was less than 3 m s−1. Mean TCHP and Z26 in the Passing-TC period were further categorized into four sets based on the relative direction from the TC center to the position of the Argo data, as inFigure 6. Ahead of a TC, the TCHP and Z26 values in the Global, Pacific10, and Pacific1 data sets agreed well with values from Argo. Behind a TC, however, TCHP and Z26 were markedly underestimated in Pacific10. Z26 was deepest in Argo among the four data sets, particularly in the right rear quadrant of a TC. In contrast, TCHP in Global had the highest values among the four data sets, except in the right rear quadrant of a TC where vertical turbulent mixing dominates. Poor reproduction of TC-induced sea surface cooling in the oceanic reanalysis data sets may be related to the high TCHP values in the right rear portion of a TC. The effects of vertical turbulent mixing and upwelling became small in Global due to poor time resolution. It is not easy to find the reason why TCHP and Z26 values were relatively small in Pacific10. Nevertheless, the Pacific1 data reproduced the TCHP and Z26 values derived from Argo observations well in the Passing-TC period. Time resolution is important for reproducing the variations in TCHP and Z26 as a TC passes by.
4.1. Effect of Profiling Float Data on Oceanic Reanalysis Data
 Our results confirm that the three oceanic reanalysis data sets used in this study can be used to investigate the relationship of ATCHP to the maximum TC intensity. However, our validation of these data sets suggests that time resolution is important for reproducing the ocean's response to a TC. The validation might be affected by the small number of Argo data points as well as by the specifications of the MOVE assimilation system (Table 1). Without Argo observations in the vicinity of TCs, the quality of these reanalysis data sets would never be reliable there: we doubt the quality of the oceanic reanalysis data sets where there are no in situ observations. In fact, however, the quality of an oceanic reanalysis data set is mostly determined from satellite altimeter data obtained once every week [Wada et al., 2008] so that its quality is guaranteed to some extent by assimilating the satellite-altimeter data.
 According to Wada et al. , who performed a 39 h numerical simulation of Typhoon Namtheun in 2004, sea surface cooling induced by the TC affected the intensity of the TC more than any other differences in preexisting oceanic conditions did (with or without satellite altimeter data). This numerical study concluded that Argo data had a small impact on TC intensity prediction, and that the oceanic reanalysis data set had a large impact, although Argo data observations were much fewer than satellite altimeter data points.
 Although Argo data did exhibit different oceanic responses to Typhoon Hai-Tang in 2005 in different locations relative to its track [Wada et al., 2009b], Argo is usually operated every 10 days, as described in section 2.2. Seven-day to ten-day observations are not sufficient to capture the time variation of the oceanic response to a TC. In order to improve the oceanic response to a TC in the reanalysis data sets, in situ observations in the vicinity of a TC are needed at least daily.
 We obtained 669 Argo data points in the western Pacific in this study. The number differed by year and season (Figure 7); the number was largest in 2005. Therefore, TCHP and Z26 values, and vertical profiles of temperature and salinity, are influenced by the imbalances in the number of Argo data observations (Figure 7). When mean atmospheric environments are calculated as a function of the position of Argo data, the profiles may have a bias affected by a few TCs that have more Argo data, and thus may not represent the atmospheric environment that influences maximum intensity of TCs.
 At any locality, the ocean's response to a TC differs according to the translation speed of the TC and the position of the locality relative to the track (section 3.3.2). In Figure 6, the difference in position relative to the TC center was responsible for the error in TCHP (Table 3) and in Z26 (Table 4). Figure 6indicates that the error in TCHP and Z26 occurred within a TC because the mean radius of 34 kt wind speed (255.4 km) was larger than a 1.5° square box for collecting Argo data. The oceanic mixed-layer deepened remarkably because of vertical turbulent mixing on the right side of the track when the translation speed of a TC was higher than 3 m s−1, but this deepening was weak on the left side of the track [Wada et al., 2009b]. Because the Argo data obtained in this study were concentrated in the right front quadrant of a TC, mean TCHP and Z26 values were mainly determined from that quadrant. This implies that the TCHP and Z26 errors were caused by the uncertainties in dynamics and thermodynamics of the oceanic response to a TC occurred in the right front quadrant, including the uncertainties in the vertical turbulent mixing scheme in the MOVE system, atmospheric wind-forcing and resultant shear instability within a mixed layer [Wada et al., 2009a].
 This uncertainty in the vertical turbulent mixing scheme is closely related to insufficient horizontal resolution of the atmospheric reanalysis data used in this study, and thus poor representation of surface wind-forcing. One of the important factors affecting the oceanic response to a TC is the strong surface wind-forcing that accompanies TCs [Wada et al., 2011]. Even though the horizontal resolution of the MOVE system became fine enough to reproduce the oceanic response to a TC, accurate surface wind-forcing is still needed to reproduce variations of water temperature, salinity, TCHP, and Z26 caused by passage of a TC. Therefore, changes in the MOVE system involving both the vertical turbulent mixing in the water and the atmospheric forcing are needed to realistically reproduce the ocean's response to a TC.
4.2. Effect of TCHP on the Atmosphere
 This study showed that the influence of ATCHP, a metric intended to represent the influence of the oceanic environment on the maximum intensity of TCs, differs between the eastern and western Pacific. Because maximum TC intensity is determined by its internal dynamics, the relationship of ATCHP to maximum TC intensity must be explained by the internal dynamics of a TC associated with TC-ocean interactions. The Rossby penetration depth (section 3.2) shows that the atmosphere over the western Pacific Ocean has high inertial and low static stability, which are favorable for a large Rossby penetration depth and thus strong TCs. This study also showed that high ATCHP and background CAPE are linked with low static stability in the lower troposphere. However, an unsolved issue remains: how do high ATCHP and background CAPE directly affect the static stability of the environment during the intensification of a TC? How does one determine the efficiency of the transformation from high ATCHP and background CAPE to low static stability in the lower troposphere? In order to clarify the influence of atmospheric and oceanic thermodynamic properties on the internal dynamics of TC-ocean interactions, numerical studies (with a sophisticated cloud-resolving atmosphere-wave-ocean model, for example) will be needed. These numerical studies are beyond the scope of this study.
 We can roughly estimate CAPE induced by a TC as 73.9 J kg−1 in the western Pacific and 54.1 J kg−1 in the eastern Pacific (section 3.2). We derived both values from the difference between CAPE calculated with six-hourly data at 23 vertical pressure levels, and that calculated with monthly data at the same pressure levels. There is a 37% difference of CAPE caused by a TC between the eastern and western Pacific, unlike the fourfold difference in background CAPE. A difference in CAPE produced by a TC between the eastern and western Pacific seems to be consistent with the difference in mean TC intensity (Table 2). However, these values and their standard deviations are very small when compared with the variation of mean CAPE in the eyewall (∼300 J kg−1), from area-mean soundings in the ring from 20 to 300 km in radius [Craig and Gray, 1996]. Later in this paper, we discuss the difference of background CAPE between the eastern and western Pacific, and particularly the high background CAPE in the western Pacific.
 Within the framework of MPI theory, Camp and Montgomery  suggested that environmental CAPE played a minor role in determining MPI. The MPI theories of Miller  and Holland , which require environmental CAPE, are inadequate for explaining CAPE modeled by Rotunno and Emanuel , while Emanuel's  theory provides insight on the controlling physics of MPI without reference to environmental CAPE [Camp and Montgomery, 2001; Persing and Montgomery, 2005]. The small regional difference in CAPE caused by a TC between the eastern and western Pacific supports the MPI theory of Emanuel in that CAPE due to a TC is calculated without regard to background or environmental CAPE. It should be noted that there are various criticisms of Emanuel's theory: Recent studies pointed out the importance of gradient wind imbalance [Smith et al., 2008] and the turbulence in the radial direction [Bryan and Rotunno, 2009] in the planetary boundary layer, which was not considered in Emanuel's  theory. However, this study does not discuss details of Emanuel's theory any longer.
 We have shown that the western North Pacific Ocean has high background CAPE where the TCHP is high and the Rossby penetration depth is deep. The Rossby depth is deep partly because static stability is low in the lower troposphere. Even though high inertial stability also contributes to high Rossby depth, low static stability in the region also plays another essential role in favoring strong TCs. Thermodynamic environmental feedbacks are important to the internal dynamics of a TC. Background CAPE can affect the Rossby penetration depth and thus maximum TC intensity.
 A difference between our conclusions and those of Camp and Montgomery  and Persing and Montgomery  may result from certain simplifications in the model of Rotunno and Emanuel , including no ice physics, a simple radiation treatment, an axisymmetrical model, and the setting of initial environmental conditions. We cannot discuss Emanuel's MPI theory using the results of this study because we do not have reliable reanalysis data of air-sea momentum and turbulent heat fluxes. If the characteristics of drag and enthalpy exchange coefficients climatologically differ between the eastern and western Pacific, they can affect not only the intensity but also the structure, and particularly the size, of TCs. We have no idea why TCs are larger in the western Pacific than in the eastern Pacific. This will be a subject for our future study.
 We do not address here the potential effects of oceanic variability on seasonal to interannual time scales (including ENSO) on background CAPE. Because other reliable oceanic reanalysis data and satellite SST data, beyond what is in Table 1, do not exist, it is beyond the scope of this study. According to Wada and Chan , mean ATCHP in the western North Pacific was estimated to be 2.3 MJ cm−2 day from 1961 to 2004, 3.0 MJ cm−2 day in an El Niño event, and 1.5 MJ cm−2 day in a La Niña event during the same period. Assuming that the oceanic reanalysis data used in Wada and Chan  were reliable, a difference of mean ATCHP between the El Niño and La Niña events caused by differences in duration and Z26 along the track of a TC was probably reflected in background CAPE: the relatively low background CAPE in the La Niña event was accompanied by less frequent convection, which is related to the high static stability in the lower troposphere. Even though TCHP in the western Pacific was relatively high even in the La Niña event, it did not trigger strong TCs. Seasonal and interannual variations in ocean properties may affect the atmosphere, even in neutral ENSO conditions, and these influences need to be studied.
4.3. SST and Sea-Surface Salinity
 A decrease in TCHP in Post-TC derived from Argo data is poorly reproduced by the three oceanic reanalysis data sets (Table 5) although the variability of TCHP went down in Post-TC. In contrast, the variability of Z26 is quite small in all data sets: Z26 seems to be quite stable. This means that poor reproduction of the decrease in TCHP is considered to be caused by an error of calculated water properties. This discussion focuses on the method for calculating SST and sea-surface salinity in the MOVE system. The three oceanic reanalysis data sets use daily COBESST as SST observations [Ishii et al., 2005] in the Global data set and daily MGDSST in the Pacific10 and Pacific1 data sets (section 2.4).
 MGDSST includes both in situ observations and satellite SST products from the Advanced Very High Resolution Radiometer (AVHRR) sensor on the NOAA-18, NOAA-19, and MetOp-A satellites, and the Advanced Microwave Scanning Radiometer for Earth observing system (AMSR-E) on the Aqua satellite. However, the frequency components that those satellite-based-SST data have are cut off by a Gaussian filter when they are shorter than 27 days. In addition, their quality control filter that is based on the standard deviation is so strict that true water temperatures in the vicinity of a TC are sometimes removed. In COBESST, only in situ observations are used, so that it is more difficult to capture the TC-induced sea surface cooling than in the MGDSST data. In order to reproduce a true decrease in TCHP and Z26 in the MOVE assimilation system, the COBESST and MGDSST data sets must be improved.
 The MOVE system reproduces reasonable salinity profiles in the ocean to some extent (see auxiliary material) and creates little difference in salinity between the three reanalysis data sets. However, the standard deviations in the Global data set (which has a time resolution of one month) are clearly smaller than those in Argo observations (not shown), as well as in the Pacific1 data set, in which the time resolution is one day. In fact, TCs cause heavy rainfall around the eyewall and spiral bands, but the MOVE system hardly captures the actual precipitation amounts nor their detailed horizontal distribution, because of coarse spatial and time resolution. If the quality of the precipitation amounts is improved in the atmospheric reanalysis data, then salinity profiles derived from the oceanic reanalysis data sets will be more reliable, and may help to improve the vertical turbulent mixing scheme in the MOVE system [Jacob and Koblinsky, 2007].
5. Concluding Remarks
 We investigated the dependence of the maximum intensity of TCs on sea surface temperature (SST) and tropical cyclone heat potential (TCHP) in the North Pacific Ocean. TCHP measures the heat content of the upper ocean from the uppermost level near the surface to the depth of the 26°C isotherm (Z26). We then computed accumulated TCHP (or ATCHP), calculated as the summation of TCHP every six hours from the genesis time of a TC to the time of first reaching minimum central pressure (MCP).
 In this study, ATCHP was highly correlated with both low values of MCP and high maximum wind speed in both the eastern and western Pacific with a correlation coefficient of 0.57–0.67, which is significant at the 99.9 level, based on the t-test. Linear regression analysis indicated that the dependence of peak TC intensity on ATCHP, and particularly the slope of the linear function, differed between the eastern and western Pacific. The western Pacific Ocean needed more ATCHP to attain a certain low MCP than the eastern Pacific Ocean did. Characteristic atmospheric environments in the western Pacific include strong vertical shear in the mid-to-upper troposphere, low static stability in the lower troposphere, high background convective available potential energy (CAPE), and high inertial stability, all derived from monthly atmospheric reanalysis data sets. High ATCHP in the western Pacific waters was linked with high background CAPE in the atmosphere, which was linked to low static stability in the lower troposphere, even though the transformation from high ATCHP and high background CAPE values to low static stability seems to be inefficient. High inertial stability, low static stability, and a larger TC in the atmosphere led to a deep Rossby penetration depth in the ocean, which was favorable for forming and intensifying strong TCs in the western Pacific. The low thermodynamic efficiency that we derived from the relationship between ATCHP and maximum TC intensity in the western Pacific probably indicates that high TCHP in the ocean accompanies or produces high values of background CAPE, because the portion of CAPE generated by the TC itself increased by a comparable amount in both the western Pacific and the eastern Pacific. Background CAPE can affect maximum TC intensity even though this effect was less than the influences of inertial stability and the size of the TC.
 We validated the TCHP and Z26 fields derived from oceanic reanalysis data sets, using the Argo profiling float observations. When the time resolution of the oceanic reanalysis data was only 10 days or a month, TCHP and Z26 values increased after the passage of TCs, but when the time resolution was daily, or actual Argo observations were used, then TCHP and Z26 values decreased (as expected). Only the daily oceanic reanalysis data reasonably reproduced the changes in TCHP and Z26 derived from the Argo observations during the passage of TCs. Our results suggest that daily oceanic reanalysis data are needed for reproducing the decrease in TCHP and Z26, associated with sea surface cooling caused by the intense surface wind curl of a TC.
 In situ observations have a strong impact on the oceanic reanalysis data and, indirectly, on TC intensity prediction. There is also a geographic imbalance in the number of in situ Argo profiling observations. The practice of relying on SST products as surface SST observations in the oceanic assimilation system needs to be questioned. More in situ observations and improvements in the oceanic reanalysis system, including vertical turbulent mixing schemes and effects of surface wind-forcing, should lead to better understanding of the relationship of maximum TC intensity to ATCHP in the world ocean. This will assist our understanding of future TC activity that may be associated with global warming.
 The authors are grateful to Greg Holland and two anonymous reviewers for comments that helped to improve the manuscript. This work was supported by the Japan Society for the Promotion of Science (JSPS) through the Grant-in-Aid for Scientific Research (C) (22540454) and by the Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) under the Grant-in-Aid for Scientific Research on Innovative Areas 2205 (in a proposed research area 23106505). The Generic Mapping Tools (http://gmt.soest.hawaii.edu/) was used to draw figures.