2012 Vol. 18, No. 2

RESEARCH PROGRESS ON THE STRUCTURE AND INTENSITY CHANGE FOR THE LANDFALLING TROPICAL CYCLONES
CHEN Lian-shou
2012, 18(2): 113-118. doi: 10.3969/j.issn.1006-8775.2012.02.001
Abstract(1742) PDF [504KB](1515)
Abstract:
Landfalling tropical cyclones (LTCs) include those TCs approaching the land and moving across the coast. Structure and intensity change for LTCs include change of the eye wall, spiral rain band, mesoscale vortices, low-layer shear lines and tornadoes in the envelope region of TC, pre-TC squall lines, remote rain bands, core region intensity and extratropical transition (ET) processes, etc. Structure and intensity change of TC are mainly affected by three aspects, namely, environmental effects, inner core dynamics and underlying surface forcing. Structure and intensity change of coastal TCs will be especially affected by seaboard topography, oceanic stratification above the continental shelf and cold dry continental airflow, etc. Rapid changes of TC intensity, including rapid intensification and sudden weakening and dissipation, are the small probability events which are in lack of effective forecasting techniques up to now. Diagnostic analysis and mechanism study will help improve the understanding and prediction of the rapid change phenomena in TCs.
INTENSITY CHANGE CHARACTERISTICS OF TROPICAL CYCLONES IN THE WESTERN NORTH PACIFIC AS REVEALED BY THREE DIFFERENT DATASETS
YU Hui, LU Yi, CHEN Pei-yan, ZHOU Wei-can
2012, 18(2): 119-126. doi: 10.3969/j.issn.1006-8775.2012.02.002
Abstract(1600) PDF [923KB](1641)
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Analyzed in this paper are the 20-yr (1991–C2010) tropical cyclone (TC) intensity from three forecast centers in the Western North Pacific, i.e. China Meteorological Administration (CMA), Japan Meteorological Agency (JMA), and Joint Typhoon Warning Center (JTWC) of the United States. Results show that there is more or less discrepancy in the intensity change of a TC among different datasets. The maximum discrepancy reaches 22 hPa/6h (42 hPa/6h, 33 hPa/6h) between CMA and JMA (CMA and JTWC, JMA and JTWC). Special attention is paid to the records for abrupt intensity change, which is currently a difficult issue for forecasters globally. It is found that an abrupt intensity change process recorded by one dataset can have, in some extreme cases, intensity change in another dataset varying from 0 to ≥ 10 hPa/6h with the same sign or the opposite sign. In a total of 2511 cases experiencing rapid intensity change, only 14% have consensus among all the three datasets and 25 % have agreement between two of the three datasets. In spite of such a significant uncertainty, the three datasets agree on the general statistical characteristics of abrupt intensity change, including regional and seasonal distribution, the relationship with initial intensity and TC moving speed, and persistence features. Notable disagreement is on very strong systems (SuperTY) and TCs moving very fast.
DYNAMIC FACTORS RELATED TO DECAY PROCESS OF OFFSHORE TROPICAL CYCLONES IN NORTHWEST PACIFIC
LEI Xiao-tu, TANG Jie, XU Xiao-lin, ZHAN Rui-fen, YU Run-ling, HUANG Rong-cheng, WU Lian-yao
2012, 18(2): 127-134. doi: 10.3969/j.issn.1006-8775.2012.02.003
Abstract(1466) PDF [605KB](1557)
Abstract:
Intensity variation of tropical cyclones (TCs), especially that of coastal or landfalling TCs, is of great concern in current research. Most of the research papers, however, focus on intensification processes of TCs; only a few discuss decay processes in the lifetime of a TC. In the daily weather operation related to TCs, it is challenging when a TC weakens and/or disappears suddenly, because it brings more difficulties than the forecast of intensifying TCs does. Overestimation of a decaying landfalling TC would lead to over-preparation of defensive measures and result in “crying wolf” mentality with adverse effects. This study summarized physical mechanisms that dominate the decaying process of TCs and listed several possible dynamical factors: reduced level of air temperature, too large or too small speed, contraction of TC size amplification of TC's core, and lightning number in a TC.
IMPACT OF SEA SPRAY ON TROPICAL CYCLONE STRUCTURE AND INTENSITY CHANGE
ZENG Zhi-hua, CHEN Lian-shou, BAO Jian-wen
2012, 18(2): 135-145. doi: 10.3969/j.issn.1006-8775.2012.02.004
Abstract(1988) PDF [661KB](1696)
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In this paper, the effects of sea spray on tropical cyclone (TC) structure and intensity variation are evaluated through numerical simulations using an advanced sea-spray parameterization from the National Oceanic and Atmospheric Administration/Earth System Research Laboratory (NOAA/ESRL), which is incorporated in the idealized Advanced Research version of the Weather Research and Forecast (WRF-ARW) model. The effect of sea spray on TC boundary-layer structure is also analyzed. The results show that there is a significant increase in TC intensity when its boundary-layer wind includes the radial and tangential winds, their structure change, and the total surface wind speed change. Diagnosis of the vorticity budget shows that an increase of convergence in TC boundary layer enhances TC vorticity due to the dynamic effect of sea spay. The main kinematic effect of the friction velocity reduction by sea spray produces an increment of large-scale convergence in the TC boundary layer, while the radial and tangential winds significantly increase with an increment of the horizontal gradient maximum of the radial wind, resulting in a final increase in the simulated TC intensity. The surface enthalpy flux enlarges TC intensity and reduces storm structure change to some degree, which results in a secondary thermodynamic impact on TC intensification. Implications of the new interpretation of sea-spray effects on TC intensification are also discussed.
NUMERICAL SIMULATION ON RE-INTENSIFICATION OF TROPICAL REMNANT RE-ENTERING THE SEA: A CASE STUDY
ZENG Zhi-hua, CHEN Lian-shou
2012, 18(2): 146-161. doi: 10.3969/j.issn.1006-8775.2012.02.005
Abstract(1655) PDF [2623KB](1166)
Abstract:
When Typhoon Toraji (2001) reached the Bohai Gulf during 1-2 August 2001, a heavy rainfall event occurred over Shandong province in China along the gulf. The Advanced Research version of the Weather Research and Forecast (WRF-ARW) model was used to explore possible effects of environmental factors, including effects of moisture transportation, upper-level trough interaction with potential vorticity anomalies, tropical cyclone (TC) remnant circulation, and TC boundary-layer process on the re-intensification of Typhoon Toraji, which re-entered the Bohai Gulf after having made a landfall. The National Centers for Environmental Prediction (NCEP) global final (FNL) analysis provided both the initial and lateral boundary conditions for the WRF-ARW model. The model was initialized at 1200 UTC on 31 July and integrated until 1200 UTC on 3 August 2001, during which Toraji remnant experienced the extratropical transition and re-intensification. Five numerical experiments were performed in this study, including one control and four sensitivity experiments. In the control experiment, the simulated typhoon had a track and intensity change similar to those observed. The results from three sensitivity experiments showed that the moisture transfer by a southwesterly lower-level jet, a low vortex to the northeast of China, and the presence of Typhoon Toraji all played important roles in simulated heavy rainfall over Shandong and remnant re-intensification over the sea, which are consistent with the observation. One of the tests illustrated that the local boundary layer forcing played a secondary role in the TC intensity change over the sea.
MICROPHYSICAL CHARACTERISTICS OF THE RAINDROP SIZE DISTRIBUTION IN TYPHOON MORAKOT (2009)
CHEN Bao-jun, WANG Yuan, MING Jie
2012, 18(2): 162-171. doi: 10.3969/j.issn.1006-8775.2012.02.006
Abstract(2450) PDF [1779KB](1728)
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Microphysical characteristics of the raindrop size distribution (RSD) in Typhoon Morakot (2009) have been studied through the PARSIVEL disdrometer measurements at one site in Fujian province, China during the passage of the storm from 7 to 10 August 2009. The time evolution of the RSD reveals different segments of the storm. Significant difference was observed in the microphysical characteristics between the outer rainband and the eyewall; the eyewall precipitation had a broader size distribution (a smaller slope) than the outer rainband and eye region. The outer rainband and the eye region produced stratiform rains while the eyewall precipitation was convective or mixed stratiform-convective. The RSD was typically characterized by a single peak distribution and well represented by the gamma distribution. The relations between the shape (μ) and slope (Λ) of the gamma distribution and between the reflectivity (Z) and rainfall rate (R) have been investigated. Based on the NW–CDm relationships, we suggest that the stratiform rain for the outer rainband and the eye region was formed by the melting of graupel or rimed ice particles, which likely originated from the eyewall clouds.
EFFECTS OF VERTICAL WIND SHEAR ON INTENSITY AND STRUCTURE OF TROPICAL CYCLONE
CHEN Qi-zhi, FANG Juan
2012, 18(2): 172-186. doi: 10.3969/j.issn.1006-8775.2012.02.007
Abstract(1715) PDF [1798KB](1648)
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In this study, the effect of vertical wind shear (VWS) on the intensification of tropical cyclone (TC) is investigated via the numerical simulations. Results indicate that weak shear tends to facilitate the development of TC while strong shear appears to inhibit the intensification of TC. As the VWS is imposed on the TC, the vortex of the cyclone tends to tilt vertically and significantly in the upper troposphere. Consequently, the upward motion is considerably enhanced in the downshear side of the storm center and correspondingly, the low- to mid-level potential temperature decreases under the effect of adiabatic cooling, which leads to the increase of the low- to mid-level static instability and relative humidity and then facilitates the burst of convection. In the case of weak shear, the vertical tilting of the vortex is weak and the increase of ascent, static instability and relative humidity occur in the area close to the TC center. Therefore, active convection happens in the TC center region and facilitates the enhancement of vorticity in the inner core region and then the intensification of TC. In contrast, due to strong VWS, the increase of the ascent, static instability and relative humidity induced by the vertical tilting mainly appear in the outer region of TC in the case with stronger shear, and the convection in the inner-core area of TC is rather weak and convective activity mainly happens in the outer-region of the TC. Therefore, the development of a warm core is inhibited and then the intensification of TC is delayed. Different from previous numerical results obtained by imposing VWS suddenly to a strong TC, the simulation performed in this work shows that, even when the VWS is as strong as 12 m s-1, the tropical storm can still experience rapid intensification and finally develop into a strong tropical cyclone after a relatively long period of adjustment. It is found that the convection plays an important role in the adjusting period. On one hand, the convection leads to the horizontal convergence of the low-level vorticity flux and therefore leads to the enhancement of the low-level vorticity in the inner-core area of the cyclone. On the other hand, the active ascent accompanying the convection tends to transport the low-level vorticity to the middle levels. The enhanced vorticity in the lower to middle troposphere strengths the interaction between the low- and mid-level cyclonical circulation and the upper-level circulation deviated from the storm center under the effect of VWS. As a result, the vertical tilting of the vortex is considerably decreased, and then the cyclone starts to develop rapidly.
ON THE RELATIONSHIPS BETWEEN THE UNUSUAL TRACK OF TYPHOON MORAKOT (0908) AND THE UPPER WESTERLY TROUGH
FEI Jian-fang, LI Bo, HUANG Xiao-gang, CHENG Xiao-ping
2012, 18(2): 187-194. doi: 10.3969/j.issn.1006-8775.2012.02.008
Abstract(1671) PDF [3331KB](1545)
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In this paper, by carrying out sensitivity tests of initial conditions and diagnostic analysis of physical fields, the impact factors and the physical mechanism of the unusual track of Morakot in the Taiwan Strait are discussed and examined based on the potential vorticity (PV) inversion. The diagnostic results of NCEP data showed that Morakot's track was mainly steered by the subtropical high. The breaking of a high-pressure zone was the main cause for the northward turn of Morakot. A sensitivity test of initial conditions showed that the existence of upper-level trough was the leading factor for the breaking of the high-pressure zone. When the intensity was strengthened of the upper-level trough at initial time, the high-pressure zone would break ahead of time, leading to the early northward turn of Morakot. Conversely, when the intensity was weakened, the breaking of the high-pressure zone would be delayed. Especially, when the intensity was weakened to a certain extent, the high-pressure zone would not break. The typhoon, steered by the easterly flow to the south of the high-pressure zone, would keep moving westward, with no turn in the test. The diagnostic analysis of the physical fields based on the sensitivity test revealed that positive vorticity advection and cold advection associated with the upper-level trough weakened the intensity of the high-pressure zone. The upper-level trough affected typhoon's track indirectly by influencing the high-pressure zone.
BOUNDARY LAYER STRUCTURE IN TYPHOON SAOMAI (2006): UNDERSTANDING THE EFFECTS OF EXCHANGE COEFFICIENT
MING Jie, SONG Jin-jie, CHEN Bao-jun, WANG Ke-fa
2012, 18(2): 195-206. doi: 10.3969/j.issn.1006-8775.2012.02.009
Abstract(2081) PDF [921KB](1294)
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Recent studies have shown that surface fluxes and exchange coefficients are particularly important to models attempting to simulate the evolution and maintenance of hurricanes or typhoons. By using an advanced research version of the Weather Research and Forecasting (ARW) modeling system, this work aims to study the impact of modified exchange coefficient on the intensity and structures of typhoon Saomai (2006) over the western North Pacific. Numerical experiments with the modified and unmodified exchange coefficients are used to investigate the intensity and structure of the storm, especially the structures of the boundary layer within the storm. Results show that, compared to the unmodified experiment, the simulated typhoon in the modified experiment has a bigger deepening rate after 30-h and is the same as the observation in the last 12-h. The roughness is leveled off when wind speed is greater than 30 m/s. The momentum exchange coefficient (CD) and enthalpy exchange coefficient (CK) are leveled off too, and CD is decreased more than CK when wind speed is greater than 30 m/s. More sensible heat flux and less latent heat flux are produced. In the lower level, the modified experiment has slightly stronger outflow, stronger vertical gradient of equivalent potential temperature and substantially higher maximum tangential winds than the unmodified experiment has. The modified experiment generates larger wind speed and water vapor tendencies and transports more air of high equivalent potential temperature to the eyewall in the boundary layer. It induces more and strong convection in the eyewall, thereby leading to a stronger storm.
IMPACTS OF UPPER-LEVEL COLD VORTEX ON THE RAPID CHANGE OF INTENSITY AND MOTION OF TYPHOON MERANTI (2010)
LI Ying, GUO Li-xia, XU Ying-long, HU Shu
2012, 18(2): 207-219. doi: 10.3969/j.issn.1006-8775.2012.02.010
Abstract(1847) PDF [2102KB](1315)
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Typhoon Meranti originated over the western North Pacific off the south tip of the Taiwan Island in 2010. It moved westward entering the South China Sea, then abruptly turned north into the Taiwan Strait, got intensified on its way northward, and eventually made landfall on Fujian province. In its evolution, there was a northwest-moving cold vortex in upper troposphere to the south of the Subtropical High over the western North Pacific (hereafter referred to as the Subtropical High). In this paper, the possible impacts of this cold vortex on Meranti in terms of its track and intensity variation is investigated using typhoon best track data from China Meteorological Administration, analyses data of 0.5×0.5 degree provided by the global forecasting system of National Centers for Environmental Prediction, GMS satellite imagery and Taiwan radar data. Results show as follows: (1) The upper-level cold vortex was revolving around the typhoon anticlockwise from its east to its north. In the early stage, due to the blocking of the cold vortex, the role of the Subtropical High to steer Meranti was weakened, which results in the looping of the west-moving typhoon. However, when Meranti was coupled with the cold vortex in meridional direction, the northerly wind changed to the southerly at the upper level of the typhoon; at the same time the Subtropical High protruded westward and its southbound steering flow gained strength, and eventually created an environment in which the southerly winds in both upper and lower troposphere suddenly steered Meranti to the north; (2) The change of airflow direction above the typhoon led to a weak vertical wind shear, which in return facilitated the development of Meranti. Meanwhile, to the east of typhoon Meranti, the overlapped southwesterly jets in upper and lower atmosphere accelerated its tangential wind and contributed to its cyclonic development; (3) The cold vortex not only supplied positive vorticity to the typhoon, but also transported cold advection to its outer bands. In conjunction with the warm and moist air masses at the lower levels, the cold vortex increased the vertical instability in the atmosphere, which was favorable for convection development within the typhoon circulation, and its warmer center was enhanced through latent heat release; (4) Vertical vorticity budget averaged over the typhoon area further shows that the intensification of a typhoon vorticity column mainly depends on horizontal advection of its high-level vorticity, low-level convergence, uneven wind field distribution and its convective activities.
DIAGNOSTIC ANALYSIS ON THE DISTRIBUTION OF RAINFALL ASSOCIATED WITH TYPHOON “MOLAVE” (0906)
GAO Shuan-zhu, LU Xin-yan
2012, 18(2): 220-227. doi: 10.3969/j.issn.1006-8775.2012.02.011
Abstract(1469) PDF [1399KB](1190)
Abstract:
This work examines the mechanism of rainfall associated with typhoon Molave (0906) in Guangdong province and Guangxi Zhuang Autonamous Region with rainfall observations, radar mosaics from China National Meteorological Center and the final analysis data of National Center of Environmental Prediction (FNL/NCEP, USA). The result shows that the mechanism is different for the rainfall in the these areas. The rainfall in eastern Guangdong is mainly associated with a convective line to the front-right of the typhoon. The convective line is about 200 km away from the typhoon center. The rainfall in western Guangdong and Guangxi appear ahead of or to the left of the typhoon and is very close to the typhoon center. Both rainfall moves forward with the typhoon anticlockwise. It was also found that the rainfall occurred in the boundary between unstable and low-level convergent areas and closer to the convergent area. The unstable area is located in the downstream of rainfall and ahead of the convective line. It is an important factor to the development and convection. Strong frontogenesis is observed in the backward or upstream convective area of rainfall and is thus an important lifting condition for the formation of rainfall. When the low-level convergent area moves to the unstable area ahead of it, the unstable energy is left behind and as a result the convection is strengthened.
A STATISTICAL ANALYSIS ON THE DIFFERENT FEATURES OF TC EXTRATROPICAL TRANSITION OVER LAND AND OCEAN
ZHONG Lin-hao, HUA Li-juan, FENG Shi-de
2012, 18(2): 228-241. doi: 10.3969/j.issn.1006-8775.2012.02.012
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The extratropical transitions (ETs) of tropical cyclones (TCs) over China and the ocean east to 150°E are investigated by the use of best-track data and JRA-25 reanalysis spanning 1979–C2008. The ET events occurring north of 25°N and in the warm season (from May to October) are extracted from the reanalysis to emphasize the interaction between TC and midlatitude circulation. Statistical analysis shows that 18.5% of the warm-season TCs go through land ETs north of 25°N in the western North Pacific. And 20.5% of the ET events occur over the ocean east of 150°E. Most (62.2%) ET TCs over China gradually die out after ET, but more (70.7%) ocean ET cases have post-ET reintensification. The evolutions in cyclone phase space and the composite fields for land and ocean ETs, as well as the ET cases with and without post-ET reintensification, are further analyzed. It is found that most TCs with ET over China and those without post-ET reintensification evolve along the typical ET phase path as follows: emergence of thermal asymmetry→losing upper-level warm core→losing lower-level cold core→evolving as extratropical cyclone. The TCs undergoing ETs over ocean and those with post-ET reintensification form a high-level cold core before the ET onset. The TCs with land ET have long distance between the landing TC and a high-level trough. That makes the TC maintain more tropical features and isolates the TC flow from the upstream and downstream jets of the midlatitude trough. The structure of circulation leads to weak development of baroclinicity in land ET. On the contrary, shorter distance between ocean TC and high-level trough makes the high-level trough absorb the TC absolutely. Under that baroclinicity-favorable environment, strong cold advection makes the TC lose its high-level warm core before ET onset. The composite fields confirm that the TC with ocean ET has stronger baroclinic features. Generally, the TC at land ET onset is located to the south of the ridge of the subtropical high, which tends to prevent the TCs from interacting with midlatitude circulation. But for the ocean ET, the situation is just the opposite. Similar analyses are also carried out for the TCs with and without post-ET reintensification over both land and ocean east of 150°E. The results further prove that the TC with stronger baroclinic characteristics, especially in the circumstance favorable to its interaction with high-level midlatitude systems, has more opportunity to reintensify as an extratropical cyclone after ET.
PREDICTION OF TROPICAL DISTURBANCE DEVELOPMENT OVER THE SOUTH CHINA SEA USING SSM/I DATA
ZHANG Chao, SHU Hai-long, ZHANG Qing-hong, WANG Lei
2012, 18(2): 242-248. doi: 10.3969/j.issn.1006-8775.2012.02.013
Abstract(1611) PDF [1793KB](2445)
Abstract:
This paper proposes a method for predicting the development of tropical disturbance over the South China Sea (SCS) based on the total latent heat release (TLHR) derived from the Special Sensor Microwave/Imager (SSM/I) satellite observations. A threshold value of daily mean TLHR (3×1014 W) for distinguishing the non-developing and developing tropical disturbances is obtained based on the analysis for 25 developing and 43 non-developing tropical disturbances over the SCS during 2000 to 2005. If the mean TLHR within 500 km of a disturbance on the latest day and its daily mean TLHR during previous life are both greater than 3×1014 W, the disturbance will be a developing one in the future. Otherwise, it is a non-developing one. A real-time testing prediction of tropical cyclogenesis over the SCS was conducted for the years 2007 and 2008 using this threshold value of TLHR. We find that the method is successful in detecting the development of 80% of all tropical disturbances over the SCS in 2007 and 2008.
STATISTICAL ANALYSIS AND NUMERICAL SIMULATION OF POYANG LAKE'S INFLUENCE ON TROPICAL CYCLONES
ZHANG Sheng-jun, CHEN Lian-shou, Li Ying
2012, 18(2): 249-262. doi: 10.3969/j.issn.1006-8775.2012.02.014
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Based on the Tropical Cyclone (TC briefly thereafter) Yearbook 1980-2009, this paper first analyzes the number and intensity change of the TCs which passed directly over or by the side of Poyang Lake (the distance of TC center is less than 1° longitude or 1° latitude from the Lake) among all the landfalling TCs in China during the past 30 years. Two cases are examined in detail in this paper. One is severe typhoon Rananim with a speed of 3.26 m/s and a change of 1 hPa in intensity when it was passing the Lake. The other is super typhoon Saomai with a faster moving speed of 6.50 m/s and a larger change in intensity of 6 hPa. Through numerical simulation experiments, this paper analyzes how the change of underlying surface from water to land contributes to the differences in intensity, speed and mesoscale convection of the two TCs when they passed the Lake. Results show that the moisture and dynamic condition above the Lake were favorable for the maintenance of the intensity when Rananim was passing through Poyang Lake, despite the moisture supply from the ocean was cut off. As a result, there was strong convection around the lake which led to a rainfall spinning counter-clockwise as it was affected by the TC movement. However, little impact was seen in the Saomai case. These results indicate that for the TCs coming ashore on Poyang Lake with a slow speed, the large water body is conducive to the sustaining of the intensity and strengthening of the convection around the TC center and the subsequent heavy rainfall. On the contrary, a fast-moving TC is less likely to be influenced by the underlying surface in terms of intensity and speed.
SURFACE OBSERVATIONS IN THE TROPICAL CYCLONE ENVIRONMENT OVER THE SOUTH CHINA SEA
LIU Chun-xia, WAN Qi-lin, LIAO Fei, ZHAO Zhong-kuo
2012, 18(2): 263-274. doi: 10.3969/j.issn.1006-8775.2012.02.015
Abstract(1546) PDF [808KB](1223)
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In this paper, the observational data from Marine and Meteorological Observation Platform (MMOP) at Bohe, Maoming and buoys located in Shanwei and Maoming are used to study the characteristics of air-sea temperature and specific humidity difference and the relationship between wind and wave with the tropical cyclones over the South China Sea (SCS). The heat and momentum fluxes from eddy covariance measurement (EC) are compared with these fluxes calculated by the COARE 3.0 algorithm for Typhoon Koppu. The results show that at the developing and weakening stages of Koppu, both these differences between the sea surface and the near-surface atmosphere from the MMOP are negative, and data from the buoys also indicate that the differences are negative between the sea surface and near-surface atmosphere on the right rear portion of tropical cyclones (TCs) Molave and Chanthu. However, the differences are positive on the left front portion of Molave and Chanthu. These positive differences suggest that the heat flux is transferred from the ocean to the atmosphere, thus intensifying and maintaining the two TCs. The negative differences indicate that the ocean removes heat fluxes from the atmosphere, thus weakening the TCs. The wind-wave curves of TCs Molave and Chanthu show that significant wave height increases linearly with 2-min wind speed at 10-m height when the wind speed is less than 25 m/s, but when the wind speed is greater than 25 m/s, the significant wave height increases slightly with the wind speed. By comparing the observed sensible heat, latent heat, and friction velocity from EC with these variables from COARE 3.0 algorithm, a great bias between the observed and calculated sensible heat and latent heat fluxes is revealed, and the observed friction velocity is found to be almost the same as the calculated friction velocity.