E 115e 120e110e 115e 120e110e 115e 120e

Fig. 4. Wind field derived from QuikSCAT during the three days.

Different atmospheric conditions in PBL_MRF (boundary condition) and CUM_G (cumulus scheme) could cause an increase in latent heat flux and precipitation, but not in storm intensity, such as maximum wind speed and center pressure. However, a warmer SST (in SST_C) could result in an increase in storm intensity in addition to the increase in latent heat flux and precipitation.

2.7 Conclusions and discussions

Model simulated precipitation and wind speed are compared with satellite data, in order to evaluate model performance and to test model sensitivity to several parameters that may impact simulation results. Atmospheric boundary condition, cumulus scheme and SST

distribution can have different influences on rainfall and wind patten during different periods of a TC process. All five model runs in this study overestimate precipitation and underestimate maximum wind speed during Chanchu (2006). Large rainfall area mainly occurs on the west or northwest side of the rainfall center. Areas around rainfall and maximum wind center are chosen to quantify the difference between model simulation and satellite observation. The model configured with Blakadar PBL, Resiner2 moisture, the BM cumulus scheme and daily-updated SST has the best simulation of precipitation. Using the MRF PBL scheme would greatly reduce TC's intensity, which can be clearly reflected in the simulation of maximum wind speed. Constant SST through the TC life cycle provides more energy to the TC, which could cause a significant increase in TC's intensity, therefore leading to the largest overestimation on rainfall and maximum wind. Longitudinally-uniform SST distribution before the RI would reduce TC's intensity and heat flux due to less energy from the ocean.

3. Bay of Bengal: cluster analysis of tropical cyclone tracks 3.1 Introduction

The Indian sub-continent is one of the worst areas in the world affected by Tropical Cyclones (TCs), although TCs in this region just account for about 7% of the total number of global TCs (Gray 1968). Unlike TCs in the western Pacific mainly occurring after the monsoon onset, TCs in the Bay of Bengal (BOB) have two seasons. The primary season is during the post-monsoon period and the second one is the pre-monsoon season (Mohanty 1994). During the monsoon, less TCs or tropical disturbances form because strong tropospheric ventilation produced by the large vertical wind shear inhibits storm development (Gray 1968). Compared with TCs in the Pacific and Atlantic, the TC genesis process in the northern Indian Ocean received little attention probably because of lacking in observations. Kikuchi et al. (2009) indicated that the incipient disturbances are virtually absent in the northern Indian Ocean and the initiation process of tropical depression is expected to be different from those in the Pacific and Atlantic Oceans.

Murty et al. (2000) examined the Effective Oceanic Layer for Cyclogenesis (EOLC) parameter, which was related with the near-surface stratified layer developed due to the spread of low salinity waters under the influence of freshwater influx. They found that EOLC should be considered for indentifying the zones of cyclogenesis and for better prediction of cyclone tracks in BOB. Their results indicated that zones of cyclogenesis and mean-cyclone tracks fairly coincide with the zones of higher EOLC. Notably, research about Cyclone Heat Potential (CHP) in BOB partly explained the cyclone genesis in this ocean basin. Sarma et al. (1990) first revealed the seasonal distribution of CHP. By means of CTD observation data sets collected from five cruises during 1993-1996, Sadhuram et al. (2004) found that high value of CHP coincided with anticyclonic gyre (ACG) and vice versa, which emphasized the importance of gyres in the distribution of CHP on the intensification of cyclones/depressions. In terms of decadal variability, Singh et al. (2000) have proved that there had been a increase trend in the enhanced cyclogenesis during November and May in BOB which account for the maximum number of severe cyclones over the north Indian Ocean. Ocean responses to TC have also been investigated in BOB, which mainly put concern on the sea surface temperature (SST) change under the passage of TC cases (Sadhram 2004). Inertial oscillations signals forced by TC were captured by time-series measurements from a moored data buoy located in BOB set in September 1997 (Joseph et al.

Fig. 5. Wind pattern simulated by the five model runs during the three days.

2007). Add to the above research, TCs case studies were carried out to find the physical explanations under the specific TC conditions which help improve the operational forecast capability, such as the disastrous TC Nargis in 2008 (Webster 2008; Lin et al. 2009; Kikuchi et al. 2009; Yanase et al. 2010; Yokoi et al. 2010; Yamada et al. 2010; McPhaden et al. 2009). The TC's track or movement is to be affected by many internal and external factors (Mohanty and Gupta 1997). Steering flow is the prominent external force on TCs, accounting for 70-90% of the motion. When steering flow is weak, TCs tend to move poleward and westward resulting from the internal force (Chan and Gray 1982; Elsberry et al. 1987). In addition, TCs have a tendency to move toward a warmer ocean surface (Orlanski 1998; Mandal et al. 2007). Several methods have been used in sorting tracks, which include K-means method (MacQueen 1967). K-means method has been applied in studying North Pacific (Elsner and Liu 2003) and North Atlantic (Elsner 2003) TCs. Nevertheless, K-means method cannot accommodate tracks in different lengths. To solve this issue, the finite mixture polynomial regression model (Gaffney 2004) was used to objectively classify the TC tracks, not only based on a few points of trajectory, but on trajectory shape. The technique has been applied to western North Pacific typhoon tracks (Camargo et al. 2007a,b), eastern North Pacific hurricane tracks (Camargo et al. 2008) and the climate modulation of North Atlantic hurricane tracks (Kossin et al. 2010). In recent years, some progresses have been made by using in models for operational track forecast in India, BOB in specific (Mohanty and Gupta 1997; Gupta and Bansal 1997; Prasad and Rao 2003). Sensitive experiments are used to examine the effective factors controlling TC tracks (Mandal et al. 2002, 2003).

These previous studies regarding TC tracks in BOB mainly focused on operational model study. However, objective and systematic analysis about TC tracks in this region remain unknown. Clarifying the physical background of TC tracks in BOB will help to minimize the error of operational forecast for similar TCs in the future, and reduce the loss of lives and properties. Therefore, the focal point of the present study is to show the TC track types classified by results from the mixture regression model, and then depict the seasonal variability and circulation field of each track type.

The study is organized as follows. Datasets used in this study are given in Section 2). Characteristic of track types is described in Section 3). Section 4) shows the seasonal variability, which help further sort tracks. Environmental flow is given in section 5).

3.2 Data and methods

TC data is derived from the Joint Typhoon TC tracks (JTWC) for the time interval 1980-2009. The year 1980 is chosen because TC data is more reliable and man-made satellites had already been launched and used for TC observation and forecast since 1980 in BOB. In this study, only TCs with landfall are included in our analysis, for the purpose of examining the environmental flows effectively.

TC track types are detected by a mixture of polynomial regression models which was developed by Gaffney et al. (2004). Compared with the previous cluster analysis methods, this model can fit the geographical "shape" of the trajectories which also allow quadratic function by extending the standard multivariate finite mixture model. Maximizing the likelihood of the parameters helps to find the best fitting mean curve. This method can easily accommodate TC tracks with different length.

Variables from the National Centers for Environmental Prediction/ National Centers for Atmospheric Research (NCEP/NCAR) reanalysis (Kalnay et al. 1996) since 1980 are used to analyze the background flows of each type of tracks. The entire data records in each case contribute to the composition of their associated track type.

3.3 Characteristics of track types

Under this mixture of polynomial regression models, as measure of goodness of fit, log-likelihood and within-cluster error values are used to obtain the optical mean regression trajectories (track types) of the observed tracks. Within-cluster error is defined as difference in latitude and longitude from the mean regression trajectories squared and summed over all tracks in the cluster for different cluster numbers (Camargo et al. 2007). Fig. 6 shows the log-likelihood values and within-cluster error for different number of clusters on different regression order. Larger log-likelihood with smaller within-cluster error indicates good fit. Here, we choose K=6 and quadratic regression order to sort tracks into six types. Fig. 7 shows the historical tracks from 1980 to 2009 of each cluster. They are (1) northeastward with recurvature; (2) westward at lower latitude; (3) longest westward; (4) longer northwestward; (5) shorter northwestward; and (6) northward.

To better find the physical relationship between TC activity and seasonal variation, all westward cases (cluster 2, 3, 4, 5) are merged into one category - here as "westward type". Hence, three new track types are listed below: westward (68 cases), northward (31 cases), and northeastward (11 cases) (Fig. 8).

3.4 Seasonal variability

Fig. 9a shows the seasonal variability which indicates total TC count during year 1980-2009. Fig. 9b gives the contribution of each cluster in each month to the total number of TCs for each cluster during 1980-2009. It shows that westward type have the largest number of cases. Most of these TCs (over 85%) occurred after winter monsoon onset (September to January), with a peak in October (over 30%). Northward type has two seasons. The primary season is after October which is similar as the westward type (but delayed for one month), and the second one is pre-summer-monsoon season (April and May). TC numbers in these two seasons are closed. Main peak took place in May, and sub-peak in November (also with one month lag compared to westward type). The northeastward type with recurvature and landing at Myanmar is unique, not only for its fewest number (only 11 cases) but for the two peaks in April and May, which implicit that connection to summer monsoon onset may be considered.

Number of Clusters

Fig. 6. Log-likelihood values and within-cluster error for different number of clusters on different regression order.

2 E 76 E SO E 84 E SS E 92 E 96 E 100 E 104-E 72 E 76 E 00 E 84 E

Fig. 7. Historical tracks from 1980 to 2009 of each of the six clusters.

2 E 76 E SO E 84 E SS E 92 E 96 E 100 E 104-E 72 E 76 E 00 E 84 E

Fig. 7. Historical tracks from 1980 to 2009 of each of the six clusters.

72 E 76 E 80 E 84 E 88 E 92 E 96 E 1 00 E 1 04 E 72 E 76 E 80 E 84 E

96 E 100 E 104 E 72 E 76 E 00 E 04 E 00 E 92 E 96 E 100 E 104 E

Fig. 8. Historical tracks from 1980 to 2009 of each of the three clusters after reclassifying.

72 E 76 E 80 E 84 E 88 E 92 E 96 E 1 00 E 1 04 E 72 E 76 E 80 E 84 E

96 E 100 E 104 E 72 E 76 E 00 E 04 E 00 E 92 E 96 E 100 E 104 E

Fig. 8. Historical tracks from 1980 to 2009 of each of the three clusters after reclassifying.

I Eastward I Westward I N-E

1 2 3 4 5 6 7 8 9 10 1 1 12

Fig. 9. Seasonal variability of (a) total TC count of year 1980-2009, (b) contribution of each cluster in each month to the total number of TCs for each cluster from 1980-2009

3.5 Environmental flow

Based on the seasonal variability discussed above, northward tracks are divided into two kinds, the one during pre-summer-monsoon (April and May) and the other during post-winter-monsoon (October to January). Figs. 10-13 show the daily vertical wind composition (600-100hPa) for TCs in each cluster, which composites on all days during the lifecycle of each TC. Demonstration of each track type in detail is given below:

Northeastward: Southerly appeared under 500hPa across large area, which seemed to be the low level cross-equatorial-flow. Above 500hPa, an anticyclonic circulation occupied IndoChina Peninsular. This system became stronger with height.

Westward: Easterly spread over wide region from northern to middle part of BOB and extend to the Arab Sea. A significant unclosed long and narrow anticyclonic circulation appeared in Indo-China Peninsular which also extended to the Arab Sea. This circulation pattern which also became stronger with height may be associated with the extension of West Pacific Subtropical High.

Northward (April and May): Remarkable southerly also appeared under 500hPa which was similar to the northeastward type. Nevertheless, this channel of wind was limited to the east of 90E (east BOB), mainly due to northward invasion of the cross-equatorial-flow and southward meander of the northerly in north BOB. These two channels of flow with different properties induced a trough. This trough should belong to the India-Burma Trough which is one of the most frequent-occurring and significant synoptic systems during the pre-monsoon season. Above 500hPa, the anticyclonic circulation still occupied Indo-China Peninsular which is weaker than the one of westward track type.

Northward (October-January): Anticyclonic circulation in Indo-China Peninsular also appeared which is similar to the westward track type but stronger. Difference is easterly could not extend to India let alone the Arab Sea. It is mainly owing to the trough activity in north India, which can constrain such anticyclone system west invasion. Compared with northward tracks in April and May, the one of this post-winter-monsoon season mostly took place in the western part of BOB.

3.6 Conclusion and discussion

By using the mixture quadratic regression model, six clusters of TC tracks in BOB are classified. To better analysis the background physical factors which can affect TC tracks of this region, all westward tracks are sorted as one type. Thereafter, three track types are obtained, northeastward, westward, and northward. After combining the analysis of seasonal variability, it is found that westward TCs which mainly occurred in the post-winter-monsoon period (September-January) were largest in amount. Northward TC were in the next place in amount. Whereas, this type of TCs should be divided by two stages (April-May and October-January), which is more suitable for examining the background controlling systems. Northeastward tracks were fewest in amount. However, this type of TCs generally took place in April and May.

The analysis of background circulation of each track type indicates that except for the northeastward one, anticyclonic circulation located in Indo-China Peninsular as well as the trough activity across the region of India-Burma played important roles on local wind pattern which assisted steering TCs. In addition, TCs happened in April and May (pre-summer-monsoon), were generally affected by the cross-equatorial-flow and prone to be with northward motion.

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