1 Introduction

Tropical cyclones (TCs) are one of the most destructive weather phenomena in the world. They cause human fatalities, structural damages, and economic losses worldwide (Pielke and Pielke 1997; Simpson et al. 2002; Manganello et al. 2012). They are large-scale rotary systems that originate over warm ocean waters in tropical or sub-tropical regions (Montgomery and Farrell 1993). They are associated with organized convections and have surface wind speeds of 34 knots or more for at least one 6-h period (Bhardwaj and Singh 2020). On average North Indian Ocean (NIO), including the Bay of Bengal (BoB) and Arabian Sea (AS), accounts for 7% of the global TCs (Neumann 1993). India is affected mainly by the TCs, which develop in the NIO, including the BoB and the AS. About 80% of these cyclones form in the BoB (Singh 2007), which tend to be the deadliest of any TCs around the globe. They develop in the pre-monsoon and post-monsoon seasons and generally move west-northwestwards to northwestwards (Chinchole and Mohapatra 2017). The average life period and frequencies of these TCs over BoB are 4–5 days and 4, respectively (Mohapatra et al. 2014; Kumar et al. 2017). India Meteorological Department (IMD) classifies TCs into five categories based on their wind speeds, starting from the cyclonic storm (CS) to the super cyclonic storm (SuCS). Very severe cyclonic storms (VSCS), extremely severe cyclonic storms (ESCS), and SuCS are the most destructive and intense TCs. Therefore, their genesis, intensification, and track are of particular significance.

Various atmospheric conditions such as strong vertical wind shear, mid-tropospheric instability and mid-tropospheric humidity influence TCs genesis and intensification. Many scientists (Gray 1968, 1979; DeMaria 1996; Emanuel et al. 2004; Kotal et al. 2009; Ganesh et al. 2020; Sanap et al. 2020; Naskar and Naskar 2021) have previously worked to find out the role of these parameters in TCs genesis and intensification. Many previous studies (Reihl 1950; Ooyama 1969; Emanuel 1986; Vinod et al. 2014; Lengaigne et al. 2019; Naskar and Naskar 2021; Singh and Roxy 2022) have also brought out the crucial role played by air–sea interaction processes in tropical cyclone genesis and intensification. As TCs primarily draw their energy from evaporation at the ocean surface, the latent heat fluxes at the air–sea interface also play an essential role in TCs intensification (Montgomery et al. 2009; Gao and Chiu 2010; Andersen et al. 2013; Chen et al. 2014; Zhou et al. 2015; Srinivas et al. 2016; Naskar and Naskar 2021; Singh and Roxy 2022). Moreover, the genesis and intensification characteristics of TCs differ from ocean basin to ocean basin (Flotz et al. 2018). Despite the above studies, the prediction of TCs genesis and intensification is still a challenge. This implies that the processes behind TCs genesis and intensification are yet to be understood. Many recent studies on TCs over BoB show that scientists have focused on a few individual dynamical and thermo-dynamical parameters to describe the genesis and intensification (Mohanty et al. 2019; Reshmi Mohan et al. 2022; Vishwakarma et al. 2022). Mohanty et al. (2019) observed a crucial role of SST in modulating the life cycle of TCs over BoB. Vishwakarma et al. (2022) observed that Amphan experienced rapid cooling during rapid intensification. Reshmi Mohan et al. (2022) observed anomalously high MRH (10–40%), upper atmospheric divergence (0–10 × 10–5 s–1), low-level cyclonic vorticity (10–50 × 10–5 s–1), and moderate shear before intensification of Amphan and Fani. They also observed higher positive SST anomaly, strong diabatic heating and increased surface fluxes during the rapid intensification of Amphan and Fani which indicates positive warm SST feedback. Sanap et al. (2020) observed that the regions of anomalously high SST, subsurface temperatures, tropical cyclone heat potential (TCHP) and ocean mean temperature (OMT) with a depth of 26°C isotherms up to 100 m favoured rapid intensification of TC Ockhi. Singh et al. (2020) showed that Madden Julian oscillation (MJO) and warm oceanic conditions helped in the genesis of Ockhi, and favourable thermodynamic conditions due to warm SST helped its intensification. Harikumar et al. (2022) observed that vorticity and RH were more favourable than VWS and potential intensity before the genesis of Ockhi and they suggested that forecasters should consider the background dynamic and thermodynamic conditions extensively in addition to model guidance for better prediction of genesis, intensity and track of TCs. Ahmed et al. (2021) observed the characteristic features of Super Cyclone Amphan through satellite images and concluded that precise changes in geometric and thermal characteristics of the ‘eye’ of Amphan are related to its intensity and these eye features can be used for very short range intensity prediction of a TC. Mohapatra and Sharma (2021) compared some vital parameters including location, movement, intensity, size, etc. for ‘Phailin’ and ‘Hudhud’ and found that higher intensity, higher rate of intensification, longer duration, lower rate of decay after landfall and larger size were responsible for higher damage potential. Most of these studies are limited to case study specific or a small group of TCs. The present study considers most of the important dynamic and thermodynamic parameters and latent heat flux for a large group of intense TCs. This study aims to find out the correlation of these parameters with TCs intensity (central pressure/maximum sustained wind speed) as well as the correlation among themselves during the life period of TCs. This will help find the most important parameter for genesis and intensification.

2 Data and methodology

The study region under consideration is BoB (0°–31°N, 79°–111°E). Three hourly 0.25° × 0.25° resolution European Center for Medium-Range Forecasts (ECMWF) ERA5 reanalysis data (Hersbach and Dee 2016) for the parameters such as wind speed and direction, temperature, relative humidity at different pressure levels, mean sea level pressure (MSLP), 200 hPa divergence, SST and SLHF for the period 1990–2019 have been obtained and used in this study. Past studies have shown that the ERA5 dataset well represents the evolution and many observed features of tropical cyclones (Malakar et al. 2020; Sanap et al. 2020; Bian et al. 2021). But ERA5 dataset is model-derived and not pure observation-based; hence for comparison purposes, we have taken three hourly 0.5° × 0.625° total latent energy flux (TLEF) and wind speed data of Modern-Era Retrospective Analysis for Research and Application, version 2 (MERRA2) (Gelaro et al. 2017) which is derived based on satellite remote sensing. Best track data of intense TCs for the period 1990–2019 have been collected from RSMC New Delhi for the track, wind speed, and MSLP. Here VSCS (maximum wind speed 64–89 kts), ESCS (90–119 kts), and SuCS (120 kts and above) have been termed intense TCs. Here we have considered several dynamic and thermodynamic parameters of TCs. The dynamic parameters are 200 hPa divergence and VWS. The thermodynamic parameters are SST, MI, MRH, TLEF and SLHF. The VWS has been calculated by taking the difference of 200 and 850 hPa winds. MRH is the mean relative humidity between 700 and 500 hPa, mid-tropospheric instability (MI) has been calculated by using MI = (T850 – T500)°C, where T850 and T500 are the temperatures at 850 and 500 hPa, respectively. The parameters such as max SLHF, max TLEF, min VWS, min MSLP, max 200 hPa divergence, mean SST, mean MI, and mean MRH have been calculated within a 6° × 6° box centering the eye of the cyclone. The composite mean of SLHF has been calculated by taking the mean of SLHFs of all TCs during their lifetime. SLHF is positive downward and negative upward. SLHF is generally denoted with a negative sign unless there is a downward energy transfer. Pearson’s correlation method has been used to derive the correlation among the parameters.

3 Results and discussions

In this study, 31 intense TCs which originated in the BoB from 1990 to 2019 have been analyzed. Figure 1 shows the genesis and landfall locations of intense TCs during this period. The red stars, dots, and triangles correspond to the genesis locations of SuCS, ESCS, and VSCS, respectively, and blue stars, dots, and triangles correspond to the landfall locations of SuCS, ESCS, and VSCS, respectively. Figure 2 shows the latitudinal and longitudinal distribution of these TCs. It is clear from figure 2(a) that almost 75% of these TCs originate between 8° and 14°N, and from figure 2(b), nearly 65% of these TCs originate between 88° and 94°E. It is also seen that almost 60% of these TCs develop within the latitude/longitude box 8°–14°N and 88°–94°E. Figure 3(b) shows the seasonal variations of these TCs. It is seen that almost 70% of these TCs form in the post-monsoon season and 30% form in the pre-monsoon season. Figure 3(c) exhibits the monthly variations of these TCs. It is observed that October month experiences the most of these TCs and it is nearly 35%. No intense TC has been formed in January, February, March, June, July, August, and September. Figure 3(a) shows the frequencies of intense TCs to their maximum SLHF values. It is observed that the frequency of TCs with SLHF values 1100–1400 KJ/m2 is maximum and above 2000 KJ/m2 is minimum.

Figure 1
figure 1

Genesis and landfall locations of intense TCs over BoB.

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Figure 2
figure 2

(a) Latitudinal and (b) longitudinal variations of intense TCs over BoB.

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Figure 3
figure 3

(a) Variations of frequency of intense TCs and maximum SLHF, (b) seasonal variations of intense TCs and (c) monthly variations of intense TCs.

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During the intensification of a tropical cyclone, the central pressure falls. Central pressure is one of the most reliable measures of TCs intensity (Chavas et al. 2017). Maximum sustained wind speed is also another important parameter for TCs intensity characterization. In fact, India Meteorological Department (IMD) categorizes TCs over NIO based on maximum sustained 10 m wind speed. Bhardwaj and Singh (2020) showed that the decrease in the central pressure of TCs and the increase in 10 m surface wind speed is proportional with a correlation coefficient of 0.97. In this study, central pressure, as well as maximum wind speed during the lifetime of TCs, have been plotted against the parameters such as SST, SLHF, 200 hPa divergence, MRH, and MI to observe if there is any relation between central pressure/maximum wind speed with these parameters during the entire life period of TCs.

Warm oceans (SST > 26.5°C) are favourable for the genesis of TCs (Palmen 1948; Gray 1998). They act as the source of energy for TCs. Using a high-resolution regional model (Lavender et al. 2018) showed that an increase (decrease) in SST was associated with an increase (decrease) in TC intensity. Ren et al. (2014) analyzed the influence of SST on TCs over four basins (Western North Pacific, North Atlantic Ocean, South Indian Ocean/Northwest Western Australian Ocean, and Southwest Pacific) and found that the intensities of TCs increased with increasing SST and warmer SST indicated more rapid intensification. Sun et al. (2017) showed that under the SST warming, TCs not only became stronger but also more prominent. Naskar and Naskar (2021) observed that under favourable conditions, abnormally high SST had rapidly intensified SuCS Amphan. Keeping in mind the influence of SST on TCs intensity as stated above, central pressures/max wind speed of all TCs have been plotted against SST values during TCs’ lifetime for the period 1990–2019 in figures 4(a)/5(a), respectively. It is seen that SST does not show any significant relation with central pressure (max wind). Though it is observed that higher SST corresponds to lower central pressure (higher max wind speed) for some intense TCs but not for all. The R2 value is –0.37 (0.31). The reason behind this may be TC-induced cooling. When a TC moves over the warm ocean, it reduces the SST along its track, mainly through vertical mixing and upwelling (Vincent et al. 2012a, b). Generally, SST remains high during the early stage of a TC and decreases with time during its lifetime. This has been observed by previous studies (Sanap et al. 2020; Naskar and Naskar 2021). If we take an area average value of SST at this genesis stage, that will be comparatively higher than the mature or dissipation stage. Whereas the pressure (max wind speed) will be comparatively higher (lower) during the early or dissipation stage than in the mature stage. This may result in higher central pressure (lower max wind speed) corresponding to higher SST (in the early stage), lower central pressure (higher max wind speed) corresponding to lower SST (in the mature stage) and higher central pressure (lower max wind speed) corresponding to lower SST (in dissipation stage). Hence in this study, it is not clear whether SST is responsible for the intensity change of TCs during their life period.

Figure 4
figure 4

Variations of central pressure of intense TCs with (a) SST, (b) 200 hPa divergence, (c) mid-tropospheric relative humidity and (d) mid-tropospheric instability.

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Figure 5
figure 5

Variations of wind speed of intense TCs with (a) SST, (b) 200 hPa divergence, (c) mid-tropospheric relative humidity and (d) mid-tropospheric instability.

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Upper-level divergence is an essential parameter for TCs intensification. It acts as the outflow in the upper level. Rappin et al. (2011) opined that an outflow layer in the upper level could modify TC’s core structure so that TC outflow could access weak inertial stability in the environment, which minimized an energy sink of the tropical cyclone secondary circulation and led to rapid intensification. Naskar and Naskar (2021) showed that 200 hPa divergence reached its peak during the maximum intensity of SuCS Amphan. In figures 4(b)/5(b), central pressures/max wind speed of all TCs have been plotted against 200 hPa divergence values during TCs’ lifetime for the period 1990–2019. It is seen that there is a decreasing (increasing) trend of 200 hPa divergence with central pressure (max wind speed) of TCs. But this trend is not uniform as many points show the high divergence corresponding to high central pressure (low max wind speed) and low central pressure (high max wind speed) corresponding to low divergence; the R2 value is –0.33 (0.44). This may be due to the divergence variations at different stages of TCs. Generally, during genesis moderate divergence, during intensification maximum divergence, and during decay weak divergence/convergence is observed (Naskar and Naskar 2021). This means the magnitude of divergence at depression during genesis will be comparatively higher than the magnitude of divergence at depression during decay. Moreover, divergence is also not uniform to central pressure/max wind during intensification in all TCs. The reason behind this is not apparent. We have tried to find out the relations between TCs intensity and divergence at different stages (figures not shown) but not found any significant correlation in the respective stages.

MRH and MI (Instability) are also essential factors for the genesis and intensification of TCs (Gray 1979; Kotal et al. 2009). High MRH ensures the moistening of the middle troposphere and helps TC’s intensification. Kotal et al. (2009) showed that MRH first increased slightly and then became stable during their lifetime for developing systems. The genesis of TCs is characterized by intense convective activity, which is associated with MI. It is the temperature difference between 850 and 500 hPa. It increases during the initial stages of TCs and then decreases (Kotal et al. 2009). Figures 4(c)/5(c) and 4(d)/5(d) show the variations of central pressure/max wind with MRH and MI. Though there are decreasing (increasing) trends of central pressure (max wind) with MRH and MI, they are not significant. The R2 values corresponding to TCs central pressure and max wind to MRH are –0.28 and 0.38, respectively. The R2 values corresponding to TCs central pressure and max wind to MI are –0.28 and 0.21, respectively. This may be because the values of MRH and MI do not change much during the lifetime of TCs. Most of the values of MRH and MI are between 70–95% and 21–23°C, respectively, during the lifetime of TCs. This suggests that though a certain amount of MRH and MI is required for the genesis and intensification, they are not explicitly related to the intensity variations of TCs during their lifetime.

VWS is also an essential factor for the genesis (Gray 1968) and intensification of TCs. It is the primary environmental control during the formation and early intensification stage over regions of significant ocean heat content (Park et al. 2012). Low VWS acts in initiating a conducive environment for cyclone movement and sustainment. Generally, VWS remains low and does not change much throughout the lifetime of a TC except in the dissipation stage (landfall). Its values remain within 5–10 m/s for most of the TCs. The relationship of VWS with central pressure/max wind has not been shown here. But from the correlation matrix (figure 9) it is seen that the relation between VWS and TCs intensity (central pressure/max wind) is not significant. The R2 values corresponding to VWS and TCs central pressure and max wind based on the ERA5 data are –0.16 and 0.14, respectively.

SLHF transfers latent heat (resulting from water phase changes, such as evaporation and condensation) between Earth’s surface and the atmosphere through turbulent air motion (Naskar and Naskar 2021). It plays a vital role in the ocean surface energy balance. It is the primary source of energy fueling TC development (Ooyama 1969) and intensification. It can provide convective instability and help develop convective activity (Cheng and Wu 2020). Like other parameters, the variations of central pressure and max wind with SLHF have also been examined. There are two seasons for TCs genesis over BoB; namely pre-monsoon and post-monsoon, the variations of central pressure with SLHF in pre-monsoon and post-monsoon seasons have been plotted separately to observe if there is any difference in the relationship during these seasons. Figure 6(a) shows a significant relationship between central pressure and SLHF for the entire period. It is seen that when there is a strong upward release of latent heat energy in the form of surface latent heat flux, the central pressure is minimum and vice versa. The variations of central pressure with the SLHF in different seasons, as depicted in figure 6(b and c) are also significant (R2 = 0.64 and 0.72) and show the same trend as figure 6(a). However, from figure 6(b and c), it is observed that SLHF is higher in the pre-monsoon season than in the post-monsoon season. This may be due to higher SST in the pre-monsoon season. The variation of SLHF with the max wind in figure 7(a) depicts a very high correlation (R2 = –0.81) in fact, this is a little higher than that with central pressure (R2 = 0.74). We have also compared this result with satellite-derived MERRA2-TLEF and MERRA2-max wind. MERRA2-max wind vs. MERRA2-TLEF in figure 7(b) also shows a very high correlation (0.62). This indicates a significant relationship between SLHF/TLEF with TCs intensity. It shows that the higher the SLHF value, the lower the central pressure (higher is the max wind). The reason may be due to the ‘evaporation-wind’ feedback mechanism known as wind-induced surface heat exchange (WISHE) (Emanuel 1994; Emanuel et al. 1994; Montgomery et al. 2009; Zhang and Emanuel 2016; Cheng and Wu 2020). We have also shown the correlation between ERA-wind and MERRA-wind in figure 7(c) to compare the ERA and MERRA winds during the lifetime of intense TCs. It is observed that the correlation between ERA-wind and MERRA-wind is very high (R2 = 0.80). This indicates that model-derived ERA-wind is in good agreement with satellite-derived MERRA-wind.

Figure 6
figure 6

Variations of central pressure of intense TCs with SLHF during (a) all the season, (b) pre-monsoon, and (c) post-monsoon.

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Figure 7
figure 7

(a) Variations of SLHF and max ERA-wind, (b) variations of TLEF and max MERRA2-wind, and (c) correlation between max MERRA2-wind and max ERA-wind.

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Scientists have observed that, generally, SLHF is closely associated with SST. Li et al. (2011) observed that an increase in SST directly contributes to the change in SLHF. Yu and Weller (2007) indicated that an increase in SLHF is mainly associated with an increase in SST. In this study, variation of SLHF with SST during the lifetime of TCs has been plotted in figure 8(a). It is seen that higher SLHF is associated with higher SST, but this relationship is not very accurate as many points depict lower SLHF as corresponding to higher SST. The R2 value of the fitted line is also –0.43. As discussed earlier, the SST value changes from high to low during a TC’s lifetime. This means the SST value in the mature stage is comparatively lower than in the genesis stage. But the value of SLHF increases with an increase in TC intensity. This may be the reason behind this low correlation. It is clear that SST is weakly correlated with SLHF whereas SLHF is strongly correlated with wind speed. Hence it can be argued that during the passage of a highly intensified cyclone over a warm-ocean and the resulting cooling of the sea surface, it is the strong aerodynamic effect under very strong winds which accelerates the evaporation process and maintains the same rate of latent flux transfer to the atmosphere.

Figure 8
figure 8

Variations of SLHF with (a) SST, (b) 200 hPa divergence and (c) MI.

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Upper-level divergence and MI are also thought to be related to SLHF. SLHF against 200 hPa divergence and MI have been plotted in figure 8(b and c), respectively. It is seen that SLHF is higher when upper-level divergence is strong and vice versa though this relation is not significant (R2 = –0.30 and 0.21). As seen earlier, the values of VWS and MI do not vary much with TC intensity. MI values are between 20–24°C for all values of SLHF. But the value of SLHF changes with TC intensity. The higher the SLHF value, the higher the intensity. This may be the reason behind this low correlation.

The correlation matrix in figure 9 summarizes all the relationships among the parameters (IMD-pressure, IMD-wind, ERA-wind, MERRA-wind, MERRA-TLEF, ERA-SHLF, ERA-pressure, ERA-200 hPa divergence, ERA-VWS, ERA-SST, ERA-MI and ERA-MRH). From this matrix, we can readily find how they correlate. It is observed that ERA-SLHF has very high correlations with ERA-pressure (R2 = 0.74), IMD-pressure (R2 = 0.64), ERA-wind (R2 = –0.81), MERRA-wind (R2 = –0.74), IMD-wind (R2 = –0.65) and MERRA-TLEF (R2 = –0.66). It is also observed that IMD-wind is highly correlated with IMD-pressure (R2 = –0.96), ERA-wind (R2 = 0.69), MERRA-wind (R2 = 0.57) and ERA-pressure (R2 = –0.66). It is also observed that ERA-wind is highly correlated with IMD-pressure (R2 = –0.65), IMD-wind (R2 = 0.69), MERRA-wind (R2 = 0.80), MERRA-TLEF (R2 = 0.60) and ERA-pressure (R2 = –0.82). There is also a good correlation between ERA-upper-level divergence and ERA-MRH (R2 = 0.52), which signifies that strong divergence in the upper level enhances moistening in the middle troposphere. The correlations among other parameters are very small or insignificant. It is clear that during the life period of a TC, intensity is highly correlated with SLHF.

Figure 9
figure 9

Correlation matrix of different parameters of intense TCs over BoB.

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Figure 10 shows the variations of SLHF and central pressure for nine different TCs in the categories of SuCS, ESCS, and VSCS, respectively. It is seen that when central pressure is minimum (976.3 mb) the SLHF is maximum, and when central pressure is maximum (1000.6 mb) the SLHF is minimum.

Figure 10
figure 10

Pictorial example of variations of SLHF with central pressure for nine different intense TCs over BoB.

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Figure 11 shows the composite mean of SLHFs during the lifetime of all TCs during the study period. In this figure, we have also overlaid the genesis locations of intense TCs on the composite mean of SLHFs. It is found that SLHF is the maximum in the regions 8–14°N and 88–94°E, which is also the location where the maximum number of the genesis of intense TCs occurs.

Figure 11
figure 11

Composite mean of surface latent heat flux for all the intense cyclones during the period 1990–2019.

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4 Conclusions

From the analysis of section 3, it is clear that the maximum number of intense TCs in the BoB form in the post-monsoon season and particularly in November. Almost 60% of these intense TCs originate in the region 8°–14°N and 88°–94°E. The composite mean of SLHF shows that the locations of higher SLHF coincide with the maximum number of genesis locations. Therefore, it can be considered an essential parameter for the genesis of TCs. The SLHF has higher values in the pre-monsoon season compared to the post-monsoon season. Almost 65% of these TCs have SLHF values between 800 and 1400 KJ m–2. Out of all the parameters like SST, SLHF, MI, MRH, VWS, and 200 hPa divergence, SLHF is mostly correlated with the central pressure/max wind of intense TCs. The increase and decrease of SLHF correspond to the increase and decrease in TCs intensity. The highest SLHF corresponds to the lowest central pressure (highest wind speed) and vice versa. Thus, SLHF is the most important among the parameters discussed above for TCs intensification.