1 Introduction

Tropical cyclones (TCs) are rapidly spinning and most significant natural hazardous systems that carry high wind speeds and rainfall (Mohanty et al. 2012; Mohapatra et al. 2015). They are generally characterized by a low-pressure center developed over a warm ocean region and intensified under favorable prevailing meteorological conditions. Warm ocean transports more energy to the atmosphere in the form of sensible and latent heat, which supports the creation of a low-pressure rotating frame via key atmospheric thermodynamics related to low-level dynamical convergence, which contributes to the intensification of the surface low to cyclonic storms (Rao and Prasad 2007).

The TCs are mainly developed throughout the pre-monsoon and post-monsoon seasons. The nearby existence of an equatorial trough over the NIO may account for a seasonal incidence of TCs in the open ocean (Ramage 1974; Vishnu et al. 2019). Among the world’s oceans, the NIO, which includes the Arabian Sea (AS) and the Bay of Bengal (BOB), is a highly active area for the growth of TCs (Balaji et al. 2018) and is responsible for 7% of all TC formations worldwide (WMO 2014). TCs significantly impact the loss of the human race, physical property, ecosystem, and environment at different levels. Therefore, accurate forecasting of cyclone tracks, intensity, and landfall is critical for reducing socioeconomic risks. According to some previous studies, the track prediction has been enhanced due to consideration of new parameterization schemes in the advanced numerical modeling and up-gradation in the data assimilation technique (Mohanty and Gupta 1997; Rao and Bhaskar Rao 2003; Mandal et al. 2004; Mohanty et al. 2019; Mohan et al. 2019). However, intensity forecasts remain a complex problem (Bender and Ginis 2000; Knaff et al. 2003; Krishnamurti et al. 2005; De Maria et al. 2005; Rogers et al. 2006) and still lag behind improvements in track prediction.

Furthermore, the modeling approach has been carried out by several studies using the ARW model to evaluate the influence of physical parameterization schemes for forecasting TC track and intensity (Raju et al. 2011; Pattanayak et al. 2012; Deshpande et al. 2012; Chandrasekar and Balaji 2012). The convective process and PBL dynamics play an essential role in the genesis and intensification of TCs among all schemes examined in the WRF-ARW model. However, microphysical parameterization has a considerable impact on TC track prediction (Raju et al. 2011; Chandrasekar and Balaji 2012). Using the ARW model, the TC track, intensity, and rainfall along with Kain–Fritsch (KF) convective and Yonsei University (YSU) PBL schemes are well simulated for TC Gonu (Osuri et al. 2012, 2013). Kanase and Salvekar (2015) show that the Bettes-Miller-Janjic (BMJ) combined with the YSU PBL scheme replicated improved results for the TC Laila. However, Sun et al. (2014) found a well-simulated TC track with the combination of Grell-Devenyi (GD) convective and Mellor-Yamada-Janjic (MYJ) PBL. The outcomes from previous studies using the Non-Hydrostatic Mesoscale Model (NMM) with the combination of KF convective parameterization scheme (CPS) and YSU PBL to forecast track and strength for TC Gonu, Sidr, and Nargis were not really adequate (Srinivas et al. 2013; Mohandas and Ashrit 2014).

From the studies mentioned above, it is still challenging to identify an appropriate convective and PBL parameterization scheme to predict the TCs over the NIO basin. In this present study, the numerical simulations have been carried out using ARW model version 3 with three convective, two PBL, and two microphysical parameterization schemes over the NIO basin. This study aims to evaluate an appropriate physical parametrization scheme within the model for the numerical simulations of TCs (to predict the track, intensity, and landfall). This assessment analysis will help to improve the operational model setup for productive use in TCs forecast.

1.1 TC case description

Since 1977, this is the first time when two very severe cyclones Luban and Titli came simultaneously to the NIO region. The cyclonic storm Luban had activated in the AS and did not affect any coast of India, while Titli had activated in BOB and was forecasted to hit the coasts of Odisha and North Andhra Pradesh. The genesis of both TCs started when the disturbance began in the open ocean as a result of the active Inter Tropical Convergence Zone (ITCZ) has begun to move southward toward the coast. Both cyclones had in common the pre-conditioning of the upper ocean in 2018 due to the co-occurrence of El Niño, the positive phase of the Indian Ocean dipole, and the cold phase of the Pacific decadal oscillation, all of which worked in tandem to warm the AS and sections of the BOB. The advent of the Madden–Julian oscillation (MJO) and the mixed Rossby-gravity wave during the first week of October caused the emergence of Luban in the AS. The eastward propagation of the MJO and the associated enhanced convection from the AS toward the region of origin of Titli, together with the arrival of the downwelling oceanic Rossby wave, prompted the birth of Titli in the BOB (Chowdhury et al. 2021; Srivastava et al. 2021).

1.2 Luban

According to the IMD report (2018), Luban was the third TC that goes up to the very severe cyclonic storm (VSCS) stage over the NIO region in 2018. Luban had been activated on 6th October in the central AS and followed a general west-northwestward path for most of its existence.

On October 6th, IMD well recognized the system as being in the depression stage. The depression stage had been upgraded to a deep depression on October 7th. The TC Luban on October 8th was designated as a cyclonic storm (CS) by the IMD classification; when it had swirling rainbands around a robust central thunderstorm region, there was clear outflow to the north. According to Joint Typhoon Warning Center (JTWC), the circulation became more distinct over time, generally steered west-northwestward by a subtropical ridge to its north (JTWC report 2018). Luban was again upgraded to a severe cyclonic storm (SCS) on October 9 by the IMD as thunderstorms started to bloom over the circulation. On October 10th, Luban was further upgraded by IMD to a VSCS, with a maximum sustained wind speed of 33 ms−1, similar to a category 1 hurricane. On the same day, both the IMD and the JTWC projected that Luban would attain a maximum wind speed peak of 39 ms−1. Besides, they also predicted that the storm would remain at its general trajectory and strike the Arabian Peninsula.

On October 13th, Luban signaling re-intensification due to increasing thunderstorm activity. On October 14th, Luban made rainfall around 6 UTC over eastern Yemen, about 30 km south of Al Ghaydah, with a wind speed of 21 ms−1. On October 15th, the storm rapidly dissipated over the dry and mountainous terrain. TC Luban caused flooding in Somalia, Yemen, and Oman. Whereas fourteen people were killed in Yemen when heavy rainfall cut off villages and destroyed roads. In Oman, a small locust outbreak occurred due to desert rainfall, and the entire country’s damage was reported to be worth $1 billion.

1.3 Titli

Titli was a deadly and devastating TC that caused a high socioeconomic loss in Eastern India and Bangladesh. The cyclonic storm emerged from low pressure in the Andaman Sea on 6th October 2018 and further moved west-northwestwards.

The depression was well identified by IMD on 8th October 2018 and upgraded to deep depression on October 9th. This was further intensified on October 10th and upgraded to a VSCS phase, and on the Saffir–Simpson scale, it was comparable to a category 3 hurricane. Titli made landfall near Palasa (Andhra Pradesh) and the south coast of Odisha from 2300 to 0000 UTC. Moving further north-northwestwards, it started weakening to an SCS on 11th October and a CS on the same evening. Furthermore, the system started progressing northeastwards under the influence of southwesterly winds from 11 p.m. on 12th October and progressively dissipated into a low-pressure area (LPA) around Gangetic West Bengal and neighboring Bangladesh on the morning of 13th October 2018. Due to heavy rainfall and landslides, it appealed to the lives of many people in Andhra Pradesh, Odisha, and other coastal regions (RSMC report 2019). The model description and methodology are discussed in the “Model description and methodology” section. Detailed information about the data used is discussed in the “Data used” section. The simulated results are discussed in the “Results and discussions” section. The conclusion and findings are discussed in the “Conclusion” section.

2 Model description and methodology

In the present study, we have considered TC Titli (October 8–12, 2018) and Luban (October 6–15, 2018). Both TCs are severe cyclones, and it is infrequent when BOB and AS host cyclonic storms of this strength at the same time. Titli has been developed over the BOB and Luban over the AS in the NIO region. Luban did not affect India’s coast, whereas Titli hit the coast of Odisha and adjoining North Andhra Pradesh.

The numerical simulations are carried out using the WRF model version 3 (release 3.9.1). WRF is a non-hydrostatic next-generation mesoscale model with a range of nesting capabilities (Skamarock and Klemp 1992; Wang et al. 2004; Skamarock et al. 2005). The WRF model offers many different physics options to signify cloud properties, solar radiation, precipitation, and surface and boundary layer process. Many previous studies already tested the performance of this WRF version over different oceanic basins and discovered that the model can reasonably predict/simulate tropical storms and rainfall occurrences (Mahala et al. 2019; Hon 2020; Baki et al. 2022; Makar and Pant 2022). Therefore, on previous considerations, this model version has been chosen for a single domain with a spatial resolution of 9 km and 35 vertical levels up to 100 hPa (Fig. 1). Presently, physical parameterization options are comprised in the WRF model (Skamarock et al. 2019), i.e., microphysics, cumulus parameterization, PBL parameterization, longwave and shortwave radiation, surface layer, and land surface parameterization (Gunwani and Mohan 2017). The twelve experiments have been designed using three convective (KF, BMJ, and GD), two PBL (YSU, and MYJ), and two microphysics Lin (Lin et al. 1983) and WDM6 (Rutledge and Hobbs 1984) schemes. The previous studies suggested that the mentioned schemes are the best suitable schemes for the prediction of TC track, intensity, and rainfall (Pattanayak and Mohanty 2008; Mohanty et al. 2010; Osuri et al. 2012 and 2013). Therefore, with the continuation and following the proposed objective of this study, these schemes’ combinations have been chosen. Detailed information about the model configuration and experiment design is discussed in Tables 1 and 2.

Fig. 1
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The topographical map indicates the model domain and terrain height (in meters)

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Table 1 The ARW-WRF model configuration parameterization schemes were used in this study
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Table 2 Experiments are designed for the simulations with the combination of PBL, MP, and Cumulus parameterizations
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The PBL schemes are different in their closure approach, such as local and nonlocal. The Mellor-Yamada-Janjić (MYJ) is classified as a local 1.5-order turbulence closure scheme (Janjic 1994). MYJ uses turbulent kinetic energy to parameterize eddy diffusivity through local vertical mixing. The Yonsei University (YSU) PBL is typically a nonlocal 1st-order turbulence closure parameterization scheme that uses k-theory to describe the role of turbulence upon the mean variables (Hong and Lim 2006). It is an updated version of the medium-range forecast (MRF) scheme (Hong and Pan 1996). The YSU PBL accompanies an explicit treatment of the entrainment process at the top of the boundary layer and rectifies systematic biases of the large-scale features such as cold bias.

Three convection schemes are tested based on target differing vertical transport strengths. First, Kain and Fritsch (KF) is a shallow and deep convection scheme used for a mass-flux approach to parameterizing both updraft and downdraft (Kain and Fritsch 1993). The mixing is permitted in all vertical levels through entrainment and detrainment processes with the CAPE removal duration. The KF scheme entails a convective triggering function (in light of grid-resolved vertical velocity), closure assumptions, and mass-flux formulation. Second, Betts, Miller, and Janjic (BMJ) is assessed as a convective adjustment scheme rather than mass flux that forces soundings toward the reference profile of specific humidity and temperature at every grid point (Betts and Miller 1986; Janjic 1994). The scheme’s structure favors enactment when substantial moisture measures are available in the low- and mid-level with flattering CAPE. Third, Grell and Devenvi (GD) is an ensemble convective parameterization scheme that incorporates several mass-flux cumulus schemes with diverse precipitation efficiencies and updraft and downdraft entrainment as well as detrainment parameters (Grell and Devenyi 2002). Moreover, the dynamic control closure depends upon moisture convergence, CAPE, and low-level vertical velocity.

3 Data used

We have considered the National Center of Environmental Prediction (NCEP) Final (FNL) operational global analysis data at 1° × 1° spatial resolution and 6-h temporal resolution for the initial and boundary condition. This item is from the global data assimilation system, which continually gathers observational information from the global telecommunication system (GTS). We have used IMD data to validate intensity, central sea level pressure (CLSP), and cyclone track. GPM data at 0.1° × 0.1° spatial resolution and half-hour temporal resolution are used to validate the rainfall distribution.

4 Results and discussions

The prediction of cyclone track, intensity, and landfall is measured as the utmost critical and challenging concern. In contrast, a misplaced forecast of the cyclonic center will produce an approximate location of rainfall and intensification of TCs, which could cause high socioeconomic loss. Therefore, a precise track forecast is significant to spot the physical position where huge damages would be expected due to high wind speed and extreme rainfall. For that purpose, numerical simulations have been carried out using the ARW model. The statistical errors have been calculated to validate the model outcomes, such as root mean square error (RMSE), mean square error (MSE), normalized mean square error (NMSE), index of agreement (IOA), and standard deviation (SD), as shown in Tables 3 and 4. The performance of schemes on different physical processes is discussed in “Cyclone intensity and track.”

Table 3 Statistical performance indexes of central sea level pressure (CSLP) and 10-m wind speed (WS10m) concerning IMD observations for Luban
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Table 4 Same as Table 3 but for Titli
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4.1 Cyclone intensity and track

The track and intensity prediction of TC by using the combination of three convection (KF, BMJ, and GD) schemes, two PBL (YSU and MYJ), and two microphysics (Lin et al. and WDM 6) schemes are discussed in this section. Figure 2 indicates that the BMJ CPS has better skill in predicting cyclone tracks with the grouping of WDM6 microphysics and MYJ PBL for Luban and YSU PBL for Titli, as compared with the IMD observations. From Fig. 3, the RMSE and vector displacement error (VDE) for the experiment MWBM are respectively < 80 km and < 8 km for TC Luban. For TC Titli, the YWBM VDE and RMSE are around < 100 km and < 10 km. The worse cyclone track is displayed by the GD scheme. When compared to other schemes, the GD scheme’s TC track for Titli is expanding substantially after 36 h of projection. As a result, the GD scheme was not chosen for the prediction of either TCs. Furthermore, in terms of predicting cyclone tracks, the KF scheme with the combination of YSU PBL and WDM6 microphysics comes in second. Over the entire forecast period, the VDE for Luban is < 130 km and the RMSE is < 12 km, while the VDE for Titli is < 200 km and the RMSE is < 13 km (see Fig. 3). The findings from the current study indicate reasonable mean track errors as compared to earlier research using simulations from the ARW model (Raju et al. 2011; Osuri et al. 2012 and 2013).

Fig. 2
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The model simulated the TC track for Luban and Titli at 12-h time intervals from different parameterization schemes

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Fig. 3
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The vector displacement error (VDEs, km) and root mean square error (RMSE, km) at 12-h time intervals for TC Luban and Titli. Here, the error bar indicates the standard deviation

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Furthermore, the TC intensity is conferred in the maximum sustained surface wind (MSW) speed and central sea level pressure (CSLP) in Fig. 4. For Luban, the observed least CSLP is around 980 hPa on 10th Oct 2018 at 12:00 UTC; however, for Titli, it is about 972 hPa at the same time (Fig. 4a,c). The results initially show that the BMJ-YSU scheme combination with WDM6 microphysics similarly followed the observation, but after midnight on 10th October, the CSLP was over-predicted. On the other hand, the KF convective with both the PBL MYJ and YSU overestimated the CSLP for the entire time frame. Figure 5a clearly shows that the CSLP for GD CPS with RMSE value ~ 9.26 hPa is close to the observation with the combination of YSU and Lin et al. scheme for Luban. However, for Titli, the BMJ convective scheme with MYJ PBL has an RMSE value is nearly 8.79 hPa (Fig. 5b). Figure 4b,d illustrates that the above-specified schemes affect the time series of maximum 10-m wind with the corresponding observations from the IMD. The maximum estimated surface wind is around ~ 38.5 ms−1 for Luban and ~ 41 ms−1 for Titli at 12:00 UTC on 10th October and 00:00 UTC on 11th October. The experiment MWKF and YWKF simulated maximum sustained surface wind ~ 25 ms−1 for Luban and Titli at 00:00 UTC on 11th October. The RMSE for the MWKF is approximately 7.13 ms−1 (Fig. 5a), and for the YWKF, it is ~ 9.75 ms−1 (Fig. 5b). The combination of BMJ and GD schemes with MYJ and YSU shows that the model is underpredicted the maximum sustained surface wind in the comparison of KF scheme (Fig. 4b,d). The KF scheme has a better ability to emphasize the small-scale features of updraft and downdraft, promoting steady convection (Kerkhoven et al. 2006; Osuri et al. 2013). BMJ is a convective adjustment scheme; therefore, the predicted convection profile (temperature and moisture) is balanced toward a reference profile in a quasi-equilibrium state because of deep convection. For this situation, the BMJ and GD scheme shows an absence of a low-level convergence, and in this way, diminishing convective activity in the improvement of the cyclonic framework.

Fig. 4
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The time series of predicted TC intensity in terms of central sea level pressure (hPa; a and c) and 10-m wind speed (ms−1; b and d) for Luban and Titli

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Fig. 5
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RMSE of CSLP (hPa; bars) and 10-m wind speed (ms−1; lines) for the different parametrization schemes combinations for (a) Luban and (b) Titli

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Tables 3 and 4 show the CSLP and 10-m wind speed statistics for several studies. The CSLP for Luban shows a low IOA magnitude for all combinations, which is below the acceptable range (0.7 hPa). The MSE, SD, and NMSE for experiment YLGD are 85.76, 6.99, and 5 × 10−6, respectively. Surface wind for MLKF, on the other hand, shows an IOA of 0.76, which is less than the acceptable range. The MSE (50.81) and NMSE (0.0075) for MLKF, as well as the SD (2.82) for YWKF, are lower than in other experiments (Table 3). Furthermore, for Titli, all combinations except MLBM for CSLP show a lower IOA magnitude than the acceptable range (0.7 hPa). The IOA, MSE, and NMSE for the experiment MLBM are in the range of 0.89, 77.32, and 7 × 10−6, respectively. The SD for the experiment MLGD is under an acceptable range than others. The MLKF’s surface wind suggests an IOA of 0.76, which is below the permissible range. The MSE (50.81), NMSE (0.0075), and SD (2.82) for MLKF and YWKF are lower than in prior studies (Table 4). The aforementioned results show that combining the KF convection scheme with the YSU and MYJ PBL schemes improves surface wind prediction, as proposed by previous studies (Raju et al. 2011; Osuri et al. 2013). However, predicting cyclone track BM convective with both PBL (i.e., MYJ and YSU) schemes has a better ability than the other schemes. Furthermore, the landfall of the cyclones is examined in terms of 24-h accumulated rainfall and statistical measures (e.g., equitable threat score (ETS), bias, percentage correct (PC), false alarm rate (FAR), and the probability of detection (POD)) and is discussed in “Rainfall prediction.”

4.2 Rainfall prediction

Figures 6 and 7 illustrate the model simulated 24-h accumulated rainfall for TC Luban and Titli along with GPM observations. The results are in agreement with Mohanty et al. (2010) and indicate that the WRF model is capable enough to simulate rainfall patterns. For TC Luban, the rainfall distribution is well captured by MLBM and very close to the GPM observations. The GD scheme with the combination of YSU and MYJ PBL has failed to predict the rainfall intensity, whereas the KF scheme is overestimated and displaced southward. BMJ CPS with YSU and MYJ PBL simulates the rainfall precisely in view of spatial distribution near the West Bengal and Bangladesh coast. Furthermore, the quantitative rainfall for TC Titli is exaggerated. The simulated rainfall using the KF scheme, on the other hand, is displaced northwards and overestimates the rainfall intensity. The GD scheme fails to reproduce the spatial distribution of precipitation, but in terms of amount, it outperforms with both PBLs (Fig. 7).

Fig. 6
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The spatial distribution of accumulated rainfall (cm) during the landfall of Luban from (a) GPM, (b) YLKF, (c) YLBM, (d) YLGD, (e) MLKF, (f) MLBM, (g) MLGD, (h) YWKF, (i) YWBM, (j) YWGD, (k) MWKF, (m) MWBM, and (l) MWGD schemes

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Fig. 7
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Same as Fig. 6 but for the Titli

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The bias and equitable threat score (ETS) for 24-h accumulated rainfall at different thresholds are evaluated to check the ability of individual experiments corresponding to the observed rainfall patterns from GPM, as shown in Fig. 8, and the observed outcomes are reasonably matched with the previous studies (Osuri et al. 2012; Mahala et al. 2019). In the case of Luban, the MLBM experiment has better skill in the prediction of quantitative rainfall with an ETS score > 0.45 at lower threshold (up to 60 mm) (Fig. 8a). The bias of MLBM is > 1 compared with MLKF from the threshold 40 mm onwards, which means the MLBM experiment overestimates the rainfall (Fig. 8c). Whereas YLKF, YLBM, MLKF, and YWKF experiment predict the quantitative rainfall well with an ETS score of more than 0.6 at the threshold of 20 mm in the case of Titli. In contrast, the YLBM experiment predicts better rainfall at the threshold of 40 mm and 60 mm with an ETS score of < 6 and < 2, respectively. The YWBM experiment indicates excellent rainfall predictability skills at a higher threshold (from 60 mm onwards) with a higher ETS score than others (Fig. 8b). The bias of YLBM and YWBM schemes are higher (> 1) compared with the MLGD at greater threshold 60 mm onwards, indicating that YLBM and YWBM experiments overestimate the rainfall (Fig. 8d).

Fig. 8
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The equitable threat score (ETS) and bias at different threshold bins for the last 24-h rainfall (i.e., during landfall)

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Tables 5 and 6 derive statistical performance indices (e.g., PC, FAR, and POD) for rainfall forecast verification at various thresholds. In the case of Luban, MLBM has higher PC skill (nearly 1), lower FAR, and higher POD in the prediction of rainfall at all thresholds (Table 5). At the 20-mm barrier for Titli, the PC for the KF scheme with MYJ is 0.969, but above the 20-mm threshold, the PC for the BMJ convective scheme with the YSU PBL is greater (close to 1). The FAR is lower for the BMJ scheme with the combination of both PBLs, and the POD is higher from the threshold of 80 mm onwards. The values, compared with that similar reported works (Federico et al. 2003, 2008; Avolio and Federico 2018), show a good performance of WRF simulations. The above result illustrates that the combination of BMJ convective with YSU and MYJ PBL scheme can better predict the rainfall distribution. Furthermore, the TC structure is analyzed to understand the dynamical and thermodynamical aspects, as discussed in “Structure of the tropical cyclones.”

Table 5 Statistical performance indexes for the rainfall forecast verification for Luban
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Table 6 Same as Table 5 but for Titli
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4.3 Structure of the tropical cyclones

The longitudinal cross-section of horizontal wind speed (ms−1) along with the cyclone center for all the experiments is presented in Figs. 9 and 10. The KF-YSU and KF-MYJ combination indicates a steady rising motion (45 ms−1) extended up to 100 hPa from the surface in the east–west plane around the storm center in the case of Luban. Moreover, the KF scheme demonstrates the well-defined TC core region and GD convection with YSU and MYJ presented weak rising motion (25 ms−1) and described the cyclone’s worst eyewall (Fig. 9). The same results have been observed in the case of the TC Titli. The KF convection shows a steady rising motion (25 ms−1) extended up to 200 hPa from the surface in the east–west plane around the storm center. The KF convective demonstrates a well-defined eyewall, and on the other hand, GD convection with YSU and MYJ represented weak rising motion (16 ms−1) and described the worst eyewall (Fig. 10). The results show that the KF scheme allows for deep convection in the air column with robust updraft and downdraft. In both cyclonic cases, all the BMJ and GD scheme simulations with YSU and MYJ are not able to determine the strong updraft except MLBM, as simulated by the KF scheme. The experiment MLBM shows a maximum rising motion of 35 ms−1 for Luban and 16 ms−1 in the case of Titli. In terms of intensity, MLBM is not good as KF with YSU and MYJ, but it shows a well-defined eyewall of the cyclone. The results indicate that the KF scheme has a better ability to predict intensity for severe weather conditions such as a TC (Pattanayak and Mohanty 2008).

Fig. 9
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The spatial distribution of east–west cross-section horizontal wind speed (ms−1) through the center of Luban from different experiments: (a) YLKF, (b) YLBM, (c) YLGD, (d) MLKF, (e) MLBM, (f) MLGD, (g) YWKF, (h) YWBM, (i) YWGD, (j) MWKF, (k) MWBM, and (l) MWGD

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Fig. 10
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Same as Fig. 9 but for the Titli

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The vertical profile of equivalent potential temperature (θe) for different convection and PBL schemes are shown in Fig. 11. The θe is generally used to analyze the thermodynamical progressions in the matured stage (very severe condition) of the TC (Dolling and Barnes 2012). According to Sikora (1976), the incredibly high equivalent potential temperature can signal a phase of subsequent explosive deepening. These characteristics of warm core structures with profound warming are most likely due to the combined effect of the following: (1) large-scale upward surface fluxes of sensible and latent heat from the underlying warm ocean due to strong updrafts in the eye wall region and (2) a significant reduction in cooler penetrative downdrafts due to increased warming tendencies in the TC core (Pattnaik and Krishnamurti 2007). The area-averaged vertical variation is shown over 100 km of radius from the TC eye. KF-YSU and KF-MYJ indicate higher θe values and intense vertical mixing throughout the pattern, whereas the GD scheme shows less θe value at the surface and mixing taking place up to 500 hPa in the case of Luban (Fig. 11a). Similarly, for TC Titli, results indicate the KF scheme with YSU and MYJ infers high θe values and intense vertical mixing up to 400 hPa. However, the GD scheme shows less θe values at the surface and vertical mixing is taking place up to 600 hPa (Fig. 11b). The θe values of the BMJ scheme with MYJ lie between KF and GD schemes. The result proposes that the boundary layer’s illustration is determined more convincingly in both the PBL (YSU and MYJ). Because of the intense vertical propelling of heat, a warmer TC core can form and increase cyclone intensity (Raju et al. 2011). The combination of the GD scheme with YSU and MYJ PBL shows the surface value of θe is less in comparison to the KF scheme, thus reducing the vertical propelling of heat around the system. The overall discussion indicates the model performed well to simulate the cyclone track, intensity, and landfall with the comparison of observational analysis.

Fig. 11
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The vertical profile of area-averaged equivalent potential temperature (°K) at a 100 km radius from the storm center for (a) Luban and (b) Titli

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5 Conclusion

The twelve experiments with three convection, two PBL, and two microphysical parameterization schemes have been designed to carry out the numerical simulations using the WRF-ARW model to forecast the TC Luban and Titli over the NIO region. The results demonstrate that the convective and PBL scheme controls the cyclone intensity, while the microphysics scheme impacts track prediction. The cyclone intensity is underestimated by the model in view of surface wind and overestimated for central sea level pressure for all sensitivity experiments. The KF convection scheme combined with WDM6 microphysics and MYJ PBL for Luban and YSU PBL for Titli has a better prediction skill of maximum sustained surface wind speed, accounting for RMSE is about 7.13 ms−1 for Luban and 9.75 ms−1 for Titli. However, The BMJ and GD scheme with the same combination of microphysics and PBL indicates that the RMSE value of maximum sustained surface wind speed is > 10 ms−1, which is more divergent from the actual. Also, the cyclone structure is well captured by MYJ–KF and YSU-KF in both space and time for Luban and Titli, respectively. The MYJ-BMJ combination is well capturing the TC track for Luban and YSU-BMJ for Titli with the WDM6 microphysics scheme. The vector displacement error and RMSE for the experiment MWBM and YWBM are < 100 km and < 10 km, respectively. MYJ-BMJ and YSU-BMJ with the Lin et al. microphysics scheme have better skills for rainfall prediction. The experiment MLBM has an equitable threat score of < 0.45 up to 60 mm, and at the higher threshold, it is < 0.3 up to 120 mm in the case of Luban. The YLBM experiment has an equitable threat score of < 0.6 up to 40 mm, and at 60 mm, it is < 0.2 for the case of Titli. The YWBM shows better predictability at a higher threshold. Overall, the tropical cyclones Luban and Titli’s track, intensity, and timing of landfall were accurately predicted by the WRF model, showing that the model has the potential to be used for operational purposes. Additionally, the model could precisely determine the spatial distribution of precipitation.

A precise prediction of cyclone track, intensity, and landfall remains a difficult issue, with much room for improvement through precise vortex relocation, initialization, and incorporation of satellites as well as other accessible information over the open ocean. The primary elements impacting cyclone prediction embrace model resolution, multiple parameterization schemes, and initial conditions including realistic steering flow. Therefore, improved initial conditions and enhanced data assimilation techniques may enable better prediction of tropical storm origin, structure, and intensity.