1 Introduction

Tropical cyclones (TCs) forming over the warm tropical oceans are major natural hazards that cause significant impacts on life, infrastructure and property over coastal regions due to the extreme winds, storm surges and flooding during their landfall. Recent climate change studies (Kossin et al., 2014; Song et al., 2020) suggest that TCs can cause increased coastal hazard due to increasing intensity of TCs under warming climate. The Bay of Bengal (BOB) of North Indian Ocean (NIO) region is highly susceptible for TCs with a high annual frequency (Rao et al., 2001). The TCs forming in the BOB cause recurring damages to the east coast due to their high frequency, low average life span and high intensity, which require development and application of advanced forecasting tools for effective disaster management (Raghavan & Sen Sarma, 2000). Numerical forecasting of TCs in the BOB is highly challenging due to the complex, non-linear scale interacting (storm scale-largescale) atmospheric processes involved (Davis et al., 2008; Gopalakrishnan et al., 2011, 2012). The physical processes such as air-sea interaction, turbulent mixing in the boundary layer, cloud microphysical and convection are important for accurate forecasting of the TCs.

An intriguing question of TC modelling is how well the models are able to resolve the convection that influences the intensity and track predictions. Convective parameterization (CP) schemes are typically employed in atmospheric models to represent the effects of deep moist convection at grid scales of ≥ 6 km (Stensrud, 2007). With the increased availability of computational resources, numerical weather prediction (NWP) models can be configured to simulate at very high resolutions, enabling the fine-scale features of the TCs to be resolved. Among the different features, the vertical circulation in the TC is crucial as it determines the potential of cyclones for further development. Recent studies reported large errors with CP schemes (Lin et al., 2008; Seifert, 2011; Song & Zhang, 2011) and suggested high resolution (≤ 3 km) models with explicit convection can better resolve the convection and precipitation processes without employing the cumulus parametrization schemes. For the NWP models operating at cloud-resolving scale (≤ 3 km), the cloud micro-physics driver will explicitly act as a cumulus driver. Numerical studies conducted for large number of TCs during the last three decades over the Atlantic basin (Davis et al., 2008; Gopalakrishnan et al., 2011, 2012) as well as in the BOB of the North Indian Ocean (Reshmi Mohan et al., 2019, 2022) suggest that high resolution models produced significant improvements in TC simulations by explicitly resolving the convection processes, thereby leading to improved intensity, track and structure prediction of TCs. However, the intensity and structure of simulated TCs in explicit model simulations are highly sensitive to the CMP schemes (Khain et al., 2016; Li et al., 2019; Makarieva et al., 2017; Maw & Min, 2017; Mooney et al., 2019; Parker et al., 2017; Reshmi Mohan et al., 2019; Zhang et al., 2019) due to their direct influence on thermodynamics of simulated storm environment and their indirect impact on the dynamical fields of horizontal and vertical winds. The CMP schemes can influence the numerical simulations via latent heating /cooling associated with condensation/evaporation processes. The lack of observational data, especially the vertical velocities in the region of TCs limits detailed evaluation of models. With the advancement of the land-based Wind Profiling Radars (WPRs) operating at very high frequency (VHF) (Dobos et al., 1995; May et al., 1995; Uma & Rao, 2009; White et al., 2015) continuous data on atmospheric vertical motions at the observation stations is now possible. Winds derived from profiling Radars are used in the past studies (Brown et al., 2009; Das et al., 2011, 2012; Dobos et al., 1995; May et al., 1995; Teshiba et al., 2004; White et al., 2015) for characterization of wind field, identification of convection, vortex stretching, precipitation and to predict the wind potential during the passage of TCs. These studies demonstrate the usefulness of WPRs in studying the dynamics of storms and for model validation studies.

In this work, the sensitivity of high resolution WRF simulations of TC Fani developed in BoB in April 2019 to various microphysics schemes: Lin, WSM6, Morrison, Thompson and Goddard is examined. The main objective of the work is to study the model ability to represent the convection associated with Fani using a range of data sets: WPR observations, multi-satellite data products of thermal anomaly and tangential winds and Doppler Radar reflectivity. The study is organized into five sections. Section 2 provides an overview of TC Fani. Section 3 gives details of the model domain and physics parameterization schemes used in this study along with brief description of various observational data used for model comparisons. Section 4 presents the results of the simulations. The conclusions of the study are provided in Sect. 5.

2 Overview of Fani Cyclone

The TC Fani, the focus of this study, formed over the BoB during the pre-monsoon season. Extremely severe cyclonic storm (ESCS) ‘Fani’ originated as a low-pressure system over eastern equatorial Indian Ocean at 0000 UTC of 25 April 2019. It became a depression in the southeast Bay of Bengal at 0300 UTC 26 April 2018 and developed into CS at 0600 UTC 27 April. It moved in the north-northwest direction and intensified into severe cyclonic storm (SCS) at 1200 UTC 29 April. It then became a VSCS in the next 12 h and ESCS in another 12 h by 12 UTC 30 April. Fani underwent rapid intensification with wind speed increase of 35 knots/18 ms−1 from 00 UTC 29 April to 00 UTC 30 April. The system had its peak intensity at 1500 UTC of 02 May with the lowest central pressure of 937 hPa and MSW of 115 knots. Subsequently, Fani gradually weakened and crossed the southern Odisha coast close to Puri between 0230 and 0430 UTC of 03 May with MSW of 85 knots (IMD, 2020).

3 Data and Methods

3.1 Numerical Simulations

The present study used the Advanced Research Weather Research and Forecasting (WRF-ARW) v.3.9. The technical description of WRF model is given in Skamarock et al. (2008). In this study, the WRF is configured with three two-way interactive nested domains with horizontal resolutions of 27 km, 9 km and 3 km and 45 vertical levels with model top at 10 hPa. The inner 3 km resolution domain covers the BOB and the adjacent continental areas. All the simulations are initialized at the stage of deep depression (intense low-pressure system with 2 or 3 closed isobars at 2 hPa interval and wind speed from 28 to 33 kts) as per the IMD best track data and the model is integrated up to dissipation to depression stage after making the landfall. Accordingly, the WRF model is initialized at 0000 UTC on 28 April 2019 and integrated for 144 h up to 0000 UTC 4 May 2019. The NCEP GFS 0.25° × 0.25° analysis data is used for model initialization and the boundary conditions are updated every 3 h with the GFS forecasts. The SST is updated from the GFS data. The model physics options used for the simulations are listed in Table 1. The cumulus parameterization is used only in the outer domains (27 km, 9 km).

Table 1 Model domain and physics configuration used in simulations
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To evaluate the model sensitivity to cloud microphysics, five bulk microphysics schemes namely WSM6, Morrison, Thompson, Lin and Goddard are tested. Lin scheme (Lin et al., 1983) is a mixed-phase single moment prognostic scheme for six classes of hydrometeors namely, water vapor, cloud water, rain water, cloud ice, rain, snow and graupel/hail. It assumes exponential particle size distribution and mass-weighted mean terminal velocity. This scheme explicitly parameterizes the collision-coalescence and collision-aggregation processes by auto-conversion and accretion processes of various liquid and solid hydrometeors. The WSM6 scheme (Hong & Lim, 2006) is a single-moment prognostic scheme with six species: water vapor, cloud water, cloud ice, rain, snow and graupel. This scheme allows supercooled water to exist and the melting of the snow as it falls below the melting layer. The Morrison scheme (2009b; Morrison et al., 2005, 2009a) is a double moment scheme with six hydrometeors namely, water vapor, cloud water, rain water, cloud ice, rain, snow and graupel/hail. It uses gamma distribution of particle size. The New Thompson scheme is a single moment scheme (Thompson et al., 2008) which predicts mixing ratio of six hydrometeors (water vapor, cloud water, cloud ice, rain, snow and graupel) along with number concentrations of ice and rain (double moment for ice and rain). Snow size distribution is assumed to depend on both ice water content and temperature. This scheme uses a generalized gamma distribution shape for each hydrometeor species. The Goddard is a one-moment scheme (Tao & Simpson, 1993) which predicts water vapor, cloud water, cloud ice, rain, snow and graupel. It uses inverse exponential size distributions and has an option to choose either graupel or hail as the third class of ice. It is based on Lin scheme for hail processes including hail riming, accretion of rain, deposition/sublimation, melting, shedding, and wet growth.

3.2 Observation Data Sets

The results from the simulations are compared against available observational data sets from different sources. Simulated central sea level pressure (CSLP) and maximum sustained wind (MSW), and track parameters are compared against the best track estimates from IMD. The error statistics (mean error) obtained as model value minus IMD intensity and track estimates is computed from 3-hourly model outputs for each microphysics experiment after the model spin up period of 12 h. Simulated hydrometeor reflectivity is compared against the available Doppler Weather Radar (DWR) products from IMD, Visakhapatnam (17.68° N, 83.21° E). The horizontal and vertical wind velocities in the region of cyclone are compared against the Mesosphere Stratosphere Troposphere (MST) radar data at National Atmospheric Research Laboratory (NARL) Gadanki station (13.45° N, 79.16° E) during the passage of cyclone close to Gadanki. In addition, the surface wind field, tangential winds and temperature anomaly are compared against the multi-satellite data products of Cooperative Institute for Research in Atmospheres (CIRA) of Colorado State University. The MST radar at Gadanki is used for atmospheric probing in the regions of Mesosphere, Stratosphere and Troposphere covering up to a height of 100 km (Rao et al., 1995). The MST Radar is highly sensitive pulse-coded coherent very high frequency phased array radar that operates with 53 MHz with an average power aperture of 7 × 108 Wm2 with a peak power of 2.5 MW. The phase antenna array consists of two orthogonal sets, one for each polarization, of 1024 three-element Yagi-Uda antennas that are arranged in a 32 × 32 matrix over an area of 130 m × 130 m (Rao et al., 1995). The MST radar observations used in the present study are obtained from a special observational campaign (Rao et al., 2020) at Gadanki (13.4593° N, 79.1684° E) during the passage of Fani from 0600 UTC of 29 April to 0300 UTC of 02 May 2019. During the observation campaign, the radar system was operated for about 60 h in the lower atmospheric mode to obtain wind parameters in the height range of 1.5 km–21 km. During the first two days of campaign (29 and 30 April 2019), the MST radar was operated only five times in a day (0500, 0700, 0900, 1100 and 1200 UTC) in multiple scan mode.

Simulated surface winds (at 10 m) are compared against the CIRA multiplatform satellite data (Knaff et al., 2011) products. The CIRA TC wind analysis is prepared at 10 km horizontal resolution at 6-h intervals using the variational technique (Knaff & DeMaria, 2006; Knaff et al., 2011) based on wind information from five data sets namely Scatterometer winds, Advanced Microwave Sounding Unit (AMSU) winds, Cloud-drift/IR/WV winds and IR-proxy winds. The objective wind analysis is available at surface (at 10 m) and mid-level (at 700 hPa) over a horizontal domain of 10° × 10° around the centre of TCs. The model derived azimuthally averaged tangential wind and temperature anomaly are compared against the CIRA products derived from the AMSU-A and B radiance (Demuth et al., 2004) data around the TC and prepared following the Demuth–DeMaria–Knaff (DDK) algorithm (Demuth et al., 2004).

4 Results and Discussion

Here we present the results of WRF simulated track and intensity parameters of Fani cyclone from different CMP experiments along with IMD estimates in Sect. 4.1. This is followed by detailed analysis of simulated horizontal and vertical wind distribution at Gadanki station and comparison of simulated vertical velocities with MST radar vertical velocity observations in Sect. 4.2. The simulated thermodynamical parameters such as theta-e, warming, diabatic heating etc. are discussed in Sect. 4.3 followed by the wind structure and simulated radar reflectivity in Sects. 4.4 and 4.5 respectively.

4.1 Track and Intensity Parameters of Fani

The simulated tracks of Fani obtained from the five microphysics experiments along with the observed track estimates are presented in Fig. 1a, and the corresponding vector track errors are shown in Fig. 1b. In general, it is found that the deviations in predicted tracks among different microphysics simulations are meagre in the initial stages but gradually increased after 24 h till the landfall. Simulated vector track errors increased to 100–150 km during rapid intensification phase (24–48 h), thereafter slightly decreased (25–125 km) till 72 h and then continuously increased until the landfall and beyond. The model captured the northward movement of Fani during the growing stages (0–48 h) of TC, and the northeast ward movement during intensification, landfall and dissipation phase after landfall. A qualitative and quantitative comparison of track errors (Fig. 1a, b; Table 2) indicates that Thompson followed by Lin, Morrison, Goddard and WSM6 produced least track errors at different time steps. The minimum landfall errors are produced by Thompson, Lin and Goddard.

Figure 1
figure 1

(a) Simulated 3-hourly vector track positions of TC ‘Fani’ along with the best track estimates of IMD (black line) starting from 0000 UTC 28 April to 0000 UTC of 4 May 2019 (b) time variation of vector track errors in km with respect to IMD track estimates

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Table 2 Track errors of Fani at 24-h interval excluding the first 12-h spin-up period computed from five microphysics simulations
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Various factors such as large-scale flow, Coriolis force, surface pressure, sea surface temperature, storm thermodynamics, wind shear etc., affect the track of a TC (Roy & Kovordányi, 2012). The differences in track forecasts produced by different CMP simulations can be related to the differences in warming in the upper layers and cooling in the lower layers produced by the microphysical processes (see subsequent discussions) affecting the temperature profile (Reshmi Mohan et al., 2019; Sun et al., 2015) thus affecting the thermodynamic and dynamic changes leading to changes in the movement of the storm.

The time evolution of simulated CSLP and MSW along with IMD estimates for TC Fani is presented in Fig. 2, and the error statistics are provided in Tables 3 and 4. All the simulations produced an increase (decrease) in wind speed associated with fall (rise) in the central pressure during the growing and intensification phases (during decay and landfall stages). As seen from Fig. 2, except Morrison all the other schemes closely captured the deepening, mature and weakening phases of TC Fani with slightly overestimation of pressure drop during mature phase (06 UTC 2 May–00 UTC 3 May). Although Morrison scheme captured the deepening of the observed storm, it considerably underestimated the pressure drop and intensity of winds during the peak stage. Lin and WSM6 schemes simulated the mature phase of the storm nearly 6 to 8 h before the actual time of attainment of peak intensity. The intensity is considerably overestimated (by 10 hPa) by Lin and WSM6. The simulation Thomson followed by Goddard CMP schemes closely captured the observed intensity of the storm during all the phases of the storm, however these schemes failed to capture the duration of mature phase (6 h). Overall, the error statistics of both mean and mean absolute errors with respect to IMD estimates (Tables 3 and 4) shows that the Thompson followed by Goddard simulations give a better agreement of intensity parameters with observations. To gain an understanding of the major factors behind producing these differences in the track and intensity predictions by CMP schemes, we further analysed the simulated vertical velocities, thermodynamics, wind field and reflectivity etc. in the following sections.

Figure 2
figure 2

Time evolution of WRF simulated a CSLP and b MSW of Fani cyclone along with IMD best track data

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Table 3 Mean CSLP errors computed from 3 hourly interval model outputs excluding the first 12-h spin-up period for the five microphysics schemes for Fani cyclone
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Table 4 Mean MSW errors computed from 3 hourly interval model outputs excluding the first 12-h spin-up period for the five microphysics schemes for Fani cyclone
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4.2 Simulated Horizontal and Vertical Winds at Gadanki Station

The time-height section of horizontal winds at Gadanki station from different CMP experiments during 28 April–4 May 2019 for Fani is presented in Fig. 3 along with data from MST-Radar during the period 1200 UTC 1 May and 1000 UTC 2 May 2019. The Gadanki station (13.46° N, 79.2° E) is situated about 100 km northwest of Chennai near Tirupati in Andhra Pradesh (Fig. 1). As per the IMD best track data, Gadanki station falls at a range of about 400 km from the centre of Fani during its passage in the east central Bay of Bengal. Simulations indicate stronger easterly/north-easterly winds between 30 April and 1 May for Fani at Gadanki station. The stronger winds are simulated in the layer 8–16 km upper tropospheric region. The strong simulated winds in the upper layers are due to the occurrence of localized thunderstorms events and meso-vortices developed in the presence of surface trough associated with the cyclone over the south-east coast. The simulations show gradual increase of winds, peaking as the cyclone approached east central Bay of Bengal and then gradual decrease of winds as the cyclone passed away. The stronger simulated winds in the upper layers are confirmed from the MST Radar data (Fig. 3f) which shows strong winds in the layer 10–18 km from 1200 UTC 1 May to 2000 UTC 2 May and slightly reducing in intensity thereafter. The radar data also shows strong winds in the lower layers (3–5 km) from 1200 UTC 1 May to 2000 UTC 2 May, which are underestimated by the model. Even though the pattern of winds is similarly produced in different CMP experiments, the intensity of simulated winds varied slightly which can be related to the differences in storm scale dynamics resulting from cloud scale—large scale processes in different microphysics simulations. Simulations with Lin, WSM6 and Goddard schemes produced stronger horizontal winds compared to other microphysics schemes.

Figure 3
figure 3

Time-height section of horizontal winds at Gadanki station from 0000 UTC 28 April to 0000 UTC of 4 May 2019 from different microphysics experiments of Fani cyclone a Morrison, b Lin, c WSM6, d Thompson, e Goddard along with f MST-Radar winds

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WRF simulated vertical velocities at Gadanki station during the passage of Fani in the east central Bay of Bengal are compared against MST Radar data. As no direct measurements of convection in the core region of cyclone are available, we have used the MST-Radar data of Gadanki away from the eye-wall of cyclone for comparison. Figure 4 shows the time-height section of simulated vertical velocities at Gadanki station from different CMP experiments along with MST Radar data from 1000 UTC 01 May 2019–1000 UTC 02 May 2019. Relatively strong vertical velocities (0.7 m/s) are simulated in the layer 8–15 km at Gadanki (Fig. 4a–e) during the passage of Fani in east central Bay of Bengal in all the experiments. The simulations also show downdrafts (− 0.2 m/s) in the upper layers. Both updrafts and downdrafts are stronger in the upper layers compared to the lower layers. The simulations Lin, WSM6 and Thompson (Fig. 4b–d) produced the strongest vertical motions at Gadanki throughout the simulation. Radar data at Gadanki (Fig. 4f) shows strong vertical motion of 0.5–0.9 m/s in the upper layers (10–17 km) and 0.1–0.5 m/s in the lower layers (2–8 km) in the period 1200 UTC 01 May–1000 UTC 02 May during the passage of the cyclone close to Gadanki. These features of strong vertical motions in the upper and lower layers in the period 1200 UTC 01 May–1000 UTC 2 May 2019 and with more intensity between 0000 and 0400 UTC are well simulated in most of the CMP experiments except Goddard which simulated downdrafts in upper layers in the period 1800 UTC 1 May to 0400 UTC 2 May and updrafts thereafter. The simulated and observed intense convective motions at Gadanki coincided with the peak intensification period of Fani as seen from the intensity plots (Fig. 2). The simulations with Thompson followed by WSM6 and Lin produced the strongest vertical motions whereas Morrison and Goddard simulated weak vertical motions in the 8 -15 km layer between 1200 UTC 01 May and 1000 UTC 2 May.

Figure 4
figure 4

Time-height section of simulated vertical velocities (ms−1) plotted for Gadanki station from 1000 UTC 1 May to 1000 UTC of 2 May 2019 from different microphysics sensitivity experiments (a) Morrison, (b) Lin, (c) WSM6, (d) Thompson, (e) Goddard schemes along with (f) MST Radar observed vertical velocities

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As the convective motions associated with storms rapidly fluctuate, to obtain a more representative comparison, the mean simulated vertical velocity profiles at Gadanki during 00 UTC 30 April – 00 UTC 1 May 2019 are compared with corresponding time-average observation profiles from MST Radar. As shown in Fig. 5, WSM6 followed by Lin and Thompson produced stronger vertical motions in different layers. The mean radar profiles indicate upward motions (0.05–0.15 m/s) in the lower 3–7 km region, and upper 10–13 km layer, and downward motion (− 0.05 m/s) in middle 8–10 km layer.

Figure 5
figure 5

(a) Time-averaged WRF simulated vertical wind profiles by different microphysics schemes compared with MST radar profiles at Gadanki and (b) vertical velocity error profile with respect to MST radar vertical wind observations during 0000 UTC 30 April – 0000 UTC 1 May 2019 for Fani

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The average errors of simulated vertical velocity (m/s) computed over different layers (1–5 km, 5–9 km, 9–13 km and 13–16 km) from different CMP experiments are presented in Table 5. Even though all the simulations captured the vertical trends similar to radar data, Thompson followed by Goddard and Morrison produced the closest agreement with average errors of − 0.014, 0.016 and 0.018 m/s respectively in the lower layers (1–5 km); Thompson followed by WSM6, and Morrison produced a closer match with mean errors of 0.005, 0.008 and − 0.034 m/s respectively in the middle layers (5–9 km); Lin followed by Morrison and Thompson simulated closely with mean errors of − 0.023, − 0.04 and − 0.061 m/s in the upper middle layers (9–13 km) and Goddard followed by Morrison and Thompson produced a better prediction with mean errors of 0.0316, − 0.070, 0.123 m/s in the upper layers (13–16 km). Overall, Thompson followed by Goddard and Morrison produced better agreement of mean vertical wind profile throughout the troposphere. The WSM6 produced overestimation of vertical winds in upper troposphere and Lin underestimated in the lower troposphere. As the Gadanki station is situated at about 400 km from the cyclone it shows weak echoes of convection.

Table 5 Mean errors in simulated vertical velocity w (m/s) at Gadanki during 00 UTC 30 April–00 UTC 1 May 2019 for the five microphysics schemes for Fani cyclone
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For a better assessment of simulated vertical motions, the deviations of simulated mean vertical wind profiles from the corresponding mean radar profiles are analyzed and shown in Fig. 5b. The central vertical line in Fig. 5b indicates ‘0 m/s’ error. As seen from Fig. 5b, even though both positive and negative errors are found in all simulations, Thompson, Goddard and Morrison produce relatively less vertical velocity errors in different layers. Among these three schemes the Thompson and Goddard schemes showed highly consistent trends of vertical motions in the lower, middle and upper layers suggesting better performance. These results suggest that the Thompson and Goddard microphysics schemes better represented the vertical motions in explicit simulations.

4.3 Storm Thermodynamics

The thermodynamic environment simulated in different CMP experiments is examined from equivalent potential temperature (theta-e) (Fig. 6), core warming (Fig. 7) and diabatic heating fields (Fig. 8). The warming produced in the upper regions of TC by subsidence and condensation and cooling produced in the lower regions by convergence and evaporation processes influence the intensity of the TC through coupling of thermodynamics and dynamics. The vertical cross-sectional view of simulated theta-e and vertical velocity (w) distribution of Fani at 1200 UTC 02 May 2019 (1800 UTC 01 May) from different CMP experiments is presented Fig. 6. The theta-e distribution suggests development of unstable layers in the lower atmosphere (below 4 km), dry regions in the middle to lower upper -troposphere and stable layers in the upper atmosphere (above 7 km). The lower regions are marked with high theta-e due to a stronger convergence of moist air to the center of the TC. The maximum theta-e is confined to an altitude of 1.0–1.5 km in Morrison and Goddard simulations, whereas it extended to slightly higher levels in the case of Thompson, Lin and WSM6 schemes suggesting more unstable layers in the latter. The middle dry regions extended slightly to deep layers in Lin and WSM6 compared to Thompson, Goddard and Morrison schemes. As shown in Fig. 8, the eye wall region of the cyclone is marked with strong updrafts in all the simulations. The biggest differences of updrafts along the eyewall are aloft. The simulations Thompson and Goddard produced stronger updrafts (3–5 m/s), while Lin, WSM6 produced moderate values of updrafts (2–4 m/s) and Morrison low updrafts (1–3 m/s) along the eye wall. The theta-e distributions suggest that Lin, WSM6 and Thompson produce relatively deep layers of high theta-e (385–390 K) in the lower atmosphere, indicating simulation of large moisture convergence. The Morrison and Goddard schemes simulated moderate values of theta-e (375–385 K). Simulated vertical velocity and theta-e distributions suggest that Lin, WSM6 produced stronger convective unstable layers compared to Thompson, Goddard and Morrison schemes.

Figure 6
figure 6

Longitude height cross section of equivalent potential temperature (theta-e) (K) and vertical velocity (m/s) around the TC centre at 1200 UTC 02 May 2019 (1800 UTC 01 May for Lin) during the peak intensification of Fani cyclone from simulations with different microphysics: a Morrison, b Lin, c WSM6, d Thompson, e Goddard

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Figure 7
figure 7

Vertical profile of simulated a theta-e, b divergence and c vertical velocity averaged over an area of 2° × 2° from the center of Fani at 1200 UTC 02 May 2019 (1800 UTC 01 May for Lin)

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Figure 8
figure 8

Zonal variation of simulated diabetic heating (°C) at 1200 UTC 2 May 2019 (1800 UTC 01 May for Lin) during peak intensification of Fani cyclone by (a) Morrison, (b) Lin, (c) WSM6, (d) Thompson, (e) Goddard schemes

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Vertical profiles of simulated theta-e, convergence/divergence, and vertical velocity fields over a 2° × 2° area around the center of Fani cyclone during its peak intensification at 1200 UTC 2 May 2019 (1800 UTC 01 May for Lin) are presented in Fig. 7. The average theta-e profile (Fig. 7a) indicates the formation of a convectively unstable region in the lower atmosphere up to 3.1 km/700 hPa and stable divergent region in the upper layers around the eye region. A local minimum in theta-e is found in the mid-troposphere, which indicates drying associated with subsidence into the eye. In both lower (< 2 km) and upper (> 10 km) levels relatively higher theta-e values are simulated indicating high enthalpy. All the CMP schemes, in general, produced a gradual vertical decrease of theta-e indicating unstable atmosphere up to 4 km and stable layer aloft with increase of theta-e. In all the CMP cases, the highly convective region of 3–5 km of the cyclone is marked with a vertical decrease of theta-e indicating strongly unstable conditions simulated in this region. Further, the increase of theta-e simulated in the upper troposphere indicates stable divergent layer of the TCs. The larger theta-e in the lower levels is due to the convergence of moisture towards the center of the TC, large water vapour flux and latent heat transport. As seen from Fig. 7, the Lin WSM6, and Morrison schemes produced highly unstable layers followed by Goodard and Thompson. The divergence profiles from simulations (Fig. 7b) indicate a stronger convergence below 4-km and a stronger divergence above 9 km in all cases except Morrison which simulated a weak divergence in the upper layers. As shown in Fig. 7c, the simulated mean vertical velocities in the core region of cyclone steadily increased from 2 km upwards; the Goddard followed by WSM6 and Lin produced a more rapid increase than the Thompson and Morrison up to 400 hPa (~ 6 km). In the upper troposphere, the Goddard, Lin, WSM6 & Thompson predicted higher updraft velocities (0.25–0.38 m/s) relative to Morrison (0.2 m/s). The maximum vertical velocities are simulated in 250–200 hPa in Lin, WSM6 and Goddard, 150 hPa in Thompson and 300 hPa in Morrison. These results suggest that Goddard, Lin, and WSM6 simulated stronger convection compared to Thompson and Morrison.

The microphysical processes involving the production and conversion of hydrometeors alter the temperature, moisture, and momentum distribution in different vertical layers. The buoyancy generated by diabatic heating associated with the deep moist convection (Smith, 2006; Zhang et al., 2019) controls the intensification of the TCs. The zonal variation of diabatic heating at different levels computed using the thermodynamic and quasi-geostrophic omega equations (Singh & Rathor, 1974) at peak intensification for Fani is presented in Fig. 8. As shown in Fig. 8, WSM6 and Lin produced a deep warmer core (up to 200 hPa) with a heating of ~ 6° C followed by Thompson and Goddard which simulated moderately deep cores extending to ~ 250 hPa with moderate heating of ~ 5 °C whereas Morrison produced relatively weak core with a heating ~ 4 °C limited to 300 hPa. The stronger diabatic heating simulated over deeper layers in WSM6, Lin suggests a stronger simulated cyclone in these cases compared to Goddard, Thompson and Morrison. The stronger warming simulated in WSM6 and Lin can be related to stronger convergence, vertical motion (Fig. 7) and the stronger convectively unstable atmosphere (Fig. 6) producing more heat of condensation relative to Goddard, Thompson and Morrison. Simulated heat distribution suggests that WSM6 and Lin produce smaller radius cores and thus more intensified cyclone compared to Thompson, Goddard and Morrison schemes. Previous studies (Mohan et al., 2023; Reshmi Mohan et al., 2019) reported that Thompson scheme simulates large amounts of cloud, rain, and snow but relatively low amounts of ice while Lin, WSM6 and Goddard produce more solid hydrometeor distributions. The frozen hydrometeors (snow/ice/graupel) in the process of freezing release large latent heat in the upper layers which is evident in Lin, WSM6 and Goddard simulations. The high warming in the case of Thompson is due to simulation of high snow mixing ratio (Mohan et al., 2023; Reshmi Mohan et al., 2019).

The intensification of a TC is closely related to the strength of its warm core represented by the magnitude of the temperature deviation from surrounding environment (also called thermal anomaly or warming) and the vertical extent of warming (Stern and Nolan, 2012). An increase of core warming leads to more intensified system by enhancing the convection. The azimuthally averaged radius-height section of warming (temperature deviation from the initial time) produced in different microphysics experiments during the peak intensity of Fani at 1200 UTC 2 May (1800 UTC 01 May for Lin) along with the CIRA data is presented in Fig. 9. As seen in Fig. 9, the CIRA data indicates a smooth temperature distribution compared to the high resolution WRF simulation due to the fact that the CIRA analysis is prepared from sensors of multiple satellites including Moderate Resolution Imaging Spectroradiometer (MODIS), Special Sensor Microwave/Imager (SSM/I), and AMSU at ground resolution of ~ 25 km (Knaff et al., 2011). The CIRA data shows a warming of 0.5–5 C extending from 8.5 to 19.5 km and with maximum warming distributed in the vertical layer 10–14 km and horizontally extending up to 100 km from the centre of the TC. Although the magnitude of warming varied, the maximum warming is simulated in the layer 8–18 km layer in all the experiments. Among different CMP schemes used, Lin followed by WSM6 produced highest warming (10–12 C); Thomson and Goddard produced moderate warming (8–10 C) while Morrison simulated low warming (6–9 C) in the core region. The simulation with Morrison produced a wider core (~ 150 km), with relatively lesser warming than other CMP cases. The simulated warming trends are consistent with the diabatic heating and intensity characteristics simulated in different CMP cases. The CMP schemes influence the simulations by vertical heat and water vapor distributions and give feed back to the largescale environment through the simulated convection. The production of solid hydrometeors such as ice, graupel significantly influence the inner core heating (Kanase & Salvekar, 2015). Among different experiments, the Lin and WSM6 produced a narrow but warmer core indicating a more intensified cyclone followed by Goddard, Thompson and Morrison. The stronger and deeper warming seen in WSM6, Lin can be partly attributed to the stronger simulated diabatic heating by the latent heat associated with strong convection and condensation in the eye wall region in these cases (Fig. 8). Atmospheric cooling is seen in the lower regions below 6 km in both CIRA data and WRF simulations. The Thompson produced a higher cooling (− 7 C) followed by WSM6, Lin, Morrison and Goddard (− 5 C) schemes. Figure 10 presents the time evolution of average warming calculated over the 2° × 2° deg area at 300 hPa (roughly at 9 km) around Fani from different CMP experiments. As seen from Fig. 10, the average warming in all the simulations progressively increased from 1200 UTC 28 April, attained its maximum during the period 0600 UTC -1500 UTC 2 May coinciding with the peak intensity period of Fani. The time series of warming also shows that Lin and WSM6 produced higher warming followed by Goddard, Thompson and Morrison throughout the life cycle of Fani and this result is consistent with the warming trends in the core region at peak intensity stage (1200 UTC 2 May in most cases; 1800 UTC 01 May for Lin) observed in Fig. 10. These differences in simulated warming distribution would influence the vertical motion simulation as seen in Figs. 6 and 7c.

Figure 9
figure 9

Azimuthally averaged radius height cross section of temperature anomaly (°C) at 1200 UTC 2 May 2019 (1800 UTC 01 May for Lin) during the peak intensification of Fani cyclone relative to the initial time by (a) Morrison, (b) Lin, (c) WSM6, (d) Thompson, (e) Goddard schemes compared with CIRA data (f)

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Figure 10
figure 10

Time evolution of simulated temperature anomaly (°C) at 300 hPa over 2° × 2° area from the center of Fani cyclone from different microphysics experiments

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Figure 11 shows the vertical distribution of area average mixing ratios of various hydrometeors (qvapor, qrain, qsnow, qice, qgraup and qcloud) over a 1.5° × 1.5° area around the center of Fani at 1200 UTC 02 May (1800 UTC 01 May for Lin) during the peak intensification. In all the cases qvapor is similarly simulated. As shown from Fig. 11, as compared to WSM6 and Morrison schemes, Goddard, Thompson and Lin schemes produced high amount of qcloud, in general, in different layers. Above 4 km (~ 600 hPa), the Morrison scheme produced larger amount of qcloud next to Lin. The qrain is mainly confined below 3 km (~ 700 hPa) (Fig. 11c). Thomson and Lin schemes produced high amount of qrain followed by WSM6, Morrison and Goddard. As for qice, which is mainly distributed in the upper layers above 6 km amsl (~ 400 hPa), the Goddard scheme produced the highest amount followed by Morrison and WSM6. The Thompson scheme produced least amount of ice similar to the result of earlier studies (Mohan et al., 2023; Reshmi Mohan et al., 2019). For qsnow which is mainly simulated in the upper layers, the Thompson scheme produced the maximum qsnow followed by Goddard, Morrison, WSM6 and Lin schemes similar to the previous studies (Mohan et al., 2023; Reshmi Mohan et al., 2019). The qgraup is concentrated mainly in the 3–6 km layer, more or less similarly simulated by all the CMP schemes except Thompson which lowest values. These results suggest that the Goddard, WSM6 and Lin schemes followed by Thompson simulate significant amount of a majority of hydrometeors (snow, ice, rain, graupel) over deep layers producing more diabatic heating, warming, high theta-e and strong vertical motions relative to Morrison which simulated relatively low quantities of these species. The present results of more diabatic heating, warming, high theta-e and strong vertical motions with WSM6, Lin and Goddard schemes are consistent with the previous study of Reshmi Mohan et al (2019) for Hudhud cyclone.

Figure 11
figure 11

Vertical profiles of hydrometeor mixing ratios (10–3 kg/kg) averaged for the peak rainfall period 1200 UTC 02 May 2019 (1800 UTC 01 May for Lin) over 1.5 × 1.5 deg area around the centre of cyclone from different microphysics experiments

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4.4 Wind Flow Pattern

Surface wind pattern simulated in different CMP experiments is compared against the CIRA wind analysis (Fig. 12) at 1200 UTC 2 May 2019 (1800 UTC 01 May for Lin) during the peak intensity stage of Fani. The WRF simulations could capture the observed wind pattern of cyclonic winds with stronger winds in the core and progressively decreasing radially outward. Simulated storms are slightly delayed in Morrison, Goddard and WSM6 with respect to the observed storm position seen in CIRA (17.5 N). The predicted storm is approximately about 50 km in Morrison and Thompson (17 N), 80 km in Lin (16.8 N), and 100 km in WSM6 and Goddard (16.5 N) to the south of the observed storm. Simulated storm in all the experiments is more intensive compared to the CIRA data. The CIRA wind data (Fig. 12f) shows stronger winds (65–95 knots) in the core region and relatively weaker winds (35 knots) in the outer core region. The CIRA winds are much stronger over land than the CMPs. Even though the simulated storm in all CMP experiments is more intensive relative to the observed storm, the Thompson and Goddard schemes simulated the intensity (90 knots) more closely interms of the distribution of isotachs and their density compared to Lin, WSM6 (> 95 knots) and Morrison (85 knots). The intensity variations among different CMP schemes can be related to the differences in microphysical processes of phase changes and latent heating which modulate inner core diabatic heating (Fig. 8), temperature, and pressure gradients (Fovell et al., 2016), which in turn influence the strength and radius of strong winds. The band of intense winds in all CMPs is simulated slightly at smaller radii (within in ~ 55 km of the center) compared to CIRA winds.

Figure 12
figure 12

Simulated surface wind and central pressure from different CMP experiments a Morrison, b Lin, c WSM6, d Thompson, e Goddard along with CIRA multi-satellite surface wind analysis data of Fani cyclone at 1200 UTC 2 May 2019

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Figure 13 shows the azimuthally averaged radius height section of tangential winds at 1200 UTC 2 May (1800 UTC 01 May for Lin) during the peak intensity stage of Fani along with CIRA estimates. The CIRA analysis shows intense tangential winds of 45–55 knots extending to 10 km in the troposphere in the core region. As compared to the CIRA analysis, tangential winds in simulations with Lin and WSM6 are slightly overestimated (45–70 knots) extending to 14 km layer, Morrison underestimated the winds (40–50 knots) up to 10 km layer whereas Thompson and Goddard schemes simulated stronger winds (45–60 km) extending to a height of 11 km. It can be seen that the core of maximum winds marked by 40 m/s contour is simulated to a radius of 100 km in Lin, WSM6, Thompson and Goddard and 90 km in Morrison against ~ 160 km noticed from CIRA data. The mismatch of radii between model and CIRA data (larger radius) is due to interpolation of coarse resolution (~ 25 km grid) satellite winds. As shown in previous studies by Wang (2009, 2012), the greater diabatic heating in rainbands simulated in the case of Lin and WSM6 (Fig. 8) produces stronger inflow and convergence in the lower levels and stronger outflow and divergence in the upper levels leading to stronger simulated upward motion in the core region (Fig. 7). The stronger simulated tangential winds in the lower troposphere in Lin and WSM6 would result in stronger inward transport of angular momentum which would produce stronger spin-up of wind near the eyewall and lead to increase in simulated TC intensity. Similar to core warming, the Thompson and Goddard schemes simulated the tangential wind distribution in better agreement with CIRA estimates compared to Morrison, Lin and WSM6 in terms of horizontal and vertical extension of maximum winds.

Figure 13
figure 13

Azimuthally averaged radius height cross section of tangential winds (m/s) for Fani cyclone at 1200 UTC 2 May 2019 during peak intensity relative to the initial time by (a) Morrison, (b) Lin, (c) WSM6, (d) Thompson, (e) Goddard schemes compared with CIRA data (f)

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4.5 Simulated Radar Reflectivity

The WRF simulated maximum reflectivity of Fani with different CMP schemes is compared with the IMD Visakhapatnam DWR reflectivity (Fig. 14) observations available at 1200 UTC 2 May. Compared to the DWR reflectivity, all the simulations predicted relatively stronger reflectivity indicating simulation of stronger convection than the observed (32–50 dBz) storm. Figure 14 indicates stronger convection in Lin, WSM6 and Goddard (37–60 dBz), whereas moderate convection in Thompson and Morrison (35–55 dBz). The DWR observed reflectivity of Fani indicates a well-defined eye and eyewall with rainbands wrapping around the southwest, northwest, and northeast sectors. However, observed reflectivity on the eastern sectors is weak indicating underestimation which is possibly due to wave attenuation effect. It can be seen that Goddard, WSM6 and Lin simulated higher dBz in the southwest, northwest and northeast sectors compared to Thompson and Morrison. The higher dBZs in Goddard, WSM6 and Lin indicate simulation of larger particle sizes/ mass, which could be due to stronger simulated convection compared to Thompson and Morrison. As seen in Fig. 14, the strong reflectivity (≥ 50 dBz) extended to deep layers (~ 10 km) in Lin, WSM6 and Goddard simulations, to moderately deep layers (8 km) in Thompson and Morrison suggesting stronger simulated convection in Lin, WSM6 and Goddard schemes. The differences in simulated radar reflectivity can be related to the differences in the vertical hydrometeor distribution in different CMP schemes. As shown by Reshmi Mohan et al (2019), the Goddard, WSM6 and Lin schemes produce significant amount of a majority of hydrometeors (snow, ice, rain, graupel) over deep layers and relatively strong vertical motions compared to Morrison and Thompson.

Figure 14
figure 14

Simulated maximum reflectivity in the region of Fani cyclone by (a) Morrison, (b) Lin, (c) WSM6, (d) Thompson, (e) Goddard schemes compared with (f) IMD DWR measured reflectivity. The colour contours of reflectivity are common to DWR and WRF plots

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5 Conclusions

In this study, the sensitivity of high resolution WRF simulations of extremely severe cyclone Fani to different cloud microphysics schemes is examined using wind profiler radar, multi-satellite data products, and DWR reflectivity data sets. Although our main objective of the study is to investigate how well the explicit simulations represent the convection, nevertheless, the results show that microphysics mainly affect the intensity and have less impact on track predictions for the Fani cyclone. From comparison of results of simulations with IMD estimates, it is found that Thompson and Goddard produced the best predictions for both tracks and intensity prediction. Results suggest that simulations using Thompson followed by Goddard schemes provide the least errors for track and intensity parameters indicating better performance.

The model could capture the radar observed strong easterly/northeasterly winds in the upper layers (8–16 km) at Gadanki station in the period from 1200 UTC 1 May to 2000 UTC 2 May during the passage of cyclone. Simulations with Lin, WSM6 and Goddard schemes produced stronger horizontal winds, Thompson moderately stronger winds and Morrison relatively weak winds. Comparison of simulated vertical velocity at Gadanki station indicated that the explicit WRF simulations could reproduce the radar observed convective motions in the outer core region of Fani on 1 and 2 May 2019. Although there are few differences among simulations in different vertical regions, overall, Thompson and Goddard schemes simulated the vertical motions in lower, middle and upper layers in better agreement with radar data.

Simulated mean vertical velocity and mean theta-e distributions in a 2 × 2 degree region around the cyclone suggest that the Goddard, Lin and WSM6 schemes produced highly convectively unstable layers in the lower 6 km layer compared to the Thompson and Morrison schemes. It has been found that the Lin and WSM6 predicted higher updraft velocities (~ 0.35 m/s) and Thompson and Goddard produced moderate updraft velocities (~ 0.25 m/s) in the upper troposphere with relatively wider area of high theta-e (385–390 K) indicating simulation of warmer cores and stronger convection compared to Morrison. Analysis of diabatic heating indicated that the WSM6 and Lin produced a deeper core (up to 200 hPa) with a stronger heating of ~ 6° C followed by Thompson and Goddard which simulated moderately deep cores extending to ~ 250 hPa with moderate heating of ~ 5 °C whereas Morrison produced relatively weak core with a heating ~ 4 °C limited to 300 hPa. The stronger diabatic heating simulated over deeper layers in WSM6, Lin suggests a stronger simulated cyclone in these cases compared to Goddard, Thompson and Morrison.

It has been found that the simulations with Lin and WSM6 produced warmer cores followed by Goddard, Thompson and Morrison throughout the life cycle of Fani. Comparison of simulated thermal anomaly with CIRA data suggest that even though all the schemes overestimated the warming, Lin followed by WSM6 produced highest warming (10–12 C); Thomson and Goddard produced moderate warming (8–10 C) while Morrison simulated low warming (6–9 C) in the core region. Similar to core warming, the Thompson and Goddard schemes simulated the tangential wind distribution in better agreement with CIRA wind analysis compared to Morrison which underestimated the strength of winds and Lin and WSM6 which overestimated the strength of tangential winds. Comparison of simulated hydrometeor reflectivity with DWR reflectivity indicated relatively strong convection in Lin, WSM6, and Goodard (37–60 dBz), and moderate convection in Thompson and Morrison (35–55 dBz). The strong reflectivity (≥ 50 dBz) extended to deep layers (~ 10 km) in Lin, WSM6, and Goddard and to moderately deep layers (9 km) in Thompson and Morrison suggesting stronger simulated convection in Lin, WSM6 and Goddard simulations.

The stronger convection in Lin, WSM6 followed by Goddard and Thompson is due to the stronger simulated diabatic heating which produces stronger inflow & convergence in the lower levels and stronger outflow & divergence in the upper levels leading to stronger simulated upward motion in the core region in these cases. Our present results of more diabatic heating, warming, high theta-e and strong vertical motions with WSM6, Lin and Goddard schemes are consistent with the previous study of Reshmi Mohan et al (2019) for Hudhud cyclone which reported that the Goddard, WSM6 and Lin schemes simulate significant amount of a solid hydrometeors (snow, ice, graupel) over deep layers producing more diabatic heating, warming, high theta-e and strong vertical motions relative to Morrison which simulated relatively low quantities of these species. The moderately strong heating and warming in the case of Thompson can be attributed to producing more snow and rain (Mohan et al., 2023; Reshmi Mohan et al., 2019). The current study used relatively older versions of microphysics for the ESCS Fani and evaluated against the wind profiler vertical velocity data at Gadanki situated very far off from the cyclone. In the context of newer model versions there is a necessity to evaluate the model simulations with more advanced schemes such as WSM7, WDM6, WDM7, aware version of Thompson, Goddard scheme with improved 4ICE etc., and with vertical velocity observations from the core region which will be attempted in future studies. Although this is a case study with microphysics sensitivity analysis for Fani, which is one of the extremely severe cyclones, the results will be useful for the prediction of cyclones in the Indian Ocean region.