1 Introduction

Accurate forecast of high impact weather events such as tropical cyclones (TC) remain a challenge to operational Numerical Weather Prediction (NWP) forecasters globally. Over the Indian region due to a long coast exposed to the Bay of Bengal and Arabian Sea and due to the vulnerability of the coastal population, the enhanced skill of TC forecast is the need of the hour. Some significant improvements have been accomplished in track error forecast of TC over the Indian seas (Deshpande et al. 2012; Mohapatra et al. 2013; Osuri et al. 2013; Kanase and Salvekar 2015a), but the intensity and heavy rainfall forecast still needs further improvement. Earlier studies (e.g., Saji and Ashrit 2014 and the references therein) have mostly used Weather Research and Forecasting (WRF) Mesoscale model and its sensitivity to different physical parameterization (cumulus, PBL, microphysics, etc.) for evaluating model skill in TC forecasting. An important issue which pertains in forecasting cyclones is the model configuration. The mesoscale models and limited area models are widely used for dynamic forecasting of tropical cyclones. While these regional models can afford very high resolution over a domain of interest, it requires artificial lateral boundary conditions to be supplied externally which can limit its performance. Several studies have highlighted the issue for lateral boundary conditions and choice of domain in mesoscale simulations (Wu et al. 2005; Rauscher et al. 2006). In case of Bay of Bengal cyclones, there is a need to consider the dynamics over a wider domain. Since the TC genesis over the BOB occurs mainly because of either in-situ (which is associated with the disturbances as part of inter-tropical convergence zone) or from the low pressure systems which generally migrate from the east (Vitart et al. 2001). Impact of large scale environmental flow on the tropical cyclone intensity is well demonstrated by Krishnamurti et al. (1989). The effects of large scale circulations (larger than domain) can be incorporated in regional mesoscale models only through the lateral boundary conditions (Velden and Leslie 1991). Cyclone being a phenomenon of multi-scale interaction, for better forecasting of cyclones, it is very important to properly represent the large scale circulation and associated processes in the models. This can be achieved with the help of global models. Goswami et al. (2011) found that the variable resolution (VR) GCM and non-linear debiasing provide a skill score of ~0.5 in the forecasting of TC intensity 2–7 days in advance for 30 cases of TC over the Bay of Bengal. Tropical cyclone is a result of variety of physical processes at different scales interacting with the inner core dynamics and the large scale flow. Ocean being one of the important energy sources for a TC, there is a need of using ocean–atmosphere coupled models in the prediction of TC genesis and intensity changes. Hardly any attempts have been made in evaluating the skill of a coupled general circulation model (GCM) forecast for TC over the Indian seas for variety of cumulus physics. This is particularly needed as currently the GCM resolution is becoming finer than the mesoscale model and the GCM is being used for the TC forecast (Goswami et al. 2006, 2011). So there is a need to evaluate the coupled GCM performance with more physics to identify better fidelity of the model for forecast application of TCs over the Indian seas.

Recent improvements in the dynamical ocean–atmosphere coupled numerical models are found to be useful for the simulation of weather phenomena involving multi-scale interaction. One of such dynamical model adopted under Monsoon Mission of Ministry of Earth Sciences, Government of India, is National Center for Environmental Prediction Climate Forecast System (NCEP CFS) which is fully coupled ocean–atmosphere–land model. NCEP CFS is extensively used for seasonal and extended range prediction (Yang et al. 2008; Abhilash et al. 2013; Sahai et al. 2014; Ramu et al. 2016; Rao et al. 2020) of the Indian Summer Monsoon and is under continuous development. Recently, the high resolution (T1534) atmospheric version of the CFSv2, i.e., GFS has been implemented for 10 days weather forecast over India (Mukhopadhyay et al. 2019).

Lim et al. (2014) had concluded that even though there is no change in the mean annual rainfall pattern due to increased spatial resolution, high resolution simulations are needed to capture short time-scale phenomenon as well as to reasonably represent the orographic precipitation. Goswami et al. (2015) explained the deficiencies in convective parameterization scheme of CFSv2 as one of the possible cause for dry precipitation bias over the Indian landmass. Recently, Abhik et al. (2017) showed that by improving the physical processes such as cloud microphysics, convection and radiation, the systematic bias of the model can improve significantly.

Accurate representation of cumulus processes in the model is one of the important factor which contributes to the model uncertainty and has large impact on the model rainfall prediction skills (Arakawa 2004; Krishnamurti 2005; Mukhopadhyay et al. 2010; Arakawa et al. 2011; Hong and Dudhia 2012; Pattanaik et al. 2013). For the purpose of proper representation of cumulus clouds, precise characterization of temperature and moisture fields in the sub-cloud layers and in the mid-troposphere is essential in the models (Yang et al. 1999). Palmer and Anderson (1994) found that large systematic errors of many models in simulating the monsoon rainfall are mainly due to convective parameterization. Similarly, Slingo et al. (1988) showed that the Asian summer monsoon and the onset dates are more sensitive to radiation and convective parameterization. Eitzen and Randall (1999) noted that increased convective adjustment time in the model leads to the improvement in simulation of precipitation and upper level circulation in GCM. Thus, knowing the importance of cumulus processes, many weather and climate prediction centres have made significant efforts to develop and update their cumulus schemes for improving precipitation forecast skills (Tiedtke 1989; Han and Pan 2011). There are very limited studies of cumulus parameterization sensitivity using CFSv2 model particularly for the high impact weather phenomena like tropical cyclones. However, it will be worth mentioning that Vitart et al. (2001) made an interesting study using GFDL atmospheric GCM at T42 with 18 vertical levels and established that simulated tropical cyclone intensity and internal variability show significant sensitivity to the cumulus parameterization. Using the same dynamical core, they tested the sensitivity of a moist adjustment scheme of Manabe et al. (1965) and mass flux based scheme of Simplified Arakawa–Schubert (SAS) (Arakawa and Schubert 1974) and revised SAS. Contrary to this, Strachan et al. (2013) showed, using a hierarchy of atmospheric GCM with increasing resolution, that higher resolution better captures the tropical cyclogenesis. Both these papers addressed the important issue that for a realistic simulation of TCs, cumulus parameterization and model horizontal resolution both play a crucial role. However, these studies are conducted using an atmospheric GCM, but the impact of cumulus parameterization and horizontal resolution on TC intensity and its internal variability is not yet studied using ocean coupled GCM.

In all the earlier studies on the monsoon rainfall using CFSv2, simulations are done using default SAS available with CFSv2 model (Goswami et al. 2015; Abhik et al. 2016 and the references therein). Ganai et al. (2015, 2016) used RSAS in CFSv2 model and examined a 15-year climate free run. They found that RSAS is able to reduce some of the prominent biases related to diurnal rainfall, daily and seasonal mean rainfall as compared to SAS. Improvement is seen in the annual cycle, onset and withdrawal, but most importantly, the rainfall probability distribution function (PDF) has improved significantly. Ganai et al. (2019) further improved the limitations of RSAS by modifying the fractional cloud condensate to precipoitation conversion. Bombardi et al. (2015, 2016) studied impact of convective trigger mechanism on the tropical cyclone and monsoon simulations using CFSv2. They concluded that heated condensation framework (HCF) as a convective trigger has improved the representation of convection vis-a-vis the monsoon rainfall and explained a way for improving the existing CP schemes by using different convection trigger mechanism. Ma and Tan (2009) have shown that slight modification in the connective trigger in CP scheme leads to large improvement in the sub-grid scale rainfall for TCs.

An attempt made by Mukhopadhyay et al. (2010) in simulating climatology of monsoon precipitation using WRF model, have shown that Betts–Miller–Janjic (BMJ) is able to simulate a reasonable heating profile, along with the realistic moist instability and seasonal cycle of evaporation and condensation and thus led to a better prediction of monsoon precipitation. Kanase et al. (2015) and Kanase and Salvekar (2015a, b), tried to understand the cloud and convective processes associated with the weak intensity storms formed over the Bay of Bengal. They found that, convective adjustment scheme such as Betts–Miller–Janjic (BMJ) is able to better reproduce the cyclone features than the mass flux based schemes. Slingo et al. (1996) showed improved simulation of UK Met Office model by the adjustment scheme as compared to mass flux scheme. Vaidya and Singh (2000) and Vaidya (2006) using limited area models showed that BMJ better simulates the rainfall and circulation features of monsoon depressions. Vaidya and Singh (1997) and Sun et al. (2015) also performed some sensitivity experiments with different adjustment parameters in BMJ and reported the impact of these parameters on different weather systems (depression, cyclones, etc.) particularly to improve the rainfall associated with these high impact weather systems.

There are some attempts (Bombardi et al. 2015, 2016) in modifying mass flux based convective schemes in CFSv2 which still could not resolve the model precipitation bias. The moist convective adjustment scheme, i.e., BMJ is able to produce the desirable forecast of the tropical cyclones in the regional mesoscale models. However, the convective adjustment scheme is not available in CFSv2 model. Here for the first time, we endeavour to implement a convective-adjustment scheme, i.e., BMJ in CFSv2 model. Fidelity of BMJ in CFSv2 model is tested and compared with the performance of SAS and RSAS schemes in CFSv2 for three Indian Ocean cyclones at three different resolutions, i.e., T126, T382 and T574.

The following questions are addressed in this study:

  1. 1.

    Do different cumulus parameterization schemes have an impact on cyclone intensity and its internal variability in coupled model?

  2. 2.

    Whether newly implemented moist convective adjustment scheme performs better for Indian Ocean cyclones especially the convective rainfall associated with the cyclones?

  3. 3.

    If yes, what could be the possible mechanisms behind the rainfall improvement?

Performance of BMJ cumulus scheme for cyclone simulation, more particularly the convective precipitation simulation, will allow us to further examine its fidelity in cyclone forecasting with a coupled model in Indian seas. Section 2 describes CFSv2 model along with experimental setup. Observed features of cyclones are mentioned in section 3. Results are discussed in section 4 followed by conclusion and future work in section 5.

2 Model description and experimental design

2.1 Model description

CFSv2 (Saha et al. 2014) used in the present study is a fully coupled ocean–atmosphere–land model. It consists of a spectral atmospheric model GFS (Global Forecast System) and Advanced version of the GFDL Modular Ocean Model, version 4p0d (MOM4). Ocean Model MOM4 (Griffies et al. 2004), is a finite difference model at 0.25–0.5° grid spacing with 40 vertical layers (10 m thickness from surface to 240 m, with 27 levels in the top 400 m to resolve the mixed layer). For the ocean model, resolution remains unchanged for all the experiments. For atmospheric model GFS, we considered three different resolutions, i.e., a spectral triangular truncation of 126 waves (T126, ~110 km), 382 waves (T382, ~35 km) and 574 waves (T574, ~25 km) in the horizontal. Out of 64 levels in the vertical direction, there are 16 levels below 800 hPa and 27 levels above 150 hPa in the stratosphere (Saha et al. 2010). CFS model has rapid radiative transfer model (RRTM) for shortwave radiation with advance cloud radiation integration scheme (Iacono et al. 2000; Clough et al. 2005; Saha et al. 2014). Coupling of CFS is also done with four-layer Noah land-surface model (Ek et al. 2003) and a two-layer sea ice model (Wu et al. 1997; Winton 2000). Cloud microphysical processes are being represented by a simple formulation based on Zhao and Carr (1997). Detailed description of model can be found in Saha et al. (2006, 2010, 2014).

The two convection schemes are available in the atmospheric component of CFSv2 such as SAS convection (Hong and Pan 1998), and RSAS convection (Han and Pan 2011). In addition to SAS and RSAS, a convective-adjustment scheme, BMJ (Betts and Miller 1986; Janjic 1994, 2000) for cumulus parameterization is implemented in CFSv2. The details of the CFSv2 model description are available in several previous studies (e.g., Goswami et al. 2015; Abhik et al. 2016).

Here, we will highlight some of the major differences that exist between SAS and RSAS cumulus parameterization as this will be more relevant to the current study. Both SAS and RSAS follow a mass-flux approach to parameterize cumulus clouds. One fundamental difference between SAS and RSAS is the type of cloud model used in each scheme. An ensemble of clouds with different cloud tops exists in RSAS, whereas a single tall cloud type representation is used on SAS. The detrainment in SAS happens only at the top, whereas for RSAS, it can occur at various levels of the cloud (Han and Pan 2011). The BMJ scheme depends on cloud efficiency which again depends on the mean temperature of cloud, entropy change and precipitation (Betts and Miller 1986; Janjic 1994, 2000). The BMJ parameterization is a convective adjustment scheme, meaning that it determines ‘reference’ profiles of temperature and dew point towards which it nudges the model soundings at individual grid points. The first step in the scheme is to locate the most unstable (highest θe) model parcel within the lowest ~200 mb above the ground. It lifts this parcel to its LCL (lifting condensation level), which it defines as cloud base. From there, the parcel is lifted moist adiabatically until the equilibrium level (EL) is reached. Cloud top is then defined as the highest model level at which the parcel is still buoyant, typically just below the EL. If the parcel is not buoyant at any level, convection is not activated and the scheme moves on to the next grid column. If the cloud is < 200 mb deep, the scheme attempts to initiate shallow (non-precipitating) convection. Otherwise, it checks to see if deep (precipitating) convection can be activated. This scheme does not include the moist processes below the cloud base or in the lower boundary layer.

2.2 Experimental design

Three cases of North Indian Ocean cyclones formed over the Bay of Bengal in 2013 are selected for the study. Out of these three cyclones, two (Phailin and Lehar) were post-monsoon and one (Viyaru) was a pre-monsoon cyclone. The initial conditions for atmosphere and ocean are taken from NCEP Climate Forecast System Reanalysis (Saha et al. 2010). The model integration started from corresponding depression stage of each cyclone, i.e., for cyclone Phailin: 00Z08102018, for cyclone Lehar: 00Z23112013 and for cyclone Viyaru: 00Z10052018. For each cyclone case, total nine experiments are carried out with three cumulus parameterization schemes such as BMJ, SAS and RSAS scheme at T126, T382 and T574 model resolutions. Thus, total 27 experiments are performed. The model is integrated for 10 days including 24 hrs spin up in all the experiments. The output is saved at 6-hr intervals. The rest of the model configuration is same as discussed in model description. The observed features of cyclones are described in section 3.

3 Cyclone description

3.1 Phailin

Very Severe Cyclonic Storm (VSCS) Phailin was the most intense landfalling cyclone over the NIO after Odisha super cyclone of 29 October 1999, originated from a remnant cyclonic circulation from the South China Sea and termed as a depression over the Bay of Bengal on 0300 UTC of 08 October 2013. It further moved in north-westwards direction crossing Odisha and adjoining north Andhra Pradesh coast near Gopalpur (Odisha) around 1700 UTC of 12 October 2013. The observed minimum central sea level pressure (CSLP) and maximum, sustained surface wind (MSW) speed of Phailin are 940 hPa and 115 knots, respectively (RSMC Report 2014).

3.2 Viyaru

Cyclone Viyaru (10–16 May 2013) has the longest track over NIO in recent period after the VSCS Phet over Arabian Sea (June 2010). Its genesis took place near 5°N on 0900 UTC of 10 May 2013. It recurved north-eastward after an initial north-westward movement. It moved very fast on the day of landfall (16 May 2013); such type of fast movement of cyclonic storm (CS) is very rare. Observed maximum, sustained surface wind speed (MSW) associated with the cyclone was ~45 knots. The observed minimum central sea level pressure (CSLP) is 990 hPa (RSMC Report 2014).

3.3 Lehar

A depression formed over the south Andaman Sea on 23 November 2013, has intensified into a VSCS Lehar on 26 November (RSMC Report 2014). It has its first landfall near Port Blair around 0000 UTC 25 November as SCS (which is very rare and after November 1989 cyclone) and second landfall at Andhra Pradesh coast around 0830 UTC of 28 November as depression. The observed CSLP and MSW of Phailin are 980 hPa and 75 knots, respectively.

4 Results and discussion

4.1 Surface parameters and vertical structure of cyclones at different resolutions

The CFSv2 is run at three different resolutions for three cyclone cases of Phailin, Viyaru and Lehar. Figure 1 shows the track (a–c), track error in km (d–f), and intensity in hPa (g–i) and error in translational speed in ms−1 (j–l) of cyclone Phailin. The first column represents results with T126, second column shows results with T382 and results with T574 are presented in third column. Black line represents the best track of respective cyclones estimated by IMD, the blue line is for SAS, the green is for BMJ and track by RSAS is shown by red line. Broadly, the north-westward movement of the cyclone Phailin is captured by all the three cumulus schemes at all resolutions. Initially up to 72 hrs of model integration (figure 1), tracks by all the three CP schemes for all the three resolutions are almost overlapping. However, beyond 72 hrs of model integration, the track with RSAS shows large deviations from the best track as compared to BMJ and SAS. At T574 (~27 km resolution), the observed track of the cyclone Phailin and model simulated track with BMJ and SAS are close to each other. The impact of CP and resolution is evident from the track error plots (figure 1d–f) for cyclone Phailin. Particularly with BMJ, the track error reduces with increase in resolution. The track error for BMJ and SAS is ~150 km up to 144 hrs of model integration at T574. Strikingly, all CP schemes underestimate the intensity of the cyclone Phailin at all the resolutions. Inter-comparison between all the CP schemes (figure 1g–i) bring out that RSAS and BMJ simulate storm with marginally higher intensity than SAS at T382 (~38 km) and T574 (~27 km). In general, the intensity increases with resolution for all the CP schemes. Overall the performance of BMJ for predicting track (track error is less for BMJ and SAS) as well as intensity (intensity is higher for BMJ and RSAS) is better than other CP schemes at higher resolution. Comparatively BMJ better predicts the track and intensity. The error in translational speed (figure 1j–l) is positive for BMJ for all lead times at all three resolutions. For SAS and RSAS, initially (for 2–3 days) the cyclone movement is very slow at all resolutions. But among all the CP schemes, with increase in resolution, the error in translational speed is (less) close to observations for BMJ. Thus, with the track, intensity and translational speed, BMJ with T574 appears to be comparable with the observations. Track and intensity results are summarized in tables 1 and 2 for cyclones Viyaru and Leher. Thus increased resolution has more impact on the intensity simulation than on the track of the cyclone. Therefore, henceforth all the results will be discussed at T574. In the following section, further the basic features of the vertical thermodynamic structure of the cyclone are also discussed.

Figure 1
figure 1

Observed and forecasted track (a–c), time evolution of track error in km (d–f), intensity in terms of CSLP (hPa) (g–i) and error in translational speed (ms−1) of cyclone (j–l) all at three resolutions T126, T382 and T574, respectively, for cyclone Phailin. Colour indicates SAS (blue), RSAS (red), BMJ (green) and IMD (black).

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Table 1 Different parameters (minimum CSLP (hPa), MSW (ms−1), daily average track errors, landfall time) for cyclone Viyaru at three different resolutions.
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Table 2 Same as table 1, but for cyclone Lehar.
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To understand the impact of CP schemes on the core structure of cyclone at the mature stage, the vertical cross section of various parameters are plotted in figure 2 . The deviation of temperature with respect to layer average (figure 2a–c), vertical variation of horizontal wind speed in ms−1 (figure 2d–f) at the corresponding mature stage of cyclone Phailin is plotted at T574 for three different CP schemes. Typical warm core structure with warming up to 9°C is observed in both RSAS and BMJ simulated cyclone, while SAS shows comparatively less warming ~4°C (figure 2c). The simulated cyclone has extended up to 200 hPa level and it has its heating maxima at the mid-tropospheric levels. In BMJ and RSAS, the warm core extends down up to the ground. From figure 2(d–f), it is evident that strong winds with higher magnitude are well simulated by BMJ and RSAS as compared to SAS. The wind maxima also lie in the lower troposphere. Similar to Phailin, the vertical structure for the cyclones Viyaru and Lehar (figure not shown) also shows that higher intensity of the cyclones are associated with a strong warming in the middle troposphere associated with strong winds surrounding the center of the cyclone. In order to examine the impact of cyclone on ocean, difference between the sea surface temperature (SST) at the time of dissipation and formation are plotted for three CP schemes along with the real time global (RTG) SST observations (figure 3) for the cyclone Phailin. RTGSST data at 0.25 × 0.25° resolution, available at 3-hr interval are used in the present study. The negative values represent the cooling of the ocean surface and vice versa. Surface cooling of 2.1°C is seen in the observation. BMJ and SAS, reasonably indicate the cooling of ocean by about 2.5°C along the cyclone path, while RSAS underestimates the cooling.

Figure 2
figure 2

Deviation of temperature with respect to layer average in °C (a–c) and vertical variation of horizontal wind speed (ms−1), (d–f) for BMJ, SAS and RSAS, respectively, at corresponding mature stage of cyclone Phailin. Mature stage for BMJ is at 21Z11Oct, SAS: 09Z12Oct, and RSAS: 09Z12Oct.

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Figure 3
figure 3

Difference between the sea surface temperature (SST) at the time of dissipation and formation of cyclone Phailin. (a) Obs, (b) RSAS, (c) BMJ, and (d) SAS.

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Although the basic structure of cyclone is well simulated by all the CP schemes and is consistent with the intensity values simulated by CFSv2, our main objective is to study the simulation of intensity and the precipitation associated with the cyclones. Hence, we will now explore the reasons behind the different intensity behaviour for all the cyclones. The results for cyclone Phailin will be explained thoroughly.

4.2 Rainfall

Tropical rainfall measuring mission (TRMM) 3B42 V7 is used as observations in the present study. It is available at 0.25 × 0.25° resolution every 3 hrs. Details about the dataset can be found at http://disc.gsfc.nasa.gov/precipitation/TRMM_README/TRMM_3B42_readme.shtml (henceforth TRMM 3B42 v7 data is referred as observations in text). Daily accumulated total rainfall (mm) at 00Z10Oct, 00Z11Oct, 00Z12Oct and 00Z13Oct for each CP scheme along with observations is plotted for the cyclone Phailin (figure 4). Observations indicate intense (>180 mm day−1) rain in the cyclone core region. For BMJ, the rainfall at the cyclone core region as well as in the rainbands is > 180 mm day−1 at most of the places, whereas it is underestimated by SAS and RSAS. The TC translational speed and intensity controls the rainfall distribution. Compared with other two schemes, BMJ better captures track, translational speed, intensity and rainfall distribution. To investigate further the contribution of the convective rain in the total precipitation, figure 5 shows the spatial pattern of convective rainfall for three CP schemes along with TRMM 3G68 as observations. TRMM 3G68 is an hourly gridded text (ascii) product containing 2A25 (Iguchi et al. 2000) rain estimates. It includes 24 hr of hourly grids into a single daily file. This information is further regridded uniformly on 0.25 × 0.25° grid for fair comparison with the model. Observations indicate heavy convective rainfall (>150 mm day−1) in the core of the cyclone. The rainfall intensity and distribution by BMJ better resembles with the observation considering the highest spatial correlation coefficient (top right corner of each panel). In SAS, the rainfall intensity is underestimated over a larger area, whereas RSAS produces a comparable amount of convective rain but largely overestimate the area of convective rain. The percentage contribution of convective rainfall to the total rainfall is plotted in figure 6 for all three convective parameterization schemes. BMJ simulates a realistic contribution of convective rain to total rain much similar to the observations. SAS and RSAS both significantly overestimate the contribution of convective rain to the total rain. The ratio of convective to non-convective rainfall averaged along the box (figure 6b) clearly indicates that SAS and RSAS overestimate the contribution of convective rain with respect to non-convective rain. The ratio simulated by BMJ is comparable with the observations. To find out the physical mechanism responsible for the different behaviour of each CP scheme in simulating the convective rainfall, we have plotted the vertical profile of total cloud condensate (cloud water and cloud ice) averaged over 2 × 2° around the cyclone center in figure 7. SAS and RSAS show lesser cloud condensate as compared to the BMJ in the lower as well as in the upper troposphere suggesting weaker convection associated with the cyclone core.

Figure 4
figure 4

Total precipitation in mm/day for cyclone Phailin at 00Z10Oct, 00Z11Oct, 00Z12Oct, 00Z13Oct2013, respectively, in each column. Observations (a–d), BMJ (e–h), SAS (i–l) and RSAS (m–p), respectively. The number in each figure shows the spatial correlation coefficient (cc) between observations and model forecast.

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Figure 5
figure 5

(a–p) Same as figure 4(a–p), but for convective precipitation (mm day−1). The number in each figure shows the spatial correlation coefficient (cc) between observations and model forecast.

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Figure 6
figure 6

(a) Percentage contribution of convective rainfall to the total rainfall averaged over the area 81–96°E and 10–25°N (covers whole cyclone path). (b) Ratio of convective to non-convective rainfall averaged over the same box for cyclone Phailin. The black line represents observations for convective rainfall compared with the BMJ (green line), SAS (blue) and RSAS (red).

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Figure 7
figure 7

Total cloud condensate (including cloud water and cloud ice) in g kg−1 averaged over cyclone path for OSAS (blue), RSAS (red) and BMJ (green).

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Underestimation of condensate by SAS and RSAS in the lower (higher) level may also affect the low (high) cloud distribution in the model compared to BMJ. It is well known from the literature (Mukhopadhyay et al. 2011; Kanase et al. 2015) that larger fraction of frozen condensate/hydrometeors may lead to enhanced latent heat release and this may produce enhanced heating (Yanai et al. 1973) in the mid-troposphere (figure not shown here). The higher amount of cloud condensate produces large amount of mid-level heating and vice-versa in each CP scheme. The cloud water which is present at the lower levels is transported to mid-levels by strong vertical motions (figure not shown) in BMJ which further helps to build the deep clouds. In RSAS and SAS, relatively weak vertical motions result in the lesser amount of cloud water being transferred to mid-troposphere and within very short interval of time it is precipitated out resulting in more drizzling and lighter rain events. BMJ, on the other hand, produces deeper convection and due to increased vertical velocity, it helps the growth of deeper cloud and heavier rainrates around the cyclones.

Based on the analysis of figure 6, we hypothesize that SAS and RSAS possibly trigger the convection more frequently (Tirkey et al. 2019) than that in BMJ and eventually contribute more convective rain. To clarify more about the rainfall patterns, we have plotted daily accumulated cloud water path (figure 8a, d), precipitation (figure 8b, e) and precipitation efficiency (figure 8c, f) for total precipitation and convective precipitation. For this purpose, we have accumulated all the daily cloud water and daily precipitation (total as well as convective) for each cyclone, corresponding to a given precipitation bin (mm day−1). The precipitation bin of mm day−1 are based on the India Meteorological Department (IMD) classification of rainfall events. The precipitation efficiency f is defined as the ratio of precipitation rate to cloud water path. It has units of day−1 and it signifies that the higher values of f correspond to the shorter time scales for the conversion process (Li et al. 2012). For each bin, precipitation efficiency f is calculated by dividing the total daily precipitation amount by the corresponding total daily cloud condensate path. For cyclone Phailin (figure 8a, d), the total cloud condensate in BMJ is higher than in SAS and RSAS in all precipitation bins. For heavy precipitation bins of 115.5–204.4 mm day−1 and >204.4 mm day−1, the cloud condensate in BMJ is one or two orders of magnitude higher than other two schemes. The precipitation amount resembles with the cloud condensate for all precipitation bins (figure 8b, d). For lighter (bins below 64.5 mm rain) precipitation bin, the precipitation rate for all the three CP schemes is broadly similar but the differences in the magnitude of three CP scheme increase with heavy precipitation bins. Only BMJ gives the heavy precipitation which is also reflected in the precipitation efficiency. Lower values of f correspond to the larger time-scale for conversion of cloud water to precipitation and vice versa. Thus for BMJ, f shows lower values for all precipitation bins which correspond to the longer time required for conversion process when compared with RSAS and SAS. One remarkable point for BMJ, is more contribution of heavy rainfall bins (>115.5 mm day−1) towards the total precipitation. In SAS and RSAS, precipitation is mostly dominated by light and medium rainfall events. The same conclusion can be drawn for cyclone Viyaru and Lehar (figures not shown). When we composite all the cyclones for the cloud water path, precipitation and precipitation efficiency, RSAS and SAS could able to convert the cloud condensate into precipitation in shorter time-scale which further add to the formation of drizzling precipitation events (figure not shown).

Figure 8
figure 8

(a) Daily cloud water path (kg/m2) for daily accumulated precipitation amount, (b) daily accumulated precipitation amount in each precipitation intensity bins of mm/day, (c) total precipitation efficiency (f) = Daily precipitation amount/Total cloud water path, (d) total cloud water path (kg/m2) for daily accumulated convective precipitation amount, (e) daily accumulated convective precipitation amount in each precipitation intensity bins of mm/day, (f) convective precipitation efficiency (f) = Daily convective precipitation amount/Total cloud water path for convective precipitation.

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The above analyses indicate that BMJ is efficient in sustaining the convective instability and generating deep convection and heavier rain rates (>64 mm/day) than the SAS and RSAS. As such, SAS and RSAS trigger the convection more frequently and thus end up in generating more lighter and moderate rain rates. Zadra et al. (2014) studied the sensitivity of TC prediction skill to trigger adjustment in the convective parameterization. They found that the prediction skill improves with reduction in the activation frequency of convective scheme. In BMJ, it seems that there are deeper convection which led to the strengthening of TC intensity and generation of more intense precipitation. To investigate further, the number of grid points in each precipitation bins (as per IMD classification of rainfall events) are counted for convective rainfall (figure 9) during the cyclone period (from depression to dissipation stage). Here, an additional ‘zero (0)’ precipitation bin is added which means that the convective scheme is not triggered for these many grid points. The careful examination of number of grid points in zero precipitation bins clearly indicates that the BMJ scheme has triggered less often than RSAS and SAS in lower precipitation bins. The frequency distribution for convective precipitation (figure 9) shows that light precipitation events are larger in numbers for SAS and RSAS, whereas the heavy rainfall events are more for BMJ scheme. Overall, from the above discussion, it seems evident that BMJ scheme triggers convection less often than SAS and RSAS, thus adjusts the atmospheric profiles less frequently, leaving the atmosphere in a convectively unstable state. This allows the PBL to moisten and grow higher. Increased moisture in PBL injects more moisture from the lower troposphere to the mid-troposphere. The increase in the atmospheric moisture results in deep convective clouds, which in turn releases latent heat and feeds back to the large scale vis-à-vis increases the intensity and precipitation of the tropical cyclones. To further establish the relation between the instability and convective precipitation, scatter plot of convective precipitation and vertically integrated (between 950 and 100 hPa) moist static energy (MSE) is shown in figure 10. ERA5 analysis is used as the reference. It shows that, overall the moist instability pattern and magnitudes are realistically matching with BMJ. SAS underestimates the rain rates and the instability, while RSAS overestimates the rain rates but BMJ appears to produce a realistic MSE and rain rate relation.

Figure 9
figure 9

Grid points count which lies in the respective convective precipitation bins.

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Figure 10
figure 10

Scatter plot of convective precipitation in (cm/day) and moist static energy (vertically integrated between 950 and 100 hPa) for (a) observations (ERA5 analysis), (b) BMJ, (c) SAS, and (d) RSAS. Colour bar indicates convective precipitation range.

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The spatial plot of outgoing long wave radiation (OLR) from the Kalpana satellite observations (https://tropmet.res.in/~mahakur/Public_Data/index.php?dir=K1OLR/3Hrly) are plotted with BMJ, SAS and RSAS (figure 11). OLR is 3 hourly data with 0.25 × 0.25° resolution. Details about the data can be found in Mahakur et al. (2013). It is evident that in the initial stages of the cyclone and at the time of landfall, BMJ captured the OLR reasonably well, though it has overestimated the convection in between. SAS produced a weaker OLR throughout the cyclone duration and RSAS simulated an overestimated OLR.

Figure 11
figure 11

The outgoing long wave radiation (Wm−2) in (a–d) observations, (e–h) BMJ, (i–l) SAS and (m–p) RSAS on 00Z10Oct, 00Z11Oct, 00Z12Oct, 00Z13Oct, respectively, in each column.

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The joint probability density distribution (JPDD) (figure 12) is plotted to understand the association of precipitation and depth of cloud. Here OLR is considered as proxy for the depth of the cloud. Lower OLR indicates deep clouds (Abhik et al. 2017). All rainfall events and OLR values are counted into 20 mm day−1 and 20 Wm−2 bins, respectively. The JPDD indicates the contribution of rainfall or OLR distribution which is expressed in percentage in a particular bin for the entire period. Lighter rain rates from the cloud with higher OLR (meaning lower level cloud) are evident in the observation and also reasonably captured by BMJ and SAS (figure 12). Probability distribution of moderate and heavier rain rate are also well captured by BMJ. SAS underestimates the deep cloud and overestimates the moderate and heavier rain rates. The RSAS also shows overestimation of moderate rain rates. Hence the most appropriate distribution of rain from the right type of clouds appears to be simulated by BMJ. Similar kind of conclusion can be drawn for Viyaru and Lehar cyclones (figures not shown).

Figure 12
figure 12

Joint probability density distribution of daily OLR (Wm−2) and convective rainfall during cyclone period over the region 10–25°N, 82–97°E. The observed (OLR and TRMM rainfall) distribution is indicated in contours. The model distribution is shaded in each plot for CP scheme. (a) BMJ, (b) SAS, and (c) RSAS.

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5 Conclusions

In the present study, for the first time, we have implemented the Betts–Miller–Janjic (BMJ) cumulus parameterization scheme in NCEP Climate Forecast System version 2 (CFSv2) model and an attempt has been made to use the coupled (CFSv2) model to simulate three cyclones. Based on the previous promising results with BMJ parameterization scheme (Slingo et al. 1996; Mukhopadhyay et al. 2011; Kanase et al. 2015; Kanase and Salvekar 2015a, b), to improve the moist physical process especially the convective parameterization (CP) schemes in CFSv2, we have added one more CP scheme, i.e., BMJ in the model. Now BMJ, SAS and RSAS are the CP options available in CFSv2. To test this newly implemented CP scheme and evaluate its performance against SAS and RSAS and to evaluate the fidelity of coupled global model (CFSv2), three cases of tropical cyclones namely Phailin, Viyaru and Lehar of year 2013 are simulated.

The CFSv2 model is run with three different resolutions, i.e., T126 (~110 km), T382 (~38 km) and T574 (~27 km) with three CP schemes. Inter-comparison between the track and intensity at three resolutions reveal that T574 better simulates the TCs than other two resolutions. It also shows that track is less sensitive to CP scheme, although CP schemes show significant sensitivity to cyclone intensity with BMJ producing highest intensity. In line with intensity, BMJ simulates a warm core and maximum wind comparable with the standard vertical structure of a cyclone. The 24 hrs accumulated rainfall when compared with the TRMM observations also shows that the rainfall in and around the cyclone centre is better represented in BMJ than SAS and RSAS. Further analyses showed that BMJ, among all the three CP schemes could able to produce a higher precipitation by converting cloud water to precipitation within relatively longer time, which helps in building and sustaining the deep convection, reducing lighter rain rate and eventually able to simulate a more intense storm. Other two CP schemes produce lighter precipitation with short interval of time in the conversion process. This result is consistent with Eitzen and Randall (1999).

Both SAS and RSAS overestimate convective rain, whereas BMJ scheme produces convective rain comparable with observation due to the fact that BMJ produces a deeper convection and does not trigger convection too often. BMJ appears to sustain the instability and deep convection longer and impact the cyclone intensity and heavy rainfall associated with it. It is also noted that BMJ is efficient in producing rain than SAS and RSAS. From the analyses of OLR and rain rate, BMJ appears to simulate a much realistic relation of cloud and precipitation. The moisture adjustment process in BMJ is efficient in sustaining the convective instability and generating deep convection and heavier rain than the SAS and RSAS. As such, SAS and RSAS trigger the convection more frequently thus end up in generating more lighter and moderate rain rates. In short, most appropriate distribution of rain from the right type of clouds are simulated by BMJ.

The paper argues that compared to available SAS and RSAS, BMJ scheme realistically produces heavy precipitation associated with the tropical cyclone over the Indian region. This study also demonstrates that higher resolution coupled model could potentially be used for high impact weather events such as cyclones and thereby can provide a seamless forecasting framework from cyclone scale through extended to seasonal scale prediction based on CFSv2.