1 Introduction

The Himalayas in northern India significantly influence the meteorological patterns (weather and climate) of the Indian subcontinent. The severe weather phenomena and extreme events such as Heavy Rainfall Events (HREs) in the northern states of India, including Jammu and Kashmir, Himachal Pradesh, and Uttarakhand, are primarily influenced by their complex topography (Dimri et al. 2017; Bharti 2015; Shekhar et al. 2010). Seasonal winds that reverse their direction and cause precipitation are monsoon winds (Rajeevan et al. 2012; Ramage 1971). The Indian summer monsoon rainfall season comes with probably the most complex air-sea interaction circulation system globally. It mainly affects India and its surrounding regions and brings a lot of rain from June to September. It is also called the southwest monsoon season (Vellore et al. 2016; Rajeevan et al. 2012; Raju et al. 2005; Raghavan 1973). The Indian summer monsoon has different types of rain, whether onset and retrieve, active spell or break (Raju et al. 2005). Before the southwesterly monsoon circulation starts, intense spring heating causes a thermal low across the northern Indian subcontinent. Due to the high altitude of the Himalayan ranges, India's wind circulation patterns change during June and July (Singh and Mal 2014). Because of the lifting through the mountain slopes, the circulation overturns, causing the moisture content in the air mass to increase. Heavy precipitation occurs in that area when an air mass with enough moisture to precipitate saturates at a specific level. Because of the interplay of monsoon currents with the slopes, most rain falls in the valleys.

In the Shivalik foothills along the Beas River, Mandi (\(31.7^\circ \mathrm{N}, 76.7^\circ \mathrm{E}\)) is located in the heart of Himachal Pradesh, surrounded by high mountains and deep terrains with significant moisture content. The HRE refers to a confined meteorological event that lasts a few hours and occurs in a narrow section (less than 20–30 square kilometers). As a result of these calamities, flash floods, landslides, home collapses, transportation disruptions, and human fatalities occur. Cumulus convective clouds grow over a given area and have the potential to deliver a large amount of rain in a short period. Cumulonimbus convection is described as a result of steep orography and moisture-induced thermodynamic instability (Das et al. 2006). On August 04 and August 08 of 2010, similar incidents occurred over Mandi at roughly 0300 and 0400 UTC. Heavy downpour water caused landslides and flash floods, resulting in the deaths of five persons and the destruction of 44 houses and 82 cowsheds (Dimri et al. 2017; Jena et al. 2020). Many people lost their lives and possessions because the incident occurred at midnight. Cattle and automobiles were washed away in great numbers. During the monsoon season, cloudbursts are common in the NWH region, resulting in severe downpours of up to 100 mm/hr. The orography of the locations simulates the convective process, resulting in severe cloudbursts. The WRF model provides a wide range of the study of meteorological applications (Kumar et al. 2017; Tiwari et al. 2019, 2022; Tiwari and Kumar 2022, 2023). Several studies with the WRF model have been done over the NWH region, as shown in Table 1.

Table 1 The literature for HRE events study using the WRF model over India
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In the present study, an HRE over the Mandi (India) is considered for the high-resolution WRF model simulations on August 07 2015 (https://www.downtoearth.org.in/). It had caused flash floods and heavy landslides, due to which loss of lives and property were faced. INSAT-3D multispectral daily rainfall from the Meteorological Satellite Data Archival Center (MOSDAC) of Space Applications Center (SAC), India valid for 05:30 Indian Standard Time on 07 August 2015 over the Mandi region is shown in Fig. 1. The model set-up was customized with two domains (outer and inner) with horizontal resolutions of 27 and 9 km, respectively, and experiments were performed for ten cloud microphysics schemes.

Fig. 1
figure 1

INSAT-3D multispectral daily rainfall from the Meteorological Satellite Data Archival Center (MOSDAC) of Space Applications Center (SAC), India valid for 05:30 Indian Standard Time on 07 August 2015

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2 Model framework and experimental design

2.1 Model description

The non-hydrostatic Advanced Research WRF model developed by the National Center for Atmospheric Research (NCAR) (Skamarock et al. 2019) is used in the study. Table 2 shows the detailed configuration of WRF model version 3.8 used in this study. The model was set up with two nested domains with a resolution of 27 km (outer domain) and 9 km (inner domain). Figure 2 depicts these domains' size and the second domain's topography. The simulations were carried out on August 07 2015, over 24 h. A total of ten experiments were conducted for ten cloud microphysics (CMPs) (Table 3).

Table 2 Description of the WRF model configuration used in the study
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Fig. 2
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a Model domains in which two boxes indicate outer and inner domains with a horizontal resolution of 27- and 9-km, respectively. The detailed topography of the inner domain is shown in (b). The plus sign represents the location of the Mandi region (31.7°N, 76.7°E)

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Table 3 Description of the numerical experiments performed in the study by using various cloud microphysics schemes
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The initial and boundary conditions for the model integration were taken from the high-resolution Global Forecast System (GFS) with \(0.25^\circ \times 0.25^\circ\) spatial resolution and 6-h temporal resolution from the National Centers for Environmental Prediction-Global Data Assimilation System (NCEP-GDAS) and NCEP-Final (NCEP-FNL). The IMDAA reanalysis dataset (Ashrit et al. 2020, https://rds.ncmrwf.gov.in/) and the GPM IMERG (Final run) satellite estimate (Huffman et al. 2019, https://gpm.nasa.gov/data/directory) are being used to validate the model.

2.2 Experimental design

WRF cloud microphysics schemes are used, each with its own set of possibilities, and sensitivity experiments have been carried out (shown in Tables 2 and 3) while the other parameterization options are fixed. The brief details about selected CMPs are provided below:

2.2.1 CAM V5.1 double moment 5-class scheme

It is the most recent of a series of global atmospheric models developed. It is a double moment 5-class scheme (Eaton 2011), which predicts ice snow graupel.

2.2.2 Goddard scheme

It predicts hail and graupel separately and provides effective radii for radiation (Tao et al. 1989, 2016).

2.2.3 Purdue Lin scheme

It is a sophisticated scheme with ice, snow and graupel processes, suitable for real-data high-resolution simulations (Chen and Sun 2002).

2.2.4 Milbrandt-Yau double moment 7-class scheme

With the double-moment cloud, rain, ice, snow, graupel, and hail, the Milbrandt-Yau double-moment 7-class scheme (Milbrandt and Yau 2005a, 2005b) gives separate categories for hail and graupel.

2.2.5 Morrison double moment scheme

It is a double-moment scheme which predicts ice, snow, rain, and graupel for cloud-resolving simulations (Morrison et al. 2009).

2.2.6 Thompson scheme

In addition, the Thompson scheme (Thompson et al. 2008) is similar to WSM6, but it includes a more accurate saturation adjustment scheme and improved snow and graupel collection (Thompson et al. 2004).

2.2.7 WRF double moment 6-class scheme (WDM6)

This scheme (Lim and Hong 2010) has double-moment rain, ice, snow, and graupel processes suitable for high-resolution simulations. It also predicts cloud and cloud condensation nuclei (CCN) for warm processes, unlike WSM6.

2.2.8 WRF single moment 3-class scheme (WSM3)

It is a simple, efficient scheme with ice and snow processes suitable for mesoscale grid sizes (Hong et al. 2004).

2.2.9 WRF single moment 5-class scheme (WSM5)

It is a slightly more sophisticated version of WSM3 that allows for mixed-phase processes and super-cooled water (Hong et al. 2004).

2.2.10 WRF single moment 6-class scheme (WSM6)

It is a simple and efficient scheme with ice, snow, and graupel processes for high-resolution grid sizes (Hong and Lim 2006). WSM6 is also the best choice for cloud-resolving grids due to its efficiency and theoretical foundation.

3 Results

3.1 Comparison of the simulated rainfall for outer and inner domains

The model outputs for the HRE over the Mandi region are computed given two reanalysis products as the proxy for observation, namely IMDAA and GPM IMERG for the outer and inner domains, as shown in Figs. 3 and 4. We consider the HRE that happened across the study region for 24 h (1 day) on August 7, 2015. In this case, IMDAA revealed less precipitation (approx. 21.83 mm/day) across the study area (Figs. 3a and 4a). GPM IMERG detected heavier rainfall/precipitation (104.82 mm/day) than IMDAA, as seen in Figs. 3b and 4b. As a result, we can use GPM IMERG as a basis for comparison from observations.

Fig. 3
figure 3

Accumulated precipitation (mm/day) of the outer domain (1st) valid for 24 h during August 07 2015 from observations a IMDAA, b satellite estimate GPM IMERG (Final run), and from model outputs with different parameterization schemes, i.e., c CAM, d Goddard, e Lin, f Milbrandt-Yau, g Morrison, h Thompson, i WDM6, j WSM3, k WSM5, and l WSM6. The box symbol represents the location of the Mandi (31.7°N, 76.7°E) region

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Fig. 4
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Accumulated precipitation (mm/day) of the inner domain valid for 24 h during August 07 2015 from observations a IMDAA, b satellite estimate GPM IMERG (Final run), and from model outputs with different parameterization schemes, i.e., c CAM, d Goddard, e Lin, f Milbrandt-Yau, g Morrison, h Thompson, i WDM6, j WSM3, k WSM5, and l WSM6. The box symbol represents the location of the Mandi (31.7°N, 76.7°E) region

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The simulation with the Morrison scheme is the best match with GPM IMERG in the outer domain (Fig. 3), closely followed by the WSM5 and WSM3 schemes over the study region. The Morrison, WSM5, and WSM3 schemes spatially overestimated the IMDAA and GPM IMERG. When dealing with higher resolution for the inner domain (as illustrated in Fig. 4), WSM3 spatially outperformed GPM IMERG. The Morrison scheme (103 mm/day) is close to GPM IMERG at the Mandi location, followed by WSM5 (102.93 mm/day) and WSM3 (117.04 mm/day). According to Fig. 4g, k, the Morrison and WSM5 schemes spatially overestimated the observed rainfall. The rest of the schemes/experiments could not identify a significant proportion of the rain when transitioning from outer to inner domains.

Overall, we can infer that as we move from coarser to higher resolution, the WSM3 scheme is most consistent with GPM IMERG. However, the GPM IMERG and IMDAA were overestimated by the Morrison and WSM5 schemes. Furthermore, the other schemes could identify the most significant rainfall west of the Mandi location. As a result, we can conclude that the WSM3 scheme could capture the high rainfall event in terms of quantity and spatial distribution throughout the study region.

3.2 Bias in the simulated rainfall concerning the best scheme

As shown in Figs. 3 and 4, the WSM3 is a substantially better scheme for capturing the high rainfall event in the study region. As a response, we have used this scheme to compute the bias for the model simulations using the other schemes. The bias in rainfall amount in the different schemes concerning the WSM3 has been estimated geographically for the outer (1st) and inner (2nd) domains, respectively, in Figs. 5 and 6. Figures 5 and 6 show that the Morrison and WSM5 schemes are reasonably similar to the WSM3. It is also noted that the WSM3 underestimates the other schemes (Fig. 5) in Mandi's west-south region, whereas the WSM3 underestimates and overestimates the other schemes (Fig. 6) in the Mandi location's west-south region and diagonal region, respectively. Overall, we can conclude that when we assess from coarser to higher resolution, Morrison and WSM5 schemes are very close to the WSM3.

Fig. 5
figure 5

Bias (mm/day) in precipitation of the outer domain valid for 24 h during August 07 2015 from the best model WSM3 with other parameterization schemes, i.e., a CAM, b Goddard, c Lin, d Milbrandt-Yau, e Morrison, f Thompson, g WDM6, h WSM5, and i WSM6. The box symbol represents the location of the Mandi (31.7°N, 76.7°E) region

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Fig. 6
figure 6

Bias (mm/day) in precipitation of the inner domain valid for 24 h during August 07 2015 from the best model WSM3 with other parameterization schemes, i.e., a CAM, b Goddard, c Lin, d Milbrandt-Yau, e Morrison, f Thompson, g WDM6, h WSM5, and i WSM6. The box symbol represents the location of the Mandi (31.7°N, 76.7°E) region

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3.3 Explanation of the rainfall patterns with various meteorological parameters

3.3.1 Simulation of cloud fraction

The fraction of low, mid, and high clouds from all the experiments have been illustrated in Figs. 7–9. It is defined as a proportion of the cloud cover over a grid box indicating the tiny droplets and/or ice particles in the lower and mid atmosphere. A cloud percentage of 1 signifies that the pixel is entirely clouded, whereas a cloud percentage of zero means the pixel is cloudless (Chen et al. 2012). The colors of clouds vary from green (no clouds) to red (clouds maxima). The high, mid, and low clouds form above the earth's surface at 6000 m, 2000 m, and 300 m, respectively.

Fig. 7
figure 7

Low cloud fraction (%) of the inner domain valid for 24 h on August 07 2015 with different parameterization schemes, i.e., a CAM, b Goddard, c Lin, d Milbrandt-Yau, e Morrison, f Thompson, g WDM6, h WSM3, i WSM5, and j WSM6. The box symbol represents the location of the Mandi (31.7°N, 76.7°E) region

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It is shown from Fig. 7 that the formation of low cloud fraction is most significant in the Morrison scheme, followed by WSM3 and CAM over the study region. On the other hand, the Lin and Thompson schemes exhibited a smaller fraction of low clouds. It can also be observed that the Morrison, CAM, and WSM5 schemes encountered a large fraction of clouds spatially in their respective regions. In addition, the analysis of Fig. 8 reveals that establishing a mid-level cloud cover percentage/fraction occurs more often in the Morrison scheme spatially. Both the WSM3 and the WSM5 experiments cannot identify the spatial distribution of cloud cover. Except for Morrison, WSM3, and WSM5, all schemes have shown considerable mid-cloud cover to the northwest of the Mandi region. The high cloud cover fraction is computed for each of the schemes, and the results are shown in Fig. 9. It has been seen that the probability of a heavy high cloud cover forming in the Morrison scheme is substantial over the Mandi area along with some other locations. In addition, it can be observed that all of the schemes, except CAM and Morrison, have shown a significant amount of heavy high cloud cover to the southeast of the Mandi location. Thus, it can be concluded that spatially, the probability of low, mid, and high cloud cover formation is prominent in the Morrison scheme.

Fig. 8
figure 8

Mid-level cloud fraction (%) of the inner domain valid for 24 h on August 07 2015 with different parameterization schemes, i.e., a CAM, b Goddard, c Lin, d Milbrandt-Yau, e Morrison, f Thompson, g WDM6, h WSM3, i WSM5, and j WSM6. The box symbol represents the location of the Mandi (31.7°N, 76.7°E) region

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Fig. 9
figure 9

High cloud fraction (%) of the inner domain valid for 24 h on August 07 2015 with different parameterization schemes, i.e., a CAM, b Goddard, c Lin, d Milbrandt-Yau, e Morrison, f Thompson, g WDM6, h WSM3, i WSM5, and j WSM6. The box symbol represents the location of the Mandi (31.7°N, 76.7°E) region

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3.3.2 Simulation of cloud reflectivity and hydrometeor

The reflectivity measures the amount of solar radiation reflectance due to the cloud bands. A large reflectivity distribution indicates the presence of clouds that may generate rainfall. The maximum reflectivity of the inner domain is plotted for ten experiments (provided in Table 3), as can be seen in Fig. 10. It has been noticed that the Morrison scheme displays the maximum reflectivity of radiations over the domain, followed by the WSM5 scheme. If we compare all the schemes, a large proportion of cloud reflectance was seen to the west of the Mandi location, except for WSM3 and WSM5. The WSM3 and WSM5 schemes indicated the maximum reflectivity when looking southeast from the HRE location. The model simulations denote that the Morrison scheme showed the highest possible reflectivity across the domain.

Fig. 10
figure 10

Maximum reflectivity (dBZ) of the inner domain valid for 24 h on August 07 2015 with different parameterization schemes i.e., a CAM, b Goddard, c Lin, d Milbrandt-Yau, e Morrison, f Thompson, g WDM6, h WSM3, i WSM5, and j WSM6. The box symbol represents the location of the Mandi (31.7°N, 76.7°E) region

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Figure 11 displays the vertical profile of model simulated hydrometeor water vapor mixing ratio (Qvapor; unit: Kg/Kg) from the experiments related to the CMP schemes (CAM, Goddard, Lin, Milbrandt–Yau, Morrison, Thompson, WDM6, WSM3, WSM5, and WSM6) over the study region valid for 07 August 2015. Qvapor is the ratio of the mass of water vapor to the mass of dry air in a given volume in the atmosphere. The behavior of the model simulations was more or less similar for all the schemes as they showed a gradual decrease of the Qvapor (~0.018 to ~0.001 kg/Kg)) from the lower troposphere to the mid-troposphere (500 to 400 hPa). In the lower atmosphere, simulations with CAM and WSM5 schemes produced relatively lesser values than others.

Fig. 11
figure 11

Vertical profile of simulated water vapor mixing ratio (Kg/Kg) valid for 07 August 2015 over the Mandi, India

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3.3.3 Simulation of maximum convective available potential energy (MCAPE)

Figure 12 depicts the simulated MCAPE (J/kg) from all experiments for the inner domain. The figure shows that Milbrandt-Yau, Thompson, WSM6, and Lin have the highest MCAPE values across the domain. Furthermore, the MCAPE value for the Mandi location is relatively high (up to 1016.82 J/kg) in the Milbrandt scheme, followed by Thompson (889.32 J/kg). The MCAPE values for the CAM, Morrison, WSM3, and WSM5 schemes were relatively lower. The figure further demonstrates the Thompson, Milbrandt-Yau, Lin, and WSM6 schemes have a high value of MCAPE in the southwest of the study location. Overall, the Thompson and Milbrandt-Yau schemes showed maximum potential to perform the convection process over the domain.

Fig. 12
figure 12

Maximum Convective Potential Energy (MCAPE) (J/kg) of the inner domain valid for 24 h during August 07 2015 with different parameterization schemes i.e., a CAM, b Goddard, c Lin, d Milbrandt-Yau, e Morrison, f Thompson, g WDM6, h WSM3, i WSM5, and j WSM6. The box symbol represents the location of the Mandi (31.7°N, 76.7°E) region

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3.3.4 Simulation of wind patterns at 850 hPa

The wind flow field is analyzed for the inner domain for all the schemes at 850 hPa. The results are shown in Fig. 13. All the schemes have the wind flow field located in the south and southwest of the domain only due to the high altitude in the north and northeast regions. The wind flow field over the study area showed a consistent pattern throughout in Fig. 13a–d, f, g, as well as (j). The Morrison, WSM3, and WSM5 schemes produced the same wind flow pattern with a speed of 10 m/s. In addition, it can be noted that the wind speed is low on the periphery of the Mandi region; however, the wind flow is vital in the western part of it and blows in a direction that is parallel to the x-axis and in the southeast direction. Aside from that, every other experiment had the same wind pattern but an abrupt and quick bend toward the north direction. Overall, the wind flow pattern is more or less similar in Morrison, WSM3, and WSM5 schemes throughout the domain, with a magnitude of 10 m/s.

Fig. 13
figure 13

Wind flow field (m/s) of the inner domain valid for 24 h during August 07 2015 with different parameterization schemes i.e., a CAM, b Goddard, c Lin, d Milbrandt-Yau, e Morrison, f Thompson, g WDM6, h WSM3, i WSM5, and j WSM6 at 850 hPa. The box symbol represents the location of the Mandi (31.7°N, 76.7°E) region

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4 Summary

In this study, the high-resolution Weather Research and Forecasting (WRF) model simulated a heavy rainfall event (HRE) over the Mandi region (31.7°N, 76.7°E) on August 07 2015. The Mandi is located in the Himachal Pradesh state of India at an elevation of 760 m from mean sea level. This weather system was quite severe regarding precipitation/rainfall, highlighted and reported by the Indian Meteorological Department and top-level national–international media. To analyze its various characteristics, we have simulated this event by performing the sensitivity experiments with ten cloud microphysics parameterization schemes, as discussed in Tables 2 and 3. The high-resolution and globally accepted reanalysis and satellite-based precipitation products IMDAA and GPM IMERG have been used as a proxy for the observation to validate the model outputs. We have evaluated this event by taking two nested domains on which lateral boundary and initial conditions have been incorporated. These conditions are taken from NCEP with \(0.25^\circ \times 0.25^\circ\) horizontal and six hourly temporal resolutions.

It was found that when we move from coarser to higher resolution (or outer to inner domain), the WSM3 scheme/experiment is the sole one that is most consistent with GPM IMERG. However, the GPM IMERG and IMDAA were overestimated by the Morrison and WSM5 schemes. Furthermore, the other schemes could identify the maximum rain proportion to the Mandi location's west. Therefore, the WSM3 scheme could capture the high rainfall event in terms of quantity and spatial distribution throughout the study region. Furthermore, the bias in simulated rainfall distribution is evaluated for both domains using all the schemes concerning WSM3. When we assess from coarser to higher resolution, Morrison and WSM5 schemes are very close to the WSM3. Moreover, other meteorological parameters are evaluated, such as cloud fraction, maximum reflectivity due to clouds, MCAPE, and wind flow field associated with rainfall patterns. The probability of low, mid, and high cloud cover formation was prominent in the Morrison scheme. Also, the Morrison scheme showed the highest possible reflectivity across the domain. In contrast, MCAPE was evaluated across the domain, and it was concluded that the Thompson and Milbrandt-Yau schemes showed maximum potential to perform the convection process over the domain. Apart from this, the wind patterns are also evaluated at 850 hPa over the region. The wind flow pattern was more or less similar in Morrison, WSM3, and WSM5 schemes throughout the domain, with a magnitude of 10 m/s.