Additional insights from convection-permitting scale ensembles in simulating spatiotemporal features of precipitation across the complex terrain of Peninsular India

Abstract

The study assesses the predictability of rainfall patterns in India through 3-day precipitation forecasts from a regional climate model ensemble framework operating at convection-permitting (CP) scales. Initially, 149 experiments are conducted across four events representing different rainfall mechanisms. The performance of a larger set of 55 ensemble members within the multi-physics ensemble framework is evaluated using quantitative metrics such as composite scaled scores and cross-correlation analyses. This evaluation led to the development of an optimally designed smaller member ensemble framework, WRF-CP7, which reduces turnaround time while maintaining the spatial and temporal performance of simulated precipitation fields. The study further assesses the reliability of this framework over an extended period, utilizing insights from 5544 simulations (792 days × 7 ensemble members running for a 90-h lead time) conducted between September 2015 and December 2017. Comparisons between WRF-CP7 and a global climate model forecasts available at coarser resolution highlight the need of parameterization and ensemble framework at convection-permitting scale. WRF-CP7 demonstrates skill in capturing spatiotemporal variability of rainfall occurrences, evidenced by a higher spread–error correlation (0.9 vs. 0.6 in the global model) among ensemble members. The correlation remains consistent even at higher lead-times, in contrast to the reducing skill of the global model with increasing lead-time. WRF-CP7 also shows reduction in spatial and temporal errors within simulated diurnal precipitation patterns, notably during Indian Summer Monsoon, Pre-Monsoon Thunderstorm activities and North-East Monsoon. A notable 30% increase in predictability for moderate to heavy rain intensities is observed across all seasons, accompanied by a 10% decrease in false alarms compared to global model ensemble forecasts. The spatial skill of WRF-CP7 for moderate-heavy intensity events remains high (50–80%) even with a longer lead time of 72-h on an intra-seasonal timescale. With a substantial sample size, the results underscore the effectiveness of using the multi-physics ensemble framework at convective scales for operational forecasting and dynamic downscaling of climatology across the Indian subcontinent.

1 Introduction

Forecasting the amount and distribution of precipitation realistically over time and space poses a significant challenge in Numerical Weather Prediction (NWP). This challenge arises from the complex interactions among various weather processes, with precipitation exhibiting more rapid and nonlinear error growth compared to other weather variables (Fritsch et al. 1998; Mullen and Buizza 2001; Ebert et al. 2003; Bei and Zhang 2007; Huang and Luo 2017). High-resolution numerical weather models, known as Convection-Permitting scale models (CPMs), have emerged as a solution to address the limitations of traditional NWP models, particularly for predicting Quantitative Precipitation Forecasts (QPFs). At a higher resolution, CPMs are expected to more effectively capture localized weather phenomena, including mesoscale convective systems, land–ocean contrasts, and orographic lifting. These features can contribute diverse feedback to larger-scale phenomena. Consequently, CPMs have demonstrated better skill compared to the NWP models at coarser scales (Weisman et al. 2008; Clark et al. 2009; Prein et al. 2015; Clark et al. 2016; Li et al. 2018; Woodhams et al. 2018; Hanley et al. 2021; Kirthiga et al. 2021; Risanto et al. 2022).

However, uncertainties increase at finer scales (Lorenz 1969; Walser and Schär 2004; Bei and Zhang 2007; Melhauser and Zhang 2012; Zhang et al. 2019), rendering deterministic forecasts with a single realization of the given atmospheric state obsolete, especially for longer lead-times (Fritsch et al. 1998; Mullen and Buizza 2001; Bei and Zhang 2007; Prakash et al. 2016; Kirthiga et al. 2021). To tackle this issue, ensemble approaches that incorporate input and model-based errors have gained popularity (Surcel et al. 2015; Frogner et al. 2019; Risanto et al. 2022) and are operational in forecasting centers worldwide (Gebhardt et al. 2011; Bouttier et al. 2012; Tang et al. 2013; Schwartz et al. 2015, 2019; Wastl et al. 2021).

Despite their advantages, CPM ensembles tend to be under-dispersive, overconfident, and computationally demanding without significantly enhancing the quality of weather forecasts (Weisman et al. 2008; Melhauser and Zhang 2012; Clark 2019). Therefore, there is a need to develop effective ensemble designs tailored explicitly for convection-permitting scales. While early research focused on sampling uncertainties in the input space (initial and lateral boundary condition) due to the abundance of research happening in the mid-latitude (extra-tropical) regions where baroclinic perturbations primarily characterized the major atmospheric disturbances (Walser and Schär 2004). Many processes seem to be under-resolved even with finer-scale ensembles, particularly in the tropics characterized mainly by warm-season weather systems (Mullen and Buizza 2001; Bei and Zhang 2007; Woodhams et al. 2018; Hanley et al. 2021). More recent studies have emphasized the importance of incorporating model uncertainty into CPM ensembles to capture the nonlinear error growth of convective events (Berner et al. 2011, 2015; Romine et al. 2014; Wang et al. 2020). Various approaches, including multi-model (Melhauser et al. 2017), multi-physics (Berner et al. 2011; Clark et al. 2010; Gebhardt et al. 2011; Kirthiga et al. 2021), multi-parameter perturbations (Yussouf and Stensrud 2012; Wang et al. 2020), and stochastic physics schemes (Berner et al. 2011; Romine et al. 2014), have been explored. However, their applicability to convection-permitting regional climate models is not well-established (Baker et al. 2014; Wang et al. 2020).

In the context of the Indian sub-continent, CPMs have shown promise in improving the predictability of major rainfall periods, such as the South-west monsoon (Prakash et al. 2016; Hazra et al. 2020; Samanta et al. 2020), North-east monsoon (Srinivas et al. 2013; Madhulatha and Rajeevan 2018; Singh et al. 2018), and Pre-monsoon thunderstorms (Madala et al. 2014; Das et al. 2015; Halder and Mukhopadhyay 2016). The uncertainty surrounding the representation of microphysical cloud processes of major rainfall mechanisms in Indian climatology by major climate models (Madhulatha and Rajeevan 2018; Kirthiga et al. 2021; Samanta et al. 2023) has led to non-overlapping findings from earlier studies. As a result, there exists a significant gap in understanding the most suitable model configurations for convection-permitting scales. Furthermore, previous studies have focused on performance evaluations for extreme events rather than examining CPM ensembles' error growth and skill in capturing the spatiotemporal variability of all rainfall categories significant to allied sectors like agriculture and water resources management. Therefore, it remains unclear how these conclusions can be applied to an operational framework that spans both intra-seasonal and inter-annual variability. It is essential to systematically investigate and quantify the ensemble properties of the multi-physics model at the convective level (Risanto et al. 2022).

In a prior study, Kirthiga et al. (2021) emphasized the significance of a multiphysics ensemble in capturing spatiotemporal variability in QPFs from diverse rainfall mechanisms at a high 4 km spatial resolution. Building on this, the primary goal of the current research is to establish an operationally feasible convective-scale ensemble, comprising: 1) Building a larger member multi-physics ensemble framework using a Regional Climate Model (RCM)—Weather Research and Forecasting (WRF) model. Devise strategies for designing effective ensemble framework with a limited number of members – WRF-CP7 (Convection Permitting 7-member ensemble from WRF, termed as WRF-CP7 in the manuscript), while maintaining spatio-temporal quality of the precipitation forecasts. The choice of a 7-member ensemble is determined through comprehensive assessments covering deterministic and probabilistic aspects across seasons, ensuring operational feasibility. 2) Quantifying the statistical significance of the suggested smaller-member framework for predicting rainy days, no-rain days and various classes of rainfall intensities over 28 months (September 2015 to December 2017), and 3) Investigative the added value by the multiphysics ensembles at convective-permitting scales against the coarser-scale Global Ensemble Forecast System (NCEP-GEFS20). This study aims to assess the uncertainty in the convection-permitting model and its representation of physical processes in the Indian domain during the important monsoon period (Indian Summer Monsoon and North-East Monsoon/ Retreating Monsoon). The results will contribute to improving the representation of physical processes in the Indian subcontinent, enhancing short to medium-range precipitation forecasts at finer scales. The structure of the manuscript includes Section 2 detailing the data and methods used, Section 3 presenting results and discussions on the benefits of the CPM multiphysics ensemble framework, and Section 4 summarizing key conclusions.

2 Methodology

The methodology is structured into two main sections: Section 2.1 "Formulation of Multiphysics ensemble framework" elaborates on the experimental design used to establish the optimal size of multi-physics ensembles, leading to the formulation of the WRF-CP7 ensemble framework. Section 2.2 "Added value by proposed limited member convective-permitting Multiphysics ensemble framework" provides an in-depth overview of the data and materials utilized to understand the consistency of the performance of the model and assess the added value of the proposed multi-physics ensemble across diverse temporal and spatial dimensions.

2.1 Formulation of multiphysics ensemble framework

2.1.1 Design of experiments

The study builds upon previous research conducted by Kirthiga et al. in 2021 (P1 hereafter). In the present study, we utilized the non-hydrostatic Weather Research and Forecasting (WRF) model version 4.0 developed by Skamarock et al. (2019). The model setup closely resembled that of P1, and any modifications will be elaborated further in the study. The lateral boundary conditions were obtained from the Global Forecast System (GFS) control run in forecast mode (ftp://ftp.ncep.noaa.gov/pub/data/nccf/com/gfs/prod). The Global Data Assimilation System (GDAS), employing a 4D hybrid ensemble-variational data assimilation scheme, generated initial conditions for the GFS forecast and was utilized in this study. The data was introduced into the model at 3-h intervals at a spatial resolution of 0.25 degrees (National Centers for Environmental Prediction/National Weather Service/NOAA/U.S. Department of Commerce 2015).

For the model configuration, two domains were used based on the conclusions drawn from P1. The parent domain – Domain 1, covered South peninsular India and encompassed 148 × 148 grid points at a resolution of 12 km (extent: 69.57E-85.63E; 0.83N-16.64N). The nested inner domain – Domain 2, used for performance assessment, was set up at a resolution of 4 km with 166 × 169 grid points (extent: 74.596E-80.604E, 5.732N-11.775N) (Fig. 1a). The model integration involved an adaptive time-step, 40 vertical levels, and a model top set at 50 hPa. The NWP models often require a user-selected constant time-step, posing a challenge as a long time-step can cause model instability for high resolution forecasts, and a shorter time-step demands excessive computing power. The optimal temporal granularity of the time-step depends on the dynamic physical processes resolved by the model at a given spatial resolution, varying daily between different rainfall and weather mechanisms. Employing an adaptive time-step dynamically adjusts to the optimal time-step supporting underlying motions, ensuring model stability and reducing total run-time compared to a static time-step. This approach was implemented in the study to improve the operational feasibility of the resulting model framework. The numerical implementation of the adaptive time-step within WRF model can be found in Hutchinson (2007).

Fig. 1

(a) Model domains and (b) Analysis Domain (represented by Domain 2 red shaded in (a)), showcasing a detailed topography map with selected evaluation zones. Western Coasts (WC) regions are termed as DOM1, Western Ghats (WG) as DOM2, Eastern Coasts (EC) as DOM3 and Central TamilNadu (CTN) as DOM4. Refer to Table 1 in supplementary material for further details

Table 1 List of physics combinations investigated in the study

Four specific moderate-extreme rainfall events were considered, consistent with P1, namely Ochki (OCH) event (00 UTC 28 Nov 2017 – 06 UTC 02 Dec 2017), the Gaja (GAJ) event (00 UTC 16 Nov 2018 – 06 UTC 20 Nov 2018), the Indian Summer Monsoon/South-West Monsoon (SWM) event (00 UTC 12 Aug 2018 – 06 UTC 16 Aug 2018), and a thunderstorm event from the Pre-monsoon (SUM) time period (00 UTC 13 Apr 2018 – 06 UTC 17 Apr 2018). The OCH and GAJ events correspond to episodes of tropical cyclones during the North-East Monsoon (NEM) or retreating monsoon period (October-December). These cyclonic events, intensified by synoptic conditions in the Bay of Bengal (BOB), resulted in heavy rainfall and strong winds, leading to significant damage in Tamilnadu and Kerala. On the other hand, the SWM event occurred during the significant Indian Summer Monsoon (ISM) period (July–September) and was driven by pressure differences between the Arabian Sea and BOB, resulting in extensive rainfall and subsequent flooding in Kerala. The SUM event represented a convective event characterized by evening thundercloud clusters across Tamilnadu, causing localized moderate to heavy rainfall. These events were selected to understand and measure the ability of the model to perform under different rainfall mechanisms covering different spatial scales and varying rainfall intensities. Detailed discussions and justification regarding the selected four events can be found in P1, not included here for brevity.

Apart from the physics schemes discussed in Sect. 2.1.2, the remaining physics schemes were maintained the same across all experiments. The radiation physics component included the RRTM Longwave Scheme by Mlawer et al. 1997, which accounted for longwave radiation processes, and the Dudhia shortwave radiation scheme developed by Dudhia 1989, which represented the shortwave component. The planetary boundary layer was represented using the Yonsei University Scheme (YSU) of Hong et al. 2006, while the surface layer formulation was used on the Revised MM5 Scheme of Jiménez et al. 2012. The model setup used the Noah Land Surface Model (LSM) (Tewari et al. 2016), which uses a four-layer soil representation to simulate the land surface processes.

2.1.2 Selection of physics schemes

In the previous study (P1), the impact of input data quality, model domain setup, and physics schemes on the model's performance was investigated. The spatiotemporal rainfall variability in the four selected events was better represented by employing multiphysics ensembles, including variants from representation of cumulus and microphysics schemes. However, it is worth noting that P1 only explored a limited range of physics combinations and did not fully examine the interaction effects between different cumulus and microphysics schemes. The present study is focused on evaluating the performance of a diverse set of physics suites, including both established and recently introduced cumulus and microphysics schemes in the WRF model. The assessment also considered their combined efficacy.

Seven cumulus schemes were considered viz. The Kain–Fritsch (KF) scheme, a slightly modified version of KF, the Kain–Fritsch cumulus potential scheme (MKF), Betts–Miller–Janjic (BMJ) scheme, Simplified Arakawa–Schubert scheme (SAS), Grell-Freitas (GF) ensemble cumulus scheme, New Tiedtke (NT) cumulus scheme and Multi–scale Kain–Fritsch (MsKF) cumulus scheme. In addition, two trigger functions for KF scheme that use moisture advection and relative humidity-based trigger were also tested. All the cumulus schemes are mass-flux schemes, except for BMJ which is an adjustment type static scheme. Detailed information about the specifications of each of the cumulus schemes can be found in the supplementary material, Section 5.2.

The primary finding of P1 was that simulations without cumulus schemes in the 4 km domain were unable to adequately represent the full range of precipitation features, especially within the Indian climatological context. Consequently, experiments were conducted in this study to evaluate the performance of major schemes with (referred to as the CUM cluster) and without implementation in domain 2 (referred to as the No-CUM cluster). The scale-aware mass-flux cumulus schemes, including Grell-Freitas (GF) ensemble cumulus scheme, New-Tiedtke cumulus scheme and Multi–scale Kain–Fritsch (MsKF), were also tested for CUM and No-CUM variants. However, only minimal differences in simulation output were observed with these schemes, attributed to their scale-aware nature. Consequently, the study presents results only from implementing the schemes in both domains (the CUM variant).

Additionally, based on the insights gained from P1, we acknowledge the role of microphysics schemes in accurately representing peak rainfall intensities by realistically representing the distribution of raindrops. The interactive behavior between each cumulus scheme and the microphysics schemes requires careful evaluation, as certain combinations have exhibited notable spatial and temporal errors (Jeworrek et al. 2019). We have considered four microphysics schemes, including two double-moment schemes (Morrison and WDM6) and two single-moment schemes (Lin and Goddard). These schemes offer a comprehensive range of options for simulating hydrometeors, encompassing water vapor, graupel, rain, cloud, cloud ice, and snow. Although they differ in their approach to simulating the number concentrations and mixing ratios of these hydrometeors, all four schemes have proven effective in the context of the Indian subcontinent. Thus, these four schemes were selected for analysis in the manuscript based on the conclusions from P1 and previous studies (Duda et al. 2014; Halder and Mukhopadhyay 2016; Pithani et al. 2019; Musaid et al. 2023).

Thus, a total of 55 combinations (mentioned as WRF-CP55 hereafters in the manuscript) were formulated and are presented in Table 1. Cases C0, C6, C8, C14, C16, C22, C24, C30, C32, C34, C36, C38, C40, C42, C44, C46, C48, C50, C52, and C54 represent explicit simulations without cumulus schemes in domain 2 which are referred to as No-CUM cluster (cases marked with * in Table 1).

2.1.3 Final set of experiments

A run-time limit of 7 h was set (based on the resource constraints elaborated in Section 5.1 of supplementary material) to enable the practical feasibility of applying the multiphysics ensemble for real-time weather forecasting. Thus, due to the dynamics of the selected events, 39 combinations practically converged for OCH, 36 combinations for GAJ, 40 combinations for SWM, and 36 combinations for SUM. The details of the individual case numbers for each event are given in Table 1. Overall, 149 experiments for the four events were evaluated, and the results are presented.

2.1.4 Methods for a comprehensive ensemble framework design

The study employed data from the Integrated Multi-satellitE Retrievals for Global Precipitation Mission (GPM-IMERG) at a spatial resolution of 10 km (referred to as GPM), as described by Huffman et al. (2014). GPM data served as a benchmark for relative comparison to evaluate the performance of the simulations. Gupta et al. (2020) highlighted the superior skill of GPM data to represent the spatial and temporal distribution of the extreme events in India. Subsequently, Kirthiga et al. (2021), in previous research, employed GPM data for the same events examined in this study. Hence, this study utilized GPM for preliminary analysis to ensure consistent evaluation across both investigations. Grid-based statistics are commonly employed for weather modeling performance assessment. While grid-to-grid comparisons offer straightforward evaluations, they can penalize model simulations that accurately represent precipitation intensity and organization but exhibit slight spatial or temporal displacement—a phenomenon known as the double penalty effect (Rossa et al. 2008). This issue is particularly pronounced in high-resolution convective-scale precipitation forecasting, necessitating the inclusion of additional statistics. Therefore, this study explores verification metrics ranging from grid-based continuous and categorical metrics to spatial performance and probabilistic skill metrics, as listed in Table 2. Rainfall intensity classification followed the India Meteorological Department (IMD) classification for hourly and daily rainfall amounts, including no rain (< 1 mm/6 h, < 2.5 mm/day), light rain (1– 10 mm/6 h; 2.5–15.5 mm/day), moderate rain (10.1–20 mm/6 h; 15.6–64.4 mm/day), and heavy to extremely heavy rainfall (> 20.1 mm/6 h; > 64.5 mm/day) (India Meteorological Department, https://mausam.imd.gov.in/imd_latest/contents/pdf/pubbrochures/Heavy%20Rainfall%20Warning%20Services.pdf).

Table 2 Performance metrics and verification strategies employed to evaluate the model simulations

2.2 Added value by proposed limited member convective-permitting Multiphysics ensemble framework

2.2.1 Design of experiments

The model configuration detailed in Section 2.1.1 was applied, with the exception of adjustments made to the cumulus and microphysics schemes from results from Section 3.2. The lateral boundary conditions and initial boundary conditions were same as those detailed in Section 2.1.1 (ftp://ftp.ncep.noaa.gov/pub/data/nccf/com/gfs/prod). An assessment of the proposed limited member ensemble framework, denoted as WRF-CP7 and comprising 7 ensemble members (see Section 3.2 for clarity on the selection of the members), was conducted over an extended period to assess the operational feasibility of the framework. The simulations spanned from September 2015 to December 2017, covering a total of 792 days (28 months), with a lead time of 90 h. A total of 5544 simulations (792 days × 7 ensemble members running for a 90-h lead time) were executed, and this study provides an assessment of the performance of the proposed framework in simulating precipitation. The evaluations focused on the prediction of various rainfall intensities during specific seasons, also considering performance across lead times (Refer to Table 2 for clarity).

2.2.2 Evaluation zones

Selected evaluation zones (DOM1, DOM2, DOM3, and DOM4) in Tamil Nadu and Kerala (Fig. 1) were chosen to assess the consistency of simulated precipitation across different agro-climatic conditions (refer to Table 1 in the supplementary material). The demarcation of these zones was primarily based on major agro-ecological classes from the Food and Agriculture Organization (FAO), Global Agro Ecological Zones v4 (GAEZv4) classification (Fischer et al. 2021), considering temperature regime, soil-moisture regime, soil/terrain class, and land-cover classes. DOM1 is predominantly in the 'Tropics, lowland humid' zones (GAEZv4 class numbers 5, 6), DOM2 in 'highland, humid with dominantly steep terrain' zones (GAEZv4 class numbers 12, 49, 50), DOM3 in 'Tropics, lowland semi-arid' zones (GAEZv4 class numbers 1, 2), and DOM4 in 'Land with ample irrigated soils' zones (GAEZv4 class numbers 51). These chosen classes are widely prevalent in the tropics and the evaluation of the predictability of precipitation in these zones allows for scaling up the findings from the study to the broader Indian and Asian context. In addition to the GAEZv4 classes, the delineation of the final four evaluation zones (Fig. 1a) also considered monsoonal patterns and local administrative boundaries (refer to the supplementary material, Section 5.2 for more details).

2.2.3 Coarser-resolution convection-parameterizing ensembles

The assessment of added value from the convection-scale multiphysics ensemble framework utilized the Global Ensemble Forecast System (GEFS) version V11.0 from the National Centers for Environmental Prediction (NCEP). This system consists of 20-member ensembles at a resolution of 0.5 degrees (NCEP-GEFS20). Data was retrieved from the THORPEX Interactive Grand Global Ensemble project (TIGGE 2021). Selecting GEFS data to benchmark the performance of the proposed ensemble framework and quantify the added value by convective-scale ensembles was conducted thoughtfully, as it utilizes the same input as used by the regional WRF model. NCEP-GEFS ensembles primarily result from perturbations in initial and lateral boundary conditions from the control member (NCEP-GFS), utilizing the Ensemble Kalman Filter (EnKF) technique. Additionally, they include recently introduced model uncertainty perturbations through the Stochastic Total Tendency Perturbation (STTP) method.

2.2.4 Verification data and methods

IMDAA reanalysis data (Indirarani et al. 2021) was used to assess the long-term performance. The reanalysis data has a horizontal resolution of 12 km (equivalent to 0.12-degree) at 3-h intervals. A resampling procedure was followed to bring other datasets to the same resolution as IMDAA. IMDAA data was chosen for its integration of a larger network of observation data from the India Meteorological Department (IMD) into the reanalysis dataset (Indirarani et al. 2021). Notably, IMDAA data has demonstrated superior performance in capturing precipitation extremes and spatio-temporal weather patterns across the Indian subcontinent compared to other reanalysis datasets (Singh et al. 2021).

An assessment was carried out across evaluation zones (Section 2.2.2) to comprehend the behavior of the model simulations across various seasons, topography, and climatology. Evaluation metrics employed for the long-term assessment are detailed in Table 2. For practical applications, determining the most useful deterministic value from the ensemble members involved utilizing both the ensemble mean (EM) and the value derived using the probability matching method (PMM) proposed by Ebert et al. (2003).

3 Results and discussion

3.1 Simulation of precipitation by multi-physics combinations across four extreme events

3.1.1 Model behavior across the different physics schemes

In this study, we classified the combinations of multiphysics simulations into two primary clusters: the CUM cluster and the No-CUM cluster. The CUM cluster incorporated cumulus schemes in domain 2, while the No-CUM cases represented explicit convection using microphysics schemes without a cumulus scheme in domain 2 (Table 1). Analysis of the domain-averaged temporal precipitation rates (mm/6 h) (Supplementary material Fig. S1) revealed a significant spread in the range of 1 mm/6 h to 5.5 mm/6 h across lead-times and events, largely evident when varying cumulus physics schemes in both domains (CUM cases). The cases within the CUM cluster (dashed lines in supplementary material Fig. S1) displayed earlier initiation of events and closely matched the intensities of peak events, aligning well with the temporal profile of GPM-IMERG data. Conversely, the No-CUM cases (C0, C6, C8, C14, C16, C22, and C24) showed a narrower spread of < 2 mm/6 h on average, suggesting lower internal variability among these cases. This indicates that the different cumulus schemes in the parent domain demonstrated minimal impact on the precipitation simulated in domain 2 for the selected events. Furthermore, No-CUM cases simulated delayed precipitation and lower peak intensities across extreme rainfall events. However, it was observed that No-CUM cases better represented weak convective activities (light rainfall of < 5 mm/6 h) with a higher success ratio exceeding 0.6. Research findings suggest that microphysics schemes are more effective in resolving stratiform clouds associated with low to moderate intensity rains (Samanta et al. 2021, 2023). The CUM clusters consistently overestimated light rainfall events, leading to a lower success ratio (< 0.5) for that category. Fractional Skill Scores (FSS) (Fig. 2) illustrate that CUM cases outperformed No-CUM cases (first 7 rows in Fig. 2) in simulating spatio-temporal patterns of moderate to higher rain thresholds across all events. The No-CUM cases exhibited low skill for higher rain thresholds with FSS ranging between 0 – 0.28.

Fig. 2

Fractional Skill Score (FSS) at 50 km radius (5 × 5 grids) across different rain thresholds. The x-axis represents the events arranged in the sequence of OCH, GAJ, SWM, and SUM. These events are reiterated for each rain threshold, namely > 1 mm/6 h, > 5.1 mm/6 h, > 10.1 mm/6 h, and 20.1 mm/6 h (indicated on the secondary x-axis located at the top). The y-axis represents case numbers arranged to depict the order of cumulus schemes, viz. KF0*, BMJ0*, MKJ0*, KF1, KF1_1, KF1_2, BMJ1, GF1, NT1, MKF1 (mapped in the secondary y-axis). Cases with no cumulus schemes used in the innermost domain D2 (No-CUM) are marked with *. Within each cumulus scheme class, microphysics schemes are sorted, and different colors on the case numbers indicate the microphysics schemes: black – Lin scheme; grey – Morrison scheme; brown – WDM6 scheme; purple – Goddard scheme. For a clearer understanding of the case numbers and various physics combinations, refer to Table 1. The lower x-axis denotes the events and y-axis denotes the case numbers. The black lines and corresponding secondary x-axis represent grouping based on the cumulus schemes. The event SUM corresponds to a moderate rainfall event, where values do not exceed 20.1 mm/6 h. Therefore, in the figure, it is represented as NA (Not Available)

The KF schemes, both the default version (cases C0, C1, C8, C9, C16, C17, C24, and C25) and those with modified triggers (cases C2, C3, C10, C11, C18, C19, C26, and C27), effectively captured the variability observed across events with FSS exceeding 0.8 for rainfall occurrences. The cases in this group demonstrated the highest skill scores of FSS > 0.65 across all rainfall categories (Fig. 2), indicating higher sensitivity and specificity in the predicted events with CSS > 0.6 across all the event and rainfall thresholds (Table 3). However, the cases that incorporated relative humidity-dependent additional perturbation for the KF scheme (cases C3, C11, C19, and C27) overestimated rainfall (positive bias of 2.5 mm/6 h) for low-moderate convective events during the GAJ and SUM episodes, with the magnitude of positive bias increasing as the lead-time increased (≥ 36 h, supplementary Table 3). It is worth noting that there was an observable difference in performance between the CUM and No-CUM variants of KF scheme, i.e. when comparing the utilization of the KF scheme in both domains (FSS of 0.6 and bias of -2 mm/6 h) versus using KF only in the parent domain (FSS of 0.35 and bias of -5 mm/6 h). The CUM cases employing the KF scheme in the 4-km domain demonstrated improved performance during the Southwest Monsoon (SWM), achieving an FSS of > 0.5 across the rainfall intensities. In contrast, the No-CUM cases showed no skill (FSS ~ 0) for rainfall intensities exceeding 20.1 mm/6 h for the SWM event (Fig. 2). Furthermore, for the OCH and SWM event, the KF-based No-CUM cases depicted a narrower spatial distribution of rainfall compared to the KF-based CUM cluster results (not shown here). An interesting finding is that during the SUM event, the CUM variant of KF schemes consistently achieved an FSS above 0.4 for rainfall intensities exceeding 5.1 mm/6 h, while the No-CUM cases recorded lower FSS values (< 0.15).

Table 3 Performance of each physics combination considered in the study across the selected events

The BMJ cases (cases C5, C6, C13, C14, C21, C22, C29, and C30) significantly under-predicted rainfall (bias of -10 mm/6 h) compared to other cumulus schemes for the four rain episodes considered, resulting in poor performance with FSS < 0.25 for higher rain thresholds (Fig. 3). The difference between the BMJ0 and BMJ1 cases were found to be very minimal, following similar spatial and temporal patterns while simulating rainfall. The MKF cumulus scheme (cases C52, C35, C47, and C53) slightly overestimated the spatial spread of rainfall during the initial periods of the SWM episode but better captured the peak event (54–90 h) during the episode (Fig. S1). Among all the events analyzed, the MKF scheme demonstrated superior performance in predicting extremes (particularly when used in domain 2), with an EES exceeding 0.45, compared to the KF schemes (EES—0.35) and other schemes (EES—0.2). The NT scheme consistently demonstrated high POD values (> 0.5) and low FAR values (< 0.3) for occurrences of low to moderate rainfall across all analyzed events. Cases involving MsKF and SAS schemes did not fully converge within the given run-time constraint (Section 2.1.3) for the four events discussed here and were therefore excluded from further discussions.

Fig. 3

Receiver Operating Characteristic (ROC) curves for various rainfall thresholds with False Positive Rate (FPR) in the x-axis and True Positive Rate (TPR) in the y-axis. The blue dashed line represents the 1:1 line. A point at the top-left corner of the ROC plot represents perfect classification (TPR = 1, FPR = 0), while a random classifier would produce a diagonal line from the bottom-left to the top-right (AUC = 0.5). The closer the ROC curve is to the top-left corner, the better the model's discrimination ability. Scatter points represent individual case skill, and black circles highlight cases with similar performance

The plots of domain-averaged temporal precipitation (mm/6 h) for different microphysics schemes (averaged across the cumulus schemes) (Fig. S2) revealed noticeable variations in the intensity of peak events and the spatial extent of rain clusters when the microphysics (MPS) schemes were modified. Particularly, for the SWM and SUM events, a deviation of ± 5 mm/6 h was noticed between the selected microphysics schemes, with Goddard (FSS – 0.35) and Morrison schemes (FSS – 0.3) recording superior performance. However, there was no significant difference in the initiation time and timing to peak of rainfall among the microphysics cases for the simulated events.

3.1.2 Spatio-Temporal attributes of rainfall events and influences on model performance

The OCH and GAJ events are tropical cyclones driven by large-scale dynamics, but the microphysical processes associated with tropical cyclones become highly complex during landfall and post-landfall as they move over the land. Tropical cyclones typically originate as clusters of thunderstorms over warm ocean waters. As these clusters intensify, warm, moist air converges toward the center of the disturbance at low levels. Further intensification leads to the formation of a deep layer of towering cumulonimbus clouds known as the Central Dense Overcast (CDO), characterized by intense convective activity and heavy rainfall consisting of numerous isolated convective elements. Tropical cyclone intensity is closely linked with Latent Heat Release (LHR), which is influenced by the distribution of hydrometeors above and below the melting layers (Nekkali et al. 2022). Studies have demonstrated that the choice of cumulus and microphysics schemes significantly impacts the track and rainfall intensities of tropical cyclones (Mahala et al. 2015; Kirthiga et al. 2021). The cyclonic storm Ockhi (OCH) is considered a rare event characterized by rapid intensification from a depression to a cyclone within a span of 9 h, further developing to a very severe cyclone within next 24 h (Singh et al. 2020). The pronounced increase in CAPE within the low to mid-level atmosphere during this event is largely linked to oceanic interactions under the influence of a prominent large-scale upper-level trough. Thus, KF, MKF and NT, which utilizes CAPE for closure assumptions was observed to perform better than other schemes. The rapid intensification was picked well by the simulations 48 h ahead of the event. Previous studies have indicated that the BMJ scheme was skillful at accurately representing the track and intensity of tropical cyclones. The scheme was reported to have simulated the typical warm core structure and wind pattern associated with these weather systems better than the other schemes (Kanase et al. 2020). However, in this study, the BMJ case, recorded late initiation for the OCH cyclone event forecasting a low intensity event. The BMJ scheme adjusts the current profile to a pre-determined convective sounding. However, as this event is a rare event which deviates from the average climatology of cyclone storms in India, resulted in lower skill of using a pre-defined reference profile in the scheme. The atmospheric sounding profiles revealed lower moisture levels and inadequately represented low-level vorticity, resulting in a slow and weaker development of the weather system. Cases that relied solely on microphysics schemes to resolve cloud processes in domain 2 (No-CUM cluster) failed to capture the full spectrum of precipitation features for OCH event (Fig. 2). This limitation may be attributed to issues with available microphysics schemes in adequately resolving isolated convective elements present in the core of the cyclone (Samanta et al. 2023). The Lin and Morrisons scheme along with KF schemes (C1, C2, C3, C9, C10 and C11) performed better in capturing the spatio-temporal pattern of the rainfall features for the event (CSS—0.6 on average; Table 3).

The conclusions drawn from the OCH event were not evidently applicable to the Gaja cyclonic event (GAJ). The GAJ event presented unique challenges, as the initial and lateral boundary conditions themselves were poorly represented from the input data system (Kirthiga et al. 2021), and the multiphysics combinations attempted here were not able to improve the simulations significantly for the major cyclonic event during the first 18 h of the simulation (Supplementary material Fig. S1). Previous studies have also highlighted the importance of near-perfect boundary forcing for accurate predictions of tropical cyclones driven mainly by synoptic-scale processes (Bucci et al. 2018). However, a significant variability of ± 7.5 mm/6 h was observed in the rainfall occurrences linked to the pull effect as the cyclone advanced westward over land during the 78–96 h lead-time.

The SWM event was part of South-West Monsoonal circulations of 2018, enhanced by presence of a low-pressure zone in Bay of Bengal. The off-shore monsoon trough was intensified by mid-tropospheric cyclonic circulation over peninsular India causing the high intensity events (Kirthiga et al. 2021). The rainfall occurred over larger spatial extent covering Kerala, Tamilnadu and parts of Karnataka, also recording highly variable rainfall intensities. Higher variability of hydrometeor distributions was noticed during the event causing huge spatio-temporal variability in the rainfall intensities (Sumesh et al. 2022). The No-CUM cases simulated high intensity events but the rainfall clusters were isolated to specific regions in the domain, thus hugely underestimating the spatial spread of the rainfall occurrence (the spatial distribution of the event simulations can be found in Kirthiga et al. 2021, not shown here for brevity). The CUM cluster was able to represent the intensification and temporal pattern of the rainfall progression, however, the areal distribution was still underestimated. The MKF1 scheme captured the accumulated rainfall for event, comparatively well when compared to GPM. However, the case simulated the event as a weak rainfall event existent for a longer duration deviating from the characteristics of the real episode.

Across the simulations, cumulus schemes influenced the spatial distribution of moderate rainfall and initiation of events, while changes to microphysics schemes introduced variability in both the intensity and spatial patterns of high-intensity rainfall occurrences within the simulated environment. Lower Convective Inhibition (CIN) and higher Convective Available Potential Energy (CAPE) values were prevalent, leading to higher skill of the CUM variant of KF schemes (implemented in two domains), with a Fractional Skill Score (FSS) exceeding 0.5 across all events considered. Cases utilizing relative humidity-based triggers with the KF scheme (C3, C11, and C19) recorded higher overall skill scores, with CSS exceeding 0.6. The Goddard, Lin, and Morrison schemes consistently demonstrated higher skill scores compared to others. For events dominated by warm rain processes like OCH and GAJ, single-moment microphysics schemes like Lin and Goddard performed well. However, for events (SWM and SUM) dominated by hydrometeors from ice and graupel categories, combinations with double-moment schemes Morrison and WDM6 schemes showed superior performance. No-CUM cases resolved precipitation intensities for events driven by large-scale dynamics and stratiform cloud processes. The ratio of simulated convective precipitation to total simulated precipitation in domain 2 consistently exceeded 0.6 across all simulated events, with contributions varying from isolated convective elements to well-structured convective processes. When microphysics schemes were used in domain 2 to explicitly resolve processes without cumulus scheme, narrow bands of precipitation, as compared to GPM, and delays in event initiation were noticed. It is noteworthy that the CUM cluster simulated a large spatial spread but weak rainfall activity, extending slightly longer than the actual duration for some events (SWM and SUM).

3.2 Reducing the number of ensemble members from an operational point of view

Figure 3 illustrates the Area Under the Receiver Operating Characteristic Curve (AUC-ROC) for precipitation across various thresholds. This metric is commonly utilized to assess the discrimination capability of forecasts for both rare and common events (Bouallègue and Richardson 2022). The KF schemes (cases C9, C10) showed higher TPR (> 0.55) and low FPR (< 0.05), particularly when paired with the Morrison microphysics scheme (Fig. 3), thus showing a superior performance for the simulated events. Case C8, a No-CUM variant, also exhibited good performance with a Critical Success Index (CSS) of 0.54. Case C11, which utilized a relative humidity perturbation with the KF scheme in both domains along with the double-moment mixed-phase Morrison scheme, exhibited a higher False Alarm Rate (FAR) exceeding 0.4 (not shown here). Conversely, case C3, employing a relative humidity trigger with the KF scheme but with a single-moment scheme (Lin) in both domains, recorded a higher True Positive Rate (TPR) exceeding 0.6 and a False Positive Rate (FPR) of less than 0.05. The NT schemes, which were scale-aware, demonstrated consistent performance across cases C7, C15, C23, and C31 with moderate CSS exceeding 0.55. The BMJ0 cluster, along with complex microphysics schemes such as cases C14 and C22, exhibited a moderate True Positive Rate (TPR ~ 0.4) across rainfall thresholds, accompanied by a slightly higher False Positive Rate (FPR ~ 0.1) with False Alarm Rate (FAR) exceeding 0.3. These cases also recorded an Extreme Event Score (EES) value not exceeding 0.2. Cases with the GF scheme (C12, C20) demonstrated a TPR not exceeding 0.3, along with FAR > 0.3, showing a lower skill when compared to other cases. The performance of the cases was largely found to be dependent on the specific event characteristics, as elaborated in Section 3.1.2.

Run-time constraints in the study were established due to resource limitations determined by the implemented cluster (supplementary material Section 5.1), aiming to ensure operational feasibility. A maximum allotted time of 3 h was set for each ensemble member to converge. The runtime of each case was influenced by the dynamics and complexity of the selected event, as well as the formulations of the physics schemes utilized. Instability in the grid sometimes led to longer runtimes for the CUM cluster due to frequent calls to the cumulus schemes at each time step. Events with mixed hydrometeors and complex cloud processes resulted in slightly longer runtime for the No-CUM variant compared to the CUM cluster. This aspect was not extensively investigated in previous studies, as most of them utilized a constant time step, except for a few studies (Jeworrek et al. 2019, 2021). To ensure operational feasibility, dynamic time steps were preferred to manage this complexity and decrease the overall turnaround time for various cases on a daily basis. The KF schemes with default trigger consistently exhibited the longest runtime among both CUM and No-CUM clusters. However, they consistently converged within the allocated 2-h runtime for all events. The KF schemes with perturbations (KF1_1 and KF1_2) recorded a runtime 10–20% shorter than KF0 and KF1 variants. Scale-aware NT schemes consistently demonstrated shorter turnaround times (18–32%) compared to other schemes. BMJ0 variants with different microphysics schemes demonstrated enhanced performance and reduced turnaround time (10–15%) compared to other schemes. However, when implemented in both domains as part of the CUM cluster, the BMJ scheme exhibited longer runtime, equivalent to the KF cluster. Furthermore, when combined with the Goddard microphysics scheme, it failed to converge for any of the event within the given time limit (Case C29). Certain combinations, such as MsKF with complex microphysics schemes, often failed to converge within the given time limit. Hence, selecting compatible cumulus and microphysics schemes for specific rain events is crucial, especially when explicitly resolving precipitation in finer domains (Yano et al. 2018). Combining KF cumulus schemes in domain 1 with the Morrison microphysics scheme in domain 2 resulted in the best performance (CSS and required less integration time than other combinations with KF scheme. However, the MKF cumulus scheme in domain 1 performed well when paired with the Goddard microphysics scheme (case C53) in domain 2 (CSS – 0.53). The WDM6 microphysics scheme showed improved performance (CSS – 0.6) when combined with the KF scheme utilizing the relative humidity-based trigger (case C19). While the Goddard scheme performed well during the SWM episode combined with the MKF (C53 – CSS of 0.53) and NT (C31 – CSS of 0.57) cumulus schemes, combinations involving the Goddard scheme failed to converge within the given time when combined with other cumulus scheme combinations across events. The MKF scheme required more runtime (20–30% more than other schemes) for implementation and occasionally failed to converge in cases with complex microphysics schemes and system dynamics (also observed by Berg et al. 2013).

The Pearson’s correlation values presented in Fig. 4 provide insights into the inter-correlation among the different members of the multiphysics approach. The degree of correlation between these members depended on the theory behind each physics scheme formulation and the underlying mechanisms driving the event. Previous studies (Charron et al. 2010; Leutbecher et al. 2017) noted that the clustering of ensemble members is a common issue associated with the multi-model or multiphysics approach, leading to multimodality in the outputs. From the results, it was observed that increasing the number of multiphysics members did not necessarily enhance the predictability of the event. The study also underscored the importance of addressing the clustering phenomenon observed among highly correlated ensembles. The highest inter-correlation was found among the cases for the GAJ event, which is more influenced by large-scale depression. Imperfect boundary conditions led to low variability between the multiphysics combinations, resulting in the highest intercorrelation exceeding 0.8 between the different cases analyzed (Fig. 4b). Moreover, a significant occurrence of high intercorrelation (> 0.7) was observed among different microphysics schemes within a given cumulus scheme cluster, as discussed in Section 3.1.1. For other events, particularly the OCH and SWM events (Fig. 4a and Fig. 4c), the KF1 variant with default trigger showed correlation (> 0.6) with KF1, NT1, and MKF1 schemes. Conversely, the BMJ0 cluster exhibited the least correlation (< 0.3) with other schemes. It is interesting to note that for SUM event there was least correlation (< 0.35) between the multi-physics members (Fig. 4d).

Fig. 4

Inter-correlation plots between cases for different events (a) OCH, (b) GAJ, (c) SWM, and (d) SUM, with light–dark shades of blue to indicate low inter-correlation (value of 0) to higher inter-correlation (value of 1). The first column presents the correlation with reference dataset GPM. The y-axis and x-axis depict correlation values, with GPM as first element, followed by the ensemble members (case numbers) of WRF-CP55. The alignment of case numbers on the y-axis corresponds to the order of cumulus schemes (labeled on the secondary y-axis, with '*' denoting No-CUM cases), and the color on the case numbers signifies the microphysics schemes similar to Fig. 2

Based on the performance assessment outlined above, including runtime analysis, correlation evaluation, and CSS scores (Fig. 3, Fig. 4 and Table 3), seven members have been selected for inclusion in the convection-allowing multiphysics ensemble of smaller size, denoted as WRF-CP7. These members, labeled as ENS1 to ENS7, correspond to case numbers C8, C9, C22, C7, C3, C10, and C23, respectively, as indicated in Table 1, 5th column (Selected ensembles and ID). The time plots presented in Fig. 5 illustrate the spread of ensembles as the lead times progress. Comparing the precipitation forecasts from WRF-CP55 with the WRF-CP7 (shaded in green), we observed that the spread was highly comparable. Furthermore, the CRPS, MAE, and RMSE values reported in Table 4 indicate that the proposed WRF-CP7 recorded similar error statistics and overall performance compared to the larger multiphysics ensembles WRF-CP55. Additionally, the outlier statistics in Table 5 demonstrate that the difference between the actual outlier base rate and the expected outlier rate for the WRF-CP7 was equivalent or even smaller when compared to the outlier statistics of WRF-CP55. Reducing the number of ensemble members did not significantly affect the distribution of the rank histogram for the four heavy rainfall events analyzed in this study (Fig. S3). However, the rank histogram, highlights skewness in both multiphysics frameworks (WRF-CP55 and WRF-CP7), indicating a tendency for the multi-physics model to slightly underestimate.

Fig. 5

Temporal plots (domain-averaged) illustrating the ensemble frameworks' spread across events, (a) OCH, (b) GAJ, (c) SWM, and (d) SUM. The x-axis of the first row represents the forecast lead time (6-hourly), while the second row displays values indicating the ratio (spread of WRF-CP7/spread of WRF-CP55) * 100. A higher ratio signifies that the spread generated by WRF-CP7 (7-member ensemble) is nearly identical to that of WRF-CP55, whereas lower values indicate a reduced spread by the WRF-CP7 model

Table 4 Performance analysis of ensemble properties across two versions of CP ensembles- WRF-CP55 and WRF-CP7 models

Table 5 Categorical error statistics across individual ensemble members during the long-term (Sep 2015 – Dec 2017) forecast simulations

It is important to note that the maximum achievable True Positive Rate (predictability), indicative of the sensitivity of the framework, consistently remains below 0.65. This suggests that the multiphysics ensemble framework accounted for a limited amount of predictability in simulated rainfall for the selected events. Addressing input and model uncertainties is imperative for enhancing the performance of ensemble frameworks, particularly in tropical regions (Prakash et al. 2016; Huang and Luo 2017). However, much of the bias in the multiphysics ensemble may stem from over-compensation of unsampled input errors.

3.3 Performance of the WRF-CP7 Framework – more extended period analysis

To assess the reliability across different seasons, rain mechanisms, and rainfall intensities, we validated 72-h ahead precipitation forecasts from WRF-CP7 for an extended period (September 2015 to December 2017). Two ensemble members from the No-CUM cluster were considered: ENS1 representing the KF0-Morrison configuration (case C8), and ENS3 representing the BMJ0-WDM6 configuration (case C22). Three members from the CUM cluster of KF schemes with different triggers were included: ENS2 representing KF1-Morrison (case C9), ENS5 representing KF1_2 (Relative humidity-dependent Additional Perturbation)-Lin (case C3), and ENS6 representing KF1_1 (Moisture–advection-based Trigger)-Morrison (case C10). Two ensemble members from the CUM cluster of NT scheme were also selected: ENS4 representing NT1-Lin (case C7) and ENS7 representing NT1-WDM6 (case C23).

As discussed in earlier sections, there was a clear distinction in the performance of individual ensemble members based on the major cumulus and microphysics schemes considered. The various categorical statistics of the performance of individual members are listed in Table 5 as a function of rainfall thresholds, and continuous statistics as a function of lead-time are available in supplementary material Table 3. The members with the NT scheme (ENS4, ENS7) recorded the lowest RMSE (3–4 mm/6 h) across the lead-times. Notably, the error progression as lead-time increases was not very prominent (< 4% increasing trend) with the NT scheme (refer to Table 3 in supplementary material). These members exhibited a slight negative bias (underestimation) with an average of -0.25 mm/6 h. However, the NT scheme with the double-moment microphysics scheme WDM6 reduced the negative bias to -0.15 mm/6 h. Highest Success Ratio (0.45) was noticed for the ENS4 across the rainfall thresholds (Table 5). The NT scheme simulations demonstrated a closer match to the observed cumulative distribution function of forecasted rainfall compared to IMDAA data across various lead-times (Fig. S4 in supplementary material). This scheme, being scale-aware exhibited faster convergence, taking 25–40% less time than the longest runtime taken by the ensemble framework. Consequently, it consistently provided reliable forecasts throughout the year. The incorporation of mid-level cumulus parameterizations, cumulus downdrafts, and cumulus momentum transports, proved highly relevant for tropical setups by earlier studies (Zhang and Wang 2017; Wang 2022; Zhou et al. 2024) and thus suggested in ‘NCAR tropical suite’(https://www2.mmm.ucar.edu/wrf/users/physics/ncar_tropical_suite.php). However, the NT scheme faces challenges in accurately simulating low clouds and shallow convection (also reported by Zhang and Wang 2018), particularly evident during the pre-monsoon (SUM) and winter (WIN) seasons. The underestimation of moderate to heavy rainfall during the onset of SWM, SUM and WIN season was widely noticed. Additionally, coastal regions, prone to onshore flow and the formation of low clouds that contribute to localized rainfall, displayed lower skill among members using the NT1 scheme.

For the No-CUM members, the KF0 and BMJ0 configurations (ENS1 and ENS3), a very similar RMSE of 5.1 mm/6 h and 5.7 mm/6 h, respectively, was recorded. The diurnal variability was adequately represented by the No-CUM members, although they failed to capture peak intensities across seasons. Research indicates that the convective precipitation to total precipitation ratio exceeds 0.5, particularly in peninsular India during the major monsoon seasons (Romatschke and Houze 2011; Sreenath et al. 2022). The explicit resolution of convective elements posed challenges within the current microphysics schemes (Samanta et al. 2023). Previous studies have suggested that utilizing cumulus parameterization at a 4-km scale performed better for certain events (Kirthiga et al. 2021; Wang et al. 2021). However, ENS1 displayed higher skill during the North-East Monsoon (NEM) season (POD – 0.7) and Winter (WIN) season (POD – 0.4), particularly for DOM3, the eastern coasts. The NEM season is mainly driven by large-scale dynamics. Initially, as easterly winds move inland from the ocean, there is minimal contribution from convective precipitation elements when precipitation happens in the coasts. However, increased convective interactions are observed as they interact with the land and penetrate further inland, resulting in a drastic reduction in the skill of ENS1 for DOM4 (POD < 0.45). The increase in RMSE values as lead-time increases was notably higher with the KF scheme, with an increasing error trend rate reaching about 30% in ENS1. It is important to highlight that that despite the BMJ0 scheme not exhibiting a linear trend (< 4% increase) in RMSE values as lead-time increases, it recorded the highest error (RMSE—6.5 mm/6 h) during the late night-early morning time. However, the BMJ scheme exhibited lower bias in simulated temperatures (< 0.5 ℃) and relative humidity, and it was noted to effectively capture rainfall from weak convective systems (also reported by Kanase et al. 2020). Specifically, the performance of ENS3 was higher (POD – 0.45) during the North-East Monsoon (NEM) season, particularly for events influenced by easterly winds and low-level convergence.

The CUM cluster with KF schemes (ENS2, ENS5, ENS6) increased rain occurrence predictability (> 1 mm/6 h) from the No-CUM variant of the KF scheme (ENS1) by about 129%, with the POD improving from 0.31 to 0.71 (Table 5). Similarly, a 35% increase in the POD of > 10.1 mm/6 h rainfall and 29% increase in the POD of > 20.1 mm/6 h rainfall was recorded. It is evident that this increase in predictability occurred without a rise in false alarms, as the false alarm ratio remained below 0.45 across the members, similar to ENS1 (Table 5). The relative humidity dependent additional perturbation (KF1_2) demonstrated higher POD, particularly for higher rainfall thresholds (POD—0.65, across seasons). However, a significant false alarm ratio (0.6) and wide overestimation (mean bias – 0.5 mm/6 h) for low-moderate rains was also noticed with this member, ENS5.

The probability distribution function (wet rain intensities > 1 mm/6 h) of the forecasts followed a similar pattern to that of IMDAA (Fig. S4). The differences in the cumulative distribution function (CDF) between the ensemble members increased with lead time. However, most ensemble members overestimated extreme events (right tail), particularly as the lead time increased. Notably, ENS3 (utilizing the BMJ cumulus scheme and WDM6 microphysics scheme) and ENS4 (employing the NT cumulus scheme and Lin microphysics scheme) outperformed in simulating low to moderate rain intensities (< 10.1 mm/6 h), even with a lead time of 72 h.

In summary, the analysis of error metrics and distribution graphs revealed that the ensemble framework slightly overestimated moderate to heavy events (> 10.1 mm/6 h) and exhibited higher uncertainty in those simulations as lead time increased. Interestingly, the findings suggest that the ensemble members exhibited similar performance during the initial forecast hours (6–24 h), but afterward, their error growth rates diverged.

3.4 Investigating the added value by the multiphysics ensembles at an intra-seasonal scale across Southern India

The added value of the proposed convection-allowing resolution multiphysics framework (WRF-CP7) was assessed by comparing the ensemble mean and spatiotemporal spread to those from NCEP-GEFS20 (refer Table 2 for more details). Figure 6 presents domain-wise averaged 6-hourly precipitation plots across different seasons. During the Southwest Monsoon/Indian Summer Monsoon (SWM) season, which exhibits higher rainfall occurrences between 6–18 UTC (11.30 AM—11.30 PM IST) in DOM1 and DOM2 (core SWM regions), the WRF-CP7 ensembles accurately represented the diurnal variability (correlation coefficient – 0.75). As mentioned earlier, the spread becomes more pronounced with increased lead time. However, the NCEP-GEFS20 performed poorly in capturing diurnal variability (correlation coefficient – 0.56), rainfall intensities, and spread among ensemble members during the SWM season. In the Northeast Monsoon (NEM) season, major rainfall occurs between 0–6 UTC (5.30 AM—12 PM Indian Standard Time (IST)) in the core monsoon domain, specifically the DOM3-Eastern Coast region. DOM3 is the first inland convergence zone, as the easterlies and associated depressions bring moisture from the Bay of Bengal. The system then moves with less intensity to Central TN (DOM4), where significant rainfall occurs between 12–18 UTC (5.30 PM—11.30 PM IST). Regarding rainfall initiation, the NCEP-GEFS20 and WRF-CP7 ensemble mean showed a slight difference, with the WRF-CP7 capturing the initiation time accurately in DOM3 but not accurately representing the peak rainfall occurrences in DOM4. Interestingly, although the NCEP-GEFS20 exhibited less spread (± 1 mm/6 h) among ensemble members, it closely followed the diurnal pattern and rain intensities observed by IMDAA for the core NEM monsoon regions (DOM3 and DOM4). NCEP-GEFS20 also captured the patterns in DOM1 and DOM2 well during the NEM period, while the WRF-CP7 slightly overestimated the peak rainfall occurrences.

Fig. 6

Diurnal variations in 6-hourly rain intensities across lead times. The observed rainfall intensities from IMDAA are represented by black lines and circle markers. Model-simulated precipitation is displayed for the ensemble mean of WRF-CP7_EM (maroon) and NCEP-GEFS20_EM (darkcyan) ensemble framework. Additionally, the results of the Probability Matching technique Mean (PMM) for WRF-CP7_PMM (maroon with + markers) and NCEP-GEFS20_PMM (darkcyan with + markers) are presented. The individual members from WRF-CP7 and NCEP-GEFS20 are depicted in shades lighter than their respective models. The rows correspond to different seasons (SWM, NEM, Pre-Monsoon, and Winter), and the columns represent various domains (DOM1: Western Coast, DOM2: Western Ghats, DOM3: Eastern Ghats, and DOM4: Central Tamilnadu). The x-axis reflects lead times at 6-h intervals, aligning with 00 UTC (5:30 AM IST), while the y-axis indicates the averaged rain intensities (mm/6 h)

Both models, WRF-CP7 and NCEP-GEFS20, capture the initiation of pre-monsoon summer (SUM) convective-type rainfall (12 UTC, 2.30 PM—5.30 PM IST) well across the domains, with slight over-prediction by the WRF-CP7 mean and slight underestimation by the NCEP-GEFS20 mean. In the DOM4 region (Central Tamilnadu—Cauvery river basin), the inland heating and local moisture fluxes enhance SUM activity, and the WRF-CP7 ensemble framework well captured this pattern. The POD for SUM events showed a 3% increase in the rain/no rain category, with the WRF simulated SUM events demonstrating a POD 30% higher than that of GEFS. However, on average, the POD of WRF ensemble mean for rain/no rain occurrences stands at 0.6. This indicates a significant opportunity exists for improving predictions in this season due to its substantial uncertainty, which arises from its shorter time-scales and greater flux transfer at low-levels. Studies have suggested that improving parameterizations of land surface processes can enhance skills at convective scales (Osuri et al. 2017).

Both models perform well in capturing the characteristics of winter precipitation (WIN). Interestingly, the NCEP-GEFS20 ensemble mean tends to be higher than the WRF-CP7 ensemble mean and more comparable to IMDAA rain rates for the WIN season. The multiphysics WRF-CP7 framework showed good performance for warm-rain type processes, while the cold-rain processes and associated mesoscale forcing during winter are slightly better represented by the NCEP-GEFS20 ensembles, including perturbed initial conditions.

The spatial maps displaying averaged daily precipitation in Fig. 7 reveal that the multiphysics ensemble mean generated by WRF-CP7 provides more detailed spatial information regarding daily precipitation distributions across seasons and domains. The NCEP-GEFS20 ensemble mean exhibits a significant dry bias for DOM2 and DOM3 in all seasons (SWM, SUM, and WIN), except for NEM. The NCEP-GEFS20 simulations failed to adequately represent the inland rainfall zone in DOM1 during the SWM season, shifting the critical rainfall zone towards the coast and ocean. Studies have also shown the lower skill of NCEP-GEFS over core monsoon regions (DOM1 and DOM2) of South-West Monsoon season with a larger dry bias (Dube et al. 2017; Saminathan et al. 2021). This dry bias was reduced in WRF-CP7 simulations, showing a 25–30% reduction in average RMSE to 6.6 mm/day across evaluation zones. The improved representation of Western Ghats terrain characteristics and better simulation of diurnal patterns of temperature and humidity profiles by the WRF-CP7 led to the improvement over NCEP-GEFS20 (not shown here). Studies have also recorded the superior performance of regional scale models in resolving the complex orographic related rainfall mechanisms (Kirthiga and Patel 2018). Interestingly, while NCEP-GEFS20 accurately simulated the spatial variability of NEM in eastern coastal zones (DOM3), the WRF-CP7 ensemble mean slightly underpredicted coastal rainfall. During the North-East monsoon season, which is characterized by tropical cyclones driven by large-scale dynamics and easterly trough-related activities, the synoptic to mesoscale processes were well represented by GEFS ensembles. Despite being driven by the control member of this system, WRF-CP7 showed minimal influence on RMSE (10–15% reduction compared to GEFS) in precipitation simulations during the NEM season for the DOM3. However, as NEM systems moved over land, microphysical processes became highly complex, with more localized convective elements, which was not well represented by coarser resolution NCEP-simulations. This resulted in a dry bias in the inland region of central Tamil Nadu (DOM4), which was better resolved by the WRF-CP7 ensemble mean at the convective scale, reducing spatial shift errors by 20–30%. During pre-monsoon convective thunderstorms, WRF-CP7 outperformed NCEP-GEFS, reducing RMSE by 20–25% in the Western Ghats regions, with an average improvement of 10–15% across other domains. However, WRF-CP7 simulations showed limitations in capturing the complexity of fluxes, with a 60% probability of detection and a 60% False Alarm Ratio. It is to be noted that the pre-summer monsoon rainfall is characterized by thunderstorm activity with huge spatial variability of mixed-phase hydrometeors. Addressing this, increasing spatial resolution to 1 km or less and improving parameterization of local fluxes through better representation of surface processes can help reduce uncertainty for this season (Kirthiga and Patel 2018; Sati and Mohan 2021; Prasad et al. 2024).

Fig. 7

Spatial averaged precipitation across seasons (unit – mm/day). The rows denote the seasons viz. SWM (a-c), NEM (d-f), SUM (g-i), and WIN (j-l). a, d, g, j denotes the IMDAA averaged precipitation climatology, b, e, h, k denotes the NCEP-GEFS20 simulated ensemble mean precipitation, and c, f, I, l denotes the WRF-CP7 multi-physics framework ensemble mean precipitation

The Fractional Skill Score (FSS) plots (Fig. 8) displayed a clear superiority of the WRF-CP7 forecasts over the NCEP-GEFS20 forecasts in representing the intra-seasonal spatial variability. When a target FSS score of 0.5 was considered satisfactory, as Woodhams et al. 2018 mentioned, the FSS values for the NCEP-GEFS20 simulations only exceeded 0.5 for the threshold > 2.5 mm/day (rain/no rain event). On the other hand, the FSS values for the WRF-CP7 ensembles exceeded 0.5 even for higher thresholds (> 10 mm/day). Analyzing the count of rain objects in Figure S5, the NCEP-GEFS20 ensembles showed significant under-prediction of the count and exhibited low spatial spread. In contrast, the WRF-CP7 members realistically simulated the count of rain objects, matching the estimated objects by IMDAA. Interestingly, the most significant deviation among the WRF-CP7 ensembles occurs in DOM3, the eastern coastal region, regarding the count of simulated rain objects. Figure S6 showcases displacement plots showing the direction and number of grids displaced for the simulated rain objects > 10.1 mm/day (moderate-very heavy rainfall category). The negative values in Figure S6a represent a northward shift in the simulated rain objects, while the positive values denote a southward shift in the objects. An ideal value of zero represents the simulated rain object centroid is near the ones from IMDAA centroids. Similarly, figure S6b represents eastward (negative) and westward (positive) direction shifts. The WRF-CP7 reduced the shifts in rain object centroids in the overall shift in the simulated rain objects, and in addition, the uncertainty with the misplaced centroid was also limited. In the SWM season, the NCEP-GEFS20 mean displayed a westward (+ ve) shift in DOM1, while the WRF-CP7 multiphysics mean reduced the spatial bias.

Fig. 8

Fractional Skill Scores (FSS) plots at different spatial scales and rain intensity thresholds for ensemble mean from WRF-CP7 and NCEP-GEFS20

Table 6 lists the RMSE, POD, and FAR values for different years, seasons, and forecast lead times (until 3 days). The WRF-CP7 ensemble mean showed a higher error growth rate than the NCEP-GEFS20 mean across lead times. Consequently, the POD was higher for the WRF-CP7 simulations, especially for higher thresholds. Additionally, the FAR was smaller for the WRF-CP7 ensemble mean throughout the seasons and years. Notably, the POD and FAR for rain occurrences (> 2.5 mm/day threshold) were higher for the NCEP-GEFS20 ensembles, particularly for NEM 2015. However, the POD and FAR for > 10 mm/day were noticeably enhanced by the WRF multi-physics ensemble simulations. Therefore, while the NCEP-GEFS20 ensembles were able to capture rain events, they significantly under-predicted moderate or higher intensity events throughout all years and seasons. A 30% increase in POD by WRF-CP7 was observed across all seasons for moderate to heavy rain intensities, accompanied by a 10% decrease in FAR against GEFS forecasts. The higher lead times of WRF-CP7 forecasts recorded higher spread and error growth rate for precipitation simulations in the coastal domains, particularly DOM1 and DOM3, during SWM and NEM seasons, respectively. The bias could be attributed either to the error in the input data (as reflected by GEFS performance) or lesser distance from the outflow boundary (Lavin-Gullon et al. 2021), or inherent issues with WRF in simulating coastline interactions (Hock et al. 2022).

Table 6 Performance metrics of the simulated daily precipitation from the proposed CP ensemble framework – WRFCP7 against NCEP-GEFS20 at intra-seasonal timescale and lead times

Figure 9 depicted the variance and MSE for day 1 forecasts of WRF-CP7, closely aligned with the 1:1 line and falling within the lower quadrant for most days across seasons. The NCEP-GEFS20 forecasts did not account for the error in simulated precipitation. The correlation plots for day 2 and day 3 multiphysics WRF forecasts also aligned with the 1:1 line. The correlation plots of NCEP-GEFS20 for longer lead times degraded compared to day 1 forecasts, deviating from the 1:1 line (not shown in the manuscript for brevity). The rank histogram (inset in correlation plots of Fig. 9) for NCEP-GEFS20 ensembles values displayed a U-shaped distribution, indicating a highly uncertain ensemble framework with both under-prediction and over-prediction. The rank histograms for WRF ensembles showed a slightly over-predicting model, with an increasing tendency to overestimate as the lead time increased. Though not discussed in detail (for brevity), it is worth noting that the Probability Matching technique Mean (PMM) did not demonstrate superior performance for either of the ensemble framework (Table 6).

Fig. 9

Correlation plots for ensemble variance (X-axis) versus the mean squared error of ensemble mean (Y-axis). The rows represent the seasons viz. SWM (a-b), NEM (c-d), SUM (e–f), and WIN (g-h). The column represents the WRF-CP7 multi-physics ensemble framework (a, c, e, g) and NCEP-GEFS20 ensemble framework (b, d, f, h). The inset shows corresponding rank histograms with reference value in horizontal dashed line. The values in the gray box denotes the Pearson’s correlation coefficient

4 Summary and conclusions

The primary focus of the study was to quantify the usefulness of convection-permitting resolution multiphysics ensemble for the simulation of year-long medium-range precipitation forecasts. The study involved three major objectives.

(i) Quantifying the predictability of precipitation across peninsular India at convection-permitting (CP) scales. The initial multi-physics members (WRF-CP55) were generated using a larger spectrum of the cumulus and microphysics parameterization combinations available with a Regional Climate Model (RCM) – Weather Research and Forecasting (WRF) model. Even though the 4 km is generally considered a convection-permitting resolution, the results from the analysis approve of the fuzziness in the usage of the cumulus scheme in the innermost domain (4 km resolution). In the present study, certain events with strong large-scale forcing, complex microphysics schemes resolved the precipitation explicitly at 4-km resolution (in agreement with studies Mukhopadhyay et al. 2010; Guo et al. 2022; Ou et al. 2020). The ratio of simulated convective precipitation to total simulated precipitation in domain 2 consistently exceeded 0.6 across all simulated events, with contributions varying from isolated convective elements to well-structured convective processes. When microphysics schemes were employed in domain 2 to explicitly resolve processes without a cumulus scheme, narrow bands of precipitation were simulated, in contrast to GPM observations, and delays in event initiation were observed. Consequently, it was observed that the simulation of intensely local or mesoscale convective events improved significantly when appropriate combinations of cumulus parameterization schemes and microphysics schemes were utilized within the 4 km domain. Studies have highlighted the challenges that current versions of microphysics schemes face in accurately capturing isolated convective elements, a common feature of significant rainfall events in subtropical climatology (Srinivas et al. 2013; Madala et al. 2014; Hazra et al. 2020; Samanta et al. 2023).

(ii) Designing a computationally efficient multiphysics ensemble framework, practically feasible from an operational point of view. Investigating the physics combinations, the resulting simulations indicated that selecting compatible schemes were essential to designing a time-efficient ensemble framework. When the convection was explicitly resolved, complex microphysics schemes were more relevant (as reported by Kirthiga et al. 2021). Some of the physics combinations were found to be highly inter-correlated. Thus, we proposed a smaller 7-member ensemble framework, WRF-CP7, based on the performances across rainfall mechanisms. A composite scaled score (CSS) that combines multiple evaluation metrics and inter-correlation analysis was used to arrive at the final seven-member ensemble. The suggested WRF-CP7 framework with smaller ensembles reduces the turnaround time without compromising the spread of the simulated precipitation fields. The study demonstrated the higher skill of No-CUM cases in simulating low-moderate rain categories (stratiform clouds and precipitation from weak convective storms). These results are comparable to previous studies with similar configurations and study regions (Mukhopadhyay et al. 2010; Srinivas et al. 2013; Das et al. 2015).

(iii) Evaluating the intra-seasonal predictability and reliability of WRF-CP7, 3-day forecasts for each day from Sep 2015 to Dec 2017. A total of 5544 simulations (792 days × 7 ensembles) were made with approximately 130–180 min of run-time for each simulation. The quantitative analysis suggested that the WRF-CP7 members represented the spatiotemporal variability of rainfall occurrences with varying thresholds and were dispersive. Higher confidence was recorded in the occurrence of a rain event with the WRF-CP7, and reduced false alarm ratios were reported. The diurnal variability was adequately represented by the No-CUM members, although they failed to capture peak intensities across seasons. Research indicates that the convective precipitation to total precipitation ratio exceeds 0.5, particularly in peninsular India during the major monsoon seasons (Romatschke and Houze 2011; Sreenath et al. 2022). The explicit resolution of convective elements posed challenges within the current microphysics schemes (Samanta et al. 2023). Previous studies have suggested that utilizing cumulus parameterization at a 4-km scale performed better for certain events (Kirthiga et al. 2021; Wang et al. 2021). The CUM cluster with KF schemes (ENS2, ENS5, ENS6) increased rain occurrence predictability (> 1 mm/6 h) from the No-CUM variant of the KF scheme (ENS1) by about 129%, with the POD improving from 0.31 to 0.71. Similarly, a 35% increase in the POD of 10.1 mm/6 h rainfall and 29% increase in the POD of 20.1 mm/6 h rainfall was recorded. It is evident that this increase in predictability occurred without a rise in false alarms, as the false alarm ratio remained below 0.45 across the members. The NT scheme recorded higher success ratio (0.45) across the rainfall intensities and lead-times. Notably, the error progression as lead-time increases was not very prominent (< 4% increasing trend) with the NT scheme. This scheme, being scale-aware exhibited faster convergence, taking 25–40% less time than the longest runtime taken by the ensemble framework. The error growth (4–44% increasing trend) of the overall ensemble framework helped in sampling the uncertainty of future atmospheric states and, thus, increasing the predictability of the extreme events. These results align with previous studies investigating precipitation simulations with multiphysics ensembles at convection-permitting resolutions (Clark et al. 2010; Duda et al. 2014; Berner et al. 2015; Francis et al. 2020). However, the overall performance of the ensemble mean suggested that the multiphysics ensemble resulted in an overpredicting model with overestimation for low-moderate rain intensities while slightly under-predicting in the heavy-very heavy rain category.

(iv) The added value of the proposed framework was assessed through the comparisons against the coarser-scale publicly-available Global Ensemble Forecast System forecasts (NCEP-GEFS20). A 30% increase in POD by WRF-CP7 was observed across all seasons for moderate to heavy rain intensities, accompanied by a 10% decrease in FAR when compared to GEFS forecasts. The NCEP-GEFS20 ensembles were less dispersive (spatially and temporally) and thus resulted in an over-confident deterministic mean which did not capture the higher intensity rains across all the seasons and years for the study domain. The spread of the simulated precipitation between the ensemble members was also not sensitive to the lead times. The mean from the WRF-CP7 simulation reduced the biases, particularly in the land regions and for heavy rain thresholds, compared to the NCEP-GEFS20 ensembles. The spatial shift from the observed rain objects was reduced with a high-resolution WRF-CP7 ensemble mean, improving the spatial accuracy of the simulated precipitation. The suggested ensemble framework gave a superior performance for SWM and SUM seasons. However, for some of the NEM events and WIN season, NCEP-GEFS20 simulation with perturbed initial conditions showed significant performance.

Physics schemes in regional/global climate models face challenges to accurately represent major rain mechanisms in the Indian subcontinent (Samanta et al. 2021, 2023), necessitating a better understanding of rain system simulations at convection-allowing scales. Intensive campaigns like CAIPEEX (Prabha et al., 2011) and INCOMPASS (Hazra et al. 2020) aid in incorporating observed features into numerical model formulations. The present study addresses model uncertainty in forecasting precipitation for a longer lead time, particularly in the convective permitting scales across India. The study uniquely evaluates the ensemble members for simulating different precipitation thresholds. Therefore, the methods employed in this study are particularly relevant for supporting vulnerability impact assessment studies (VIA), especially in agriculture and water resources. However, in the present ensemble configuration, the deterministic ensemble mean over-predicted the low-moderate rainfall, particularly the bias becoming dominant with an increase in lead time. Some studies like Thornes and Stephenson 2001 have argued that missing a heavy rainfall event was more damaging than anticipated. Since the resulting model has a systematic wet bias, post-processing techniques like bias correction can effectively be explored to improve the precipitation forecasts for a longer lead time (Clark et al. 2016). Increasing the spatial resolution to 1 km or less can also help reduce the uncertainty induced by parameterizing convection (Schwartz et al. 2017; Frogner et al. 2019; Sofokleous et al. 2021). Techniques to address the input and model uncertainties are necessary for the ensemble framework, particularly in the tropics (Prakash et al. 2016; Huang and Luo 2017). The results from the study strongly advocate for extensive sampling within the model uncertainty space, coupled with input uncertainty, to capture better the entire spectrum of rainfall mechanisms occurring in the tropics.