1 Introduction

Regional climate models (RCMs) have been extensively used for high-resolution climate information to regional scales to account for fine-scale processes that regulate the spatial structure of climate variable. Several RCMs studies (Ratnam and Kumar 2005; Rupa Kumar et al. 2006; Dobler and Ahrens 2010; Lucas-Picher et al. 2011; Kumar et al. 2013; Hong and Kanamitsu 2014) have been carried out to simulate the summer monsoon over south Asia. All have reported an improvement in the simulation of spatial and temporal distribution compared to coarser global models, but showed a general overestimation of orographic rainfall. In fact, most of the studies have focused on mean precipitation climatology, examining in particular the ability of RCMs to improve, variability, interactions between the different dynamical features affecting the monsoon, land use changes, fine-scale topography, monsoon circulation, and El Niño Southern Oscillation (ENSO) dynamics on future climate over monsoonal (Paeth et al. 2009; Sylla et al. 2009, 2012; Mariotti et al. 2011; Zaroug et al. 2013) areas.

The performance of RCMs in simulating spatial and temporal variability at several atmospheric scales, as well as in simulating extreme meteorological events, has been evaluated in many studies through comparison of historical climate simulations against meteorological observations (Hong et al. 2010; Chang and Hong 2011; Ahn et al. 2012, Suh et al. 2012; Im et al. 2012a, b; Lee et al. 2013). However, most RCMs have uncertainties associated with domain, model resolution, lateral boundary conditions, and physics parameterizations. Oh et al. (2013) has compared the impacts of lateral boundary conditions (LBCs) using regional climate model for climate extreme events over Korea. Regional climate models (RCMs) based on dynamical downscaling of coupled general circulation models (CGCMs) are more appropriate for capturing sub-grid scale meteorological processes (e.g., sea breezes, mountain precipitation, etc.) over heterogeneous land surfaces, according to high-resolution surface forcing (Hong and Kanamitsu 2014). Additionally, the parameterization scheme is the basis of climate modeling, which plays an increasingly important role in RCM performance with increasing model resolution (Lee et al. 2013; Hong and Kanamitsu 2014; Lee and Hong 2014). Accurately evaluating the degree of added value in the RCM against the corresponding GCM result has remained under debate in the last few years (Hong and Kanamitsu 2014). Therefore, a comprehensive assessment of the performance of RCMs is key for regional climate dynamical downscaling.

This is particularly the case for precipitation, which shows very complex spatial patterns in regions of steep topographic gradients such as Sahyadri Mountain (Western Ghats) in the southern parts and the Himalayas in the northern parts of India. Another expectation from RCMs is that the physical and dynamical processes controlling the precipitation may be improved at high resolution (Duffy et al. 2006; Pal et al. 2007). In particular, a number of previous studies of RCMs have shown significant biases in precipitation for both the winter and summer seasons (Tadross et al. 2006; Dimri and Mohanty 2009; Engelbrecht et al. 2009; MacKellar et al. 2009; Tummon et al. 2010; Lee et al. 2011). During winter, northern India receives precipitation due to eastward moving low pressure synoptic weather system originating from the Mediterranean Sea called the western disturbances (WDs). Dash et al. (2002) explain that each subregion is important because it has its own regional climatic characteristics and the precipitation analysis over these subregions should be studied separately. Their study included five different homogenous monsoon regions. Pattnayak et al. (2013) used an RCM to study the regional precipitation characteristic of the six homogenous monsoon regions; they also reported that the surplus moisture flux over the Arabian Sea causes the prolonged rainy season in the model. Lucas-Picher et al. (2011) studied the ability of four different regional climate models to reproduce the summer monsoon. Therefore, a contribution to the biases may be derived from the lateral boundary forcing (Staniforth 1997; Noguer et al. 1998; Sylla et al. 2009; Wang et al. 2010). As a matter of fact, Sylla et al. (2010) argued that the specification of lateral boundary conditions of sufficient quality can improve RCM simulations of convection over Africa. They reported that the model processes are more dominant in determining the rainfall variability than the initial and boundary conditions.

It is a well-known fact that the simulation of precipitation sensitively depends on the option of cumulus parameterization schemes available in the model. Therefore, it is important to identify the most suitable convective parameterization schemes for a given high-resolution model to improve the simulation of the monsoon precipitation. Evaluations of the sensitivity of convective parameterization schemes for monsoon simulation have been performed in the past (Ratnam and Kumar 2005; Dash et al. 2006; Singh and Oh 2007). They inferred that the simplified Arakawa–Schubert approach is more suitable to produce realistic north–south and east–west precipitation distributions and circulation features compared to the other cumulus parameterization schemes. Dash et al. (2006) have run RegCM3 model at 55 km horizontal resolution only for the four selected year from 1993 to 1996 from April to September (summer monsoon months only) using initial and boundary conditions from ECMWF (using only two convective schemes, i.e., Kuo-type and mass flux schemes). The effect of different green house gases was not included at that time and also only two parameterization schemes were available. Maharana and Dimri (2014) have also run RegCM3 at 50 km horizontal resolution for 22 years (1980–2002) using initial and boundary conditions of the National Centre for Environmental Prediction/National Centre for Atmospheric Research, US (NCEP-NCAR) reanalysis 2 (NNRP2) and mentioned that the model has a very poor relationship with IMD data set over India and most of its regions using different statistical analysis. In all the above-mentioned studies, it can be seen that the typical range of the horizontal resolutions used for the simulation of the Asian monsoon precipitation remains around 50 km. At this resolution, large-scale monsoonal features can be captured, but to resolve the physiographical heterogeneity and the mesoscale cloud clusters in the region, high-resolution RCMs are required (Im et al. 2006, 2008).

In the present study, an attempt has been made to see how well the RegCM3 simulates the observed interannual variability of precipitation over India and its homogeneous regions using various statistical methods. To understand the possible cause of annual and seasonal precipitation biases, water vapor mixing ratio (WVMR) from surface to top of the atmospheric levels has been studied in detail from the period of 1982–2006. Detailed descriptions of the model, experimental design and used data are described in Sect. 2. While model results and observational analysis are illustrated in Sects. 3 and 4 discussed the important conclusions.

This study focuses on the evaluation of the performance of RegCM3 in the simulation of variability of precipitation over India and its homogeneous regions using various statistical methods and cause of annual and seasonal precipitation biases during the period 1982–2006. Detail descriptions of the model experiment and data are described in Sect. 2. The analysis of observed precipitation is illustrated in Sect. 3.1. RegCM3 simulation results are shown in Sect. 3.2 and variability is described in Sects. 3.3 and 3.4. The possible precipitation biases of the model may be lower near surface temperature and WVMR at surface to top level (1σ–18σ level) has been studied in detail in Sect. 3.5 and important conclusions are given in Sect. 4.

2 Experimental design

The RegCM3 is simulated from 1st November 1981 to 31st January 2007 (2 months spin-up time) for continuously run at a grid spacing of 40 km with 18σ vertical pressure level. Central point of the model is kept at 23.5°N and 80°E, with 111 grids in the north–south and 125 grids in the west–east directions. The model domain covers the area of 58°E–102.5°E and 5°N–40°N. The grids were defined on a Normal Mercator (NORMER) map projection. The terrain height and land-use data for the given domain were generated from the Global Land Cover Characterization (GLCC) global 2 min resolution terrain. The monthly averaged Optimum Interpolated Sea-Surface Temperature (OISST) available from the National Oceanic and Atmospheric Administration (NOAA) for the whole year was horizontally interpolated into the specified domain and also in each time step for the model integration. The lateral boundary conditions for wind, temperature, surface pressure, and water vapor were interpolated from 6-hourly National Centre for Environmental Prediction/National Centre for Atmospheric Research, US (NCEP-NCAR) reanalysis 1 (NNRP1). The NCEP data have a spatial resolution of 2.5° × 2.5°. Soil moisture is initialized as a function of vegetation type. The lateral boundary conditions were updated every 6 h and the time step of the integration has been kept at 75 s. The parameterization of convective precipitation remains one of the most important sources of errors in climate models. The experiments were conducted for Grell (1993) cumulus parameterization schemes (Sinha et al. 2012) with Arakawa–Schubert (Krishnamurti and Sanjay 2003) as the closure scheme.

The boundary layer physics is formulated following the non-local vertical diffusion schemes of (Holtslag et al. 1990). RegCM3 was the latest version of the community climate model version 3 (CCM3) (Kiehl et al. 1996). In the CCM2 package, the effects of H2O, O3, O2, CO2 and clouds were accounted for by the model. The solar radiative transfer was treated with a δ-Eddington approach and cloud radiation depended on three cloud parameters, the cloud fractional cover, the cloud liquid water content, and the cloud effective droplet radius. The CCM3 scheme retains the same structure as that of the CCM2, but it includes new features such as the effect of additional greenhouse gases (NO2, CH4, and CFCs), atmospheric aerosols, and cloud ice.

Various statistical methods like mean bias error (MBE), root mean square error (RMSE) and mean percentage error (MPE) have been applied for comparisons. Observed daily precipitation data of India Meteorological Department (IMD) of Rajeevan et al. (2006) have been used at 1° longitude × 1° latitude grid over India from 1951 to 2007. Other observed precipitation from CPC merged analysis of precipitation (CMAP) developed by the Climate Diagnostic Center (US Department of Commerce) following the methodology of Xie and Arkin (1997) has also been used for the verification purposes (horizontal resolution of 2.5° × 2.5° longitude by latitude). We have validated the profiles of temperature and water vapor mixing ratio from RegCM3 and National Centre for Environmental Prediction (NCEP) reanalysis observations. We have used area average precipitation of six homogeneous regions of India viz., Hilly region of India (HRI), northwest India (NWI), central northeast India (CNEI), northeast India (NEI), west central India (WCI) and peninsular India (PI) can be seen at Indian Institute of Tropical Meteorology (http://www.tropmet.res.in/) and shown in Fig. 1. The whole year is classified by IMD into four seasons, viz., winter (January–February or JF) pre-monsoon (March–May or MAM) summer monsoon (June–September or JJAS) and post-monsoon (October–December or OND).

Fig. 1
figure 1

Model domain used in RegCM3 and the six homogeneous regions of India such as Hilly region of India (HRI), North West India (NWI), Central Northeast India (CNEI), North East India (NEI), West Central India (WCI), and Peninsular India (PI)

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3 Results and discussion

3.1 Analysis of observed precipitation over India

To study the annual and seasonal precipitation climatology, daily precipitation data at 1° × 1° grids of IMD from 1951 to 2007 (57-years) have been used. Figure 2 shows the mean annual climatology (mm) and regression trend (mm/57 years) of annual precipitation over India. Figure 2a shows the mean annual precipitation in the range of 1500–3000 mm over the NEI, approximately 3000 mm over the Western Ghats (WGs), 1000–1500 mm over the Western Himalaya (WH) and 100–500 mm over NWI. Figure 2b shows that the decreasing trend of annual precipitation in the range of 50–300 mm was found over the WGs, central India and HRI and increasing trend in the range of 20–300 mm was noticed over the NWI, NEI and PI. These changes in precipitation heavily affect the agricultural activity of those regions and in turn the economy of the country.

Fig. 2
figure 2

a Observed (IMD) mean annual precipitation (mm) and b trend (mm/57 years) over India during 1951–2007

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Figure 3a–d illustrates the climatology of mean seasonal precipitation and Fig. 3e–h shows the corresponding trend (mm/57 years) over India using IMD gridded data from 1951 to 2007. Figure 3a shows the mean precipitation of 50–100 mm over the HRI during JF (Fig. 3a), 50–300 mm over the HRI, 100–500 mm over the NEI during MAM (Fig. 3b), above 2000 mm over the WGs, 1000–2000 mm over the NEI, 500–1000 mm over the WH and 100–500 mm over the NWI during JJAS (Fig. 3c) and 50–100 mm over the HRI, CNEI, NEI, WCI and 100–300 mm over the PI during OND (Fig. 3d). Figure 3e shows an increasing trend in precipitation of 20–100 mm over the west WH and the decreasing trend of 20–100 mm over the east WH during JF. While increasing precipitation of 20–100 mm can be seen over the west WH, north NWI, NEI and decreasing precipitation of 20–100 mm over the east WH, east coast of India and eastern Himalaya during MAM (Fig. 3f). Figure 3g shows a decreasing trend of 50–300 mm over the WGs, central India, HRI and an increasing trend was found in the range of 20–300 mm over the NEI and PI during JJAS. Figure 3h shows a decreasing trend in the range of 20–100 mm over large parts of India.

Fig. 3
figure 3

a–d Observed (IMD) seasonal mean precipitation (mm) and e–h corresponding trend (mm/57 years) over India during 1951–2007

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The analysis of annual precipitation clearly showed large variations over different parts of India. Highest precipitation can be seen over the WGs and eastern part of India and the lowest precipitation was found over the NWI. The primary reason for high precipitation over the mountainous regions could be attributed to the strong convection, which undergoes a diurnal cycle in which these mesoscale mountains play an important role (Xie et al. 2006). The highest precipitation was found during JJAS over India followed by OND, MAM and JF. Overall, an increased precipitation was found during JF and MAM seasons and decreased precipitation was noticed in JJAS and OND seasons over large parts of India.

Annual and inter-annual variability of precipitation has been illustrated in the annual time series plots of precipitation anomalies over India from 1951 to 2007 (solid thick line shows 5-year running mean) as shown in Figs. 4 and 5 respectively. An analysis of annual variability of mean precipitation over India showed an unequal pattern with high and low precipitations (Fig. 4). The long-term mean value of annual averaged precipitation over India was about 1416 mm and standard deviation of 113 mm (coefficient of variation; CV of 8 %) of the long-term mean value. High and low rain years are identified on the basis of IMD criteria. Those years having mean annual percentage departure less than −10 % (more than +10 %) are considered as deficient (excess) years and the remaining years are considered as normal rainy years. The annual precipitation records over India have shown that there were 7-excess rainy years and 9-deficient rainy years during 1951–2007 (57 years). The trend analysis showed a decreasing trend of 0.31 mm/year in mean annual precipitation over India, while 5-year moving average reveals the existence of low-frequency variability of time scales of the order of approximately 5–10 years (positive: 1954–63, negative: 1965–1969 and 1997–2004).

Fig. 4
figure 4

Observed (IMD) inter-annual precipitation variability and 5 years running mean (black solid line) over India during 1951–2007

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Fig. 5
figure 5

Same as in Fig. 4 except for different seasons

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An analysis of inter-annual variability in precipitation for the different seasons (JF, MAM, JJAS and OND) from 1951 to 2007 has been shown in Fig. 5. Observed seasonal variability averaged over India was about 46 mm and standard deviation was about 14.7 mm (CV of 31.8 %) with increasing precipitation of 0.073 mm/year during JF. While mean precipitation was of 167.5 mm and standard deviation was about 26.3 mm (CV of 15.7 %) with increasing precipitation rate of 0.18 mm/year during MAM. Long-term mean of JJAS precipitation was about 1050 mm and CV was about 8.6 % (standard deviation of 90 mm) with a decreasing trend of −0.26 mm/year. The averaged precipitation during OND was about 152 mm, standard deviation of 35 mm (CV of 23.3 %) and a decreasing trend of −0.304 mm/year. The spatial distribution of precipitation trend indicated that the precipitation exhibits an increasing trend during JF and MAM seasons and decreasing trends during JJAS and OND seasons. While annual precipitation showed a decreasing trend over India during 1951–2007.

Figure 6 shows the temporal analysis of the daily precipitation along with composite floods and droughts years during the period of study. Figure 6 clearly shows that the amount of daily precipitation was increasing from January to July and precipitation started decreasing from the beginning of August to December. Figure 6 also shows that the amount of precipitation is less than 4 mm/day in January to May and mid of October to December. The daily precipitation event is about 4–12 mm/day during JJAS (up to mid of October) and the highest daily precipitation was noted in July (about 12 mm/day). The analysis of composite floods/droughts year shows a daily precipitation of 4–18/4–12 mm/day during the JJAS. The highest daily precipitation of 18 mm/day has been observed during mid July in composite flood cases and 12 mm/day during August in composite drought cases. It suggests that the monsoon was most active during early July to the mid of August compared to June and September. Figure 6 (marked with circles) clearly shows that in the case of droughts low precipitation was noted from July to early August approximately duration of 30–40 days which corresponds to the long-term intraseasonal variability of Maden–Julian type.

Fig. 6
figure 6

Temporal plot of the IMD daily precipitation (mm) along with composite floods (blue) and droughts (red) years over India during 1951–2007

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It is a well-known fact that, even during a particular year, large spatial and intraseasonal variability in the seasonal precipitation over India is evident. This is primarily due to the occurrence of precipitation associated either with monsoon disturbances (referred to as monsoon lows and monsoon depressions) that form over the adjoining seas and move over land, or with an intensification and/or displacement of the monsoon trough (summer season equivalent to the intertropical convergence zone) that generally lies over the northern plains of India during the monsoon season. The day-to-day variability in precipitation is thus characterized by “active” periods with high precipitation over the central India when the monsoon trough is over the northern plains, and “break” periods with weak or no precipitation over the central India and high precipitation over the north India when the monsoon trough is close to the foothills of the Himalaya.

3.2 Model simulated mean precipitation

The present study compared the simulated annual and seasonal mean precipitation climatology over India with the observed gridded data set of IMD and CMAP for the period of 25 years (1982–2006).

3.2.1 Simulated mean annual precipitation

Figure 7 shows the highest mean annual precipitation over the NEI and WGs and lowest precipitation over the NWI in IMD (Fig. 7a), CMAP (Fig. 7b) and RegCM3 (Fig. 7c). The mean annual precipitation amount of 1500–3000 mm over the NEI and WGs, 1000–1500 mm over the WH, west CNEI, 500–1000 mm over the east CNEI, east NWI, WCI and PI and below 500 mm over west parts NWI has been observed in IMD data (Fig. 7a). CMAP showed the mean annual precipitation of 1500–2500 mm over the NEI and WGs, 1000–1500 mm over the east CNEI and east WCI, 500–1000 mm over the west CNEI, east NWI, WCI, PI and WH and below 500 mm over west NWI (Fig. 7b). While RegCM3 showed the mean annual precipitation of 1500–3000 mm over the eastern Himalaya, NEI and WGs, 1000–1500 mm over the foothills of Himalaya and NEI, 500–1000 mm over the large parts of central India, PI and below 500 mm over the west parts of NWI (Fig. 7c). The mean annual precipitation of above 2000 mm can be seen over the large part of NEI and WGs in IMD and RegCM3 while the amount of precipitation more than 2000 mm was found only over the small parts of north NEI in CMAP. Overall, RegCM3 has been able to simulate the mean annual precipitation well patterns over India.

Fig. 7
figure 7

Spatial distribution of mean annual precipitation in mm (a) IMD, (b) CMAP, (c) RegCM3, respectively for the period 1982–2006

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3.2.2 Simulated seasonal mean precipitation

After detailed study of annual and seasonal mean (JF, MAM, JJAS and OND), precipitation climatology from IMD, CMAP and RegCM3 over India during 1982–2006 has been presented Fig. 8a–l. The RegCM3 simulated mean precipitation of 150–300 mm was found over the HRI and PI during JF (Fig. 8c). The highest difference in the amount of precipitation was noted over the PI where the model overestimated the precipitation. RegCM3 showed (Fig. 8f) the mean precipitation of 300–1000 mm over the HRI and NEI, 50–300 mm over the large parts of central India, east NWI and PI during MAM. The largest difference was noted over the HRI and NEI. Figure 8i shows the RegCM3 in JJAS mean precipitation of 1000–3000 mm over the foothills of Himalayas and WGs, 500–1500 mm over the NEI, large parts of CNEI and east coast of India and below 500 mm over the large parts of the central India, PI and WH. A comparison of model and observed mean precipitation showed the highest precipitation in IMD and approximately the same precipitation amount in RegCM3, but CMAP showed the slightly lower precipitation amount over the large parts of India. Figure 8 shows the RegCM3 mean precipitation of 50–300 mm over the HRI and NEI, large parts of CNEI and PI during OND.

Fig. 8
figure 8

Same as in Fig. 7 except for different season

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3.3 Interannual variability of precipitation

The previous sections have mainly focused on the mean precipitation climatology or climate conditions. But much less is known about how well the RegCM3 can simulate the interannual variability. The goal of this study is to provide a detailed comparison between the RegCM3 simulated and the observed interannual precipitation variability over India from 1982 to 2006. The year-to-year variations in precipitation between model and observed interannual variability are important as it is one way to test for the RegCM3. Therefore, it is critical to evaluate when and where climate anomalies are predictable and to assess the performance of RegCM3 in reproducing them. Before incorporating the RegCM3 for the predictions of variability and for the impact assessments, we must first evaluate how well these models simulate the present-day variability. To evaluate how well an RegCM3 simulates the year-to year precipitation variability, one method is to compare the magnitudes of observed and simulated variability. Table 1 shows model and observed precipitation averaged (mm), regression trend (mm/years) and correlation coefficients (CCs) in different seasons over India and annually over India and six homogenous regions.

Table 1 Model and observed precipitation averaged (mm), regression trend (mm/year) and correlation coefficients (CCs) in different seasons over India and annually over India and six homogenous regions
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Figure 9a–e presents that annual and seasonal anomalies over India were approximately similar to the RegCM3 and observed anomalies of IMD and CMAP both during 1982–2006. Figure 9a shows that the magnitudes of positive and negative annual precipitation anomalies have been found to be the highest in IMD followed by RegCM3 and CMAP in most of the years. RegCM3 underestimated the annual variability compared to IMD and overestimated compared to CMAP over the India. The regression trend (Table 1) analysis showed a decreasing annual precipitation amount of the order of 0.67 mm/year in IMD, 2.04 mm/year in RegCM3 and 2.85 mm/year in CMAP over India. The analysis of JF and MAM (Fig. 9b, c) precipitation anomalies was slightly higher (positive or negative magnitude) in RegCM3 followed by CMAP and IMD. The trend analysis showed a decreasing rate in precipitation of 0.35 mm/year in IMD, 0.27 mm/year in RegCM3, 0.61 mm/year in CMAP during JF and 0.23 mm/year in IMD, 0.83 mm/year in RegCM3 and 0.67 mm/year in CMAP during MAM. Figure 9d shows that most of the precipitation anomalies (positive/negative) having similar patterns. It was found that in most of the years high magnitudes of anomalies (positive or negative) were found with IMD followed by CMAP and RegCM3. The analysis also indicated that the model underestimated the precipitation anomalies compared to the IMD and CAMP and decreasing rate of 0.52 mm/year in IMD, 1.81 mm/year in RegCM3 and −1.16 mm/year in CMAP over India. In most of the years, the precipitation anomalies during OND have been found to be the highest by IMD followed by CMAP and RegCM3 as shown in Fig. 9e. It means that RegCM3 underestimated the precipitation anomalies as compared to those by the IMD and CMAP and decreasing rate of 0.03 mm/year in IMD, 1.13 mm/year in RegCM3 and 0.63 mm/year in CMAP over India.

Fig. 9
figure 9

All India annual and seasonal precipitation anomalies (mm) for the period 1982–2006 (solid line shows 5-years running mean)

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The analysis of correlation coefficients (CCs) shows a significant level of the order of 95 % (CC = 0.396) and 99 % (CC = 0.505), respectively, shown in Table 1. The CCs between all India precipitation of the model with respect to IMD (CMAP) are 0.79 (0.67), 0.57 (0.43), 0.59 (0.52), 0.42 (0.46) and 0.65 (0.57) during JF, MAM, JJAS, OND and annual, respectively [CCs are higher than Maharana and Dimri (2014)]. The simulated precipitation anomalies compared well with the observed anomalies over the India and for each season. However, the regional model overestimates the interannual variability during winter- and pre-monsoon seasons and underestimates the interannual variability during the summer and pre-monsoon seasons. The RegCM3 shows that the winter- and pre-monsoon seasons produce more variability than the observed ones (IMD and CMAP). This type of behavior of RegCM3 is in agreement with results found by Giorgi et al. (2004) who discussed the scale dependence of interannual variability. He showed that during the summer months, the mesoscale forcing has an important role in regulating the simulated interannual variability, while in the winter months the simulated interannual variability is mostly regulated with the boundary forcing fields. In particular, a number of previous studies have shown the substantial overestimates of precipitation over the near-equatorial convergence zone for both the winter and summer seasons (MacKellar et al. 2009; Tummon et al. 2010). Such deficiency may be due to the inability of the models to correctly simulate realistic large-scale conditions or to properly respond to such conditions via their convective parameterization (Crétat et al. 2012).

3.4 Scale of variability

The standard deviation and coefficient of variation are generally used to study the scale of variability. Figure 10 shows a comparison of RegCM3 and observed (IMD and CMAP) precipitation variability (standard deviation) over India and six homogeneous regions. Figure 10 shows the highest standard deviation during JJAS, OND as well as in annual precipitation over India compared to the IMD and maximum values of standard deviation were found during JF and MAM over India in RegCM3. As far as homogeneous regions are concerned, the highest standard deviations were with IMD over all the homogeneous regions of India followed by RegCM3 mainly over the HRI and PI and CMAP over the NWI, CNEI, NEI and WCI. During OND, simulated and observed standard deviations were almost equal over India.

Fig. 10
figure 10

Standard deviation of precipitation (mm) over the India and six homogeneous regions: IMD (aqua), RegCM3 (slate blue) and CMAP (dark violet)

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Figure 11a shows the CV of precipitation for IMD, CMAP and RegCM3 over India and six homogeneous regions. Figure 11a shows highest CV during JF, OND and MAM and low variability during JJAS and in annual precipitation over India. Comparing the magnitudes of the simulated and observed CV, Fig. 11a shows high CV over the NWI and low variability over the HRI, CNEI and NEI. A close relationship between the model and observed CV can be seen over the CNEI and NEI. Figure 11b shows the ratio of CV between model and observed (IMD and CMAP) precipitation over India and six homogeneous regions. The ratio of CV is noticeably less than one in all the seasons and more than one in annual precipitation over India. Figure 11b shows that the model reproduced the observed pattern of large variability. Figure 11b also shows that the model reproduced the high CV over the NWI and CNEI and low CV over the NEI and WCI. The largest difference in the ratio of simulated and observed CV was found over the HRI and PI in IMD and CMAP. The magnitude of the ratio of CV was 0.74 and 0.90 in IMD and 1.41 and 1.58 in CMAP over the HRI and PI, respectively. It suggests that the RegCM3 shows high CV over the HRI and NWI while low CV is found over the NEI and WCI as compared to IMD and high CV over the NWI and low CV over the HRI and PI as compared with the CMAP. The above analysis indicates that model well captured the scale of variability reasonably well, except over the northern parts of the India.

Fig. 11
figure 11

a Coefficient of variation of precipitation (%) and b ratio of coefficient of variation (model and observed) over the India and six homogeneous regions: IMD (aqua), RegCM3 (slate blue), CMAP (dark violet) and RegCM3/IMD (aqua) and RegCM3/CMAP (dark violet)

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3.5 Evaluation of model performance

After the detailed study of mean precipitation variability over India and its homogeneous regions, we have computed the different quantitative performance measures, such as the MBE, RMSE and MPE using the simulated and observed variables over India. Such quantitative measures are very useful in the evaluation of model performance and it is well described by Sylla et al. (2010). We have already computed the CCs (Table 1) between RegCM3-simulated precipitation and observed precipitation and found significant CCs. The model is validated using observed precipitation from IMD and CMAP. Figure 12a–c shows the MBE (mm), RMSE (mm) and MPE (%) over India and six homogeneous regions from 1982 to 2006. The computation of MBE and RMSE (for evaluating the model performance) showed the magnitude of −319 and 329 mm with the IMD, while −18 and 79 mm were found with the CMAP over India. Figure 12a shows that the RegCM3 underestimated the mean annual precipitation as compared to IMD and CMAP over India. The analysis also showed that the value of MBE was negative while RMSE was always positive but the magnitude was nearly same as in IMD and a large difference was found with the CMAP. This analysis suggests that there is a very close relationship between RegCM3 and IMD and close relationship with the CMAP over India. The MPE test clearly shows that the RegCM3 underestimates the mean annual precipitation of the order of −22.44 % as compared to IMD and −1.41 % compared to CMAP during the period of study.

Fig. 12
figure 12

Comparison of simulated and observed precipitation over India and six homogeneous regions; (IMD (aqua), RegCM3 (slate blue) and CMAP (dark violet). a Mean bias error (MBE), b root mean square error and c mean percentage error

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The analysis shows that the RegCM3 overestimated the precipitation during JF, MAM and underestimated during JJAS, OND as compared with those of IMD and CMAP. The analysis of MBE and RMSE reveals that the RegCM3 simulated precipitation has a close relationship with IMD during JF, MAM, JJAS and JF, MAM, OND with the CMAP. The MPE test clearly shows the mean precipitation of 24.99, 42.30, −35.44 and −19.62 % with IMD and 42.30, 69.96, −10.13 and 30.97 % with the CMAP during JF, MAM, JJAS and OND seasons, respectively, over India. These results suggest that the RegCM3 overestimates the precipitation during JF and MAM, while it underestimates during JJAS and OND with IMD and CMAP both over India. The RegCM3 shows a very close relationship with the IMD and CMAP both over the NWI and PI, while approximately close relationship can be seen over the HRI, VNEI, NEI and WCI. Over the mountainous regions of India, RegCM3 has approximately close relationship with the IMD and CMAP. The MPE test clearly shows that the mean annual precipitation was overestimated of the order of 4.97 % over the PI with IMD and 62.22, 4.97, and 0.79 % over the HRI, NWI and PI, respectively, with the CMAP. The analysis also shows that the RegCM3 underestimated the order of 18.39 % over the HR, 1.38 % over the NWI, 24.25 over the CNEI, 40.26 % over the NEI and 30.37 % over the WCI with IMD and 17.98 % over the CNEI, 22.14 % over the NEI and 17.20 % over the WCI with the CMAP.

The mean bias error is 95 % confidence intervals computed using a two-tailed t test applied to the annual (all India and its homogeneous regions) and seasonal (AI) time series of the difference between the RegCM3 and observed (IMD and CMAP) dataset in Fig. 13. The IMD and CMAP showed low and equal bias during JF, MAM and OND over India and annually over the NWI and PI. The high bias was over the HRI and NEI to the IMD, while these regions are same as in CMAP dataset. This would cause a high bias predominantly in mountainous terrain. It is quite interesting to note that RegCM3 is significantly over predicting JF and MAM over India and under predicting JJAS over India in IMD and annually over the HRI, CNEI, NEI and WCI in IMD. Consistency between RegCM3 and observed is an important cause of fundamental to the dynamical downscaling approach rather than arising from the details of a particular code. It is also worth noting that the RegCM3 has a systematic bias; the IMD bias is the highest and the CMAP bias is among the smallest.

Fig. 13
figure 13

Precipitation biases at 95 % confidence intervals for annual and seasonal (JF, MAM, JJAS and OND) precipitation (RegCM3-IMD show blue and RegCM3-CMAP show green) over AI and its homogeneous regions during 1982–2006

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The simulated total moisture transport is illustrated by the vertically integrated temperature and water vapor mixing ratio (WVMR). Giorgi et al. (2004) also have studied over European regions. The annual and seasonal moisture transports at 18σ levels have been shown in Fig. 14 along with their respective differences (RegCM3-NCEP) averaged over the land regions of India. The negative differences of averaged air temperature at first σ level have largest during JF and MAM and smallest during JJAS and OND (left panel of Fig. 14). Similarly, the WVMR (right panel of Fig. 14) shows the positive differences during JF and MAM and negative differences during JJAS and OND at first σ level. As a consequence, model having the total moisture convergence is highest compared to the NCEP during JF and MAM. This is consistent with the stronger lower level convergence and upward motion of the model from 1σ level to 10σ level. Figure 14 (right panel) clearly shows high WVMR during JF and MAM in RegCM3, which caused high precipitation and low WVMR in RegCM3 during JJAS and OND can be linked with low precipitation of RegCM3. Figure 14 also shows that an increased mean WVMR resulting from the exclusion of increase simulated mean precipitation and vice versa. The analysis also shows that an increased mean precipitation decreases the average surface temperature and vice versa. Hence, high negative biases in RegCM3 simulated seasonal temperature during JF and MAM can be linked with the RegCM3 overestimated WVMR and precipitation and slightly lower negative biases of the model during JJAS and OND can be linked with the underestimated WVMR and precipitation with RegCM3.

Fig. 14
figure 14

Annual and seasonal vertical profile differences between RegCM3 and NCEP reanalysis: air temperature (left) and water vapor mixing ratio (right) averaged over India at 18σ level

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Figure 15 compares the difference (RegCM3-NCEP) in vertically integrated average annual temperature and WVMR over the six homogeneous regions of India at 18σ levels (simulated total moisture transport is illustrated by the vertically integrated temperature and water vapor mixing ratio). Figure 15 (right panel) shows high positive values of WVMR over PI, WCI and CNEI where strong negative biases were found in the analysis of temperature. This can be linked with the cooling during the same season. The negative value of WVMR can be seen over the NEI and HRI. A comparison of model simulated and observed mean precipitation showed that the RegCM3 strongly underestimates the precipitation over the NEI. These regions showed the high negative WVMR. While over the regions of overestimated mean precipitation (over PI), a high value of positive WVMR can be seen.

Fig. 15
figure 15

Same as in Fig. 14 except for the homogeneous regions of India

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These results indicate that the RegCM3 has a more transport of vertical air temperature and WVMR from the lower boundary to the upper boundary of troposphere compared to NCEP. One reason for this behavior is the use of different planetary boundary layer schemes in the models. The RegCM3 adopts a non-local boundary layer representation in which the vertical profile between the surface and the boundary layer top is calculated from the temperature and WVMR of the lower troposphere. Giorgi et al. (2004) showed that non-local schemes tend to enhance the vertical heat and moisture transport compared to the local schemes, thereby leading to a relative cooling and drying of the surface. A second reason may be attributed to the use of different convection schemes. The net effect of convection is to redistribute vertically and in particular transport upward, energy and moisture. However, the schemes adopt different closures and parameter assumptions, and as a result their efficiency in redistributing heat and moisture may be different. This effect would be especially important in the warm season, when cumulus convection is more active.

4 Conclusions

In this paper, the means, interannual variability, trends and various statistical measures have been used to test the RegCM3 performance over India and its homogeneous regions. Highest precipitation was found over the east part of India and WGs and lowest precipitation was found over the NWI. The spatial distribution of precipitation trend indicated an increasing trend during JF and MAM and decreasing trends during JJAS and OND. While annual precipitation showed a decreasing trend over India during 1951–2007. The annual change in precipitation shows a decreasing trend over WGs, central India, HRI and an increasing precipitation was noticed over the NWI, a large part of the PI and NEI. Temporal analysis of daily precipitation shows less than 4 mm/day of rain from January to May and mid October to December. The precipitation variation was noted in the range of about 4-12mm/day during month of June to September (up to mid of October) but highest precipitation was found in July (12mm/day). It suggests that the monsoon was more active during early July to the mid of August compared to June and September. In the case of droughts, low precipitation was noted from July to early August, approximately 30–40 days duration.

The seasonal simulated precipitation anomalies compared well with the observed anomalies over India. However, the regional model overestimated the interannual variability during JF and MAM and underestimated the interannual variability during JJAS and OND. RegCM3 shows more variability than the observed ones (IMD and CMAP) during JF and MAM. RegCM3 shows the high coefficient of variation over the HRI and NWI while low over the NEI and WCI compared to IMD and high CV over NWI and low CV over the HRI and PI as compared to CMAP. The above analysis indicates that model well captured of inter-annual variability reasonably well except over the northern parts of the India. The MPE analysis clearly shows that the RegCM3 underestimated the mean annual precipitation of the order of −22.44 % compared to IMD and −1.41 % compared to CMAP during the period of study. The analysis also shows that the RegCM3 overestimated the precipitation during JF, MAM and underestimated during JJAS, OND compared to IMD and CMAP. Over the mountainous regions of India, RegCM3 has close values with the IMD and CMAP. The RegCM3 is capable of simulating the highest value of WVMR during JF and MAM (caused high precipitation in JF and MAM) and low WVMR during JJAS and OND.