Introduction

The winter season over India is characterized by dominating influence of cool continental air of low humidity and is therefore the period of generally cool and dry weather over most of the country (Pant and Rupa Kumar 1997). This fine weather is occasionally interrupted by the arrival of low pressure waves or weak depressions from the far west, these disturbances appear as troughs or low pressure areas at the surface or as cyclonic circulation in the upper air in the regime of westerly winds north of the sub-tropical high pressure belt (Dutta and Gupta 1967; Singh 1979; Singh et al. 1981). These migratory systems originate at frequent intervals in the Mediterranean Sea and sometimes as far west as the Atlantic ocean and there after traveling eastwards across Iraq, Iran, Afghanistan and Pakistan, they enter north India and move away further eastwards giving rise to extended cloudiness, precipitation and cold wind over northwest and north India (Rao and Srinivasan 1969). These disturbances are called western disturbances (WD) as it travels from west to east and it is also defined as an eastward moving extra-tropical upper air trough in the subtropical westerly often extending down to the lower atmospheric level of the north Indian latitudes during the winter months (Pisharoty and Desai 1956).

The arrival of western disturbance throws the life out of gear in Northwest India, causing heavy precipitation followed by chill. Therefore, forecasting the intensity of western disturbance is useful for disaster mitigation (Dimri et al. 2004). In addition to complex orography, paucity of data has made numerical weather prediction very challenging over the region (Hatwar et al. 2005). Studies on Western Disturbances over North West India using numerical models are limited. Azadi et al. (2001) used NCAR high resolution mesoscale model to simulate active western disturbance during 1997. Dimri et al. (2004) used a mesoscale MM5 model to simulate heavy precipitation associated with an intense WD over Western Himalayas during 21–25 January 1999 when a WD affected NW India. Hatwar et al. (2005) and Dimri and Mohanty (2009) carried out prediction of western disturbance and associated weather systems over Western Himalayas using the IMD’s operational limited area analysis and forecast system and MM5 model respectively.

The model used in this study is the Weather Research and Forecasting (WRF) model (Version v3.5.1) which uses the Eulerian mass coordinate and is referred to as the Advanced Research WRF (ARW). The WRF physics options have a range of physical parameterization configurations which can be used for simulation. Thus, one of the essential steps in the simulation is to choose the most appropriate combination of physics options (Optimal setup) for the region and time period under consideration. Previous studies by William and James (2006), Borge et al. (2008), Krieger et al. (2009), Flaounas et al. (2010), Kim and Wang (2011), Raju et al. (2011), Crétat et al. (2012) and others have showed that, the model forecast is sensitive to choice of physical parameterization schemes. Though previous studies have attempted to determine the sensitivity of the model and best physics options over many different regions, their conclusions may not be necessarily applicable to this region due to its different geographical features (Krieger et al. 2009). Thus, the purpose of this paper is to examine model sensitivity and identify best physics options suited for this region during the Western Disturbance. Dimri and Chevuturi (2014) have studied model sensitivity for WDs with the old version (3.0) of WRF model using five different cloud microphysics schemes. Two intense cases of WDs during the period 13–17 January 2002 (case-1)and 05–08 February 2002 (case-2) have been investigated by Hatwar et al. (2005) and Dimri and Chevuturi (2014). In addition, two more cases of WDs that affected northwest India during period of 16–19 January 2013(case-3) and 4–7 February 2013 (case 4) (see Table 1) which have occurred after a decade have been selected for the present study. During these cases of WDs, heavy precipitation has been reported from the many stations in Northern India and the Western Himalayan region. The synoptic situations associated with Case-3 and Case-4 has been discussed by Medha et al. (2014).

Table 1 List of episode selection
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Five experiments have been carried out using the different Micro Physics (MP) schemes while keeping the other parameterization schemes fixed (see Tables 2, 3a). In the present study, three nested domains of resolutions 81, 27 and 9 km with five different model configurations were simulated for all four WDs. Sensitivity and error statistics of three important parameters have been studied to examine model sensitivity and identify best physics options suited for simulating the weather system over this region during WD.

Table 2 Description of the model configuration used
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Table 3 Microphysics schemes used with (a) combination of other parameterization schemes in 1–5 experiments and (b) summary
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Model, data, experimental design and evaluation methodology

Model used

The model used in this study is the Weather Research and Forecasting (WRF) model (Version v3.5.1) which is a widely used community mesoscale model. This version of the WRF model uses the Eulerian mass coordinate and is referred to as the Advanced Research WRF (ARW) developed by the National Center for Atmospheric Research (NCAR). It uses the fully compressible non-hydrostatic equations with hydrostatic option and mass-based terrain following coordinate. The horizontal grid is the Arakawa-C grid. The model can simulate both idealized and real-data cases with various lateral boundary condition options. The model supports one way, two-way, and moving nest options (Skamarock et al. 2008). A brief description of the model configuration and the different nested domains used in this study is given in Table 2 and Fig. 1 respectively. In the present study, three nested domains with resolutions of 81, 27 and 9 km cover northwest and north India. Domain 1 is the mother domain and there are two inner domains within domain 1. All the domains are provided with feedback option.

Fig. 1
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WRF modeling domains (black box) covers northwest and north India

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Data used

Initial and boundary conditions for the model integration are taken from the NCEP High Resolution Global Forecast System (GFS) with 1° × l° spatial resolution and temporal resolution of 6 h. For model validation different observational datasets have been used. For precipitation verification, a spatial resolution 0.25° × 0.25° long period (1901–2013) daily gridded rainfall data over the Indian main land (Pai et al. 2014) by the India Meteorological Department (IMD) has been used.

Other parameters were validated with ERA-Interim of the European Centre for Medium-Range Weather Forecasts (ECMWF). This is a global atmospheric reanalysis data from 1979 to present. The spatial resolution of the data set is approximately 80 km (T255 spectral) on 60 vertical levels from the surface up to 0.1 hPa (Dee et al. 2011).

Experimental design

The WRF physics options fall into several categories, each contains several choices. In the present study, Numerical experiments have been carried out by changing the Microphysics (MP) Category (shown in Tables 2, 3a) while keeping the other parameterization schemes fixed. Microphysics schemes have commonly been referred to as grid-scale precipitation schemes. A full description (Mass variables, Number variables, various processes etc.) of Microphysics Category with each scheme is available in the model description document (Skamarock et al. 2008).

In addition to the microphysics schemes the role of various other parameterization schemes, which represents the processes at a subgrid scale is also very important.

Based on previous simulation studies by Azadi et al. (2001), Dimri and Chevuturi (2014) done for the WDs over the same region, the following parameterization schemes have been selected: Kain–Fritsch (KF) (Kain 2004) for cumulus; unified Noah land-surface model (Noah) (Chen and Dudhia 2001) for land surface; Yonsei University (YSU) (Hong and Lim 2006) for planetary boundary layer; MM5 (Monin–Obukhov) scheme (Paulson 1970) for surface layer; rapid radiative transfer model (RRTM) (Mlawer et al. 1997) for longwave radiation and Dudhia (1989) for shortwave radiation. Five experiments for producing 24-h forecasts have been carried out using the different Physics options as shown in Table 3a.

Evaluation methodology

Sensitivity and error statistics of precipitation (PREC; mm/day), wind (CIRC; m/s) and geopotential heights (GPH; m) are analyzed to examine model sensitivity and identify best physics options suited for this region during the passage of the weather system.

Root mean square error is used to examine model sensitivity. It is mathematically defined, (Singh et al. 2004; Wilks 2006) as

$$RMSE = \sqrt {\frac{{\mathop \sum \nolimits_{i = 1}^{n} \left( {X_{i} - O_{i} } \right)^{2} }}{n}} .$$

Standard deviation of observed data (STDEVobs) is mathematically defined,

$${\text{STDEV}}_{\text{obs}} = \sqrt {\frac{{\mathop \sum \nolimits_{i = 1}^{n} \left( {O_{i} - O_{mean} } \right)^{2} }}{n}}$$

where n is the total number of evaluated grid points over space, Xi and Oi are the model and observed precipitation for ith point O mean is the value averaged over space for observed analysis.

RMSE is calculated over the domain area 26°N–40°N and 70°E–85°E which covers the north west and north India. In each grid or grid point model output is compared with the observation in order to calculate RMSE. The Model accumulated rainfall was compared with IMD observational dataset. For geopotential height and winds, ERA interim observational dataset is used. In addition to these statistics RMSE-observations standard deviation ratio (RSR) is also evaluated.

$$RSR = \frac{RMSE}{{{\text{STDEV}}_{\text{obs}} }}$$

RSR standardizes RMSE using the observations standard deviation. RSR varies from the optimal value of 0, which indicates zero RMSE or residual variation and therefore perfect model simulation, to a large positive value. Lower RSR and lower RMSE indicate better model simulation. If RSR greater than or equal to 1 (high) then Skill of the model is poor so it does not make any sense to evaluate the best physics options suited for this region during the weather system (Morias et al. 2007). An experiment that gives the Lowest RMSE (RSR) will be determined from the five simulations. The configuration of this experiment may be the best combination of physics options suited for the region to capture the main characteristics of the various parameters associated with the WDs.

Results and discussion

Sensitivity of the model forecast and to identify best physics options

The model forecasts of precipitation (PREC; mm/day), wind (CIRC; m/s) and geopotential heights (GPH; m) from five physics configurations have been assessed with respective observational datasets for the four cases of WDs that affected the northwest India. Table 4a, b show RMSE and RSR in bracket based on the Model forecasts of precipitation (mm/day) (PREC), 500 hpa geopotential height (m) (GPH) and 500 hPa wind (m/s) (CIRC) from different experiments (physics configurations) for WD case 1, 2 and WD case 3, 4 respectively.

Table 4 RMSE and RSR in bracket based on the model forecasts of precipitation (mm/day) (PREC), 500 hpa geopotential height (m) (GPH) and 500 hPa wind (m/s) (CIRC) from different experiments (physics configurations) for (a) WD case 1, 2 and (b) WD case 3, 4
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RMSE and RSR are evaluated for all the model domains, but for the sake of brevity the Table 4 illustrates the values of the first model domain (81 km) only. It is seen that RSR is always less than one which shows that the means skill (performance) of the model is good for forecasting these cases of WDs. It is observed that, most of the time RMSE and RSR has been the lowest for Experiment 5.

In the Experiment 5, National Severe Storms Laboratory (NSSL) 1-moment (Gilmore et al. 2004) scheme used as a microphysics parameterization scheme. It is developed at the National Severe Storms Laboratory. A single-moment bulk microphysics scheme with multiple ice precipitation categories is described. It has in addition two liquid hydrometers, snow (ice crystal aggregates), and various categories of graupel with different densities and intercepts. It also has predictive equations for the specific humidity of forms of particle like cloud water (q c ), cloud ice (q i ),snow (q s ), rain (q r ) and graupel (qg) (see Table 3b). The specific humidity for the larger precipitation categories (graupel, hail, and rain) are defined by Marshall–Palmer exponential size distributions (Marshall and Palmer 1948). These features may be responsible for proper depiction of sub grid level phenomenon over the region and hence lower the errors.

The performance of the combination of NSSL one moment, KF, Noah, YSU, MM5 schemes as microphysics, cumulus parameterization, Land surface, Planetary Boundary layer and Surface layer respectively are best compared to the other schemes used in this study. Thus discussions on dynamical structure of WDs are based on these combinations of the model physics.

To study dynamical structure of WDs

Dynamical structure of the WDs simulated by the model with the Physics configuration of experiment 5 is discussed here. Figure 2a–d shows daily rainfalls (mm/day) for 15th and 16th January 2002, of WD case 1 and 7th and 8th February 2002, of WD case 2 respectively based on IMD’s gridded rainfall data and Fig. 2e–f shows for model simulated rainfall.

Fig. 2
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Daily rainfalls (mm/day) based on a–d IMD’s and e–h model simulated for 15th January 2002, 16th January 2002 of WD case 1 and 7th February 2002, 8th February 2002 of WD case 2 respectively

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On 15th January 2002, the observed rainfall distribution (see Fig. 2a) shows widespread rainfall over many places over NW India and the model simulation also shows almost the same pattern which can be seen in the observed rainfall (see Fig. 2a, e). On 16th January 2002, the observed rainfall distribution shows, the maxima of precipitation has shifted towards South-East direction (see Fig. 2b). The model could produce the maxima of precipitation which can be seen in the observed rainfall (see Fig. 2b, f). On 7th February 2002, moderate rainfall in the range 1–2 cm over some parts of Western Himalayan region were observed (see Fig. 2c). Model could produce rainfall of the same range over the same region as seen in observed spatial distribution pattern (see Fig. 2c, g). On 8th February 2002, rather heavy rainfall is seen over many places of East India (see Fig. 2d). The Model could produce rainfall over the region but over-predicted the rainfall (see Fig. 2d, h).

Figure 3a–d shows daily rainfalls (mm/day) for 18th and 19th January 2013, of WD case 3 and 5th and 6th February 2013 of WD case 4 respectively based on IMD’s gridded rainfall data and Fig. 3(e–f) shows the model simulated rainfall. On 18th January 2013, the observed rainfall distribution (Fig. 3a) shows a belt of moderate to heavy rainfall over the Western Himalayan region with peak centered near lat 32°N and 79°E (Approximately 10 cm) was observed. Figure 3e presents the model forecast for same period. The model could produce moderate to heavy rainfall over Western Himalayan region with peak centered near lat 32°N and 77°E (Approximately 10 cm). The model simulated spatial distribution pattern shows widespread light to moderate rain over parts of North West India, which can be clearly discernible in the observed rainfall (see Fig. 3a, e). On 19th January 2013, again Precipitation belt (1–6 cm) was confined mainly over the Western Himalayan region. Also light to moderate rain was observed over parts of eastern India (see Fig. 3b). From Fig. 3f, it is seen that, the model could produce the precipitation belt over the Western Himalayan region, light to moderate rain is seen over parts of eastern India. On 5th February 2013, Precipitation belt (2–9 cm) was confined mainly over the Western Himalayan region with peak centered near lat 33°N and 75°E (>9 cm) light to rather heavy rain over parts of North West India can also be seen (see Fig. 3c). The model simulation could also produce the Precipitation belt over the same region, but over predicted the rainfall over some parts of the Western Himalayan region (see Fig. 3c, g). On 6th February 2013, heavy rainfall persisted over the Western Himalayan region (see Fig. 3d). From Fig. 3h, it is seen that the model could produce the Precipitation belt over same region. Figure 4a–d presents 500 hPa geopotential height (m, contour) and wind (m/s, arrow) based on Era-interim data and region with wind speed more than 25 m/s is depicted in grey shade. Figure 4e–h shows the model simulated values for 15th and 16th January 2002 of WD case 1 and 7th and 8th February 2002, of WD case 2 respectively. Geopotential height approximates the actual height of a pressure surface above mean sea-level. Since cold air is denser than warm air, it causes pressure surfaces to be lower in colder air masses, while less dense, warmer air allows the pressure surfaces to be higher (Stull 2012). Thus, heights are lower in cold air masses, and higher in warm air masses. A line drawn in the presented figures connecting points of equal height (in meters) is called a height contour. That means, at every point along a given contour, the values of geopotential height are same. Geopotential height is valuable for locating troughs and ridges which are the upper level counterparts of surface cyclones and anticyclones (Daniel et al 1997). From Fig. 4a, it is seen that on 15th January 2002, a trough lay along longitude about 66°E. Model simulation could produce the trough along longitude about 68°E (see Fig. 4e). Figure 4b shows the trough has deepened and moved rapidly eastwards on 16th January 2002 and lay along longitude about 72°E. Model simulation could produce the trough at the same position (see Fig. 4f). From Fig. 4c, it is seen that on 7th February 2002, the associated cyclonic circulation is over 30°N to 34°N and 68°E to 72°E region. The Model could capture the cyclonic circulation over the same region (see Fig. 4g). The model simulation shows that on 8th February 2002, the cyclonic circulation moved eastward (see Fig. 4h) which can also be seen in observed analysis (see Fig. 4d).

Fig. 3
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Daily rainfalls (mm/day) based on a–d IMD’s and e–h model simulated for 18th January 2013, 19th January 2013 of WD case 3 and 5th February 2013, 6th February 2013 of WD case 4 respectively

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Fig. 4
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500 hPa geopotential (m, contour), wind (m/s, arrow) and region with wind speed more than 25 m/s depicted in grey shade a–d with Era-interim data and e–h model simulation valid for 00UTC for 15th January 2002, 16th January 2002 of WD case 1 and 7th February 2002, 8th February 2002 of WD case 2 respectively

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Figure 5a–d presents 500 hPa geopotential height (m, contour) and wind (m/s, arrow) based on Era-interim data and region with wind speed more than 25 m/s is depicted in grey shade. Figure 5e–h shows the model simulated values for 18th and 19th January 2013 of WD case 3 and 5th and 6th February 2013 of WD case 4 respectively. On 18th January 2013, well intensified trough lay along longitude about 70°E (see Fig. 5a). Model simulation could produce the trough at the same position (see Fig. 5e). The system became less marked on 19th January 2013 (see Fig. 5b) and model simulation could produce the same synoptic conditions (see Fig. 5f). From Fig. 5c, it is seen that the cyclonic circulation is over 30°N to 34°N and 68°E to 72°E region on 6th February 2013. The cyclonic circulation moved eastward and it became less marked on 7th February 2013 (Fig. 5d). The Model could produce the same synoptic conditions associated with the system (see Fig. 5c–f). During all the WDs, the model simulated geopotential height shows good accuracy in predicting low pressure area over the region. Figure 6a–h presents the forecast error (model-observation) in 500 hpa wind (m/s, arrow) and the region with bias (forecast error) more than 5 m/s depicted in grey shade for 15th and 16th January 2002 (of WD case 1), 7th and 8th February 2002 (of WD case 2), 18th and 19th January 2013 (of WD case 3) and 5th and 6th February 2013 (of WD case 4) respectively. From Fig. 6a–h it is observed that, the model simulated wind pattern agrees very closely with the observation analysis. However, over western Himalayan region it shows a south westerly bias.

Fig. 5
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500 hPa geopotential (m, contour), wind (m/s, arrow) and region with wind speed more than 25 m/s depicted in grey shade a–d with Era-interim data and e–h model simulation valid for 00UTC for 18th January 2013, 19th January 2013 of WD case 3 and 5th February 2013, 6th February 2013 of WD case 4 respectively

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Fig. 6
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Forecast error (model-observation) for 500 hPa wind (m/s, arrow) and region with wind speed error more than 5 m/s depicted in grey shade for a–h for 15th January 2002, 16th January 2002 of WD case 1, 7th February 2002, 8th February 2002 of WD case 2, 18th January 2013, 19th January 2013 of WD case 3 and 5th February 2013, 6th February 2013 of WD case 4 respectively

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Conclusions

The present study shows that performance of the combination of NSSL one moment, KF, YSU, RRTM and Dudhia schemes as a microphysics, cumulus, planetary boundary layer, longwave radiation and shortwave radiation parameterization schemes respectively gives a better simulation of the weather during WD’s over North West India.

The characteristics of the various parameters associated with the WDs have been thoroughly studied. It is found that the intensity and movement of the precipitation distribution and circulation over the region is well predicted by the model. However, it shows a bias over the Himalayan region. During all the WDs, the model simulated geopotential height shows good accuracy in predicting low pressure areas over the region. The model simulated wind pattern agrees very closely with the observation analysis. However, over western Himalayan region it shows a south westerly bias. Further improvement in the model resolution (less than 1 km), high resolution mountainous region and assimilation of satellite data in the analysis system are expected to improve the forecast accuracy further.