Abstract

In a variational data assimilation system, background error statistics (BES) spread the influence of the observations in space and filter analysis increments through dynamic balance or statistical relationships. In a data-sparse region such as the Bay of Bengal, BES play an important role in defining the location and structure of monsoon depressions (MDs). In this study, the Indian-region-specific BES have been computed for the Weather Research and Forecasting (WRF) three-dimensional variational data assimilation system. A comparative study using single observation tests is carried out using the computed BES and global BES within the WRF system. Both sets of BES are used in the assimilation cycles and forecast runs for simulating the meteorological features associated with the MDs. Numerical experiments have been conducted to assess the relative impact of various BES in the analysis and simulations of the MDs. The results show that use of regional BES in the assimilation cycle has a positive impact on the prediction of the location, propagation, and development of rainbands associated with the MDs. The track errors of MDs are smaller when domain-specific BES are used in the assimilation cycle. Additional experiments have been conducted using data from the Interim European Centre for Medium-Range Weather Forecasts Re-Analysis (ERA-Interim) as initial and boundary conditions (IBCs) in the assimilation cycle. The results indicate that the use of domain-dependent BES and high-resolution ERA-I data as IBCs further improved the initial conditions for the model leading to better forecasts of the MDs.

1. Introduction

The east coast and central parts of India receive 80%–90% of their annual rainfall during the summer monsoon season (June–September). A major portion of this rainfall is associated with monsoon depressions (MDs) moving across India. During a monsoon season, an average of six or seven monsoon depressions form over the northern Bay of Bengal (BoB) and move along the monsoon trough. These depressions produce widespread and heavy to very heavy rainfall during their passage over India. In fact, MDs are the most important synoptic-scale disturbances on the monsoon trough. So, they play a very important role in the space and time distribution of the Indian summer monsoon rainfall. For improved predictions of monsoon rainfall, better understanding of these depressions is required.

High-resolution nonhydrostatic mesoscale models and data assimilation techniques have shown great potential in predicting weather events associated with mesoscale convective systems (MCSs). Such MCSs influence synoptic-scale features of the Indian monsoon (Chang et al. 2009; Vinodkumar et al. 2009; Routray et al. 2010a,b). Operational weather forecasting centers in India are using three-dimensional variational (3DVAR) data assimilation methods. Variational data assimilation requires the knowledge of model forecast error statistics for the computation of the background cost function. The background errors determine the level of influence of each observation in the analysis and how this influence is distributed in space and among various analysis variables. In a regional data assimilation and forecast system, improper specification of the background error covariances leads to too large or too small analysis increments.

In the past few years, ensemble-based data assimilation methods such as the ensemble Kalman filter (EnKF) (Evensen 1994) are becoming more popular than variational approaches in the data assimilation community. The EnKF technique uses short-term ensemble forecasts to estimate the flow-dependent background errors. This technique has been recently implemented in various atmospheric and oceanic models at various leading operational centers in the world (Houtekamer and Mitchell 2001; Zhang and Anderson 2003; Houtekamer et al. 2005, 2009; Whitaker et al. 2008; Buehner et al. 2010a). These studies show the effectiveness of the EnKF method for different scales of interest and the advantages over existing data assimilation schemes, which assume stationary, isotropic background error covariance. Whitaker et al. (2008, 2009) and Buehner et al. (2010b) have examined the EnKF and variational assimilation methods. They found that the forecast skill of the models improved when the EnKF method is used in the analysis procedure. Buehner (2005) has evaluated the performance of six different types of background error and concluded that model skill is improved in the variational approach using flow-dependent error covariances produced at regular intervals by the EnKF.

The EnKF technique requires that flow-dependent error covariances are produced at regular intervals and is dependent on the ensemble members. In addition, it is computationally challenging to estimate the full covariance matrix. As an alternative, the National Meteorological Center [NMC, now known as the National Centers for Environment Prediction (NCEP)] method provides an approximation of model forecast error covariances. The background error is computed on a set of differences of model forecasts for the same validating time (Parrish and Derber 1992). This information gives insight into the dynamics of the numerical model itself. Several studies have revealed the drawbacks of the NMC method. However, the advantage of the NMC method is that it provides background errors that are easy to implement in a variational scheme. The background variances are weighted by a scalar in order to tune the strength of the feedback toward the observations. Buehner (2005) has estimated the homogeneous and isotropic background error using the NMC method.

The Weather Research and Forecasting (WRF) modeling system uses the 3DVAR method for data assimilation. The background error statistics (BES) provided with this system have been computed using forecasts from the global model of NCEP. Thus, the WRF assimilation procedure does not consider the bias of the WRF Model while assimilating the data. The region and model specific error covariances involve time-consuming computations, and researchers prefer to use the default BES available with the model. Many data impact studies have been carried out for the Indian region using this default BES in the WRF system (Vinodkumar et al. 2009; Rakesh et al. 2009; Routray et al. 2010a; Deb et al. 2010). Robustness of the NMC method for computing BES has been established in literature. This method has also been implemented in the WRF system to compute the regional BES. However, there has been no research study on the computation of regional BES for the WRF Model and the assessment of its impact for the Indian region.

In a regional assimilation and modeling system, initial and lateral boundary conditions (IBCs) are either prescribed from global numerical weather prediction models, other limited-area models, or reanalysis datasets with coarse resolution. Accuracy of the lateral boundary conditions is important because the atmospheric waves and disturbances generated at the boundary can rapidly propagate throughout the domain and affect the model forecasts. Moreover, errors can enter the domain of a regional model from the lateral boundaries that may themselves suffer from limited data, such as over the oceans. This error then propagates through the regional domain, negatively affecting the predictive skill of the regional model and reducing the benefits of high-resolution and sophisticated physics. There are a number of previous studies that have dealt with the treatment of lateral boundary conditions (Williamson and Browning 1974; Perkey and Kreitzberg 1976; Davies 1976; Majewski 1997). Mohanty et al. (2010) examined the impact of initial and boundary conditions on the simulations of tropical cyclones in the BoB. Most of these types of studies relate to downscaling or predictions of severe weather systems from the global analysis and forecasts. The forecasted track and intensity of monsoon systems (e.g., monsoon depressions) greatly depend on the initial specifications of the location and intensity of such systems, which in turn, depend on the quality of observation data and their assimilation techniques. Rupa et al. (2002) and Kar et al. (2003) have highlighted the uncertainties in available observed data over the BoB region and their assimilation into models. However, there has been no research study examining the impacts of initial and lateral boundary conditions on the analysis and predictions of monsoon depressions in the BoB using regional models.

In this study, domain-specific BES, have been computed using the WRF Model for the Indian region for the monsoon season as well as for winter. Single-point observation studies have been carried out to evaluate the seasonal variations of the BES. The spread of the observation information to other regions owing to characteristic properties of the WRF Model and its error distribution over the region has been estimated. The impact of the different BES on the analysis and forecasts of MDs has been evaluated. Even though the EnKF method has not been used in our study, this study makes a case for and is a step toward implementing a flow-dependent background error for the South Asian region in a regional data assimilation system. Therefore, this study complements the study of Buehner (2005). In addition to experiments with various BES performed with the NCEP–National Center for Atmospheric Research (NCAR) reanalysis dataset (Kalnay et al. 1996), several additional experiments have been carried out using the Interim European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-Interim) dataset as IBCs. ERA-Interim uses a 4DVAR methodology and a high-resolution global model at T255 resolution (www.ecmwf.int) as compared to the NCEP–NCAR reanalysis, which was carried out at coarser horizontal resolution (T62) using the 3DVAR method. The present study is a part of the South Asian Regional Reanalysis (SARR) project for which the WRF system is being used to carry out this retrospective analysis using both conventional and satellite radiance data.

Section 2 provides details related to the BES used in the study. Section 3 describes the synoptic features of the MDs being studied while section 4 presents the model description and the numerical experiments performed in this study. Section 5 provides the results and discussions, while section 6 briefly describes conclusions drawn from this study.

2. Background error statistics

In this study, two different types of background error statistics are considered in the assimilation cycle. The first experiment uses the default (global) BES, which can be used for any regional domain. This global BES from NCEP is estimated on grid points (physical space) based on recursive filters through the NMC method (Parrish and Derber 1992; Wu et al. 2002). The background error covariance matrices through the NMC method are calculated as described below:

 
formula

where the overbar denotes an average over time and/or geographical area, is the background error covariance matrix, and A is the tuning parameter. The true background error is not known in reality, but is assumed to be statistically well represented by the covariance matrix of short-range forecast perturbations . In the standard NMC method, the perturbation is given by the difference between two forecasts (e.g., 24 h minus 12 h) verifying at the same time. Climatological estimates of background error are obtained by averaging such forecast differences over a period of time. Skamarock et al. (2005) have suggested that the calculation of background error in the NMC method should be carried out using the forecast differences of 48 h minus 24 h for global models, and 24 h minus 12 h for regional models; that is, = 48 h, = 24 h forecasts for global models and = 24 h, = 12 h forecasts for regional models. Empirical multiplicative tuning factors are applied to the length scales calculated using the NMC method to obtain an optimal horizontal component of background error covariance. The scale lengths used in the horizontal background error covariances via a recursive filter are tuned in terms of the WRF-VAR control variables, namely, streamfunction, unbalanced velocity potential, unbalanced temperature, unbalanced surface pressure, and pseudo–relative humidity. The details about the tuning parameter are described in Barker et al. (2004) and Jianfeng et al. (2005). The global BES has been estimated with the differences of 24- and 48-h NCEP Global Forecast System (GFS) global forecasts at T170L42 resolution valid at the same time for 357 cases distributed over a period of 1 yr.

For our study, a second set of domain-dependent regional BES has been computed from the WRF forecasts using the NMC method. For the computation of BES, the WRF Model is configured with 25-km horizontal resolution with 286 × 332 (15°S–45°N, 40°–120°E) grid size over the South Asian region (Fig. 1a). More details regarding the numerical experiments, systematic errors of the WRF Model over the region, and the result of sensitivity experiments are described in Sowjanya et al. (2013). A summary of the relevant model physics and options used in the present study is given in Table 1. The WRF Model was run for the whole monsoon period of 1999 (June–September) and for January 1999 to produce 12- and 24-h forecasts at 0000 and 1200 UTC initial conditions. Then, a domain-dependent set of BES is computed by averaging these WRF forecast differences valid at the same hour.

Fig. 1.

(a) Model domain chosen for the experiments and (b) observed tracks of the MDs.

Fig. 1.

(a) Model domain chosen for the experiments and (b) observed tracks of the MDs.

Table 1.

Model configuration used in the present study.

Model configuration used in the present study.
Model configuration used in the present study.

Both sets of BES are applied on the same set of the control variables, namely, streamfunction, unbalanced velocity potential, unbalanced temperature, unbalanced surface pressure, and pseudo–relative humidity. With the NCEP BES, the control variables are in physical space while, for the newly computed domain-specific BES, the control variables are in eigenvector space. In the NCEP BES, the vertical scales are estimated through the statistics of the vertical correlation of each variable and are applied locally using recursive filters (RFs). However, computation of the domain-specific BES used the empirical orthogonal function (EOF) to represent the vertical covariance. Therefore, the major differences between these two kinds of BES are in the vertical covariance. The details of the implementation of the RF for global BES can be found in the study by Wu et al. (2002).

In regional BES, the representation of the horizontal component of background error is via horizontally isotropic and homogeneous RF (Hayden and Purser 1995; Purser et al. 2003). The version of the RF used in WRF-VAR possesses only two free parameters for each control variable: the number N of applications of the filter [N = 2 defines a second-order autoregressive (SOAR) function response, as N the response approximates a Gaussian] and the correlation length scale s of the filter. Barker et al. (2004) suggested N = 6 for all applications; this was the minimum number of passes required to remove unphysical ‘‘lozenge’’-shaped correlations in the wind field. The background error correlation length scale s is specified for each variable and for each vertical mode. It is important that the RFs have good amplitude control so that the estimated background error variances can be applied precisely. In both sets of BES, a localized correlation between the velocity potential and the streamfunction is also used to account for the positive correlation between the vorticity and divergence in the planetary boundary layer.

3. Synoptic overview of the MDs

During the monsoon season of 1999, there were four monsoon depressions over the Indian region. Out of these, two deep depressions during 27–29 July 1999 (case 1) and 17–18 June 1999 (case 2) had formed over the BoB. The depression during 11–12 June 1999 (case 3) had formed over land and the depression of 6–8 August 1999 (case 4) formed over the BoB. The best tracks from the India Meteorological Department (IMD) for all the MD cases are shown in Fig. 1b. A brief description of the synoptic situations that prevailed during these periods is given below.

a. Case 1

A well-marked low pressure area formed over the northwest BoB and adjoining West Bengal coast on 26 July 1999. It concentrated into a depression at 0300 UTC 27 July and was centered near 21°N, 89°E, about 200 km southeast of Kolkata, where it further intensified into a deep depression on the same day close to Sand Heads (22°N, 88.5°E). It moved northwestward and crossed the West Bengal–Odisha coast during the morning of 28 July. It weakened to become a depression 29 July, and moved toward the west-northwest and lay centered at Satna (24.5°N, 81°E).

b. Case 2

A well-marked low pressure area formed over the northwest BoB off the West Bengal–Odisha coast on 16 June 1999. It concentrated into a depression at 0300 UTC 17 June, centered near 18.5°N, 86°E and intensified into a deep depression at 1200 UTC 17 June near 19°N, 85.0°E. It moved west-northwestward and crossed the Odisha coast near Gopalpur (19.2°N, 84.9°E). On 18 June, it weakened into a depression and continued to move toward the west-northwest as a well-marked low pressure area.

c. Case 3

Under the influence of an upper-air cyclonic circulation pattern, a well-marked low pressure area formed over the West Bengal coast and adjoining North Bay on 10 June 1999. It moved in a northwestward direction and concentrated into a depression at 0300 UTC 11 June close to Purulia (23°N, 86.5°E). It continued to move in the same direction and lay centered about 50 km northwest of Varanasi (25.2°N, 82.9°E). It weakened into a well-marked low pressure area on 12 June.

d. Case 4

A well-marked low pressure area formed over the northwest BoB off the West Bengal–north Odisha coast on 6 August 1999. It concentrated into a depression and lay centered at 1200 UTC 6 August near 21°N, 88.5°E, about 160 km south of Kolkata (22.5°N, 88.3°E). Its direction of movement was toward the west-northwest and it crossed the West Bengal coast near Digha (22.5°N, 87.5°E) at 0300 UTC 7 August. It moved farther toward the west-northwest and weakened into a well-marked low pressure area on 9 August.

4. Modeling system and numerical experiments

The WRF Model with the Advanced Research core (ARW, version 3.1.1) is based on an Eulerian solver for the fully compressible nonhydrostatic prognostic equations, designed in conservation of mass, momentum, entropy, and scalars using flux form, with mass (hydrostatic pressure) vertical coordinates as well as a third-order Runge–Kutta time integration scheme. A detailed description of the model equations, physics, and dynamics is available in Skamarock et al. (2005). As described in Barker et al. (2004), the variational data assimilation algorithm adopted in WRF-VAR is a model-space, incremental formulation of the variational problem. In this approach, observations, previous forecasts, their errors, and physical laws are combined to produce analysis increments, which are added to the first guess to provide an updated analysis.

Several experiments have been carried out in this study to document the impact of BES and IBCs on the analyses and predictions of the MDs. Three numerical experiments were carried out to assess the impacts of different BES on the simulations of the MDs. These experiments are CNTL, BG-3DV, and BR-3DV, and they use NCEP–NCAR reanalyses as initial and lateral boundary conditions. In the CNTL experiment, the model is integrated without any data assimilation. In the BG-3DV experiment, the default BES (global BES) available within the WRF-VAR are used in the 6-hourly assimilation cycle. In the BR-3DV experiment, the newly computed domain-specific BESs are used in the 6-hourly assimilation cycle. The assimilation experiments are performed using the archived data obtained through the Global Telecommunication System [GTS: radiosondes, surface synoptic observations (synops), buoys, ships, geoamv, aircraft reports (aireps), etc.]. Figure 2 shows the distribution of selected observations used in the assimilation experiments for case 1. Observation datasets used in the assimilation cycle are given in Table 2. These observations are preprocessed using the WRF-VAR observation preprocessor package and a variety of quality control (QC) checks are performed. These QC checks include the removal of observations outside the time range and domain (horizontal and top); reordering and merging the duplicate data reports in time location, excluding location/time duplicates and incomplete observations (e.g., no location); and ensuring vertical consistency of radiosonde profiles and superadiabatic properties for multilevel observations, etc. The details about the QC checks performed within the WRF-VAR simulations are described in Barker et al. (2004) and Jianfeng et al. (2005).

Fig. 2.

Distribution of observations used in the assimilation experiments valid at 0000 UTC 27 Jul 1999 for case 1.

Fig. 2.

Distribution of observations used in the assimilation experiments valid at 0000 UTC 27 Jul 1999 for case 1.

Table 2.

Descriptions of observation datasets used in the assimilation cycle.

Descriptions of observation datasets used in the assimilation cycle.
Descriptions of observation datasets used in the assimilation cycle.

For data assimilation in tropical regions, periods of assimilation, spinup, and balance issues at initial time play important roles. To address these issues, a comparative study has been carried out between the “cold start” (CLD, i.e., NCEP–NCAR reanalyses used as IBCs in the model) and “warm start” (CYC, i.e., 6-h forecasts obtained from previous cycles used as the first guess in the next cycle) runs for the two MD cases using the regional BES and default BES. For CYC, the assimilation cycle began in June 1999 and continued for the months from June through September 1999. For the CLD run, the system is initialized at model initial time by assimilating the available observations. The mean track errors (mean error at particular forecast time from all the cases) of the MDs and the percent improvement of the errors are provided in Table 3. It is noticed that in CYC the track errors are significantly less than in the CLD runs. A warm start run characterizes the convective system at model initial time in a better way (Routray et al. (2010a,b), and divergence and moisture fields are in better balance. Skamarock (2004) and Osuri et al. (2013) have found that the WRF Model needs up to 12 h to spin up. However, spinup time of a model depends on the grid spacing and the time step. In our study, all experiments were carried out using warm start (cyclic) conditions, so the spinup and balance issues of the WRF modeling system are addressed properly. In addition to the above experiments, additional experiments have been carried for two MD cases from the 2003 and 2004 monsoon seasons to study the impact of regional BES. These experiments used the BES computed using forecast data from 1999.

Table 3.

Mean track errors (km) and percentage improvement of MDs from different simulations with cold start and cyclic assimilation.

Mean track errors (km) and percentage improvement of MDs from different simulations with cold start and cyclic assimilation.
Mean track errors (km) and percentage improvement of MDs from different simulations with cold start and cyclic assimilation.

To examine the impact of IBCs, additional experiments have been carried out using ERA-Interim datasets as the model IBCs. Three experiments that were carried out—CNTL-ERA, BG-ERA, and BR-ERA—are similar to the CNTL, BG-3DV, and BR-3DV experiments, respectively, but they use the ERA-Interim data. The assimilation experiments with ERA-Interim used the same set of observed data as in the experiments with the NCEP–NCAR reanalysis.

5. Results and discussion

Various aspects of the computed BES are studied with single-observation tests. Results of these tests with temperature and wind components at different locations and at different sigma levels are briefly discussed in section 5a. As mentioned earlier, the main objective of the present study is to evaluate the impact of domain-dependent BES in the WRF-VAR assimilation system as well as lateral boundary conditions for simulations of the MDs. The initial conditions of the model are improved through assimilation of available observations using the assimilation system and the domain-dependent BES. The predicted meteorological fields associated with the MDs are also compared with the available observations. The predicted rainfall is verified against the IMD station observations and also with Tropical Rainfall Measuring Mission dataset and other satellite precipitation products like 3B42 version 6 (TRMM-3B42V6).

a. Single-observation test

Several single-observation tests at various locations (latitude, longitude and sigma level) are performed over the Indian region using the calculated domain-dependent BES and default BES available within the WRF-VAR. This is done to understand the response of BES in the WRF-VAR system over the Indian region. The single-observation perturbation tests are applied for the temperature and u-wind component, of a 1-K and 1 m s−1 innovation [observation minus background (OB)], respectively, at the middle of the domain (17.5°N, 76.5°E, sigma level = 19). The analysis increments of temperature and wind components obtained from single-observation tests using both sets of BES are shown in Figs. 3 and 4. In Fig. 3, the horizontal spreading of the increments of temperature and the u and υ components of wind is the same in both cases. However, the temperature response is an order of magnitude higher in the regional BES as compared to the global BES. Figures 4a–c and 4d–f show the analysis increments in response to the single u-wind component (1 m s−1) innovation applied at the middle of the domain using both sets of BES, respectively. Similar to the temperature field, the magnitudes of the analysis increment response from the innovation of the single u-wind component are more easily seen in Figs. 4d–f as compared to the Figs. 4a–c, respectively. The responses of the υ increments (Fig. 4f) support cyclonic and anticyclonic circulation patterns to the north and south of the u-increment location, respectively. However, this feature is not clearly brought out with the default BES (Fig. 4c). Both cold and warm temperature increments seen in Fig. 4d are not noticed in Fig. 4a. As seen in Fig. 4, the response in the global BES is asymmetric (stronger to the north and weaker to the south) while it is more symmetric in the regional BES. The symmetric responses in C(u, T), C(u, u), and C(u, υ) etc. are consistent with those of Daley (1993, Fig. 3) and Daley (1991, Fig. 5.4). Therefore, the responses obtained in the BR-3DV case in this study are closer to those of Daley and these symmetric responses are not seen in the BG-3DV case. As a result, the response of analysis increments from single innovation is propagated properly in the surrounding area when newly computed domain-dependent BES are used as compared to the default BES.

Fig. 3.

Response of the analysis increments to a single temperature observation (1 K) at 17.5°N, 76.5°E and sigma level = 19 (a)–(c) from default BES and (d)–(f) from the domain-specific BES.

Fig. 3.

Response of the analysis increments to a single temperature observation (1 K) at 17.5°N, 76.5°E and sigma level = 19 (a)–(c) from default BES and (d)–(f) from the domain-specific BES.

Fig. 4.

As in Fig. 3, but the response of the analysis increments to a single u-wind perturbation of 1 m s−1. (g) As in (e), but the response of analysis increments [C(u, u)] computed for the month of January.

Fig. 4.

As in Fig. 3, but the response of the analysis increments to a single u-wind perturbation of 1 m s−1. (g) As in (e), but the response of analysis increments [C(u, u)] computed for the month of January.

Figures 3 and 4 show how the methodology followed to estimate the background error matrix gives rise to the extended impact of single wind or mass observations in the tropical region. In our study, we find that, for both sets of BES, the effect of a single wind observation is consistent with theoretically derived wind correlations for nondivergent flow. The 〈u, u〉 patterns for domain-specific BES and global BES are not similar in this study. For domain-specific BES (Fig. 4e), a strong (−4 × 10−2 m s−1) easterly response is seen to the south of central latitudes as compared to the global BES (Fig. 4b) case (−0.5 × 10−2 m s−1). Moreover, for the domain-dependent BES, we find that the C(u, u) pattern is not similar to that seen in theoretical analysis of Daley (1993) and this study shows two local maxima over the BoB and Arabian Sea in the C(u, u) analysis increment.

In our study, the BES have been calculated using the forecasts for the whole monsoon period of 1999 (June–September). At lower levels (e.g., at 850 hPa) strong monsoon winds prevail over the Arabian Sea, reaching the west coast of India and over the BoB flowing over to the north Indian plains. Strong convective activity also occurs during this period over the region. Wind errors in the models are linked to errors in convective activity over the Indian subcontinent during monsoon seasons. Two local maxima over the BoB and Arabian Sea found in the C(u, u) analysis increment in this study (Fig. 4e) include a specific feature of the season and the WRF Model. To examine the seasonality of the C(u, u) pattern, we repeated the same experiment for the winter period (using WRF Model forecast data for January 1999). In a single-observation experiment for this period, the C(u, u) structure is similar to that presented in Daley (1993). The C(u, u) pattern for the month of January for a single-observation test is shown in Fig. 4g. These results suggest that regional BES show a double maximum during the monsoon season and this double maximum is related to the convective activity over the BoB and the Arabian Sea. During nonmonsoon months (e.g., in January) such a double maximum is not seen. Therefore, seasonally varying regional BES should be used for the Indian region in the WRF modeling system.

The impact of a single temperature innovation in the present study has been to generate an isotropic response in the temperature field. Daley (1996) has noted that at higher latitudes the wind–mass covariance is asymmetric about the latitude where the single observation is performed. However, equatorial error covariance is weaker than that at higher latitudes and similar to that obtained by equatorial beta plane theory. By suppressing the erroneous tropical wind–height coupling, Daley (1996) did not find the covariance pattern to the south of the central latitude in the tropical domain. Addition of slow Kelvin modes effectively reduces the mass–wind correlations, as noted by Parrish (1988). Figure 4 shows the C(u, u), C(u, T), and C(u, υ) correlations. The salient features of these correlations are similar to those obtained for nondivergent flow in Daley (1996). Therefore, in this study, the computed BES do not adequately represent tropical wind errors for divergent flow. The geostrophic coupling (mass–wind balance) decreases near the equator, which makes the circulation in the tropics different from other regions. The real error fields have both zonal and meridional structures and are different from the one assumed in the linear balance equations (Daley 1991, 1996). In this study, it is seen that different BES yield analysis increment responses to a single observation that are not qualitatively different. However, differences in the magnitude of the observation impact due to domain-specific BES shall have a large impact on the initial position, intensity, and forecast skill of the monsoon depressions.

Results of single-observation tests with higher innovation of wind (4 m s−1) and temperature (4 K) are also examined. One may notice that the horizontal spread and magnitude of analysis increments from higher innovation of temperature and wind are larger (figure not shown) as compared to the analysis increments obtained from smaller innovation of wind and temperature.

Further diagnoses of the roles of the global BES (BG-3DV) and the domain-specific BES (BR-3DV) have been made to examine how the influence of the observations spreads at small and large radii and document the role of different BES on the analysis at distances away from (and in between) the observations. For this purpose, the differences of the wind fields between the BR-3DV and BG-3DV analyses, along with the available radiosonde/rawinsonde (RS/RW) observations, have been examined. As the number of analysis cycles increases, the flow pattern gets modified owing to the effects of the model, as well as the large number of observations available at various locations at different times. Therefore, the difference in the wind field after just one analysis has been plotted. At this time, the model first guess, as well as the number of observations, are the same for both the BG-3DV and BR-3DV analyses.

The differences between the wind analysis (between BR-3DV and BG-3DV) at 850 hPa on 25 July 1999 and the observation data used in the analysis are shown in Figs. 5a and 5b. Stronger westerly and easterly winds are seen in the BR-3DV analysis as compared to that of BG-3DV over the central and northern parts of India, which are to the south and north of the observations. The large-scale westerly and easterly flow difference creates a monsoonal low pressure area over the northern BoB. This feature supports the formation or intensification of monsoonal low pressure systems in the BoB. As seen in the single-observation study, northeasterly and southwesterly winds are seen over the eastern and western regions of the equatorial Indian Ocean, respectively (away from observation locations). It is also seen that the BR-3DV analysis produces stronger wind (~8–12 m s−1) over oceanic regions and cyclonic circulation over the northern BoB as compared to the BG-3DV analysis. Therefore, the large-scale pattern of wind obtained after assimilation of many observations is similar to the pattern obtained with the single-observation test (Figs. 4e,f). It may be noted here that this difference is not due to a shift in the location of the cyclonic circulation in the analyses. The vortex develops over the northern BoB in the BR-3DV analysis and the observations also show a cyclonic circulation pattern over the region that is not noticeable in the BG-3DV analysis. Therefore, the BR-3DV analysis represents the large-scale flow during the MD better than the BG-3DV analysis.

Fig. 5.

(a) Analyzed wind difference (m s−1) at 850 hPa (BR-3DV minus BG-3DV) and (b) observed wind (RS/RW; m s−1) data valid on 25 Jul 1999.

Fig. 5.

(a) Analyzed wind difference (m s−1) at 850 hPa (BR-3DV minus BG-3DV) and (b) observed wind (RS/RW; m s−1) data valid on 25 Jul 1999.

b. Impact of BES

As mentioned earlier, four MD cases have been considered in this study. For all of these cases, assimilation and forecast experiments were conducted using default BES and domain-specific BES with data from the NCEP–NCAR and ERA-Interim reanalyses used to set the initial and boundary conditions. However, for brevity, detailed results for the structures of the MDs are discussed here only for MD cases 1 and 2.

1) Analyzed and forecast structures of the MD

Figures 6 and 7 show the model initial time (analysis), simulated, and verified analysis of winds at 850 hPa and MSLP (contour) for cases 1 and 2 obtained from the three experiments. First, we analyze the impact of different BES on the analysis before discussing the impact on the model simulations. For comparison purposes, the meteorological fields of the low-resolution NCEP–NCAR reanalysis have been interpolated into the resolution of the final WRF-VAR analysis through bilinear interpolation. Figures 6a–c and 7a–c show the initial wind fields for the model at 850 hPa and MSLP for cases 1 and 2 from different analyses. The magnitude of the wind speed is considerably higher surrounding the MDs in BG-3DV and BR-3DV as compared to the NCEP–NCAR reanalyses for these cases. By using the regional BES, an increase in wind speed of around ~5 m s−1 is observed over the region influenced by MDs as compared to the analyses obtained using global BES. The MSLP patterns over the domain are clearly seen in all the analyses for both cases but the magnitude of the central pressure is found to be higher in the regional analyses than that in the NCEP–NCAR reanalysis. This feature in BR-3DV is also closer to the actual observations.

Fig. 6.

Winds (m s−1) at 850 hPa and MSLP (hPa) for (a) NCEP, (b) BG-3DV, and (c) BR-3DV valid at 0000 UTC 27 Jul 1999 (initial time). The 24-h model-simulated wind fields (m s−1) at 850 hPa and MSLP (hPa) from (d) CNTL, (e) BG-3DV, and (f) BR-3DV. (g) Verifying analysis valid at 0000 UTC 28 Jul 1999. (h)–(k) As in (d)–(g), but for 36 h valid at 1200 UTC 28 Jul 1999. Shading levels for wind speed are 10, 12, 15, and 20 m s−1 and the contour interval for MSLP is 1 hPa.

Fig. 6.

Winds (m s−1) at 850 hPa and MSLP (hPa) for (a) NCEP, (b) BG-3DV, and (c) BR-3DV valid at 0000 UTC 27 Jul 1999 (initial time). The 24-h model-simulated wind fields (m s−1) at 850 hPa and MSLP (hPa) from (d) CNTL, (e) BG-3DV, and (f) BR-3DV. (g) Verifying analysis valid at 0000 UTC 28 Jul 1999. (h)–(k) As in (d)–(g), but for 36 h valid at 1200 UTC 28 Jul 1999. Shading levels for wind speed are 10, 12, 15, and 20 m s−1 and the contour interval for MSLP is 1 hPa.

Fig. 7.

Winds (m s−1) at 850 hPa and MSLP (hPa) for (a) NCEP, (b) BG-3DV, and (c) BR-3DV valid at 0000 UTC 17 Jun 1999 (initial time). The 24-h model simulated wind fields (m s−1) at 850 hPa and MSLP (hPa) from (d) CNTL, (e) BG-3DV, and (f) BR-3DV. (g) Verifying analysis valid at 0000 UTC 18 Jun 1999. Shading levels for wind speed are 10, 12, 15, and 20 m s−1 and the contour interval for MSLP is 1 hPa.

Fig. 7.

Winds (m s−1) at 850 hPa and MSLP (hPa) for (a) NCEP, (b) BG-3DV, and (c) BR-3DV valid at 0000 UTC 17 Jun 1999 (initial time). The 24-h model simulated wind fields (m s−1) at 850 hPa and MSLP (hPa) from (d) CNTL, (e) BG-3DV, and (f) BR-3DV. (g) Verifying analysis valid at 0000 UTC 18 Jun 1999. Shading levels for wind speed are 10, 12, 15, and 20 m s−1 and the contour interval for MSLP is 1 hPa.

The initial positions of the MDs are well represented in the BR-3DV experiment (case 1: 20.8°N, 89.3°E; case 2: 18.8°N, 86.5°E) as compared to BG-3DV (case 1: 21.6°N, 88.8°E; case 2: 18.9°N, 87.1°E). The observed locations of the storms at 21.0°N, 89.0°E for case 1 and at 18.5°N, 86.0°E for case 2 are reported in the Indian Daily Weather Report (IDWR) published by IMD. The initial position errors are reduced by 23% in case 1 and 28% in case 2 owing to the use of regional BES in the 3DVAR system compared to the BG-3DV experiment. Therefore, the BR-3DV analysis provides improved location and intensity information for the MDs as initial conditions for model simulations.

The impact of different BES used in the WRF-VAR analysis system on the model simulations of MDs has been examined. Figures 6d–f and 6h–j show the 24- and 36-h model-simulated wind fields and MSLP for case 1 obtained from the CNTL, BG-3DV, and BR-3DV experiments. The simulated wind fields and MSLP are compared with the verified analyses obtained from regional analysis (BR-3DV analyses) along with IMD observations. Figures 6g,k depict the verified analyses for 24 and 36 h valid at 0000 and 1200 UTC 28 July 1999. In each experiment, the wind flow around the depression is simulated satisfactorily by the model. The positions of the depression are better simulated in the BR-3DV experiment than in the CNTL and BG-3DV simulations. One of the important characteristics of the MDs is the presence of the strong winds over the northern quadrant (Sikka 1977; Rao 1976). This feature can be seen in the verifying analyses (Figs. 6g,k) and is reasonably well simulated in the assimilation experiments. However, the increased magnitude of the wind (~5–8 m s−1) over a large area is simulated on the northern side of the vortex throughout the forecast periods in BR-3DV.

As the default BES were calculated using very low resolution (T170, ~75 km) global model forecasts, the mesoscale features associated with MDs are not well represented in the initial conditions of the model. It was also noticed that the response of the single innovation of the wind and temperature increment in the default BES was less as compared to the domain-specific BES (Figs. 3 and 4). As mentioned earlier, BG-3DV provides a poorer set of initial conditions for the WRF Model as compared to the BR-3DV assimilation. As a result, during the forecast period, the position and northwestward movement of the MD are consistently well simulated in the BR-3DV experiments. In particular, landfall of the MD is not well simulated in the CNTL experiment.

For case 2, the 24-h forecasts of the wind fields and MSLP obtained from CNTL, BG-3DV, and BR-3DV experiments and verified analysis are illustrated in Figs. 7d–f and 7g. The large-scale features associated with the MD, and the locations and magnitudes of winds around the depression, at different forecast times are better simulated in BR-3DV. As in the case 1, the BR-3DV also provides stronger winds (around 25–30 m s−1) in the lower-tropospheric westerlies at 900–850 hPa in the 12- and 24-h forecasts for this MD case. In the assimilation experiments, the northward movement of the MD is simulated well as compared to the CNTL simulation. In the day-1 forecast, the BR-3DV experiment has simulated that the location of the vortex (20.5°N, 84.3°E) is closer to that of the observed (20.5°N, 82.0°E) as compared to other experiments.

Figures 8a–c and 8d–f illustrate the longitudinally averaged (over the monsoon depression) vertical cross section (latitude and pressure) of vorticity (10−5 s−1) and moisture convergence (10−5 g kg−1 s−1) valid at 0000 UTC 27 July 1999 from the three analyses for case 1. In the BR-3DV analysis, the vorticity and moisture convergence are stronger by 3 × 10−5 s−1 and 4 to 6 × 10−5 g kg−1 s−1, as compared to the CNTL and BG-3DV analyses. Cyclonic vorticity is seen up to 300 hPa and moisture convergence extends up to 700 hPa from the surface around the center of the MD in the BR-3DV analysis. Moisture divergence is seen to the north and south of the MD in this analysis. These features—mainly northern moisture divergence as well as the amount (southern part)—are not seen in CNTL analysis. Generally, the vertical structure (cross section) of all the MDs is similar to the one shown in Fig. 8. The MDs have warm cores at upper levels, cold cores at lower levels, and the axes of the MDs tilt southwestward in the vertical. However, MDs have vorticity maxima at lower levels, and this structure is similar to results found in previous studies by Krishnamurti et al. (1975), Sikka (1977), Godbole (1977), and Jianying et al. (2007). Therefore, the vertical structure of the MD is well represented in the BR-3DV analysis owing to the use of the regional BES in the assimilation cycle.

Fig. 8.

Vorticity (10−5 s−1) from the analyses (a) NCEP, (b) BG-3DV, (c) BR-3DV, and (d) BR-ERA for case 1 valid at 0000 UTC 27 Jul 1999. (e)–(h) As in (a)–(d), but for moisture convergence (10−5 g kg−1 s−1).

Fig. 8.

Vorticity (10−5 s−1) from the analyses (a) NCEP, (b) BG-3DV, (c) BR-3DV, and (d) BR-ERA for case 1 valid at 0000 UTC 27 Jul 1999. (e)–(h) As in (a)–(d), but for moisture convergence (10−5 g kg−1 s−1).

2) Rainfall

The model-simulated precipitation amounts obtained from the CNTL, BG-3DV, and BR-3DV experiments and the corresponding TRMM satellite estimates are shown in Figs. 9 and 10 for cases 1 and 2, respectively. It is seen that the spatial distribution of the rainfall simulated by CNTL is shifted southward as compared to the TRMM observations during all forecast periods for both the cases. None of the simulations get the rainfall at the right location and magnitude for both of the cases. However, the BR-3DV experiment provides better rainfall prediction as compared to the CNTL and BG-3DV simulations for both of the MD cases.

Fig. 9.

Accumulated precipitation (cm) for 12 h from (a) TRMM, (b) CNTL, (c) BG-3DV, (d) BR-3DV, and (e) BR-ERA valid at 1200 UTC 27 Jul 1999. (f)–(j) As in (a)–(e), but for 24 h valid at 0300 UTC 28 Jul 1999. (k)–(o) As in (a)–(e), but for 36 h valid at 1200 UTC 28 Jul 1999.

Fig. 9.

Accumulated precipitation (cm) for 12 h from (a) TRMM, (b) CNTL, (c) BG-3DV, (d) BR-3DV, and (e) BR-ERA valid at 1200 UTC 27 Jul 1999. (f)–(j) As in (a)–(e), but for 24 h valid at 0300 UTC 28 Jul 1999. (k)–(o) As in (a)–(e), but for 36 h valid at 1200 UTC 28 Jul 1999.

Fig. 10.

Accumulated precipitation (cm) for 12 h from (a) TRMM, (b) CNTL, (c) BG-3DV, (d) BR-3DV, and (e) BR-ERA valid at 1200 UTC 17 Jun 1999. (f)–(j) As in (a)–(e), but for 24 h valid at 0300 UTC 18 Jun 1999.

Fig. 10.

Accumulated precipitation (cm) for 12 h from (a) TRMM, (b) CNTL, (c) BG-3DV, (d) BR-3DV, and (e) BR-ERA valid at 1200 UTC 17 Jun 1999. (f)–(j) As in (a)–(e), but for 24 h valid at 0300 UTC 18 Jun 1999.

In the day-1 forecast for case 1, all model simulations show widespread intense rainfall over the oceanic region except BR-3DV (Fig. 9i), which is also not evident in the TRMM observations (Fig. 9f). Simulated precipitation from BR-3DV is closer to the observations but there is a southward shift from the observed satellite-derived precipitation in the simulated rainfall from CNTL and BG-3DV. Similar results are found for case 2 (Fig. 10), where the spatial distribution and intensity of the precipitation are better in the BR-3DV experiments as compared to the CNTL and BG-3DV. Heavy rainfall is concentrated along the track of the MDs in both cases throughout the forecast time when regional domain-specific BES are used in the 3DVAR simulations. Comparisons of the day-1 model-simulated rainfall and stationwise observed precipitation of all four cases are provided in Table 4. The positions of the maximum precipitation in all four cases are not accurately captured in the model simulations. However, the rainfall amounts are better and closer to the observations over the region in BR-3DV as compared to the CNTL and BG-3DV simulations. From Table 4, it is also seen that the observed amount of rainfall over a larger number of stations is closer to the BR-3DV simulated amount.

Table 4.

Comparison between stationwise observed and model simulated rainfall (cm) in day-1 forecasts.

Comparison between stationwise observed and model simulated rainfall (cm) in day-1 forecasts.
Comparison between stationwise observed and model simulated rainfall (cm) in day-1 forecasts.

c. Impact of ERA-Interim IBCs

1) Analyzed and forecast structures of the MDs

A set of experiments similar to those described in the previous subsection was carried out using ERA-Interim datasets as the initial and boundary conditions for the model. Figures 11 and 12 show the model initial time (analysis), as well as the simulated and verified analyses of winds at 850 hPa and MSLP (contour), for cases 1 and 2, as obtained from the three experiments using ERA-Interim IBCs. Figures 11a–c show the model initial wind fields at 850 hPa and MSLP for case 1. The magnitude of the wind speed is considerably higher surrounding the MD in the BG-ERA (Fig. 11b) and BR-ERA (Fig. 11c) analyses, as compared to the ERA reanalysis (Fig. 11a). As in the case of experiments with NCEP–NCAR data as IBCs, use of the regional BES in assimilations leads to an increase in wind speed of around ~5 m s−1 over the region influenced by MD as compared to BG-ERA. The BR-ERA analysis (Fig. 11c) shows a stronger MD as compared to BR-3DV (Fig. 6c). But the initial position error is significantly reduced in BR-ERA (Fig. 11c, 30 km) as compared to BR-3DV (Fig. 6c, 65 km). In case 2, the magnitude of the wind speed and the initial position of the MD are well characterized in the ERA analyses (Figs. 12a–c). In this case, the initial position error of the MD is around 55 km in the BR-ERA analysis (Fig. 12c) as compared to that in BR-3DV (Fig. 7c, 90 km). This result clearly demonstrates that the initial position errors of the MDs are less in experiments with regional BES when ERA-Interim IBCs are used (54% improvement for case 1 and 40% for case 2). Therefore, domain-specific BES have improved the assimilation of the available observations and improved the model initial conditions with ERA-Interim as the IBCs. The MSLP patterns over the domain are brought out well in all of the analyses for both of the cases in BR-ERA. Therefore, the BR-ERA analysis provides improved locations and intensity of the MDs as the initial conditions for the model simulations.

Fig. 11.

As in Fig. 6, but from ERA-Interim IBCs runs and ERA-Interim verifying analyses in (g),(k).

Fig. 11.

As in Fig. 6, but from ERA-Interim IBCs runs and ERA-Interim verifying analyses in (g),(k).

Fig. 12.

As in Fig. 7, but from ERA-Interim IBCs runs and ERA-Interim verifying analyses (g).

Fig. 12.

As in Fig. 7, but from ERA-Interim IBCs runs and ERA-Interim verifying analyses (g).

Figures 11d–f and 11h–j show the 24- and 36-h model-simulated wind fields and MSLP results obtained from ERA-Interim experiments for case 1. The simulated wind fields and MSLP are compared with the verifying analyses (ERA-Interim) and IMD observations. Figures 11g and 11k depict the verifying analyses for 24 and 36 h valid at 0000 and 1200 UTC 28 July 1999. The positions of the depression are better simulated in the domain-specific BES experiments than in the corresponding CNTL and BG simulations. The model simulates a stronger MD with ERA-Interim as the IBCs in all of the simulations (Figs. 11d–f and 11h–j), as compared to the corresponding simulations using NCEP–NCAR reanalysis data (Figs. 6d–f and 6h–j). The vector display errors (VDEs) are more prominent in CNTL-ERA (272 and 286 km) for the 24- and 36-h forecasts, respectively, as compared to the BG-ERA (131 and 190 km) and BR-ERA (108 and 189 km) simulations. The magnitude of the wind in the simulations with the regional BES has increased by around 5–10 m s−1 over the MD region. This feature is also seen in the verifying analyses (Figs. 11g,k). However, the position of the MD is well represented and is closer to the IMD observations in the BR-3DV verifying analyses (Figs. 6g,k) as compared to BR-ERA (Figs. 11g,k).

For case 2, the 24-h forecasts of wind fields and MSLP obtained from ERA experiments and the verifying analyses are shown in Figs. 12d–g. The large-scale features associated with the MD are well characterized in all of the simulations. However, the locations and magnitudes of the winds around the depression at different forecast time are better simulated in the BR-ERA simulations as compared to the other experiments. The VDEs are less in BR-ERA (87 km) for the 24-h forecast as compared to CNTL-ERA (206 km) and BG-ERA (185 km). The magnitude of the wind speed is higher in the ERA-Interim experiments (Figs. 12d–f) as compared to the corresponding NCEP–NCAR experiments (Figs. 7d–f). The mean VDEs from BR-ERA are less in both cases as compared to the CNTL-ERA and BG-ERA experiments (Table 5).

Table 5.

Mean track errors (km) and percentage improvement of MDs from different simulations with ERA-Interim and NCEP–NCAR IBCs.

Mean track errors (km) and percentage improvement of MDs from different simulations with ERA-Interim and NCEP–NCAR IBCs.
Mean track errors (km) and percentage improvement of MDs from different simulations with ERA-Interim and NCEP–NCAR IBCs.

Figures 8d,h illustrate the longitudinally averaged (over the monsoon depression) vertical cross section of vorticity (10−5 s−1) and moisture convergence (10−5 g kg−1 s−1) valid at 0000 UTC 27 July 1999 from the BR-ERA analyses for case 1. In this analysis, the vorticity and moisture convergence are stronger in the lower troposphere around 3–7 × 10−5 s−1 and 7–12 × 10−5 g kg−1 s−1 as compared to BR-3DV (Figs. 8c,g). Cyclonic vorticity is seen up to 300 hPa and moisture convergence extends up to 500 hPa from the surface around the center of the MD in the BR-ERA analysis as compared to BR-3DV. Similarly, moisture divergence is prominent to the north and south of the MD in the BR-ERA analysis as compared to the other analyses.

2) Rainfall

The model-simulated precipitation results obtained from the BR-ERA experiments are shown in Figs. 9e,j,o and 10e,j for cases 1 and 2. The BR-ERA simulations provide better rainfall prediction for both of the MD cases as compared to the corresponding simulations with the NCEP–NCAR reanalysis data as the IBCs. In case 1, the spatial distribution and convective rainbands in the BR-ERA experiments for all forecasts agree well with the TRMM rainfall pattern over the region. In the BR-3DV experiments, all of the 12-h simulations show patches of heavy rainfall over oceanic region, which is not seen in the BR-ERA simulations (Fig. 9e) and matches well with the observed rainfall (Fig. 9a). For case 2, the amount of rainfall over the oceanic region is also higher in the NCEP–NCAR simulations (Figs. 10b–d) as compared to the BR-ERA simulation (Fig. 10e), which is not seen in the observed rainfall plot (Fig. 10a).

In the day-1 forecast for case 1, all of the model simulations show widespread intense rainfall over the oceanic region except for the BR-3DV and BR-ERA simulations (Figs. 9i,j). This widespread intense rainfall, however, is not seen in the TRMM observations (Fig. 9f). Similar results are found for case 2, where the spatial distribution and intensity of the precipitation are better in the BR-ERA and BR-3DV experiments. The simulated precipitation pattern from BR-ERA is closer to the observations in both cases. The distribution and amount of the rainfall in the 36-h forecast are well simulated in the BR-ERA experiment (Fig. 9o), as compared to BR-3DV, and matches well with the TRMM results (Fig. 9k). It is very clearly seen from Table 4 that the rainfall amounts are further improved in the BR-ERA simulation as compared to BR-3DV in all four cases and that the BR-ERA-simulated amount is closer to the observed amount of rainfall over the maximum number of stations.

d. Skill measures

After each cycle of assimilation, the analyzed datasets have been examined in detail to check the data ingestion and its impact. Figure 13 shows the averaged rms error (RMSE) of the wind (u and υ components) and temperature from all types of observations [observation minus analysis (OA)] after analysis at the initial time of the model run for the BG-3DV, BR-3DV, and BR-ERA experiments. It is seen that the domain-specific BES have improved the assimilation of available observations and improved the model initial conditions with both NCEP–NCAR and ERA-Interim data as IBCs. The mean rms of the OA of the variables in Figs. 13a–c are less for the BR-3DV and BR-ERA experiments. Among these two experiments, the RMSEs obtained in BR-ERA experiments are smaller. Therefore, in BR-ERA, the amount and propagation of observation information in the data assimilation system is properly reflected.

Fig. 13.

Mean RMSEs from BG-3DV, BR-3DV, and BR-ERA of OA for (a) U (m s−1), (b) V (m s−1), and (c) T (K).

Fig. 13.

Mean RMSEs from BG-3DV, BR-3DV, and BR-ERA of OA for (a) U (m s−1), (b) V (m s−1), and (c) T (K).

The RMSEs for wind components (u and υ) are computed from the four analyses against the available radiosonde observations (20 stations) in the domain at model initial time for cases 1 and 2. The RMSEs at different pressure levels are provided in Table 6. The error statistics show that the analyses with regional BES produced fewer errors at all the pressure levels as compared to the BG-3DV analyses for both of the MD cases. However, the RMSEs of wind components are significantly reduced in the BR-ERA analysis as compared to BR-3DV. It is clearly seen that assimilation using domain-specific BES in the 3DVAR simulations with ERA-Interim data as IBCs provides improved initial conditions and has a positive impact on simulations of wind structures associated with the MDs.

Table 6.

RMSEs of wind components (m s−1) at different pressure levels.

RMSEs of wind components (m s−1) at different pressure levels.
RMSEs of wind components (m s−1) at different pressure levels.

As a measure of forecast accuracy, the RMSE, correlation coefficients (CC), equitable threat score (ETS), and biases of rainfall have been calculated using the TRMM rainfall data as the observations. The details of the formulation of these skill scores can be found in Jankov et al. (2005). The ETS and bias range from 0 to 1, with a value of 1 indicating a perfect forecast. The spatial (15°–25°N, 75°–90°E) CC and RMSE of rainfall between the observations and the model outputs from different experiments for all of the MD cases are calculated over land (by masking out the oceanic region) for the day-1 forecasts (Table 7). The RMSE and CC values are better in the simulations with data assimilation than in the CNTL runs. It is seen that the RMSE and CC are also significantly improved in BR-3DV as compared to the CNTL and BG-3DV simulations. The mean improvements of 27% (16%) in RMSE and 88% (29%) in CC are obtained in the BR-3DV experiment as compared to CNTL (BG-3DV). In BR-ERA, the mean RMSE and CC (18.6 mm and 0.59) are better than those from BR-3DV (22.16 mm and 0.49). It is very clearly seen that the percentage of the mean improvement of the BR-ERA simulation for RMSE (16%) and CC (20%) is higher than that obtained from the BR-3DV simulation.

Table 7.

Spatial RMSE (mm) and CC of rainfall over the area (15°–25°N, 75°–90°E) for all cases.

Spatial RMSE (mm) and CC of rainfall over the area (15°–25°N, 75°–90°E) for all cases.
Spatial RMSE (mm) and CC of rainfall over the area (15°–25°N, 75°–90°E) for all cases.

Figures 14a–d show the day-1 forecasts of ETS and bias of rainfall for various threshold values (mm) obtained from the four experiments for all four MD cases. The ETS and bias scores are better in the experiments with regional BES for each threshold value of rainfall as compared to the CNTL and BG-3DV experiments. However, the skill scores are significantly improved in the domain-specific BES with ERA-Interim as the IBCs as compared to the BR-3DV simulations for all the cases, as seen in Fig. 14e. Therefore, while regional BES improved the simulation of the rainfall amount and pattern for the MD cases, use of ERA-Interim as IBCs further improved the simulations.

Fig. 14.

ETS (bar) and bias (line) of rainfall with different thresholds (mm) from CNTL, BG-3DV, BR-3DV, and BR-ERA for day 1 in (a) case 1, (b) case 2, (c) case 3, and (d) case 4, as well as (e) mean ETS and bias.

Fig. 14.

ETS (bar) and bias (line) of rainfall with different thresholds (mm) from CNTL, BG-3DV, BR-3DV, and BR-ERA for day 1 in (a) case 1, (b) case 2, (c) case 3, and (d) case 4, as well as (e) mean ETS and bias.

The use of ERA-Interim data not only impacts the lateral boundary conditions, but also the initial conditions. However, when assimilation of observation data is carried out in cyclic mode using the WRF-3DVAR model, the impact of the initial conditions used at the beginning of the assimilation is reduced. It can be seen from the figures depicting CNTL-ERA, BG-ERA, and BR-ERA (Figs. 9e,j,o, 10e,j, 11, and 12) that the use of domain-specific BES contributes positively to the analysis and forecasts of monsoon depressions. However, the impact of the BES in the ERA experiments is less than that from the NCEP–NCAR experiments.

e. Track predictions

Figures 15a–h show the model-simulated tracks of the four MDs along with the IMD-observed tracks and the corresponding vector display errors. It is seen that for all cases, the model-simulated tracks do not exactly match with the IMD best tracks, but the BR-3DV-simulated tracks are better than the CNTL and BG-3DV tracks. Significant reductions in the initial position errors of the MDs are noticed by using the regional BES as compared to the CNTL and BG-3DV simulations. It is interesting to note that the simulated tracks from CNTL in cases 1 and 2 show no landfall. In particular, the movement of the MDs in CNTL during the forecast period is totally different from what is observed. Therefore, the VDEs from the CNTL simulations are higher throughout the forecast period as compared to the assimilation experiments. The maximum VDEs are about 810 km (351 km) in case 1 at 48 h and about 477 km (324 km) in case 2 at 24 h for the CNTL (BG-3DV) simulations. Corresponding VDEs in the BR-3DV experiment are about 233 and 249 km in cases 1 and 2. The VDEs are further reduced in BR-ERA to about 179 km (48 h) and 87 km (24 h) in cases 1 and 2, respectively. Therefore, the errors are significantly smaller in the BR-ERA simulations for these cases when the ERA-Interim analyses are used as IBCs.

Fig. 15.

The 12-hourly track (observed and simulated) and VDEs (km) from CNTL, BG-3DV, BR-3DV, and BR-ERA. (a) Track and (b) VDEs for case 1 (initial time 0000 UTC 27 Jul 1999). (c),(d) As in (a),(b), but for case 2 (0000 UTC 17 Jun 1999). (e),(f) As in (a),(b), but for case 3 (0000 UTC 11 Jun 1999). (g),(h) As in (a),(b), but for case 4 (0000 UTC 6 Aug 1999). (i) Mean VDEs (km) and gains in skill of the experiments.

Fig. 15.

The 12-hourly track (observed and simulated) and VDEs (km) from CNTL, BG-3DV, BR-3DV, and BR-ERA. (a) Track and (b) VDEs for case 1 (initial time 0000 UTC 27 Jul 1999). (c),(d) As in (a),(b), but for case 2 (0000 UTC 17 Jun 1999). (e),(f) As in (a),(b), but for case 3 (0000 UTC 11 Jun 1999). (g),(h) As in (a),(b), but for case 4 (0000 UTC 6 Aug 1999). (i) Mean VDEs (km) and gains in skill of the experiments.

For the cases 3 and 4, the model-simulated monsoon depressions from the CNTL experiments move more slowly than for the observation as compared to other simulations. The BR-3DV-simulated tracks match reasonably well with the observed track throughout the forecast period as compared to the BG-3DV simulations. The VDEs increase as the forecast length increases in all of the cases. However, the errors in the BR-3DV simulation are comparatively smaller than those in the CNTL and BG-3DV simulations. The gain in skill in the BR-3DV experiment compared to the CNTL experiment ranges from 46% to 50% throughout the forecast period, while it is from 25% to 42% in the case of BG-3DV. The skill of BR-3DV over BG-3DV varies from 12% to 30% during the forecast period. It is worth mentioning here that the mean initial position errors of the MDs are significantly reduced (to 74 km) in BR-3DV as compared to CNTL (149 km) and BG-3DV (107 km).

The BR-ERA-simulated tracks match better with the observed tracks throughout the forecast period as compared to the BR-3DV simulations. The mean (at a particular time from all of the cases) VDEs are smaller in the BR-ERA simulations than in the CNTL, BR-3DV, and BG-3DV simulations in Fig. 15i. The percentage improvement in the average VDEs of the MDs from the BR-ERA simulation is about 50% with respect to BR-3DV. The gain in skill in BR-ERA ranges from 44% and 53% and is considerably improved over BR-3DV. The mean initial position errors of the MDs are significantly reduced to 42 km in BR-ERA as compared to BR-3DV (74 km). The mean VDEs of the simulated MDs have been evaluated from various experiments (ERA-Interim and NCEP) and percentage improvements are shown in Table 5. It is noticed that the VDEs are smaller and percentage improvement is greater in the ERA experiments as compared to the corresponding NCEP–NCAR experiments. Therefore, we may conclude that assimilation using the domain-specific BES provides improved forecast tracks when ERA-Interim boundary conditions are used for simulating the monsoon depressions.

f. Additional MD cases

The results from the above four MD cases during the 1999 monsoon period indicate that the use of domain-specific BES in the assimilation cycle improved the performance of the model. This improvement was seen in the model dynamical fields as well as in the locations, movements, and amounts of rainfall associated with the MDs. Improved simulations were obtained with both NCEP–NCAR and ERA-Interim reanalysis data as initial and boundary conditions when the domain-specific BES were used. Since, the BES were computed using the model simulations of 1999, it is possible that the improvement in the forecasts of these MDs could be due to the use of BES of that year. Examination of several independent cases (other than in 1999) is necessary to develop better statistics related to the improvement in the model performance owing to domain-specific BES over the Indian monsoon region.

For this purpose, two additional MD cases have been investigated that occurred during 2003 and 2004: 25–28 July 2003 (case 5) and 11–14 June 2004 (case 6). The low pressure areas formed over north parts of the Bay of Bengal and the adjoining land area (case 5) and over the east-central Bay of Bengal (case 6) and, subsequently, were concentrated into deep depressions. Being monsoon systems, these moved toward the west-northwest after crossing the coast. Widespread rainfall occurred along the coastal states as well as in interior parts of India. Data assimilation experiments were carried out for these two cases using the default BES as well as domain-specific BES computed for 1999 with NCEP–NCAR and ERA-Interim analyses as IBCs. The WRF Model was integrated for 78 h for both cases 5 and 6 with the same model configuration discussed in section 4. The analysis fields valid for 0000 UTC 25 July 2003 and 11 June 2004 were used as the initial conditions for the model for these two cases. The tracks and VDEs obtained from cases 5 and 6 are shown in Figs. 16a,b and 16c,d. It is seen that the simulated tracks with the regional BES are better than the CNTL simulation and runs with default BES. The initial position errors of the MD in both cases are less in BR-ERA compared to other experiments.

Fig. 16.

As in Fig. 15, but for two independent MD cases occurring during 2003 and 2004 (a) Track and (b) VDEs for case 5 (initial time 0000 UTC 25 Jul 2003). (c),(d) As in (a),(b), but for case 6 (initial time 0000 UTC 11 Jun 2004).

Fig. 16.

As in Fig. 15, but for two independent MD cases occurring during 2003 and 2004 (a) Track and (b) VDEs for case 5 (initial time 0000 UTC 25 Jul 2003). (c),(d) As in (a),(b), but for case 6 (initial time 0000 UTC 11 Jun 2004).

The model-simulated speed of the MDs is simulated well in the BR-3DV and BR-ERA runs as compared to CNTL and to runs with default BES. It is also seen that the movement of the MDs is also well simulated in BR-3DV compared to BG-3DV and CNTL. The VDEs are significantly less in BR-ERA for both cases. For case 5, the maximum VDEs are about 512 km (60 h) and 470 km (36 h) for the CNTL and BG-3DV simulations, respectively. Corresponding VDEs in the BR-3DV experiment are about 80 km (36 h) and 298 km (60 h). However, the VDEs ranged from 15 to 95 km in the BR-ERA simulation throughout the forecast hours. Similar results are also noticed for case 6, where the VDEs are less in the simulation using the regional BES. The simulated MD is a little faster in BR-3DV as compared to BR-ERA. During day-1 and day-2 forecasts for case 5, the intensity and structure of the MDs are well represented in the BR-ERA simulations. Therefore, this study suggests that even for independent cases (for the MDs in other years and not only 1999) the use of domain-specific BES improves the analyses and simulations of the MDs. Use of higher-resolution ERA-Interim data further improves the characteristics of the MDs for these cases.

6. Conclusions

Within a variational data assimilation system, BES spread the influence of the observations in space and filter analysis increments through dynamic balance or statistical relationships. In a data-sparse region such as the BoB, background error statistics (BES) and initial and lateral boundary conditions (IBCs) play an important role in defining the location, structure, and movement of MDs within the context of regional modeling. In this study, domain-specific BES (for the Indian region) have been computed using the NMC method for the WRF-VAR system. An assessment has been made on the impact of different BES (global BES available within the WRF-VAR system and domain-specific BES). In addition, experiments have been conducted to evaluate the impact of IBCs by using NCEP–NCAR reanalysis as well as ERA-Interim data as IBCs on the assimilation and forecasts of the monsoon depressions (MDs). Single-observation tests over India show that analysis increments respond well to the assimilation of the temperature and wind over the region when domain-specific BES are used compared to the global BES. Propagation of observation information in the data assimilation system is properly reflected in the final analysis of MDs and improvement in the model predictions has been obtained.

Large impacts on the analyses of MSLP and winds associated with MDs are noticed when domain-specific BES are used in the analysis forecast system. The intensity, initial position, and movement of the MDs are reasonably well characterized in both BR-ERA and BR-3DV experiments as compared to control runs or experiments with the default global BES. It is seen that the initial position errors are less in the regional BES runs, and are further reduced when using the ERA-Interim analyses as IBCs in the model. It is found that the model underestimates the rainfall due to the MDs in all of the experiments compared to the observed amount. However, the rainfall amounts and distribution are closer to the observations in the BR-ERA experiment compared to the CNTL, BG-3DV, and BR-3DV simulations. The track errors of the forecasted MDs are significantly less in simulations with regional BES as compared to other experiments.

It may be noted that use of analyses, rather than forecasts, as boundary conditions significantly improves the verification statistics for all metrics. In this study, analysis is used as the boundary conditions in all the experiments as the objective is to document the sensitivity of the analyses and predictions to background error statistics and initial/boundary conditions. Therefore, the experiments are simulation experiments and not prediction experiments.

The present study highlights aspects of the assimilation process that limit or improve the skill of prediction of MDs. It is well known that prediction of the environmental flow, building of the vertical structure of the vortex, the moisture analysis and initialization of the vortex, and construction of the primary and secondary circulation patterns all contribute to the analysis and prediction of MDs. The results of this study show that the use of domain-dependent BES in the WRF-VAR analysis system provides improved initial conditions and forecasts relative to using global BES. It is also clearly shown that use of high-resolution ERA-Interim data as the initial and lateral boundary conditions along with the domain-specific BES further improved the analysis and forecasting of the MDs. However, the use of ensemble-flow-dependent BES in the assimilation cycle (Fisher 2003; Houtekamer and Mitchell 2001; Hamill and Snyder 2000) should further improve the analysis and prediction of MDs. Therefore, this study makes a case for and is a step toward implementing a flow-dependent background error for the South Asian region in a regional data assimilation system.

Acknowledgments

The authors acknowledge the Mesoscale and Microscale Meteorology Division at NCAR, NCEP, and ECMWF for making available their WRF and 3DVAR systems as well as reanalyses datasets used as IBCs for models in public domain. Thanks also to the IMD for providing the station-wise observed rainfall and best tracks of the MDs that are used to validate the model results of this study. Thanks also to the editor and the anonymous reviewers for many useful comments and suggestions that have helped to improve the paper.

REFERENCES

REFERENCES
Barker
,
D. M.
,
W.
Huang
,
Y.-R.
Guo
,
A.
Bourgeois
, and
X. N.
Xiao
,
2004
:
A three-dimensional variational data assimilation system for MM5: Implementation and initial results
.
Mon. Wea. Rev.
,
132
,
897
914
, doi:.
Buehner
,
M.
,
2005
:
Ensemble-derived stationary and flow-dependent background-error covariances: Evaluation in a quasi-operational NWP setting
.
Quart. J. Roy. Meteor. Soc.
,
131
,
1013
1043
, doi:.
Buehner
,
M.
,
P. L.
Houtekamer
,
C.
Charette
,
H. L.
Mitchell
, and
B.
He
,
2010a
:
Intercomparison of variational data assimilation and the ensemble Kalman filter for global deterministic NWP. Part I: Description and single-observation experiments
.
Mon. Wea. Rev.
,
138
,
1550
1566
, doi:.
Buehner
,
M.
,
P. L.
Houtekamer
,
C.
Charette
,
H. L.
Mitchell
, and
B.
He
,
2010b
:
Intercomparison of variational data assimilation and the ensemble Kalman filter for global deterministic NWP. Part II: One-month experiments with real observations
.
Mon. Wea. Rev.
,
138
,
1567
1586
, doi:.
Chang
,
H.-I.
,
D.
Niyogi
,
A.
Kumar
,
C. M.
Kishtawal
,
J.
Dudhia
,
F.
Chen
,
U. C.
Mohanty
, and
M.
Shepherd
,
2009
:
Possible relation between land surface feedback and the post-landfall structure of monsoon depressions
.
Geophys. Res. Lett.
,
36
,
L15826
, doi:.
Daley
,
R.
,
1991
: Atmospheric Data Analysis. Cambridge University Press, 457 pp.
Daley
,
R.
,
1993
:
Atmospheric data assimilation on the equatorial beta plane
.
Atmos.–Ocean
,
31
,
421
450
, doi:.
Daley
,
R.
,
1996
:
Generation of global multivariate error covariances by singular-value decomposition of the linear balance equation
.
Mon. Wea. Rev.
,
124
,
2574
2587
, doi:.
Davies
,
H. C.
,
1976
:
A lateral boundary formulation for multi-level prediction models
.
Quart. J. Roy. Meteor. Soc.
,
102
,
405
418
, doi:.
Deb
,
S. K.
,
C. M.
Kishtawal
, and
P. K.
Pal
,
2010
:
Impact of Kalpana-1-derived water vapor winds on Indian Ocean tropical cyclones forecast
.
Mon. Wea. Rev., 138, 987–1003
, doi:.
Evensen
,
G.
,
1994
:
Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics
.
J. Geophys. Res.
,
99
,
10 143
10 162
, doi:.
Fisher
,
M.
,
2003
: Background error covariance modeling. Proc. Seminar on Recent Development in Data Assimilation for Atmosphere and Ocean, Reading, United Kingdom, ECMWF, 45–63.
Godbole
,
R. V.
,
1977
:
The composite structure of the monsoon depression
.
Tellus
,
29A
,
25
40
, doi:.
Hamill
,
T. M.
, and
C.
Snyder
,
2000
:
A hybrid ensemble Kalman filter—3D variational analysis scheme
.
Mon. Wea. Rev.
,
128
,
2905
2919
, doi:.
Hayden
,
C. M.
, and
R. J.
Purser
,
1995
:
Recursive filter objective analysis of meteorological fields: Applications to NESDIS operational processing
.
J. Appl. Meteor.
,
34
,
3
15
, doi:.
Houtekamer
,
P. L.
, and
H. L.
Mitchell
,
2001
:
A sequential ensemble Kalman filter for atmospheric data assimilation
.
Mon. Wea. Rev.
,
129
,
123
137
, doi:.
Houtekamer
,
P. L.
,
H. L.
Mitchell
,
G.
Pellerin
,
M.
Buehner
,
M.
Charron
,
L.
Spacek
, and
B.
Hansen
,
2005
:
Atmospheric data assimilation with an ensemble Kalman filter: Results with real observations
.
Mon. Wea. Rev.
,
133
,
604
620
, doi:.
Houtekamer
,
P. L.
,
H. L.
Mitchell
, and
X.
Deng
,
2009
:
Model error representation in an operational ensemble Kalman filter
.
Mon. Wea. Rev.
,
137
,
2126
2143
, doi:.
Jankov
,
I.
,
W. A.
Gallus
Jr.
,
M.
Segal
,
B.
Shaw
, and
S. E.
Koch
,
2005
:
The impact of different WRF Model physical parameterizations and their interactions on warm season MCS rainfall
.
Wea. Forecasting
,
20
,
1048
1060
, doi:.
Jianfeng
,
G. U.
,
Q.
Xiao
,
Y.-H.
Kuo
,
D. M.
Barker
,
X.
Jishan
, and
M. A.
Xiaoxing
,
2005
:
Assimilation and simulation of Typhoon Rusa (2002) using the WRF system
.
Adv. Atmos. Sci.
,
22
,
415
427
, doi:.
Jianying
,
J.
,
J.
Jixi
,
B.
Yalin
, and
L.
Nianqing
,
2007
:
Heavy rainfall associated with a monsoon depression in South China: Structure analysis
.
Acta Meteor. Sin.
,
22
,
51
65
.
Kalnay
,
E.
, and Coauthors
,
1996
:
The NCEP/NCAR 40-Year Reanalysis Project
.
Bull. Amer. Meteor. Soc.
,
77
,
437
471
, doi:.
Kar
,
S. C.
,
K.
Rupa
,
M.
Das Gupta
, and
S. V.
Singh
,
2003
: Analyses of Orissa super cyclone using TRMM (TMI), DMSP (SSM/I) and OceanSat-I (MSMR) derived data. J. Atmos. Ocean Sci.,9, 1–18, doi:.
Krishnamurti
,
T. N.
,
M.
Kanamitsu
,
R.
Godbole
,
C. B.
Chang
,
F.
Carr
, and
J. H.
Chow
,
1975
:
Study of a monsoon depression, (I), Synoptic structure
.
J. Meteor. Soc. Japan
,
53
,
227
240
.
Majewski
,
D.
,
1997
:
Operational regional prediction
.
Meteor. Atmos. Phys.
,
63
,
89
104
, doi:.
Mohanty
,
U. C.
,
K. K.
Osuri
,
A.
Routray
,
M.
Mohapatra
, and
S.
Pattanayak
,
2010
:
Simulation of Bay of Bengal tropical cyclones with WRF model: Impact of initial and boundary conditions
.
Mar. Geod.
,
33
,
294
314
, doi:.
Osuri
,
K. K.
,
U. C.
Mohanty
,
A.
Routray
,
M.
Mohapatra
, and
D.
Niyogi
,
2013
:
Real-time track prediction of tropical cyclones over the North Indian Ocean using the ARW model
.
J. Appl. Meteor. Climatol.,
52, 2476–2492, doi:.
Parrish
,
D.
,
1988
: The introduction of Hough functions into optimal interpolation. Preprints, Eighth Conf. on Numerical Weather Prediction, Baltimore, MD, Amer. Meteor. Soc..
Parrish
,
D.
, and
J. C.
Derber
,
1992
:
The National Meteorological Center’s spectral statistical interpolation analysis system
.
Mon. Wea. Rev.
,
120
,
1747
1763
, doi:.
Perkey
,
D. J.
, and
W.
Kreitzberg
,
1976
:
A time-dependent lateral boundary scheme for limited area primitive equation models
.
Mon. Wea. Rev.
,
104
,
744
755
, doi:.
Purser
,
R. J.
,
W.-S.
Wu
,
D. F.
Parrish
, and
N. M.
Roberts
,
2003
:
Numerical aspects of the application of recursive filters to variational statistical analysis. Part I: Spatially homogeneous and isotropic Gaussian covariances
.
Mon. Wea. Rev.
,
131
,
1524
1535
, doi:.
Rakesh
,
V.
,
R.
Singh
,
P. K.
Pal
, and
P. C.
Joshi
,
2009
:
Impact of satellite-observed surface wind and total precipitable water on WRF short-range forecasts over Indian region during monsoon 2006
.
Wea. Forecasting
,
24
,
1706
1731
, doi:.
Rao
,
Y. P.
,
1976
: Southwest Monsoon. Meteor. Monogr. (Synoptic Meteorology), No. 1/1976, India Meteorological Department, 366 pp.
Routray
,
A.
,
U. C.
Mohanty
,
D.
Niyogi
,
S. R. H.
Rizvi
, and
K. K.
Osuri
,
2010a
:
Simulation of heavy rainfall events over Indian monsoon region using WRF-3DVAR data assimilation system
.
Meteor. Atmos. Phys.
,
106
,
107
125
, doi:.
Routray
,
A.
,
U. C.
Mohanty
,
S. R. H.
Rizvi
,
D.
Niyogi
,
K. K.
Osuri
, and
D.
Pradhan
2010b
: Impact of Doppler weather radar data on numerical forecast of Indian monsoon depressions. Quart. J. Roy. Meteor. Soc.,136, 1836–1850, doi:.
Rupa
,
K.
,
S. R. H.
Rizvi
,
S. C.
Kar
,
U. C.
Mohanty
, and
R. K.
Paliwal
,
2002
:
Assimilation of IRS-P4 (MSMR) meteorological data in the NCMRWF global data assimilation system
.
Proc. Indian Acad. Sci. (Earth Planet. Sci.)
,
111
,
351
364
.
Sikka
,
D. R.
,
1977
:
Some aspects of the life history, structure and movement of monsoon depressions
.
Pure Appl. Geophys.
,
115
,
1501
1529
, doi:.
Skamarock
,
W. C.
,
2004
:
Evaluating mesoscale NWP models using kinetic energy spectra
.
Mon. Wea. Rev.
, 132,
3019
3032
, doi:.
Skamarock
,
W. C.
,
J. B.
Klemp
,
J. Dudhia
,
D. O.
Gill
,
D. M.
Barker
,
W. Wang
, and
J. G.
Powers
,
2005
: A description of the advanced research WRF version 2. NCAR Tech. Note NCAR/TN-468+STR, 88 pp. [Available online at http://www.mmm.ucar.edu/wrf/users/docs/arw_v2.pdf.]
Sowjanya
,
K.
,
S. C.
Kar
,
A.
Routray
, and
P.
Mali
,
2013
:
Impact of SSM/I retrieval data on the systematic bias of analyses and forecasts of the Indian summer monsoon using WRF assimilation system
.
Int. J. Remote Sens.
,
34
,
631
654
, doi:.
Vinodkumar
,
A.
Chandrasekar
,
K.
Alapaty
, and
D.
Niyogi
,
2009
:
Assessment of data assimilation approaches for the simulation of a monsoon depression over the Indian monsoon region
.
Bound.-Layer Meteor.
,
133
,
343
366
, doi:.
Whitaker
,
J. S.
,
T. M.
Hamill
,
X.
Wei
,
Y.
Song
, and
Z.
Toth
,
2008
:
Ensemble data assimilation with the NCEP Global Forecast System
.
Mon. Wea. Rev.
,
136
,
463
482
, doi:.
Whitaker
,
J. S.
,
G. P.
Compo
, and
J.-N.
Thépaut
,
2009
:
A comparison of variational and ensemble-based data assimilation systems for reanalysis of sparse observations
.
Mon. Wea. Rev.
,
137
,
1991
1999
, doi:.
Williamson
,
D. L.
, and
G. L.
Browning
,
1974
:
Formulation of the lateral boundary conditions for the NCAR Limited Area Model
.
J. Appl. Meteor.
,
13
,
8
16
, doi:.
Wu
,
W.-S.
,
R. J.
Purser
, and
D. F.
Parrish
,
2002
:
Three-dimensional variational analysis with spatially inhomogeneous covariances
.
Mon. Wea. Rev.
,
130
,
2905
2916
, doi:.
Zhang
,
S.
, and
J. L.
Anderson
,
2003
:
Impact of spatially and temporally varying estimates of error covariance on assimilation in a simple atmospheric model
.
Tellus
,
55A
,
126
147
, doi:.