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  • View in gallery
    Fig. 1.

    Flowchart of applying the improved observation operator in GSI.

  • View in gallery
    Fig. 2.

    Distributions of wind increment (m s−1) of the single analysis unit test using two different observation operators with various analysis unit sizes. (left) Experiments using the traditional observation operator: (a) RW1 (1 km × 1 km), (c) RW2 (12 km × 12 km), (e) RW3 (24 km × 24 km), and (g) RW4 (48 km × 48 km). (right) Experiments using the improved observation operator: (b) IVAP1 (1 km × 1 km), (d) IVAP2 (12 km × 12 km), (f) IVAP3 (24 km × 24 km), and (h) IVAP4 (48 km × 48 km).

  • View in gallery
    Fig. 3.

    Raw radar radial velocity observations and results from different thinning methods of the lowest elevation (0.5°) in Zhejiang province at 1200 UTC 06 Oct 2013. (a) Raw radar data from the Wenzhou radar. (b) Results of the traditional thinning method using the data from only the Wenzhou radar. (c) Results of the improved observation operator with an analysis unit of 12 km × 12 km using the data from only the Wenzhou radar. (d) As in (c), but using the data from all five radars. The location of each radar station (filled star) and the center of Typhoon Fitow (green dot) are indicated.

  • View in gallery
    Fig. 4.

    Analysis and prediction domain at 3-km horizontal resolution, with the best track locations of Typhoon Fitow marked at 1-h intervals from 0600 UTC 6 Oct to 0000 UTC 7 Oct 2013. The locations of the radar stations (filled stars), the maximum Doppler range of the radar data (circle), and the terrain (m, gray shading) are indicated.

  • View in gallery
    Fig. 5.

    Flowchart of Exp CTL and the Exps assimilating radar data via the traditional observation operator (RW) and the improved observation operator (IVAP). Each upward arrow indicates the time when the radar radial velocity is assimilated. A 12-h forecast is carried out, following the final analysis at 1200 UTC 6 Oct 2013 in each Exp.

  • View in gallery
    Fig. 6.

    The (a) MSLP and (b) MWS during the data assimilation period from Exps CTL, RW, and IVAP.

  • View in gallery
    Fig. 7.

    Horizontal wind increments at z = 3 km for the last analysis (1200 UTC) from (a) Exp RW and (b) Exp IVAP. The wind speed (shading), the location of the radar stations (filled stars), and the typhoon centers in the background (purple dot) and observation fields (green dot) are indicated.

  • View in gallery
    Fig. 8.

    The radial velocity (shading) and wind field (vector) at the lowest elevation (0.5°) of the Wenzhou radar station at 1200 UTC 6 Oct 2013: (a) observed radar radial velocity (no vector), (b) Exp CTL, (c) Exp RW, and (d) Exp IVAP. The location of the radar station (filled star) and the approximate center of the observed typhoon (green dot), near the lower-right corner of each panel, are indicated.

  • View in gallery
    Fig. 9.

    The radial and tangential velocities (shading) and wind field (vector) at the lowest elevation (0.5°) of the Wenzhou radar station at 1200 UTC 6 Oct 2013: (a) observed radar radial velocity and the background wind field from Exp CTL, (b) the tangential velocity and its direction from Exp CTL, (c) the increment of tangential velocity between Exps RW and CTL, and (d) the increment of tangential velocity between Exps IVAP and CTL. The location of the radar station (filled star) and the approximate center of the observed typhoon (green dot), near the lower-right corner of each panel, are indicated.

  • View in gallery
    Fig. 10.

    Analyzed SLP (thick solid contour, hPa), surface wind speed (shading, m s−1), and wind barbs for Typhoon Fitow at 1200 UTC 6 Oct 2013 from (a) Exp CTL, (b) Exp RW, and (c) Exp IVAP. The approximate center of the observed typhoon (black dot), near the domain center in each panel, is indicated.

  • View in gallery
    Fig. 11.

    Azimuthally averaged tangential wind (contours with 2.5 m s−1 intervals) and reflectivity (shading, dBZ) from (a) Exp CTL, (b) Exp RW, and (c) Exp IVAP at 1200 UTC 6 Oct 2013; (d)–(f) as in (a)–(c), but for horizontal temperature deviation (contours with 1.0°C intervals) and absolute vorticity (shading, 10−5 s−1).

  • View in gallery
    Fig. 12.

    The 12-h predicted (a) tracks, (b) track errors, (c) MSLP (hPa), and (d) MWS (m s−1) of Typhoon Fitow from 1200 UTC 6 Oct to 0000 UTC 7 Oct 2013.

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Application of IVAP-Based Observation Operator in Radar Radial Velocity Assimilation: The Case of Typhoon Fitow

Feng ChenState Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing, and Zhejiang Institute of Meteorological Sciences, Hangzhou, China

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Xudong LiangState Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing, China

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Hao MaZhejiang Province Meteorological Observatory, Hangzhou, China

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Abstract

An improved Doppler radar radial velocity assimilation observation operator is proposed based on the integrating velocity–azimuth process (IVAP) method. This improved operator can ingest both radial wind and its spatial distribution characteristics to deduce the two components of the mean wind within a given area. With this operator, the system can be used to assimilate information from tangential wind and radial wind. On the other hand, because the improved observation operator is defined within a given area, which can be uniformly chosen in both the observation and analysis coordinate systems, it has a thinning function. The traditional observation operator and the improved observation operator, along with their corresponding data processing modules, were implemented in the community Gridpoint Statistical Interpolation analysis system (GSI) to demonstrate the superiority of the improved operator. The results of single analysis unit experiments revealed that the two operators are comparable when the analysis unit is small. When the analysis unit becomes larger, the analysis results of the improved operator are better than those of the traditional operator because the former can ingest more wind information than the latter. The results of a typhoon case study indicated that both operators effectively ingested radial wind information and produced more reasonable typhoon structures than those in the background fields. The tangential velocity relative to the radar was retrieved by the improved operator through ingesting tangential wind information from the spatial distribution characteristics of radial wind. Because of the improved vortex intensity and structure, obvious improvements were seen in both track and intensity predictions when the improved operator was used.

Denotes content that is immediately available upon publication as open access.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Xudong Liang, xdliang@camscma.cn

Abstract

An improved Doppler radar radial velocity assimilation observation operator is proposed based on the integrating velocity–azimuth process (IVAP) method. This improved operator can ingest both radial wind and its spatial distribution characteristics to deduce the two components of the mean wind within a given area. With this operator, the system can be used to assimilate information from tangential wind and radial wind. On the other hand, because the improved observation operator is defined within a given area, which can be uniformly chosen in both the observation and analysis coordinate systems, it has a thinning function. The traditional observation operator and the improved observation operator, along with their corresponding data processing modules, were implemented in the community Gridpoint Statistical Interpolation analysis system (GSI) to demonstrate the superiority of the improved operator. The results of single analysis unit experiments revealed that the two operators are comparable when the analysis unit is small. When the analysis unit becomes larger, the analysis results of the improved operator are better than those of the traditional operator because the former can ingest more wind information than the latter. The results of a typhoon case study indicated that both operators effectively ingested radial wind information and produced more reasonable typhoon structures than those in the background fields. The tangential velocity relative to the radar was retrieved by the improved operator through ingesting tangential wind information from the spatial distribution characteristics of radial wind. Because of the improved vortex intensity and structure, obvious improvements were seen in both track and intensity predictions when the improved operator was used.

Denotes content that is immediately available upon publication as open access.

© 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Xudong Liang, xdliang@camscma.cn

1. Introduction

Limited-area models (LAMs) with high spatial and temporal resolution, mainly focusing on precise nowcasting, tend to have poor forecast skills. This is mostly due to energy imbalance and the lack of local information (Schwitalla and Wulfmeyer 2014). By specifying the thermodynamic structure and providing hydrometer information in a convective-permitting system, assimilating radar data into LAMs can improve short-range quantitative precipitation forecast (QPF) (Sheng et al. 2006; Xiao 2007; Zhao and Xue 2009). However, unconventionally observed parameters and mismatched resolutions between model and observation make radar data assimilation difficult to implement (Fabry and Kilambi 2011; Thompson et al. 2012).

Radar radial velocity can be directly assimilated using an observation operator. In an example used by the community Gridpoint Statistical Interpolation analysis system (GSI), the data assimilation system of the National Centers for Environmental Prediction (NCEP) (Wu et al. 2002; Purser et al. 2003a,b; Hu et al. 2015; Shao et al. 2016) is as follows:
e1
where are model wind components in the Cartesian coordinate of (x, y), is the azimuth of the radar observation (zero refers to north and it increases clockwise), is the radar elevation angle, and is the radar radial velocity with the mass-weighted terminal velocity deducted. This type of observation operator has been used in many studies in which the radar radial winds were assimilated directly (Sun et al. 1991; Sun and Crook 1997, 1998; Snyder and Zhang 2003; Tong and Xue 2005; Caya et al. 2005; Xu et al. 2006; Li et al. 2012; Sun and Wang 2013; Wang et al. 2013). Many studies showed improved short-range QPF (Barker et al. 2004; Hu and Xue 2007; Schenkman et al. 2011; Abhilash et al. 2012; Maiello et al. 2014; Srivastava and Bhardwaj 2014). Meanwhile, the majority of operational or research models use this method to assimilate radar data, such as the three-dimensional variational data assimilation (3DVAR) system of HIRLAM (HIRLAM-3DVAR; Lindskog et al. 2004), the MM5-3DVAR (Xiao et al. 2005), the ARPS-3DVAR (Hu et al. 2006), the Application of Research to Operations at Mesoscale (AROME)-3DVAR (Montmerle and Faccani 2009), and the Beijing Rapid Update Cycle (BJ-RUC) system [based on WRF and the WRF data assimilation system (WRFDA); Chen et al. 2014]. Nevertheless, Doppler radar can provide only the radial component of wind velocity, namely, without the tangential component (refers to as the cross-beam wind component, the same as below). The observing system simulation experiment (OSSE) study (Sugimoto et al. 2009) showed that this method needs improvement because it is limited in retrieving the tangential wind component.

Doppler radar can give only the radial component of the wind velocity at each point, but the spatial distribution characteristics of the radial wind can provide some information about the tangential wind component. For example, the velocity–azimuth display (VAD) method (Lhermitte and Atlas 1961; Browning and Wexler 1968; Lindskog et al. 2002; Benjamin et al. 2010) can be used to obtain the whole-domain-averaged wind within the radar scan range using the spatial distribution characteristics of radial wind. Therefore, besides the radial wind, assimilating the spatial distribution characteristics of the radial winds should help improve the model wind field. The traditional observation operator given in Eq. (1) however cannot incorporate the spatial distribution characteristics into a data assimilation system.

Rather than the VAD method that can provide only the whole-domain-averaged wind field, the integrating velocity–azimuth processing (IVAP) method proposed by Liang (2007) can provide locally averaged wind within a given area. In this study, a new observation operator based on the IVAP method is proposed to assimilate the radar radial wind and its spatial distribution characteristics.

In the meantime, the resolution mismatch of observation and model must be handled before radar data assimilation. Generally, a thinning method is used to match the two resolutions. The existing thinning methods (Purser et al. 2000; Alpert and Kumar 2007) used in radar data assimilation discard massive observations and induce interpolation errors. Such as that in GSI, the mean radial velocity in a box (e.g., 5 km in range, 5° in azimuth, and 0.25° in elevation) is used to represent the whole area, which is called super-observations. Meanwhile, the pointwise measurements used in the traditional observation operator require that the radial velocity is averaged in a box within the radar volume, which produces large errors when the system is far away from the radar center (Wood et al. 2009). Because the IVAP method uses a given area to obtain the information about local wind, the size of the area can be uniformly set in both radar and model coordinates; therefore, it has a thinning function automatically without having to discard observations and induce interpolation errors.

In this study, single analysis unit experiments and a case study of Typhoon Fitow (2015) are used to make detailed comparative analyses, to show the superiority of this improved operator. The paper is organized as follows. The formula of the improved observation operator is described in section 2. The single analysis unit experiments to demonstrate the improved observation operator are analyzed in section 3. Data processing procedures and elaboration on the outcome of the selected typhoon case are given in section 4, followed by a summary and a discussion in section 5.

2. Observation operators for radar radial velocity assimilation

The traditional observation operator for Doppler radar radial velocity is similar to Eq. (1) and is given below:
e2
where are wind components in the Cartesian coordinate of (x, y, z). Equation (2) introduces the radar radial wind directly; sometimes, the vertical velocity term is omitted, such as in Eq. (1) used by the GSI. As discussed in section 1, besides the radial wind, the spatial distribution characteristics of radial wind are also useful for retrieving the tangential wind, which cannot be observed by the radar directly. According to Liang (2007) and Luo et al. (2014), there are two spatial distribution characteristics of radial wind that can be obtained by multiplying or on both sides of Eq. (2) and summing within a given area :
e3
If we define the averaged wind within using , then Eq. (3) can be expressed as follows:
e4
Dividing both sides of Eq. (4) by or , we have
e5
As shown in Liang (2007), Eq. (5) can be used to retrieve all components of the mean wind within . The left and right sides of Eq. (5) are defined in the observation and analysis spaces, respectively, as follows:
e6
and
e7
The area-averaged wind can be obtained using the operator . For example, , where N is the total number of the grid points within . Equation (7) can be used as an observation operator instead of Eq. (2) in radar radial wind assimilation; it can provide the spatial distribution characteristics of radial wind besides the radial wind itself. As a consequence, the observations are reorganized using Eq. (6), which can be seen as the weighted average of radial wind, instead of having radial wind only in Eq. (2). As shown by Liang (2007), if using the equations and , we can retrieve using the radial winds . The winds in the Cartesian coordinate are equal to the radial and tangential winds in the radar coordinate. In other words, Eqs. (6) and (7) have partial information about tangential wind besides the radial wind observed by radar. In the data assimilation system, Eqs. (6) and (7) are not equal exactly, and the differences between Eqs. (6) and (7) are minimized during the minimization process and are controlled by background and other observations.
Then, Eqs. (6) and (7) can be introduced into the 3DVAR cost function
e8
where and are background and observation terms, respectively. In this study, the GSI data assimilation was used and the observation operator was added. Because the vertical velocity is not a control variable in GSI and, in general, the eigenvalues of horizontal wind components in a mesoscale system (except for some deep convections) are much larger than that of vertical wind components, we omit in Eq. (7) in this study. As a result, the radar wind part in is
e9
where and are the observations defined by Eq. (6); and are the new observation operators defined by Eq. (7), and are the background error covariance and observation error variance matrices, respectively, and
e10
The default background error covariance derived from the North American Mesoscale Forecast System (NAM; Hu et al. 2015) is used in this study. A constant observation error similar to that used in Min et al. (2007) and Zhao et al. (2012) is used in this study. The area used in Eq. (10) is uniform in both the radar observation and analysis fields (model) coordinates. It should be pointed out that the observation errors of radial winds and the new observations ( and ) are not the same. We simply used the same values in this study by assuming that the differences between the errors do not ruin the performance of the operator obviously. Meanwhile, the observation errors of and should be studied in the future.

The improved observation operator can be applied in GSI, as shown in Fig. 1. First, the observations of and are calculated using Eq. (6) based on the radial velocity in the radar coordinate system; and two coefficients and ( and , respectively, in Fig. 1) are recorded. Second, the area-averaged wind components of and are obtained from the model wind field. Third, the values of and are computed based on Eq. (7). Finally, we minimize the cost function to obtain the final analysis field.

Fig. 1.
Fig. 1.

Flowchart of applying the improved observation operator in GSI.

Citation: Monthly Weather Review 145, 10; 10.1175/MWR-D-17-0002.1

Generally, a thinning method should be used because of the resolution differences between the observation and the model mentioned in the introduction. In Eqs. (6) and (7), the size and shape of are the same, even though they are different coordinate systems. Therefore, the resolutions of the observation and analysis fields are matched by the selected . In other words, the operators in Eqs. (6) and (7) have a thinning function automatically. For example, if in the model coordinate system is 12 km × 12 km, then a similar should be chosen in the radar coordinate system. The resolution of the radial winds observed by radar varies with range and the number of observations in also varies with range, but the resolution of observations and remains 12 km × 12 km.

In summary, compared with the traditional operator, which introduces radial velocity using point-to-point “super observations (super-obs),” the improved operator absorbs more observed information, including both radial wind and its spatial distribution characteristics. In addition, compared with single-point measurements, the improved observation operator, calculating the observation variables in , can reduce interpolation errors during artificial data thinning. Finally, as in Liang (2007), if is reduced to one observation point, then the improved operator becomes the traditional observation operator [see Eq. (2)].

3. Single analysis unit experiments

To compare the performances of the two observation operators in the GSI system, single analysis unit experiments were conducted. A domain with 725 × 625 horizontal grid points, 3-km resolution, and 51 vertical levels is used. The model top is at 10 hPa. The background wind is uniform, with and being 5 and 1 m s−1, respectively. A uniform westerly wind field with a speed of 10 m s−1 was assumed as the observed wind field. Thus, the radial velocity with the resolution of 1° in azimuth and 125 m in range can be obtained [setting the radar at the same location as the Wenzhou radar (i.e., 27.9°N, 120.74°E; 755 m)] and an observation error of 1 m s−1 was assumed. A point with an elevation of 0.5°, an azimuth of 176°, and a range of 446 (the range interval is 125 m) was selected as the center of the analysis unit (or in section 2). Four analysis unit sizes were chosen: 1 km × 1 km, 12 km × 12 km, 24 km × 24 km, and 48 km × 48 km. Two categories of single analysis unit experiments (Exp) were designed: one group used the traditional observation operator and its corresponding thinning method along with the four analysis unit sizes (referred to as RW1, RW2, RW3, and RW4, respectively), and the other used the improved observation operator with the same four analysis unit sizes (referred to as IVAP1, IVAP2, IVAP3, and IVAP4, respectively).

The wind speed increments were computed between the observation and background fields [observation minus background (OMB)] and between the observation and analysis fields [observation minus analysis (OMA)] in each experiment (Table 1). The OMBs were mostly in the westerly direction with a slight southerly increment, with the values of 5 and −1 m s−1 in the x and y directions, respectively. By using the traditional observation operator, an innovation against the radar center can be found in Exp RW1 that reduced the radial velocity error from 1.34 m s−1 (OMB) to 1.13 m s−1 (OMA). With the analysis unit size increased from 1 km × 1 km to 48 km × 48 km, the number of super-obs points increased from 1 to 119, while the OMA decreased from 1.13 to 0.72 m s−1. However, the tangential velocity showed almost no improvement, which only changed from −4.92 to −4.43 m s−1. Figures 2a, 2c, 2e, and 2g show that the wind increments had little improvements in the east–west direction, and the directions of the innovation appeared mainly toward or against the radar center, since the traditional observation operator can ingest only radial velocity; in other words, it did not have information about tangential velocity. By using the improved observation operator, the observation parameters, calculated in the given area using Eqs. (6) and (7), ingested both radial velocity and its spatial distribution characteristics into the assimilation system, which contained the information about tangential velocity. Thus, the improvements appeared not only in radial velocity but also in tangential velocity. With the analysis unit size increased from 1 km × 1 km to 48 km × 48 km, the radial velocity error decreased from 1.34 m s−1 (OMB) to about −0.25 m s−1 (OMA) in Exp IVAP4, while the tangential velocity decreased from −9.98 m s−1 (OMB) to −4.92 m s−1 in Exp IVAP1, and to 0.65 m s−1 in Exp IVAP4. As mentioned in section 2, when the analysis unit was small, the improved observation operator was similar to the traditional one, which was demonstrated by the similar results of IVAP1 (Fig. 2b) and RW1 (Fig. 2a). Since there were fewer observations in a smaller analysis unit, less tangential information could be deduced and less advantage the improved observation operator had compared to the traditional one. When the analysis unit became bigger, the abundance of observed radial velocity provided more tangential information through the improved observation operator; the holonomic wind field made the analysis results closer to the observation (Figs. 2d,f,h). These analyses indicate the essential differences of these two observation operators and demonstrate the superiority of the improved observation operator. As shown by the results of the single analysis unit experiments, the traditional observation operator cannot improve the wind in the tangential direction by assimilating radar observation even in the case of a uniform wind field.

Table 1.

Wind increments between the observation (OBS) and background fields and between the observation and analysis fields.

Table 1.
Fig. 2.
Fig. 2.

Distributions of wind increment (m s−1) of the single analysis unit test using two different observation operators with various analysis unit sizes. (left) Experiments using the traditional observation operator: (a) RW1 (1 km × 1 km), (c) RW2 (12 km × 12 km), (e) RW3 (24 km × 24 km), and (g) RW4 (48 km × 48 km). (right) Experiments using the improved observation operator: (b) IVAP1 (1 km × 1 km), (d) IVAP2 (12 km × 12 km), (f) IVAP3 (24 km × 24 km), and (h) IVAP4 (48 km × 48 km).

Citation: Monthly Weather Review 145, 10; 10.1175/MWR-D-17-0002.1

4. Case study

a. Data processing

Because nonmeteorological echoes can ruin the observation and analysis results, it is essential to process the observation data before assimilation. We processed the radar data using the following methods.

1) Suppression of ground clutters

Ground clutters show nonzero data in areas with zero velocity in low elevation of the radial velocity field (Yu 2006). Therefore, we omit all velocities smaller than 0.5 m s−1.

2) Removal of isolated data

To ensure the consistency of the radar radial field, we removed all isolated observations, around which the number of no-data points was more than N (N = 4 in this study).

3) Exclusion of mass-averaged terminal velocity

As mentioned in section 2, we do not consider vertical velocity in this study. Five low-level scans (with elevation angles of 0.5°, 1.5°, 2.4°, 3.4°, and 4.3°) were chosen, as suggested by Liu et al. (2010), to reduce errors from neglecting the vertical wind component. Because the mass-averaged terminal velocity of rainwater cannot be neglected (Wan et al. 2005), it was calculated based on the equation derived by Sun and Crook (1997), and it was removed from the radar radial velocity using
e11
where is the observed radar radial velocity, is the mass-averaged terminal velocity, and is the elevation angle (Alberoni et al. 2000).

4) Data thinning

The mismatch in resolutions between the observation and model coordinate systems imposes a burden for the assimilation system. It is desirable to maximize the compression of radar data while minimizing the degradation of the information content (Alpert and Kumar 2007).

A thinning method is used for the traditional observation operator. The GSI rarefied the high-density radar data to super-obs points, which are comparable to the model’s resolution, to reduce the amount of redundant data. The mean radial velocity and other properties (such as azimuth, range, longitude, latitude, and height) in a box (e.g., 5 km in range, 5° in azimuth, and 0.25° in elevation) were selected to represent all the data as one super-obs point. This thinning method usually introduces interpolation errors and discards a lot of data manually.

For the improved observation operator, the thinning process can be done during the process of calculating the observation parameters. A super-obs point was extended to an analysis unit, and the observation field was segmented into a series of squares (analysis units). All the data within the squares were used by the operator [Eq. (6)].

Figure 3a shows the raw radar radial velocity data at the elevation of 0.5° of the Wenzhou radar. Figures 3b and 3c show the results after different processing procedures; both results correctly represent the observation field. Figure 3b implies that the observed field was divided into many super-obs points, which discarded many observations. However, Fig. 3c shows that the observed radar radial velocity field was divided into many squares, which kept the spatial distribution information about the raw data. The shaded grids in one rectangle formed one analysis unit and were used to calculate the observation parameters, which implied a large amount of data was processed. In addition, the IVAP can filter out short waves (Liang 2007), and therefore it is unnecessary to smooth the pulsation in data processing. The analysis units at the 0.5° elevation of the five radars are shown in Fig. 3d.

Fig. 3.
Fig. 3.

Raw radar radial velocity observations and results from different thinning methods of the lowest elevation (0.5°) in Zhejiang province at 1200 UTC 06 Oct 2013. (a) Raw radar data from the Wenzhou radar. (b) Results of the traditional thinning method using the data from only the Wenzhou radar. (c) Results of the improved observation operator with an analysis unit of 12 km × 12 km using the data from only the Wenzhou radar. (d) As in (c), but using the data from all five radars. The location of each radar station (filled star) and the center of Typhoon Fitow (green dot) are indicated.

Citation: Monthly Weather Review 145, 10; 10.1175/MWR-D-17-0002.1

b. Numerical modeling system configuration

The WRF Model was used to conduct the numerical simulations; it is a state-of-the-art atmosphere modeling system designed for both meteorological research and numerical weather prediction (Skamarock et al. 2008; http://www2.mmm.ucar.edu/wrf/users). The prognostic variables in WRF include velocity components u and υ in the Cartesian coordinate, vertical velocity w, perturbation potential temperature, perturbation geopotential, perturbation surface pressure of dry air, and hydrometeors (water vapor mixing ratio, rain/snow mixing ratio, and cloud water/ice mixing ratio).

The model physics of the numerical modeling system include the new Thompson microphysics scheme (Thompson et al. 2008), the new Rapid Radiative Transfer Model for GCMs (RRTMG) shortwave and longwave radiation parameterizations (Iacono et al. 2008), the Yonsei University planetary boundary layer scheme (Hong et al. 2006), the revised Monin–Obukhov mixed-layer scheme (Jiménez et al. 2012), and the unified Noah land surface model (Chen and Dudhia 2001). With a horizontal resolution of 3 km, the cumulus parameterization is turned off (Schwitalla and Wulfmeyer 2014). The same domain as that used in the single analysis unit experiments was used (see Fig. 4). The background of initial conditions and the lateral boundary conditions (LBCs) are from 6-hourly ERA-Interim reanalysis (Dee et al. 2011) at 0.75° resolution.

Fig. 4.
Fig. 4.

Analysis and prediction domain at 3-km horizontal resolution, with the best track locations of Typhoon Fitow marked at 1-h intervals from 0600 UTC 6 Oct to 0000 UTC 7 Oct 2013. The locations of the radar stations (filled stars), the maximum Doppler range of the radar data (circle), and the terrain (m, gray shading) are indicated.

Citation: Monthly Weather Review 145, 10; 10.1175/MWR-D-17-0002.1

GSI, the same as the single analysis unit experiments, was used with the default background error covariance derived from NAM (Hu et al. 2015). In addition, a constant observation error (2 m s−1) is used in this study, similar to that used in Min et al. (2007) and Zhao et al. (2012). The analysis unit for the new operator was chosen to be 4 times the model resolution (i.e., 12 km × 12 km).

c. Experimental setup

To facilitate the comparison of the two operators, we designed three experiments: Exps CTL, RW, and IVAP (Fig. 5). Exp CTL was designed to give the reference results without any radar data, was started at 0600 UTC 6 October 2013 from the ERA-Interim data, and was followed by 18-h forecasts covering the landfall and postlandfall periods of Fitow (2013). Exp RW used the traditional observation operator in Eq. (2), and by cycling assimilated radar data from 0600 to 1200 UTC with an interval of 1 h, 12-h forecasts were then launched from 1200 UTC. Exp IVAP was the same as Exp RW, except it used the improved observation operator in Eqs. (6) and (7). The impacts on the horizontal wind, track, and intensity of Typhoon Fitow were compared and analyzed when using the two observation operators that assimilated radar radial velocity.

Fig. 5.
Fig. 5.

Flowchart of Exp CTL and the Exps assimilating radar data via the traditional observation operator (RW) and the improved observation operator (IVAP). Each upward arrow indicates the time when the radar radial velocity is assimilated. A 12-h forecast is carried out, following the final analysis at 1200 UTC 6 Oct 2013 in each Exp.

Citation: Monthly Weather Review 145, 10; 10.1175/MWR-D-17-0002.1

d. Results and discussion

1) Analysis increments

The impacts of radar data during the assimilation cycles were analyzed first. The minimum seal level pressure (MSLP) (Fig. 6a) and the maximum wind speed (MWS) (Fig. 6b) in the ERA-Interim background before the first analysis were about 37 hPa higher and 21 m s−1 weaker, respectively, than the observations from the official best track data from the China Meteorological Administration (CMA). The intensity increased in all three experiments, especially in Exps RW and IVAP, which frequently assimilated radar radial velocities. The MSLP (MWS) error decreased to 35 hPa (−8 m s−1) at the end of the cycles (1200 UTC) in Exp RW, while it decreased to 31.5 hPa (−8 m s−1) in Exp IVAP. It is worth noting that the analysis error in MWS decreased more significantly than that in MSLP. This is because the GSI is a univariate analysis system, and the wind field was updated by directly absorbing radial velocity observations through the data assimilation, while the change in surface pressure is the result of model adjustment to the analysis. In additional, there was larger uncertainty in estimating MSLP errors than in estimating MWS errors (Zhao et al. 2012).

Fig. 6.
Fig. 6.

The (a) MSLP and (b) MWS during the data assimilation period from Exps CTL, RW, and IVAP.

Citation: Monthly Weather Review 145, 10; 10.1175/MWR-D-17-0002.1

To better understand the behavior of radar radial velocity assimilation, the horizontal wind component increments at 3-km height after the last analysis cycle were plotted in Fig. 7. For Exp RW, the analysis produced larger wind increments with a much better organized cyclonic structure (Fig. 7a) than that in CTL, which is consistent with the larger decrease in MWS error shown in Fig. 6b. We can see that there were two clear regions with increasing wind speed to the east and south of Wenzhou radar station that were associated with the large negative and positive radial velocities observed, respectively. This is because the wind field was directly updated by ingesting the observed large radial velocity via the traditional observation operator. Similar behavior can be seen in Exp IVAP, except that the magnitude was larger (Fig. 7b). Furthermore, obvious increments can be found in the region between the Wenzhou radar station and the center of the enhanced cyclone, which can be shown more clearly in the next subsection of the analysis of tangential velocity. It is worth noting that the wind direction was orthogonal to the radial direction in this region and that the observed radial velocity was nearly zero. Thus, larger wind increments could be found in Exp IVAP but not in Exp RW, since additional tangential wind information was ingested by the improved observation operator.

Fig. 7.
Fig. 7.

Horizontal wind increments at z = 3 km for the last analysis (1200 UTC) from (a) Exp RW and (b) Exp IVAP. The wind speed (shading), the location of the radar stations (filled stars), and the typhoon centers in the background (purple dot) and observation fields (green dot) are indicated.

Citation: Monthly Weather Review 145, 10; 10.1175/MWR-D-17-0002.1

2) Radial and tangential velocities of the analysis wind field

Figure 8a shows the observed radial velocity at the lowest elevation (0.5°) of the Wenzhou radar (which was the nearest radar to the typhoon center), with one large negative velocity region to the east and one large positive velocity region to the south, indicating an intense cyclone system. However, two extreme velocity regions appeared to the northeast and southwest of the Wenzhou radar in CTL that were associated with the underestimation of intensity and the southwest position error of the typhoon (Fig. 8b). With the assimilation of radial velocity by the traditional observation operator, a more reasonable distribution of radial velocity was simulated in Exp RW; especially, the extreme velocity regions were reproduced as a result of directly absorbing the large radial velocity observations in these two regions (Fig. 8c). Further improvement of the distribution of radial velocity can be found in the IVAP Exps (Fig. 8d). Reasonable cyclone structure and position were produced as a result, namely, the extreme velocity regions matched the observation much better. These increments (Figs. 8c,d) illustrate that both operators can ingest radar radial data but that the new observation operator is better.

Fig. 8.
Fig. 8.

The radial velocity (shading) and wind field (vector) at the lowest elevation (0.5°) of the Wenzhou radar station at 1200 UTC 6 Oct 2013: (a) observed radar radial velocity (no vector), (b) Exp CTL, (c) Exp RW, and (d) Exp IVAP. The location of the radar station (filled star) and the approximate center of the observed typhoon (green dot), near the lower-right corner of each panel, are indicated.

Citation: Monthly Weather Review 145, 10; 10.1175/MWR-D-17-0002.1

Correspondingly, the tangential wind field (relative to the radar) and its increments are retrieved and plotted in Figs. 9b–d. Figure 9b shows the calculated background tangential velocity as the baseline, and indicates large tangential velocities appeared to the northwest and south of the Wenzhou radar. It is not surprising that small tangential velocity increments in Exp RW can be found (Fig. 9c). On the other hand, larger increments were found to the southeast of the Wenzhou radar in Exp IVAP (Fig. 9d), where the radial velocity was nearly zero (Fig. 9a). The reason is that the tangential velocity information was ingested through spatial distribution characteristics of the radial velocity within the analysis unit, as implied by Eqs. (6) and (7). The increments of tangential velocity were related to the northeast adjustment of the typhoon position and the enhanced intensity in IVAP (Fig. 7b).

Fig. 9.
Fig. 9.

The radial and tangential velocities (shading) and wind field (vector) at the lowest elevation (0.5°) of the Wenzhou radar station at 1200 UTC 6 Oct 2013: (a) observed radar radial velocity and the background wind field from Exp CTL, (b) the tangential velocity and its direction from Exp CTL, (c) the increment of tangential velocity between Exps RW and CTL, and (d) the increment of tangential velocity between Exps IVAP and CTL. The location of the radar station (filled star) and the approximate center of the observed typhoon (green dot), near the lower-right corner of each panel, are indicated.

Citation: Monthly Weather Review 145, 10; 10.1175/MWR-D-17-0002.1

3) Typhoon structures

Figure 10 shows the sea level pressure and surface wind speed from CTL after a 6-h integration, and from Exps RW and IVAP after the last analysis cycle (at 1200 UTC 6 October 2013). The intensity was too weak in CTL, with an MSLP bias of 37 hPa and an MWS bias of −21 m s−1 compared to the CMA best track data. Fitow was significantly stronger in Exps RW and IVAP, with the MWS error reduced to about −8 m s−1 in both experiments. The vortex in Exp IVAP was the strongest with larger wind speed north of the typhoon center and with the MSLP error reduced to about 31.5 hPa (Fig. 10).

Fig. 10.
Fig. 10.

Analyzed SLP (thick solid contour, hPa), surface wind speed (shading, m s−1), and wind barbs for Typhoon Fitow at 1200 UTC 6 Oct 2013 from (a) Exp CTL, (b) Exp RW, and (c) Exp IVAP. The approximate center of the observed typhoon (black dot), near the domain center in each panel, is indicated.

Citation: Monthly Weather Review 145, 10; 10.1175/MWR-D-17-0002.1

The azimuthally averaged vertical structure of the typhoon is presented in Fig. 11. In CTL, the vortex was weak and broad (Fig. 11a), characterized by a large radius of maximum tangential wind (RMTW, relative to the typhoon center) of ~170 km (contours in Fig. 11a) and by a weak warm core at 350 hPa (contours in Fig. 11d). These deficiencies were improved in Exps RW and IVAP, with the RMTW reduced to 130 and 100 km, respectively. Although the RMTW was still too large [this value was only about 28 km in the Joint Typhoon Warning Center (JTWC) best track data; http://www.usno.navy.mil/NOOC/nmfc-ph/RSS/jtwc/best_tracks/wpindex.php], the improvements can be found when ingesting radial velocity in both Exps RW and IVAP. With the improvement of vortex strength, the stronger absolute vorticity can be found near the typhoon eye, especially in Exp IVAP. Thus, larger reflectivity was produced that was associated with stronger vertical convection. These results illustrate that assimilating radial velocity can improve typhoon circulation when using the tradition observation operator, which is consistent with the findings of existing studies (e.g., Zhao and Jin 2008; Zhao et al. 2012), and that the improvements are more significant when using the improved observation operator.

Fig. 11.
Fig. 11.

Azimuthally averaged tangential wind (contours with 2.5 m s−1 intervals) and reflectivity (shading, dBZ) from (a) Exp CTL, (b) Exp RW, and (c) Exp IVAP at 1200 UTC 6 Oct 2013; (d)–(f) as in (a)–(c), but for horizontal temperature deviation (contours with 1.0°C intervals) and absolute vorticity (shading, 10−5 s−1).

Citation: Monthly Weather Review 145, 10; 10.1175/MWR-D-17-0002.1

4) Track and intensity predictions

The predicted typhoon track, MSW, and MSLP from Exps CTL, RW, and IVAP are compared with the best track data in Fig. 12 for the 12-h forecast period from 1200 UTC 6 October to 0000 UTC 7 October 2013. As shown in Fig. 12a, the predicted typhoon in CTL moved southward along the coastline, made landfall at about 120 km southwest of the observed landfall site, and then moved westward and disappeared 5 h later. The 12-h mean track error in CTL was about 75.9 km, and the track error increased obviously after 1600 UTC (2 h before the landfall; Fig. 12b). After assimilating the radial velocity in Exp RW using the traditional observation operator, the 12-h mean track error decreased to about 59.7 km, with clearly shown track improvement in Fig. 12a. By using the improved observation operator, Exp IVAP gave the best results, with the predicted typhoon track being the closest to the best track data (Fig. 12a) and the smallest 12-h mean track error of 46.1 km. Note that the error forecasted by the CMA’s operational NWP system (T639 model, whose resolution is about 50 km) was 82.1 km. These results indicate that the assimilation of radar radial velocity had a positive impact on the track forecast and demonstrate the superiority of the improved observation operator.

Fig. 12.
Fig. 12.

The 12-h predicted (a) tracks, (b) track errors, (c) MSLP (hPa), and (d) MWS (m s−1) of Typhoon Fitow from 1200 UTC 6 Oct to 0000 UTC 7 Oct 2013.

Citation: Monthly Weather Review 145, 10; 10.1175/MWR-D-17-0002.1

Figure 12c compares MSLPs in Exps CTL, RW, and IVAP. Although there were still large overestimations of MSLP, Exp IVAP reproduced an MSLP of about 980 hPa, which was better than both Exps CTL and RW; specifically, Exp IVAP reduced the error by about 11 and 5.3 hPa compared to Exps CTL and RW, respectively. Greater improvement can be found in MWS (Fig. 12d). The MWS in CTL reached only about 35 m s−1, while the MWS in Exps RW and IVAP increased to about 38 and 43 m s−1, respectively; the observation was 42 m s−1. These improvements can be attributed to the improved vortex intensity and structure in the radar radial wind assimilation experiments, especially when using the improved observation operator.

5. Summary and perspectives

In this study we examined an improved observation operator for Doppler radar radial velocity assimilation using the GSI system and compared it with the traditional observation operator. Unlike the traditional observation operator, which simply ingests radial information about super-obs points, the new observation operator has the following advantages. It assimilates observation parameters calculated from radial velocity and its spatial distribution characteristics, and it can then provide information about tangential wind, which cannot be observed by the radar directly. In addition, the improved observation operator uses a uniform area in both radar and model coordinates; therefore, it has a thinning function without inducing interpolation errors and retains the spatial distribution information about the raw data.

The performance of the improved observation operator was evaluated through single analysis unit experiments using different analysis units. The distribution of the analysis wind increment of the improved operator became closer to the observation as the analysis unit became wider, as a result of ingesting more wind information into the assimilation system. Note that the traditional observation operator can be treated as a specific form of the improved observation operator when the analysis unit becomes small.

Three experiments, based on the WRF Model, were carried out in a case study of Typhoon Fitow (2013), to examine the performances of different operators in assimilating Doppler radial velocity. The increments of the results indicated that both operators had the capability to ingest radial velocity information and produced a more reasonable typhoon structure, which was weak in Exp CTL. The radial and tangential velocities were further improved by using a new observation operator in Exp IVAP. Because of the improved vortex intensity and structure, greater improvements were realized in the track and intensity predictions of the 12-h forecast.

All of these analyses indicated that the improved observation operator had good performance in Doppler radar radial velocity assimilation. However, there are still problems that need further research. The vertical wind component should be considered and its effects should be examined in case studies. From the results of the single analysis unit experiments, we noticed that different analysis unit sizes could affect the analysis results. In this study, the analysis unit size was chosen to be 4 times the model resolution. However, if the analysis unit size is too small relative to the model grid size, then limited tangential information can be obtained. When the analysis unit size becomes too big, a lot of detailed information about mesoscale or convective-scale weather events will be abandoned. The impact of the size of the analysis unit on a real case should be investigated in future research.

Acknowledgments

This work is supported by the National Basic Research Program of China (Grant 2013CB430101), the National Natural Science Foundation of China (Grant 41375056), the National Key Technology R&D Program of China (Grant 2012BAC22B02), and the National Innovation Project for Meteorological Science and Technology of China: Quality Control, Fusion, and Reanalysis of Meteorological Observations. We gratefully acknowledge Prof. Fang Zhao and Prof. Chunxiao Ji for providing the radar data, Dr. Meiyin Dong for assistance in data analysis, and Dr. Zuojun Yu for English editing. The initial and lateral boundary conditions used in the model are from the ECMWF (http://apps.ecmwf.int/datasets/data/interim-full-daily), and the raw radar data are obtained from the Zhejiang Meteorological Bureau.

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