1. Introduction
The accuracy of convection-permitting numerical weather prediction (NWP) relies not only on resolving the convective storms themselves, but also on properly representing the large-scale environments where the storms initiate, evolve, and dissipate. There is a wide variety of meteorological observations available, either sampling the environmental conditions or representing the convective systems themselves. It is a crucial challenge to accurately estimate the atmospheric state from synoptic scale to convective scale by properly assimilating these different scale observations and is also one of the keys to improving short-term convection-permitting NWP (Gustafsson et al. 2018).
Early studies on convective-scale data assimilation (DA) focused more on how to effectively utilize Doppler radar data that provide high-resolution dynamical and microphysical information within convection for improving short-term convective-scale forecasting with NWP models. Various methods were applied to radar DA and promising results were obtained in a large number of studies, demonstrating the vital role of radar DA in convection-permitting NWP (see Sun et al. 2014; Gustafsson et al. 2018 for review). However, it has also been found that the benefits of assimilating high-resolution radar data may decline rapidly because the emphasis of convective-scale high-resolution DA can cause distortion of large-scale environments, resulting only in a short-lived forecast skill enhancement (Majumdar et al. 2021). Therefore, it is vitally important to optimally assimilate both the large-scale and convective-scale observations such that an accurate convective-scale analysis is produced while the balance in the convective environment is maintained.
Different multiscale DA strategies have been developed to assimilate multisource observations to improve multiscale analysis. The two-step assimilation method is a common multiscale DA strategy and has been successfully applied to both the three-dimensional variational (3DVar) DA method (Xie et al. 2011; Gao et al. 2013; Xu et al. 2016; Tong et al. 2016; Gao et al. 2018) and four-dimensional variational (4DVar) DA method (Carrier et al. 2019; Sun et al. 2020). In the two-step assimilation method, conventional observations are assimilated first, followed by a second step to assimilate high-resolution observations, such those from radar. In the different assimilation steps, the background error covariance (BEC) is adjusted to correspond to different observation types, either by tuning the BEC length scales (Xie et al. 2011) or splitting BEC into different scales (Li et al. 2015). Despite the successful application of the two-step assimilation method in variational DA methods, the 3DVar method has limited capability in convection-permitting NWP due to its static, homogeneous, and isotropic BEC (Gao and Stensrud 2014). For the ensemble Kalman filter (EnKF; Evensen 1994) DA method, studies on multiscale DA focused more on resolving synoptic- to convective-scale features with different localization scales for different observation types (Zhang et al. 2009), which is possible because observations at a given time are sequentially assimilated in EnKF. The EnKF-based multiscale DA method has obtained promising results by assimilating multisource observations, especially radar data, in various studies (Snook et al. 2015; Johnson et al. 2015; Degelia et al. 2018). However, due to the high computational cost, the EnKF with limited ensemble members suffers from the issue of sampling errors (Evensen 2004), limiting its applications to operational convection-permitting NWP.
The hybrid ensemble–variational (EnVar; Lorenc 2003) DA method has been used widely in recent years, thanks to its ability to combine advantages and mitigate disadvantages of the variational and EnKF DA methods. While the hybrid EnVar technique has been shown promising results for large-scale analysis and prediction and implemented in operational applications (Bonavita et al. 2016; Clayton et al. 2013; Lorenc et al. 2015; Kleist and Ide 2015a,b; Buehner et al. 2013, 2015), its application to convection-permitting NWP, however, is still undergoing (Gao and Stensrud 2014; Gao et al. 2016; Benjamin et al. 2016; Wang and Wang 2017; Tong et al. 2020; Kong et al. 2021). As in the case of variational or ensemble DA, one of the keys for success in the convective-scale application of the hybrid EnVar method is to obtain accurate multiscale analysis by considering the different representative scales of radar and conventional observations.
In this study, a two-step approach following Tong et al. (2016) was developed for a hybrid 3D-EnVar system in an attempt to obtain improved analyses for atmosphere convection as well as convective environment. The hybrid EnVar system was based on the 3DVar in WRFDA (Barker et al. 2012) and the EnKF in DART (Data Assimilation Research Test bed) (Anderson et al. 2009). This two-step approach enables the applications of different BEC tuning factors and different hybrid weights for radar and conventional observations. Furthermore, the EnKF run that is used to generate the ensemble BEC excludes radar DA in order to avoid producing a flow-dependent BEC dominated by convective-scale uncertainty. The multiscale hybrid EnVar strategy was evaluated using a convective rainfall case occurred on 15 July 2015 during the PECAN (Plains Elevated Convection At Night; Geerts et al. 2017) field campaign first by comparing it with 3DVar and EnKF and then through a series of sensitivity experiments.
The rest of the paper is organized as follows. In section 2, the methodology of the multiscale hybrid EnVar is described. The model configuration, experimental design, and case description are given in section 3. The multiscale hybrid EnVar is evaluated with the convective rainfall case in section 4 by comparing it with 3DVar and EnKF. Section 5 conducts a series of sensitivity experiments to evaluate the role of the two-step assimilation strategy and the influence of radar data assimilation in the EnKF update on hybrid EnVar. The summary and conclusions are given in section 6.
2. Methodology
a. Cost function of hybrid EnVar
b. Design of the multiscale hybrid EnVar
The hybrid EnVar algorithm used in this study is from a research version of WRFDA similar to V3.9.1 but with a few upgrades including a neighborhood-based low reflectivity assimilation scheme (Gao et al. 2018) and a background-dependent microphysics partition reflectivity assimilation scheme (Chen et al. 2020). The ensemble BEC was provided by forecasts initialized by the ensemble adjustment Kalman filter (EAKF; Anderson 2003) ensemble data assimilation system in DART. The dynamic blending scheme of Feng et al. (2020) that blends WRF forecast with Global Forecast System (GFS) forecast was implemented to the ensemble forecasts as well as the hybrid EnVar deterministic forecast to reduce large-scale errors commonly found in limited-area models. Schwartz et al. (2021) has recently reported the positive impact of a similar blending scheme on the performance of EnKF, and Feng et al. (2021) also showed the benefits of employing the dynamic blending scheme in an operational regional 3DVar system.
The conventional observations, including aircraft reports, meteorological aerodrome reports, surface synoptic observations, ship reports, and soundings from the Global Transmission System (GTS) were assimilated to retrieve synoptic-scale and mesoscale weather conditions. Radar radial velocity and reflectivity data were assimilated to resolve the dynamic and microphysical states within convective systems. A total of 17 NEXRADs were assimilated in the inner domain D02 (see Fig. 1 for the radar locations). The radar radial velocity data were directly assimilated following Xiao et al. (2005) and the radar reflectivity data were assimilated using an indirect method following Wang et al. (2013). A background-dependent microphysics partition scheme was employed to retrieval rainwater, snow, and graupel species from radar reflectivity observations (Chen et al. 2020; Chen et al. 2021). The neighborhood-based no-rain assimilation scheme (Gao et al. 2018) was applied to assimilate the reflectivity observations below −5 dBZ to suppress spurious convection.
Experimental domains of 15 km (D01) and 3 km (D02). The black dots indicate radar sites, and the topography height (m) is shaded.
Citation: Monthly Weather Review 150, 9; 10.1175/MWR-D-21-0325.1
The flowchart of the multiscale hybrid EnVar is shown in Fig. 2a. The data assimilation was conducted on a nested domain (see Fig. 1) with 15- and 3-km grid spacings for the outer and inner domains, respectively. The background for the first cycle was from the 0.25° × 0.25° GFS analysis, and the conventional and radar observations were assimilated from T (start time of the first assimilation cycle of hybrid EnVar) to T + 9 with continuous hourly cycles. In the outer domain, only conventional observations were assimilated. Starting from T + 3, the dynamic blending scheme was applied to the outer domain every 3 h prior to DA. In the inner domain, radar data and conventional observations were assimilated separately in two successive steps to obtain the multiscale analysis. Different from previous studies which assimilated conventional data in the first step (Gao et al. 2013; Tong et al. 2016; Gao et al. 2018), in this study, the radar data were assimilated in the first step, and the conventional observations were assimilated in the second step. The reason for reversing the order is to retain more large-scale analysis obtained from conventional DA, and it will be explained in more details in section 5.
Flow charts of (a) multiscale hybrid EnVar and (b) EAKF for the generation of 50 ensemble forecast members. In both charts, T indicates the first analysis time of inner domain DA and is 1800 UTC 14 Jul 2015 for the study case. BLD indicates dynamic blending applied in the outer domain.
Citation: Monthly Weather Review 150, 9; 10.1175/MWR-D-21-0325.1
The key to a successful hybrid EnVar analysis lies in the flow-dependent BEC it introduces, so the quality of the ensemble members is of vital importance. In this study, we used the EAKF in DART, an EnKF-based ensemble DA method, to update ensemble members for ensemble BEC generation in our multiscale hybrid EnVar. Shen et al. (2018) showed that using the EnKF to update ensemble members for ensemble BEC generation in hybrid EnVar may have some advantages over the Ensemble of data assimilation (EDA; Houtekamer et al. 1996) method. A total of 50 ensemble members were initialized at T − 30 (hours) by perturbing the Global Ensemble Forecast System (GEFS) 21-member ensemble analyses using the WRFDA Random-CV tool (Barker 2005). Each of the ensemble members was updated with the process illustrated by the flowchart in Fig. 2b. A 24-h spinup was carried out in the coarser domain taking into consideration that the 1° × 1° GEFS analysis was much coarser than our experimental model resolution. The ensemble in the outer domain was then updated every 3 h by assimilating conventional observations using the EAKF starting from T − 6, and the dynamic blending scheme was applied in the outer domain prior to DA. At the second assimilation cycle (T − 3), the ensemble members of the inner domain were initialized from the analysis of the outer domain. After a 3-h spinup, inner domain data assimilation was conducted from T to T + 6 with hourly cycles and 3-h ensemble forecasts were carried out valid at T, T + 3, and T + 6. In the EAKF updating, the RTPS (Relaxation to prior spread) covariance inflation method (Whitaker and Hamill 2012) was employed to keep the analysis spread 95% of the background spread. The horizontal ensemble covariance localization scale for conventional observation assimilation was 150 km, while no vertical localization was applied. For the first cycle valid at T, the ensemble BEC was calculated from the 3-h ensemble forecasts initialized at T − 3, while for the cycles from T + 1 to T + 9, the 1-, 2-, or 3-h ensemble forecast, whichever was the latest, was used to calculate the ensemble BEC. Considering that the 1-h ensemble forecasts tend to have spinup problems and be less balanced, we used the 1- to 3-h ensemble forecasts to compute the flow-dependent BEC rather than the 1-h ensemble forecasts refreshed at each hourly analysis cycle. It is worth noting that the ensemble members and the hybrid EnVar were one-way coupled, i.e., the ensemble members were used to calculate the flow-dependent BEC without being re-centered around the hybrid EnVar analysis.
c. Background error covariance
The climatology BEC was calculated by the WRFDA GEN_BE (Barker et al. 2004) tool with samples generated by the National Meteorological Center (NMC) method (Parrish and Derber 1992) using the differences between 24- and 12-h forecasts valid at the same time during a 1-month period (15 June–15 July 2015). The selected control variables in this study are eastward and northward velocity components (U, V), surface pressure (Ps), temperature (T), pseudo relative humidity (RHs), cloud water mixing ratio (Qc), ice water mixing ratio (Qi), rainwater mixing ration (Qr), snow mixing ratio (Qs), and graupel mixing ratio (Qg). No multivariate correlations were considered among these control variables. U and V were selected as the momentum control variables in order to better assimilate radar radial velocity observations (Sun et al. 2016), and the five hydrometeor control variables enabled the assimilation of retrieved hydrometeors from radar reflectivity data. The nine control variables in the climatology BEC were also used as the alpha control variables in the flow-dependent BEC except that water vapor mixing ratio (Qv) instead of RHs was applied as the humidity alpha control variable.
Because of uncertainties involved in the climatology BEC modeling, it is a common practice to tune the BEC empirically (Xu et al. 2020). The two-step procedure enables different tuning factors for the assimilations of radar and conventional observations. It also allows the choice of different weighting ratios between the climatology and ensemble BECs. Table 1 lists the climatology BEC rescaling factors for variance (var_scaling) and length scale (len_scaling) along with the ensemble BEC localization scale and weight in the hybrid EnVar. The climatology BECs for conventional DA in both domains and for radar DA in D02 were tuned based on a general assumption that the BEC varies with respect to model resolution and representative scale of observation. The specific tuning factors in Table 1 were determined via single observation tests by making the spread of the increment of a single observation from the climatology BEC similar to that from the ensemble BEC that was localized with a scale of 150 km for conventional data, and a smaller scale of 30 km for radar to extract convective-scale information. The 150-km horizontal localization scale used for conventional DA is close to that used in Montmerle et al. (2018), and the 30-km horizontal localization scale used for radar DA is a middle value between 60 km for radial wind (Li et al. 2012) and 18 km for reflectivity data (Kong et al. 2018). No vertical localization was applied in conventional DA, while a 1.5-km vertical localization scale was applied in radar DA. The weighting of ensemble BEC was set larger for radar DA considering that the convective-scale motion that is attained by assimilating radar observations is more flow-dependent. For an illustrative example, the increments for u-wind, temperature, and water vapor mixing ratio from a set of 3DVar, hybrid EnVar, and EnVar single observation tests in the inner domain are shown in Fig. 3 using the parameters given in Table 1. Compared with hybrid EnVar and EnVar, the increments from 3DVar have a centric structure, while the increments from EnVar and hybrid EnVar show obvious flow-dependent patterns thanks to the ensemble BEC it employed. It is also shown that the extents of the significantly large increments of all three variables in 3DVar are generally comparable to those in hybrid EnVar, indicating that the tuning of the climatology BEC was properly done. It is also worth noting that the hybrid EnVar gets rid of the noisy increments in EnVar, indicating that the hybrid EnVar method is effective in removing spurious spatial correlations in the ensemble BEC and could be advantageous over the pure EnVar method.
Analysis increments of (a)–(c) U, (d)–(f) T, and (g)–(i) Q from assimilating a set of single observations of U, T, and Q using (left) 3Dvar, (center) hybrid EnVar, and (right) EnVar methods. The weights of ensemble BEC used in 3DVar, hybrid EnVar, and EnVar are 0, 0.5, and 1, respectively, and the localization scale of ensemble BEC is 150 km. The innovations of T, U, and Q are 1 m s−1, 1 K, and 10 g kg−1, respectively, and the observation errors are the same as the innovations.
Citation: Monthly Weather Review 150, 9; 10.1175/MWR-D-21-0325.1
Specifications of the climatology and flow-dependent BEC. The Var_scaling and Len_scaling are factors that multiply the variance and length scale of the climatology BEC. Conv stands for conventional, and “—” means no vertical localization was applied.
3. Descriptions of model configuration, experiments, and case
a. Model configuration
The Weather Research and Forecasting (Skamarock et al. 2008) Model V3.9.1 was used as the numerical model in this study. All experiments were conducted on the same experimental domains shown in Fig. 1. It has two nested domains with the horizontal resolutions of 15 km (outer domain) and 3 km (inner domain) and numbers of horizontal grid points of 212 × 160 and 411 × 321, respectively, and the two-way nesting was applied. The number of vertical levels is 51 and the model top is set to 50 hPa. The selected physical parameterizations for both domains are Mellor–Yamada–Janjić (MYJ) planetary boundary layer model (Janjić 1994), Thompson microphysics scheme (Thompson et al. 2004), Noah land surface model (Chen and Dudhia 2001), Rapid Radiative Transfer Model for GCMs (RRTMG) longwave radiation, and RRTMG shortwave radiation (Iacono et al. 2008). The Kain–Fritsch (KF) cumulus parameterization scheme (Kain and Fritsch 1990) is only applied in the outer domain.
b. Experimental design
In this study, six experiments (summarized in Table 2) were conducted. The experiment Exp-HYB used the multiscale hybrid EnVar strategy described in section 2 and regarded as the “optimal” configuration. The experiments Exp-3DVar and Exp-EAKF were conducted as benchmarks for Exp-HYB to demonstrate the benefits of hybrid EnVar on analysis and forecasting. The experiment Exp-3DVar was the same as Exp-HYB except that the flow-dependent BEC was not used, reducing it to a 3DVar experiment. The 50-member hourly cycling EAKF experiment Exp-EAKF followed the same strategy as shown in Fig. 2a but used DART to assimilate radar and conventional observations sequentially in the inner domain from T to T + 9. Considering that the radar data contain mainly localized information, the ensemble covariance localization scale used in Exp-EAKF was set to 30 km horizontally and 1.5 km vertically for radar DA. Even though various studies have shown the benefits of assimilating radar data using EnKF methods with a very high frequency like 15 min or less (Chang et al. 2014; Wheatley et al. 2015; Bick et al. 2016; Putnam et al. 2019), we used hourly cycling configuration in Exp-EAKF to make a fair comparison with 3DVar and hybrid EnVar. An hourly cycle system with less computation cost makes a DA system more likely to be implemented operationally.
Summary of experiments.
The other three experiments were designed to examine the impact of the multiscale strategy in the hybrid EnVar. The experiments HYB-OneStep and HYB-GTSRad were conducted to evaluate the impact of the two-step assimilation approach. In HYB-OneStep, conventional data and radar data were assimilated simultaneously with the same BEC parameters as for radar DA in Exp-HYB, in contrast to the two-step procedure used in Exp-HYB and HYB-GTSRad where the BEC and ensemble weight were tuned differently for conventional and radar observations as shown in Table 1. The experiment HYB-GTSRad was the same as Exp-HYB but radar data were assimilated after conventional observations rather than vice versa. The experiment HYB-EnRad was similar to Exp-HYB but with radar data assimilated in the EAKF ensemble updates. The comparison between Exp-HYB and HYB-EnRad is to explore whether it is necessary to update ensemble members with radar DA in the EAKF for ensemble BEC generation in hybrid EnVar.
c. Case description
The convective rainfall case occurred from 1800 UTC 14 July to 1500 UTC 15 July 2015 during the PECAN field campaign. The convective system was initiated in the Colorado mountain region and then developed as it moved to the plains under large-scale environmental forcing. The evolution of the observed composite radar reflectivity for this convective case is shown in Fig. 4. At 2100 UTC 14 July (Fig. 4a), scattered convective cells initiated on the mountains in Colorado. In the next 3 h, more convective cells developed and moved eastward, and a north–south line system was organized at 0000 UTC 15 July (Fig. 4b). The convective line system were further enhanced and moved to the east border of Colorado at 0300 UTC 15 July (Fig. 4c). At 0600 UTC 15 July (Fig. 4d), the main body of the convective system moved farther eastward to the west-northwest of Kansas and meanwhile a west–east thin convective line occurred in Nebraska. At 0900 and 1200 UTC 15 July, the main system moved northeastward across the border of Nebraska and Kansas becoming broader at the rear of the leading convection and weakened (Figs. 4e,f).
The composite radar reflectivity observations (dBZ) valid at (a) 2100 UTC 14 Jul, (b) 0000 UTC 15 Jul, (c) 0300 UTC 15 Jul, (d) 0600 UTC 15 Jul, (e) 0900 UTC 15 Jul, and (f) 1200 UTC 15 Jul 2015.
Citation: Monthly Weather Review 150, 9; 10.1175/MWR-D-21-0325.1
For this study case, the cold start time of data assimilation (T in Fig. 2) is 1800 UTC 14 July 2015. A total of 10 hourly cycles with three 9-h forecasts launched at 2100 UTC 14 July, 0000 UTC 15 July, and 0003 UTC 15 July were conducted.
4. Comparing hybrid EnVar with 3DVar and EAKF
To evaluate the performance of the multiscale hybrid EnVar, we first compare the Exp-HYB with EXP-3DVar and Exp-EAKF in terms of both analysis and forecast for the heavy rainfall case. In section 5, we will then examine the sensitivity experiments to evaluate the impact of the hybrid EnVar design strategy.
a. Analysis increments
The wind, temperature, and humidity increments from Exp-3DVar, Exp-HYB, and Exp-EAKF at 0300 UTC 15 July are shown separately for radar data assimilation (Fig. 5) and for conventional data assimilation (Fig. 6). It should be noted that the three DA analyses at 0300 UTC did not have the same forecast background due to continuous cycling. To compare the increment fields of the three experiments relative to a same background, we reran these experiments at 0300 UTC using the same background, i.e., the ensemble mean, assimilating radar data only (Fig. 5) and conventional data only (Fig. 6).
Analysis increment of (top) wind (m s−1), (middle) temperature (K), and (bottom) water vapor mixing ratio (g kg−1) from radar data assimilation at AGL 1.8 km valid at 0300 UTC 15 Jul 2015 for (left) Exp-3DVar, (center) Exp-HYB, and (right) Exp-EAKF. For Exp-EAKF, the fields are from the ensemble mean.
Citation: Monthly Weather Review 150, 9; 10.1175/MWR-D-21-0325.1
As in Fig. 5, but from conventional data assimilation at 1.0 km AGL.
Citation: Monthly Weather Review 150, 9; 10.1175/MWR-D-21-0325.1
By examining the increments from radar DA alone, it is found that Exp-3DVar and Exp-HYB (Figs. 5a,b) produced similar wind increments, mainly due to the assimilation of dense radar radial data in both experiments; however, the impacts of the spatial and multivariate correlations from ensemble BEC were also shown by the larger and wider spread wind increments in Exp-HYB than in Exp-3DVar. In contrast, the wind increments in Exp-EAKF (Fig. 5c) are much localized and concentrated around the high-reflectivity region (see Fig. 4c), which could be due to the fact that radial velocity observations are assimilated only in the regions where there exist large spreads of reflectivity-weighted terminated velocity in DART’s EAKF method. Unlike the wind increments, the temperature increments (Figs. 5d–f) from the three experiments are markedly different. The small increments in both value and coverage in Exp-3DVar resulted from the indirect radar reflectivity assimilation method (Wang et al. 2013) in which the temperature responded to pseudo humidity assimilation within convection. Since there was no multivariate correlation in the climatology BEC, the radar DA in Exp-3DVar was unable to produce temperature increments outside the convective region. In comparison, much larger and wider-spread increments of temperature in Exp-HYB and Exp-EAKF were produced through contributions of multivariate correlation in the flow-dependent BEC. For the water vapor increments (Figs. 5g–i), both Exp-3DVar and Exp-EAKF clearly show the impact of radar reflectivity DA by the high increments in the high-reflectivity region (see Fig. 4c); nevertheless, Exp-HYB not only captured the increments within convection from radar DA but also the relatively large-scale environmental increments from the multivariate correlations and spatial correlations in the flow-dependent BEC. Since Exp-HYB obtained relatively broader wind increments than Exp-EAKF, the multivariate and spatial correlations in the ensemble BEC enabled the wind increments to be transferred to temperature and water vapor fields with broader coverage in Exp-HYB. Although the ensemble BECs for both Exp-HYB and Exp-EAKF were generated by ensemble forecasts via EAKF, the former was from 3-h ensemble forecasts without radar DA but the latter was from 1-h ensemble forecasts with radar DA, which could be another reason for the broader increment coverage in Exp-HYB for both temperature and water vapor.
To illustrate the effect of conventional DA in the multiscale hybrid EnVar scheme, the three experiments were rerun using the same background as in the above radar DA experiments but assimilating conventional data only. Their increment fields are compared in Fig. 6. The main conventional observations at 0300 UTC were from surface stations and aircraft reports, so the increments in Exp-3DVar were obtained mainly through the vertical spread of surface DA and partly from aircraft DA, which generated some large increments in temperature where observations were relatively dense. With the flow-dependent BEC employed in Exp-HYB and Exp-EAKF, however, the cross-correlation produced greater increments in all three fields with multiscale patterns. While both Exp-HYB and Exp-EAKF obtained large positive increments in northwestern Kansas and across the Kansas–Nebraska border, Exp-HYB produced stronger negative temperature increments along the Colorado–Kansas border where the convection occurred. Because of the omission of radar DA in the ensemble BEC of Exp-HYB, larger uncertainties in the convective region were estimated, which enabled larger negative temperature increments by spreading the observed surface cold pool upward via vertical correlation. Since the ensemble BEC in Exp-EAKF were produced with radar DA, it missed the large uncertainties in the observed convection region due to the disturbance of the model forecasted convection with obvious location errors.
The wider increment spread and larger increments around the convective region in Exp-HYB suggests that the strategy in which ensemble BEC is generated without radar DA using EAKF could be one of the important features for a successful multiscale hybrid EnVar system. Our results indicate that the Exp-HYB increments in all three fields can produce increment patterns within convection (mainly from radar DA in hybrid EnVar) as well as in the environment (mainly from ensemble BEC generated without radar DA). In the next section, a sensitivity experiment in which radar DA is included in the ensemble BEC will be compared to further examine the difference made by excluding radar DA in the ensemble BEC generation using EAKF.
b. Quantitative precipitation forecast
To evaluate the performance of the multiscale hybrid EnVar strategy in forecasting precipitation, we first show the 9-h (Fig. 7) and 1-h (Fig. 8) accumulated precipitation forecasts from Exp-3DVar, Exp-HYB, and Exp-EAKF initialized at 0300 UTC and then their quantitative verification results. For Exp-EAKF, we present the “best member” and “worst member” selected by computing the fractions skill score (FSS; Roberts and Lean 2008) of 9-h accumulated precipitation averaged over the three forecasts initialized at 2100, 0000, and 0300 UTC (0.497 and 0.327, respectively, for the 40-mm threshold). The radius of influence for the FSS calculation is 15 km throughout this paper. It is seen from Fig. 7 that the experiment Exp-3DVar under-forecasted the major rainband in Kansas but over-forecasted the precipitation in Nebraska. While the best member from Exp-EAKF forecasted the rainband in Kansas quite well, it over-forecasted the precipitation in Nebraska (Fig. 7e). Moreover, the worst member from Exp-EAKF significantly over-forecasted the precipitation in a large region north of Kansas and south of Nebraska (Fig. 7d). In comparison with the other forecasts, Exp-HYB captured the rainband in Kansas with the right location, although somewhat weaker than that in the observation, and the precipitation in Nebraska without overprediction (Fig. 7c).
The 9-h accumulated precipitation (mm) valid at 1200 UTC 15 Jul 2015 for (a) observations from Stage IV and forecast initialized from 0300 UTC 15 Jul 2015 for (b) Exp-3DVar, (c) Exp-HYB, (d) worst Exp-EAKF member, and (e) best Exp-EAKF member. The contours in (b)–(e) represent observed precipitation over 20 mm.
Citation: Monthly Weather Review 150, 9; 10.1175/MWR-D-21-0325.1
The hourly accumulated precipitation (mm) valid at (left) 0600, (center) 0900, and (right) 1200 UTC 15 Jul 2015 for (a)–(c) observations from Stage IV and forecast initialized from 0300 UTC 15 Jul 2015 for (d)–(f) Exp-3Dvar, (g)–(i) Exp-HYB, (j)–(l) worst Exp-EAKF member, and (m)–(o) best Exp-EAKF member. The contours in (d)–(o) represent observed precipitation over 1 mm.
Citation: Monthly Weather Review 150, 9; 10.1175/MWR-D-21-0325.1
The 1-h precipitation forecasts from the last cycle are compared in Fig. 8 to show their temporal evolution. At 0600 UTC, the main precipitation system was located at the west of Kansas and some weaker precipitations were observed in Nebraska. Exp-3DVar over-forecasted precipitation in southwest Nebraska and southwest of Kansas but missed the strong precipitation in the west of Kansas. Both Exp-HYB and the best EAKF member improved the forecast by successfully capturing the west Kansas precipitation. However, Exp-EAKF’s worst member over-forecasted the main precipitation area in Kansas and the location had a northward bias. At 0900 UTC, both Exp-3Dvar and Exp-EAKF (best and worst) forecasted the precipitation system with obvious northward location biases. In contrast, Exp-HYB not only forecasted the system’s location well but also the structure with the heavier precipitation in the east and the lighter precipitation to its west. By 1200 UTC, a northwest–southeast precipitation band appeared across Kansas–Nebraska border, while an east–west precipitation band appeared in Nebraska. The location errors in both the worst Exp-EAKF member and Exp-3Dvar further increased, while Exp-HYB and the best Exp-EAKF member had relatively smaller location errors even though the former slightly underpredicted the northwest–southeast rainband and the latter overpredicted both bands.
To quantitatively evaluate the precipitation forecast skills of the three DA methods, the categorical performance diagram (Roebber 2009) of 9-h accumulated precipitation against the NCEP Stage IV precipitation data for the three experiments are shown in Figs. 9a–c. The categorical performance diagram combines the probability of detection (POD), the critical success index (CSI), the frequency bias (BIAS), and the success ratio [1 − false alarm ratio (FAR)] in one diagram to overall evaluate the forecast performance. For the 10-mm threshold, Exp-HYB had a slightly better performance than Exp-3Dvar, and both Exp-HYB and Exp-3Dvar performed better than most Exp-EAKF members with higher CSI and POD, and lower FAR. For the 20-mm threshold, most Exp-EAKF members had higher POD than Exp-HYB but with a high-frequency bias, while Exp-3Dvar had lower POD and a low-frequency bias. Exp-HYB performed slightly better than the other two experiments with a frequency bias value close to 1 and a slightly higher CSI. The largest difference among the three experiments appears in the 40-mm threshold diagram where the improved performance by Exp-HYB is evident as the red dot is located closer to the diagonal line and to the top-right corner, indicating higher CSI, smaller precipitation bias, and higher success ratio. Exp-EAKF has higher POD than Exp-HYB but at the expenses of high-frequency bias, lower CSI, and higher FAR, and all Exp-EAKF members have better performance than Exp-3DVar. Figures 9d–f compares the FSSs with respect to forecast hour of the 1-h accumulated precipitation forecasts from the three experiments against the NCEP Stage IV precipitation data. For the 1-mm threshold, the FSS for Exp-HYB was higher than most members of Exp-EAKF up to 6 h and it was also higher than Exp-3DVar in nearly all forecast hours. For the precipitation thresholds of 5 and 10 mm, the FSSs for Exp-HYB were still the highest among the three experiments, and most members of Exp-EAKF show higher skill than Exp-3DVar over the nine forecast hours, especially for the threshold of 10 mm where the all-member mean FSS was higher than Exp-3DVar.
The categorical performance diagram of 9-h accumulated precipitation with thresholds of (a) 10, (b) 20, and (c) 40 mm, and time series of FSS of hourly accumulated precipitation with thresholds of (d) 1, (e) 5, and (f) 10 mm for Exp-3DVar, Exp-HYB, and Exp-EAKF. In (a)–(c), the purple line represents CSI, and the black line represents bias. The light blue dots in (a)–(c) and light blue shading in (d)–(f) indicate the scores of all members, while the blue represents the scores averaged from all members of Exp-EAKF.
Citation: Monthly Weather Review 150, 9; 10.1175/MWR-D-21-0325.1
Generally, Exp-HYB had relatively better forecast skills of precipitation than other two experiments, while Exp-3DVar had the worst performance in precipitation forecasts of higher threshold. It is not surprising that Exp-3DVar had comparable precipitation forecast skills with other two experiments in small threshold because the assimilation of pseudo water vapor observations from reflectivity data provided the convection with suitable water vapor conditions. The improved precipitation forecast skills for higher threshold in Exp-HYB and Exp-EAKF could be the result of the flow-dependent BECs used in these two experiments. They adequately transferred information from radar observations to the model variables through multivariate and spatial correlations, providing the convection with more favorable temperature and humidity conditions.
c. Forecast verification against conventional and radar observations
To further examine the impact of the multiscale hybrid EnVar scheme on short-term forecasts in Exp-HYB, we calculated the forecast errors from the three experiments against conventional observations and radar observations, respectively. All diagnosis results were averaged over the 1–9-h forecasts from the three cycles at 2100 UTC 14 July, 0000 UTC 15 July, and 0300 UTC 15 July.
Since the aircraft observations have better temporal continuity and spatial coverage, it was used to evaluate the large-scale forecast errors for wind and temperature fields. Note that aircraft observations do not have moisture observations, so the moisture field is not verified. The vertical profiles of forecast RMSE and BIAS from the three experiments against aircraft observations (U, V, and T) are shown in Fig. 10. Compared to Exp-3DVar, the forecast errors in Exp-HYB are smaller for all three variables at nearly all levels, indicating the hybrid EnVar produced better large-scale forecasts than the 3DVar method. Compared to Exp-EAKF, Exp-HYB has relatively smaller RMSE for wind fields in the low-level except near the surface and temperature fields below 850 hPa and above 300 hPa. The BIAS curves of Exp-3DVar and Exp-HYB are very close, while Exp-EAKF shows relatively larger positive BIAS for U and T and larger negative BIAS for V.
Vertical profiles of (a)–(c) RMSE and (d)–(f) BIAS of (a),(d) U (m s−1); (b),(e) V (m s−1); and (c),(f) T (K) of 1–9-h forecast against aircraft observations for Exp-3DVar (black line), Exp-HYB (red line), and Exp-EAKF (blue line) averaged over three cycles. For EAKF, the light blue shade indicates the coverage of the RMSE of all members, while the blue line represents the RMSE averaged over 50 members.
Citation: Monthly Weather Review 150, 9; 10.1175/MWR-D-21-0325.1
To evaluate the forecast performances of the three DA methods at convective-scale, radial velocity and reflectivity fields computed from model forecast variables were verified against their radar observations. Figure 11 shows the vertical profiles of RMSE and BIAS of radial velocity and reflectivity, respectively. For radial velocity, the RMSE in Exp-HYB is the least among the three experiments, and Exp-EAKF has slightly smaller forecast errors than Exp-3DVar almost at all levels. Exp-HYB also has the least BIAS of radial velocity, while Exp-EAKF has relatively larger positive BIAS near 3 km and larger negative BIAS above 4 km than Exp-3DVar. For radar reflectivity, the three curves are very close but Exp-HYB shows slightly smaller RMSE over the other two experiments even though with relatively larger negative BIAS below 3 km, and Exp-EAKF has relatively smaller RMSE and BIAS than Exp-3DVar above 5 km.
Vertical profiles of (a),(b) RMSE and (c),(d) BIAS of 1–9-h forecast against (a),(c) radial velocity (RV) and (b),(d) reflectivity (RF) observations for Exp-3DVar (black line), Exp-HYB (red line), and Exp-EAKF (blue line) averaged over three cycles. For Exp-EAKF, the light blue shade indicates the RMSE coverage of all members, while the blue line represents the RMSE averaged of all members.
Citation: Monthly Weather Review 150, 9; 10.1175/MWR-D-21-0325.1
The above verification results against Stage IV precipitation, radar, and aircraft observations indicate that the multiscale hybrid EnVar scheme can improve short-term precipitation prediction, presumably as a result of improved predictions of radial velocity and reflectivity mainly over the convective region as well as wind and temperature variables over a larger region of aircraft observations.
5. Sensitivity experiments of the multiscale hybrid EnVar strategy
In this section, three additional experiments similar to Exp-HYB are presented to examine the sensitivities of three key features in the multiscale hybrid EnVar scheme by excluding each of them, respectively, in each of the experiments. The experiment HYB-OneStep conducted the assimilation of conventional observations and radar observations simultaneously in one step, HYB-GTSRad assimilated conventional data in the first step and radar data in the second step in contrast to Exp-HYB, and HYB-EnRad included radar DA in ensemble updating for ensemble BEC generation contrary to Exp-HYB in which radar DA was not included in the BEC generation.
a. Impact of the two-step assimilation approach
By comparing HYB-OneStep with Exp-HYB, we can obtain an assessment of the contribution of the two-step procedure in improving convective forecasting. In the previous two-step DA approach using 3DVar by Tong et al. (2016), conventional observations were assimilated in the first step and radar data in the second step. However, assimilating high-resolution radar data with reduced length scales in the second step may disturb the large-scale environmental conditions obtained in the first step and lead to decreased forecasting skills in later hours. Here we evaluate the two-step assimilation approach with hybrid EnVar and demonstrate that assimilating radar data before conventional observations is preferable.
Figure 12 shows the time series of FSSs and frequency bias scores of hourly accumulated precipitation forecasts for HYB-OneStep, HYB-GTSRad, and Exp-HYB. The two experiments using the two-step approach (Exp-HYB and HYB-GTSRad) have larger FSSs than HYB-OneStep for the thresholds of 1 and 5 mm in nearly all forecast hours, and Exp-HYB had higher FSS in most hours than HYB-GTSRad except for the hours 2–4. For the higher threshold of 10 mm, both experiments using the two-step assimilation approach have higher FSSs than HYB-OneStep in the first 5 h. For the rest 4 h, HYB-OneStep has relatively higher FSSs than HYB-GTSRad, while Exp-HYB still maintained the benefits of the two-step DA approach with highest FSSs. Unlike the FSS verification, the results of the bias scores are mixed.
(a)–(c) FSS and (d)–(f) frequency bias of hourly accumulated precipitation with thresholds of (a),(d) 1; (b),(e) 5; and (c),(f) 10 mm averaged over three cycles (2100 UTC 14 Jul, 0000 UTC 15 Jul, and 0300 UTC 15 Jul) for Exp-HYB, HYB-GTSRad, and HYB-OneStep.
Citation: Monthly Weather Review 150, 9; 10.1175/MWR-D-21-0325.1
To evaluate why the two-step procedure and assimilating radar data first improved the precipitation forecast, we computed the RMSE and BIAS of DA analyses against aircraft observations averaged over all 10 hourly assimilation cycles in Fig. 13. For the wind fields, the final analyses after both steps from Exp-HYB and HYB-GTSRad have smaller RMSEs than that from HYB-OneStep. Assimilating radar data in first step in Exp-HYB has largest RMSE and BIAS for both U and V in the middle levels (around 700 hPa) and upper levels (around 200 hPa), but the errors are greatly reduced after the conventional data were assimilated in the second step. While in HYB-GTSRad, the radar DA in the second step made the final RMSE and BIAS from HYB-GTSRad greater than that in Exp-HYB, suggesting that the large-scale analysis obtained from the first step may have been disturbed after the radar DA in the second step. Similarly, the second step assimilation of conventional data reduced the RMSE and BIAS in Exp-HYB for temperature, while the errors were increased in the second step in HYB-GTSRad. Nevertheless, HYB-OneStep resulted in smallest RMSE and BIAS errors for temperature likely because a smaller var_scaling for temperature (see Table 1) was used in Exp-HYB and HYB-GTSRad, making the data assimilating system trust less on observations and thus larger analysis errors were obtained.
Averaged profiles of (a)–(c) RMSE and (d)–(f) BIAS of (a),(d) U; (b),(e) V; and (c),(f) T of analysis against aircraft observations during 10 hourly cycles from 1800 UTC 14 Jul to 0300 UTC 15 Jul for HYB-OneStep, HYB-GTSRad, and Exp-HYB. For Exp-HYB and HYB-GTSRad, the solid line represents the final analysis, while the dotted line represents the analysis from the first step.
Citation: Monthly Weather Review 150, 9; 10.1175/MWR-D-21-0325.1
We further show the analysis fields of wind, perturbed potential temperature, and relative humidity at the surface from the last cycle of HYB-OneStep, HYB-GTSRad, and Exp-HYB in Fig. 14. Both HYB-OneStep and HYB-GTSRad produced spurious wind disturbances ahead of the precipitation system in the northwest of Kansas, which were coupled with fake cold pools in the temperature fields. Exp-HYB not only got rid of the spurious disturbance but also analyzed relatively larger winds and a stronger cold pool in the observed precipitation region near the Colorado–Kansas border. Consequently, the Exp-HYB analyzed stronger relative humidity in the observed precipitation region than the other two experiments, especially as compared to that of HYB-OneStep.
Analysis of (top) wind (m s−1), (middle) perturbed potential temperature (K), and (bottom) relative humidity (%) at surface level valid at 0300 UTC 15 Jul 2015 for (left) HYB-OneStep, (center) HYB-GTSRad, and (right) Exp-HYB. The contour indicates the Stage-IV hourly accumulated precipitation of 1 mm valid at 0300 UTC 15 Jul.
Citation: Monthly Weather Review 150, 9; 10.1175/MWR-D-21-0325.1
b. Impacts of radar DA on ensemble updating
Radar DA in EAKF can help improve the analysis and uncertainty estimate in the flow-dependent BEC for the convective scale. However, noises from updating ensemble members with frequent radar DA may disturb the large-scale balance and its uncertainty estimate if no adequate observations to constrain the convective environment, which can bring negative impacts to the hybrid EnVar analysis. By comparing the experiments with (HYB-EnRad) and without (Exp-HYB) radar DA in EAKF for generating the ensemble BEC, we explore the impact of radar DA during ensemble member updating on the hybrid EnVar performance.
Figure 15 shows the time series of FSS and frequency bias scores of hourly accumulated precipitation forecasts for Exp-HYB and HYB-EnRad. In the first 4 h, the FSSs in both experiments are comparable, but the FSS values in Exp-HYB are steadier than HYB-EnRad among the different precipitation thresholds. For the remaining 5 h, the FSS values in Exp-HYB are larger than HYB-EnRad for the low precipitation threshold of 1mm and slightly larger for the other two thresholds. The main difference between the two experiments is observed in the frequency bias score, in which the Exp-HYB produced less low bias (closer to 1), suggesting improved bias properties.
(a)–(c) FSS and (d)–(f) frequency bias of hourly accumulated precipitation with thresholds of (a),(d) 1; (b),(e) 5; and (c),(f) 10 mm averaged over three cycles (2100 UTC 14 Jul, 0000 UTC 15 Jul, and 0300 UTC 15 Jul) for HYB-EnRad and Exp-HYB.
Citation: Monthly Weather Review 150, 9; 10.1175/MWR-D-21-0325.1
The different precipitation forecast skills in Exp-HYB and HYB-EnRad were resulted from the different uncertainty estimate by the flow-dependent BEC in the two experiments. Figure 16 compares the ensemble spreads of 1-h accumulated precipitation, wind, and temperature of the flow-dependent BECs at 1.8 km AGL for the two experiments. Assimilating radar data for ensemble updating in HYB-EnRad introduced some spurious precipitation spreads in the area across the border of Nebraska with Kansas, which corresponded to the large spreads of wind speed and temperature in the same area and could have been the main reason for the forecast precipitation bias in Nebraska (see Figs. 8j–o). These spurious spreads in the ensemble BEC worsened the hybrid EnVar analysis with unreasonable multivariate correlation and spatial correlations and led to the reduced precipitation forecast skill in HYB-EnRad. Our results therefore suggest that it may be not necessary to use radar DA in ensemble updating to generate ensemble BEC for hybrid EnVar.
Ensemble spread of (a),(d) 1-h accumulated precipitation; (b),(e) wind speed; and (c),(f) temperature valid at 0300 UTC 15 Jul from the 50-member ensemble forecasts for (a)–(c) Exp-HYB and (d-f) HYB-EnRad. The black contours indicate the observed precipitation over 1 mm.
Citation: Monthly Weather Review 150, 9; 10.1175/MWR-D-21-0325.1
6. Summary and conclusions
In this study, we explored how to design an effective multiscale hybrid EnVar strategy with the aim to improve short-term convective-scale precipitation forecast. The two-step assimilation approach was employed in the rapid hourly updating cycled hybrid EnVar, and radar and conventional data were assimilated in two sequential steps to obtain the multiscale analysis. To get proper flow-dependent BEC, the ensemble members used in this study were initialized from GEFS analysis and updated using EAKF by assimilating conventional observations only with hourly assimilation interval. The designed multiscale hybrid EnVar strategy was evaluated through a rainfall case during the PECAN field campaign.
The performance of the multiscale hybrid EnVar strategy was first evaluated by comparing it with the 3DVar and EAKF methods in terms of convective-scale analysis increments and precipitation forecast. The analysis increments showed that the multiscale hybrid EnVar could well assimilate the multiscale information from radar and conventional observations and properly transfer the information from observed variables to unobserved variables through the flow-dependent BEC. The improved multiscale analysis enabled the hybrid EnVar to produce higher precipitation forecast skills than the 3DVar and EAKF methods. The verification of forecast against conventional and radar data further showed that the multiscale hybrid EnVar method generally had smaller forecast errors in wind, temperature, and radial velocity than 3DVar and EAKF, which led to improved precipitation forecast.
A series of sensitivity experiments were then carried out to investigate the impacts of three key features in the multiscale hybrid EnVar strategy. The results indicated that the two-step assimilation approach had advantages over the one-step approach and assimilating radar data in the first step produced less spurious disturbances, resulting in more favorable environmental conditions for convective systems and improved precipitation forecast at the later hours of the 1–9-h forecast range. Our sensitivity study also suggested that radar DA in the EAKF ensemble member updating may not be a necessity in hybrid EnVar. Radar DA in ensemble updating may produce errors at convective-scale and contaminate the estimate of large-scale uncertainty in the flow-dependent BEC, which will introduce noises into the hybrid EnVar analysis and bring negative impacts to the subsequent precipitation forecast.
The multiscale hybrid EnVar method was only evaluated through an individual case in this study, and its applications in more cases and in other areas need further research. In this study, the flow-dependent BEC was the same for conventional and radar DA even though the weight and localization scales were different, so one of our future plans is to explore how to separate the ensemble BEC into different scales for the assimilation of radar and conventional data in different steps. Last, to further enhance the multiscale capacity of the hybrid EnVar method, it is necessary to consider scale-dependent information in both climatology and flow-dependent BEC (Buehner and Shlyaeva 2015; Huang et al. 2021), and it will be explored in near future.
Acknowledgments.
This work was jointly sponsored by the National Natural Science Foundation of China (42075148), the Outreach Projects of the State Key Laboratory of Severe Weather (2021LASW-A08), the Joint Open Project of KLME & CIC-FEMD, Nanjing University of Information Science and Technology (NUIST) (KLME202209), and the National Center for Atmospheric Research (NCAR). The numerical calculations of this study are supported by the Computational and Information Systems Laboratory of NCAR and the High Performance Computing Center of NUIST.
Data availability statement.
The Global Transmission System (GTS) conventional observations are obtained from NCAR’s Research Data Archive (RDA) (https://rda.ucar.edu/datasets/ds351.0 and https://rda.ucar.edu/datasets/ds461.0). The Global Forecast System (GFS) analysis and forecast are obtained from NCAR’s RDA (https://rda.ucar.edu/datasets/ds083.3). The Global Ensemble Forecast System (GEFS) data are obtained from NOAA’s Archive Information Request System (https://www.ncei.noaa.gov). The radar data are obtained from NCAR’s Short Term Explicit Prediction (STEP) Program.
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