The E3DVAR method is one of the hybrid DA methods that use a static climatological background error covariance (BEC) and ensemble-based flow-dependent BEC, and couples the EnKF and 3DVAR (Zhang et al., 2013). E3DVAR is based on a cost function of 3DVAR. In E3DVAR, EnKF provides flow-dependent BEC as well as updates on perturbations for ensemble members. Following Zhang et al. (2013), 1Jb=Jsb+Jeb=12δxT(1-β)B+βPf∘C-1δx, where Jsb is a traditional cost function based on a static climatological BEC B and Jeb is an additional cost function based on ensemble-based BEC Pf. C is a correlation matrix for localization of the ensemble covariance Pf. The weighting coefficient β between static and ensemble-based BEC is set to 0.8 in this study. To account for model error for E3DVAR, a multi-physics scheme is applied to 40-member ensembles. Yang and Kim (2021a) found that E3DVAR is the most appropriate DA method among 3DVAR, EnKF, and E3DVAR methods over East Asia. More detailed information on E3DVAR implemented in this study can be found in Yang and Kim (2021a).

In the last decade, the traditional hybrid methods have been widely used for many operational centers and research institutes. Recently, Penny (2014) proposed a new class of hybrid gain methods combining desirable aspects of both variational and EnKF families of algorithms by weighting analyses from 3DVAR and LETKF for an optimal analysis in the Lorenz 40-component model. Since then, this algorithm has been implemented at ECMWF (Bonavita et al., 2015) and at a hybrid global ocean DA system in the National Centers for Environmental Prediction (NCEP) (Penny et al., 2015).

The hybrid gain algorithm can be described with the following equations: 2xHyba=αxDeta+(1-α)xa‾, where xHyba, xDeta, and xa‾ denote the hybrid analysis, deterministic analysis, and the ensemble mean analysis from the ensemble-based assimilation method, and α is a tunable parameter (Penny, 2014; Houtekamer and Zhang, 2016).

The hybrid gain method is different from traditional hybrid methods, in that a hybrid gain approach linearly combines analysis fields from EnKF and variational DA methods to produce a hybrid gain analysis rather than linearly combining respective BECs (Penny, 2014). Basically, the hybrid gain method is used to hybridize two different Kalman gain matrices of ensemble-based (Eq. 4) and variational DA systems (Eq. 5) as in Eq. (3): 3K^=β1Kf+β2KB+β3KBHKf, where 4Kf=PfHT(HPfHT+R)-1,5KB=BHT(HBHT+R)-1. H is an observation operator mapping the model state vector to observation space and R is the observation error covariance matrix. The matrices Pf and B indicate the ensemble-based and the static climatological BEC, respectively. By choosing the specific coefficients (β1=1, β2=α, β3=-α), it can be written as in Eq. (6) and it can give an algebraically equivalent result with Eq. (2) (Penny, 2014): 6K^=Kf+αKB(I-HKf). One of the advantages of the hybrid gain algorithm with respect to its development is that preexisting operational systems can be used without significant modification for a hybrid analysis (Penny, 2014) and independent parallel development of respective methods is allowed (Houtekamer and Zhang, 2016). Furthermore, the hybrid gain approach can be considered a practical and straightforward method in the foreseeable future to combine advantageous features of both ensemble- and variational-based DA algorithms (Houtekamer and Zhang, 2016). More detailed information on this algorithm can be found in Penny (2014).

In this study, based on the hybrid gain approach, an advanced hybrid gain DA method (AdvHG) is newly proposed as follows: 7XAdvHGa=αXERA5f(6h)+(1-α)X‾E3DVARa, where XERA5f(6h) denotes the 6 h forecast of ERA5 reanalysis based on the WRF model and X‾E3DVARadenotes the analysis of E3DVAR (Fig. 2). In Eq. (7), α is a tunable parameter and is assigned to be 0.5 in this study. This advanced hybrid gain approach is different from the hybrid gain approach in that (1) E3DVAR analysis is used instead of EnKF, (2) 6 h forecast of ERA5 is used instead of deterministic analysis from the variational DA method, and (3) the preexisting and state-of-the-art reanalysis data (i.e., ERA5) are simply used instead of producing deterministic analysis by assimilation. The reasons for these different approaches proposed in this study are as follows:

E3DVAR is used instead of EnKF because Yang and Kim (2021a) confirmed that E3DVAR outperforms EnKF for winter and summer seasons over East Asia.

Therefore, the approach proposed in this study is called “advanced hybrid gain method” (denoted as “AdvHG”).

The analysis and forecast RMSEs of E3DVAR, AdvHG, the WRF-based ERA-I, and WRF-based ERA5 are calculated for zonal wind, meridional wind, temperature, and Qvapor (water vapor mixing ratio in WRF) variables against sonde observations at 00:00 and 12:00 UTC in verification domain (dashed box in Fig. 1) for January and July 2017 and averaged over each month (Figs. 3, 4, and 5).

For the analysis RMSE (Fig. 3), E3DVAR is smaller than AdvHG for all pressure levels and variables, except for temperature in July at 1000 hPa and Qvapor in January and July at 1000 hPa. In general, the analysis RMSE of AdvHG for all variables is comparable to or greater than that of ERA5. The analysis RMSE of ERA5 is smaller than that of ERA-I for all levels and variables; in particular, the analysis RMSE difference between ERA5 and ERA-I is distinctive for wind.

Regarding wind variables of analysis (Fig. 3a, b, c, and d), E3DVAR is the most closely fitted to observations except for the wind in the upper troposphere in January, followed by ERA5, AdvHG, and ERA-I. For the temperature RMSE (Fig. 3e and f), E3DVAR is smaller than AdvHG. For Qvapor, RMSE in July is much larger than that in January due to a monsoonal flow carrying moist air to East Asia. In general, the Qvapor RMSE of E3DVAR is the smallest, followed by ERA5, AdvHG, and ERA-I. Therefore, for all variables, E3DVAR analysis fields are generally the most closely fitted to observations. Since the analysis RMSE implies how much the analysis fields are fitted to observations rather than the accuracy of analysis itself, not only the analysis RMSE but also the forecast RMSE should be considered.

For 24 h forecast fields in January (Fig. 4a, c, e, and g), overall, the RMSEs of AdvHG and E3DVAR are greater than those of ERA5 and smaller than those of ERA-I, and the AdvHG RMSE is smaller than the E3DVAR RMSE for all levels and variables. Meanwhile, for July (Fig. 4b, d, f, and h), AdvHG and E3DVAR show comparable RMSE to ERA-I.

Furthermore, the general features of the 36 h forecast RMSE (Fig. 5) are similar to the 24 h forecast RMSE (Fig. 4). However, particularly in January, the 36 h forecast RMSE differences between ERA5 and ERA-I are more distinctive than those of the 24 h forecast. In January, the vertically averaged 36 h forecast RMSE differences of ERA5 and ERA-I are 0.52 m s-1 for wind, 0.16 K for temperature, and 0.08 g kg-1 for Qvapor, whereas those of the 24 h forecast are 0.4 m s-1 for wind, 0.11 K for temperature, and 0.06 g kg-1 for Qvapor. In addition, the 36 h forecast RMSE differences between ERA5 and AdvHG for January are on average 0.1 m s-1 for wind, 0.05 K for temperature, and 0.02 g kg-1 for Qvapor, which are even smaller compared to those of the 24 h forecast, implying that AdvHG is much more accurate than ERA-I for January 2017. For July, the 36 h forecast RMSE of ERA5 is the smallest and the RMSEs of AdvHG and E3DVAR are similar to those of ERA-I.

In this section, the EARR produced in this study is verified for a longer period with WRF-based ERA5. The RMSE and spread of reanalyses and reforecasts based on the AdvHG method are calculated and averaged over the period 2010–2019. The reanalyses and (re)forecast fields are evaluated by calculating RMSE valid at 00:00 and 12:00 UTC and spread at 00:00, 06:00, 12:00, and 18:00 UTC.

The averaged RMSEs of reanalysis for ERA5 and EARR (denoted as AdvHG in Fig. 6) and spread of analysis and 6 h forecast fields of EARR (AdvHG) are shown in Fig. 6. With respect to spread, the ensemble spreads of analysis fields are smaller than those of 6 h forecast fields, on average, by 0.15 m s-1 for wind, 0.04 K for temperature, and 0.02 g kg-1 for Qvapor, which is the well-known characteristic of ensemble-based DA methods. Specifically, the wind spread (Fig. 6a and b) is similar to or greater than the wind RMSE except for the upper troposphere above 200 hPa, implying the ensemble spread for wind is well represented below 200 hPa. On the contrary, the ensembles for temperature and Qvapor (Fig. 6c and d) are underdispersive compared to their RMSEs.

Regarding the reanalysis RMSE, overall AdvHG RMSE is greater than ERA5 RMSE for all variables (Fig. 6). The vertically averaged RMSEs of AdvHG are greater by 0.16 m s-1 for wind, 0.09 K for temperature, and 0.01 g kg-1 for Qvapor than those of ERA5. Nonetheless, the wind RMSEs of AdvHG are similar to those of ERA5 for the middle of the troposphere (400–850 hPa), and the Qvapor RMSEs of AdvHG are similar to those of ERA5 except for 1000 hPa.

In addition, regarding the 24 h forecast RMSE, AdvHG shows a larger RMSE than ERA5 for all variables (Fig. 7). The vertically averaged RMSE differences of wind, temperature, and Qvapor variables between AdvHG and ERA5 are approximately 0.2 m s-1, 0.07 K, and 0.03 g kg-1, respectively. These differences are smaller, compared to the 24 h forecast RMSE difference between ERA-I and ERA5 shown in Fig. 4 (i.e., wind, temperature, and Qvapor RMSE difference: 0.4 m s-1, 0.11 K, and 0.06 g kg-1 for January 2017, 0.25 m s-1, 0.05 K, and 0.04 g kg-1 for July 2017).

In​​​​​​​ this section, for the point-based equitable threat score (ETS) and frequency bias index (FBI) based on Table 4, the 6 h accumulated precipitation fields based on the 6 h forecast of E3DVAR, AdvHG, WRF-based ERA-I, WRF-based ERA5, ERA-I_fromECMWF, and ERA5_fromECMWF are evaluated every 6 h (00:00, 06:00, 12:00, and 18:00 UTC) for January and July 2017 (Fig. 8). Here, all the WRF-based precipitation fields are based on 12 km horizontal resolution, and ERA-I_fromECMWF and ERA5_fromECMWF have 79 and 31 km horizontal resolutions, respectively. Generally, ETS decreases as a threshold increases for both months (Fig. 8a and c). For January 2017 (Fig. 8a), AdvHG ETS is the greatest among others. Compared to precipitation reforecasts from ECMWF (i.e., ERA-I_fromECMWF, ERA5_fromECMWF), AdvHG shows the higher ETS, indicating that AdvHG is able to simulate more accurate precipitation fields than ERA-I and ERA5 from ECMWF in January 2017. Surprisingly, ETS of ERA5_fromECMWF for January 2017 is the lowest among all the results and is even lower than that of ERA-I_fromECMWF.

Since the precipitation reforecasts from ECMWF have not only coarser resolutions but also a different forecast model (i.e., the forecasting system of ECMWF), the precipitation forecasts of ERA5 and ERA-I are additionally produced by using the same forecast model with the same resolution as AdvHG and E3DVAR in this study, as explained in Sect. 2.4. For January 2017 (Fig. 8a), ETS of ERA5 (i.e., WRF-based ERA5) is higher than that of ERA5_fromECMWF for all thresholds, whereas ETS of ERA-I (i.e., WRF-based ERA-I) is lower than that of ERA-I_fromECMWF except for high thresholds (8 and 16 mm per 6 h). The ERA5 ETS is greater than the ERA-I ETS, but is smaller than the AdvHG ETS. The AdvHG shows the greatest ETS among others with the same resolution and forecast model, and E3DVAR, ERA5, and ERA-I follow.

Regarding FBI in winter (Fig. 8b), for 4, 8, and 16 mm per 6 h thresholds, all the results show that FBI is smaller than 1, implying an underestimation of the frequency of precipitation for high-threshold events. In general, AdvHG shows the FBI closest to 1 among all the results, which is consistent with the greatest ETS of AdvHG. The E3DVAR FBI is similar to the AdvHG FBI, and ERA5 and ERA-I FBIs are similar to each other.

Overall, the ETS values for January, whose maximum is around 0.4 (Fig. 8a), are much greater than those for July 2017, whose maximum is around 0.2 (Fig. 8c), implying that the precipitation forecast in summer is more difficult than that in winter. The ETS difference between the results in July is smaller than that in January. Particularly, for the thresholds 4 and 8 mm per 6 h, the ETSs in July are similar to each other (Fig. 8c). Except for those two thresholds, the ETS of ERA-I_fromECMWF is the smallest. At the threshold of 16 mm per 6 h, ERA5 ETS is the highest, followed by AdvHG, E3DVAR, ERA-I, ERA5_fromECMWF, and ERA-I_fromECMWF. At the threshold of 0.5 and 1 mm per 6 h, the E3DVAR ETS is the greatest, followed by ERA5, AdvHG, ERA5_fromECMWF, ERA-I, and ERA-I_fromECMWF.

With respect to FBI in July 2017, the WRF-based results yield FBIs greater than 1, whereas reforecast from ECMWF yields FBIs greater than 1 for 0.5, 1, and 4 mm per 6 h thresholds and smaller than 1 for higher thresholds (8 and 16 mm per 6 h) (Fig. 8d). For July 2017, in general, ERA5_fromECMWF FBI is the closest to 1, followed by E3DVAR, AdvHG, ERA5, ERA-I, and ERA-I_fromECMWF FBI.

The probability of detection (POD or hit rate) and false alarm ratio (FAR) are calculated for precipitation simulated from E3DVAR, AdvHG, WRF-based ERA-I, WRF-based ERA5, ERA-I_fromECMWF, and ERA5_fromECMWF for January and July 2017 (Fig. 9). For January 2017, AdvHG POD is the greatest among the WRF-based results, followed by E3DVAR, ERA5, and ERA-I (Fig. 9a). In addition to the lowest ETS of ERA5_fromECMWF for January 2017 as discussed in the Sect. “Equitable threat score and frequency bias index”, the FAR of ERA5_fromECMWF is extremely high with a low POD in winter. Therefore, especially for January 2017, the precipitation fields simulated from EARR (AdvHG) over East Asia are much more accurate than those from ERA5_fromECMWF.

For July 2017, generally, AdvHG shows the largest POD, except for ERA5 (Fig. 9c). The FAR values in July are much greater than those in January, which is consistent with the ETS difference between these two seasons.

The neighborhood sizes are chosen to be 3Δx, 5Δx, 9Δx, and 11Δx, which are 36, 60, 108, and 132 km, respectively, and the thresholds 0.5, 1, 4, 8, and 16 mm per 6 h are considered. The probabilistic precipitation forecasts are calculated at every model grid point depending on neighborhood sizes and thresholds. Regarding each observation, the nearest model grid point to observations is considered as the center of the neighborhood. For verification, 6 h accumulated precipitation fields are extracted from the first 0–6 h forecast fields of WRF-based ERA-I, WRF-based ERA5, E3DVAR, and AdvHG every 6 h (00:00, 06:00, 12:00, and 18:00 UTC). The BSSs of ERA5_fromECMWF and ERA-I_fromECMWF are not calculated, because they have a different resolution from WRF-based results.

Based on the neighborhood approach, the BSS is calculated depending on different neighborhood sizes for January and July 2017, respectively (Fig. 10). Because the reference of BS is chosen as the ERA-I, the positive BSS suggests a better accuracy than ERA-I. In general, for both months, the AdvHG BSS is greater than the ERA5 BSS. Although the E3DVAR BSS is the greatest in July 2017, the AdvHG BSS is the greatest in January 2017.

For January 2017, as a neighborhood size increases, the AdvHG and E3DVAR BSSs tend to increase except for ERA5. Overall, the AdvHG BSS is the greatest among other BSSs for all thresholds for all neighborhood sizes. The ERA5 BSS is greater than the E3DVAR BSS except for 16 mm per 6 h. The highest BSS of AdvHG and the lowest BSS of ERA-I are consistent with the ETS result. Unlike the greater E3DVAR ETS than ERA5 ETS, the ERA5 BSS is greater than the E3DVAR BSS in January 2017.

For July 2017, while the ETS difference between the WRF-based results is not distinct (Fig. 8c), the BSS difference is rather noticeable. Generally, the E3DVAR BSS is the greatest among other BSSs for all thresholds except for 16 mm per 6 h for neighborhood sizes 9 and 11. Although the E3DVAR BSS is the largest, AdvHG outperforms ERA5 and ERA-I. The worst performance of ERA-I precipitation is consistent with the ETS result. At 0.5, 1, and 4 mm per 6 h thresholds, E3DVAR BSS is the greatest, which is similar to ETS. At 8 and 16 mm per 6 h thresholds, ERA5 ETS is the highest, followed by AdvHG and E3DVAR, whereas overall, the E3DVAR BSS is the highest, followed by AdvHG and ERA5.

In this section, the spatial distributions of 6 h accumulated precipitation from the WRF-based forecast and reforecast from ECMWF are compared. In addition, pattern correlation coefficients (PCC) are calculated and shown at the bottom right of Figs. 11 and 12.

The PCC is computed according to the usual Pearson correlation operating on the N observed point pairs of 6 h accumulated precipitation fields simulated from (re)forecast and observations at the specific time. For the calculation of PCC, 6 h accumulated precipitation fields from (re)forecast fields are interpolated bilinearly to the N observed points.

First, on 29 and 30 January 2017 (Fig. 11), it is noticeable that the precipitation fields of AdvHG match observations well over East Asia, whereas, in particular, those of ERA5_fromECMWF do not. For example, ERA5_fromECMWF overestimates precipitation over the inland area of China (Fig. 11zz), while AdvHG simulates precipitation similar to observations regarding its position and intensity (Fig. 11x). ERA5_fromECMWF also shows a noticeably smaller PCC (Fig. 11g, n, and zz). Although PCC does not represent the exact accuracy or predictability of precipitation, the overall feature of PCC is consistent with the results found so far. For January 2017, the averaged PCC of AdvHG is the greatest (i.e., 0.61) and that of ERA5_fromECMWF is the smallest (i.e., 0.46; not shown).

For 1 and 2 July 2017 (Fig. 12), in general, AdvHG, E3DVAR, and ERA5 simulate well not only the overall features of precipitation fields but also their intensity. During July 2017, ERA5 and ERA-I simulate heavier precipitation than AdvHG (not shown), which is consistent with the larger FBI of ERA5 and ERA-I at higher thresholds. For the 1-month period of July 2017, the averaged PCC of ERA5 is the greatest (i.e., 0.37) and that of AdvHG is 0.34, but the PCC difference between ERA5 and AdvHG is not distinctive. Moreover, the overall range of averaged PCC of different datasets in summer (i.e., 0.29–0.35) is smaller than that in winter (i.e., 0.46–0.61), which is consistent with the seasonal difference of ETS in this study.

In this section, the monthly accumulated precipitation fields of rain gauge-based observations, E3DVAR, AdvHG, ERA-I, ERA5, ERA-I_fromECMWF, and ERA5_fromECMWF are compared with each other for two 1-month periods in January and July 2017, respectively.

The monthly accumulated precipitation fields simulated by E3DVAR and AdvHG (Fig. 13b and c) are similar to each other, and E3DVAR and AdvHG produce the best fit to observed fields. Especially for the northwestern part of Japan (e.g., Chugoku and Kinki), E3DVAR and AdvHG are able to represent precipitation correctly, whereas ERA-I_fromECMWF and ERA5_fromECMWF fail to do so (Fig. 13). Moreover, although all the results similarly represent overall features of precipitation in January (Fig. 13), ERA5_fromECMWF (Fig. 13g) simulates the overestimated precipitation over South China, which is consistent with the results in the previous section as well as its larger FBI at lower thresholds (0.5 and 1 mm per 6 h) shown in Fig. 8b. It is noticeable that all results fail to represent the observed precipitation area over the Tibetan Plateau (25–40∘ N, 95–105∘ E).

For the monthly accumulated precipitation in July 2017, overall, the ERA5_fromECMWF (Fig. 14g) and the WRF-based results (Fig. 14b, c, and e) except for ERA-I (Fig. 14d) simulate precipitation well, similar to observations. The WRF-based results including AdvHG overestimate precipitation over the western and southern parts of Japan, while ERA-I_fromECMWF and ERA5_fromECMWF simulate similar precipitation fields to observed fields. The WRF-based results tend to overestimate precipitation in South China, Korea, and Japan, compared with ERA-I_fromECMWF and ERA5_fromECMWF. This is consistent with the result in Fig. 8d, in which FBIs from WRF-based results are generally greater than for higher thresholds (8 and 16 mm per 6 h), whereas those from ECMWF are smaller than 1.

Even though the detailed precipitation features of WRF-based results are different, the overall features of precipitation from WRF-based results are similar to each other, which implies that predictability of precipitation strongly depends on the physics schemes as well as on the NWP model, especially for the summer season. According to Que et al. (2016), depending on the combinations of physics options in the WRF model, the spatial distribution of precipitation can be significantly different over the Asian summer monsoon area, and the YSU PBL scheme which is used in this study tends to overestimate precipitation over the same area. Thus, different physics options could simulate the different spatial distribution of precipitation.

In addition, compared to ERA5 based on the WRF model (Fig. 14e), the ECMWF model for ERA5_fromECMWF (Fig. 14g) seems to suppress precipitation. Thus, the WRF model with the physics schemes used in this study might simulate more precipitation than the ECMWF model, although the initial condition is the same. Therefore, it is important to consider the consistency of the systems for DA and the forecast model for a good performance of forecast weather variables such as precipitation.