1. Introduction
Spurious high-frequency oscillations occur in primitive equation model integrations (Daley 1993). Imbalances caused by data assimilation procedures, especially intermittent data assimilation schemes, usually lead to unrealistic pressure oscillation, excessive rainfall, and data rejection. Initialization schemes capable of producing balanced initial conditions that do not excite inertia–gravity oscillations in a model integration have been designed and implemented in most operational numerical weather prediction (NWP) systems.
Nonlinear normal mode initialization (Machenhauer 1977) and digital filter initialization (DFI; Lynch and Huang 1992) are two well-known methods characterized by suppressing gravity wave modes in the initial states or filtering high-frequency oscillations in the model integrations around the analysis time. Another widely used initialization scheme is the incremental analysis updates (IAU; Bloom et al. 1996), which is similar to nudging and uses the dynamic model to distribute the analyses increments over a time window centered at the analysis time. Bloom et al. (1996) demonstrated IAU as a low-pass time filter, as a nudging method is supposed to do (Bao and Errico 1997). Polavarapu et al. (2004) demonstrated the equivalence of IAU and incremental DFI, which applied a digital filter to the time evolution of analysis increments, for the case of linear models and indicated that the constant weights, typically used in most IAU applications, were shown to result in too much damping of long waves.
IAU has been employed in global NWP and climate modeling, e.g., the U.S. National Aeronautics and Space Administration (NASA) Physical-space Statistical Analysis System (PSAS) (Zhu et al. 2003), the Met Office three-dimensional variational (3D-Var) data assimilation system (Lorenc et al. 2000; Clayton 2003), the Canadian Seasonal to Interannual Prediction System (CanSIPS) (Merryfield et al. 2013), and the Model for Prediction Across Scales (MPAS) (Ha et al. 2017). A four-dimensional IAU was shown to effectively reduce imbalances in the ensemble Kalman filter (EnKF) analyses in the U.S. National Centers for Environmental Predictions (NCEP) Global Forecasting System (GFS) (Lei and Whitaker 2016). IAU was implemented in the NASA four-dimensional variational (4D-Var) data assimilation system and was shown to remove the initial precipitation spikes and reduce other discontinuities in the data assimilation experiments (Zhang et al. 2015).
IAU has also been used in regional NWP systems, e.g., the Fifth-generation Pennsylvania State Univeristy–National Center for Atmospheric Research Mesoscale Model (MM5) (Lee et al. 2006), the Advanced Regional Prediction System (ARPS) (Stratman and Brewster 2017), and the convective-scale NWP system for Singapore (SINGV) (Huang et al. 2019). The real-time configuration of the 1-km ARPS, which uses IAU to handle the increments produced by 3DVAR with cloud analysis, had the success of providing a good baseline forecast (Stratman and Brewster 2017). IAU has also been used in the evaluation of vertically integrated cloud liquid water (CLW) transport (Shay-El et al. 2000) and in the research of high-quality leaf area index (LAI) products retrieved from satellite observations (Jiang et al. 2014).
Recently, with the data assimilation cycling stepping into high frequency, initialization procedures become crucially important for the numerical models to achieve mesoscale balance within very short integration period to avoid the numerical noise accumulation, which may lead to unreasonable data rejection and worse forecast performance. For the operational NWP systems from the Rapid Update Cycle (RUC), the first hourly update cycling NWP system implemented at any operational center in the world (Benjamin et al. 2004, 2016) to Rapid Refresh (RAP), DFI has been used and shown to provide noise-free 1-h forecasts. However, the performance of IAU with high update frequency is still to be evaluated and documented.
We developed a WRF/WRFDA-based hourly cycling data assimilation system, Rapid-refresh Multiscale Analysis and Prediction System–Short-Term (RMAPS-ST) (Wang et al. 2022; Xie et al. 2019) and implemented it in operation in 2021. Within the hourly RMAPS-ST system, IAU is applied as an initialization step. The time-varying weights are used in IAU in this research to avoid the overdamping of long waves. In this article, the development of IAU for WRF model is described and its impacts on the efficacy to reduce the inertia–gravity waves and spinup is investigated. Section 2 describes the IAU implementation and the experiment configurations. Section 3 presents the results and assessments of the impact of IAU on noise control, model spinup phenomena, and data assimilation. A comparison between IAU and DFI is discussed in section 4. The verification results of the 3-month preoperational hourly cycling forecasts with IAU are shown in section 5. A summary and some conclusions are given in section 6.
2. WRF–IAU coupling
The selection of λ(t), the IAU weighting coefficients, is very similar to determining the filter coefficients for a digital filtering scheme (Clayton 2003). Although λ(t) could be freely chosen with the Eq. (2) as the only constraint, the distribution and filtering feature of IAU determined by the time-weighted coefficients should be carefully inspected. In addition to constant weights, a practical method is to use digital filter to generate the candidate time series of λ(t). We use the Dolph–Chebyshev window (Lynch 1997) to construct λ(t). The filter has two parameters, filter span and filter cutoff period. With filter span Δtc = 2 h, time step Δt = 15 s (corresponding to a WRF/ARW model forecast with 3-km grid distance), there are a total of 481 steps from [−240, 240] centered around the analysis time t = 0 h.
To illustrate the sensitivities to choices in IAU coefficients as well as their impacts on the hourly cycling forecasts, retrospective hourly cycling experiments with uniform IAU coefficients (UNIFORM) and the IAU coefficients based on the Dolph–Chebyshev window (DOLPHWIN), were performed, and compared against the cycling experiment without IAU (NOIAU). The NOIAU experiment was a regular continuous hourly cycling assimilation and forecast runs without initialization step. The DOLPHWIN and UNIFORM experiments were identical except their IAU coefficient λ(t). For UNIFORM, λ(t) was simply assigned the constant of the reciprocal of the total forecast steps over the time span. For DOLPHWIN, the time weighting of λ(t) was assigned by the Dolph–Chebyshev window filter configured with a 2-h time span and 2-h cutoff period.
Two configurations of λ(t), UNIFORM and DOLPHWIN are listed in Table 1 and shown in Fig. 1a. The amplitude responses for different time series of λ(t) are compared in Fig. 1b. As digital filters, IAU configurations attenuate the waves with periods shorter than 1 h. DOLPHWIN, obviously, has a similar shape to a triangle (Clayton 2003) by distributing more weights around the analysis time. Compared to DOLPHWIN, UNIFORM causes extra Gibbs oscillations for the high-frequency periods and damps too much (over 50%) within the transition bands from 2 to 6 h.
List of experiments and the configurations of λ(t) used in this study.
(a) The IAU coefficients as functions of time (time step = 15 s) and (b) the amplitudes of IAU response functions as functions of period (h).
Citation: Weather and Forecasting 38, 7; 10.1175/WAF-D-22-0127.1
Briefly, IAU runs within each 1-h assimilation cycle as follows. (i) The analysis increments of all prognostic variables including the hydrometers produced by the data assimilation procedure are stored. (ii) Model starts to integrate from the model state valid at t = −1 h, which is the analysis time of the previous cycle, for the entire 2-h IAU time span while applying the λ(t) fraction of analysis increments at every time step. (iii) With the analysis increments used up by the end of the 2-h IAU integration, the model state valid at t = 1 h are stored as the background of the next cycle and model’s regular free forecast starts. It should be noted that the IAU procedure requires one extra integration hour compared with a regular model integration.
Additionally, it should also be mentioned that the 2-h time span used in this study is an overlaid IAU window for hourly cycling runs, as the integration starts with the 1-h forecast of model state from the previous cycle, in which only half of last cycle’s analysis increments are added. The decision is based on the consideration that a longer time span may produce better filtering results and that there are no obvious negative effects as each cycling run absorbs full analysis increments. Regardless, if shorter time-span filtering results is acceptable, 1 h is a reasonable time span configuration that ensures the analysis increments will be used up exactly within the time window.
An hourly updating version of the cycling analysis and forecast system, RMAPS-ST, which was developed at the Institute of Urban Meteorology of the China Meteorological Administration (CMA/IUM) is used in this study. It provides short-term forecasts over the limited-area domains at mesoscale (9-km horizontal) covering China (D01) and a one-way nested 3-km domain covering part of Northern China (D02) (Fig. 2). Its model and data assimilation components are based on WRF-ARW version 3.8.1 (Skamarock et al. 2008) and WRF Data Assimilation (WRFDA) version 3.8.1 (Barker et al. 2012), respectively.
Domains and observations used in RMAPS-ST system.
Citation: Weather and Forecasting 38, 7; 10.1175/WAF-D-22-0127.1
RMAPS-ST assimilates multisource data, including the conventional observations (Fig. 2) from the Global Telecommunications System (GTS) and the surface observations from local automated weather station (AWS) networks. The national-wide radar mosaic reflectivity data are assimilated in D01, while the superobservations of the radial velocity and reflectivity observations from eight Doppler radars are assimilated in D02. To assimilate the radar reflectivity data for both domains, an indirect method employing proxy observations of various hydrometeor mixing ratios transformed from reflectivity mosaic data based on background temperature is utilized (Wang et al. 2013; Fan et al. 2013).
The 3DVAR version of WRFDA was used for all three experiments. The system configurations can be found in Wang et al. (2022). All experiments were conducted over the 7-day period from 0000 UTC 12 July to 2300 UTC 18 July 2018. The lateral boundary conditions generated from the 12-h ECMWF global forecasts were updated for the cycling runs initiated at 0000 and 1200 UTC. At 0000 UTC each day, a restart of the cycling was performed with the background of data assimilation from a 6-h cold start run initialized from the ECMWF forecast at 1800 UTC the previous day.
3. Results
a. Impact on model dynamic balance
Domain-averaged absolute surface pressure tendency (DPSDT; hPa h−1): (a) for D01 from t = 0 h to t = 1 h; (b) for D02 from t = 0 h to t = 1 h, of all the forecasts from 0000 UTC 12 Jul to 2300 UTC 18 Jul 2018; and (c) for D02 from t = −1 h to t = 6 h averaged over all 168 cycles over the 7-day period.
Citation: Weather and Forecasting 38, 7; 10.1175/WAF-D-22-0127.1
All the IAU runs started the model integration from −1 h. As shown in Fig. 3c, the noise level in the IAU runs was also high at t = −1 h, although it was lower than NOIAU. These results indicate that the 2-h span was a good choice and at the end of IAU at t = 1 h both IAU runs reached their DPSDT levels which can be considered as for a balanced model state. DPSDT for NOIAU took much longer time to drop to its final level. It could take longer than 12 h to reach to a similar level as those of the IAU experiments.
b. Impact on background for data assimilation
Performance of the data assimilation can be affected by the quality of the background fields. High frequency oscillations due to the imbalances in the background fields, in particular in the surface pressure fields, could lead to large differences between background (1-h forecasts in the hourly cycle experiments) and observations. The large differences not only damage short-term forecasts, but can also lead to observation rejections as results of the checks against background fields. In the experiments, surface pressure observations were rejected if they differed from their corresponding background values by more than 5 hPa, i.e., 5 times the observation error of surface pressure (1 hPa) used in all three experiments.
In Fig. 4, we show the numbers of assimilated surface synoptic observations (SYNOP) at every 1-h cycle from 0000 UTC 12 July to 2300 UTC 18 July 2018 for D01. In all three experiments, the first DA cycle of each day at 0000 UTC, the same number of observations was assimilated as they were compared against the same backgrounds, which were the 6-h forecasts initialized from previous day ECMWF forecasts at 1800 UTC. Imbalances can be introduced due to interpolation, insert of WRF model terrain too, in addition to via DA and, without an initialization step, the numerical noises remain in the 1-h model forecasts which became the background fields for the next data assimilation cycle. As the cycles continued, the noisy backgrounds and further DA-added imbalances were accumulated, leading to data rejections at later DA cycles. The diurnal variation of convection also affected the model imbalance as the large data rejection rate occurred in the late afternoon and early evening. For the NOIAU experiment, diurnal variations can be clearly identified in that nearly 100% of the surface pressure observations were able to be assimilated in the first few cycles, such as from the first cycle (0000 UTC) to the fourth cycle (0400 UTC) of each day, while in later cycles, less surface pressure observations were absorbed by the data assimilation procedure, and the worst situation occurred in the late afternoon or early evening cycles characterized by active convection, e.g., from 1200 UTC (2000 local time) 14 July and 1000 UTC (1800 local time) 15 July, where more than 50% of the observations were rejected. Both IAU experiments showed nearly 100% of the absorption rate of the surface pressure observations over the entire period indicating the capability of IAU schemes in controlling the initial model noises and maintaining the model balances (Fig. 4a).
The numbers of assimilated (a) surface pressure, (b) u component, and (c) temperature from SYNOP observations at each hourly cycle for D01, during the period from 0000 UTC 12 Jul to 2300 UTC 18 Jul 2018.
Citation: Weather and Forecasting 38, 7; 10.1175/WAF-D-22-0127.1
For 10-m wind observations, we found diurnal variations of the observation absorption rate and IAU experiments absorbed more observations than NOIAU (Fig. 4b). However, the numbers of assimilated 2-m temperature observations were the same for all three experiments (Fig. 4c), indicating no impact of IAU on the background check of the 2-m temperature observations.
Considering the fact that the backgrounds against which DA performs at 0000 UTC are identical, only the amounts of the upper-air observations assimilated at 1200 UTC from 10 to 18 July 2018 for D01 are displayed in Fig. 5. Obviously, for all variables, more upper-air observations were assimilated by the IAU initialization procedures, which were shown to have less noise accumulation and provide better backgrounds for data assimilation not only for the surface level observations, but also for upper-air observations.
The numbers of assimilated (a) U/V components, (b) temperature, and (c) qvapor of TEMP observations for D01 at 1200 UTC from 12 Jul to 18 Jul 2018.
Citation: Weather and Forecasting 38, 7; 10.1175/WAF-D-22-0127.1
We show the root-mean-squares of observation minus background (OMB) and observation minus analysis (OMA) for SYNOP observations in Fig. 6 at each hourly cycle from 0000 UTC 12 July to 2300 UTC 18 July 2018 and for radiosonde (TEMP) observations in Fig. 7 at 1200 UTC every day during the period. Note that OMBs and OMAs were computed using the observations after the background check. For SYNOP OMBs and OMAs, clear diurnal variations in OMBs occurred in all three experiments, and convective activities caused larger 1-h forecast errors. For all SYNOP and TEMP observations, NOIAU had much larger OMBs than UNIFORM and DOLPHWIN, indicating both IAU schemes produced better 1-h forecasts than NOIAU. Although 3D-Var managed to bring the analysis closer to observations than background, OMA < OMB, for all the cycles and all the experiments, the OMAs in IAU experiments were consistently smaller than OMAs in NOIAU, indicating that the IAU schemes bring the analyses closer to the observations.
OMB and OMA of assimilated surface (a) pressure, (b) u component, and (c) temperature from SYNOP observations for D01 at each hourly cycle during the period from 0000 UTC 12 Jul to 2300 UTC 18 Jul 2018.
Citation: Weather and Forecasting 38, 7; 10.1175/WAF-D-22-0127.1
OMB and OMA of (a) U/V components, (b) temperature, and (c) qvapor from TEMP observations for D01 at each hourly cycle, during a convection-active period from 0000 UTC 12 Jul to 2300 UTC 18 Jul 2018.
Citation: Weather and Forecasting 38, 7; 10.1175/WAF-D-22-0127.1
c. Impact on precipitation forecasts
For most NWP models, the precipitation forecasts need some time to spinup due to the inconsistency between the initial dynamic and the moisture fields (Puri 1985; Kasahara et al. 1988; Lee et al. 2006). In data assimilation cycles, the quick drop of the precipitation rate during the initial integration period, i.e., spindown, is another feature of model imbalance.
The domain-averaged precipitation rates DARDTs (mm h−1) from t = 0 h to t = 1 h for all hourly cycling runs from 0000 UTC 12 July to 2300 UTC 18 July 2018 for D01 and D02 are shown in Figs. 8a and 8b, respectively. All three experiments showed similar precipitation diurnal features. The NOIAU experiment displayed much larger precipitation rates than the two IAU experiments and its sharp and intense spikes of the precipitation rate were triggered by the hourly data assimilation processes. Both UNIFORM and DOLPHWIN experiments had lower and smoother precipitation rates than NOIAU. The precipitation rate in the UNIFORM experiments was shown to be almost continuous from cycle to cycle.
Domain-averaged precipitation rate (DARDT; mm h−1): (a) for D01 from t = 0 h to t = 1 h; (b) for D02 from t = 0 h to t = 1 h, of all the forecasts from 0000 UTC 12 Jul to 2300 UTC 18 Jul 2018; and (c) for D02 from t = −1 h to t = 6 h averaged over all 168 runs over the 7-day period.
Citation: Weather and Forecasting 38, 7; 10.1175/WAF-D-22-0127.1
The D02 DARDTs averaged over all 168 runs, from 0000 UTC 11 July to 2300 UTC 18 July 2018, are shown in Fig. 8c. Even after averaging out the diurnal variability, the typical spindown and spinup features were still clearly shown in the NOIAU runs and the precipitation rate remained high for a few hours, which could impact the precipitation scores for the short-term forecasts. The IAU runs also showed some spindown and spinup features in the model runs between t = −1 h and t = 0 h, but their precipitation rate after hour 0 is much more constant, a desirable result from cycling. DARDTs of the two IAU experiments were much lower than that of NOIAU during the first few hours of model integrations, but gradually became higher. The difference between UNIFORM and DOLPHWIN, although not very large, was clearly shown in the first 5 h.
The lower precipitation rate brought by the application of IAU can also be demonstrated by comparing the radar reflectivity forecasts. Figure 9 shows the radar reflectivity observations (only over China) at 0100 UTC 15 July 2018 and 1-h radar reflectivity forecasts by NOIAU, UNIFORM and DOLPHWIN from 0000 UTC 15 July 2018. No significant differences were identified among the three 1-h forecasts valid at 0100 UTC, as they had the same analysis at 0000 UTC 15 July 2018, the first cycling runs of the day. The imbalance of hydrometeors in NOIAU amplified and was accumulated from one cycle to the next and showed severe overprediction of the reflectivity in the later cycles.
The radar composite reflectivity over the entire D01 domain at 0100 UTC 15 Jul 2018 from (a) observation and 1-h forecasts of three retrospective runs, initiating at 0000 UTC 15 Jul 2018, in the (b) NOIAU, (c) DOLPHWIN, and (d) UNIFORM experiments.
Citation: Weather and Forecasting 38, 7; 10.1175/WAF-D-22-0127.1
Figure 10 shows the radar reflectivity observations at 1800 UTC 15 July 2018 and 1-h radar reflectivity forecasts by NOIAU, UNIFORM, and DOLPHWIN from 1700 UTC 15 July 2018, the 18th cycling run of the day. Compared to the observed, scattered weak convections over Southeast China (Fig. 10a), NOIAU had much stronger and more widely spreading simulated reflectivity (Fig. 10b). The successive hourly cycling allowed the unbalanced forecasts, especially the hydrometeor forecasts highly impacted by the radar data assimilation, continued to influence the subsequent cycles and eventually the accumulated error in the initial conditions resulted in widespread strong convection in the model forecast. Using a similar hourly continuous cycle strategy, the radar reflectivity forecasts in UNIFORM and DOLPHWIN experiments (Figs. 10c,d) were found to have the structures and locations in closer approximation to the observations. The IAU technique effectively suppressed the accumulative growth of erroneous precipitation forecasts, even after 17 hourly continuous cycling runs of the day.
The radar composite reflectivity over the entire D01 domain at 1800 UTC 15 Jul 2018 from (a) observation and 1-h forecasts of three retrospective runs, initiating at 1700 UTC 15 Jul 2018, in the (b) NOIAU, (c) DOLPHWIN, and (d) UNIFORM experiments.
Citation: Weather and Forecasting 38, 7; 10.1175/WAF-D-22-0127.1
The hourly precipitation forecasts for the first 6 h of the 168 cycles in each retrospective experiment were verified against the observed 1-h accumulated precipitation from the automated weather station (AWS). The general critical success index (CSI) and the frequency bias (BIAS) scores were calculated and intercompared to evaluate the impact of IAU on the hourly cycling analyses and forecasts, especially on the quality of short-range forecasts and nowcasting of precipitation. CSI and BIAS scores of the three experiments with thresholds of 0.1, 1, 5, 10, and 25 mm h−1 are shown in Fig. 11. For all the thresholds and all six 1-h intervals, IAU experiments had consistently higher CSI scores than NOIAU. For light rainfall thresholds such as 0.1 mm h−1, the improvements were around 10%. For the heavy precipitation with the threshold of 10 mm h−1 the improvements of CSI scores can be higher than 20%. All three experiments had BIAS scores above 1, especially for heavy precipitation classes. However, IAU experiments had lower BIAS than NOIAU for almost all thresholds and all six 1-h intervals, indicating that IAU schemes help to reduce the overprediction caused by spinup especially at the beginning of forecasts (also see Figs. 8a,b). For heavy precipitation with the threshold of 25 mm h−1, NOIAU had BIAS larger than 5 for the first hour and close to 5 for the second hour, indicating that too much precipitation was forecast in NOIAU due to the noisy initial conditions. For the same threshold, 25 mm h−1, both IAU experiments had only slight overprediction of precipitation and the BIAS scores of both IAU experiments were about 1.5.
The precipitation scores (a) CSI for D01, (b) BIAS for D01, (c) CSI for D02, and (d) BIAS for D02 of the hourly precipitation forecasts for thresholds of 0.1, 1, 5, 10, and 25 mm h−1 during the 0–6-h period averaged over all 168 forecasts from 0000 UTC 12 Jul to 2300 UTC 18 Jul 2018.
Citation: Weather and Forecasting 38, 7; 10.1175/WAF-D-22-0127.1
A closer comparison between the two IAU schemes slightly favored UNIFORM for D01. For CSI, UNIFORM had in general slightly higher scores than DOLPHWIN. For BIAS, UNIFORM had in general slightly lower scores (closer to 1) than DOLPHWIN. However, for D02 the scores slightly favored DOLPHWIN.
Given that the two IAU schemes have comparable performances, and more importantly, because DOLPHWIN adds more analysis increments to the model around the analysis time, which is more physical and may help reduce the hydrometeor displacement error by adding the increments evenly into the model in the time span as Uniform does, it is chosen as the IAU scheme in the following study.
4. Comparison with DFI
DFI is a standard initialization scheme for the WRF Model and has been widely used. It requires the model to perform a backward-forward two-pass integration, during which the digital filter is applied to attenuate the high-frequency oscillations with large amplitudes. To further demonstrate the initialization efficiency and performance of IAU, the results of the IAU technique (DOLPHWIN) were compared to the results obtained from a 2-day hourly cycling parallel experiment using DFI initialization during the period of 0000 UTC 16 July–2300 UTC 17 July 2018. A regular diabatic DFI (DDFI) scheme was applied using a Dolph filter with a 2-h time span and a 1-h cutoff period in the DFI experiment.
The D02 DPSDT and DARDT time series averaged over 48 cycles are shown in Fig. 12. The precipitation forecast scores, CSI and BIAS, of the hourly precipitation forecasts during the 0–6 h for D02 from the NOIAU, IAU, and DFI experiments are shown in Fig. 13. The results of D01 were quite similar and hence omitted. Judging from the DPSDT both DFI and IAU had similar noise control capability. However, the DARDT results indicate that the spinup problem related to the imbalance between hydrometeors and dynamical fields were not well addressed by DFI. DARDT of DFI started from a lower value than IAU and NOIAU, followed by a quick spindown and spinup process thereafter, becoming larger than IAU and NOIAU after t = 2 h and t = 3.5 h, respectively. As a result, DFI had the lowest BIAS at t = 1 h and BIAS quickly rise since t = 2 h (Fig. 13b), especially for the larger thresholds such as 5 and 10 mm h−1. No such BIAS jump from 1 to 2 h in the IAU experiment. In general, IAU had higher CSI (Fig. 13a) scores and better (closer to 1) BIAS scores than DFI for all the thresholds and through the first 6 h.
The time series of the domain-average DPSDT (hPa h−1) and DARDT (mm h−1) averaged over 48 forecasts during 0000 UTC 16 Jul–2300 UTC 17 Jul 2018 for D02.
Citation: Weather and Forecasting 38, 7; 10.1175/WAF-D-22-0127.1
The precipitation forecast scores, (a) CSI and (b) BIAS, of the hourly precipitation forecasts during the 0–6-h period for D02 from the NOIAU, IAU, and DFI experiments, averaged over 48 forecasts during 0000 UTC 16 Jul–2300 UTC 17 Jul 2018 for D02.
Citation: Weather and Forecasting 38, 7; 10.1175/WAF-D-22-0127.1
In addition to better filtering performance, IAU has the following advantages over DFI: IAU does not need to perform backward integration, so it avoids inconsistencies caused by the adiabatic process of backward integration; and for a same time-span window, IAU can save from 1/2 to 2/3 of the integration time. However, the model state at hour 0 when using IAU cannot be treated as a true initialized analysis, thus limiting its use on certain applications, e.g., reanalysis.
5. Preoperational results
Two continuous hourly cycling data assimilation and forecasting systems with and without IAU technique, namely, IAU and NOIAU, respectively, were conducted in parallel during the summertime from 8 May to 31 August 2019. Their basic cycling configurations were the same as the aforementioned NOIAU experiment, and the only difference between the two experiments was that DOLPHWIN was used as the initialization method in the IAU experiment. The precipitation verification results, CSI and BIAS, for the summer of 2019 and D01 are shown in Fig. 14. During the long experiment period, improved scores from the IAU experiment were found for all thresholds and up to 12 h. It became operational after this preoperational test and IAU remains as the initialization scheme in further system upgrades since then.
The precipitation forecast scores, (a) CSI and (b) BIAS, of the hourly precipitation forecasts for D01 during 12 h for the two parallel continuous hourly cycling data assimilation and forecasting systems during the period of 8 May–31 Aug 2019.
Citation: Weather and Forecasting 38, 7; 10.1175/WAF-D-22-0127.1
6. Summary and discussion
An IAU-based initialization method was developed for the WRF model and implemented in an operational hourly update cycling analysis and forecasting system. In addition to the constant time coefficients as in most IAU implementations, the time-varying weights based on a digital filter were tested. To examine the behaviors of the IAU in terms of initialization performance, spinup phenomena, and its impacts on data assimilation and precipitation performance, 7-day hourly update cycling retrospective tests were performed with and without IAU initializations. The simulation results suggest that IAU, designed as an initialization method, has successfully achieved the goals to suppress numerical noise to a reasonable level and alleviate the spinup/spindown problem with much more stable precipitation rates during the model integration. Moreover, IAU’s positive impact on data assimilation can be seen in terms of more observations being assimilated due to better balanced backgrounds. The detailed hourly precipitation and radar reflectivity forecast comparison also indicated that IAU effectively corrected the large overprediction of the regular hourly cycling forecasts caused by the spinup problems, leading to better precipitation forecast. It has also been discovered that the time-varying weights based on a digital filter of the Dolph–Chebyshev window (DOLPHWIN) perform similarly to the constant IAU coefficients in terms of filtering effectiveness and forecast. DOLPHWIN is ultimately decided upon as the upcoming operational IAU coefficients due to its greater theoretical plausibility. Finally, long-term runs by the two continuous hourly cycling data assimilation and forecasting systems with and without IAU technique were evaluated. The results of positive impact using IAU initialization on the rainfall forecast for all the thresholds and long forecast length further confirm its implementation in an operational hourly cycling system.
Acknowledgments.
This research is sponsored by the National Key Research and Development Project of China (2022YFC3004003, 2018YFC1506804) and the Key Innovation Team of China Meteorological Administration (CMA2022ZD09).
Data availability statement.
The radar, GTS, and AWS data are from China Meteorological Administration. The WRF Model output upon which this study is based are too large to archive or to transfer. Instead, the IAU code, compilation script, initial and boundary condition files, and the namelist settings, etc. are available upon request.
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