1. Introduction
Severe weather often leads to significant societal losses, making its accurate prediction crucial for short-range weather forecasting. Specifically, convective clouds can develop in less than 10 min in urban areas like Tokyo, Japan, during summer, leading to localized torrential rainfall (e.g., Takahashi et al. 2019; Kato et al. 2017). To predict such severe weather with numerical weather prediction (NWP), it is essential to obtain accurate initial conditions through data assimilation (DA). Indeed, previous studies indicated that assimilating weather radar observations improves analyses and forecasts of convective clouds (e.g., Snyder and Zhang 2003; Dowell et al. 2004; Zhang et al. 2004; Tong and Xue 2005; Aksoy et al. 2009). Furthermore, recent studies have successfully assimilated frequent observations by state-of-the-art phased-array weather radars (PAWRs) (Miyoshi et al. 2016a,b; Maejima et al. 2017; Honda et al. 2022a,b; Taylor et al. 2023; Miyoshi et al. 2023; Supinie et al. 2017; Stratman et al. 2020).
It is well known that Earth’s atmosphere possesses a chaotic nature, which limits the predictability of weather. The predictability limits can be categorized into the practical and intrinsic predictability limits (e.g., Zhang et al. 2019; Sun and Zhang 2016). The former refers to how we can predict a weather phenomenon with the current state-of-the-art NWP systems and realistic uncertainties in the initial and boundary conditions, whereas the latter refers to such ability using nearly perfect NWP systems and idealized tiny uncertainties in the initial and boundary conditions (e.g., Zhang et al. 2019; Sun and Zhang 2016). In particular, the intrinsic predictability limit can be regarded as the theoretical limit of atmospheric predictability. Investigating the intrinsic predictability and associated processes enhances our understanding of the atmosphere and could provide valuable implications for improving operational NWP.
The predictability limits differ across weather phenomena due to their unique dynamics and levels of nonlinearity. Consequently, numerous studies have explored the predictability limits of a variety of weather phenomena. For instance, Zhang et al. (2002, 2003) investigated the predictability of an intense snow storm and found that small changes in the initial conditions can greatly affect the mesoscale distribution of precipitation. Similar findings but with reduced upscale error growth were reported for a warm-season precipitation event (Zhang et al. 2006). Zhang et al. (2007) indicated a multistage error-growth process in baroclinic waves. In addition, other studies investigated the predictability limits of tropical cyclones and associated differences in large-scale environments and the initial conditions (e.g., Zhang and Tao 2013; Zhang et al. 2017; Tao and Zhang 2014, 2015; Tao et al. 2022; Nystrom and Zhang 2019; Minamide et al. 2020).
Several studies have examined the predictability limits of severe weather related to convective clouds. For instance, Zhang et al. (2015) investigated the practical predictability limit of a tornadic supercell, showing that small differences in low-level moisture affect convection initiation and subsequently modify the development of convective systems. This is consistent with later studies on mesoscale convective systems (MCSs) (Peters et al. 2017; Schumacher and Peters 2017). Zhang et al. (2016) focused on the same supercell and revealed its intrinsic predictability limit through ensemble simulations with a horizontal grid spacing (Δx) of 250 m. Markowski (2020) has indicated that tornadoes are largely affected by subtle differences in the initial conditions using high-resolution (Δx = 75 m) idealized ensemble simulations. Additionally, using a convection-permitting NWP model (Δx = 2 km), Bachmann et al. (2019, 2020) have indicated that the practical predictability limit of summertime deep convection can be extended by orography and the assimilation of radar observations.
Although many studies have focused on the intrinsic predictability limit of various weather phenomena, our knowledge of the predictability limits of localized convective rainfall in the summer is still limited. This is because such rainfall is associated with convective clouds, which are small scale (<10 km) and exhibit rapid (e.g., Fig. 5 of Miyoshi et al. 2016b) and nonlinear (e.g., Ruiz et al. 2021) development. To investigate the predictability limits of localized convective rainfall, it would be necessary to use high-resolution simulations with appropriate initial conditions that include realistic high-resolution uncertainty.
This study investigates the intrinsic and practical predictability limits of a localized torrential rainfall event near Tokyo, Japan, in 2019. During this event, a convective system was rapidly developed and was observed in detail by the multiparameter PAWR (MP-PAWR; Takahashi et al. 2019). This study uses a high-resolution NWP model (Δx = 50 m), which can be regarded as a large-eddy simulation (LES) of the target convective system if its length scale l is ∼5 km or more (i.e.,
The rest of this article is structured as follows. Section 2 offers an overview of the target convective rainfall event. Section 3 outlines the methods. Section 4 assesses the assimilation of MP-PAWR observations. Section 5 presents the main results and discussion in terms of predictability limits. Finally, section 6 summarizes our findings and provides some additional remarks.
2. Case overview
The target convective precipitation event on 24 August 2019 near Tokyo, Japan, has been used as a test case for the assimilation of MP-PAWR observations (Honda et al. 2022a,b; Taylor et al. 2023). As shown in Fig. 1a, the synoptic-scale environment during this event was characterized by an extratropical cyclone to the east of Japan (black contours). An upper-level cold air mass (blue contour) and warm air from the south (color shading) resulted in a convectively unstable atmosphere near Tokyo.
Horizontal maps of (a) the temperature at 850 hPa (color shading; K), mean sea level pressure (MSLP) (black contours; every 4 hPa), and temperature at 500 hPa (blue contour; 265 K) from the initial conditions of the NCEP GFS valid at 1200 UTC 24 Aug 2019 and (b) the previous 1-h accumulated precipitation amount (mm) from the JMA radar observations valid at 1500 UTC 24 Aug 2019. The black mark and dashed contours in (b) indicate the location of MP-PAWR and the distance from it (20, 40, and 60 km).
Citation: Journal of the Atmospheric Sciences 82, 1; 10.1175/JAS-D-24-0022.1
MP-PAWR observed the rapid development of a convective precipitation system (Fig. 2). Up until 1340 UTC, MP-PAWR observed discrete convective clouds (Figs. 2a–c). These clouds rapidly developed within 10 min, formed a convective system by 1350 UTC, and continued to develop until 1400 UTC (Figs. 2d,e). This convective system was maintained for over 30 min, causing localized rainfall (Figs. 2e–h). The 1-h accumulated precipitation amount estimated by the Japan Meteorological Agency (JMA) operational C-band radars was over 30 mm (Fig. 1b), the definition of torrential rainfall by JMA. According to JMA (2024), in Japan, extreme precipitation events with the rainfall amount of ≥50 mm h−1 are observed approximately 330 times per year. In general, as precipitation intensity decreases, the frequency of such events increases (e.g., JMA 2024; Martinez-Villalobos and Neelin 2019). Thus, convective precipitation similar to the target event would be frequently observed in the warm season in Japan. Previous studies (Honda et al. 2022a,b; Taylor et al. 2023) have focused on another new convective system that developed later on 24 August, but its development was likely affected by the preceding convective system. Therefore, this study focuses on the preceding convective system that developed around 1400 UTC.
Horizontal maps of MP-PAWR radar reflectivity observations (dBZ) on 24 Aug 2019 within a height (z) range of 2.0 ± 0.2 km within the height (z) range of 1.8–2.2 km (z = 2.0 ± 0.2 km) at (a) 1320:00, (b) 1330:00, (c) 1340:00, (d) 1350:00, (e) 1400:00, (f) 1410:00, (g) 1420:00, and (h) 1430:00 UTC. Gray dashed curves indicate the distance from MP-PAWR (20, 40, and 60 km).
Citation: Journal of the Atmospheric Sciences 82, 1; 10.1175/JAS-D-24-0022.1
3. Methodology
a. Model
We used a regional model from the Scalable Computing for Advanced Library and Environment (SCALE; Nishizawa et al. 2015; Sato et al. 2015). As depicted in Fig. 3, this study employed quadruply nested domains with Δx = 9 km for domain 1 (D1), 1.5 km for domain 2 (D2), 300 m for domain 3 (D3), and 50 m for domain 4 (D4). Similar to Sueki et al. (2019), the model top was set at 37.9 km for D1 and at 36.4 km for the other domains (Table 1). Since the length scale of the target convective system was
Horizontal maps of the computational domains for (a) D1, D2, and D3 and for (b) D3 and D4. The innermost rectangle in (a) indicates D3. Color shading is the terrain height (m) for D1 in (a) and D3 in (b). The blue mark and dashed contours in (b) indicate the location of MP-PAWR and the distance from it (km).
Citation: Journal of the Atmospheric Sciences 82, 1; 10.1175/JAS-D-24-0022.1
Model and DA configurations in each domain.
The model configuration largely follows that of Honda et al. (2022a,b) and Sueki et al. (2019). All four domains used a single-layer urban canopy model (Kusaka et al. 2001), a Beljaars-type bulk surface-flux model (Beljaars and Holtslag 1991), and the model simulation radiation transfer code (MSTRN) X (Sekiguchi and Nakajima 2008). Subgrid-scale turbulence was represented using a Smagorinsky-type scheme (Lilly 1962; Smagorinsky 1963). Additionally, D1 and D2 incorporated the level-2.5 closure of the Mellor–Yamada–Nakanishi–Niino scheme (Nakanishi and Niino 2004). For D1, D2, and D3, we used the single-moment six-category Tomita (2008) cloud microphysics scheme, which predicts ratios of water vapor mass qυ, cloud water mass qc, rain mass qr, cloud ice mass qi, snow mass qs, and graupel mass qg to total mass. D1 also utilized the Kain–Fritsch cumulus parameterization scheme (Kain and Fritcsh 1990; Kain 2004). Preliminary experiments using the Tomita (2008) microphysics scheme in D4 revealed an unrealistic overintensification of the target convective system. Therefore, for D4, we used the double-moment microphysics scheme developed by Seiki and Nakajima (2014), which predicts the specific contents of the aforementioned six categories and the number densities of cloud water (Nc), rain (Nr), cloud ice (Ni), snow (Ns), and graupel (Ng).
b. Data assimilation system
This study used the SCALE–local ensemble transform Kalman filter (LETKF) system (Lien et al. 2017), which consists of the SCALE model and the LETKF (Hunt et al. 2007; Miyoshi and Yamane 2007). In general, the accuracy of EnKF analyses is improved as the ensemble size increases due to reduced sampling errors (e.g., Miyoshi et al. 2014; Kondo and Miyoshi 2016). However, using a larger ensemble size requires a larger amount of computing resources. In this study, by considering the amount of available computing resources and the success of the previous studies with Δx = 100 m (Miyoshi et al. 2016a,b; Maejima et al. 2017), we set the ensemble size at 100. Similar to Lien et al. (2017), SCALE–LETKF analyzes the three components of velocity (u, υ, and w for x, y, and z directions), temperature (T), pressure (p) and the ratios of six-category water mass to the total mass. For D4, SCALE–LETKF also analyzes the number densities of the five hydrometeors.
The DA configuration for each domain is summarized in Table 1. Similar to Lien et al. (2017) and Honda and Miyoshi (2021), D1 assimilates conventional (nonradiance) National Centers for Environmental Prediction (NCEP) prepared data in Binary Universal Form for Representation of Meteorological Data (PREPBUFR) observations every 6 h. Unlike Honda et al. (2022b), the mesoscale domain (D2) also assimilated conventional PREPBUFR and MP-PAWR observations every 10 min to provide better boundary conditions for high-resolution domains. By considering the sparsity of conventional PREPBUFR observations in D3 and D4, these domains assimilated MP-PAWR observations only. Covariance inflation was achieved by the relaxation-to-prior-spread (RTPS) method (Whitaker and Hamill 2012). We tested a few coefficients (such as 0.8 and 0.9) and then set the coefficient to 0.9 for all domains.
A Gaussian-like function (Gaspari and Cohn 1999) was used for localization. Characteristic length scales for localization (σh for horizontal and σv for vertical) were set as shown in Table 1. Here, the cutoff radius corresponds to
Assimilation of MP-PAWR observations generally follows Honda et al. (2022b). This study used the observation operator developed by Amemiya et al. (2020) for MP-PAWR radar reflectivity Z observations. Similar to Aksoy et al. (2009), Z observations of <10 dBZ were assimilated as zero-precipitation observations with 5 dBZ to suppress spurious convection effectively. This treatment would also contribute to reducing negative values in analyzed hydrometeors (Janjić and Zeng 2021). When the number of precipitating ensemble members was smaller than five, we discarded the zero-precipitation (Z < 10 dBZ) observations and applied an additive inflation method (Yokota et al. 2018; Honda et al. 2023) for the precipitation (Z ≥ 10 dBZ) observations. The observation error standard deviation was set at 3 dBZ for Z observations and 1.5 m s−1 for Doppler radial velocity Vr observations. Similar error settings were used in Jung et al. (2012) and Snook et al. (2015). These values were found to improve the forecast accuracy and the consistency ratio (Dowell et al. 2004) based on preliminary sensitivity experiments with larger observation errors such as 5 dBZ and 3 m s−1 (not shown).
Localization for MP-PAWR observations generally follows previous studies. Similar to Wang et al. (2022) who set the horizontal cutoff radius at 12 km with Δx = 1 km, D2 employed σh = 4 km and σv = 4 km. Following Maejima et al. (2017), D3 used σh = 1 km and σv = 1 km. D4 also employed σv = 1 km because appropriately representing the vertical structure of convection with a larger σv would be important for accurate prediction (Wu et al. 2020). To effectively suppress spurious convection, similar to Aksoy et al. (2009), this study used a larger σh of 400 m for nonprecipitating Z observations and a smaller σh of 200 m for precipitating Z and Vr observations in D4.
c. Preprocessing of MP-PAWR observations
As shown in Figs. 4a and 4e, MP-PAWR observations are very dense especially near MP-PAWR, so that superobbing and thinning are necessary. This study generally followed the superobbing method used by Zhang et al. (2009). Their method averages raw observations within a bin at each radar elevation angle. The radial length of each bin was set at 2 km for D2, 500 m for D3, and 75 m for D4 by considering different Δx for each domain (Table A1). The azimuth angle of each bin was set at 1.2°, approximately corresponding to the azimuth interval of the original MP-PAWR data (Takahashi et al. 2019). When averaging, Vr observations with |Vr| > 70 m s−1 or Z ≤ 5 dBZ were discarded. Similar to Zhang et al. (2009), raw observations close to MP-PAWR (the distance to MP-PAWR is <5 km) were not used. Before the superobbing procedure, attenuation for Z observations was corrected by the method of Maesaka et al. (2011). In addition, quality control (QC) was applied to exclude raw observations affected by the terrain and buildings (Honda et al. 2022b).
(a)–(d) Horizontal maps and (e)–(h) vertical cross sections of MP-PAWR radar reflectivity observations (dBZ) (a),(e) without thinning; (b),(f) with adaptive thinning for D4; (c),(g) with adaptive thinning for D3; and (d),(h) with adaptive thinning for D2 valid at 1400 UTC 24 Aug 2019. Horizontal maps in (a)–(d) are constructed by the observations at a height (z) of z = 2 ± 0.2 km within the height range of 1.8–2.2 km shown by the blue shading in (e)–(h). Vertical cross sections in (e)–(h) are constructed by the observations with the radar azimuth angle ϕ of ϕ = 14° ± 0.6° shown by the blue shading in (a)–(d). Black dashed contours indicate the distance from MP-PAWR (km).
Citation: Journal of the Atmospheric Sciences 82, 1; 10.1175/JAS-D-24-0022.1
Superobbed observations would still have correlated components of the observation errors (e.g., Janjić et al. 2018). These components degrade the performance of LETKF, which generally uses a diagonal observation-error covariance matrix (e.g., Terasaki and Miyoshi 2024). To suppress the effects of the correlated components of the observation errors, this study used an adaptive thinning method for superobbed MP-PAWR observations. The method is applied in the radar polar coordinates. The thinning method ensures that the spatial distance of superobbs in each direction is longer than a prescribed threshold. The threshold distance was separately set for precipitation (Z > 15 dBZ), no-precipitation (Z ≤ 15 dBZ), and Vr observations in each domain. Namely, following Aksoy et al. (2009), the thinning distance for no-precipitation observations was set to be longer than that for precipitation observations.
We tested several settings of the threshold distance, such as 200 and 400 m for the elevation direction, and then set the values as in Table A1 in the appendix, considering Δx in each domain. As shown in Figs. 4b–d and 4f–h, the thinning method effectively reduces the number of observations than that without thinning (Figs. 4a,e), especially near MP-PAWR, while maintaining the general characteristics such as a taller convective cloud with a reflectivity core below the height of 6 km and a weak shallower cloud.
d. Ensemble perturbations
Following Necker et al. (2020) and Honda (2023), this study generated ensemble perturbations for D1 using past NCEP Global Forecast System (GFS) data (see Fig. 2 of Honda 2023). First, a pair of GFS initial conditions at 0000 UTC on different dates in August 2018, 2020, 2021, and 2022 was randomly chosen for each ensemble member. The difference between each pair represents ensemble perturbations for each member. Second, the ensemble mean of the aforementioned perturbations was subtracted such that the ensemble perturbations were unbiased. Third, as in Honda (2023), the ensemble perturbations were rescaled by a multiplicative factor of 0.3. This factor was chosen by Honda (2023), who tested factors of 0.1, 0.3, 0.5, and 1.0. Following Necker et al. (2020) and Honda (2023), a smooth evolution of the ensemble perturbations was achieved by using sequential GFS data. For example, if the ensemble perturbations at time t for the ensemble member X were based on GFS data at dateX1 and dateX2, the next perturbations at time t + 6 h were generated by GFS data at dateX1 + 6 h and dateX2 + 6 h.
e. Workflow
The workflow for each domain is illustrated in Fig. 5. This study initiated D1 at 0000 UTC 9 August 2019 and started assimilating 6-hourly conventional PREPBUFR observations at 0600 UTC 10 August 2019. The spinup period for D1 was approximately 2 weeks because D1 was initiated from the ensemble perturbations generated by the random pairs of the GFS data (section 3d). Indeed, previous studies with similar methods for the ensemble perturbations used approximately 1 week as spinup (Necker et al. 2020; Honda 2023). D2 was initiated at 1200 UTC 24 August, assimilated PREPBUFR observations only as a spinup, and then assimilated both PREPBUFR and MP-PAWR observations from 1230 UTC. D3 and D4 were initiated at 1230 and 1300 UTC, respectively. Following their spinup ensemble forecasts, D3 and D4 started assimilating MP-PAWR observations at 1300:00 and 1330:30 UTC, respectively. Longer spinup periods especially for finer grid-spacing domains could improve the performance of the EnKF, but this study set the aforementioned workflow due the limitation of available computing resources.
General workflow of the four domains. Periods with slanted lines are for spinup. Time unit is UTC.
Citation: Journal of the Atmospheric Sciences 82, 1; 10.1175/JAS-D-24-0022.1
f. Ensemble forecasts
This study investigates the practical and intrinsic predictability limits of the target convective precipitation event by comparing four 30-min ensemble forecasts initiated from 100-member analyzed ensemble states in D4 (Table 2). The first ensemble forecast, referred to as ALL1.0, was initiated using the analyzed ensemble states rescaled by a factor of 1.0 for all analyzed variables. This rescaling does nothing because it multiplies the ensemble perturbations by a factor of 1.0 and adds them to the ensemble mean. This process does not change the analyzed ensemble spread, which represents a practical level of initial-condition uncertainty. ALL1.0 was utilized to assess the practical predictability limit. The second ensemble forecast, named ALL0.1, was initiated by rescaling all analyzed variables with a factor of 0.1. In ALL0.1, the initial ensemble spread at a height of 2 km was approximately 0.2 m s−1 (u), 0.05 K (T), and 0.07 g m−3 (qυ) in the vicinity of the target convective precipitation system. To exclude the effects of ensemble perturbations in the unanalyzed variables, all variables except for the analyzed ones, such as the land temperature, were replaced with their ensemble mean during rescaling.
List of four ensemble forecasts with configurations of their initial conditions. All variables include the total density (ρ), three components of the momentum (ρu, ρυ, ρw), mass-weighted potential temperature (ρθ), qυ, qc, qr, qi, qs, qg, Nc, Nr, Ni, Ns, and Ng. Precipitation variables include qr, qs, qg, Nr, Ns, and Ng. Wind variables include ρu, ρυ, and ρw. See Nishizawa et al. (2015) for more details of each variable.
The initial conditions in ALL0.1 have a highly reduced level of uncertainty, with only 10% of the ensemble perturbations compared to those in ALL1.0. As noted by Zhang et al. (2019), achieving this level of uncertainty in the foreseeable future would be impossible. In contrast to ALL1.0 with a practical level of initial-condition uncertainty, this idealized scenario with nearly perfect initial conditions (ALL0.1) offers an estimate of the intrinsic predictability limit. These parameter values of 1.0 and 0.1 simply follow Zhang et al. (2016) who investigated the predictability limits of a tornadic thunderstorm. To investigate the intrinsic predictability limit, a smaller factor (e.g., 0.001) could be used; however, such a scenario may yield a similar estimate to that of ALL0.1, as smaller errors tend to grow faster (Zhang et al. 2003). Indeed, Selz et al. (2022) have demonstrated that reducing initial errors from 10% to 0.1% of their magnitude (equivalent to factors of 0.1 and 0.001 in the present study) yields only a minor gain in predictability. A larger factor, such as 0.5, raises ambiguity as to whether it represents practical or intrinsic. Therefore, this study chooses a factor of 0.1, as in Zhang et al. (2016), to represent an idealized level of initial-condition uncertainty that would be impossible to achieve even in the future.
The other two forecasts were used to assess which variables (precipitation-related or wind variables) need reduced uncertainty in the initial conditions to improve forecast accuracy. The third ensemble forecast, referred to as DBZ0.1, used the initial conditions rescaled by a factor of 0.1 for precipitation-related variables (i.e., qr, qs, qg, Nr, Ns, Ng) and a factor of 1.0 for the other variables. The fourth ensemble forecast, referred to as UVW0.1, used a rescaling factor of 0.1 for the three components of the momentum and 1.0 for the other variables including total density ρ.
As commonly done in previous studies (e.g., Zhang et al. 2006, 2019), in section 5, this study assumes that the forecast (SCALE) model and the boundary conditions are perfect. Namely, we used the single-member boundary conditions from deterministic forecasts initiated from the ensemble-mean analysis in D3. In this idealized scenario, a reduction in the forecast ensemble spread by changing initial-condition perturbations corresponds to an improvement in forecast accuracy, as forecasts without initial-condition perturbations are assumed to be perfect. Such changes in initial conditions could be achieved by advancing DA procedures and observing systems in the future. In reality, however, the forecast model and boundary conditions are definitely imperfect. Therefore, this study estimates an upper bound of the predictability limit in the idealized scenario.
In this study, the predictability limit was measured by the ensemble spread, which represents forecast uncertainty. When the ensemble spread exceeds a threshold, the ensemble forecast can be regarded as too uncertain and loses its value. For the threshold, this study uses the observation error standard deviation in LETKF (i.e., σoLETKF = 3 dBZ), which represents a practical level of observation uncertainty. The ensemble spread at each grid point can be large when the same convective clouds are slightly dislocated. Furthermore, even if the overall behavior of a convective system was generally predictable, a small portion of it may have a large ensemble spread. Therefore, this study uses the fraction of the precipitating grid points (Z ≥ 15 dBZ) that have the ensemble spread in Z of ≥σoLETKF to assess the predictability limits. The fraction was calculated within the range of 139.6°–140.15°E and 36.1°–36.4°N, where the target convective system remained until 1420 UTC. When the fraction becomes almost 100%, the entire convective system can be regarded as unpredictable.
4. Assessing the assimilation of MP-PAWR observations
Before exploring the predictability limit, we briefly assess the performance of SCALE–LETKF in D4. As illustrated in the horizontal maps in Fig. 6, the spatial pattern of the analyzed radar reflectivity in SCALE–LETKF is generally similar to the observation, except for unobservable areas. Namely, SCALE–LETKF successfully analyzed discrete clouds at 1340 UTC, two developing convective systems (denoted as A and B in Fig. 6e) at 1350 UTC, and further development of A and dissipation of B until 1400 UTC. These characteristics could not be found when the MP-PAWR observations were not assimilated in D4 (Figs. 6g–i). In addition, sawtooth patterns were found in the time series of the root-mean-square errors (e.g., Fig. 3 of Miyoshi et al. 2016a) against MP-PAWR’s radar reflectivity and Doppler velocity observations (not shown). These results indicate that we have successfully assimilated the MP-PAWR observations every 30 s with Δx = 50 m.
Horizontal maps of radar reflectivity (dBZ) from (a)–(c) MP-PAWR observations, (d)–(f) analyzed ensemble-mean states, and (g)–(i) those without assimilating MP-PAWR observations (NODA) at (a),(d),(g) 1340:00 UTC; (b),(e),(h) 1350:00 UTC; (c),(f),(i) 1400:00 UTC 24 Aug 2019. The height z is set at z = 1.8–2.2 km in (a)–(c) and z = 2.0 km in (d)–(i). The dark gray shading represents the unobservable area of MP-PAWR in (a)–(c) and areas outside of D4 in (d)–(i). Black dashed contours indicate the distance from MP-PAWR (km). Black dashed circles in (e) indicate the convective system A and B.
Citation: Journal of the Atmospheric Sciences 82, 1; 10.1175/JAS-D-24-0022.1
The analysis accuracy of SCALE–LETKF is also evident by comparing its forecast with the MP-PAWR observations (Fig. 7). We performed a single-member forecast from the analyzed ensemble mean at 1400:00 UTC. SCALE–LETKF predicted the development of the convective systems A and B up to the forecast time (FT) of 20 min even though the convective system B dissipated in the MP-PAWR observations (Figs. 7b,e). At FT = 30 min, the simulated convective systems seem to be affected by the advection of other convective clouds from the lateral boundaries (Fig. 7f). Thus, in section 5, we will discuss only up to FT = 20 min. In summary, SCALE–LETKF was not able to accurately predict the evolution of the convective systems A and B, but it simulated the development of the convective systems. Considering the clear differences between the SCALE–LETKF forecasts and observations, we will focus on evolution of the ensemble spread in the following section. Improving the forecast accuracy of SCALE–LETKF is an important subject for our future research.
As in Fig. 6, but for (d)–(f) the forecast initiated from the ensemble mean at 1400:00 UTC and (a)–(c) corresponding MP-PAWR observations valid at (a),(d) 1410:00, (b),(e) 1420:00, and (c),(f) 1430:00 UTC. The FTs are 600 s in (d), 1200 s in (e), and 1800 s in (f).
Citation: Journal of the Atmospheric Sciences 82, 1; 10.1175/JAS-D-24-0022.1
5. Predictability limits
a. Intrinsic and practical predictability limits
As mentioned in section 3f, we performed ALL1.0 and ALL0.1 to assess the practical and intrinsic predictability limits. We initiated these forecasts at 1340:00, 1350:00, and 1400:00 UTC and obtained similar results regardless of the initial time. Therefore, we will focus on the results from the initial conditions at 1400:00 UTC. Since averaging ensemble forecasts involving highly nonlinear processes would result in an unrealistically smooth state, this study investigates selected individual members and the ensemble spread.
Before quantitatively assessing the predictability limits using the ensemble spread, we investigate differences in three selected ensemble members. Large differences among the members within a short FT would imply that predictability is strictly limited by fast forecast error growth. In ALL1.0, the three members predicted very similar patterns of radar reflectivity (Figs. 8a–c). However, nonnegligible differences are found in fine-scale structures even within the 10-min ensemble forecast. For example, the development of a new convective cell in the east and the convective system B is different among the selected members. These members also have slightly different distributions of high radar-reflectivity areas (>55 dBZ) in the core of the convective system A. This indicates that the forecast error growth is very fast when the initial conditions have a practical level of uncertainty, and fine-scale characteristics would be practically unpredictable even within 10 min in the target event. In contrast, ALL0.1 does not exhibit as large differences by FT = 10 min (Figs. 8d–f), indicating that the intrinsic predictability limit would be longer than 10 min and that improving the initial conditions could extend the practical predictability limit of the target event.
Horizontal maps of radar reflectivity (dBZ) from forecasts initiated at 1400:00 UTC 24 Aug 2019 in members (a),(d) 1, (b),(e) 2, and (c),(f) 3 of (a)–(c) ALL1.0 and (d)–(f) ALL0.1. The FT and height z are 10 min and 2.0 km, respectively. Gray dashed contours indicate the distance from MP-PAWR (40 and 60 km). Black dashed ovals in (a)–(c) show the location of the convective core, new cell, and convective system B.
Citation: Journal of the Atmospheric Sciences 82, 1; 10.1175/JAS-D-24-0022.1
Horizontal maps of the ensemble spread of radar reflectivity also indicate that the intrinsic predictability limit of the target precipitation event would be much longer than the practical predictability limit. As shown in snapshots of the ensemble spread, many areas in ALL1.0 exhibit fast growth of the ensemble spread even within 10 min (Figs. 9a,b). In particular, the ensemble spread is large in the core of the convective system A and the new convective cell (Fig. 9b). In these areas, the ensemble spread further grows until FT = 20 min (Fig. 9c). On the other hand, ALL0.1 exhibits slow growth of the ensemble spread in 10 min, indicating that the intrinsic predictability limit would be longer than 10 min. Even at FT = 20 min, ALL0.1 has a small ensemble spread, except in the core and an eastern area of the convective system A (Fig. 9f). The eastern area would be associated with a merging process between the convective system A and new convective cell. Therefore, in the target event associated with the convective systems A and B, highly nonlinear processes such as the rapid development in the convective core and the cell merger would be intrinsically unpredictable, whereas general characteristics of these convective systems would be intrinsically predictable at least up to FT = 20 min.
Horizontal maps of the ensemble spread (color shading; dBZ) and ensemble mean (contours; 15 dBZ) in radar reflectivity at a height z of 2 km for (a)–(c) ALL1.0, (d)–(f) ALL0.1, (g)–(i) DBZ0.1, and (j)–(l) UVW0.1 at the FTs of (a),(d),(g),(j) 0; (b),(e),(h),(k) 10; and (c),(f),(i),(l) 20 min. The initial time is 1400:00 UTC 24 Aug 2019. Black dashed ovals in (b) indicate the location of the convective core and new cell.
Citation: Journal of the Atmospheric Sciences 82, 1; 10.1175/JAS-D-24-0022.1
The differences in the forecast error growth between ALL1.0 and ALL0.1 are further evident in a time series of the fraction of the precipitating grid points (Z ≥ 15 dBZ) that have the ensemble spread in Z of ≥σoLETKF (Fig. 10). Namely, the ensemble spread in ALL1.0 exceeds the threshold value for the predictability limits in this study across the whole area of the target precipitation system within 10 min (black curve in Fig. 10), whereas most areas have the ensemble spread of <σoLETKF in ALL0.1 as of FT = 10 min (magenta curve in Fig. 10).
Time series of the fraction of the precipitating grid points (Z ≥ 15 dBZ) within the region of 139.6°–140.15°E and 36.1°–36.4°N at a height of 2 km that have the ensemble spread Z of ≥σoLETKF in ALL1.0 (black), ALL0.1 (magenta), DBZ0.1 (cyan), and UVW0.1 (orange). The initial time is 1400 UTC 24 Aug 2019.
Citation: Journal of the Atmospheric Sciences 82, 1; 10.1175/JAS-D-24-0022.1
As shown in Figs. 9f and 10, some areas in ALL0.1 still have the ensemble spread of <σoLETKF as of FT = 20 min, indicating that the target system would be intrinsically predictable to some extent at FT = 20 min. The difference between the estimated practical and intrinsic predictability limits implies a large room for improvement for convective-scale NWP. Specifically, the practical predictability limit with the current NWP system could be extended toward the intrinsic predictability limit by improving the NWP model and DA system to obtain more accurate initial conditions.
Although we have focused on a low-level representative height of 2 km so far, the aforementioned differences in the forecast error growth can be found in the entire troposphere. As shown by vertical profiles of the area-averaged ensemble spread, the ensemble spread in ALL0.1 at FT = 20 min is much smaller than that in ALL1.0 for all vertical levels (solid magenta and solid black curves in Fig. 11). By comparing the dashed and solid black curves in Fig. 11, their differences (i.e., forecast error growth) below the midtroposphere are larger (faster) than those in the upper troposphere. This is probably because the convective core of the target convective system is located below the midtroposphere (Fig. 4). As indicated by previous studies (e.g., Peters and Schumacher 2015; Peters et al. 2017; Schumacher and Peters 2017), low-level characteristics such as convergence, vertical shear, moisture, and stability play a dominant role in the development of convective systems. Therefore, it would be important to reduce the initial-conditions errors, especially below the midtroposphere, to improve the forecast accuracy of the target convective event.
Vertical profiles of the area-averaged ensemble spread of radar reflectivity (dBZ) over the precipitating grid points (Z ≥ 15 dBZ) within the region of 139.6°–140.15°E and 36.1°–36.4°N in ALL1.0 (black), ALL0.1 (magenta), DBZ0.1 (cyan), and UVW0.1 (orange) at the FT of 20 min (solid curves). Dashed curves are those at FT = 0 min in ALL1.0 and ALL0.1. The initial time is 1400 UTC 24 Aug 2019. Computations were carried out at 1-km intervals in height.
Citation: Journal of the Atmospheric Sciences 82, 1; 10.1175/JAS-D-24-0022.1
Figure 11 also indicates that forecast error growth rate increases as the amplitude decreases. Specifically, the error doubling time in ALL0.1 is shorter than that in ALL1.0. This is consistent with the findings by Zhang et al. (2002, 2003), who showed that the growth rate depends on the error amplitude.
b. Which variables do we need to reduce their uncertainty for improving forecast accuracy?
In section 5a, we have found the gap between the intrinsic and practical predictability limits of the target convective precipitation event, which indicates room for improvement in practical NWP. A natural question that arises is which variables we need to reduce their initial-condition uncertainty to improve the forecast accuracy of the target event. Indeed, Reynolds et al. (2019) addressed a similar question regarding atmospheric rivers (ARs) using adjoint sensitivity analysis and indicated that low-level winds and precipitation associated with ARs were more sensitive to moisture in the initial conditions compared to horizontal winds. For a tornadic supercell in Japan, Yokota et al. (2016) performed an ensemble-based sensitivity analysis and showed that a low-level mesocyclone was sensitive to low-level winds and humidity.
To answer the above question, we performed two additional ensemble forecasts that use the initial conditions with ideally reduced uncertainty only for either precipitation-related variables (DBZ0.1) or wind variables (UVW0.1), but the other variables contain a practical level of uncertainty of the initial conditions. These experiments would provide implications for future development of NWP systems and observing networks for accurate short-range prediction of convective clouds. For example, if DBZ0.1 exhibited much slower forecast error growth than UVW0.1, it would be more promising to focus on reducing uncertainty of the reflectivity-related variables than doing so for the wind variables in future research. It is technically possible to perform more ensemble forecasts with ideally reduced uncertainty for a single variable, but this approach requires a large amount of additional computing resources. Therefore, this study focuses on the comparison between the wind- and precipitation-related variables.
Both DBZ0.1 and UVW0.1 show faster error growth than ALL0.1, indicating that both the precipitation and wind variables are important for improving the forecast accuracy (Figs. 9d–l). At the initial time (FT = 0 min), the fraction of the ensemble spread of ≥σoLETKF is the same between DBZ0.1 and ALL0.1 (UVW0.1 and ALL1.0) because the precipitation-related variables are rescaled by the same factor of 0.1 (1.0) in these experiments. In DBZ0.1, the fraction of the ensemble spread of ≥σoLETKF and area-averaged ensemble spread increases faster and becomes larger than those in UVW0.1 (cyan and yellow orange curves in Figs. 10 and 11).
UVW0.1 generally shows slower error growth than DBZ0.1 (Figs. 10 and 11), likely due to reduced uncertainty in advection and associated nonlinear processes. Indeed, the ensemble spread in UVW0.1 is generally smaller than that in DBZ0.1 for FT ≥ 10 min (Figs. 9g–l). As shown in Figs. 12b and 12d, a single member of DBZ0.1 has large westerly and broad positive Z perturbations at the initial time. At FT = 5 min, the same member has a broad westerly perturbation, a negative Z perturbation at the western edge, and a positive Z perturbation on the eastern side of the convective system (Figs. 12f,h). The negative Z perturbation at the western edge is unclear in the same member of UVW0.1, in which westerly perturbations are weak (Figs. 12a,c,e,g). Another ensemble member with a southerly perturbation has a negative Z perturbation at the southern edge of the convective system (not shown). These characteristics indicate that advection plays a dominant role in the short-range forecast error growth. Even if uncertainty in the precipitation variables was drastically reduced, the remaining uncertainty in the wind variables would result in a rapid forecast error growth due to advection. Therefore, reducing uncertainty in the wind variables could be more promising for improving the forecast accuracy in the target event than doing so for the precipitation variables, although the initial-condition errors in both variables largely contribute to the chaotic behavior of the target convective system.
Horizontal maps of the forecast perturbations in terms of the (a),(b),(e),(f) radar reflectivity (dBZ) and (c),(d),(g),(h) zonal wind speed (m s−1) against the ensemble mean at the FT of (a)–(d) 0 and (e)–(f) 5 min in the ensemble member 1 of (a),(c),(e),(g) UVW0.1 and (b),(d),(f),(h) DBZ0.1. The initial time and height are 1400 UTC and 3.0 km, respectively. Black contours are the ensemble-mean radar reflectivity (15 dBZ) in each ensemble forecast.
Citation: Journal of the Atmospheric Sciences 82, 1; 10.1175/JAS-D-24-0022.1
c. Sensitivity to Δx
An important difference between this study and the previous studies by Zhang et al. (2017, 2016) is Δx. Namely, this study has used Δx = 50 m, which is smaller than that used by these previous studies. To assess the impact of Δx on estimating the predictability limits of the target event, we performed an additional experiment with Δx = 300 m for D4 (hereafter DX300m). The model and DA configurations for DX300m were set the same as D4, except for its Δx and the use of the MP-PAWR preprocessing and localization settings for D3. In DX300m, analyzed radar reflectivity patterns were generally consistent with the corresponding MP-PAWR observations (Figs. 13a,d), indicating that SCALE–LETKF has successfully assimilated the MP-PAWR observations even with Δx > 50 m, as in the previous studies (Miyoshi et al. 2016a,b, 2023; Maejima et al. 2017; Honda et al. 2022a,b; Taylor et al. 2023). Figure 13 also shows that the forecast accuracy of SCALE–LETKF has room for improvement.
As in Fig. 6, but for the (d) ensemble-mean analysis at 1400:00 UTC 24 Aug 2019 and (e),(f) forecast initiated from it in the DX300m experiment. The FTs are 600 s in (e) and 1200 s in (f).
Citation: Journal of the Atmospheric Sciences 82, 1; 10.1175/JAS-D-24-0022.1
The intrinsic predictability limit estimated with Δx = 300 m seems longer than that estimated with Δx = 50 m. We performed ALL1.0 and ALL0.1 ensemble forecasts using the analyzed states from DX300m. In both ALL1.0 and ALL1.0 (DX300m), the fraction of the precipitating grid points with the ensemble spread of ≥σoLETKF becomes almost 100% within the first 10 min (black curves in Fig. 14). This indicates that the entire area of the target system would be practically unpredictable beyond FT = 10 min regardless of Δx. In contrast, the fraction of the ensemble spread of ≥σoLETKF at FT = 20 min in ALL0.1 (DX300m) is smaller than that in ALL0.1 (magenta curves in Fig. 14). Namely, we might overestimate the intrinsic predictability limit of the target event if we used DX300m only.
As in Fig. 10, but for the DX300m (solid curves) and DX300m experiment (dashed curves) without DBZ0.1 and UVW0.1.
Citation: Journal of the Atmospheric Sciences 82, 1; 10.1175/JAS-D-24-0022.1
The slow growth of the ensemble spread in ALL0.1 (DX300m) could have two potential interpretations. First, smaller-scale errors resolved with Δx = 50 m might grow faster than relatively larger-scale errors in Δx = 300 m. The scale dependence of forecast error growth has been reported by recent studies (Weyn and Durran 2019; Zhang 2023). In particular, Weyn and Durran (2019) have indicated that small-scale errors exhibit a larger growth rate than larger-scale errors if synoptic-scale forcing is weak. The target event can be regarded as a weak-forcing case because it occurred far from the synoptic-scale low-pressure system (Fig. 1a). To obtain more robust conclusions on the sensitivity to Δx, it would be necessary to perform more case studies with different synoptic-scale forcing in future research. Second, the results could be affected by suboptimal DA. In both Δx experiments, it would be possible to further improve the analyses and subsequent forecasts by using a larger ensemble size and optimizing DA parameters such as the localization scales. By doing so, the analyzed perturbations and their growth could be changed. In future research, it would be beneficial to use observing system simulation experiments (OSSEs), as they provide a robust means of controlling synoptic-scale forcing and initial-error characteristics. Furthermore, OSSEs enable the use of a large ensemble size when the computational domain is small. In summary, it is necessary to carefully assess the sensitivity to Δx in future research, although our results indicate that Δx could largely affect the estimation of the intrinsic predictability limit.
6. Summary and concluding remarks
This study has investigated the intrinsic predictability limit of the localized convective precipitation event near Tokyo, Japan, in August 2019 (Figs. 1, 2, and 4). We have used a high-resolution NWP model [horizontal grid spacing (Δx) of 50 m], which can be regarded as an LES of the target convective system, to capture small-scale forecast error growth (Table 1 and Fig. 3). To obtain the initial conditions with a practical level of uncertainty, we have assimilated the MP-PAWR observations every 30 s. The resulting analyses and forecasts were generally consistent with the MP-PAWR observations (Figs. 6 and 7).
To assess the practical and intrinsic predictability limits, we have performed a series of high-resolution ensemble forecasts (Table 2). The first ensemble forecast (ALL1.0) has been initialized by the initial conditions obtained by DA without rescaling their ensemble spread. ALL1.0 represents the practical predictability limit. The second ensemble forecast (ALL0.1) has used the same initial conditions, but their ensemble spread has been rescaled by a factor of 0.1. This rescaling corresponds to a large error reduction of the initial conditions (i.e., error amplitude in terms of energy is 1% of the original), and ALL 0.1 provides an estimate of the intrinsic predictability limit. The third (DBZ0.1) and fourth (UVW0.1) ensemble forecasts have employed the initial conditions in which only the precipitation-related variables or the wind variables have been rescaled by a factor of 0.1. These forecasts would imply which variables we need to reduce their uncertainty in the initial conditions to extend the practical predictability limit.
The intrinsic predictability limit of the target localized precipitation event would be much longer than its practical predictability limit. ALL0.1 shows slow error growth in terms of radar reflectivity for most areas up to FT = 20 min, indicating that the intrinsic predictability limit would be longer than 20 min (Figs. 9d–f and 10). In contrast, ALL1.0 exhibits fast error growth even within 10 min and indicates that the practical predictability limit would be shorter than 10 min (Figs. 9a–c and 10). These differences between ALL1.0 and ALL0.1 imply that the current NWP system has a large room for improvement of its forecast accuracy for the target event.
A natural question that arises is which variables we need to reduce their uncertainty in the initial conditions to improve the forecast accuracy. To answer this question, we have performed two additional ensemble forecasts (DBZ0.1 and UVW0.1). Both forecasts show faster error growth than ALL0.1, indicating that both the precipitation-related and wind variables would play important roles in forecast error growth (Fig. 9). UVW0.1 exhibits slower forecast error growth than DBZ0.1 especially below the midtroposphere (Figs. 10 and 11), probably due to reduced uncertainty in nonlinear processes related to advection (Fig. 12). Therefore, to improve the forecast accuracy, it could be more promising to focus on reducing uncertainty in the wind variables by refining assimilation procedures or advancing wind observing systems rather than doing so for the precipitation-related variables.
The estimated length of the intrinsic predictability limit depends on Δx. We performed the additional experiment with Δx = 300 m for D4 (Fig. 13). The intrinsic predictability limit estimated with Δx = 300 m seems longer than that with Δx = 50 m (Fig. 14). It should be noted that this result could be affected by suboptimal DA for Δx = 300 m. In addition, the growth of forecast errors on different spatial scales is case dependent and sensitive to synoptic-scale forcing. Nevertheless, it would be important to pay attention to the sensitivity of estimating the intrinsic predictability limit to Δx, especially in the convective scale.
Although this study has used the finest-ever horizontal-resolution simulations for exploring the intrinsic predictability limit of a localized convective precipitation event, several limitations still remain. For example, we have focused on a single case with a limited period (i.e., 20 min of FT). It is difficult to generalize the predictability limits of convective precipitation from one case. Therefore, it is necessary to investigate more convective precipitation events to assess the robustness of the findings, although it requires massive computing resources. Indeed, previous studies have indicated that the intrinsic predictability limit would vary with each event (e.g., Bachmann et al. 2020). Although this study has focused on the sensitivity of the predictability limits to perturbation amplitude only, investigating the sensitivity to perturbation regions could provide further insights. For example, perturbations in some limited regions might play a dominant role in forecast error growth. Similarly, it might be possible to assess the potential impacts of chaos seeding (Ancell et al. 2018) by perturbing a variable far from target convection. In addition, analyzing the forecast error growth through scale decomposition could offer further insights into the predictability limits (e.g., Selz and Craig 2015; Zhang 2023), although this study did not do so because the domain size seems too small. Furthermore, this study has relied on the performance of the SCALE–LETKF system in terms of the structure of analyzed ensemble perturbations. The SCALE–LETKF system would be still suboptimal because its ensemble size was limited and the observation operator was not optimal for the two-moment microphysics parameterization scheme in the SCALE model. Therefore, it would be desirable to investigate the intrinsic predictability limit by using other convective-scale DA systems or an improved version of SCALE–LETKF in future research.
This study would provide an example of the intrinsic and practical predictability limits of a localized convective precipitation event and implications for further improving the forecast accuracy. In particular, reducing uncertainty in the wind variables could be more promising for extending the forecast lead time than doing so for the precipitation variables. It is interesting to investigate what future observing networks could contribute to improving convective-scale NWP in observing-system simulation experiments (e.g., Maejima et al. 2022).
Acknowledgments.
The author thanks Shinsuke Sato of NICT for providing the MP-PAWR observation data and Shigenori Otsuka of RIKEN for supporting the preprocessing of the data. The author also thanks Yasumitsu Maejima of RIKEN for valuable discussion. This work used computational resources of the supercomputer Fugaku provided by the RIKEN Center for Computational Science through the HPCI System Research Project (Project: hp220207 and hp230244). This research was partially supported by the Research Field of Hokkaido Weather Forecast and Technology Development (endowed by Hokkaido Weather Technology Center Co. Ltd.) and JSPS KAKENHI (JP20K14558 and JP20H04196). The author would like to thank the editor and anonymous reviewers for their valuable comments.
Data availability statement.
MP-PAWR data are available from NICT (https://pawr.nict.go.jp/index_en.html). NCEP GFS data are available from the NCEP GFS 0.25 Degree Global Forecast Grids Historical Archive (https://rda.ucar.edu/datasets/ds084.1/). NCEP PREPBUFR observations are available from the Research Data Archive at the NCEP (https://rda.ucar.edu/datasets/ds337.0/). The source code and document of SCALE and LETKF are available from RIKEN (https://scale.riken.jp/) and GitHub (https://github.com/SCALE-LETKF-RIKEN/scale-letkf). Plotting scripts and configuration files are available at https://zenodo.org/records/14219420.
APPENDIX
Superobbing and Thinning Configurations for MP-PAWR
Table A1 summarizes the setting of superobbing and thinning distance for MP-PAWR observations.
Superobbing setting and thinning distance for MP-PAWR observations in each domain.
REFERENCES
Aksoy, A., D. C. Dowell, and C. Snyder, 2009: A multicase comparative assessment of the ensemble Kalman filter for assimilation of radar observations. Part I: Storm-scale analyses. Mon. Wea. Rev., 137, 1805–1824, https://doi.org/10.1175/2008MWR2691.1.
Amemiya, A., T. Honda, and T. Miyoshi, 2020: Improving the observation operator for the phased array weather radar in the SCALE-LETKF system. SOLA, 16, 6–11, https://doi.org/10.2151/sola.2020-002.
Ancell, B. C., A. Bogusz, M. J. Lauridsen, and C. J. Nauert, 2018: Seeding chaos: The dire consequences of numerical noise in NWP perturbation experiments. Bull. Amer. Meteor. Soc., 99, 615–628, https://doi.org/10.1175/BAMS-D-17-0129.1.
Bachmann, K., C. Keil, and M. Weissmann, 2019: Impact of radar data assimilation and orography on predictability of deep convection. Quart. J. Roy. Meteor. Soc., 145, 117–130, https://doi.org/10.1002/qj.3412.
Bachmann, K., C. Keil, G. C. Craig, M. Weissmann, and C. A. Welzbacher, 2020: Predictability of deep convection in idealized and operational forecasts: Effects of radar data assimilation, orography, and synoptic weather regime. Mon. Wea. Rev., 148, 63–81, https://doi.org/10.1175/MWR-D-19-0045.1.
Beljaars, A. C. M., and A. A. M. Holtslag, 1991: Flux parameterization over land surfaces for atmospheric models. J. Appl. Meteor., 30, 327–341, https://doi.org/10.1175/1520-0450(1991)030<0327:FPOLSF>2.0.CO;2.
Bryan, G. H., J. C. Wyngaard, and J. M. Fritsch, 2003: Resolution requirements for the simulation of deep moist convection. Mon. Wea. Rev., 131, 2394–2416, https://doi.org/10.1175/1520-0493(2003)131<2394:RRFTSO>2.0.CO;2.
Dowell, D. C., F. Zhang, L. J. Wicker, C. Snyder, and N. A. Crook, 2004: Wind and temperature retrievals in the 17 May 1981 Arcadia, Oklahoma, supercell: Ensemble Kalman filter experiments. Mon. Wea. Rev., 132, 1982–2005, https://doi.org/10.1175/1520-0493(2004)132<1982:WATRIT>2.0.CO;2.
Gaspari, G., and S. E. Cohn, 1999: Construction of correlation functions in two and three dimensions. Quart. J. Roy. Meteor. Soc., 125, 723–757, https://doi.org/10.1002/qj.49712555417.
Honda, T., 2023: Development of a polar mesocyclone and associated environmental characteristics during the heavy snowfall event in Sapporo, Japan, in early February 2022. J. Geophys. Res. Atmos., 128, e2022JD037774, https://doi.org/10.1029/2022JD037774.
Honda, T., and T. Miyoshi, 2021: Predictability of the July 2018 heavy rain event in Japan associated with Typhoon Prapiroon and southern convective disturbances. SOLA, 17, 113–119, https://doi.org/10.2151/sola.2021-018.
Honda, T., and Coauthors, 2022a: Advantage of 30-s-updating numerical weather prediction with a phased-array weather radar over operational nowcast for a convective precipitation system. Geophys. Res. Lett., 49, e2021GL096927, https://doi.org/10.1029/2021GL096927.
Honda, T., and Coauthors, 2022b: Development of the real-time 30-s-update big data assimilation system for convective rainfall prediction with a phased array weather radar: Description and preliminary evaluation. J. Adv. Model. Earth Syst., 14, e2021MS002823, https://doi.org/10.1029/2021MS002823.
Honda, T., Y. Sato, and T. Miyoshi, 2023: Regression-based ensemble perturbations for the zero-gradient issue posed in lightning-flash data assimilation with an ensemble Kalman filter. Mon. Wea. Rev., 151, 2573–2586, https://doi.org/10.1175/MWR-D-22-0334.1.
Houtekamer, P. L., and F. Zhang, 2016: Review of the ensemble Kalman filter for atmospheric data assimilation. Mon. Wea. Rev., 144, 4489–4532, https://doi.org/10.1175/MWR-D-15-0440.1.
Hunt, B. R., E. J. Kostelich, and I. Szunyogh, 2007: Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter. Physica D, 230, 112–126, https://doi.org/10.1016/j.physd.2006.11.008.
Janjić, T., and Y. Zeng, 2021: Weakly constrained LETKF for estimation of hydrometeor variables in convective-scale data assimilation. Geophys. Res. Lett., 48, e2021GL094962, https://doi.org/10.1029/2021GL094962.
Janjić, T., and Coauthors, 2018: On the representation error in data assimilation. Quart. J. Roy. Meteor. Soc., 144, 1257–1278, https://doi.org/10.1002/qj.3130.
JMA, 2024: Climate change monitoring report 2023. JMA Tech. Rep., 94 pp., https://www.jma.go.jp/jma/en/NMHS/ccmr/ccmr2023.pdf.
Jung, Y., M. Xue, and M. Tong, 2012: Ensemble Kalman filter analyses of the 29–30 May 2004 Oklahoma tornadic thunderstorm using one- and two-moment bulk microphysics schemes, with verification against polarimetric radar data. Mon. Wea. Rev., 140, 1457–1475, https://doi.org/10.1175/MWR-D-11-00032.1.
Kain, J. S., 2004: The Kain–Fritsch convective parameterization: An update. J. Appl. Meteor., 43, 170–181, https://doi.org/10.1175/1520-0450(2004)043<0170:TKCPAU>2.0.CO;2.
Kain, J. S., and J. M. Fritcsh, 1990: A one-dimensional entraining/detraining plume model and its application in convective parameterization. J. Atmos. Sci., 47, 2784–2802, https://doi.org/10.1175/1520-0469(1990)047<2784:AODEPM>2.0.CO;2.
Kato, R., S. Shimizu, K.-I. Shimose, T. Maesaka, K. Iwanami, and H. Nakagaki, 2017: Predictability of meso-γ-scale, localized, extreme heavy rainfall during the warm season in Japan using high-resolution precipitation nowcasts. Quart. J. Roy. Meteor. Soc., 143, 1406–1420, https://doi.org/10.1002/qj.3013.
Kondo, K., and T. Miyoshi, 2016: Impact of removing covariance localization in an ensemble Kalman filter: Experiments with 10 240 members using an intermediate AGCM. Mon. Wea. Rev., 144, 4849–4865, https://doi.org/10.1175/MWR-D-15-0388.1.
Kusaka, H., H. Kondo, Y. Kikegawa, and F. Kimura, 2001: A simple single-layer urban canopy model for atmospheric models: Comparison with multi-layer and slab models. Bound.-Layer Meteor., 101, 329–358, https://doi.org/10.1023/A:1019207923078.
Lien, G.-Y., T. Miyoshi, S. Nishizawa, R. Yoshida, H. Yashiro, S. A. Adachi, T. Yamaura, and H. Tomita, 2017: The near-real-time SCALE-LETKF system: A case of the September 2015 Kanto-Tohoku heavy rainfall. SOLA, 13, 1–6, https://doi.org/10.2151/sola.2017-001.
Lilly, D. K., 1962: On the numerical simulation of buoyant convection. Tellus, 14, 148–172, https://doi.org/10.3402/tellusa.v14i2.9537.
Maejima, Y., M. Kunii, and T. Miyoshi, 2017: 30-second-update 100-m-mesh data assimilation experiments: A sudden local rain case in Kobe on 11 September 2014. SOLA, 13, 174–180, https://doi.org/10.2151/sola.2017-032.
Maejima, Y., T. Kawabata, H. Seko, and T. Miyoshi, 2022: Observing system simulation experiments of a rich phased array weather radar network covering Kyushu for the July 2020 heavy rainfall event. SOLA, 18, 25–32, https://doi.org/10.2151/sola.2022-005.
Maesaka, T., M. Maki, and K. Iwanami, 2011: Operational rainfall estimation by X-Band MP radar network in MLIT, Japan. 35th Conf. on Radar Meteorology, Pittsburgh, PA, Amer. Meteor. Soc., 142, https://ams.confex.com/ams/35Radar/webprogram/Paper191685.html.
Markowski, P. M., 2020: What is the intrinsic predictability of tornadic supercell thunderstorms? Mon. Wea. Rev., 148, 3157–3180, https://doi.org/10.1175/MWR-D-20-0076.1.
Martinez-Villalobos, C., and J. D. Neelin, 2019: Why do precipitation intensities tend to follow gamma distributions? J. Atmos. Sci., 76, 3611–3631, https://doi.org/10.1175/JAS-D-18-0343.1.
Minamide, M., F. Zhang, and E. E. Clothiaux, 2020: Nonlinear forecast error growth of rapidly intensifying Hurricane Harvey (2017) examined through convection-permitting ensemble assimilation of GOES-16 All-Sky Radiances. J. Atmos. Sci., 77, 4277–4296, https://doi.org/10.1175/JAS-D-19-0279.1.
Miyoshi, T., and S. Yamane, 2007: Local ensemble transform Kalman filtering with an AGCM at a T159/L48 resolution. Mon. Wea. Rev., 135, 3841–3861, https://doi.org/10.1175/2007MWR1873.1.
Miyoshi, T., S. Yamane, and T. Enomoto, 2007: Localizing the error covariance by physical distances within a local ensemble transform Kalman filter (LETKF). SOLA, 3, 89–92, https://doi.org/10.2151/sola.2007-023.
Miyoshi, T., K. Kondo, and T. Imamura, 2014: The 10,240-member ensemble Kalman filtering with an intermediate AGCM. Geophys. Res. Lett., 41, 5264–5271, https://doi.org/10.1002/2014GL060863.
Miyoshi, T., and Coauthors, 2016a: “Big data assimilation” revolutionizing severe weather prediction. Bull. Amer. Meteor. Soc., 97, 1347–1354, https://doi.org/10.1175/BAMS-D-15-00144.1.
Miyoshi, T., and Coauthors, 2016b: “Big data assimilation” toward post-petascale severe weather prediction: An overview and progress. Proc. IEEE, 104, 2155–2179, https://doi.org/10.1109/JPROC.2016.2602560.
Miyoshi, T., and Coauthors, 2023: Big data assimilation: Real-time 30-second-refresh heavy rain forecast using Fugaku during Tokyo Olympics and Paralympics. SC ’23: Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, Association for Computing Machinery, 1–10, https://doi.org/10.1145/3581784.3627047.
Nakanishi, M., and H. Niino, 2004: An improved Mellor–Yamada level-3 model with condensation physics: Its design and verification. Bound.-Layer Meteor., 112, 1–31, https://doi.org/10.1023/B:BOUN.0000020164.04146.98.
Necker, T., S. Geiss, M. Weissmann, J. Ruiz, T. Miyoshi, and G.-Y. Lien, 2020: A convective-scale 1,000-member ensemble simulation and potential applications. Quart. J. Roy. Meteor. Soc., 146, 1423–1442, https://doi.org/10.1002/qj.3744.
Nishizawa, S., H. Yashiro, Y. Sato, Y. Miyamoto, and H. Tomita, 2015: Influence of grid aspect ratio on planetary boundary layer turbulence in large-eddy simulations. Geosci. Model Dev., 8, 3393–3419, https://doi.org/10.5194/gmd-8-3393-2015.
Nystrom, R. G., and F. Zhang, 2019: Practical uncertainties in the limited predictability of the record-breaking intensification of Hurricane Patricia (2015). Mon. Wea. Rev., 147, 3535–3556, https://doi.org/10.1175/MWR-D-18-0450.1.
Peters, J. M., and R. S. Schumacher, 2015: Mechanisms for organization and echo training in a flash-flood-producing mesoscale convective system. Mon. Wea. Rev., 143, 1058–1085, https://doi.org/10.1175/MWR-D-14-00070.1.
Peters, J. M., E. R. Nielsen, M. D. Parker, S. M. Hitchcock, and R. S. Schumacher, 2017: The impact of low-level moisture errors on model forecasts of an MCS observed during PECAN. Mon. Wea. Rev., 145, 3599–3624, https://doi.org/10.1175/MWR-D-16-0296.1.
Reynolds, C. A., J. D. Doyle, F. M. Ralph, and R. Demirdjian, 2019: Adjoint sensitivity of North Pacific atmospheric river forecasts. Mon. Wea. Rev., 147, 1871–1897, https://doi.org/10.1175/MWR-D-18-0347.1.
Ruiz, J., G.-Y. Lien, K. Kondo, S. Otsuka, and T. Miyoshi, 2021: Reduced non-gaussianity by 30-second rapid update in convective-scale numerical weather prediction. Nonlinear Processes Geophys., 28, 615–626, https://doi.org/10.5194/npg-2021-15.
Sato, Y., S. Nishizawa, H. Yashiro, Y. Miyamoto, Y. Kajikawa, and H. Tomita, 2015: Impacts of cloud microphysics on trade wind cumulus: Which cloud microphysics processes contribute to the diversity in a large eddy simulation? Prog. Earth Planet. Sci., 2, 23, https://doi.org/10.1186/s40645-015-0053-6.
Schumacher, R. S., and J. M. Peters, 2017: Near-surface thermodynamic sensitivities in simulated extreme-rain-producing mesoscale convective systems. Mon. Wea. Rev., 145, 2177–2200, https://doi.org/10.1175/MWR-D-16-0255.1.
Seiki, T., and T. Nakajima, 2014: Aerosol effects of the condensation process on a convective cloud simulation. J. Atmos. Sci., 71, 833–853, https://doi.org/10.1175/JAS-D-12-0195.1.
Sekiguchi, M., and T. Nakajima, 2008: A k-distribution-based radiation code and its computational optimization for an atmospheric general circulation model. J. Quant. Spectrosc. Radiat., 109, 2779–2793, https://doi.org/10.1016/j.jqsrt.2008.07.013.
Selz, T., and G. C. Craig, 2015: Upscale error growth in a high-resolution simulation of a summertime weather event over Europe. Mon. Wea. Rev., 143, 813–827, https://doi.org/10.1175/MWR-D-14-00140.1.
Selz, T., M. Riemer, and G. C. Craig, 2022: The transition from practical to intrinsic predictability of midlatitude weather. J. Atmos. Sci., 79, 2013–2030, https://doi.org/10.1175/JAS-D-21-0271.1.
Smagorinsky, J., 1963: General circulation experiments with the primitive equations. Mon. Wea. Rev., 91, 99–164, https://doi.org/10.1175/1520-0493(1963)091%3C0099:GCEWTP%3E2.3.CO;2.
Snook, N., M. Xue, and Y. Jung, 2015: Multiscale EnKF assimilation of radar and conventional observations and ensemble forecasting for a tornadic mesoscale convective system. Mon. Wea. Rev., 143, 1035–1057, https://doi.org/10.1175/MWR-D-13-00262.1.
Snyder, C., and F. Zhang, 2003: Assimilation of simulated Doppler radar observations with an ensemble Kalman filter. Mon. Wea. Rev., 131, 1663–1677, https://doi.org/10.1175//2555.1.
Stratman, D. R., N. Yussouf, Y. Jung, T. A. Supinie, M. Xue, P. S. Skinner, and B. J. Putnam, 2020: Optimal temporal frequency of NSSL phased array radar observations for an experimental warn-on-forecast system. Wea. Forecasting, 35, 193–214, https://doi.org/10.1175/WAF-D-19-0165.1.
Sueki, K., T. Yamaura, H. Yashiro, S. Nishizawa, R. Yoshida, Y. Kajikawa, and H. Tomita, 2019: Convergence of convective updraft ensembles with respect to the grid spacing of atmospheric models. Geophys. Res. Lett., 46, 14 817–14 825, https://doi.org/10.1029/2019GL084491.
Sun, Y. Q., and F. Zhang, 2016: Intrinsic versus practical limits of atmospheric predictability and the significance of the butterfly effect. J. Atmos. Sci., 73, 1419–1438, https://doi.org/10.1175/JAS-D-15-0142.1.
Supinie, T. A., N. Yussouf, Y. Jung, M. Xue, J. Cheng, and S. Wang, 2017: Comparison of the analyses and forecasts of a tornadic supercell storm from assimilating phased-array radar and WSR-88D observations. Wea. Forecasting, 32, 1379–1401, https://doi.org/10.1175/WAF-D-16-0159.1.
Takahashi, N., and Coauthors, 2019: Development of multi-parameter phased array weather radar (MP-PAWR) and early detection of torrential rainfall and tornado risk. J. Disaster Res., 14, 235–247, https://doi.org/10.20965/jdr.2019.p0235.
Tao, D., and F. Zhang, 2014: Effect of environmental shear, sea-surface temperature, and ambient moisture on the formation and predictability of tropical cyclones: An ensemble-mean perspective. J. Adv. Model. Earth Syst., 6, 384–404, https://doi.org/10.1002/2014MS000314.
Tao, D., and F. Zhang, 2015: Effects of vertical wind shear on the predictability of tropical cyclones: Practical versus intrinsic limit. J. Adv. Model. Earth Syst., 7, 1534–1553, https://doi.org/10.1002/2015MS000474.
Tao, D., P. J. van Leeuwen, M. Bell, and Y. Ying, 2022: Dynamics and predictability of tropical cyclone rapid intensification in ensemble simulations of Hurricane Patricia (2015). J. Geophys. Res. Atmos., 127, e2021JD036079, https://doi.org/10.1029/2021JD036079.
Taylor, J., T. Honda, A. Amemiya, S. Otsuka, Y. Maejima, and T. Miyoshi, 2023: Sensitivity to localization radii for an ensemble filter numerical weather prediction system with 30-second update. Wea. Forecasting, 38, 611–632, https://doi.org/10.1175/WAF-D-21-0177.1.
Terasaki, K., and T. Miyoshi, 2024: Including the horizontal observation error correlation in the ensemble Kalman filter: Idealized experiments with NICAM-LETKF. Mon. Wea. Rev., 152, 277–293, https://doi.org/10.1175/MWR-D-23-0053.1.
Tomita, H., 2008: New microphysical schemes with five and six categories by diagnostic generation of cloud ice. J. Meteor. Soc. Japan, 86A, 121–142, https://doi.org/10.2151/jmsj.86A.121.
Tong, M., and M. Xue, 2005: Ensemble Kalman filter assimilation of Doppler radar data with a compressible nonhydrostatic model: OSS experiments. Mon. Wea. Rev., 133, 1789–1807, https://doi.org/10.1175/MWR2898.1.
Wang, Y., N. Yussouf, C. A. Kerr, D. R. Stratman, and B. C. Matilla, 2022: An experimental 1-km Warn-on-Forecast System for hazardous weather events. Mon. Wea. Rev., 150, 3081–3102, https://doi.org/10.1175/MWR-D-22-0094.1.
Weyn, J. A., and D. R. Durran, 2019: The scale dependence of initial-condition sensitivities in simulations of convective systems over the southeastern United States. Quart. J. Roy. Meteor. Soc., 145, 57–74, https://doi.org/10.1002/qj.3367.
Whitaker, J. S., and T. M. Hamill, 2012: Evaluating methods to account for system errors in ensemble data assimilation. Mon. Wea. Rev., 140, 3078–3089, https://doi.org/10.1175/MWR-D-11-00276.1.
Wu, P.-Y., S.-C. Yang, C.-C. Tsai, and H.-W. Cheng, 2020: Convective-scale sampling error and its impact on the ensemble radar data assimilation system: A case study of a heavy rainfall event on 16 June 2008 in Taiwan. Mon. Wea. Rev., 148, 3631–3652, https://doi.org/10.1175/MWR-D-19-0319.1.
Yokota, S., H. Seko, M. Kunii, H. Yamauchi, and H. Niino, 2016: The tornadic supercell on the Kanto Plain on 6 May 2012: Polarimetric radar and surface data assimilation with EnKF and ensemble-based sensitivity analysis. Mon. Wea. Rev., 144, 3133–3157, https://doi.org/10.1175/MWR-D-15-0365.1.
Yokota, S., H. Seko, M. Kunii, H. Yamauchi, and E. Sato, 2018: Improving short-term rainfall forecasts by assimilating weather radar reflectivity using additive ensemble perturbations. J. Geophys. Res. Atmos., 123, 9047–9062, https://doi.org/10.1029/2018JD028723.
Zhang, F., and D. Tao, 2013: Effects of vertical wind shear on the predictability of tropical cyclones. J. Atmos. Sci., 70, 975–983, https://doi.org/10.1175/JAS-D-12-0133.1.
Zhang, F., C. Snyder, and R. Rotunno, 2002: Mesoscale predictability of the “surprise” snowstorm of 24–25 January 2000. Mon. Wea. Rev., 130, 1617–1632, https://doi.org/10.1175/1520-0493(2002)130<1617:MPOTSS>2.0.CO;2.
Zhang, F., C. Snyder, and R. Rotunno, 2003: Effects of moist convection on mesoscale predictability. J. Atmos. Sci., 60, 1173–1185, https://doi.org/10.1175/1520-0469(2003)060<1173:EOMCOM>2.0.CO;2.
Zhang, F., C. Snyder, and J. Sun, 2004: Impacts of initial estimate and observation availability on convective-scale data assimilation with an ensemble Kalman filter. Mon. Wea. Rev., 132, 1238–1253, https://doi.org/10.1175/1520-0493(2004)132<1238:IOIEAO>2.0.CO;2.
Zhang, F., A. M. Odins, and J. W. Nielsen-Gammon, 2006: Mesoscale predictability of an extreme warm-season precipitation event. Wea. Forecasting, 21, 149–166, https://doi.org/10.1175/WAF909.1.
Zhang, F., N. Bei, R. Rotunno, C. Snyder, and C. C. Epifanio, 2007: Mesoscale predictability of moist baroclinic waves: Convection-permitting experiments and multistage error growth dynamics. J. Atmos. Sci., 64, 3579–3594, https://doi.org/10.1175/JAS4028.1.
Zhang, F., Y. Weng, J. A. Sippel, Z. Meng, and C. H. Bishop, 2009: Cloud-resolving hurricane initialization and prediction through assimilation of Doppler radar observations with an ensemble Kalman filter. Mon. Wea. Rev., 137, 2105–2125, https://doi.org/10.1175/2009MWR2645.1.
Zhang, F., D. Tao, Y. Q. Sun, and J. D. Kepert, 2017: Dynamics and predictability of secondary eyewall formation in sheared tropical cyclones. J. Adv. Model. Earth Syst., 8, 89–112, https://doi.org/10.1002/2016MS000729.
Zhang, F., Y. Qiang Sun, L. Magnusson, R. Buizza, S.-J. Lin, J.-H. Chen, and K. Emanuel, 2019: What is the predictability limit of midlatitude weather? J. Atmos. Sci., 76, 1077–1091, https://doi.org/10.1175/JAS-D-18-0269.1.
Zhang, Y., 2023: Sensitivity of intrinsic error growth to large-scale uncertainty structure in a record-breaking summertime rainfall event. J. Atmos. Sci., 80, 1415–1432, https://doi.org/10.1175/JAS-D-22-0231.1.
Zhang, Y., F. Zhang, D. J. Stensrud, and Z. Meng, 2015: Practical predictability of the 20 May 2013 tornadic thunderstorm event in Oklahoma: Sensitivity to synoptic timing and topographical influence. Mon. Wea. Rev., 143, 2973–2997, https://doi.org/10.1175/MWR-D-14-00394.1.
Zhang, Y., F. Zhang, D. J. Stensrud, and Z. Meng, 2016: Intrinsic predictability of the 20 May 2013 tornadic thunderstorm event in Oklahoma at storm scales. Mon. Wea. Rev., 144, 1273–1298, https://doi.org/10.1175/MWR-D-15-0105.1.