1. Introduction
Predicting severe convective weather by numerical weather prediction (NWP) is challenging because convective clouds have small scales and develop rapidly. To improve convective-scale NWP, it is important to obtain accurate initial conditions by effectively assimilating available observations, such as weather radars and satellite radiances. Indeed, previous studies have shown that the assimilation of observations from weather radars or satellite radiances improves the forecast accuracy of convective systems (Aksoy et al. 2010; Snook et al. 2011; Honda et al. 2022a,b; Sawada et al. 2019; Zhang et al. 2018; Dowell et al. 2004, 2011; Snyder and Zhang 2003; Zhang et al. 2004; Tong and Xue 2005; Xue et al. 2006; Putnam et al. 2019; Snook et al. 2016; Yussouf et al. 2013, 2015; Zhu et al. 2020; Maejima et al. 2017; Miyoshi et al. 2016a,b).
Lightning flashes are another potentially useful observation for improving convective-scale NWP because they are closely associated with the development of convective clouds. Lightning flashes have been detected by ground-based sensor networks (e.g., Lay et al. 2004; Cummins and Murphy 2009; Yoshida et al. 2014) and sensors onboard satellites. In particular, the Geostationary Lightning Mapper (GLM; Goodman et al. 2013), on board the Geostationary Operational Environmental Satellite (GOES) series of the National Oceanic and Atmospheric Administration (NOAA), observes total lightning flashes with a high spatiotemporal resolution (8-km mesh at the nadir every 2 ms).
Several studies have attempted to assimilate lightning flash observations. For example, Fierro et al. (2016, 2019) used a variational system for the assimilation of pseudo–water vapor observations derived from lightning observations and successfully improved short-term forecasts. Allen et al. (2016) assimilated pseudo-GLM observations using an ensemble Kalman filter (EnKF; Houtekamer and Zhang 2016; Evensen 1994). They used statistical relationships between model variables and lightning flashes as the observation operator and showed promising results. Using the statistical relationships obtained by Allen et al. (2016), Kong et al. (2020) successfully assimilated real GLM data. More recently, Honda et al. (2021) showed positive impacts of the assimilation of lightning flash observations in idealized observing system simulation experiments (OSSEs).
To effectively assimilate lightning flash observations with an EnKF-based system, it is important to address the so-called zero-gradient issue (or zero ensemble spread). Figure 1a shows a schematic of the zero-gradient issue. All ensemble members may have zero lightning flashes. In this case, the ensemble mean in the observation space is zero. Furthermore, the ensemble perturbations in the observation space (y′) are completely zero, so that observations cannot be related to the ensemble perturbations in the model space (x′). In other words, the ensemble perturbations in the observation space have the zero gradient against the model-space counterpart, and the ensemble spread in the observation space is zero. As a result, no analysis increments are obtained. If a few members predict an event (e.g., nonzero lightning flash), the gradient of y′ is not completely zero. However, in this case the EnKF relies on outliers of an ensemble to obtain the forecast error covariance and could be suboptimal. Therefore, in this paper, we relax the zero-gradient issue to include the situations in which only a small portion (<10%) of an ensemble predicts nonzero lightning flashes.
Schematic showing (a) the zero-gradient issue in which background ensemble perturbations in the observation space (y′) are zero regardless of background ensemble perturbations of a model variable (x′), (b) the regression slope (blue line) between x′ and y′ obtained from a large sample (black circles), and (c) y′ (blue marks) regressed from x′ (gray marks) using the regression slope (blue line) in (b).
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
Schematic showing (a) the zero-gradient issue in which background ensemble perturbations in the observation space (y′) are zero regardless of background ensemble perturbations of a model variable (x′), (b) the regression slope (blue line) between x′ and y′ obtained from a large sample (black circles), and (c) y′ (blue marks) regressed from x′ (gray marks) using the regression slope (blue line) in (b).
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
Schematic showing (a) the zero-gradient issue in which background ensemble perturbations in the observation space (y′) are zero regardless of background ensemble perturbations of a model variable (x′), (b) the regression slope (blue line) between x′ and y′ obtained from a large sample (black circles), and (c) y′ (blue marks) regressed from x′ (gray marks) using the regression slope (blue line) in (b).
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
The zero-gradient issue can be found in other observations such as radar reflectivity and precipitation. For example, Lien et al. (2013, 2016) and Kotsuki et al. (2017) applied a threshold of the minimum number of precipitating ensemble members for the assimilation of global precipitation observations. Lien et al. (2013) performed sensitivity experiments for this threshold and showed that assimilating precipitation observations with a small threshold (at least 1 precipitating member out of 32 ensemble members) degrades the analysis accuracy compared to that with a larger threshold.
Recently, Yokota et al. (2018) proposed a remedy for the zero-gradient issue for the assimilation of radar-reflectivity observations. First, as shown in Fig. 1b, their method obtains regression coefficients between x′ and y′ using a large sample from all grid points in all ensemble members. This large data are expected to include many nonzero y′. Here, because both x′ and y′ are the ensemble perturbations and their means are zero, the regression line (blue line in Fig. 1b) paths the origin. Second, x′ with the zero-gradient issue is regressed onto the observation space by the obtained regression coefficients (Fig. 1c). Third, the resulting regression-based ensemble perturbations (blue marks in Fig. 1c) are replaced with the original ensemble perturbations in the observation space (gray marks in Fig. 1c). As a result, the ensemble spread in the observation space increases, and it would be possible to obtain nonzero analysis increments. Unlike standard additive inflation using random noise (e.g., Dowell and Wicker 2009), this method adds flow-dependent ensemble perturbations correlated with model variables. Without such correlations, it would be necessary to grow the random noise until it achieves clear correlations between x′ and y′. In this regard, the Yokota et al. (2018) method provides an alternative to standard additive inflation to address the zero-gradient issue. Yokota et al. (2018) applied the method to two tornadic supercells in Japan and showed that their method clearly improved the forecast accuracy.
Following the success of Yokota et al. (2018) for the zero-gradient issue posed in the data assimilation (DA) of radar reflectivity, this study aims to apply their regression-based ensemble perturbations method for the assimilation of lightning flash observations. This study targets a single heavy precipitation event in Japan during which a large amount of precipitation and active lightning flashes were observed (Kawano and Kawamura 2020; Sato et al. 2022). Because effective bias correction and quality control methods have not been established for lightning flash observations, this study focuses on a proof of concept based on OSSEs.
This paper is structured as follows. Section 2 provides an overview of the target event and explains the methodology. Section 3 provides the results and discussion. A summary and future perspectives are presented in section 4.
2. Case overview and experimental design
a. Case overview
This study focuses on the heavy precipitation event in Kyushu, Japan on 5 and 6 July 2017 (hereafter referred to as the Kyushu-2017 event). During this event, a quasi-stationary mesoscale convective system (MCS) developed in the northern part of Kyushu Island and caused a large amount of precipitation. In particular, a surface gauge station recorded 6-h accumulated precipitation of >600 mm on 5 July (Kawano and Kawamura 2020). This precipitation was associated with abundant moisture supply from the East China Sea and an upper-level trough located over the Korean Peninsula (Kawano and Kawamura 2020; Tsuji et al. 2020). During this event, many lightning flashes were observed (Sato et al. 2022). Refer to Kawano and Kawamura (2020) and Tsuji et al. (2020) for more details on the Kyushu-2017 event.
b. Nature run
1) model configuration
A nature run uses the atmospheric regional model from scalable computing for advanced library and environment (SCALE version 5.4.3; Nishizawa et al. 2015; Sato et al. 2015) with a domain that covers the northern part of Kyushu (blue rectangle in Fig. 2a). As detailed later, the same domain is used for OSSEs that assimilate synthetic lightning observations. The experimental design follows Sato et al. (2022), who successfully simulated precipitation and lightning flashes during the Kyushu-2017 event. The horizontal grid spacing is 1 km. As shown in the workflow in Fig. 2b, the nature run is initiated at 0000 UTC 5 July 2017, using the initial and boundary data given by the Japan Meteorological Agency (JMA) Mesoscale Analysis data every 3 h. The SCALE model employs a single-layer urban canopy model (Kusaka et al. 2001), a Beljaars-type bulk surface-flux model (Beljaars and Holtslag 1991), the model simulation radiation TRaNsfer code (MSTRN) X (Sekiguchi and Nakajima 2008), and a Smagorinsky‐type scheme (Smagorinsky 1963; Lilly 1962; Brown et al. 1994). A double-moment microphysics scheme (Seiki and Nakajima 2014), which predicts the mixing ratios and number concentrations of cloud water, rain, cloud ice, snow, and graupel, is used.
(a) Computational domains for the domain 1 (black) and domain 2 (blue) and the geographical location of Kyushu Island. (b),(c) Schematic showing the workflow for (b) the nature run and (c) OSSEs.
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
(a) Computational domains for the domain 1 (black) and domain 2 (blue) and the geographical location of Kyushu Island. (b),(c) Schematic showing the workflow for (b) the nature run and (c) OSSEs.
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
(a) Computational domains for the domain 1 (black) and domain 2 (blue) and the geographical location of Kyushu Island. (b),(c) Schematic showing the workflow for (b) the nature run and (c) OSSEs.
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
2) Lightning parameterization
The SCALE model can predict lightning flashes by using a bulk lightning model implemented by Sato et al. (2019). This scheme predicts the electric charges in each hydrometeor category based on the noninductive charge separation process (Takahashi 1978) and neutralizes (discharges) them by the Fierro et al. (2013) scheme. During the neutralization process, this parameterization scheme iterates the following steps. First, the electric field (E) is calculated by solving the Poisson equation for the electric charge and electric potential [see Eqs. (5) and (6) in Sato et al. 2019]. Second, target grid points with |E| > Eint are searched, where Eint is a prescribed threshold of |E| for the initiation of discharges. Each target grid point is used as the center of a vertical cylinder. Third, within the vertical cylinders, the electric charge in each grid is neutralized. In other words, the parameterization scheme neutralizes the grid points that are close to the target grid points with a horizontal distance smaller than the radius of the vertical cylinder. The parameterization scheme iterates the above steps until all grid points satisfy |E| ≤ Eint. Following Fierro et al. (2013), the radius of the vertical cylinder is set at 3 km, 3 times larger than the model grid spacing. A larger radius can be employed and would lead to more efficient neutralization (smaller numbers of lightning flashes), but results are expected to be qualitatively similar (Fierro et al. 2013). We set Eint at 150 kV. More details of the lightning parameterization scheme can be found in Fierro et al. (2013) and Sato et al. (2019).
Throughout this study, lightning activity is measured by flash origin density (FOD; Fierro et al. 2013). FOD is a proxy of lightning activity and represents the number of flashes within each grid cell per time interval. FOD is normalized by the areas of each grid cell and the vertical cylinder, so that FOD is a float number rather than an integer. In this study, by summing 9 × 9 horizontal grid points, FOD is convolved into an observation grid with 9-km grid spacing, which approximately corresponds to the horizontal spacing of GLM at the nadir (Goodman et al. 2013). For simplicity, FOD is not forced to be an integer value. For real GLM data, flash extent density (FED) would be more useful than FOD because FED contains information on the extent of electric charge. However, Fierro et al. (2013)’s scheme does not explicitly predict individual lightning channels like Mansell et al. (2002). Therefore, it is not straightforward to obtain FED from the Fierro et al. (2013)’s scheme. Advanced parameterization schemes that explicitly calculate lightning channels have not been implemented into the SCALE model and further model development is required to assimilate FED without statistical observation operators used in previous studies (e.g., Allen et al. 2016; Kong et al. 2020, 2022).
The accumulation time interval of FOD is set at 1 h because Honda et al. (2021) indicated that the longer accumulation time interval, the higher correlations between the lightning activity and hydrometeors. As shown below, the accumulation time interval of 1 h seems acceptable for the target event caused by the MCS that stayed for 9 h (Kawano and Kawamura 2020). However, to improve the forecast accuracy of shorter-lived convective systems, it would be suitable to use a short accumulation time interval. Investigating such sensitivity in various events is an important topic for future research.
3) Overview of the results
The nature run successfully simulates the heavy precipitation and active lightning flashes. Figures 3a and 3b present the horizontal maps of accumulated precipitation and lightning activity. A large amount of precipitation and high flash activity are simulated near the center of Kyushu Island, consistent with the observations (Sato et al. 2022). As expected, active lightning occurs only where precipitation is simulated, and most of the observation grid points are zero flashes as indicated by the large spike near zero in the histogram shown by Fig. 3c.
Horizontal maps of the 18-h accumulated (a) precipitation amount (mm) and (b) lightning activity measured by the flash origin density (FOD; Fierro et al. 2013) from the nature run. The accumulation period is between 0600 UTC 5 Jul and 0000 UTC 6 Jul 2017. (c) Number of grids points (9-km horizontal grid spacing) as a function of the hourly accumulated FOD.
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
Horizontal maps of the 18-h accumulated (a) precipitation amount (mm) and (b) lightning activity measured by the flash origin density (FOD; Fierro et al. 2013) from the nature run. The accumulation period is between 0600 UTC 5 Jul and 0000 UTC 6 Jul 2017. (c) Number of grids points (9-km horizontal grid spacing) as a function of the hourly accumulated FOD.
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
Horizontal maps of the 18-h accumulated (a) precipitation amount (mm) and (b) lightning activity measured by the flash origin density (FOD; Fierro et al. 2013) from the nature run. The accumulation period is between 0600 UTC 5 Jul and 0000 UTC 6 Jul 2017. (c) Number of grids points (9-km horizontal grid spacing) as a function of the hourly accumulated FOD.
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
c. OSSE
1) Data assimilation system
This study uses the ensemble-based DA system that consists of the SCALE model and the local ensemble transform Kalman filter (Hunt et al. 2007; Miyoshi and Yamane 2007). The system is referred to as SCALE-LETKF and was originally developed by Lien et al. (2017). SCALE-LETKF has been widely used to assimilate observations from various platforms such as conventional (nonradiance) observations (Lien et al. 2017; Taylor et al. 2021b; Honda and Miyoshi 2021), satellite infrared radiances (Honda et al. 2018b,a, 2019), radar reflectivity and Doppler velocity from phased-array weather radars (Miyoshi et al. 2016b; Honda et al. 2022a; Amemiya et al. 2020; Maejima et al. 2019; Honda et al. 2022b; Ruiz et al. 2021; Taylor et al. 2023), and a geostationary radar satellite (Taylor et al. 2021a). This study sets up the SCALE-LETKF system with the ensemble size of 100 and uses 18- and 3-km grid-spacing domains (hereafter D1 and D2). D1 is run first and provides the boundary conditions for D2.
2) Domain 1
D1 is the same as the near-real-time SCALE-LETKF system (Lien et al. 2017) and covers East Asia (shown by black curves in Fig. 2a). The DA configuration for D1 is the same as Lien et al. (2017), except for a minor update of the coefficient (1.25) of the multiplicative covariance inflation method. In D1, the National Centers for Environmental Prediction (NCEP) PREPBUFR conventional (nonradiance) observations are assimilated every 6 h. The model configuration for D1 is the same as Lien et al. (2017), except for the use of a new version (5.4.3) of SCALE, the Kain–Fritsch cumulus parameterization scheme (Kain and Fritsch 1990; Kain 2004), the double-moment microphysics scheme developed by Seiki and Nakajima (2014), and higher-resolution (0.25°) NCEP Global Forecast System (GFS) data as the boundary conditions.
Following Lien et al. (2017), this study initiates D1 at 0000 UTC 15 June 2017, by using arbitrarily chosen NCEP GFS analyses and forecasts data in June 2018, 2019, and 2020. Although this initiation method leads to a large ensemble spread at the beginning, continuous DA would constrain the atmospheric state effectively in terms of the root-mean-squared differences and ensemble spread (see Figs. 3, S2–2h, and S2–3h of Lien et al. 2017). After a 30-h-spinup ensemble forecast, D1 starts 6-hourly assimilation of the conventional observations at 0600 UTC 16 June and continues DA cycles until 0000 UTC 5 July 2017. After the DA cycles, this study performs a 100-member extended ensemble forecast in D1 from 0000 UTC 5 July 2017. The resulting forecast data are used as the initial and boundary conditions for D2.
3) Domain 2
This study performs OSSEs in D2. The initial conditions at 0600 UTC 5 July 2017, are obtained by a 6-h spinup ensemble forecast initiated at 0000 UTC 5 July 2017, using the D1 forecast data. The model configuration for D2 is generally the same as that for the nature run, except for the horizontal grid spacing, the boundary layer scheme, and the configuration of the lightning parameterization scheme. For D2, the SCALE model uses a 3-km domain that covers the same area as the nature run (shown by the blue rectangle in Fig. 2a). To represent subgrid-scale turbulence in the boundary layer, the level-2.5 closure of the Mellor–Yamada–Nakanishi–Niino turbulence scheme (Nakanishi and Niino 2004) is employed. Following Fierro et al. (2013), the radius of a vertical cylinder for the lightning parameterization scheme is set at 9 km, 3 times larger than the model grid spacing for D2. FOD is not fully scaled with the radius. Thus, the model imperfection in OSSEs is increased by using a radius different from that in the nature run.
By design, all ensemble members explicitly predict lightning flashes in D2. This configuration requires approximately twice the computation resources for ensemble forecasts compared to similar ensemble forecasts without lightning processes. Nevertheless, it can provide flow-dependent relationships between lightning flashes and atmospheric variables. Indeed, diagnostic observation operators for lightning observations (e.g., Fierro et al. 2016; Allen et al. 2016; Wang et al. 2017; Hu et al. 2020) would be computationally less expensive and practically useful, but they require tuning coefficients using many events (Kong et al. 2022).
In D2, this study hourly assimilates the 9-km mesh lightning flash observations (FOD) simulated from the nature run. Similar to Maejima et al. (2017) for OSSEs with weather radars, synthetic lightning flash observations are created by adding a Gaussian noise N(0, 1) multiplied by 10% of FOD at each 9-km grid point except where FOD is zero. The resulting synthetic FOD observations are set to zero if the sum of FOD and the observation noise is negative. This study performs three experiments: one without DA (hereafter NODA); another without regression-based perturbations (hereafter CTRL); the other with regression-based ensemble perturbations (hereafter TEST). To focus on the impact of assimilating lightning flashes, this study assimilates no observation data other than the synthetic lightning flashes in D2. Assimilating lightning flashes together with other observation data, such as conventional data, satellite infrared radiances, and weather radars, will be investigated in our future work.
For DA in D2, by considering the representation error (Janjić et al. 2018), the standard deviation of the observation error in LETKF is set at 6.0. This is generally larger than the added Gaussian noise and roughly corresponds to 10% of the maximum of FOD in the nature run (Fig. 3c). This study employs a Gaussian-like function for covariance localization (Gaspari and Cohn 1999). The characteristic horizontal length scale for this function [see Eq. (13) in Miyoshi and Yamane 2007] is chosen to be 40 km, corresponding to the cutoff radius of approximately 146 km. This scale was selected after a few sensitivity experiments and is larger than that used in the previous studies with shorter (≤5 min) assimilation windows (Allen et al. 2016; Kong et al. 2020). No vertical localization is applied in D2. Similar to Lien et al. (2017) and Honda et al. (2018a), as a simple gross-check quality control (QC) method (e.g., Kalnay 2003), observations with large absolute values of innovations by more than five standard deviations (i.e., 6.0 × 5 = 30.0) are discarded. This QC is applied even if the ensemble mean of lighting is zero, but most lighting observations are <30.0 (Fig. 3c) and would pass this QC.
d. Lightning flash assimilation method
This study uses regression-based ensemble perturbations as a remedy for the zero-gradient issue. As shown in Fig. 1b, in this method, a regression coefficient between observed quantity (i.e., FOD) and model-variable perturbations is obtained by using a large sample from the entire domain of all ensemble members. By doing so, as indicated by Yokota et al. (2018), the sample is expected to contain nonzero lightning and allows obtaining regression coefficients. With a large model bias, however, the entire domain of all ensemble members could be zero lightning. Future research with real observation data might require remedy for such situation. Using the regression coefficient, ensemble perturbations in the model space are regressed to nonzero ensemble perturbations in the observation space (Fig. 1c). This method is applied if the number of ensemble members with nonzero lightning flashes is smaller than a prescribed threshold (Nmem). Yokota et al. (2018) did not use such a threshold for the assimilation of radar observations, meaning that they applied regression-based ensemble perturbations only if the ensemble spread (slope of y′ in Fig. 1) is completely zero. In contrast, this study sets Nmem at 10 members out of 100 members. Section 3c discusses the sensitivity to Nmem.
Calculation of the regression coefficients for each model variable generally follows Yokota et al. (2018), except that FOD is two-dimensional (2D). The regression coefficients between FOD and each three-dimensional (3D) model variable are separately calculated at each model level. The resulting vertical profiles of the regression coefficients for each model variable are used to regress the ensemble perturbations at each model level separately onto the observation space. A sum of the regressed values from each model level and each variable is used as the regression-based ensemble perturbations in the observation space. The regression coefficients are calculated at each cycle and are used regardless of the coefficient of determination. The model variables used for the regression coefficients include the zonal, meridional, and vertical velocities, temperature, and mixing ratio of water vapor. Mixing ratios of hydrometeors are not used because ensemble perturbations in these model variables should be close to zero where simulated lightning flashes are zero. Indeed, including hydrometeor variables for the regression-based ensemble perturbations did not show large impacts (not shown). Furthermore, if the standard deviation of model-variable perturbations [the square root of the denominator of Eq. (7) in Yokota et al. (2018) divided by the number of samples minus one] is too small, the regression coefficients can be very large. To avoid this issue, the regression coefficients are calculated only where the standard deviation of each model variable is larger than a prescribed threshold. The thresholds for each model variable are chosen to 0.1 m s−1 for the zonal, meridional, and vertical velocities, 0.1 K for the temperature, and 0.1 g kg−1 for the mixing ratio of water vapor. By design, a single lightning observation at the 9-km grid should include nine grid columns at the 3-km grid. Among these grid columns, only the center column, which is at the observation location, is used for calculating the regression coefficients. Because the ensemble perturbations in the stratosphere are not expected to be closely associated with lightning, this study uses the ensemble perturbations below a height of 14 km.
3. Results and discussion
In this section, we first check the impacts of regression-based ensemble perturbations on analyses, followed by those on forecasts. Then, we discuss the sensitivity to Nmin.
a. Impacts on analyses
Figures 4a and 4b show the horizontal distributions of observation-minus-background (O − B) in lightning flashes and the number of ensemble members with nonzero lightning flashes at the first analysis time (0700 UTC 5 July 2017). O − B is generally positive, indicating that the number of lightning flashes in the first guess is smaller than the synthetic observations (Fig. 4a). Indeed, at many observation locations, the number of nonzero lightning members is ≤5 (Fig. 4b). In the middle of Kyushu (32.5°N, 131°E), O − B is large because the number of nonzero lightning members is ≤5, indicating that the standard EnKF without regression-based ensemble perturbations could not effectively assimilate lightning observations.
Horizontal maps of (a) observation minus background (O − B) and (b) the number of ensemble members with nonzero lightning flashes valid at the first analysis time (0700 UTC 5 Jul 2017). Zero-flash observations are omitted if no ensemble members have nonzero lightning flashes.
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
Horizontal maps of (a) observation minus background (O − B) and (b) the number of ensemble members with nonzero lightning flashes valid at the first analysis time (0700 UTC 5 Jul 2017). Zero-flash observations are omitted if no ensemble members have nonzero lightning flashes.
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
Horizontal maps of (a) observation minus background (O − B) and (b) the number of ensemble members with nonzero lightning flashes valid at the first analysis time (0700 UTC 5 Jul 2017). Zero-flash observations are omitted if no ensemble members have nonzero lightning flashes.
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
In the middle of Kyushu, the first-guess ensemble mean has lesser graupel and weaker updraft than those in the nature run. Figures 5a and 6a show the differences in the mixing ratio of graupel and vertical velocity between the first-guess ensemble mean and nature run. These differences are generally positive, meaning that the first-guess ensemble mean misses developed convective clouds in the middle of Kyushu. As mentioned above, however, in the middle of Kyushu the number of nonzero lightning members is few, so it would be difficult to obtain analysis increments associated with deep convection using the standard EnKF (without regression-based ensemble perturbations) due to the zero-gradient issue.
Horizontal maps of (a) the differences in the mixing ratio of graupel between the nature run and the ensemble mean of the first guess and (b),(c) analysis increments of the mixing ratio of graupel in (b) CTRL and (c) TEST at the first analysis time (0700 UTC 5 Jul 2017) at a height of 6 km.
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
Horizontal maps of (a) the differences in the mixing ratio of graupel between the nature run and the ensemble mean of the first guess and (b),(c) analysis increments of the mixing ratio of graupel in (b) CTRL and (c) TEST at the first analysis time (0700 UTC 5 Jul 2017) at a height of 6 km.
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
Horizontal maps of (a) the differences in the mixing ratio of graupel between the nature run and the ensemble mean of the first guess and (b),(c) analysis increments of the mixing ratio of graupel in (b) CTRL and (c) TEST at the first analysis time (0700 UTC 5 Jul 2017) at a height of 6 km.
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
As in Fig. 5, but for the vertical velocity (W; m s−1).
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
As in Fig. 5, but for the vertical velocity (W; m s−1).
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
As in Fig. 5, but for the vertical velocity (W; m s−1).
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
To deal with the zero-gradient issue, this study applied regression-based ensemble perturbations in TEST. To do so, we obtained the flow-dependent regression coefficients between each model variable and simulated lightning flash at each height. Figure 7 shows the vertical profiles of the regression coefficients at the first analysis time. The regression coefficients for the vertical velocity and temperature indicate that lightning flashes are closely associated with developed convective clouds having a strong updraft and a stabilized temperature profile due to diabatic heating (Figs. 7c,d). A strong updraft within convective clouds would transport low-level moisture upward, so that the regression coefficients for moisture indicate that the more moisture aloft, the more lightning flashes (Fig. 7e). According to Yokota et al. (2018), the regression coefficients for the horizontal winds exhibit more flow-dependent characteristics than the above three variables. At the first analysis time, low-level westerly and southerly are associated with active lightning flashes (Figs. 7a,b).
Vertical profiles of the regression coefficients for (a) zonal velocity [(m s−1)−1], (b) meridional velocity [(m s−1)−1], (c) vertical velocity [(m s−1)−1], (d) temperature (K−1), and (e) the mixing ratio of water vapor [(g kg−1)−1] at the first analysis time (0700 UTC 5 Jul 2017).
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
Vertical profiles of the regression coefficients for (a) zonal velocity [(m s−1)−1], (b) meridional velocity [(m s−1)−1], (c) vertical velocity [(m s−1)−1], (d) temperature (K−1), and (e) the mixing ratio of water vapor [(g kg−1)−1] at the first analysis time (0700 UTC 5 Jul 2017).
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
Vertical profiles of the regression coefficients for (a) zonal velocity [(m s−1)−1], (b) meridional velocity [(m s−1)−1], (c) vertical velocity [(m s−1)−1], (d) temperature (K−1), and (e) the mixing ratio of water vapor [(g kg−1)−1] at the first analysis time (0700 UTC 5 Jul 2017).
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
Using the obtained regression coefficients, this study intends to increase the ensemble spread in the observation space. Figure 8 shows scatterplots between ensemble perturbations in the model space (mixing ratio of water vapor) and those in the observation space at an observation location in the middle of Kyushu. The scatterplot for CTRL exhibits the zero-gradient issue and the ensemble spread in the observation space is completely zero (Fig. 8a). In contrast, regression-based ensemble perturbations increase the ensemble spread in TEST (Fig. 8b). In this case, the larger amount of water vapor, the more lightning. The coefficient of determination (r2) is not high because y′ is affected by not only the ensemble perturbations in water vapor at a single height but also those in other variables at various heights. The increase in the ensemble spread would contribute to obtaining nonzero analysis increments in TEST.
Scatterplots between the background ensemble perturbations in the model space (x′) (mixing ratio of water vapor at a height of 6 km; g kg−1) and those in the observation (lightning flash) space (y′) in (a) CTRL and (b) TEST for the observation located at 32.49°N, 130.99°E, at the first analysis time (0700 UTC 5 Jul 2017). The black line is the regression line for the scatterplot in (b) with the correlation coefficient (r) and its square (r2) in the upper-left corner.
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
Scatterplots between the background ensemble perturbations in the model space (x′) (mixing ratio of water vapor at a height of 6 km; g kg−1) and those in the observation (lightning flash) space (y′) in (a) CTRL and (b) TEST for the observation located at 32.49°N, 130.99°E, at the first analysis time (0700 UTC 5 Jul 2017). The black line is the regression line for the scatterplot in (b) with the correlation coefficient (r) and its square (r2) in the upper-left corner.
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
Scatterplots between the background ensemble perturbations in the model space (x′) (mixing ratio of water vapor at a height of 6 km; g kg−1) and those in the observation (lightning flash) space (y′) in (a) CTRL and (b) TEST for the observation located at 32.49°N, 130.99°E, at the first analysis time (0700 UTC 5 Jul 2017). The black line is the regression line for the scatterplot in (b) with the correlation coefficient (r) and its square (r2) in the upper-left corner.
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
Regression-based ensemble perturbations result in analysis increments associated with convective clouds even where the number of nonzero lightning members is few. Figures 5b and 5c show the horizontal distributions of the analysis increments for graupel at the first analysis time. TEST has positive analysis increments in the middle of Kyushu where the first guess misses developed convective clouds (Figs. 5a,c), whereas CTRL does not (Fig. 5b). Although the ensemble mean of graupel is close to zero in the middle of Kyushu, some ensemble members still have nonzero graupel there (not shown). These ensemble perturbations in graupel are related to the ensemble perturbation in the observation space by the Yokota et al. (2018) method, resulting in the analysis increments in graupel. Similarly, assimilating lightning flashes intensifies the updraft in the middle of Kyushu in TEST, not in CTRL (Fig. 6). These analysis increments in TEST are consistent with the differences between the first guess and nature run although the former is far smaller than the latter partially due to the large observation error in LETKF. Therefore, regression-based ensemble perturbations successfully improve the analysis by mitigating the zero-gradient issue.
Assimilation of zero lightning observations effectively suppresses spurious convection associated with lightning. Such convection is located where negative values of O − B are found (Fig. 4a). In these areas, analysis increments of graupel and vertical velocity are generally negative, indicating that spurious convection is suppressed by DA with the EnKF, like Mansell (2014).
b. Impacts on the precipitation distribution
In this section, we assess the impacts of regression-based ensemble perturbations on the forecast accuracy. We focus on the precipitation distribution because heavy rain in the center of Kyushu is missed in CTRL, as will be shown in Fig. 9. This study performs six ensemble forecasts in each experiment with 1-h increments between 0700 and 1200 UTC 5 July 2017. To quantitively measure the forecast accuracy, this study uses the fractions skill score (FSS) (Roberts and Lean 2008) for the hourly accumulated precipitation amount with a horizontal scale of 30 km and a threshold of 5 mm h−1.
Horizontal maps of the probability of precipitation of >5 mm h−1 initiated at the first analysis time (0700 UTC 5 Jul 2017) for (a) NODA, (b) CTRL, and (c) TEST. The valid time and forecast time (FT) are at 0800 UTC and 1 h. Gray broken curves show precipitation of 5 mm h−1 in the nature run.
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
Horizontal maps of the probability of precipitation of >5 mm h−1 initiated at the first analysis time (0700 UTC 5 Jul 2017) for (a) NODA, (b) CTRL, and (c) TEST. The valid time and forecast time (FT) are at 0800 UTC and 1 h. Gray broken curves show precipitation of 5 mm h−1 in the nature run.
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
Horizontal maps of the probability of precipitation of >5 mm h−1 initiated at the first analysis time (0700 UTC 5 Jul 2017) for (a) NODA, (b) CTRL, and (c) TEST. The valid time and forecast time (FT) are at 0800 UTC and 1 h. Gray broken curves show precipitation of 5 mm h−1 in the nature run.
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
Regression-based ensemble perturbations improve the forecast accuracy of precipitation. Figure 9 shows the horizontal maps for the probability of precipitation (>5 mm h−1) obtained from the ensemble forecasts initiated at 0700 UTC. The nature run has a precipitation region in the middle of Kyushu (gray dashed curves in Fig. 9). This precipitation region is almost missing in CTRL, whereas TEST shows a slightly higher probability. In addition, spurious precipitation over the ocean found in NODA is suppressed in CTRL and TEST. This indicates that the assimilation of zero lightning flashes contributes to reducing false alarms, consistent with the analysis increments shown in Figs. 5 and 6.
Regression-based ensemble perturbations further improve the forecast accuracy of precipitation by continuously cycling DA. Figure 10 shows the probability of precipitation from the ensemble forecasts initiated after six DA cycles. The nature run has a band-shaped precipitation system in the middle of Kyushu. This precipitation system is successfully predicted in TEST with a high probability (>90%), whereas CTRL predicts a low probability (<30%).
As in Fig. 9, but for the ensemble forecasts in (a) CTRL and (b) TEST initiated at 1200 UTC 5 Jul 2017.
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
As in Fig. 9, but for the ensemble forecasts in (a) CTRL and (b) TEST initiated at 1200 UTC 5 Jul 2017.
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
As in Fig. 9, but for the ensemble forecasts in (a) CTRL and (b) TEST initiated at 1200 UTC 5 Jul 2017.
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
The forecast accuracy of precipitation in TEST is improved compared to CTRL in all the forecasts. Figure 11 presents box plots of FSS for the ensemble forecasts in each experiment. TEST shows higher FSSs for all the forecasts than CTRL, indicating that regression-based ensemble perturbations clearly contribute to improving the forecast accuracy of precipitation. The forecast improvement in TEST is found even at the forecast time of 4 h (not shown). In CTRL, the zero-gradient issue limits the impacts of assimilating lightning flash observations, so that FSSs for CTRL are almost the same as those for NODA (Fig. 11).
Boxplots of the fractions skill scores (FSSs) for 1-h ensemble precipitation forecasts in NODA, CTRL, and TEST. Each experiment contains six ensemble forecasts initiated hourly from 0700 to 1200 UTC 5 Jul 2017.
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
Boxplots of the fractions skill scores (FSSs) for 1-h ensemble precipitation forecasts in NODA, CTRL, and TEST. Each experiment contains six ensemble forecasts initiated hourly from 0700 to 1200 UTC 5 Jul 2017.
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
Boxplots of the fractions skill scores (FSSs) for 1-h ensemble precipitation forecasts in NODA, CTRL, and TEST. Each experiment contains six ensemble forecasts initiated hourly from 0700 to 1200 UTC 5 Jul 2017.
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
c. Sensitivity to the number of nonzero lightning members
This study applies regression-based ensemble perturbations if Nmem < 10, whereas Yokota et al. (2018) applied them for the assimilation of radar reflectivity observations if there are zero precipitating members. In this section, we investigate the sensitivity of the results to Nmem. This study performs two additional TEST experiments with Nmem = 1 (hereafter MEM01) and Nmem = 20 (hereafter MEM20).
The TEST experiment (Nmem = 10) gives the best forecast accuracy among the three experiments. Figure 12 compares FSSs for two additional experiments and TEST. Although MEM01 corresponds to the setting used in Yokota et al. (2018), MEM01 has the lowest FSSs among the three experiments and its improvement of FSSs against CTRL is limited (Figs. 11 and 12). TEST shows slightly higher FSSs than MEM20 in terms of the median.
As in Fig. 11, but for MEM01, MEM10 (i.e., TEST), and MEM20.
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
As in Fig. 11, but for MEM01, MEM10 (i.e., TEST), and MEM20.
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
As in Fig. 11, but for MEM01, MEM10 (i.e., TEST), and MEM20.
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
Analysis increments depend on Nmem. Figure 13 shows the horizontal maps of the analysis increments for the vertical velocity in each experiment. MEM01 has the smallest analysis increments. The analysis increments for TEST and MEM20 are similar in the middle of Kyushu where the number of nonzero lightning members < 5 (Fig. 4b). In the north of Kyushu, where the number of nonzero lightning members is between 5 and 20 (Fig. 4b), MEM20 has larger analysis increments than TEST (MEM10) (Figs. 13b,c). These large analysis increments in MEM20 could result in imbalance and slightly degrade the forecast accuracy than that in TEST.
Horizontal maps of the analysis increments of vertical velocity (W; m s−1) at the first analysis time (0700 UTC 5 Jul 2017) in (a) MEM01, (b) MEM10 (TEST), and (c) MEM20 at a height of 6 km.
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
Horizontal maps of the analysis increments of vertical velocity (W; m s−1) at the first analysis time (0700 UTC 5 Jul 2017) in (a) MEM01, (b) MEM10 (TEST), and (c) MEM20 at a height of 6 km.
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
Horizontal maps of the analysis increments of vertical velocity (W; m s−1) at the first analysis time (0700 UTC 5 Jul 2017) in (a) MEM01, (b) MEM10 (TEST), and (c) MEM20 at a height of 6 km.
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
When Nmem is nonzero and smaller than 10 (out of 100 members), the ensemble spread in the observation space is nonzero but could be too small to obtain enough analysis increments. Figure 14 shows the horizontal maps of the ensemble spread in each experiment. In MEM01 and MEM10 (TEST), regression-based ensemble perturbations result in larger ensemble spread and larger analysis increments in the middle of Kyushu than CTRL (Figs. 13 and 14). The ensemble spread in MEM01 in the middle of Kyushu is smaller than that in TEST. This is because TEST applies regression-based ensemble perturbations even where 1 ≤ Nmem < 10, whereas MEM01 does not. As a result, in MEM01 the impacts of assimilating lightning flash observations are limited (Fig. 13). Furthermore, when the number of nonzero lightning members is few, the EnKF relies on few outliers to obtain the forecast error covariance and its performance could be suboptimal. These reasons could explain why MEM10 and MEM20 outperform MEM01.
Horizontal maps of the ensemble spread in the observation space at the first analysis time (0700 UTC 5 Jul 2017) in (a) CTRL, (b) MEM01, and (c) MEM10 (TEST).
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
Horizontal maps of the ensemble spread in the observation space at the first analysis time (0700 UTC 5 Jul 2017) in (a) CTRL, (b) MEM01, and (c) MEM10 (TEST).
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
Horizontal maps of the ensemble spread in the observation space at the first analysis time (0700 UTC 5 Jul 2017) in (a) CTRL, (b) MEM01, and (c) MEM10 (TEST).
Citation: Monthly Weather Review 151, 10; 10.1175/MWR-D-22-0334.1
4. Summary
Assimilation of lightning flash observations could have a positive impact on NWP because these observations are closely associated with the development of convective clouds. Lightning flashes are generally zero if no developed clouds, resulting in the zero-gradient issue in which only a small portion of ensemble members have nonzero lightning flashes. To address the zero-gradient issue in lightning flash DA, this study has applied regression-based ensemble perturbations, originally proposed by Yokota et al. (2018) for the assimilation of radar reflectivity observations.
This study has evaluated the impacts of regression-based ensemble perturbations on the assimilation of lightning flash observations in OSSEs for the Kyushu-2017 event. This study has obtained the following findings:
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Regression-based ensemble perturbations increase the ensemble spread and contribute to obtaining reasonable analysis increments associated with convective clouds even if only a few members have nonzero lightning flashes.
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The forecast accuracy is sensitive to the threshold of the number of ensemble members with nonzero lightning flashes (Nmin). When at least a few ensemble members have nonzero lightning flashes, the ensemble spread in the observation space is not completely zero but is too small to obtain enough analysis increments. Furthermore, in such a case the EnKF relies on a few outliers to obtain the forecast error covariance and could be suboptimal. In this regard, Nmin = 10 (out of 100 members) provides a better forecast accuracy than Nmin = 1, which was used in Yokota et al. (2018) for radar reflectivity observations.
This study has focused on a proof of concept with the OSSEs for a single case. In future research, it is essential to evaluate the impacts of regression-based ensemble perturbations on the assimilation of real lightning flash observations for many cases. For example, the development of tropical cyclones is known to be associated with lightning activity (e.g., Sato et al. 2021), so assimilating lightning flashes could improve the forecast accuracy of tropical cyclones. Although this study has evaluated the impacts on the precipitation distribution, assimilating lightning flashes with weather radar data could further improve quantitative precipitation forecast (e.g., Fierro et al. 2019). However, to deal with real lightning observations, we should develop a preprocessing procedure of real lightning observations, evaluate their quality and bias, and implement a bias correction method if necessary. In addition, the use of FED instead of FOD could enhance the positive impacts of assimilating lighting observations even though it requires further model development. These are a subject of our future research. Nevertheless, the zero-gradient issue can be found not only in lightning-flash DA but also in the assimilation of all-sky satellite radiances in terms of clouds. Applying regression-based ensemble perturbations to all-sky satellite radiances is an interesting subject of future research.
Acknowledgments.
The authors thank the editor and anonymous reviewers for providing constructive comments that helped improve the manuscript. TH also thanks Hideyuki Sakamoto of RIKEN for his kind support during the revision. This research was partially supported by the RIKEN Special Postdoctoral Researchers Program, JSPS KAKENHI (Grants JP20K14558, JP20H04196, and JP19H05605), JST AIP (JPMJCR19U2), MEXT (JPMXP1020200305) as “Program for Promoting Researches on the Supercomputer Fugaku” (Large Ensemble Atmospheric and Environmental Prediction for Disaster Prevention and Mitigation), JST SICORP (JPMJSC1804), JST CREST (JPMJCR20F2), COE research grant in computational science from Hyogo Prefecture and Kobe City through Foundation for Computational Science, JAXA EO-RA2, RIKEN Pioneering Project “Prediction for Science,” and RIKEN Engineering Network Project. This research used computational resources of Supercomputer Fugaku provided by the RIKEN Center for Computational Science (ID: hp210166). YS was supported by Research Field of Hokkaido Weather Forecast and Technology Development (endowed by Hokkaido Weather Technology Center Co. Ltd.).
Data availability statement.
The NCEP GFS data and PREPBUFR data are available online at https://rda.ucar.edu/datasets/ds084.1/ and https://rda.ucar.edu/datasets/ds337.0/. The MANL data are available via the Meteorological Research Consortium between the JMA and Meteorological Society of Japan. The source code and documentation of SCALE are available online at https://scale.riken.jp/. The source code of the LETKF and plotting scripts are available online at https://doi.org/10.5281/zenodo.8012034.
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