The Tornadic Supercell on the Kanto Plain on 6 May 2012: Polarimetric Radar and Surface Data Assimilation with EnKF and Ensemble-Based Sensitivity Analysis

Sho Yokota Meteorological Research Institute, Japan Meteorological Agency, Tsukuba, Japan

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Hiromu Seko Meteorological Research Institute, Japan Meteorological Agency, Tsukuba, and Japan Agency for Marine-Earth Science and Technology, Yokohama, Japan

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Masaru Kunii Meteorological Research Institute, Japan Meteorological Agency, Tsukuba, Japan

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Hiroshi Yamauchi Meteorological Research Institute, Japan Meteorological Agency, Tsukuba, and Observations Department, Japan Meteorological Agency, Tokyo, Japan

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Hiroshi Niino Atmosphere and Ocean Research Institute, The University of Tokyo, Kashiwa, Japan

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Abstract

A tornadic supercell and associated low-level mesocyclone (LMC) observed on the Kanto Plain, Japan, on 6 May 2012 were predicted with a nonhydrostatic mesoscale model with a horizontal resolution of 350 m through assimilation of surface meteorological data (horizontal wind, temperature, and relative humidity) of high spatial density and C-band Doppler radar data (radial velocity and rainwater estimated from reflectivity and specific differential phase) with a local ensemble transform Kalman filter. With assimilation of both surface and radar data, a strong LMC was successfully predicted near the path of the actual tornado. When either surface or radar data were not assimilated, however, the LMC was not predicted. Therefore, both surface and radar data were essential for successful LMC forecasts. The factors controlling the strength of the predicted LMC, defined as a low-level maximum vertical vorticity, were clarified by an ensemble-based sensitivity analysis (ESA), which is a new approach for analyzing LMC intensification. The ESA showed that the strength of the LMC was sensitive to low-level convergence forward of the storm and to low-level relative humidity in the rear of the storm. Therefore, the correction of these low-level variables by assimilation of dense observations was found to be particularly important for forecasting and monitoring the LMC in the present case.

Corresponding author address: Sho Yokota, Forecast Research Department, Meteorological Research Institute, Japan Meteorological Agency, 1-1 Nagamine, Tsukuba, Ibaraki 305-0052, Japan. E-mail: syokota@mri-jma.go.jp

Abstract

A tornadic supercell and associated low-level mesocyclone (LMC) observed on the Kanto Plain, Japan, on 6 May 2012 were predicted with a nonhydrostatic mesoscale model with a horizontal resolution of 350 m through assimilation of surface meteorological data (horizontal wind, temperature, and relative humidity) of high spatial density and C-band Doppler radar data (radial velocity and rainwater estimated from reflectivity and specific differential phase) with a local ensemble transform Kalman filter. With assimilation of both surface and radar data, a strong LMC was successfully predicted near the path of the actual tornado. When either surface or radar data were not assimilated, however, the LMC was not predicted. Therefore, both surface and radar data were essential for successful LMC forecasts. The factors controlling the strength of the predicted LMC, defined as a low-level maximum vertical vorticity, were clarified by an ensemble-based sensitivity analysis (ESA), which is a new approach for analyzing LMC intensification. The ESA showed that the strength of the LMC was sensitive to low-level convergence forward of the storm and to low-level relative humidity in the rear of the storm. Therefore, the correction of these low-level variables by assimilation of dense observations was found to be particularly important for forecasting and monitoring the LMC in the present case.

Corresponding author address: Sho Yokota, Forecast Research Department, Meteorological Research Institute, Japan Meteorological Agency, 1-1 Nagamine, Tsukuba, Ibaraki 305-0052, Japan. E-mail: syokota@mri-jma.go.jp

1. Introduction

Strong tornadoes are often generated in supercells (Browning 1964), which are known to develop in an environment with strong vertical wind shear and unstable stratification. In particular, a veering shear tends to enhance right-moving storms and associated midlevel (above 1-km height) mesocyclones by means of the relatively upward pressure gradient force that results from the interaction of the vertical shear and updraft (Rotunno and Klemp 1982).

Strong low-level (below 1-km height) mesocyclones (LMCs) play an important role in the formation of tornadoes. If the low-level air has no initial vertical vorticity, tilting of horizontal vorticity by a downdraft is required for the genesis of LMCs (Davies-Jones 1982; Rotunno and Klemp 1985; Wicker and Wilhelmson 1995; Adlerman et al. 1999). Both observational and numerical studies (Markowski et al. 2002, 2003, 2008; Straka et al. 2007) have suggested that horizontal vorticity is mainly generated baroclinically by the rear-flank downdraft (RFD) of the storm. In this baroclinic genesis mechanism of horizontal vorticity, environmental low-level vertical shear and water vapor are important (Craven and Brooks 2004; Markowski and Richardson 2014; Parker and Dahl 2015). A gradient of vertical shear across the storm (Richardson et al. 2007) and a cold pool that is neither too strong nor too weak (Markowski and Richardson 2014) have also been pointed out as favorable conditions for the intensification of right-moving supercells associated with strong LMCs.

Although the mechanisms of LMC genesis have already been clarified, important conditions for the genesis of actual LMCs might not be detected or identified by observational studies and numerical sensitivity experiments not conducted under realistic conditions. Therefore, sensitivity analyses of LMCs successfully reproduced by ensemble experiments with a large number of members and realistic conditions are required to characterize more accurately the relationship between LMCs and the surrounding environment; such a sensitivity analysis can be accomplished by a “warn-on-forecast” approach (Stensrud et al. 2009, 2013; Cintineo and Stensrud 2013), that is, ensemble forecasts of storm features made by assimilating dense surface and radar observations around the tornadoes.

Surface meteorological data directly capture the dynamic and thermodynamic characteristics of the planetary boundary layer, and these characteristics are closely related to low-level convergence and static instability. Therefore, assimilation of surface data can potentially improve the modeled state of the planetary boundary layer and associated forecasts of convective systems (Hacker and Snyder 2005; Zhang et al. 2006; Meng and Zhang 2007, 2008; Fujita et al. 2007; Ancell et al. 2011; Ha and Snyder 2014; Sobash and Stensrud 2015). Doppler radar data assimilation is also useful for improving forecasts of convective systems because distributions of Doppler velocity and reflectivity observed by radar contain information on the structure and development of convective systems (Snyder and Zhang 2003; Zhang et al. 2004; Dowell et al. 2004, 2011; Caya et al. 2005; Tong and Xue 2005; Xue et al. 2006, 2014; Hu et al. 2006a,b; Hu and Xue 2007; Stensrud and Gao 2010; Schenkman et al. 2011a,b; Dawson et al. 2012; Marquis et al. 2012, 2014; Snook et al. 2012, 2015; Yussouf et al. 2013a,b; Tanamachi et al. 2013; Putnam et al. 2014). Although polarimetric radar information also has large potential to improve short-term forecasts of convective systems, their assimilation does not necessarily improve forecasts because quantitative forecasting of cloud microphysics is difficult (Jung et al. 2008a,b, 2010a,b; Li and Mecikalski 2010, 2012, 2013).

To forecast tornadic supercells by assimilating dense surface and radar observations, three-dimensional variational (3DVAR) and ensemble Kalman filter (EnKF) methods are widely used. While 3DVAR assimilation is useful for forecasting supercell storms easily with high resolution (Hu et al. 2006a,b; Hu and Xue 2007; Stensrud and Gao 2010; Schenkman et al. 2011a,b; Xue et al. 2014), EnKF assimilation can produce dynamically balanced analyses of supercell storms from the flow-dependent (varying according to the atmospheric field) forecast error covariance estimated by ensemble forecasts (Dowell et al. 2004, 2011; Dawson et al. 2012; Marquis et al. 2012, 2014; Snook et al. 2012, 2015; Yussouf et al. 2013a,b; Tanamachi et al. 2013; Putnam et al. 2014). Caya et al. (2005) have shown that EnKF assimilation can produce better analyses than 4DVAR assimilation after several assimilation cycles in observation system simulation experiments using radar observations of a supercell storm.

These previous studies of surface and radar data assimilation have shown that modification of small-scale fields before the genesis of LMCs by assimilation of low-level dense observations helps to improve the predictability of LMCs. However, it is not yet clear which physical variables distributed in what areas are important to assimilate for LMC forecasts. Convective available potential energy (CAPE) and storm-relative environmental helicity (SREH; Davies-Jones et al. 1990) are known to be useful parameters for estimating the potential intensity of convective updrafts and the production of vertical vorticity through the tilting of horizontal vorticity associated with environmental vertical wind shear, respectively. However, even when these parameters suggest that conditions are favorable for LMC genesis, LMCs are not necessarily generated.

The objectives of this study are to show the impacts of dense surface and radar data assimilation on the forecast of an LMC and to clarify which variables are important for intensification of the LMC by performing a sensitivity analysis with realistic conditions. To fulfill these objectives, we performed ensemble forecasts using EnKF analyses and determined the sensitivity of the LMC strength to environmental parameters such as SREH and CAPE by conducting an ensemble-based sensitivity analysis (ESA; Ancell and Hakim 2007; Torn and Hakim 2008).

The rest of the paper is structured as follows. The design of the assimilation experiment is presented in section 2, and the experimental results are presented in section 3. In section 4, these results are compared with those of sensitivity experiments in which dense surface or radar observations were not assimilated. In section 5, the ESA method used to examine the sensitivity of the strength of the generated vortex to environmental variables is described, and the results are presented. In section 6, the ESA results are discussed. Finally, section 7 is a summary with conclusions.

2. Experimental design

a. The tornadoes on 6 May 2012

In this study, we focused on three tornadoes that occurred almost simultaneously on the Kanto Plain at about 1230 Japan standard time (JST; 0900 JST corresponds to 0000 UTC) on 6 May 2012 (Japan Meteorological Agency 2012). These tornadoes passed through Tsukuba, Chikusei, and Moka cities in order from the south (paths are shown by black solid lines in Figs. 13), and they are hereafter called the Tsukuba, Chikusei, and Moka tornadoes, respectively. We focused particularly on the Tsukuba tornado, which caused the most severe damage of the three along a path that was 17 km long and 500 m wide. It was spawned by a classic supercell (Yamauchi et al. 2013) and was ranked F3 on the F-scale (Fujita 1971) by the Japan Meteorological Agency (JMA).

Fig. 1.
Fig. 1.

Observations at 1200 JST used in the inner-LETKF analysis: (a) horizontal winds (m s−1), (b) temperature (K), and (c) relative humidity (%) at 20-m height. Black lines denote the paths of the Tsukuba, Chikusei, and Moka tornadoes in order from south to north. (d) Roughness length of the modeled surface z0 (color shading, m) and altitude in the model zm (thin contours = 100 m; thick contours = 1000 m) used in Eqs. (1)(3).

Citation: Monthly Weather Review 144, 9; 10.1175/MWR-D-15-0365.1

Fig. 2.
Fig. 2.

Radial velocity (m s−1) at 1.0° elevation used in the inner-LETKF analysis observed by (a) Kashiwa, (b) Haneda, and (c) Narita radars and by (d) MACS-POL at 1200 JST. The black dot denotes the position of each radar site. Black lines are as in Fig. 1. The red circles denote the position of cyclonic shear line.

Citation: Monthly Weather Review 144, 9; 10.1175/MWR-D-15-0365.1

Fig. 3.
Fig. 3.

(a) Z (dBZ) and (b) ϕDP (degrees) at 1.0° elevation observed by MACS-POL at 1200 JST, and (c) QRZ (g m−3) and (d) QR (g m−3) estimated from Z and KDP at 1.0° elevation. The black dot and the black lines are as in Fig. 1. The red circle denotes the position of QR peaks.

Citation: Monthly Weather Review 144, 9; 10.1175/MWR-D-15-0365.1

At 0900 JST on 6 May 2012, southerly winds prevailed near the surface of the Kanto Plain because a low pressure system was centered over the Japan Sea, northwest of the Kanto Plain (Fig. 4a). At that time, both a cold air mass and a low pressure system were located in the upper troposphere over the Japan Sea (Fig. 4b). Subsequently, a group of cumulonimbus clouds began to develop west of the Kanto Plain, and they moved northeastward across the Kanto Plain while continuing to develop. Cold advection due to northwesterly winds in the upper troposphere and warm advection due to southerly winds near the surface increased static instability and contributed to the intensification of the storm. The detailed synoptic-scale field around the tornadoes has been described by Seko et al. (2015).

Fig. 4.
Fig. 4.

(a) Temperature (color shading, K) and pressure (contours, hPa) at the surface and (b) temperature (color shading, K) and height (contours, m) on the 500-hPa surface in the global analysis of JMA at 0900 JST 6 May 2012.

Citation: Monthly Weather Review 144, 9; 10.1175/MWR-D-15-0365.1

On the Kanto Plain, a considerable number of observations captured the structure and environment of the tornadoes. In particular, the Meteorological Research Institute advanced C-band solid-state polarimetric radar (MACS-POL) observed the detailed structure and behavior of the tornado’s parent storm. MACS-POL has radial and azimuthal resolutions of 150 m and 0.7° (Adachi et al. 2013), and the Tsukuba tornado passed only about 15 km north of MACS-POL. Radial velocity observed by MACS-POL showed that a low-level vortex at the tip of a hook echo moved above the path of the Tsukuba tornado (southernmost solid black line in Figs. 13). The diameter and vorticity of this vortex, calculated from the local minimum and maximum velocities and their locations, were O(1) km and O(10−2) s−1, respectively, at about 1230 JST, and they became O(10−1) km and O(10−1) s−1, respectively, by 1250 JST (Yamauchi et al. 2013). In addition, the high-resolution surface observation network, comprising Automated Meteorological Data Acquisition System (AMeDAS; operated by JMA) and Environmental Sensor Network (ESN; operated by NTT DOCOMO, Inc.) stations, recorded the horizontal distributions of surface winds, temperature, and relative humidity on the Kanto Plain before and after the genesis of each of the three tornadoes. The average spatial interval of these surface observations was about 10 km (Figs. 1a–c).

Shoji et al. (2015) and Mashiko (2016) simulated an LMC and a tornado corresponding to the Tsukuba tornado by a numerical simulation using the operational analyzed fields of JMA’s mesoscale model. Although Shoji et al. (2015) and Mashiko (2016) did not discuss the predictability of LMCs, Seko et al. (2015) simulated three LMCs corresponding to the three tornadoes and discussed their predictability by conducting ensemble experiments with EnKF assimilation. However, owing to model bias and inaccurate initial conditions due to the assimilation of spatially coarse conventional observations, the LMC outbreaks simulated by Seko et al. (2015) were about 45 min earlier than the actual outbreak, and the position of the LMC associated with the Tsukuba tornado was shifted 15–20 km north of the actual tornado.

b. Nested LETKF system

To clarify the variables that affect LMC genesis, we forecast a realistic LMC through assimilation of dense surface and radar observations. Such a realistic forecast can be attained when both large-scale (more than several tens of kilometers) environments (e.g., the convergence of low-level winds) and the convective-scale (less than a few tens of kilometers) structure of severe events (e.g., cumulus convection) are well reproduced simultaneously. To reproduce them, we used a nested, four-dimensional local ensemble transform Kalman filter (nested LETKF; Seko et al. 2013), a multiscale EnKF, as the data assimilation system (Fig. 5).

Fig. 5.
Fig. 5.

Schematic of the calculation procedure and the calculation domains of the nested-LETKF system.

Citation: Monthly Weather Review 144, 9; 10.1175/MWR-D-15-0365.1

In this system, the analysis and the analysis perturbations are calculated at each analysis point. Observation localization factors, which are required to reduce unrealistic correlations due to too few ensemble members, are defined to enlarge the observation error variance at observation points far from the analysis point both spatially and temporally (Hunt et al. 2007). To enlarge the underestimated forecast error, we adopted multiplicative inflation (Anderson and Anderson 1999). After the analysis, we performed an ensemble forecast with the JMA nonhydrostatic model (Saito et al. 2006)1 using the LETKF-analyzed field for the initial conditions, and repeated the forecast–analysis cycle. In this study, the number of the ensemble members was 32.

In the outer LETKF, the grid interval was 15 km horizontally, and it varied vertically from 40 m near the surface to 886 m near the top of the calculation domain. The number of vertical levels was 50. For the boundary conditions, the mesoscale analysis (until 0900 JST 6 May) and the global forecast (after 0900 JST 6 May) of JMA without any ensemble perturbations were used by all members. A bulk-type single-moment cloud microphysics scheme with water vapor, cloud water, rain, cloud ice, snow, and graupel (Lin et al. 1983) and Kain–Fritsch cumulus parameterization (Kain and Fritsch 1990; Kain 2004) were adopted. A second-order turbulence closure scheme based on Nakanishi (2001) and Nakanishi and Niino (2004, 2006) was also adopted. Hourly observations of surface stations (pressure), radiosondes (horizontal winds, temperature, and relative humidity), aircraft (horizontal winds and temperature), wind profiler radars (horizontal winds), and Doppler radars [Doppler velocity and relative humidity estimated from reflectivity (Ikuta and Honda 2011; Ikuta 2012)], which are used in the mesoscale analysis of JMA (Honda et al. 2005), were assimilated in a 6-h assimilation window.

In the inner LETKF, the grid interval was 1875 m horizontally, which is 8 times finer than that of outer LETKF. The vertical grid interval was the same as the outer-LETKF interval to avoid inconsistency with the horizontally coarse lateral boundary. No cumulus parameterization was used. Surface and radar data observed every 10 min were assimilated in an hourly assimilation window. The hourly 32-member outer-LETKF analyses and forecasts were used for the boundary conditions of the 1-h inner-LETKF ensemble forecasts. Surface observations consisted of horizontal winds, temperature, and relative humidity observed at meteorological observatories and by AMeDAS and ESN. Radar observations consisted of radial velocity observed by MACS-POL and three operational C-band Doppler radars, in Kashiwa city and at Haneda and Narita airports (hereafter the Kashiwa, Haneda, and Narita radars, respectively) and the amount of rainwater estimated by MACS-POL. The methods used to assimilate surface and radar observations are explained in the following subsections. An ensemble Kalman smoother (EnKS; Kalnay et al. 2007; Yang et al. 2009) was used in the assimilation of observations from 1100 to 1200 JST, in addition to those before 1100 JST, only in the analysis at 1100 JST 6 May 2012; EnKS is a simple extension of EnKF in a time direction because in the LETKF formulation any time in the assimilation window can be an analysis time. With EnKS, requirements for a long spinup time and the assimilation of observations just before the tornado outbreak are accomplished simultaneously.

In the downscale ensemble experiments (350m-EXPs) used to forecast the LMC associated with the Tsukuba tornado, the grid interval was 350 m horizontally, and it varied vertically from 40 m near the surface to 609.5 m near the top of the calculation domain. The number of vertical levels was 70. A first-order turbulence closure scheme based on Deardorff (1980) was adopted, and no cumulus parameterization was used. The 32-member inner-LETKF analyses and their ensemble mean at 1100 JST 6 May 2012 and their forecasts were used as the initial and boundary conditions, respectively, for the 33 members of 350m-EXP. Figure 5 outlines the calculation procedures and shows the computational domains of the nested-LETKF system, and the settings are summarized in Table 1.

Table 1.

Setting of the nested LETKF.

Table 1.

The experiments performed in this study differ from those of Seko et al. (2015) with respect to the following points: (i) dense surface and radar data were assimilated by inner LETKF; (ii) the number of ensemble members was increased from 12 to 32; (iii) multiplicative inflation parameters were increased from 1.1 to 1.5 in outer LETKF and from 1.1 to 1.2 in inner LETKF to increase the impact of the assimilation of dense observations; (iv) the horizontal domain of inner LETKF was increased from 300 km × 300 km to 450 km × 450 km to assimilate the dense surface observations in the larger domain; (v) observations assimilated by outer LETKF were not assimilated again by inner LETKF, and the inner-LETKF analyses did not affect the outer-LETKF analyses, to facilitate interpretation of the impact of the assimilation of dense observations; (vi) the initial time of the 350m-EXPs was changed from 1030 to 1100 JST, and EnKS (Kalnay et al. 2007; Yang et al. 2009) was used to assimilate the dense observations near the time when the actual tornadoes were generated; and (vii) the JMA global forecast was used for the boundary conditions of outer LETKF after 0900 JST 6 May 2012 to demonstrate the predictability of the LMC.

c. Assimilation of surface observations

In inner LETKF, zonal and meridional winds, temperature, and relative humidity (u20, υ20, T20, RH20) at 20-m height, the lowest model level (Figs. 1a–c), were assimilated. These variables were transformed from the corresponding surface data (uobs, υobs, Tobs, RHobs) with the following equations:
e1
e2
e3
where z0 (Fig. 1d) is the roughness length of the model surface (m); zm (Fig. 1d) and zs are altitudes of the model and the actual surface, respectively, above sea level (m); zobs is the height of the observation instruments above the surface (m); p(z) and es(z) are pressure and saturated water vapor pressure, respectively, at height z (m) of the model; cp = 1.01 × 103 J K−1 kg−1 is the specific heat at constant pressure; R = 2.87 × 102 J K−1 kg−1 is the gas constant; and Γ = 6.5 × 10−3 K m−1 is the temperature lapse rate. ESN observations from only those sites that passed quality check procedures (u20 and υ20 from 228 and T20 and RH20 from 215 of 332 total sites) were assimilated in the experiments; for details, see the appendix.

Equation (1) assumes a neutrally stratified atmosphere in which vertical changes of horizontal winds are logarithmic. However, the assumption of neutral stratification is not appropriate for temperature and relative humidity because differences in their values at 20-m height between the model and the observation were mainly caused by the difference between zm and zs. Therefore, Eqs. (2) and (3) assume a constant Γ instead of neutral stratification. Equation (3) also assumes a constant water vapor mixing ratio.

In the present study, variables at the lowest model level (20-m height above the surface) were diagnosed from the surface observations and assimilated. This assimilation method is different from that used by previous studies, in which variables at 10 or 2 m above the surface were diagnosed from model grid values to assimilate surface observations directly (e.g., Hacker and Snyder 2005; Fujita et al. 2007; Ancell et al. 2011; Ha and Snyder, 2014; Sobash and Stensrud 2015). We used our method so that the impacts of observations made at various heights would be all at the same level. Moreover, the present study also considered the difference between zm and zs.

Figures 1a–c show the distributions of (u20, υ20, T20, RH20) assimilated at 1200 JST 6 May 2012. A mesoscale cold front dividing the northwestern region from the southeastern region was analyzed near the actual paths of the tornadoes (black lines): a warm, humid southerly flow prevailed south of the front, whereas a cold, dry, northerly flow prevailed on its northern side.

Figures 6a–d show (OF) (observation minus forecast) histograms of all surface observations during 1100–1200 JST assimilated by the inner LETKF. All (OF) distributions were close to Gaussian, and, although the (OF) averages were not zero because of biases of the model or observations, their standard deviations were larger than the averages and close to the radiosonde observational error variances at the surface used in the JMA operational mesoscale data assimilation system (2.2 m s−1 for u20 and υ20, 1.3 K for T20, and 10.8% for RH20; Honda 2010). Therefore, we used these observational error variances in the JMA system (Honda 2010) for the surface observations in this experiment.

Fig. 6.
Fig. 6.

Frequency distributions of (OF) (observation minus forecast) results of the inner-LETKF analysis during 1100–1200 JST: (a) zonal wind (m s−1), (b) meridional wind (m s−1), (c) temperature (K), and (d) relative humidity (%) at 20-m height, (e) radial velocity (m s−1) observed by four radars, and (f) rainwater (g m−3) observed by MACS-POL. “AVE” and “STD” are average and standard deviation, respectively.

Citation: Monthly Weather Review 144, 9; 10.1175/MWR-D-15-0365.1

The observational error variances were partly caused by the assumption of neutral stratification in Eq. (1) and of constant Γ and water vapor mixing ratio in Eqs. (2) and (3). Typical scales of these transformation errors caused by Eqs. (1)(3) were estimated as the difference of the schemes between Eqs. (1)(3) and the empirical functions proposed by Beljaars and Holtslag (1991). First, horizontal winds at 10-m height and temperature and relative humidity at 1.5-m height were obtained hourly from the 1-h forecasts of inner LETKF from 0400 to 1200 JST 6 May. Then, the root-mean-square (RMS) differences of variables at 20-m height were diagnosed by both schemes hourly from the 1-h forecasts. These RMS differences, 0.32 m s−1 for u20, 0.62 m s−1 for υ20, 0.47 K for T20, and 3.7% for RH20, are smaller than the observational error variances given in the previous paragraph.

d. Assimilation of radar observations

Radial velocity VR (m s−1) observed by four radars (Fig. 2), and reflectivity Z (dBZ) (Fig. 3a) and specific differential phase KDP (° km−1) observed by MACS-POL were also assimilated in inner LETKF. The velocity VR was obtained by the dual pulse-repetition frequency technique (Dazhang et al. 1984) and dealiased by the hybrid multiple pulse-repetition interval method (Yamauchi et al. 2006). Here KDP is defined as
e4
where r is the distance from the radar, and ϕDP is the differential phase. Because the observed ϕDP (Fig. 3b) is a noisy measurement (Sachidananda and Zrnić 1986, 1987; Chandrasekar et al. 1990; Hubbert and Bringi 1995), in this study KDP was calculated as the 6-km moving average of ϕDP in the radial direction. The backscatter differential phase included in the observed ϕDP, which is caused by large raindrops or small melting hail (Hubbert and Bringi 1995; Carey et al. 2000; Tabary et al. 2009; Borowska et al. 2011; Tromel et al. 2013), was ignored because the observed ϕDP until 1200 JST increased almost monotonically in the radial direction, even when the backscatter differential phase was not removed.

Because the radar data were not uniformly distributed, we adopted the “superobservation” method for the radar data assimilation: uniform data of VR, Z, and KDP were produced by interpolation to the model grid points of inner LETKF within a 1-km influence radius (Cressman 1959; Seko et al. 2004) on the plan position indicator surface at each elevation angle. Data for elevation angles larger than 5.4° were not used (cf. Seko et al. 2004) because (i) vertical air motion and hydrometeor fall speeds at high elevation angles cannot be ignored and (ii) Z and KDP above the environmental 0°C level, which were observed at high elevation angles, cannot be caused by rainwater only.

In this study, Z and KDP were not themselves assimilated directly, but rainwater, QR, retrieved from Z and KDP, was assimilated (cf. Kawabata et al. 2011). To retrieve QR (g m−3) from Z (dBZ) and KDP (° km−1), we used the following equations:
e5
(Sun and Crook 1997) and
e6
(Bringi and Chandrasekar 2001), respectively, where f = 5.370 GHz is the frequency of the MACS-POL (Adachi et al. 2013). Data with values of Z < 15 dBZ or KDP < 0 were not used because such echoes may not be caused by rainwater. Although Z is affected by radar wave attenuation, Z in Eq. (5) was not corrected for this effect. In general, QRK is more accurate than QRZ because KDP in Eq. (6) is less affected by the drop size distribution than Z in Eq. (5), and it is not affected by radar wave attenuation caused by rainfall. When KDP is small, however, KDP is noisier than Z because the amount of noise of KDP, which is calculated by finite-difference approximation of ϕDP, is not small even when KDP is small (Sachidananda and Zrnić 1986, 1987; Chandrasekar et al. 1990; Hubbert and Bringi 1995). Therefore, as the equation for the retrieval of QR we used
e7
where r = QRK − 1. The quality control of QR mentioned above is very simple, and there is room for its improvement. However, the impact of improving the quality of QR is expected to be small because the impact of assimilating QR was not remarkable, as described later in section 4b.

Figure 2 shows the distribution of VR for the four radars, and Figs. 3c and 3d show that of QRZ and QR, respectively, for MACS-POL at an elevation angle of 1.0° at 1200 JST 6 May 2012. A precipitation band elongated in the meridional direction was located at around 139.5°E (Fig. 3d). This precipitation system was accompanied by a cyclonic shear line (red circles in Fig. 2), and QR peaks that corresponded to the parent storms of the three tornadoes were present near the shear line (red circle in Fig. 3d). These three QR peaks are clearer than the QRZ peaks (Fig. 3c) because they were estimated by using KDP as well as Z.

Because the (OF) distribution of VR is close to Gaussian (Fig. 6e) and its standard deviation is larger than the averages and standard deviations of u20 and υ20 (Figs. 6a and 6b), a constant value of 3.0 m s−1 was used for the observational error variance of VR in this experiment. However, the (OF) distribution of QR is far from Gaussian (Fig. 6f). Therefore, to set the observational error variance of QR we used a similar method to Koizumi et al. (2005). Because the absolute value of (OF) increases when QR is larger, the observational error variance of QR set in this experiment should be varied according to QR. However, it is expected to have a certain finite value even if QR is small because the radar wave attenuation caused by rain introduces some error. Thus, the observational error variance of QR was set to 0.1QR (QR ≥ 1 g m−3) and 0.1 (QR < 1 g m−3).

3. Predicted LMC and environmental parameters

a. Process of LMC genesis

Figure 7 shows the generation process of the predicted LMC in 350m-EXP, where we regarded an LMC as having been generated when the maximum vertical vorticity at 0.8-km height, ξ0.8km, exceeded 0.03 s−1. At 1100 JST, the weak convective system that later spawned the LMC was already present (region C in Fig. 7a). This convective system was a “right-moving storm”: it moved to the right of the averaged horizontal wind at 0–6-km height, and a strong LMC was generated at its southern edge at about 1140 JST (Fig. 7b). The variable ξ0.8km reached a maximum at 1150 JST (Fig. 7c), and by this time, the region of large vertical vorticity reached from the surface to a height of over 6 km. The path of the LMC was several kilometers north of the actual path of the Tsukuba tornado and closer than the LMC path of Seko et al. (2015) (Figs. 7c and 8a). The LMC, which was accompanied by a hook-shaped rainwater distribution, started to dissipate after 1150 JST, and had disappeared by about 1210 JST (Fig. 7d).

Fig. 7.
Fig. 7.

The total of rain, snow, and graupel (color shading, g m−3) and horizontal winds (arrows, m s−1) at 0.8-km height at (a) 1100, (b) 1142, (c) 1150, and (d) 1206 JST in 350m-EXP (CTL). Red dots denote the location of maximum vertical vorticity [value given below (b)–(d)]. Black lines are as in Fig. 1. Region C denotes the position of the convective system.

Citation: Monthly Weather Review 144, 9; 10.1175/MWR-D-15-0365.1

Fig. 8.
Fig. 8.

The total of rain, snow, and graupel (color shading, g m−3) and horizontal winds (arrows, m s−1) at 0.8-km height when ξ0.8km reached a maximum in (a) the experimental design of Seko et al. (2015), (b) NSRF, (c) NRAD, (d) NQR, and (e) NSMT. (f) The term QR (g m−3) estimated from Z and KDP at 1.0° elevation at 1230 JST. In the gray area, 0 g m−3 rainwater was estimated.

Citation: Monthly Weather Review 144, 9; 10.1175/MWR-D-15-0365.1

Figure 9 shows the time series of ξ0.8km within the region 36.0°–36.4°N and 139.4°–140.2°E for the 33 members of 350m-EXP. Temporal fluctuations of ξ0.8km were so large that it was not appropriate to estimate the vortex strength from ξ0.8km at a particular time. If “strength of the LMC” is defined as the 20-min moving average of ξ0.8km around the time of the maximum ξ0.8km in each member (hereafter, ), then = 0.052 s−1 at 1150 JST for a member in which the mean of the LETKF analyses at 1100 JST is used for the initial conditions (red line in Fig. 9). The radius of the maximum horizontal wind and maximum vorticity of the predicted LMC at that time were O(1) km and O(10−2) s−1, respectively, which agree with those of the observed low-level vortex at about 1230 JST (Yamauchi et al. 2013). Note that no tornado vortices were predicted near the surface in this experiment because the horizontal grid interval of 350 m is too large to resolve tornadoes. The period with ξ0.8km > 0.04 s−1 (1142–1206 JST) was about 45 min before the Tsukuba tornado was observed (Japan Meteorological Agency 2012); this timing is similar to that of Seko et al. (2015).

Fig. 9.
Fig. 9.

Time series of maximum vertical vorticity (s−1) at 0.8-km height within the region of 36.0°–36.4°N and 139.4°–140.2°E in 350m-EXP (CTL) (red line, member with mean initial condition; blue line, member with maximum ; green line, member with minimum ).

Citation: Monthly Weather Review 144, 9; 10.1175/MWR-D-15-0365.1

A probability map that LMCs appear within 5 km from each point between 1100 and 1300 JST is shown in Fig. 10 based on the 33 members of 350m-EXP. In Fig. 10, the genesis points of the Tsukuba, Chikusei, and Moka tornadoes are located in areas with a probability of more than 50%, 10%, and 0%, respectively; this result confirms the potential of the warn-on-forecast approach for the tornadoes (Stensrud et al. 2009, 2013; Cintineo and Stensrud 2013) in this case, and it also suggests that the LMC generated at the southern edge of the storm was more easily predicted than the weak northern LMCs.

Fig. 10.
Fig. 10.

Probability map that high vertical vorticity (exceeding 0.03 s−1) at 0.8-km height appears within 5 km of each point, based on the 33 members of 350m-EXP (CTL) (%). Black lines denote the paths of Tsukuba, Chikusei, and Moka tornadoes in order from the south. The gray rectangle indicates the region where ξ0.8km was calculated (see Fig. 9).

Citation: Monthly Weather Review 144, 9; 10.1175/MWR-D-15-0365.1

b. Environmental parameters related to the LMC genesis

To clarify the cause of the LMC genesis, we focused on the inner-LETKF analysis at 1100 JST, which was used for the initial conditions of 350m-EXP. Figure 11a shows the distribution of the ensemble mean SREH at 0–3-km height at that time. SREH is a measure of the environmental vertical wind shear for the development of a right-moving storm, and large SREH suggests an increased threat of tornadoes with supercells. In this study, SREH was calculated for each member from a storm motion vector estimated on some assumptions: the speed of the storm was assumed to be 75% of the averaged horizontal wind velocity at 0–6-km height, and the storm was assumed to move at 30° to the right of this averaged wind (Maddox 1976). Because this storm motion vector was consistent with the motion of the simulated LMC (Figs. 7b–d), the distribution of SREH calculated with this storm motion vector is almost the same as that with the motion of the simulated LMC (not shown).

Fig. 11.
Fig. 11.

Horizontally smoothed (a),(c),(e) SREH (color shading, m2 s−2) and horizontal wind (arrows, m s−1), and (b),(d),(f) MLCAPE (color shading, J kg−1) and water vapor (contours, g kg−1) at 1100 JST in 350m-EXP: (a),(b) CTL; (c),(d) NSRF; and (e),(f) NRAD. Thick black lines in (a) and (b) indicate the path of the predicted LMC. Variables shown here have been averaged below the height of 1 km. Region C is as in Fig. 7. Regions H+, H, and E+ denote the positions of large SREH, small SREH, and large MLCAPE, respectively. Region e+ is explained in Fig. 12.

Citation: Monthly Weather Review 144, 9; 10.1175/MWR-D-15-0365.1

SREH was large, particularly in the area south of the convective system [region H+ (large SREH) in Fig. 11a]. This large-SREH region corresponds to the region of strong, low-level southerly wind (arrows in Fig. 11a). This large-SREH field, which is favorable for development of a right-moving storm (Rotunno and Klemp 1982), is consistent with the genesis point of the LMC.

Static stability is another important factor in LMC genesis. Figure 11b shows the distribution of the ensemble mean mixed-layer CAPE (MLCAPE) of the inner-LETKF analysis at 1100 JST. MLCAPE is the maximum energy available to a lifted air parcel, which is averaged in the lowest 100 hPa, and gives an estimate of the maximum vertical velocity once convection is initiated.

In the inner-LETKF analysis at 1100 JST, the ensemble mean MLCAPE was particularly large around the path of the predicted LMC [region E+ (large MLCAPE) in Fig. 11b]. This distribution is similar to that of the low-level water vapor (contours in Fig. 11b).

4. Impacts of assimilation of dense observations

Four additional experiments were performed to clarify the impacts of dense surface and radar data assimilation by inner LETKF on the genesis of the LMC: In the first experiment, surface horizontal winds, temperature, and relative humidity were not assimilated. In the second experiment, radar data (both radial velocity and rainwater) were not assimilated. In the third experiment, only rainwater data were not assimilated. In the fourth experiment, observations during 1100–1200 JST 6 May were not assimilated. These experiments are hereafter called “no surface data” (NSRF), “no radar data” (NRAD), “no QR” (NQR), and “no smoother” (NSMT), respectively. The experiment with all surface and radar data as described in section 3 is called “CTL.”

a. Impacts of assimilation of surface observations

In NSRF, in which no surface data were assimilated, an LMC still appeared at the southern edge of the storm in 350m-EXP (Fig. 8b), but the precipitation distribution in CTL (Fig. 7c) was more similar to QR at 1230 JST (Fig. 8f) than that in NSRF (Fig. 8b). The LMC generated in NSRF was shifted northward compared with that in CTL (Fig. 7c), and = 0.036 s−1 was weaker in NSRF than it was in CTL.

In the initial conditions of 350m-EXP (NSRF), SREH and low-level southerly wind velocity (Fig. 11c) were smaller than those in CTL in the area south of the convective system (region H+ in Fig. 11a). MLCAPE and low-level water vapor (Fig. 11d) were also smaller along the path of the predicted LMC (region E+ in Fig. 11b) than those in CTL. Therefore, the assimilation of surface observations contributes to an increase in the low-level southerly wind velocity in the area south of the convective system and to an increase in water vapor near the path of the predicted LMC. These increments of low-level southerly wind and water vapor improved the predictability of the LMC.

b. Impacts of the assimilation of radar observations

In 350m-EXP without radar data assimilation (NRAD), storms were not as well developed as in CTL (Fig. 7c) or observations (Fig. 8f), although a weak LMC was generated (Fig. 8c). The strength of the LMC ( = 0.025 s−1) was weaker in NRAD than it was in either CTL or NSRF.

In the initial conditions of 350m-EXP (NRAD), as in NSRF, SREH and low-level southerly wind velocity (Fig. 11e) were smaller than those in CTL in the area south of the convective system (region H+ in Fig. 11a). These differences in SREH and wind indicate that both radar and surface data assimilation contributes to the increase in the low-level southerly wind velocity in this region. The increase in the low-level southerly wind velocity in the area south of the convective system causes SREH to increase there and thus affects supercell development (cf. Schenkman et al. 2011b).

The distributions of MLCAPE and low-level water vapor (Fig. 11f) were mostly similar to those in CTL (Fig. 11b). This similarity shows that radar data assimilation hardly affects low-level water vapor and associated MLCAPE. However, MLCAPE and low-level water vapor in some regions, especially southwest of the precipitation system (region e+ in Fig. 11b), were smaller than those in CTL. These differences indicate that low-level water vapor is related to horizontal wind and rainwater, and that radar data assimilation in region e+ increased low-level water vapor there.

Low-level water vapor in places where rainwater was assimilated was greater in the inner-LETKF analysis (CTL) at 1100 JST than it was in NQR (not shown). This result suggests that rainwater assimilation affected the predicted precipitation distribution associated with low-level water vapor (Figs. 8d). However, the LMC predicted in 350m-EXP (NQR) was very similar to that predicted in CTL. These findings indicate that the impact of rainwater assimilation on development of the LMC was not large in this experimental design.

In NSMT, the generated LMC was weaker than that in CTL ( = 0.029 s−1; Figs. 7c and 8e). Therefore, the assimilation of observations during 1100–1200 JST with EnKS, including radar data on the forward side of the storm, importantly modified the variables at 1200 JST in a reliable manner.

5. Ensemble-based sensitivity analysis

In 350m-EXP (CTL), the predicted LMC was closer to the path of the Tsukuba tornado than the LMC predicted by Seko et al. (2015) or in NSRF, NRAD, and NSMT. The southward shift of the path of the LMC in CTL indicates that dense surface and radar data assimilation and other differences between CTL and the experiment of Seko et al. (2015), described in section 2, improved the LMC forecast. To clarify further the factors important in LMC genesis, we conducted an ESA.

The maximum and minimum “strengths” of the LMC among (j = 1, …, 33: indices of ensemble members) of the 350m-EXP ensemble (CTL), in which the 32 LETKF analyses and their ensemble mean were used as the initial conditions, were 0.107 s−1 (blue line in Fig. 9) and 0.036 s−1 (green line in Fig. 9), respectively. Therefore, we investigated the relationship between and environmental parameters simulated in the 350m-EXPs with an ESA.

a. Sensitivity analysis method

In the ESA, the sensitivity of to variable xij that characterizes the environment at each point i (i = 1, …, n) was calculated as
e8
(Ancell and Hakim 2007; Torn and Hakim 2008), where the overbar denotes the ensemble mean. This method gives quantitative information about the impacts of xij on . In this study, environmental parameters horizontally smoothed over 15.75 km × 15.75 km (45 × 45 grid points) were used as xij to discuss impacts of the mesoscale environment on the forecast of the strength of the LMC.

b. Sensitivities of the strength of the LMC to environmental parameters in the composite field

First, environmental parameters when was largest were composited relative to the LMC (the point of ) to clarify the no-time-lag relationship between and these parameters. Figures 12a and 12b show the ensemble means of SREH and MLCAPE, respectively, in the composite field around the LMC (region C). SREH was large in the area south of the LMC (region H+ in Fig. 12a) and small in the area north of the LMC (region H in Fig. 12a); this distribution indicates that the large SREH (the clockwise-turning vertical wind shear) south of the LMC was favorable for the development of a supercell. Similar to the distribution of SREH, the low-level southerly wind velocity was large (small) south (north) of the LMC. This wind distribution also indicates convergence of low-level horizontal winds at the position of the LMC (region C in Fig. 12a). Low-level water vapor and associated MLCAPE were large southeast of the LMC (region E+ in Fig. 12b). These large MLCAPE and water vapor values were caused by the low-level southerly winds, which had previously blown from Tokyo Bay to the Kanto Plain.

Fig. 12.
Fig. 12.

Ensemble mean of horizontally smoothed (a) SREH (color shading, m2 s−2) and horizontal winds (arrows, m s−1) and (b) MLCAPE (color shading, J kg−1) and water vapor (black contours, g kg−1), and sensitivities of (s−1) to (c) SREH [color shading, s−1 (102 m2 s−2)−1] and horizontal winds [arrows, s−1 (m s−1)−1] and (d) MLCAPE [color shading, s−1 (103 J kg−1)−1] and water vapor [black contours, s−1 (g kg−1)−1] in the composite field to the position of for 350m-EXP (CTL). Variables shown here have been averaged below a height of 1 km. Region C denotes the position of . Regions h+(−) and e+(−) denote the positions of positive (negative) sensitivities to SREH and MLCAPE, respectively. The other letters are as in Fig. 11.

Citation: Monthly Weather Review 144, 9; 10.1175/MWR-D-15-0365.1

The two-dimensional vectors in Fig. 12c show the sensitivity of the LMC strength to low-level zonal and meridional winds. The stronger the winds were in the direction of the two-dimensional vectors, the stronger the LMC was in the same direction. The vectors point toward the LMC, indicating that a strong low-level convergence was associated with a strong LMC. The distribution of the sensitivity to SREH, which was positive southeast of the LMC (region h+ in Fig. 12c) and negative northwest of the LMC (region h in Fig. 12c), was similar to that of the sensitivity to the low-level southerly wind.

Sensitivities to low-level water vapor and associated MLCAPE (Fig. 12d) were positive in almost the whole region around the LMC, except to its west (region e in Fig. 12d). These positive sensitivities were larger on the low-level windward side of the LMC (region e+ in Fig. 12d) than in the region where the ensemble means of MLCAPE and low-level water vapor were large (region E+ in Fig. 12b). West of the LMC, where the sensitivity to MLCAPE was negative (region e in Fig. 12d), low-level water vapor and associated MLCAPE were relatively small (Fig. 12b).

c. Sensitivities of the strength of the LMC to environmental parameters of the initial field

The sensitivities in the composite field described in the previous section resulted from the initial and boundary conditions. Clarification of the regions, in which the sensitivities of to the initial perturbations are large before the occurrence of the LMC, is important for forecasting the LMC. Figures 13a and 13b show the sensitivities to initial conditions (1100 JST), which were much larger from those to the composite field (Figs. 12c and 12d).

Fig. 13.
Fig. 13.

Sensitivities of (s−1) to (a) SREH [color shading, s−1 (102 m2 s−2)−1] and horizontal winds [arrows, s−1 (m s−1)−1] and (b) MLCAPE [color shading, s−1 (103 J kg−1)−1] water vapor [black contours, s−1 (g kg−1)−1] in the initial (1100 JST) field in 350m-EXP (CTL). The thick black line denotes the path of the predicted vortex. Letters are as in Figs. 11 and 12.

Citation: Monthly Weather Review 144, 9; 10.1175/MWR-D-15-0365.1

In the initial field, the sensitivity to SREH was positive on the southeastern (forward right) side of the storm, which corresponds to the area south of the path taken later by the generated LMC (region h+ in Fig. 13a). In contrast, the sensitivity to SREH was not large near the storm (region C in Figs. 13a and 13b), and it was negative on the northeastern (forward left) side of the storm (region h in Fig. 13a). The sensitivity to MLCAPE was positive in almost the whole area, and it was especially large on the southwestern (rear) side of the storm (region e+ in Fig. 13b).

Sensitivities to SREH and MLCAPE correspond to those to the low-level southerly wind and water vapor, respectively (Figs. 13a and 13b), in both the initial and composite fields. These distributions of sensitivities to wind and water vapor indicate that the LMC became strong when the initial low-level horizontal winds converged toward the forward side of the storm (between region h+ and h in Fig. 13a) and initial low-level water vapor was large to the rear of the storm (region e+ in Fig. 13b).

6. Discussion

The ensemble-based sensitivities of the strength of the predicted LMC to SREH and MLCAPE before the genesis of the LMC (Figs. 13a and 13b) were larger than those when the LMC was strongest (Figs. 12c and 12d). This result indicates that SREH and MLCAPE were highly correlated with the strength of the LMC even before LMC genesis, as well as when the LMC was strongest. These larger sensitivities before the LMC genesis can be explained by the increase with time of the spread of SREH or MLCAPE in the denominator of Eq. (8) without a noticeable increase in the covariance between the strength of the LMC and SREH and MLCAPE in the numerator of Eq. (8) in the ensemble forecasts.

In the studied case, the sensitivity to SREH and MLCAPE was large in the region where SREH and MLCAPE were relatively small in the initial field (region h+ in Fig. 13a and region e+ in Fig. 13b); this result suggests that areas with high SREH or high MLCAPE are not necessarily the most important for the strength of the LMC. Furthermore, the sensitivities to SREH and MLCAPE, as well as their distributions, were similar to the sensitivities to the low-level southerly wind and water vapor, respectively, both before and after LMC genesis (Figs. 12c, 12d, and 13); from this result, we inferred that large-scale, low-level southerly wind and water vapor played especially important roles in determining the strength of the LMC in this case.

The sensitivity to the low-level southerly wind before LMC genesis was positive on the forward right side in relation to the storm’s direction of movement (region h+ in Fig. 13a) and negative on the forward left side (region h in Fig. 13a). This sensitivity distribution shows that convergence of low-level meridional winds within the storm and high SREH on the forward right side relative to storm movement direction strengthened the predicted LMC. In a numerical model that assumes a horizontally uniform environment, an environment with veering shear (i.e., high SREH) is suitable for development of a right-moving supercell (Rotunno and Klemp 1982). Richardson et al. (2007) additionally showed in idealized numerical experiments that the meridional gradient of vertical shear can intensify the supercell. The present study showed that, when horizontal inhomogeneity exists in the real atmosphere, a large high-SREH region just on the forward right side of the storm (i.e., low-level southerly winds toward the storm's position at a later time) should contribute to the strengthening of the LMC. The negative sensitivity to SREH (region h in Fig. 13a) indicates that large SREH associated with strong southerly winds to the northeast of the LMC would weaken the LMC, because low-level convergence would be weak if southerly winds were strong northeast of the LMC.

The sensitivity to low-level water vapor both before and after LMC genesis was positive in almost the whole region and was particularly large to the rear of the storm (region e+ in Figs. 12d, 13b, and 14b). However, sensitivity to low-level potential temperature was negative there (Fig. 14a). When low-level water vapor and potential temperature of a parcel are larger and lower, respectively, relative humidity is higher, lifted condensation level and level of free convection are lower (Fig. 14c), and the parcel is more easily lifted despite negative buoyancy in the updraft area. Therefore, these sensitivities may indicate that tilting of baroclinically generated horizontal vorticity (Markowski et al. 2002, 2003, 2008; Straka et al. 2007) and stretching of vertical vorticity by the convection associated with large amounts of low-level water vapor behind the rear-flank gust front are important for LMC genesis. The negative sensitivity to low-level water vapor and the positive sensitivity to potential temperature in the region indicated by e in Figs. 12d and 14 were caused by low-level, dry and high potential temperature air that was advected from above by downdrafts in the precipitation area (Figs. 14b and 14c), which are more intense in the case of a relatively strong LMC. Although this positive sensitivity to potential temperature shows that cold pool in the RFD area tends to be weaker in the stronger LMC, the cold pool in the strongest LMC was not weakest (not shown). These results are consistent with the idealized experiments, which showed that a cold pool in the strong supercell is neither too strong nor too weak (Markowski and Richardson 2014).

Fig. 14.
Fig. 14.

Ensemble mean of horizontally smoothed (a) potential temperature (color, K) and horizontal wind relative to that of the center (arrows, m s−1); (b) water vapor (color, g kg−1), updraft (white contours, >0.2 m s−1), and downdraft (black contours, <−0.2 m s−1); and (c) level of free convection (color, km) and the total of rain, snow, and graupel (white contours, >0.2 g kg−1) in the composite field to the position of for 350m-EXP (CTL). Red and blue contours are sensitivities of to potential temperature (s−1 K−1), water vapor [s−1 (g kg−1)−1], and level of free convection (s−1 km−1). Variables shown here have been averaged below a height of 1 km. Letters are as in Fig. 12.

Citation: Monthly Weather Review 144, 9; 10.1175/MWR-D-15-0365.1

In the inner-LETKF analysis at 1100 JST 6 May, the low-level southerly wind velocity and associated SREH in CTL were larger (smaller) than those in NSRF or NRAD on the southern (northern) side of the storm [region H+ (H) in Fig. 11], and sensitivities to low-level southerly wind and SREH were positive (negative) there (Fig. 13a). Low-level water vapor and associated MLCAPE in the inner-LETKF analysis at that time in CTL were larger than those in NSRF in almost the entire calculation domain, and larger than those in NRAD just on the southwestern side of the storm (region e+ in Fig. 11). Sensitivities to low-level water vapor and MLCAPE were positive in almost the entire region and were especially large on the southwestern side of the storm (region e+ in Fig. 13b). These results show that the modifications of low-level southerly wind and water vapor by assimilation of dense surface and radar data contributed to the strengthening of the LMC that was generated later.

7. Summary and conclusions

The low-level mesocyclone (LMC) associated with the Tsukuba tornado was predicted in 350m-EXPs, where the initial conditions were obtained by assimilation of surface and radar data with local ensemble transform Kalman filter (LETKF). The surface data included zonal and meridional winds, temperature, and relative humidity at 20-m height transformed from the observations. The radar data were radial velocity from a polarimetric Doppler radar and three operational Doppler radars, and rainwater estimated from the reflectivity and specific differential phase of the former.

In the ensemble-based sensitivity analysis (ESA), sensitivities of the strength of the LMC to SREH and MLCAPE were similar to the sensitivities to low-level southerly winds and water vapor, respectively. The ways in which the LMC was intensified, as revealed by the ESA, are illustrated in Fig. 15. Before the generation of the LMC (Fig. 15a), large amounts of low-level water vapor and associated static instability on the rear side of the storm (region e+ in Fig. 15a) had a large effect on the storm’s development (region C in Fig. 15a). Meanwhile, strong low-level southerly winds and the associated veering shear on the forward right side relative to the storm motion (region h+ in Fig. 15a) created a favorable environment for the development of a supercell. Low-level convergence associated with weak southerly winds on the forward left side (region h in Fig. 15a) also contributed to the development of the supercell by strengthening the forward-flank gust front. After the formation of the LMC (Fig. 15b), low-level relative humidity to the rear of the storm also played an important role in strengthening the LMC (region e+ in Fig. 15b). Convergence of low-level winds to the rear of the storm (between regions h+ and h in Fig. 15b) was also important for development of the LMC.

Fig. 15.
Fig. 15.

Schematic illustrations of the development of the LMC on maps of water vapor (color shading, g kg−1) and horizontal winds averaged below 1-km height (arrows, m s−1) in (a) the initial (1100 JST) field and (b) the composite field (relative to the position of ) in 350m-EXP (CTL).

Citation: Monthly Weather Review 144, 9; 10.1175/MWR-D-15-0365.1

These sensitivities show that information of low-level convergence on the forward side of the storm and low-level relative humidity to the rear of the storm greatly improved the predictability of the LMC in this tornadic supercell event. In the present case, without assimilation of either surface or radar data, the LMC was not predicted near the path of the Tsukuba tornado, because these important low-level variables were not modified by assimilation. These results suggest that observations of the forward horizontal winds and the rear relative humidity of the storm in the lower layer make LMC forecasts better.

To our knowledge, this is the first study to have examined the sensitivities of a predicted LMC to physical variables in the real atmosphere by using realistic ensemble forecasts. This study confirmed that the factors suggested by previous studies and their horizontal distributions are important for the development of LMCs (e.g., Richardson et al. 2007; Schenkman et al. 2011b). Because this article describes a single case study, however, the sensitivities found may not necessarily be the same for all tornadic supercells. To obtain more conclusive results regarding the mechanism of LMC genesis, similar ESAs of multiple cases should be carried out.

As a next step, it is also desirable to perform ensemble experiments with higher resolution, because the tornado vortex was not resolved in the 350m-EXPs. The impact of cloud microphysics used in this study (Table 1) should also be clarified since the effectiveness of multimoment schemes has been pointed out (Dawson et al. 2010, 2015, 2016). Another problem to be considered is that, in the present study, dense observations affected only nearby points of observation because of the localization of the LETKF analysis. To use EnKF without localization, a larger number of members would be required (e.g., Kunii 2014). In ensemble forecasts with a small number of members, only the sensitivities of the “LMC strength” to variables near the LMC or windward of it are reliable. Therefore, it would be desirable to perform experiments with a larger number of members to improve the forecast and to calculate meaningful sensitivities of the strength of the generated LMC and tornado to environmental parameters.

Acknowledgments

The authors thank Dr. Kazuo Saito, Dr. Teruyuki Kato, and Dr. Wataru Mashiko for many important suggestions that improved this study and anonymous reviewers for thoughtful comments on the original manuscript. This work was supported in part by the research project “HPCI Strategic Program for Innovative Research (SPIRE) Field 3,” “social and scientific priority issues (Theme 4) to be tackled by using post K computer of the FLAGSHIP2020 Project,” “Tokyo Metropolitan Area Convection Study for Extreme Weather Resilient Cities (TOMACS),” a Grant-in-Aid for Scientific Research (A) 24244074, and the Cooperative Program (No. 131, 2014; No. 136, 2015; No. 138, 2016) of Atmosphere and Ocean Research Institute, The University of Tokyo. The outer and inner LETKFs were conducted using the Fujitsu PRIMEHPC FX10 System (Oakleaf-FX, Oakbridge-FX) at the Information Technology Center, The University of Tokyo, and the 350m-EXPs were conducted using the K computer at the RIKEN Advanced Institute for Computational Science through the HPCI System Research Project (Project ID: hp120282, hp130012, hp140220, hp150214, hp150289, hp160229). ESN data were from NTT DOCOMO, Inc., which is Japan’s mobile service provider.

APPENDIX

Quality Control of ESN Surface Data

In the present experiments, surface observation data from AMeDAS and ESN were transformed to data at 20-m height before they were assimilated. AMeDAS instruments are located at about 10-m height, which is high enough for them to be applied in Eq. (1) for transformation to 20-m height. However, some ESN instruments are located at a height of just a few meters, which is too low for the data to be transformed to data at 20-m height. In addition, some ESN stations are located in an environment that is not suitable for surface observations. Therefore, we controlled the quality of ESN surface data for reliable assimilation results.

To evaluate the ESN data, surface zonal and meridional winds and temperature of the JMA hourly analysis (Muroi et al. 2008) were first interpolated to the horizontal positions of the ESN instruments. Because the heights of the interpolated winds (uA and υA) and temperature (TA) were 10 and 1.5 m, respectively, the ESN data (uobs, υobs, Tobs) were transformed to data at heights of 10, 10, and 1.5 m for comparison with (uA, υA, TA), respectively. The differences between the transformed ESN data and (uA, υA, TA) are given as
ea1
and
ea2
In this study, u20 and υ20 were not assimilated at points where the bias of δu or δυ was more than 2.0 m s−1 or the RMS of δu or δυ was more than 1.5 m s−1. Similarly, T20 was not assimilated at points where the bias or RMS of δT was more than 1.0 K. These thresholds are the same as those used by Nishi et al. (2015). Biases and RMSs were calculated from hourly surface data for 29 April–13 May 2012 and 26 August–9 September 2013; both of these periods include the time when tornadoes were generated on the Kanto Plain.

Relative humidity data from ESN were not evaluated in this study because the horizontal interval between JMA meteorological observatories where relative humidity is observed is too coarse (50–100 km) to be used as a reference for the ESN data. In the present study, relative humidity was assimilated only at points where temperature data were used, because ESN hygrometers are located at the same locations as ESN thermometers.

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