Since lightning quantity is not a regular variable in most numerical weather prediction models, lightning observations cannot be directly used for model initialization. It is necessary to convert lightning data to model variables or other related diagnostic variables by using empirical or semi-empirical relations before the LDA. The relationship among the lightning flash rate, water vapor, and graupel mixing ratio established by Fierro et al. (2012) has been utilized in many convective events studies and shown promising results (Fierro et al., 2014, 2015; Lynn et al., 2015; Lynn, 2017; Zhang et al., 2017); however, the adjustment magnitude of humidity in this relationship depends heavily on the lightning flash rate. Considering the relatively low lightning detection efficiency of WWLLN (about 10%), the flash rate is less reliable or insignificant in providing information about the strength of convection. Therefore, a simplified method with the adjustment of humidity independent of the lightning flash rate, which was developed by Dixon et al. (2016), was used in this study. For the grids where lightning occurred, the relative humidity (RH) values at all levels in the troposphere (levels where atmospheric pressure exceeded 200 hPa) were adjusted to 90% if the simulated RH values were below 85%. This method does not restrict the adjustment of humidity to any specific vertical layer of the troposphere; rather, it enhances both the surface-based and elevated convection by adjusting RH at all vertical levels within the troposphere.
The basic rationale of this method is based on the concept that lightning can be used to indicate deep moist convection. When lightning occurs, if the necessary RH condition of deep moist convection (in this study, RH ≥ 85%) in the troposphere is not satisfied, the RH value is adjusted to 90%, ensuring that the RH value at positions where the lightning happens is no less than 90%. The increased RH will stimulate the processes of condensation and freezing, thus increasing the release of latent heat and accelerating the cloud updraft, and eventually lead to the production of convection in areas where lightning occurs.
As mentioned above, the detection efficiency of WWLLN is relatively low. WWLLN mainly detects strong lightning pulses, and hence some weak lightning will inevitably be missed. Additionally, there are location errors (< 10 km) for lightning positions detected by WWLLN. Therefore, the strategy of artificially increasing the radius of lightning influence used by Dixon et al. (2016) was adopted. For each 3 km × 3 km grid (as described in the next section, LDA was performed on the 3-km resolution innermost domain), if there was lightning observed within 1 h prior to the assimilation time in the circular region with a radius of 5 km from the typhoon center, it was assumed that lightning occurred in this grid. As shown in Fig. 3, for the blue 3 km × 3 km grid, if there is lightning within the circular region with a 5-km radius, i.e., the green shaded circle with a blue outline, it is considered that there is lightning in the blue grid. Similarly, for the red grid, if there is lightning within the circular region with a 5-km radius, i.e., the green shaded circle with a red outline, it is considered that there is lightning in the red grid.
Figure 3. A schematic showing how to determine if there is lightning within each grid of 3 km × 3 km.
A flowchart illustrating the LDA process is shown in Fig. 4. First, we checked if lightning was observed within the model grid 1 h prior to the LDA time. If there was lightning within a model grid, the RH value at levels of the troposphere in this grid column was checked. If the RH value was below 85%, it was adjusted to 90%; otherwise, it was simply skipped. After this step was completed for all the grids, the adjusted RH was output together with the model temperature and pressure as a pseudo sounding observation in LITTLE_R format [an American Standard Code for Information Interchange (ASCII)-based standard format required by WRF Data Assimilation (WRFDA)], which was then processed through the observation preprocessor (OBSPROC) module provided in WRFDA to prepare a suitable observation file (ob.ascii) for the WRF’s three-dimensional variational (3DVAR) framework, and finally assimilated in the WRFDA-3DVAR system.
The numerical model used in this study was the three-dimensional compressible nonhydrostatic WRF model with the Advanced Research dynamic solver (WRF-ARW version 3.5.1). Simulations were conducted in three nested domains with horizontal resolutions of 27, 9, and 3 km, respectively. The parent domain (the outermost domain) remained fixed during the whole simulation period, whereas the inner two domains were automatically moved by using WRF’s vortex-following algorithm, which updated positions of the inner two domains every 15 minutes so that they moved with and remained centered on the storm’s center. The initial and boundary conditions were provided by the NCEP Final (FNL) analysis dataset, with 1° × 1° spatial and 6-h temporal resolutions. All simulations were run with 30 vertical levels, with a 50-hPa model top. More details about the model configuration can be found in Table 1.
Parameter Domain 1 Domain 2 Domain 3 Grid points 211 × 124 271 × 211 241 × 241 Horizontal grid distance (km) 27 9 3 Time step (s) 60 20 6.67 Microphysics scheme WSM6 WSM6 WSM6 Cumulus scheme Kain–Fritsch Kain–Fritsch No Shortwave radiation scheme Dudhia Dudhia Dudhia Longwave radiation scheme RRTM RRTM RRTM Boundary layer scheme YSU YSU YSU Surface layer scheme Monin–Obukhov Monin–Obukhov Monin–Obukhov Note: WRF single-moment 6-class—WSM6, Rapid Radiative Transfer Model—RRTM, Yonsei University—YSU.
Table 1. Model configuration
To examine the impact of LDA on the subsequent prediction of typhoon intensity, three LDA experiments that started at different moments were conducted: LDA_0406 started at 0600 UTC 4 November, LDA_0518 at 1800 UTC 5 November, and LDA_0606 at 0600 UTC 6 November. For comparison, a control experiment with-out assimilation of any observational data was conducted for each LDA experiment: CTL_0406 started at 0600 UTC 4 November, CTL_0518 at 1800 UTC 5 November, and CTL_0606 at 0600 UTC 6 November. For all the LDA experiments, the lightning data were assimilated only in the innermost domain for LDA experiments, by using the default NCEP global background error covariance (the “CV3” option in WRFDA), which was estimated from a year of differences in 24- and 48-h Global Forecast System (GFS) forecasts valid at the same time and was applicable for any regional domain (Barker et al., 2004). Also, the observation error used in this study was from the default error file “obserr.txt” provided in WRFDA, in which the RH observation error is 10% (tests with the RH observation error of 15% were also conducted, and the results were generally consistent to those with 10%; figure omitted). The results presented in the following sections are from the innermost domain of the simulations.
To investigate the impact of spatial range of lightning data on the LDA results, experiment LDA_0606 was further divided into three: LDA_0606_All, which assimilated all the typhoon lightning; LDA_0606_Innercore, which assimilated only the inner-core lightning; and LDA_0606_Rainband, which assimilated only the rainband lightning. Whereas, sensitivity experiments that assimilated lightning data in different spatial ranges were not conducted for experiments LDA_0406 and LDA_0518, since the lightning data in experiment LDA_0406 were all rainband lightning and those in experiment LDA_0518 were nearly all inner-core lightning. The lightning data assimilated in LDA experiments were those that occurred within the previous one hour. In order to investigate the impact of number of LDA cycles on the subsequent forecast, four consecutive cycles at the 1-h interval were performed for each LDA experiment, and the forecasts produced by using the analysis based on different LDA cycles as the initial field were compared.