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The numerical simulations of SB convection presented in this paper were performed using the Advanced Research WRF (WRF-ARW) model (version 3.7.1, Skamarock et al., 2008). A four-level, one-way nested domain configuration centered over the Florida peninsula is employed for the simulation. The outermost, two middle, and innermost horizontal domain grids consist of grid spacings of 27 km (d01), 9 km (d02), 3 km (d03), and 1 km (d04), respectively (not shown). Note that the spatial resolutions of d03 and d04 are both at the gray-zone scale. The outermost domain (d01) and d02 were chosen to cover the southeastern US and the surrounding Atlantic Ocean in order to capture dynamics that might influence the SB and convection. The innermost domain covers the Florida peninsula and its surrounding local waters (see areas covered by d03 and d04 in Figs. 3a and 3b).
Figure 3. Terrain heights and water body locations for (a) d03 and (b) d04. Red lines indicate the locations of the vertical cross sections cut west-to-east through MacDill, Air Force Base (MCF, northernmost) and Lake Okeechobee (OBE, southernmost). The colored boxes indicate locations used later in the study for a zoomed-in analysis. The locations of the 23 observing stations used to aid in the verification of the WRF simulation are also plotted. Note the increased number of lakes in (b) compared to (a). Water body names and locations are annotated in panel (c). The left corner inset of panel (c) is a zoomed-in area over Tampa Bay. (d) Locations of WRF model domains for all four-level nested domains.
All four domains contain 62 vertical eta levels with 26 levels in the lower atmospheric region (below 850 hPa). The model top is set at 5 hPa. The physics options used in this study include the Unified Noah land surface model (LSM, Chen and Dudhia, 2001), Mellor-Yamada-Janjić (MYJ, Mellor and Yamada, 1974) PBL, New Thompson microphysics (Thompson et al., 2008), New Kain-Fritsch (KF, Kain, 2004) cumulus (d01 and d02 only), MM5 Dudhia shortwave radiation (Dudhia, 1989), and Rapid Radiative Transfer Model (RRTM) longwave radiation (Iacono et al., 2008). Table 1 gives a full list of the configurations used for each of the four domains. Different configurations of physical parameterization impact the onset, intensity, and merging of the SBFs. The selection of the physical parameterization options was based on sensitivity experiments with various physical schemes in the early phase of this study (not shown).
Parameter d01 d02 d03 d04 Physical domain 139 × 97 (lon. × lat.) 253 × 202 (lon. × lat.) 343 × 313 (lon. × lat.) 502 × 661 (lon. × lat.) Horizontal resolution 27 km 9 km 3 km 1 km Vertical resolution 62 levels with variable Δz (26 levels below 850 hPa): model top 50 hPa* Time integration 120-sec time step; 36-h duration* Boundary conditions Damping depth over top 500 m* Lateral boundary 21 600-sec time interval* Surface layer physics Monin-Obukhov Janjić Eta (MO-JE)* Microphysics New Thompson* Longwave radiation Rapid Radiative Transfer Model (RRTM)* Shortwave radiation MM5 (Dudhia)* PBL physics Mellor-Yamada-Janjić (MYJ)* Land-surface physics Noah land surface model (LSM)* Cumulus physics New Kain-Fritsch New Kain-Fritsch None None Vertical Diffusion 2nd order diffusion* Time-integration Runge-Kutta 3rd order* Eddy coefficient Horizontal Smagorinsky 1st order closure* *Values are the same for all four grids. Table 1. WRF model parameter settings for domains d01, d02, d03, and d04.
The model initial and boundary conditions are provided by the NCEP North American Mesoscale (NAM) Forecast System analysis at 12-km grid spacing from 0000 UTC 6 September 2012 to 1200 UTC 7 September 2012 at six-hour intervals. After initialization, the model was integrated into a one-way nested mode for 36 hours until 1200 UTC 7 September 2012. The simulated SB events are verified using surface parameters obtained from local aviation routine weather reports (METARs) and aviation special weather reports (SPECIs) from 23 locations across the peninsula. A detailed comparison of the simulated results is made with NCEP’s Stage IV precipitation analysis (Lin and Mitchell, 2005) and the Climatology-Calibrated Precipitation Analysis (CCPA) (Hou et al., 2014). Furthermore, NCEP’s 32-km horizontal grid spacing/45-level vertical resolution North American Regional Reanalysis (NARR; Mesinger et al., 2006) is also used to verify the WRF simulation output.
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The SB and its associated convection were examined on a five-minute basis for the WRF simulation. As both the d03 and d04 grid scales were very similar in their ability (spatially and temporally) to resolve the SB, only the results from d03 are shown in this section. It is noteworthy that the higher resolution of d04 did allow the SBF to more closely follow the coastline shape upon initiation and produced a more intense and narrower SBF, which will be discussed in later sections.
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Figure 4 shows the initiation and evolution of the WRF-simulated ECSB and WCSB as seen by the zonal surface winds and total wind vectors. Specifically, the WRF-simulated SB is initiated between 1405 and 1435 UTC 6 September 2012 on both sides of the peninsula (Figs. 4a and 4b), as seen in the turning of the coastal winds, which is in line with the SB initiation time in the surface observations and NARR data. By 1500 UTC, both SBs are well established (Fig. 4c) and continue to strengthen and propagate through the afternoon. Due to the opposing low-level synoptic flow, the ECSB is quite discernible in the simulation, while the WCSB that is parallel to the synoptic flow becomes much harder to discern in the analysis (Fig. 4d). Simulated surface temperature also indicates that coastal areas are warmer than the nearby ocean before the SB, which leads to surface pressure decreases over land and then the land breeze turning into an SB (not shown).
Figure 4. WRF-simulated zonal (u-component) winds (color: red easterly, blue westerly; units: m s–1) and total wind (black arrows; unit reference vector 2.5 m s–1) at surface level for a zoomed-in region of d03 (yellow box in Fig. 3a) at: (a) 1300 UTC, (b) 1400 UTC, (c) 1500 UTC, and (d) 1600 UTC 6 September 2012.
Figure 5 shows a temporal evolution of the zonal wind cross sections, indicating the inland progression and height of the ECSB and WCSB during the afternoon. Initially, the simulated WCSB extends higher (700 m) than the ECSB (400 m, Fig. 5a). However, by 1700 UTC 6 September 2012, the ECSB has reached 700 m at its frontal head, while the WCSB extends 900 m (Fig. 5b). The two SBFs reach a maximum height of around 1 km by 1930 UTC (Fig. 5c). The two SBs gradually approach each other (Fig. 5d) and eventually meet inland of the eastern coast of Florida at 2120 UTC 6 September 2012, which is 50 minutes after the SB frontal merger in surface observations.
Figure 5. Cross section (through northernmost red line in Fig. 3a) of d03 WRF-simulated zonal (u-component) winds (color: red easterly, blue westerly; units: m s–1) and total horizontal wind (black arrows represent horizontal winds at each height level along longitude, reference vector 10 m s–1; upward arrows mean north direction) at: (a) 1600 UTC, (b) 1700 UTC, (c) 1930 UTC, and (d) 2030 UTC 6 September 2012. Red contour lines indicate the zero-wind contour heights, which are indicative of approximate SBF heights.
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Figures 6a and 6b compare the WRF-simulated accumulated precipitation to CCPA data from 1200 UTC 6 September 2012 to 0600 UTC 7 September 2012 (18-h accumulated precipitation in total) for domains d03 and d04. Both of the WRF simulation domains and the CCPA analysis observe relatively sparse areal coverage of rainfall along the west coast and in northern Florida, while distinct patterns of rainfall are observed along the east coast and in central Florida. In addition, an obvious lack of rainfall occurs northeast of Lake Okeechobee in both the CCPA analysis and the WRF simulations, although the “rain shadow” is more pronounced in d03 (Fig. 6a) than in d04. Meanwhile, light rainfall occurs across the north-central and northeast portions of the Florida peninsula in the d04 simulation (Fig. 6b), while the d03 grid scale shows almost no precipitation in those areas (Fig. 6a).
Figure 6. 18-h rainfall accumulation totals from 1200 UTC 6 September 2012 to 0600 UTC 7 September 2012 for (a) d03 WRF-simulated precipitation accumulation totals (blue contours; units: mm) and CCPA data (color; units: mm). Panel (b) is the same as (a) but for d04. WRF-simulated precipitation accumulation totals (color; units: mm) for (c) d03 and (d) d04 for the same times as (a) and (b).
Figure 7 further compares the hourly WRF precipitation accumulations for d03 and d04 with hourly Stage IV data. Simulated timing of the initial convection along the west coast of Florida at 1400 UTC 6 September 2012 for an inland location just northeast of Waccasassa Bay (see Fig. 3c for the location of the bay) in d03 and d04 (Figs. 7a and 7b) is concurrent with observations; however, d03 fails to resolve the convection produced east of Waccasassa Bay, contrary to the Stage IV analysis. In contrast, the higher resolution d04 is able to capture the convection east of Waccasassa Bay (Fig. 7b) but also overestimates the WCSB convection just north of Naples (APF in Figs. 3a and 3b). At this time, there are also small convective cells not associated with the SBF in the central portion of the peninsula in d04 (Fig. 7d) that are not present in d03 (Fig. 7c). By 1800 UTC 6 September 2012, d04 resolves the convection along the east coast of Florida, while d03 has only a small convective cell in the southeast corner of the peninsula associated with the ECSB (Figs. 7c and 7d). It is not until 1900 UTC 6 September 2012 that d03 begins to resolve significant convection along the ECSB.
Figure 7. Stage IV precipitation accumulation (color; units: mm) and d03 (left column) and d04 (right column) WRF-simulated precipitation accumulation (black contours; units: mm) at: (a–b) 1400 UTC, (c–d) 1800 UTC, (e–f) 2100 UTC, and (g–h) 2300 UTC 6 September 2012. The red arrows in (e) and (f) indicate squall lines.
The WRF-simulated SBFs collide and merge at 2030 UTC 6 September 2012 and produce an enhanced convective squall line that is clearly visible at 2100 UTC 6 September 2012, which is markedly similar to the Stage IV analysis convective pattern (Figs. 7e and 7f). However, from 2230 UTC 6 September 2012 until 0200 UTC 7 September 2012, the orientation of the convection in the d03 WRF simulation becomes north-to-south, while the Stage IV analysis data clearly show the convective line in southern Florida maintaining a northeast-to-southwest orientation (Fig. 7g). The convection produced in d04 better captures this northeast-to-southwest convective orientation (Fig. 7h). Finally, the duration of the convection across the Florida peninsula in the d03 simulation lasts until 0530 UTC 7 September 2012, rather than 0500 UTC 7 September 2012 as seen in Stage IV and CCPA analyses, or 0400 UTC as seen in the d04 simulation (not shown). A comparison of 18-h accumulated precipitation (1200 UTC 6 September 2012 to 0600 UTC 7 September 2012) between the d03 and d04 WRF simulations (Figs. 6c and 6d) and the CCPA analysis (Figs. 6a and 6b) shows that despite good spatial coverage of the WRF-simulated convective precipitation, the maximum precipitation accumulations produced by the WRF simulation cover much smaller spatial areas than what is observed in the CCPA analysis.
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To further examine the intensity differences between the two spatial resolutions at the gray-zone scale, a quantitative precipitation forecasting (QPF) analysis was conducted using the Equitable Threat Score (ETS), also known as the Critical Success Index (CSI), and Bias Score (BS) calculations. The values used to calculate these scores are given in a 2 × 2 contingency table (Table 2). Four specific precipitation thresholds are used in the QPF statistics calculations: 2.54 mm, 6.35 mm, 12.7 mm, and 25.4 mm. Knowing information about the forecast area (F), observed area (O), and the correctly forecasted “hits” (H), the CSI seeks to answer the question of how well the forecasted “hits” correspond to the observed “hits”. The BS seeks to answer the question of how similar the frequencies of forecasted and observed “hits” are. The BS is mathematically defined as:
Forecast Observed Yes No Sum Yes Hits (H) False alarms All forecasted (F) No Misses Correct rejections No forecasted
(N−F)Sum All observed (O) No observed
(N−O)Total (N) Table 2. Contingency table illustrating the counts used in verification statistics of dichotomous (e.g., Yes/No) forecasts and observations.
The ETS score can be obtained using the following equation:
For a given threshold, A represents the number of grid points that exceed the threshold in both the model forecast and the CCPA data; B denotes the number of grid points that exceed the threshold in the model forecast, but not in the CCPA data; and C is the number of grid points that do not reach the threshold in the model forecast, but that exceed the threshold in the CCPA analysis.
ETS values range from 0 to 1, with 0 indicating no skill in the forecast. BS values range from 0 to infinity, with a bias of less than 1 indicating a tendency to underforecast, while a bias greater than 1 indicates a tendency to overforecast in the forecast system. The ETS and BS values for the d03 and d04 simulation results are given in Table 3. As seen by the relatively low ETS values in both domains for all four precipitation thresholds, the simulations are relatively poor at forecasting the correct intensities for the SB event, and the BS shows that the simulations underforecast the precipitation intensity events. d04 performs slightly better than d03 at nearly all precipitation thresholds.
Precipitation
Threshold (mm)Domain d03 d04 Equitable Threat Score (ETS) 2.54 0.12 0.28 6.35 0.1 0.19 12.7 0.08 0.15 25.4 0 0.04 Bias Score (BS) 2.54 0.12 0.26 6.35 0.11 0.2 12.7 0.12 0.17 25.4 0.14 0.23 Table 3. Equitable Threat and Bias Score values for four rainfall thresholds over an 18-h forecast period (1200 UTC 6 September 2012 to 0600 UTC 7 September 2012).
Thus, it is evident that the WRF simulation is able to capture the overall spatial locations and timing of the convective mesoscale systems (MCSs) that occurred during the 6–7 September 2012 SB event reasonably well. However, the intensities of the WRF-simulated convective precipitation are overall much weaker as compared to the CCPA and Stage IV analyses in subjective and QPF evaluations. It is also found that increasing spatial resolution at the gray-zone scale has impacts on convection activities: namely, increasing the spatial resolution at the gray-zone scale can reasonably reproduce and capture the timing of the CI, as well as the orientation of the convection after the SBF merger into the squall line over the peninsula, although it degrades the simulation of the size and organization of convective cells.
The spatial resolution of the gray-zone scale commonly ranges from 1 km to 5 km; therefore, different spatial resolutions mean different geophysical features, which in turn affect atmospheric features. In order to further understand the geophysical features at different spatial resolutions and their impacts on the simulation of spatial, timing, and intensity of MCSs and precipitation, additional analysis of the atmospheric and convective features resolved at these two grid scales (d03 and d04 domains) is performed in the next section.
Parameter | d01 | d02 | d03 | d04 |
Physical domain | 139 × 97 (lon. × lat.) | 253 × 202 (lon. × lat.) | 343 × 313 (lon. × lat.) | 502 × 661 (lon. × lat.) |
Horizontal resolution | 27 km | 9 km | 3 km | 1 km |
Vertical resolution | 62 levels with variable Δz (26 levels below 850 hPa): model top 50 hPa* | |||
Time integration | 120-sec time step; 36-h duration* | |||
Boundary conditions | Damping depth over top 500 m* | |||
Lateral boundary | 21 600-sec time interval* | |||
Surface layer physics | Monin-Obukhov Janjić Eta (MO-JE)* | |||
Microphysics | New Thompson* | |||
Longwave radiation | Rapid Radiative Transfer Model (RRTM)* | |||
Shortwave radiation | MM5 (Dudhia)* | |||
PBL physics | Mellor-Yamada-Janjić (MYJ)* | |||
Land-surface physics | Noah land surface model (LSM)* | |||
Cumulus physics | New Kain-Fritsch | New Kain-Fritsch | None | None |
Vertical Diffusion | 2nd order diffusion* | |||
Time-integration | Runge-Kutta 3rd order* | |||
Eddy coefficient | Horizontal Smagorinsky 1st order closure* | |||
*Values are the same for all four grids. |