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The model used in this study is WRF, version 3.9.1.1 (Skamarock et al., 2008). All domains used one-way nesting without feedback and the same vertical discretization of 51 levels, including 11 layers within the boundary layer (below 1500 m). The model was driven by the NCEP FNL Operational Global Analysis Data (1° × 1° grid) as initial and boundary conditions for the outer domains. The 30-arc-second USGS terrain data and 21-category, 2-m resolution MODIS land use/cover data were prescribed for static surface conditions. The model physics included the Kain−Fritsch (KF) cumulus scheme for the outer grids, the Morrison microphysics scheme (Morrison et al., 2009), the Noah Land Surface Model (Tewari et at., 2004), and the RRTMG longwave and shortwave radiation scheme (Iacono et al., 2008).
Liang et al. (2019) put forward a pragmatic and effective approach in precipitation forecasting to avoid the challenge in representing convection across the gray zone. The convective gray zone refers to the model grid spacing around 1−10 km, where parameterized and resolved convective clouds could exist simultaneously. In the gray zone, many widely used cumulus parameterization assumptions become invalid and it is difficult to realistically represent the convection (Yano et al., 2010). Liang et al. (2019) found that double-nesting simulations using the WRF model with a large grid ratio (15:1 or 9:1) outperformed the traditional triple nesting with a middle (3- or 5-km) grid in forecasting the extreme rainfall of Jiangsu province. In particular, the outer grid using the KF scheme (Kain, 2004) to parameterize cumuli at 15 km with explicitly resolving convection at 1 km produced the best forecast of hourly rainfall variation. Therefore, we followed the same double-nesting experiments using the KF cumulus scheme in the outer coarse (15- and 9-km) grids and explicitly resolving convection at the inner 1-km grid. Our focus, however, is to examine the PBL effects on the prediction of extreme rainfall.
Three PBL schemes were used and the related diffusion equations and eddy diffusivity coefficient computations are listed in Table 1. These schemes are all based on the K-gradient transport theory, which determines the turbulent flux by multiplying the eddy moment or heat diffusivity coefficient with the vertical gradient of grid-mean variables. Their main differences are the closure assumptions used to define the eddy diffusivity coefficient and the non-local effect for the energy exchange between model layers. The YSU scheme is a first-order closure scheme that determines the K-profile in the mixed layer by introducing the PBL height [Eq. (3)] but depends on the mixing length and Richardson number above the entrainment zone [Eqs. (1) and (2)]. A counter gradient transport term [Eq. (7)] related to surface buoyancy flux is included for the nonlocal effect, especially for unstable boundary layers (Hong et al., 2006). As higher-order schemes, both MYNN (which hereafter refers to MYNN 2.5 in WRFv3.9.1.1) and MYJ (Janjić, 1994) are based on TKE closure to parameterize the eddy diffusivity but without considering the nonlocal effect in the unstable layer. They differ in the diagnostic equations for dimensionless stability function (S) and turbulent length scale (
$ l $ ). The MYJ (Janjić, 1994) scheme represents a non-singular implementation of the Mellor−Yamada level-2.5 turbulence closure model by adding limitation to the turbulent length scale. The MYNN scheme was considered to better represent the mixing in the convective boundary layer than MYJ because it considers the buoyancy effect on the stability function and turbulent length scale (Srinivas et al., 2018). In WRFv3.9.1.1, the MYNN scheme includes several options to improve the coupling of the PBL scheme with radiation (icloud_bl=1) and microphysics (bl_mynn_cloudmix=1), and two options (bl_mynn_edmf=1, bl_mynn_mixlength=2) to use the cloud-specific and scale-aware mixing length following Ito et al. (2015). As suggested by the WRF physics documentation (Wang and Bruyere, 2017), the YSU scheme adopts the MM5 (Jiménez et al., 2012) surface layer scheme, and the MYJ and MYNN2.5 schemes both use the Monin−Obukhov (Monin and Obukhov, 1954) surface layer scheme.PBL parameterization schemes YSU MYNN MYJ Reference(s) Hong et al. (2006) Mellor and Yamada (1982);
Nakanishi and Niino (2004);
Olson et al. (2019)Janjić, 1994 Eddy diffusivity coefficient ${K}_{{\rm{m}},t\_\mathrm{l}\mathrm{o}\mathrm{c} }={l}^{2}{f}_{{\rm{m}},t}\left(\mathrm{R}\mathrm{i}\mathrm{g}\right)\left(\dfrac{\partial U}{\partial \mathrm{z} }\right)$ (1)
$\mathrm{R}\mathrm{i}\mathrm{g}=\dfrac{\mathrm{g}\left[\theta-\theta_{\mathrm{s} }\right]\left(h-{Z}_{\mathrm{m}\mathrm{i}\mathrm{x} }\right)}{\theta {\left[U\left(h\right)-U\left({Z}_{\mathrm{m}\mathrm{i}\mathrm{x} }\right)\right]}^{2} }$ (2)
${K}_{{\rm{m}}}=k{w}_{s}z{\left(1-\dfrac{z}{h}\right)}^{P}$ (3)
${K}_{{\rm{h,m}}}=lq{S}_{{\rm{h,m}}}$ (4) $ K=Slq $ (5) Diffusion equation $ \dfrac{\partial C}{\partial t}=\dfrac{\partial }{\partial \mathrm{z}}\left[{K}_{c}\left(\dfrac{\partial C}{\partial z}-{\gamma }_{c}\right)-{\left(\overline{{w}'{c}'}\right)}_{h}{\left(\dfrac{z}{h}\right)}^{3}\right] $ (6)
${\gamma }_{c}= {b}\dfrac{ {\left(\overline{ {w}'{c}'}\right)}_{0} }{ {w}_{s}h}$ (7)$ \dfrac{\left(\dfrac{{q}^{2}}{2}\right)}{\partial t}=\dfrac{\partial }{\partial z}\left[lqS\dfrac{\partial \left(\dfrac{{q}^{2}}{2}\right)}{\partial z}\right]+{P}_{\mathrm{s}}+{P}_{\mathrm{b}}+D $ (8) Description of variables ${K}_{{\rm{m}},t\_\mathrm{l}\mathrm{o}\mathrm{c} }$ denotes the diffusivity coefficient used above the entrainment zone;
${K}_{{\rm{m}}}$ denotes the momentum eddy diffusivity in the mixed-layer;
Kc denotes the eddy diffusivity;
Z is the height from the surface and h is the height of the PBL;
C denotes the prognostic variables for wind fields (u, v, w), water vapor (q) and potential temperature ($ \theta $);
$ {w}'{c}' $ denotes the flux for prognostic variables (u, v, q, $ \theta $);
b is a constant of proportionality;
${\gamma }_{{\rm{c}}}$ is a local gradient correction item.${S}_{{\rm{h,m}}}$ is a dimensionless stability item that is a function of the Richardson number (Rig);
${K}_{{\rm{h,m}}}$ denotes the heat, water vapor and momentum eddy diffusivity;
$ l $ denotes the turbulent length;
${ {q}^{2} }/{2}$ denotes the TKE;
Ps denotes the TKE induced by wind shear;
Pb denotes the TKE induced by buoyancy;
D denotes the dissipation of TKE.$ S $ is a dimensionless stability item that is a function of the Richardson number (Rig);
K denotes the eddy diffusivity.Table 1. Diffusion equations and vertical diffusivity coefficient computations for the three PBL parameterization schemes used in the model experiments.
Table 2 summarizes the configurations for two groups of double-nesting simulations. The mesoscale grids (15 and 9 km) used KF-parameterized convection, while the 1-km grid used fully explicit convection (EC). All experiments were initialized at 0800 LST 24 May 2018, and integrated for 48 h up to 0800 LST 26 May 2018. For convenience, D1 and D2 are denoted as the outer and inner domains, respectively. Nesting grid configurations are denoted directly by the grid spacing in km in sequential order. For example, 15-1 km denotes a double nesting configuration between D1 at 15 km and D2 at 1 km. The model results were bilinearly interpolated to the AWS stations to facilitate the comparison.
Outer domain [D1] Inner domain [D2] 15 km 9 km 15-1 km 9-1 km CUP KF KF EC EC PBL YSU/MYJ/MYNN YSU/MYJ/MYNN YSU/MYJ/MYNN YSU/MYJ/MYNN Grid cells 407 × 297 677 × 494 1156 × 1141 1153 × 1135 Table 2. Two groups of model experiments using different configurations of grid nesting and PBL parameterization schemes as well as convection treatments. 15-1 km and 9-1 km denote the experiments in 1-km grid nested with the 15 km- and 9 km-grid, respectively.
The evaluation methods include pattern correlations (COR; Barnston, 1992), root-mean-square errors (RMSE; Barnston, 1992), threat score (TS; Wilks, 2011), and bias score (BS; Wilks, 2011) for different precipitation intensity thresholds (i.e., 0.1, 10, 25, 50, 100 mm, representing light, moderate, large, heavy, and extreme rain respectively). Larger COR and smaller RMSE indicate a better forecast of the spatial pattern of rainfall amount. The TS is also called the Critical Success Index, and a larger TS indicates higher predictive skill (perfect = 1) for the corresponding precipitation intensity. The bias score (Bias) denotes the frequency of rainfall forecasts compared with observations, and BS = 1 indicates an ideal prediction of the relative area size of corresponding precipitation intensity. The equations of COR, RMSE, TS, and BS are as follows:
where “
$ \stackrel{-}{F} $ ” denotes the daily mean precipitation simulations, “$ \stackrel{-}{O} $ ” denotes the daily mean precipitation observations, and$ N $ denotes the number of observed stations. Four categories of hit (a), miss (b), false alarm (c) and correct non-rain forecast (d) are used to refer to the occurrence/non-occurrence of a rain event at each threshold, listed in Table 3. For example, both observed and predicted precipitation between 0.1 and 10 denote a hit for light rain.Rainfall Event Forecast yes no yes a c no b d Table 3. Four categories of the occurrence/non-occurrence for a rain event at each threshold. Four categories of hit (a), miss (b), false alarm (c) and correct non-rain forecast (d) are used to refer to the occurrence/non-occurrence of a rain event at each threshold.
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Figure 7 compares the time−height sections of vertical eddy transport of equivalent potential temperature and water vapor mixing ratio. They are averaged over the core rainband from the double nesting of 9-1 km using the three PBL schemes. The simulated vertical transport of heat and water vapor in the boundary layer all gradually became stronger from the early morning to noon, corresponding to the time when the primary rainfall peak occurred. The major difference existed with the vertical transport and mixing process at the top of the boundary layer between the nonlocal (YSU) and local (MYNN & MYJ) PBL schemes. The YSU scheme includes the nonlocal effect with the counter gradient transport and produced stronger vertical mixing below 2000 m than that of the local MYNN scheme before 1200 LST. The MYJ scheme showed intermediate vertical mixing between the YSU and MYNN schemes, as supported by Srinivas et al. (2018). This would cause differences in the vertical distribution of heat and water vapor from the boundary layer to the lower troposphere, and thus affect the stability of the atmosphere as well as the development of convection and precipitation, which will be discussed as follows. It is noteworthy that there was high vertical equivalent potential temperature and moisture transport at 2000 LST in the experiment with the MYNN scheme, which may explain the high precipitation at 2100 LST shown in Fig. 6.
Figure 7. Time−height cross sections of the vertical eddy transport of (a−c) equivalent potential temperature (unit: K s−1) and (d−f) water vapor [units: kg (cm hPa s)−1] averaged over the core rainband on 25 May in the inner 1-km grids (9-1) simulations using YSU, MYJ and MYNN.
Figure 8 compares the hourly variation of vertical distributions of equivalent potential temperature, water vapor mixing ratio, horizontal wind speed, and vertical velocity averaged over the core rainband from the surface to the lower troposphere. The vertical profiles of these corresponding variables at 1200 LST in Fig. 9 are also combined to discuss the different effects of the PBL schemes. For the thermal structures, the three PBL schemes all produced an inversion layer near the surface and the depth was decreasing from the early morning till noon, but the local MYNN scheme produced the shallowest inversion layer at 1200 LST around 1000 m compared to the nonlocal YSU scheme (1200 m) or the local MYJ scheme (1300 m) (Fig. 9a). Meanwhile, they all produced a warm layer in the middle-upper boundary layer, resulting in an unstable layer above. For the water vapor distribution, the three PBL schemes showed relatively little difference, but the water vapor was still more evenly distributed within the inversion layer (< 1000 m) during morning till noon in the nonlocal YSU scheme. The local MYJ and MYNN schemes both showed a more concentrated water vapor center in the bottom layer, but the MYJ scheme produced slightly higher water vapor mixing ratios from the top of the boundary layer to the middle troposphere at 1200 LST (Fig. 9b). For the wind structure, the local MYNN scheme produced stronger horizontal wind speed and upward motion than the nonlocal YSU scheme from the lower troposphere to the upper levels. The wind fields simulated by the MYJ scheme were strong at the lower troposphere; however, they rapidly reduced from the lower troposphere to upper levels (Figs. 9c and d). However, the nonlocal YSU scheme produced the lowest wind speed from the low-level troposphere (2500 m; 13.60 m s−1) to upper levels (6000 m; 17.42 m s−1) owing to its strongest vertical mixing at the top of the unstable boundary layer (Figs. 7a and d).
Figure 8. Time−height sections of the (a−c) equivalent potential temperature (units: K), (d−f) water vapor mixing ratio (units: g kg−1), (g−i) horizontal wind speed (unit: m s−1), and (j−l) vertical velocity (units: m s−1) averaged over the core rainband 1-km grids (9-1) using YSU, MYJ and MYNN.
Figure 9. Profiles of (a) equivalent potential temperature (θe, units: K), (b) water vapor mixing ratio (QV, units: g kg−1), (c) horizontal wind speed (wspd, units: m s−1), and (d) vertical velocity (W, units: m s−1) from 100 to 6000 m over the core rainband at 1200 LST in the 1-km (9-1) grids using YSU, MYJ and MYNN.
Therefore, the local MYNN scheme produced the shallowest and most humid inversion layer in the bottom layer, the least warm middle boundary layer, but stronger horizontal wind and upward motion from the top of the boundary layer to the upper levels. YSU produced a deeper inversion layer than MYNN in the bottom layer, a relatively warm and humid middle boundary layer, and the weakest wind fields due to the strongest vertical mixing at the top of the boundary layer. The local MYJ scheme produced an inversion layer with a depth between the other two schemes, but the warmest middle boundary layer, and the wind fields of MYJ at the boundary layer top were strong but quickly weakened above 5000 m. The MYJ scheme had slightly higher wind speeds in the boundary layer compared to the others, but caution should be taken here considering the uncertainty of wind observations and computational errors. In the following we focus on the effects of these different boundary layer structures on the development of convection.
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Figure 10 compares the hourly variations of simulated convective available potential energy (CAPE) and convective inhibition energy (CIN) averaged over the core rainband from the double nesting of 9-1 km simulations with the three PBL schemes. CAPE is defined as the accumulated buoyancy energy from the level of free convection to the equilibrium level, which represents the net kinetic energy that a rising air parcel can gain from the environment and hence reflects the potential strength of convective systems and associated precipitation. CIN is defined as the accumulated negative buoyant energy from the air parcel’s starting position to the level of free convection, which represents the inhibition energy that the rising air parcel has to overcome to become free convection. Under stormy conditions, the PBL height could be defined by some alternative methods such as using a cloud base or lifting condensation level (LCL) (Wisse and de Arellano, 2004; Stull, 2011), and a higher LCL usually denotes a stronger vertical mixing. Table 4 also lists the simulated values of CAPE, CIN and LCL, as well as the horizontal wind speed and upward motions at the top of the boundary layer (around 1500 m), the low-level troposphere (around 2500 m), and the middle troposphere (around 6000 m) at 1200 LST for a quantitative comparison.
PBL CAPE
(J kg−1)CIN
(J kg−1)LCL (m) Height of
inversion
layer (m)Vertical velocity
(m s−1)Horizontal wind speed
(m s−1)Water vapor mixing ratio
(g kg−1)1500 m 2500 m 6000 m 1500 m 2500 m 6000 m 1500 m 2500 m 6000 m YSU 216.93 11.04 1438 1200 0.01 0.10 0.34 9.99 13.60 17.42 13.80 10.90 4.70 MYJ 402.97 7.86 1411 1300 0.02 0.21 0.37 9.63 13.93 18.44 14.10 11.40 4.70 MYNN 236.6 11.08 1381 1000 0.03 0.17 0.43 9.39 13.94 18.9 13.40 10.80 4.90 Table 4. Simulated values of CAPE, CIN and LCL, as well as the horizontal wind speed, vertical velocity and water vapor mixing ratio, at the top of boundary layer (around 1500 m), the low-level troposphere (around 2500 m), and the middle troposphere (around 6000 m) at 1200 LST.
Figure 10. Hourly variations of simulated (a) CAPE (units: J kg−1), (b) CIN (units: J kg−1) and (c) LCL (units: m) averaged over the core rainband at 1-km (9-1) grids on 25 May using three PBL schemes.
The nonlocal YSU scheme produced the lowest CAPE peak at around 0800 LST, which was two hours earlier than the primary rainfall peak. Although the YSU scheme produced comparable CIN with the MYNN scheme, it systematically had the highest LCL compared to the other two schemes. This implies that, compared to the local MYNN scheme, the air parcel in the YSU scheme needs to be uplifted to a higher altitude to achieve condensation; nevertheless, the unstable energy in the upper boundary layer is insufficient to sustain the development of convection.
However, the local MYJ scheme systematically produced the largest CAPE and CIN during the morning through the afternoon, indicating that the convection was strongly suppressed and the CAPE was slowly released. The LCL in the MYJ scheme was also higher than in the MYNN scheme. The larger CIN, the slower release rate of CAPE, and the higher LCL with the MYJ scheme all determine that it is more difficult for the convection to initiate and develop compared to using the MYNN scheme. The atmospheric instability, low-level moisture convergence and vertical motion are the prerequisites for the development and maintenance of deep convection and mesoscale convective systems that often lead to heavy rainfall events (Srinivas et al., 2018). Therefore, in the following, we discuss the PBL effects on the large-scale forcings, including the low-level moisture supply and the upward motions.
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Figure 11 compares the time−height sections of horizontal and vertical fluxes of water vapor mixing ratio and vertical velocity averaged over the core rainband from the surface to the troposphere in the double nesting of 9-1 km simulations with the three PBL schemes. The water vapor transport simulated by these three PBL schemes mainly differed in its contributions to the primary rainfall peak at noon. The local MYNN scheme systematically produced the strongest horizontal water vapor transport, as well as upward motion from the top of the boundary layer to the middle troposphere during 1000−1200 LST. This can also be identified from Table 4, in which the MYNN scheme shows slightly stronger wind speeds and vertical velocity at the boundary layer top and the middle troposphere at 1200 LST compared to YSU. Although the MYJ scheme produced higher wind speeds and upward motion at 1200 LST at the top of the boundary layer, they weakened rapidly and produced less moisture transport to the upper levels. Therefore, the MYJ scheme also predicted a lower intensity of the primary rainfall peak compared to the MYNN scheme.
Figure 11. Time−height sections of (a−c) horizontal water vapor mixing ratio flux [units: kg (cm hPa s)−1] and (d−f) vertical water vapor mixing ratio flux [units: kg (cm hPa s)−1] and vertical velocity (black solid contours; units: m s−1) averaged over the core rainband on 25 May in the inner 1-km (9-1) grids using YSU, MYJ and MYNN.
Figure 12 presents longitude−height sections of moisture convergence and zonal−vertical wind averaged over 31°−33°N in the inner 1-km grid from the double nesting of 9-1 km simulations at 1200 LST and 1400 LST using the three PBL schemes. Here, we chose to demonstrate the moisture convergence at 1400 LST because of the availability of ECMWF reanalysis data. In the ECMWF data, at 1400 LST, there was strong low-level moisture convergence over the region 120°−122°E associated with strong upward motion from the lower to upper troposphere, corresponding to the east rainband. MYNN produced stronger upward motion than the other PBL schemes, which affected the amount of vertical moisture transport and produced the strongest low-level moisture convergence over this region. Weak low-level moisture convergence and upward motion in the lower troposphere were also shown in the ECMWF data over the region 117°−118°E, corresponding to the relatively weak rainfall in the west rainband. However, using the MYNN scheme could only partly capture the upward motion and moisture convergence over this region, and with underestimated intensity; and yet, the other two schemes could barely capture the upward motion, and the MYJ scheme even produced weak moisture divergence in the lower troposphere. This also explains why the experiments with the YSU and MYJ schemes largely underestimated the extreme rainfall over the west rainband. Besides, at 1200 LST, MYNN also produced stronger low-level moisture convergence and upward motion in the lower troposphere over the regions 120°−122°E and 117°−118°E.
Figure 12. Longitude−height sections of moisture convergence [shaded; units: 10−7 g (cm2 hPa s)−1] and U-W wind (black vectors; units: U × 100 W m s−1) averaged over 31°−33°N on 25 May in the inner 1-km nested with 9-km grid using three PBL schemes at 1200 LST (a-c) and 1400 LST (d-f).
Therefore, the nonlocal YSU scheme, with the strongest vertical mixing, produced the deepest inversion layer in the bottom layer with the highest LCL, the lowest CAPE, and the weakest wind fields, as well as low-level moisture transport. The MYJ scheme, with intermediate vertical mixing, produced larger CIN, slower release of CAPE, and higher LCL compared to the MYNN scheme, which suppressed the development of convection. The wind fields in the MYJ scheme at the low-level troposphere were the strongest but quickly weakened upwards, resulting in less moisture transport and convergence in the lower troposphere, especially over the west rainband. However, the MYNN scheme, with the weakest vertical mixing, produced the shallowest and most humid inversion layer in the bottom layer with the lowest LCL, but stronger wind fields and upward motions from the boundary layer top to upper levels. These all facilitated the development of deep convection and moisture transport for intense precipitation.