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The Advanced Research core of the Weather Research and Forecasting (WRF) model, version 3.7.1 (Skamarock et al., 2008), is utilized as the numerical model. A one-way nested framework is designed with 180 × 180 and 258 × 258 horizontal grid points for 18- and 3-km grid spacing, respectively (Fig. 2). There are 41 terrain-following hydrostatic-pressure vertical levels and a model top of 10 hPa in both outer and inner domains.
Figure 2. (a) Model domain configuration: the black square indicates the outer domain (18-km resolution); the red square indicates the inner domain (3-km resolution); black dots show the distribution of simulated sounding datasets; blue circles show locations of the seven radar sites. (b) Terrain height within the inner domain, the Dabie Mountains (31°N, 116°E), Huang Mountains (30°N, 117.5°E), and Mu-fu Mountains (29°N, 115°E).
The ICs and lateral boundary conditions (LBCs) are derived from the U.S. National Centers for Environmental Prediction Global Forecast System (GFS) operational analysis data. The physical parameterization schemes include the WSM6 microphysics scheme (Hong and Lim, 2006), Yonsei University boundary layer scheme (Hong et al., 2006), RRTM longwave radiation scheme (Mlawer et al., 1997), and Goddard shortwave radiation scheme (Chou and Suarez, 1999). Additionally, the Grell-3 cumulus scheme (Grell and Dévényi, 2002) is used in the inner domain.
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Following Zhuang et al. (2020), an ensemble data assimilation and forecast system (Wang et al., 2013) is constructed (Fig. 3) to generate flow-dependent IC and LBC perturbations. The Ensemble Square Root Filter approach proposed by Whitaker and Hamill (2002) is employed as the data assimilation method. For the present study, the system is modified to run in an OSSE setup to remove model uncertainties (Yussouf and Stensrud, 2012; Gasperoni et al., 2013; Johnson and Wang, 2016; Madaus and Hakim, 2017).
Figure 3. Schematic of the ensemble data assimilation configuration. The outer-domain ensemble data assimilation is initialized at 0000 or 1200 UTC for each case, while the inner domain ensemble data assimilation is initialized 21 h after the outer domain initialization using the outer-nest ensemble for both the initial and boundary conditions. “Obs” indicates observations.
To create a “true” atmospheric state, we first perform a 36-h nature run initialized from the GFS analysis 24 h before the analysis time for each case with a 3-km resolution covering the outer domain (Fig. 2a). The mesoscale sounding datasets are then generated at randomly chosen locations within China’s mainland (Fig. 2a) and interpolated from the “true” run with observation errors of 2.5 m s−1, 1.2 K, and 0.005 kg kg−1 for wind velocity, temperature, and water vapor, respectively (Snook et al., 2015). For the inner domain, the “true” run is interpolated to seven real CINRAD-SA radars (Zhu and Zhu, 2004) (Fig. 2b) with observation errors of 2 m s−1 and 5 dBZ for radial velocity and reflectivity (Johnson et al., 2015).
We then generate the initial ensemble in the outer domain, by adding analysis perturbations from the first 30-member European Centre for Medium-Range Weather Forecasts global ensemble prediction products (Hagedorn et al., 2008; Hagedorn et al., 2012) to temperature, horizontal wind, and water vapor mixing ratio in the ICs and LBCs. After that, the mesoscale sounding data assimilation for the outer domain is initialized at 0000 or 1200 UTC (0008 or 2000 LST) for each case (Table 1) over a 24-h period with 3-h intervals. For the inner domain, the initial ensemble is obtained by downscaling the analysis states at the seventh assimilation cycle in the outer domain using the WRF “ndown” tool (Daniels et al., 2016). The radar data (including reflectivity and radial velocity) are then assimilated for 3-h with 10-min intervals in the inner domain, while the outer domain provides larger-scale LBC perturbations every 15-min during the assimilation cycles.
Number Start time Subset 1 0000 UTC 23 June 2013 Weak forcing 2 0000 UTC 5 July 2013 Weak forcing 3 1200 UTC 6 July 2013 Strong forcing 4 0000 UTC 7 July 2013 Weak forcing 5 0000 UTC 21 July 2013 Weak forcing 6 0000 UTC 22 July 2013 Weak forcing 7 0000 UTC 1 June 2014 Strong forcing 8 0000 UTC 15 June 2014 Strong forcing 9 0000 UTC 25 June 2014 Strong forcing 10 0000 UTC 26 June 2014 Weak forcing 11 1200 UTC 1 July 2014 Strong forcing 12 0000 UTC 12 July 2014 Weak forcing 13 1200 UTC 24 July 2014 Strong forcing Table 1. Summary of cases.
The horizontal and vertical covariance localization radii for the outer domain are 120 km and 6 km, and the corresponding values in the inner domain are 20 and 5 km (Wang et al., 2013; Snook et al., 2015), respectively. To maintain spread within the assimilation cycles, a multiplicative covariance inflation of 1.15 (Anderson and Anderson, 1999; Tong and Xue, 2005) and a relaxation inflation of 0.5 to prior ensemble variability (Zhang et al., 2004) are applied to the outer and inner domains.
The control experiment (CTRL) uses the first 20 members of the ensemble analysis in the inner domain and the LBC perturbations are provided by the outer domain ensemble forecasts and perform 12-h convective-scale ensemble forecasts (Fig. 3). Several sensitivity experiments (IC_MULTI, IC_SMALL, IC_TRANS, and IC_LARGE) are conducted to further clarify the scale-based sensitivity of errors. These experiments employ the same LBCs from the ensemble mean analysis of the outer domain (no LBC perturbations) and differ in initial perturbations that are constructed in three steps: (i) subtract the ensemble mean from each analysis state to obtain intermediate perturbations; (ii) scale each perturbed variable by retaining information at determined spatial scales; and (iii) add the scaled perturbations back to the ensemble mean (Table 2). Specifically, IC_MULTI uses the same IC perturbations as CTRL with LBC perturbations excluded to investigate the sensitivity of larger-scale LBC errors. By retaining the small-scale components of the flow-dependent IC perturbations, the up-amplitude and upscale processes of small-scale initial errors and the associated impact on precipitation can be isolated and examined via IC_SMALL. By retaining the larger-scale components of the IC perturbations, the evolution and the associated impact of larger-scale initial errors on precipitation can be isolated and examined via IC_LARGE. The definition of scale range is specified in section 2.3.
Experiment IC perturbations LBC perturbations CTRL Flow-dependent_3 km Flow-dependent_18 km IC_MULTI Flow-dependent_3 km None IC_SMALL Filtered information < 36 km from Flow-dependent_3 km None IC_TRANS Filtered in formation > 36 km and < 120 km from Flow-dependent_3 km None IC_LARGE Filtered information > 120 km from Flow-dependent_3 km None Table 2. Summary of IC perturbations and LBC perturbations used in the ensemble experiments.
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The forecast error is quantified using the difference total energy (DTE; Zhang et al., 2007):
where
$ {u}' $ ,$ {v}' $ , and$ {t}' $ are the differences of zonal wind, meridional wind, and temperature from the ensemble mean, respectively ($ {C}_{p}=1004.9\;{\rm{J\;kg}}^{-1}{\rm{K}}^{-1} $ and${T}_{\rm{r}}=270\;{\rm{K}}$ ). The subscripts i, j, k, t, m, and λ represent the x-direction, y-direction, vertical level, forecast time, ensemble member, and the spatial scale.To measure the scale-dependent error growth, we classify the spatial scale into three scale ranges (Zhuang et al., 2020): small scale (36 km ≥ wavelength); transition scale (120 km ≥ wavelength > 36 km); and larger scale (wavelength > 120 km). To obtain variable fields at different scales, the discrete cosine transform (DCT) ( Denis et al., 2002; Surcel et al., 2015; Wu et al., 2020) method is used. Compared to traditional Fourier transform methods, DCT is able to avoid discontinuity problems at domain boundaries.
We also introduce a vertical function (Nielsen and Schumacher, 2016) to calculate the two-dimensional root-mean vertically integrated DTE (RMDTE). To compare the error growth between different convective regimes, the normalized root-mean vertically integrated DTE (NRMDTE) (Nielsen and Schumacher, 2016; Klasa et al., 2019) at different scales is calculated to eliminate the variability independent of the magnitude of the total background flow (Appendix A).
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To evaluate spatial precipitation uncertainties, the decorrelation scale method proposed by Surcel et al. (2015) is applied. As described in that study, complete decorrelation of ensemble forecasts can be considered as a lack of precipitation predictability by the ensemble at a given scale λ0. For the scale λ ≤ λ0, there is no precipitation predictability. For the scale λ ≥ λ0, the precipitation fields of ensemble members are correlated, indicative of some predictability. The power ratio is used to quantitatively assess the precipitation uncertainty (Wu et al., 2020):
where
$ {\rm{Var}}\left({p}_{m}\left(\lambda \right)\right) $ is the variance of the precipitation field$ {p}_{m}(m=1,\dots,n) $ at spatial scale λ. The value of$ R\left(\lambda \right) $ varies from 1 / n to 1, with a larger value corresponding to higher uncertainty and lower precipitation predictability. In general, a threshold value of$ R\left(\lambda \right) $ = 1 means the complete loss of predictability at scale λ, while in this study, the threshold is set to 0.9 to eliminate noise without introducing any significant bias (Judt, 2018; Wu et al., 2020). Quantitative investigations of precipitation uncertainty are then conducted by comparing$ R\left(\lambda \right) $ for different ensemble designs at different forecast lead times. -
Thirteen mei-yu-season heavy-rainfall events (June and July 2013–2014) (Liu et al., 2012; Sun and Zhang, 2012; Luo and Chen, 2015) over the YHRB are selected, ranging from local self-organized convective events to synoptically driven mei-yu-front events. Based on the convective adjustment timescale
$ {\rm{\tau }}_{\rm{c}} $ (Appendix B) calculated with the deterministic forecast in the inner domain (initialized with the ensemble mean analysis), all 13 cases are quantitatively classified into two categories based on the convective adjustment timescale. The typical 6-h (Zimmer et al., 2011; Keil et al., 2014) threshold is used to distinguish strong-forcing events from weak-forcing events (Table 1).Figure 4a shows the evolution of
$ {\rm{\tau }}_{\rm{c}} $ with corresponding convective available potential energy (CAPE; Fig. 4b) for cases in each subset. Note that$ {\rm{\tau }}_{\rm{c}} $ for the weak-forcing subset is markedly higher than that of the strong-forcing subset with a more remarkable semidiurnal cycle of CAPE. Figures 5c and d show the frequency of 1-h precipitation exceeding 0.5 mm h−1 in both strong- and weak-forcing regimes for the true state. The strong-forcing events exhibit a southwest–northeast frequency belt along the mei-yu front (Fig. 5c), which is consistent with the frontal rainfall events (Sun and Zhang, 2012). The weak-forcing events exhibit a scattered pattern near the Dabie Mountains, Huang Mountains, and Mu-fu Mountains (Chen et al., 2016), with frequency maxima 1°–3° to the south of the northeast–southwest-oriented weak mei-yu front (Fig. 5d). The wind fields also differ between strong- and weak-forcing regimes, with the strong-forcing cases having stronger wind speed (Fig. 4c) and cyclonic shear (Fig. 5a) while the weak-forcing cases are generally characterized by weaker large-scale advection (Fig. 4d and Fig. 5b) in which the CAPE is higher (Figs. 4a). These environmental features are in accordance with Klasa et al. (2019), as they also found stronger large-scale advection and lower CAPE for strong-forcing events, supporting our application of$ {\rm{\tau }}_{\rm{c}} $ .Figure 4. The (a) convective-adjustment time scale
$ {\rm{\tau }}_{\rm{c}} $ (units: h) and (b) CAPE (units: J kg−1) averaged over areas with rainfall higher than 0.5 mm h−1. The black line in (a) is the 6 h threshold for regime classification. The dashed lines indicate each case while the thick solid lines represent average value for each subset. (c, d) Wind rose variation between 1000 and 100 hPa for (c) strong-forcing and (d) weak-forcing cases. The concentric rings show the frequency of wind direction and the colors indicate the magnitude of wind speed.Figure 5. (a, b) Ensemble-mean 850-hPa wind vector (units: m s−1) and equivalent potential temperature (blue solid contours lines, 344–348 K, 2 K interval, indicating the location of the mei-yu front) averaged over cases for the (a) strong- and (b) weak-forcing regime calculated from the outer domain ensemble. The red boxes indicate the inner domain. (c, d) Precipitation frequency computed from the observed hourly precipitation exceeding 0.5 mm h−1 for the (c) strong- and (d) weak-forcing regime. The black triangles indicate the mountains shown in Fig. 2.
2.1. Model configuration
2.2. OSSE framework and ensemble generation
2.3. Representation of scale-dependent error growth
2.4. Representation of spatial precipitation uncertainty
2.5. Case selection
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CONVECTIVE ADJUSTMENT TIMESCALE
The convective adjustment timescale is defined as the rate at which CAPE is removed by diabatic heating associated with precipitation (Done et al., 2006):
where
${C}_{p}$ is the specific heat capacity of air at constant pressure,$ {\rho }_{0} $ and$ {T}_{0} $ are the reference density and temperature,$ {L}_{\rm{v}} $ is the latent heat of vaporization, g is the acceleration of gravity, and$ {p}_{\rm{rate}} $ is the precipitation rate. In this study, the deterministic forecast for the inner domain is used to calculate$ {\rm{\tau }}_{\rm{c}} $ . Prior to calculation, the CAPE and$ {p}_{\rm{rate}} $ are both spatially smoothed using a Gaussian method (Keil et al., 2014) with a spatial scale of 36 km and masked with a threshold of 0.5 mm h−1 to avoid dry events (Surcel et al., 2016).