Abstract

Using the interior spectral nudging and update cycle (SN+UIC) methods in the regional Weather Research and Forecasting (WRF) Model, the numerical predictions of four persistent severe rainfall (PSR) events during the preflood season in south China were investigated, based on the fact that the global model has an advantage in predicting the large-scale atmospheric variation and the regional model is better in terms of simulating small-scale changes. The simulation results clearly indicated that the SN+UIC improved the prediction of the PSR events’ daily precipitation for moderate, heavy, and torrential rains (10–100 mm day−1). It also improved the simulative forecasts of the two categories of rain with accumulated precipitation above 50 and 100 mm at lead times of 5–11 days. Moreover, the longer the forecast lead time is, the larger the decrease in the Brier score. Additionally, the SN+UIC method decreased the root-mean-square error for accumulated rainfall (6.2%) and relative humidity (5.67%).

1. Introduction

Persistent severe rainfall (PSR) is a highly disruptive and damaging weather phenomenon; it usually causes severe impacts over larger areas and longer durations than “normal” torrential rain. In the last 60 years, PSR events have been occurring with increasing frequency and at a relatively higher mean intensity in China (Chen and Zhai 2013), which poses a considerable threat to human safety and economic stability. Therefore, studying the predictability of such high-impact weather is of great significance.

PSR is different from normal torrential rain events. In general, the PSR’s water vapor transportation and thermal dynamic conditions are very special; these conditions are produced within the context of an abnormal large-scale circulation pattern with less variation (e.g., Ding and Reiter 1982; Samel and Liang 2003; Zhai et al. 2013). As far as numerical weather prediction is concerned, the large-scale circulations also possess better predictability than smaller-scale ones (e.g., Lorenz 1969; Chen et al. 2010). Plus, the small-scale wave error grows rapidly, which interacts nonlinearly with the large-scale wave forecasts. Thus, for regional models, achieving a more efficient use of large-scale forecasts of the forcing fields, and retaining simultaneously the small-scale features in the regional model domain, are critical for better forecasting of PSR events.

Spectral nudging (SN) is a technique that can be used to constrain the interior of the regional model domain toward the large-scale driving data in the Weather Research and Forecasting (WRF) Model (e.g., Waldron et al. 1996; Von Storch et al. 2000; Miguez-Macho et al. 2004) and can be applied to the horizontal wind components, potential temperature, and geopotential height. A number of previous studies have investigated the performance of SN in regional climate models, revealing that its application significantly improves the prediction of temperature and atmospheric circulation (e.g., Liu et al. 2012; Feser and Barcikowska 2012; Xu and Yang 2015), but does not improve the forecasting of precipitation in all situations (Alexandru et al. 2009), possibly leading to overprediction (e.g., Otte et al. 2012; Bowden et al. 2012, 2013). It has been hypothesized that such overprediction may be caused by the lack of moisture in the SN of the WRF implementation, meaning the horizontal and vertical variations of moisture are likely to be misrepresented by the coarse input (Miguez-Macho et al. 2004), and adjusting the SN approach toward moisture could improve the precipitation forecast (e.g., Kanamaru and Kanamitsu 2007; Radu et al. 2008; Spero et al. 2014). However, these studies have focused on longer-term forecasting, while little research has been carried out on medium-range forecasting of PSR.

An accurate small-scale forecast is also important and can be produced by the regional model with the use of a high-resolution model as the background, although it may not be produced by the coarser global fields in the short-range forecast (Schwartz and Liu 2014). Some studies have combined the large-scale part of the global forecast with smaller scales from the regional model to improve the accuracy of the rainfall forecasts (e.g., Wang et al. 2013; Wang et al. 2014; Hsiao et al. 2015; Zhang et al. 2015). However, these studies directed against the regional ensemble prediction within 3-day forecasts.

In the present study, to explore new methods for improving the numerical prediction of PSR during the preflood season in south China, the SN was used to make efficient use of large-scale forecasts of the forcing fields for inner fields, with the “update cycle” method used to retain the small-scale features for the initial conditions (ICs). Meanwhile, the multiscale blending (MSB) method was adopted for a forecast within 3 days, while using the GFS global forecast after 3 days. In addition, the update cycle method took into account the water vapor mixing ratio as well.

2. Data and methodology

The data used in this study for providing the model ICs and boundary conditions were taken from the 2.5° × 2.5° Global Forecast System (GFS) dataset with an initial forecast time at 0000 UTC for 15-day forecasts during May–June 2011 and April–May 2013. The temporal resolution of the first 8 days of forecasting was in the interval of 6 h, and for the last 7 days it was an interval of 12 h. Four PSR cases (case 1, 0000 UTC 12 May–0000 UTC 15 May 2011; case 2, 0000 UTC 4 June–0000 UTC 8 June 2011; case 3, 0000 UTC 6 May–0000 UTC 10 May 2013; and case 4, 0000 UTC 19 May–0000 UTC 22 May 2013) in the preflood season in south China were selected, based on the precipitation dataset of basic daily meteorological variables from Chinese national surface weather stations. This dataset was also used for verifying the forecasted rainfall. For verification of the circulation field, the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) Final (FNL) Operational Global Analysis dataset (Kalnay 1996) was used (horizontal resolution, 1° × 1°; temporal resolution, 6 h), covering May–June 2011, and April–May 2013.

The regional model used was WRF-ARW (version 3.7.1). The model physics employed included the Kain–Fritsch cumulus convection parameterization scheme (Kain 2004), the WRF double-moment 6-class microphysics scheme (Lim and Hong 2010), the Rapid Radiative Transfer Model longwave radiation scheme (Mlawer et al. 1997), the Dudhia shortwave radiation scheme (Dudhia 1989), the Monin–Obukhov surface layer scheme (Beljaars 1995), the Yonsei University boundary layer scheme (Hong et al. 2006), and the Noah land surface scheme (Tewari et al. 2004). Double-deck nesting was used, as shown in Fig. 1, with the respective horizontal grid spacings of 36 km (270 × 190 grids) and 12 km (274 × 190 grids). WRF was run with a 63-layer configuration that extended to a model top at 10 hPa. Aside from when the SN technique was employed, the physical configuration in WRF was kept the same for all experiments.

Fig. 1.

The nested model domains, with terrain shaded.

Fig. 1.

The nested model domains, with terrain shaded.

The interior SN was applied to the horizontal wind components, potential temperature, and geopotential height at all the levels above the planetary boundary layer, with an interval of 6 h, and the nudging fields were from the GFS predictions. The nudging coefficients for all variables were set to be 0.0003 s−1. SN is applied in WRF to wavelengths longer than a threshold that is a function of the domain size. The preliminary choice of wavenumber in this study was made based on two considerations. First, on the horizontal resolution of the driving field (GFS), the threshold wavelength was not allowed to be less than the shortest wavelength resolved by the driving fields, which is at least 4 × Dx (Pielke 1984) (~1100 km). Second, on the size of the WRF domain, a wavelength of about 2000 km is an appropriate choice in WRF runs (Liu et al. 2012), and the sizes of domains 1 and 2 were about 9720 km × 6840 km and 3300 km × 2280 km (zonal × meridional direction) in this study, respectively. Hence, the wavenumbers in the two domains were set to be 4 and 2 in both the zonal and meridional directions, capturing the driving field features at a scale about 1140–2430 km.

Based on the SN experiments, the update cycle for the ICs (UIC) was conducted for every 72-h forecast with a 12-h running-in period. This was done using MSB, which combined the large scales from the GFS with the small scales from the WRF Model at the first UIC, and the GFS forecast from the second to the fourth UICs (Fig. 2). This was based on the fact that GFS shows better predictability for larger scales as in a longer-term forecast, while the WRF model shows better results for smaller-scale features as in a short-range forecast. The MSB cutoff wavenumber was chosen to be the same as the threshold wavelength of SN, which was wavenumber 4 in domain 1. Hereafter, this method is referred to as SN+UIC.

Fig. 2.

A diagram of the SN+UIC forecast flow with the update cycle.

Fig. 2.

A diagram of the SN+UIC forecast flow with the update cycle.

The MSB process was composed of two steps (Fig. 2). In step 1, wavenumber 4 was filtered using the two-dimensional discrete cosine transform method (Denis et al. 2002), which is suitable for spectral filtering of data in a limited area, for all variables that SN applied to, as well as the water vapor mixing ratio at 62 layers (except the first ground layer). In step 2, the spectral blending was performed as follows:

 
formula

where WRF represents the WRF regional ICs from the preceding WRF forecast, and WRFLS and GFSLS are the filtered large-scale regional ICs and the global forecast, respectively.

Against each of the events, three sets of numerical experiments—control experiments without SN and UIC (CTL), and the other two comparative experiments [one with both SN and UIC (SN+UIC) and another with SN only (SN)]—were conducted with 15-day runs done for the different initial forecast times, at the lead times of 1, 3, 5, 7, 9 and 11 days prior to the PSR. The term lead time in this study denotes the forecast start time (number of days) prior to the whole PSR event. The four PSR cases were selected for the numerical experiments with a total of 24 forecast runs in each experiment set.

The circulation field was verified using the root-mean-square error (RMSE):

 
formula

where Fi is the model forecast variable; Oi is the observational variable, taken from the FNL data; and N is the number of verification grids for the evaluation region (21°–35°N, 105°–118°E) in domain 2.

Precipitation verification is always based on the threat score (TS) or Brier score (BS). The TS and BS can be expressed as

 
formula
 
formula

where and denote the k-component probability value of the forecast and observation, respectively. BS ranges from 0 to 1 with BS = 0 indicating a perfect forecast. The 24-h precipitation TS and the accumulated precipitation BS were used for verifying the PSR forecast for the different precipitation rate categories, with the same evaluation range as the RMSE method. The whole precipitation process TS was obtained by averaging the daily score of the PSR case period, as well as averaging the four PSR cases to obtain the overall scores of the precipitation verification. The rainfall categories for TS were divided into light rain (<10 mm day−1), moderate rain (10–24.9 mm day−1), heavy rain (25–49.9 mm day−1), torrential rain (50–100 mm day−1), and rainstorm (>100 mm day−1). In addition, the RMSE and the linear regression coefficient (RC) were also used for the daily and accumulated precipitation verification, and the improvement rates (IRs) of TS, BS, RMSE, and RC were calculated, with TS as an example:

 
formula

The IRs of BS and RMSE are multiplied by −1.

3. Results

For the 24-h precipitation TS, the improvement seen through using SN and SN+UIC, compared with CTL, was mainly reflected in the precipitation rate categories above light rain (>10 mm day−1) (Fig. 3). SN+UIC produced better results than SN for lead times of 3–11 days for moderate and heavy rains (10–49.9 mm day−1), and achieved slightly better results for lead times of 7–11 days for the categories above heavy rain (>50 mm day−1). The averaged TS also showed that SN+UIC produced superior results compared with SN for moderate and heavy rain (Fig. 3g).

Fig. 3.

Averaged TSs at (a) 1-, (b) 3-, (c) 5-, (d) 7-, (e) 9-, and (f) 11-day lead times prior to PSR, and using the different methods. (g) Averaged TSs over the different forecast lead times for the PSR events.

Fig. 3.

Averaged TSs at (a) 1-, (b) 3-, (c) 5-, (d) 7-, (e) 9-, and (f) 11-day lead times prior to PSR, and using the different methods. (g) Averaged TSs over the different forecast lead times for the PSR events.

The improvement rates of TS, BS, RMSE, and RC were calculated and are shown in Table 1. SN+UIC improved the 24-h precipitation outcomes for moderate, heavy, and torrential rains (10–100 mm day−1) when compared with CTL, with the greatest improvement rate (46.2%) reached for heavy rain (25–49.9 mm day−1). The improvement was also reflected in the rate categories above light rain (>10 mm day−1) when compared with SN. For the accumulated precipitation BS, SN+UIC produced better results at the different lead times for the rainfalls above 10 and 25 mm, and yielded a decrease in BS with lead times of 5–11 days for the accumulated rainfalls above 50 and 100 mm. Moreover, the longer the forecast time is, the larger the decrease in BS. The accumulated precipitation improvement rates of RMSE and RC were 6.2% and 12.4%, respectively, when compared with CTL forecasts. Moreover, the higher improvement rates were gained as compared with the SN, which proved that SN+UIC improved more the SN.

Table 1.

The improvement rates realized for TS, BS, RMSE, and RC. Boldface text indicates the positive value.

The improvement rates realized for TS, BS, RMSE, and RC. Boldface text indicates the positive value.
The improvement rates realized for TS, BS, RMSE, and RC. Boldface text indicates the positive value.

The total accumulative rainfall distribution of the four PSR cases for 3- (Fig. 4) and 5-day (Fig. 5) lead times was analyzed in detail. For case 1, SN+UIC and SN with a forecast lead time of 3 days (Figs. 4c1,d1) predicted a better rainband range than CTL, with SN+UIC (Fig. 5d1) better than the other two methods (Figs. 5b1,c1) for 5-day lead time. The forecasted rainband in case 2 as a whole showed a southward deflection by using SN+UIC for a forecast lead time of 3 days (Fig. 4d2), which was closer to the observations. Among the rest, the accumulated rainfall above 100 mm was relatively well forecasted for lead time of 5 days (Fig. 5d2). Although the rainband ranges for case 3 were smaller than the observations, as shown in the results by using all of the methods, SN+UIC was slightly better. The rainband of case 4 also showed a southward deflection with a forecast lead time of 3 days when using SN+UIC (Fig. 4d4) compared with SN. The accumulated rainfall of case 4 for the category above 50 mm when using SN+UIC at a lead time of 5 days was closer to the observations compared with those using SN (Fig. 5d4). We note that, for the time series of daily precipitation (figures not presented here), the persistence characteristics of precipitation were improved by using SN and SN+UIC as compared with CTL, especially for the duration length.

Fig. 4.

Total accumulative rainfall distribution of the PSR cases in the preflood season in south China for (a1–a4) the observations and for the forecast experiments at 3-day lead time, with the following different experiment methods: (b1)–(b4) CTL, (c1)–(c4) SN, and (d1)–(d4) SN+UIC.

Fig. 4.

Total accumulative rainfall distribution of the PSR cases in the preflood season in south China for (a1–a4) the observations and for the forecast experiments at 3-day lead time, with the following different experiment methods: (b1)–(b4) CTL, (c1)–(c4) SN, and (d1)–(d4) SN+UIC.

Fig. 5.

As in Fig. 4, but for 5-day lead time.

Fig. 5.

As in Fig. 4, but for 5-day lead time.

Next, the improvement realized by SN+UIC was analyzed using the averaged RMSE profiles of relative humidity (Fig. 6), which was also compared with the GFS forecast. As can be seen, SN+UIC led to improvements at the various heights compare with SN, but this is more obviously so at altitudes above 800 hPa with lead times of 3–5 days (Figs. 6b,c). Compared with the CTL experiments for the levels below 500 hPa at lead times of 5–11 days (Figs. 6c–f), SN+UIC yielded the greatest decrease in RMSE, followed by SN. For the levels above 500 hPa, SN+UIC also demonstrated better predictability than SN at the different lead times, with smaller RMSEs than CTL at lead times of 9–11 days. In general, the longer the forecast time, the larger the decrease in RMSE at a wider range of heights for SN and SN+UIC, as compared with CTL. The averaged improvement rates for heights and lead times were 5.67% and 1.49%, compared with CTL and SN, respectively. The GFS forecast produced smaller RMSEs than the other methods over the different forecast lead times, especially in the upper levels, which could be due to the fact that the reanalysis data (FNL) for the verification in this study might have larger uncertainties at upper levels (Moradi et al. 2013; Noh et al. 2016). As for the improvement in the relative humidity when using SN+UIC, this might be attributable to the better predictability of the GFS, as well as the lack of the water vapor mixing ratio in the WRF implementation using SN, which suggests that the inclusion of humidity is an important contribution to enhancing the precipitation verification scores.

Fig. 6.

Averaged relative humidity RMSE (%) changes with height for the PSR period at (a) 1-, (b) 3-, (c) 5-, (d) 7-, (e) 9-, and (f) 11-day lead times prior to PSR, with the different methods used (the green line is the NCEP GFS forecast). (g) Averaged RMSEs over the different forecast lead times.

Fig. 6.

Averaged relative humidity RMSE (%) changes with height for the PSR period at (a) 1-, (b) 3-, (c) 5-, (d) 7-, (e) 9-, and (f) 11-day lead times prior to PSR, with the different methods used (the green line is the NCEP GFS forecast). (g) Averaged RMSEs over the different forecast lead times.

In terms of the RMSEs of the geopotential height field (Figs. 7a1d1) and temperature field (Figs. 7a2d2), a decrease when using SN and SN+UIC was mainly found above 900 and 700 hPa, respectively, compared with CTL; moreover, the longer the forecast time is, the larger the decrease in RMSE. Especially, the decrease for the PSR period (Figs. 7a1a2) was larger than the other averaged forecast periods. On the other hand, the two methods had similar effects on the forecast outcomes. For the zonal (Figs. 7a3d3) and meridional (Figs. 7a4d4) wind fields, SN+UIC achieved slightly better results than SN from 800 to 400 hPa for the 6–15-day forecast period (Figs. 7c3d3 and 7c4d4) and the PSR period (Figs. 7a3a4). GFS yielded smaller RMSEs than CTL for all variables, which were even smaller than SN and SN+UIC for wind fields at the various heights as well as the geopotential height field below 400 hPa. This further proved that GFS provided more accurate extended forecasts than WRF, and, on the other hand, that the WRF spectral nudging distinctly achieved a better prediction of rainfall.

Fig. 7.

Vertical profiles of the averaged RMSEs of (a1)–(d1) the geopotential height field H (gpm), (a2)–(d2) the temperature field T (°C), (a3)–(d3) the zonal wind field U (m s−1), and (a4)–(d4) the meridional wind field V (m s−1) for (top row) the PSR period, and (second row) the 1–5-, (third row) 6–10-, and (bottom row) 11–15-day forecasts, with the different methods used (the green line is the NCEP GFS forecast).

Fig. 7.

Vertical profiles of the averaged RMSEs of (a1)–(d1) the geopotential height field H (gpm), (a2)–(d2) the temperature field T (°C), (a3)–(d3) the zonal wind field U (m s−1), and (a4)–(d4) the meridional wind field V (m s−1) for (top row) the PSR period, and (second row) the 1–5-, (third row) 6–10-, and (bottom row) 11–15-day forecasts, with the different methods used (the green line is the NCEP GFS forecast).

4. Conclusions

A new method for improving the numerical prediction of four PSR events during the preflood season in south China using SN and UIC within WRF version 3.7.1 was explored, and the forecast simulations were analyzed and verified in terms of accumulated rainfall and related meteorological variables. The main conclusions can be summarized as follows.

The use of SN+UIC led to clear improvements in the 24-h precipitation simulations, particularly for moderate, heavy, and torrential rains (10–100 mm day−1), and yielded the greatest improvement rate (46.2%) for heavy rains compared with CTL. The improvement was also reflected in the accumulated precipitation above 50 and 100 mm with lead times of 5–11 days; moreover, the longer the forecast lead time is, the larger the decrease in BS. In addition, higher improvement rates of RMSE and RC were produced by using SN+UIC. The precipitation pattern and intensity of the accumulated rainfall were also better than the SN outcomes for lead times of 3–5 days.

The SN+UIC method decreased the RMSEs for relative humidity at the various heights when compared with SN, and the longer the forecast time is, the larger the decrease in the RMSEs with a wider range of heights for SN and SN+UIC, as compared with CTL. The averaged improvement rates were 5.67% and 1.49%, compared with CTL and SN, respectively. In terms of the other variables, SN+UIC achieved slightly better results at 800–400 hPa for the wind fields during the 6–15-day forecast and during the PSR period. For the geopotential height and temperature fields, SN and SN+UIC had similar effects on the forecast outcomes. GFS provided more accurate extended forecasts than WRF, and resulted in SN and SN+UIC in WRF achieving a better prediction.

The results clearly indicated that SN+UIC improved the precipitation prediction of PSR during the preflood season in south China. The improvement realized by SN+UIC was particularly associated with the better predictability of the GFS for the larger-scale circulations, as well as with the update cycle of the water vapor mixing ratio for the ICs, which fixed the lack of SN in the WRF implementation. However, there was no obvious improvement seen for the geopotential height, temperature, and wind fields, and further research into these areas is needed. Indeed, using different initial conditions may lead to differing levels of performance, and further experiments using various sources of global model forecasting data are needed for comparison. Additionally, long-term statistical studies are needed as well on the effects of SN+UIC for PSR events over different regions of Asia. Such research efforts should involve the analysis of the dynamics, thermodynamics, and many other aspects of the precipitation systems, enabling a better selection of the SN+UIC parameters and a deeper understanding of the function of these methods so as to further improve the forecasting of PSR.

Acknowledgments

This study was jointly supported by the National Natural Science Foundation of China (Grant 91437221), the National Key Basic Research Program of China (Grant 2012CB417204), China Special Fund for Meteorological Research in the Public Interest (Grant GYHY201506002), and the China Scholarship Council. The authors are grateful to the editors and three reviewers for their invaluable and constructive suggestions and comments, which helped to improve the manuscript.

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