The Liujiang River basin (LRB) is selected as the studied area, which is the largest first-order tributary of the Pearl River with a drainage area of 58 270 km2 (Chen et al., 2017). LRB is in the monsoon area with heavy storms that induced severe flooding in the watershed and caused huge flood damages in the past centuries. Figure 1 is a sketch map of the LRB.

Precipitation of 68 rain gauges within the watershed in 2011, 2012 and 2013 was collected and used in this study to compare with the WRF QPF. Precipitation data are at 1 h intervals. River discharge near the watershed outlet is collected also for this same period. As this study focuses on watershed flood forecasting, so only the precipitation and river discharge during the flood events are prepared. There is one flood event in each year. The flood events are numbered as flood event no. 2011, flood event no. 2012 and flood event no. 2013, respectively.

All simulations for this study were conducted with the Advanced Research WRF (WRF-ARW) model version 3.4 (Skamarock et al., 2008). The WRF-ARW model is 3-D, non-hydrostatic, and fully compressible, and has the terrain-following sigma coordinate system. The model is considered the next generation's medium-range weather forecasting model, and can simulate different weather processes from cloud scale to synoptic scale, especially at a horizontal resolution of 1–10 km. The model also integrates the advanced numerical methods and data assimilation techniques, a variety of physical process schemes, and multiple nested methods and the capability of being used in different geographical locations. The WRF-ARW model satisfies the needs of scientific research and practical applications for this study.

Prior studies have been shown in quantitative precipitation forecasting by using the WRF-ARW model. For instance, Pennelly et al. (2014) employed the WRF model to predict three precipitation events of Alberta, Canada, and compared the precipitation with the 48 h leading time predicted by the model with rain gauges. The results showed that Kain–Fritsch cumulus parameterization overestimated the value of precipitation invariably. Eiserloh and Chiao (2015) used WRF-ARW with data assimilation to investigate an atmospheric river event over northern California. Maussion et al. (2011) compared the capability of the WRF model in retrieving monthly precipitation and snowfall at three different spatial resolutions, including the 30, 10 and 2 km domains over Tibet. Their results showed that the model was able to recapture monthly precipitation and snowfall. Pan et al. (2012) used two WRF simulation groups between pre-process and post-process in the Heihe River basin, and compared and analyzed the mean bias error, root mean square error and correlation coefficient of the two WRF groups. Huang et al. (2011) found that variations in the microphysical process parameterization schemes had much more influence on precipitation than that of cumulus parameterization schemes, especially for a torrential rain attributed to large-scale forcing that mainly resulted from stratus clouds. Kumar et al. (2001) used the WRF model to study a heavy rain in 2005; their results showed that the WRF model could reproduce the storm event and its dynamical and thermo-dynamical characteristics. Hong and Lee (2009) conducted a triply nested WRF simulation for convective initiation of a thunderstorm. Givati et al. (2012) predicted the hiemal precipitation events of 2008 and 2009 based on the WRF model in the upstream of the Jordan River, and coupled the WRF model with hydrological model HYMKE to simulate the velocity and discharge of the Jordan River. Sensitivity experiments of WRF microphysical schemes by Niu and Yan (2007) have shown the adequate performance of precipitation predicted associated with region, center location and rainfall intensity. Xu et al. (2007) compared the hiemal continuous precipitation process predicted with the estival results by the WRF model; the results showed that the KF scheme was better than the BM scheme in summer. Hu et al. (2008) found that the parameterization scheme of the WRF model was related to the model resolution, and the parameterization scheme should be selected by the resolution of the WRF model.

The WRF-ARW was applied to the LRB following the configurations by Li et al. (2015). More information about the LBR can be found in Li et al. (2015) and Chen et al. (2017). The model domain is centered at 23.8∘ N, 109.2∘ W with the Lambert conformal projection. The vertical structure includes 28 levels, with the focus on the lower levels of the troposphere. The initial and time-dependent lateral boundary conditions are supplied from NCEP Global Forecast System (GFS) 3-hourly global analysis at 0.5∘ horizontal resolution. The model domain has a 20 km grid resolution. The single-moment 3-class microphysics (WSM3) parameterization (Hong and Lim, 2006) is adopted for this study. Kain–Fritsch cumulus parameterization (Kain, 2004) as well as the YSU boundary layer microphysics scheme (Hong and Lim, 2006) are used. Other physics schemes used include the NOAH scheme for the land surface physics (Ek et al., 2003), the Goddard scheme for the shortwave radiation physics (based on Chou and Suarez, 1994), and the Rapid Radiative Transfer Model (RRTM) scheme for the longwave radiation physics (Mlawer et al., 1997).

The spatial and temporal resolution of WRF is at 20 km × 20 km and 1 h, respectively. The entire Liujiang River basin is covered by a total of 156 grid points of the WRF model. The simulated QPF for flood events in years 2011 to 2013 was produced with three different lead times (i.e., 24, 48 and 72 h), respectively. Shown in Figs. 2–4 are the WRF QPF products in 3 different years.

Comparisons of WRF QPF and rain gauge precipitation are performed. From the simulated results, as shown in Figs. 2–4, it appears that the temporal precipitation pattern of both products is similar, although there are some insignificant differences. To make further comparison, the accumulated precipitation of the three flood events averaged over the watershed is calculated and listed in Table 1.

As summarized in Table 1, it could be found that the WRF QPF accumulated precipitation has obvious bias with rain gauge accumulated precipitation. For all three flood events, the WRF QPF accumulated precipitation is higher than that measured by rain gauges. In other words, the WRF QPF overestimates the precipitation. For flood event no. 2011, the overestimated watershed averaged precipitations of the WRF QPF with lead times of 24, 48 and 72 h are 23, 32 and 55 %, respectively. For the flood event no. 2012, they are 16, 37 and 71 %, respectively. They are 50, 73 and 95 %, respectively, from the event no. 2013. The results suggest that the longer the WRF QPF lead time, the higher the chance of overestimation.

From the simulated results (cf. Figs. 2–4 and Table 1), the WRF QPF has significant bias compared to rain gauge precipitation. Assuming the rain gauge precipitation is correct, the WRF QPF needs to be further calibrated. In order to do so, the WRF QPF is further post-processed based on the rain gauge precipitation to correct the systematic error of the WRF QPF. The principle of WRF QPF statistical calibrations proposed in this study is to keep the areal averaged event accumulated precipitation from both model and rain gauge products equivalent. In other words, the statistical approach is to nudge the WRF QPF precipitation to rain gauge results.

Based on this principle, the WRF QPF post-processing procedure is summarized as follows.

Calculate the areal average precipitation of the WRF QPF for each flood event over the watershed as the following equation:P‾WRF=∑i=1NPiFiN,

where P‾WRF is the areal average precipitation of the WRF QPF of one flood event, Pi is the precipitation on WRF grid i, Fi is the surface area of WRF grid i divided by the whole watershed drainage area, and N is the total number of WRF grids.

The Liuxihe model is a physically based fully distributed hydrological model proposed mainly for watershed flood forecasting (Chen, 2009; Chen et al., 2011), and has been used in a few watersheds for flood forecasting (Chen, 2009; Chen et al., 2011, 2013, 2016; Liao et al., 2012a, b; Xu et al., 2012a, b). In the Liuxihe model, runoff components are calculated at grid scale, runoff routes at both grid and watershed scale. Runoff routing is divided into hillslope routing and river channel routing by using different computation algorithms. The Liuxihe model proposed an automatic parameter optimization method using the PSO algorithm (Chen et al., 2016), which largely improves the model's performance in watershed flood forecasting. Now the Liuxihe model is deployed on a supercomputer system with parallel computation techniques (Chen et al., 2013) that largely facilitates the model parameter optimization of the Liuxihe model.

Chen et al. (2017) set up the Liuxihe model in the LRB with freely downloaded terrain property data from the website at a spatial resolution of 200 m × 200 m, and optimized model parameters with observed hydrological data. The model was validated by observed flood event data, and the model performance was found to be rational and could be used for real-time flood forecasting. The model only uses rain gauge precipitation, so its flood forecasting lead time is limited. In this study, the Liuxihe model was set up in the LRB and the optimized model parameters were used in this study as the first attempt. Figure 5 shows the model structure.

While the model parameter optimization by Chen et al. (2017) is done by using the rain gauge precipitation, this study uses the WRF QPF as the precipitation input. So the parameters of the Liuxihe model that were set up in the LRB may not be appropriate for coupling the WRF QPF. For this reason, considering the Liuxihe model is a physically based distributed hydrological model, the parameters were optimized again by using the WRF QPF flood event no. 2011. Hence, the WRF QPF is the post-processed one, not the original one. Results of parameter optimization are shown in Fig. 6. Among them, (a) is the objective function evolution result, (b) is the parameter evolution result, and (c) is the simulated flood process by using the optimized model parameters. To compare, the simulated flood process of flood event no. 2011 was also drawn in Fig. 6c.

From the result of Fig. 6c, it may be seen that the optimized model parameters with the WRF QPF improved the flood simulation when compared to the corresponding flood simulation based on gauge precipitation. This means parameter optimization with the WRF QPF is necessary.

When the Liuxihe model set up for LRB flood forecasting (Chen et al., 2017) was employed to couple with the WRF QPF, the model spatial resolution remained 200 m × 200 m. As the spatial resolution of the WRF QPF is 20 km × 20 km, the WRF QPF was downscaled to the resolution of 200 m × 200 m by using the nearest downscaling method, the same spatial resolution of the flood forecasting model.

The original WRF QPF and the post-processed QPF were used to couple with the Liuxihe model. In this simulation, the original model parameters that were optimized with the rain gauge precipitation were employed, not the re-optimized model parameters. The simulated results are shown in Figs. 7–9.

From the above results, it could be seen that the simulated flood discharges with the original WRF QPF are much lower than the observed ones. But with the post-processed WRF QPF used, the simulated flood discharge increased and became much closer to the observation. This implies that the flood forecasting capability has been improved by post-processing of the WRF QPF. To further compare the three results, five evaluation indices, including the Nash–Sutcliffe coefficient (C), correlation coefficient (R), process relative error (P), peak flow relative error (E) and water balance coefficient (W), were calculated and listed in Table 2.

From the results of Table 2, it has been found that all five evaluation indices have been improved by coupling the post-processed WRF QPF. For example, for flood event no. 2011 with 24 h lead time, the Nash–Sutcliffe coefficient/C, correlation coefficient/R, process relative error/P, peak flow relative error/E and coefficient of water balance/W with the original WRF QPF are 0.65, 0.88, 35, 14 % and 1.44, respectively, but those with the post-processed WRF QPF are 0.75, 0.93, 23, 8 % and 1.15, respectively. For flood event no. 2012 with 48 h lead time, the above five evaluation indices with the original WRF QPF are 0.63, 0.75, 48, 12 % and 1.43, respectively, and are 0.75, 0.84, 26, 8 % and 1.32, respectively, with the post-processed WRF QPF. For flood event no. 2013 with 72 h lead time, the above five evaluation indices with the original WRF QPF are 0.44, 0.75, 129, 45 % and 1.66, respectively, and are 0.55, 0.82, 98, 23 % and 1.25, respectively, with the post-processed WRF QPF. It is obvious that with the post-processed WRF QPF, the evaluation indices are improved substantially. These results show that WRF QPF post-processing could improve the flood forecasting capability because the WRF QPF is closer to the observed precipitation after post-processing. So it should be practiced for real-time flood forecasting.

The model parameters optimized with rain gauge precipitation and the WRF QPF are different, so different parameter values will result in different model performances. To analyze this effect, the flood events no. 2012 and no. 2013 with two different sets of model parameter values are simulated, and are shown in Figs. 10 and 11, respectively. Only the post-processed WRF QPF is coupled in this simulation.

From the above figures it may be that the simulated flood results with re-optimized model parameters are better than those simulated with the original model parameters. The simulated flood discharge with the re-optimized model parameters matches the observed discharge. To further compare the two results, five evaluation indices, including the Nash–Sutcliffe coefficient (C), correlation coefficient (R), process relative error (P), peak flow relative error (E) and water balance coefficient (W), are calculated and listed in Table 3.

From the results of Table 3, it is found that the results of flood simulation based on the re-optimized model parameters have better evaluation indices. All evaluation indices for those based on re-optimized model parameters are improved. For example, for flood event no. 2012 with 24 h lead time, the Nash–Sutcliffe coefficient/C, correlation coefficient/R, process relative error/P, peak flow relative error/E and coefficient of water balance/W with the original model parameters are 0.58, 0.82, 35, 12 % and 1.08, respectively, but those with the re-optimized model parameters are 0.74, 0.86, 28, 8 % and 0.95, respectively. For flood event no. 2013 with 48 h lead time, the five indices with the original model parameters are 0.62, 0.86, 22, 13 % and 1.24, respectively, and are 0.68, 0.89, 18, 9 % and 1.06, respectively, for those with re-optimized model parameters. So it could be said that in coupling the WRF QPF with a distributed hydrological model, the model parameters need to be re-optimized with the WRF QPF. This finding implies that the precipitation pattern has an obvious impact on model parameters. It should be considered, and model parameter optimization is a rational way to consider this effect.

To compare the model performance with different lead times, the flood events with three different lead times are simulated and shown in Fig. 12. The model parameters are the re-optimized ones, and the QPF is the post-processed QPF.

From the results of Fig. 12, it could be seen that the flood simulation result gets worse as the lead time increases; i.e., the model performance with 24 h lead time is better than that with 48 h lead time, and the model performance with 48 h lead time is better than that with 72 h lead time. The simulated hydrological process with 24 h lead time is very similar to that simulated with rain gauge precipitation. To further compare the results, five evaluation indices, including the Nash–Sutcliffe coefficient (C), correlation coefficient (R), process relative error (P), peak flow relative error (E) and water balance coefficient (W), were calculated and listed in Table 4.

From the results of Table 4, it is found that the simulated flood events with 24 h lead time have the best evaluation indices, and are very close to those simulated with rain gauge precipitation. For flood event no. 2012, the Nash–Sutcliffe coefficient/C, correlation coefficient/R, process relative error/P, peak flow relative error/E and coefficient of water balance/W with the rain gauge are 0.82, 0.89, 20, 5 % and 0.8, respectively, while those with 24 h lead time are 0.74, 0.86, 28, 8 % and 0.95, respectively, those with 48 h lead time are 0.63, 0.84, 48, 12 % and 1.32, respectively, and are 0.56, 0.56, 56, 18 % and 1.54, respectively, for 72 h lead time. For flood event no. 2013, the Nash–Sutcliffe coefficient/C, correlation coefficient/R, process relative error/P, peak flow relative error/E and coefficient of water balance/W with the rain gauge are 0.95, 0.92, 8, 6 % and 1.08, respectively, while those with 24 h lead time are 0.87, 0.87, 9, 12 % and 1.02, respectively, those with 48 h lead time are 0.62, 0.86, 22, 13 % and 1.24, respectively, and are 0.61, 0.87, 75, 17 % and 1.66, respectively, for 72 h lead time. This finding means that the current WRF QPF capability is lead-time-dependent, and with the increasing lead time, the practical value of the WRF QPF gets lower.