A DRR model was applied to the Kasahori dam catchment. The DRR model applied is that originally developed by Kojima and Takara (2003) called CDRMV3. The details of this DRR model can be seen in the work by Apip et al. (2011). In the DRR model, the surface and river flows are simulated using a 1-D kinematic wave model. The subsurface flow is simulated using a q–h relationship developed by Tachikawa et al. (2004). The schematic of the q–h relationship is shown in Fig. 7, where q is the discharge per unit width and h is the water depth, as shown in Fig. 7a. The mathematical expression is as follows: qh=vmdmhdmβ,(0≤h≤dm)vmdm+va(h-dm),(dm<h≤da)vmdm+va(h-dm)+α(h-da)m,m=53,(da<h), where vm=kmi, va=kai, α=i/Nslope, and D is the thickness of the layer, shown in Fig. 7a; da-dm is the area of the saturated flow; dm is the area of unsaturated flow; vm is the unsaturated flow velocity; km is the hydraulic conductivity in dm; i represents the slope gradient; va is the saturated flow velocity; ka is the hydraulic conductivity in da-dm; and Nslope represents the equivalent roughness coefficient of the slope. βkm=ka needs to be satisfied to establish the continuity of the q–h relationship. The initial discharge Qi is set at the catchment outlet of the river. Normally Qi is the observed discharge in the beginning of the simulation. Then, the Qi is converted to the water depth h in each grid of the entire catchment depending on the ratio of the flow accumulation value for the particular grid and the flow accumulation value at the outlet. Thus, before the simulation, all the grids already have the initial water depth hi depending on Qi. This could be considered as the base flow in the model concept. As mentioned in Sect. 4, the parameters of the DRR model are identified using the RC. The equivalent roughness coefficient of the forest, the Manning coefficient of the river, and identified soil-related parameters are described in Table 1.

Two 11-member ensemble forecasts with different horizontal resolutions (10 and 2 km) were conducted for the 2011 Niigata–Fukushima heavy rainfall event using JMA-NHM (Saito et al., 2006; Saito, 2012) as the forecast model. The 10 km ensemble prediction system (EPS) uses the JMA's operational mesoscale 4D-Var analysis of 12:00 UTC (21:00 JST) on 28 July and the JMA's global spectral model (GSM) forecast from the same time as the initial and boundary conditions of the control run, respectively. As for the initial and lateral boundary conditions, perturbations from the JMA's 1-week global ensemble prediction from 12:00 UTC (21:00 JST) on 28 July were employed, whose detailed procedures are given in Saito et al. (2010, 2011). The 2 km EPS is a downscaling of the 10 km EPS with a 6 h time lag, using the forecasts of the 10 km EPS as the initial and boundary conditions (Fig. 8).

The bulk method that predicts the mixing ratios of six water species (water vapor, cloud water, rainwater, cloud ice, snow, and graupel) and the number density of cloud ice was adopted as the cloud microphysical process. The 10 km EPS applied the modified Kain–Fritsch convective parameterization scheme, while the 2 km EPS did not use convective parameterization. Other physical processes of the two systems were almost the same to those of the operational mesoscale model and the local forecast model of JMA (JMA, 2013b). The verification of the statistical performance of similar double-nested EPSs has been given by Duc et al. (2013).

Figure 9 (upper left) shows the 3 h accumulated rainfall from 12:00 to 15:00 JST (21:00 to 24:00 JST) by the control run of the 10 km EPS. Although the maximum value of the predicted rainfall (74 mm) is somewhat weaker than the observation (right panel of Fig. 1), the region of intense rainfall is simulated well. The upper right panel of Fig. 9 indicates the forecast by each member of the 10 km EPS. Seemingly, the result of each ensemble member resembles the others, and the basic characteristic features of the observed rainfall are simulated well. The maximum rainfall was obtained by member p02 (89 mm). A common feature seen in these figures is that weak fake rainfall appears over the coastal region facing the Sea of Japan, which is likely produced by the Kain–Fritsch convective parameterization.

Figure 9 lower panels shows the corresponding results by the 2 km EPS. The concentration of intense precipitation is produced more clearly, the maximum rainfall of which reaches 237 mm. The areas of weak rainfall over the western coastal region, appearing in Fig. 9 upper panels, no longer develop because of the removal of the convective parameterization. A detailed analysis of the two EPSs (ensemble spread and fraction skill scores) and the result of a sensitivity experiment to the orography have been presented by Saito et al. (2013a).

The inflow to the Kasahori dam is simulated using the DRR model. The RG, RC, and RR data are used as the inputs to the runoff simulations. The three hydrographs with the parameters identified by the RC are shown in Fig. 10. The simulated hydrograph with the RC rainfall is in relatively good agreement with the observations, which is to be expected because the model parameters are calibrated against the RC rainfall. Using a straight line method for the base flow separation, the total discharge with RC in mm becomes 556.3 mm while the total rainfall is 568.5 mm.

The simulated hydrographs for the other two rainfalls are larger than the observations. We do not address the magnitude of the relationship in this paper because it is not possible to determine more accurate rainfall data. The RG, RC, and RR measurements all have strengths and weaknesses; however, we focus on the consideration of RC for use because of the frequency of the data, i.e., 10 min interval.

Using the ensemble rainfalls from JMA-NHM, explained in Sect. 5.2, the ensemble flood simulation focusing on the Kasahori dam catchment was performed. A flowchart is shown in Fig. 11 to explain briefly again the overall procedure of the methodology for the ensemble simulations used in the paper.

The catchment-averaged ensemble rainfalls obtained from the 10 and 2 km resolution NHM are shown in Fig. 12. Figure 12 (upper) shows the control run and five negatively perturbed members, m01–m05 (m indicates minus), and five positively perturbed members, p01–p05 (p indicates positive), for the 10 km resolution.

It is apparent from the figure that the magnitude of the 10 km resolution ensemble rainfall is basically lower than the RC rainfall. Thus, the dam inflows, obtained from the RC parameters in Table 1 with the 10 km resolution ensemble rainfall, lead to lower magnitude discharge compared with the ground observations (shown later in the paper).

Figure 12 shows the control run, m01–m05, and p01–p05 for the 2 km resolution NHM. The figures reveal that the first peak in the 2 and 10 km resolution ensemble simulations appears 2–4 h earlier than that in the observation. The magnitudes of some 2 km resolution ensemble rainfalls are equivalent to that of the RC rainfall. Thus, dam inflows using the RC parameters in Table 1 with the 2 km resolution ensemble rainfall can indicate discharge with equivalent magnitude (shown later in the paper). Figure 13 shows the spatial patterns of the cumulative ensemble rainfalls from 03:00 JST on 29 July 2011 to 03:00 JST on 30 July 2011 by the 11 ensemble simulations (upper: 10 km resolution; lower: 2 km resolution). The figures indicate that the 2 km resolution NHM rainfalls are apparently larger than the 10 km resolution rainfalls. Tables 2 and 3 show the cumulative and maximum hourly rainfalls from the 10 and 2 km resolution NHMs, respectively, averaged over the Kasahori dam catchment, which show that the 10 km resolution rainfalls are smaller than the 2 km resolution rainfalls. The maximum cumulative rainfall of the 2 km resolution NHM is realized in p02: 175.5 mm. Table 2 also shows the average cumulative rainfalls of both the 10 and 2 km resolution NHMs. The average cumulative rainfall in the 2 km resolution NHM is greater than in the 10 km resolution NHM. With regard to the maximum hourly rainfall in Table 3, p02 shows the highest values in both the 10 and 2 km resolution NHMs. The maximum hourly rainfall in the 2 km resolution NHM is also greater than that in the 10 km resolution NHM. This tendency is also true in the average maximum hourly rainfall shown in Table 3.

Figure 14 (upper) shows the simulated inflow to the Kasahori dam with the control run and positively/negatively perturbed rainfalls of the 10 km resolution NHM. Figure 14 (upper) shows that all the inflows to the Kasahori dam are lower than the observations; however, these inflows exceed the flood discharge of 140 m3 s-1, which is the threshold for the flood control operation (see Sect. 3 for the details of the operation).

Figure 14 (lower) shows the simulated discharge with the 2 km resolution ensemble rainfalls. Figure 14 (lower) shows that at least the first peak of the dam inflow in p02 shows a comparable value with that of the observed inflow; the peak discharge of the observation is 843 m3 s-1, whereas it is 779 m3 s-1 with the p02 of the 2 km resolution NHM. However, the occurrence of the first peak in the simulation is 4 h earlier than indicated by the observations. The fact that one of the ensemble flood discharges with the 2 km resolution NHM shows approximately equivalent magnitude of discharge with the observed first peak discharge, despite the forward shift in occurrence time, implies that the ensemble flood prediction with the 2 km resolution NHM could potentially be used as a reference in dam operations, although the discharge reproduction is still not fully satisfactory both in quality and quantity. The ensemble flood simulations with the 10 km resolution NHM could not reproduce the peak at all. Moreover, the first peak of the simulated inflow with the control run of the 2 km resolution NHM attains only 614 m3 s-1. A single value from a deterministic (i.e., control run only) NWP (i.e., prevailing prediction) might fail to capture a realistic discharge, whereas ensemble simulations produce additional prediction ranges that cover the higher observed discharge values.

In the actual operation of the Kasahori dam, the dam gate opening is fixed once the inflow exceeds 140 m3 s-1. The dam inflows from the control run and the other 10 ensemble rainfall predictions of both the 2 and 10 km resolution NHMs all predict that the dam inflow is above the flood discharge threshold (i.e., 140 m3 s-1). The single weather simulation produces solely a deterministic value, which does not reflect the uncertainty of the initial conditions, whereas ensemble simulations enhance confidence in the prediction by incorporating the uncertainty. The exceedance probability of 11/11 by the ensemble simulations is numerically the same as the probability of 1/1 by a single simulation. However, the physical implications of these two values are different in terms of confidence and significance.

All the dam inflow simulations, however, show that the second and third peaks of the inflow are much smaller than indicated by the observations. In the actual flood event, the so-called Tadashigaki operation was implemented at around the time of the second and third peaks. In the Tadashigaki operation, the dam outflow has to equal the inflow to avoid dam failure as the water level approaches overtopping of the dam body. The runoff simulations did not reproduce such a critical situation this time because the second and third discharge peaks are not properly reproduced. This is a deficiency of the ensemble forecast method at this time. The accumulated inflow volume to the dam of both the observation and 2 km ensemble simulation from 03:00 JST, 29 July 2011, to 03:00 JST, 30 July 2011, is shown in Fig. 15. It can be seen that the inflow volumes are somehow comparable with the observations until the first peak is observed, though the discrepancy becomes larger afterwards. This will cause critical hardship for dam operation if the ensemble flood prediction were used in isolation, especially after the first peak.

Numerical weather prediction have inevitable forecast errors. The current case has a large amount of accumulated rainfall within a limited area and is sensitive to the position error. Although ensemble simulation represents the uncertainty to some extent, the ensemble spread tends to be under-dispersive because of imperfect model/initial condition representations and limited ensemble sizes. Duc et al. (2013) verified the spatial–temporal fractions skill score of 10 km/2 km ensemble forecasts for heavy rainfall events occurring over central Japan from 3 July 2010 to 2 August 2010. They showed that a spatial scale of 60 km (positional lag of 30 km) should be considered to obtain a reasonable reliability from a high-resolution ensemble forecast. Thus, it is important to take into account the position error within a reasonable distance before input to the runoff model.

To improve the ensemble rainfalls in quantity and timing, the cumulative rainfalls of each ensemble member are calculated and the rain distribution is translated within 30 km from the original position so that the catchment-averaged cumulative rainfall for the Kasahori dam maximizes. The analysis is carried out using the 2 km resolution, 30 h rainfall after the simulation. This position change corresponds to consideration of a 30 km positional lag to detect a risk of the maximum rainfall amount. Figure 16 shows the examples of the position shifts for cntl, m02, p03, and p04. Although the ensemble forecasts produce high cumulative rainfall, the original peak lies to the south of the Kasahori dam in all four members shown in Fig. 16. Figure 17 shows the spatial distribution of the position-shifted cumulative ensemble rainfalls with the 2 km resolution. Comparing Figs. 13 and 17, it is apparent that the rainfall intensity becomes higher. The simulated discharges with these position-shifted rainfalls are shown in Fig. 18. Figure 18 indicates that the first peak discharge simulated becomes high enough compared with the observed discharge. Timing of the first peak is also improved, and, in particular, some members reproduce the exact timing. Figure 18 shows the ensemble mean of the discharge as well since the ensemble mean becomes more informative compared to that in the experiment without position shifting. Figure 19 shows the inflow volume into the reservoir based on the observation and position-shifted ensemble simulations; the simulated inflow volume becomes comparable to the observed inflow volume. These results indicate that the ensemble rainfall simulation with position shift brings better performance although testing with more cases is desirable to confirm that.

As indicated in Sect. 5.2, it is known that ensemble weather simulations can be useful in adding value to weather forecasts. In the current operational weather forecasting, it is not necessarily expected that the weather will be predicted accurately for any specific location. However, accurate prediction over dam catchments is the main concern of river dam administrators. In this regard, this paper shows clearly that although the original 2 km prediction forecast provides much better results than that with the 10 km resolution prediction, greater accuracy is still desirable. For example, in dam/reservoir operations, the reliable prediction of the peak timing, flood duration, and runoff volume is extremely important parameters necessary to avoid erroneous operation. The results with original ensemble rainfalls here do not match the current requirements; however, the position-shifted 2 km resolution ensemble rainfall could be a useful tool for supporting operational decisions after statistical validation with various rainfall events, which would not be possible based on previous simulations with coarser resolutions.