Real-time flash flood forecasting approach for development of early warning systems: integrated hydrological and meteorological application

Abstract This study proposes an integrated hydrometeorological modelling framework approach and methodology for flash flood Early Warning Systems in the Chugoku region of Japan. Unprecedented rainfall-induced hydrometeorological disasters and flash floods are increasingly occurring worldwide. Comprehensive efforts are conducted to simultaneously combine multiple disciplines into integrated modelling framework approaches to reduce disaster resilience. This enables more accurate hindcasts, reanalyses, real-time forecasts or nowcasts for flash floods. This study integrates proposed hydrological calibration approach with meteorological input. Two real-time rainfall forecasts by the Weather Research and Forecasting model forced by the Atmospheric Reanalysis v5 (ERA5) and the Japanese 55-year Reanalysis (JRA55) were used as input data to the hydrological model ensemble parameterized previously. This approach was applied to seven major rivers to evaluate river discharges real-time forecasts accuracy during the Heavy Rainfall Event of July 2018. Long lead-times of up to 29 h with a satisfactory reproducible range of Nash-Sutcliffe Efficiency were obtained using both meteorological forecast for all rivers cumulatively. This indicates that the proposed integrated hydrometeorological approach enables accurate flash flood real-time forecasting for this event. Similarly, the joint hydrometeorological approach enables framework for development of real-time flash food forecasting application in Japan and presumably worldwide. HIGHLIGHTS Development of integrated hydrometeorological river discharge forecasts in real time. This study integrates hydrological ensemble calibration and meteorological forecasts. Weather Research and Forecasting (WRF) outputs with ensemble hydrological parameters. Long lead-times of 29 h with satisfactory accurate reproducibility were obtained. Our integrated hydrometeorological approach enables accurate river discharge nowcasts.


Challenges in real-time forecasting of hydrometeorological disasters
Global mean temperature has increased by around 1 � C above pre-industrial levels (IPCC 2018) and climate change now presents one of the most serious and immediate threats to human wellbeing.The unprecedented increase in the number and magnitude of natural disasters associated with extreme precipitation, such as floods and flash floods due to climate change, leads to devastating societal and economic consequences worldwide.The rate of occurrence of extreme precipitation events and floods is now four times higher than in the 1980s (UNESCO, UN Water 2020).Regionally, future river discharges are expected to increase in highly-urbanized basins of Japan.Mori et al. (2021) projected that the 200-year future annual maximum 24-h rainfall is about 1.3-1.4times larger than the historical and consequently the annual maximum river discharge is about 1.5-1.7 times larger over Japan, resulting in a significant increase of flood risk with large variability.
Many studies have been conducted in order to understand the synoptic-scale pattern, atmospheric driving factors and convective systems of the flash flood events over different regions across the globe (e.g.Ranalkar et al. 2016;Olsson et al. 2017;Takemi 2018;Tsuguti et al. 2019;Nayak and Takemi 2021).Torrential rainfall events generally occur due to the organization and maintenance of stationary connective systems (Takemi 2018) and/or the prolonged concentration of very moist airstreams (Nayak and Takemi 2021).The prominent moisture flux convergence and well-developed moist conditions mainly maintain the heavy rainfall events over downpour affected areas (Nayak and Takemi 2021).Although a flood event at a place depends on many factors as stated above, the torrential rainfall events that caused flooding depend on its dynamic and thermodynamic features such as wind speed and direction, moisture content, temperature etc. which characterize the maintenance of intense rainfall.Thus, the atmospheric models are used to understand these factors from a mesoscale point of view.Weather Research and Forecasting (WRF) model, one of the atmospheric models, is widely used for real-time forecasting around the world.Its performance is well recognized in simulating the convective rainfalls that caused flash floods and/or landslides due to unstable atmospheric conditions.Simultaneous integration of atmospheric model outputs as inputs in hydrological modelling to be applied in a real-time forecasting framework faces numerous challenges mostly in terms of both meteorological and hydrological uncertainties, spatiotemporal resolutions, and the applied approach of meteorological forecasts (deterministic or ensemble).
Hydrometeorological real-time forecasting (also referred to as nowcasting), which involves the integration of meteorological forecasts into hydrological models, plays a considerable role in the mitigation of negative climate impacts as a tool to predict extreme river water levels and discharges before and during flooding events and has therefore significant potential to contribute to the development of flash flood Early Warning Systems (EWS).Kuang and Liao (2020) emphasized increasing needs for approaching flood disasters management by learning-based approach from past events and experiences using multidisciplinary frameworks.Dimri et al. (2016) comprehensively reviewed atmospheric and land surface processes generating floods in Himalayas and found that a catastrophic flooding was caused by the simultaneous peaking of floods in the Ganges and Brahmaputra Rivers, emphasizing the necessity of developing a robust real-time flood forecasting framework.However, hydrometeorological forecast uncertainties, largely due to errors in precipitation forecasts especially with longer leadtimes, represent fundamental challenges towards the development of EWS (Cuo et al. 2011;Hapuarachchi et al. 2011;Emerton et al. 2016;Adams and Dymond 2019).Nonetheless, several flash flood EWS have been successfully developed and implemented worldwide to produce warnings at regional scale (Corral et al. 2019) including the European Flood Awareness System (EFAS; Thielen et al. 2009;www.efas.eu)and the US National Weather Service Flash Flood Guidance system (FFG; Clark et al. 2014), which has been extended to the Global Flash Flood Guidance system (GFFG) covering other regions (Georgakakos 2018).As flash floods are characterized by sudden, rapid increases in flood peaks due to high-intensity rainfalls (Georgakakos 1986), the ongoing development of EWS is crucial in the effort to improve disaster reducing policies which allows reducing human casualties, economical and ultimately societal damages from disasters.

Recent modelling advancements on forecasting heavy rainfall disasters
The increasing importance of developing more sophisticated hydrometeorological approaches and methodologies for natural disaster risk reduction is emphasized in Sahani et al. (2019).Many recent studies (Alfieri et al. 2012;Huang et al. 2012;Hsiao et al. 2013;Alfieri et al. 2014;Brown et al. 2014;Demargne et al. 2014;Yang et al. 2015;Jhong et al. 2017;Chang et al. 2018;Adams and Dymond 2019;Berkhahn et al. 2019;Corral et al. 2019;Silvestro et al. 2019;Tien Bui et al. 2019;Roux et al. 2020;Wijayarathne and Coulibaly 2020;Wu et al. 2020;Zhai et al. 2021) have used various hydrological or hydrometeorological approaches to develop real-time forecasting or nowcasting models worldwide.They applied deterministic and ensemble approaches with regards to only meteorological modelling, where ensemble approaches usually showing better performance.However, to our best knowledge, ensemble forecasts with such analogical approach have not yet been applied with regards to hydrological modelling, particularly to its parameter calibration.Development of methodology for conducting such ensemble parameter calibration approach to hydrological modelling is the main scientific contribution from Tro� selj et al. (2023), whereas applying such approach to a hydrometeorological real-time flash flood forecasting framework for development of EWS is proposed and discussed in this study.
Spatial and temporal resolutions for meteorological models applied as input data in integrated hydrometeorological forecasting typically range between 2.5-20 km and 1-6 h, whereas for hydrological simulations temporal resolutions are in range of 1-hourly, 3-hourly and 6-hourly or 12-houry data while spatial resolutions from 200 m to 5 km are commonly applied (Alfieri et al. 2012;Hsiao et al. 2013;Liechti et al. 2013;Yang et al. 2015;Li et al. 2017;Corral et al. 2019;Roux et al. 2020;Wijayarathne and Coulibaly 2020;Wu et al. 2020).Scholars have reported reasonable model performances of deterministic hydrometeorological flood forecasts with various lead-times.Liechti et al. (2013) derived Nash-Sutcliffe Efficiency (NSE) values of 0.14 � NSE � 0.71 by applying deterministic precipitation input data to a semidistributed rainfall-runoff model, and Wijayarathne and Coulibaly (2020) reported Kling Gupta Efficiency (KGE) values of 0.42 � KGE � 0.75 for deterministic hydrometeorological forecasts with 24-h lead-times of five hydrological models with varying complexity.However, NSE and KGE values bigger than 0.7 are generally considered satisfactory in terms of forecasting performance, thus a methodology and knowledge gap for the enhancement of model performances as well as lead-times is apparent and both meteorological and hydrological experts put large efforts to contribute towards proposing improved methodologies.
In July 2018, an unprecedented rainfall-induced disaster resulting from the interaction of Typhoon Prapiroon with the seasonal Baiu rain front occurred in western Japan, resulting in 224 casualties, 8 missing people and 459 injured people (JMA 2018).On the particular study site, several meteorological studies conducted for this Heavy Rainfall Event of July 18 (HRE18) estimated extreme rainfall events occurrence in future to be of a similar scale as that of the HRE18.Osakada and Nakakita (2018) and Nayak and Takemi (2020) estimated that the intensity and frequency of extreme precipitation associated with the HRE18 and Baiu heavy rainfall will increase under a warming climate in the future.Therefore, developing models for the real-time forecasting of such rainfall-induced disasters is increasingly important in comprehensive meteorological, hydrological and coastal ocean contexts.Developing robust and accurate real-time meteorological forecasting tools is a first step towards conducting associated integrated hydrolometeorological forecasts.Several studies (Enomoto 2019;Kotsuki et al. 2019;Oizumi et al. 2019;Nayak and Takemi 2020;Ono et al. 2020;Nayak and Takemi 2021) have developed meteorological forecasts for the HRE18.
Recently, there has been an increasing trend towards the development of methodologies that can extend lead-times of hydrometeorological real-time forecasts.Lead-times most commonly applied by scholars for hydrometeorological ensemble forecasting lie within the short (i.e. less than 48 h) and medium (i.e. between 3 and 15 days) range (Wu et al. 2020).While the implementation of deterministic meteorological forecast inputs into hydrometeorological real-time forecasts is generally less challenging due to less complex data pre-and post-processing requirements, its performance compared to ensemble meteorological forecasts is usually lower (Cloke and Pappenberger 2009;Pappenberger et al. 2015;Siddique and Mejia 2017;Roux et al. 2020).Moreover, ensemble forecasts are more advantageous in terms of decision support system efficiency and therefore highly relevant to early-warning decision makers (Ferretti et al. 2020).Liechti et al. (2013) obtained considerably more accurate forecast performances for two flash flood events when using radar ensemble meteorological input, which added significant value and advantages over forecasts with deterministic meteorological input in their hydrological model.Therefore, future technological as well as methodological advancements regarding the accuracy of deterministic forecasts are necessary to allow for a more straightforward implementation and operation of EWS.Additionally, ensemble forecasting, as an alternative to deterministic forecasting, can offer ways to increase model performance for longer lead-times while better representing forecast uncertainties by producing multiple possible forecast outcomes.This enables estimation of their occurrence probability for effective risk management and it is therefore suggested that deterministic quantitative precipitation forecasts are replaced by ensemble methods in hydrometeorological forecasting (Adams and Dymond 2019;Zhong et al. 2019;Ferretti et al. 2020;Roux et al. 2020;Sayama et al. 2020;Wu et al. 2020).However, deterministic meteorological forecasts are still more readily available worldwide than ensemble forecasts, thus proper approach and methodology for developing real-time forecasting Early Warning System is desirable to be first established with a deterministic forecasts, and later eventually upgraded and extended to an ensemble forecast.

Objectives, hypothesis and new contributions of this study
This study investigates optimal range of hydrometeorological real-time forecasting lead-times which can reproduce and forecast a satisfactorily accurate river discharge hydrographs for the implementation into the flash flood Early Warning Systems in the Chugoku Region of Japan.In particular, the specific questions addressed in this study can be summarized as follows: 1. How accurately can our integrated hydrometeorological framework reproduce the river discharges from the HRE18, with various initial real-time forecasting leadtimes?2. How long lead-times from our meteorological forecasts until the peak of a river discharge hydrograph can be reproduced with satisfactory accuracy?3. How can our findings be used for real-time forecasting a flash flood river discharges from extreme future rainfall events?
We hypothesize that combination of ensemble calibrated river basin parameters of hydrological models from several historical extreme discharge events of similar scale and forecasted meteorological data can accurately predict river discharge hydrographs of extreme rainfall-induced future events in real time before the flood.

Materials and methods
The ensemble hydrological parameter calibration methodology and approach as developed in the Tro� selj et al. ( 2023) was applied to every river.The observed hourly rainfall data were collected from the online database of the Japan Meteorological Agency (JMA 2020) as point data from all rain gauges of the associated river basin with available published data.The observed discharge data were collected from the online database of the Ministry of Land, Infrastructure, Transport and Tourism (MLIT 2020).After calibration and validation of the hydrological model, real-time forecasted meteorological rainfall output data with various lead-times were used as input to the hydrological model instead of the observed rainfall data to show applicability of the proposed methodology to EWS.
The materials and datasets used for conducting hydrological modelling hindcasts and parameterizations are explained in details in Tro� selj et al. ( 2023), while those for meteorological modelling in Nayak and Takemi (2021).Hereafter, we will introduce study site and explain applied hydrological and meteorological model configuration methodologies, as well as methodology of their integration into an integrated hydrometeorological framework.

Study sites
The extreme river discharges from the HRE18 in the Chugoku region of Japan were projected for all seven first-class river basins flowing into the Seto Inland Sea.From east to west, these rivers are the Saba, Oze, Ota, Ashida, Takahashi, Asahi, and Yoshii Rivers.Arranged by the catchment area of the station farthest downstream with observed discharge data, these rivers are classified as follows: Takahashi (2644 km 2 ), Yoshii (1996 km 2 ), Asahi (1587 km 2 ), Ota (1527 km 2 ), Ashida (798.8 km 2 ), Saba (423.1 km 2 ) and Oze (323 km 2 ).The total spatial distance from the eastern (Saba) to the western (Yoshii) river basin is approximately 300 kilometres.Supplementary Material A shows the Digital Elevation Model (DEM) of the seven targeted river basins, their associated mean centres, locations of the observed and simulated discharges near the river mouths, information on the position of the study domain within Japan, Typhoon Prapiroon's track, and observed rainfall of all seven rivers during the HRE18 at their mean rainfall centres.JMA rainfall averaged for all river basins for the seven modelled days during the HRE18 are shown on the lower right corner of the Supplementary Material A.

Hydrological model
The hydrological Cell Distributed Runoff Model version 3.1.1(CDRM) (Kojima et al. 1998;Sayama et al. 2003;Tachikawa et al. 2004;Sayama and McDonnell 2009;Apip et al. 2012;Luo et al. 2014;Sasaki 2014;Troselj et al. 2017;Tro� selj and Lee 2021;Tro� selj et al. 2023), calibrated by the Shuffled Complex Evolution optimization method developed at the University of Arizona (SCE-UA; Duan et al. 1992;Sorooshian et al. 1993;Duan et al. 1994;Harada et al. 2006;Sasaki 2014;Troselj et al. 2017;Tro� selj and Lee 2021;Tro� selj et al. 2023) was applied to the seven first-class rivers in the Chugoku region of Japan at a spatial resolution of approximately 500 m (15 arc-sec) and a 1 h time step.River discharges were in principle simulated for the most downstream discharge stations with available observed data records.The detailed process of obtaining the river discharge data and choosing the corresponding observation station location is described in more detail in Tro� selj and Lee (2021).
However, if tidal effects were great enough to reduce observed data reliability, then the closest upstream discharge station without a significant tidal effect was selected as the observation and simulation location (hereafter, river mouth).The particular river mouth location for each river is noted in the corresponding results section for that river.
The surface flow of each individual cell in the CDRM model is represented by Equation (1) and calculated by the Kinematic Wave method (Tachikawa et al. 2004;Sayama and McDonnell 2009;Sasaki 2014;Tro� selj and Lee 2021;taken from Tro� selj et al. 2023).
where q is the discharge per unit width, h is the water depth, r e is the effective rainfall, S is the slope gradient, N is the equivalent roughness, and m is the slope constant.
The slope S is obtained from the DEM, while the equivalent roughness N is generally a value or observation in the Kinematic Wave method, where it is treated as a model parameter by setting an upper limit.The relationship between q and h with applied parameterization simplifications in the 5 Calibrated Parameter Method (5-CPM) and without applied parameterization simplification in the 7 Calibrated Parameter Method (7-CPM) is graphically represented in Supplementary Material B, alongside with its relationship with Equation (1).This relationship enables us to track the rainwater propagation speed in combination with the continuous basic equation (Equation (1)).The very detailed model configurations related to the Supplementary Material B and the Equation (1) are explained in (Sayama and McDonnell 2009;modified from Tro� selj et al. 2023).
In post-processing, five (for 5-CPM) or seven (for 7-CPM) parameter sets provided one model run for one event.Total number of simulated events was six for extreme events different than HRE18, and the HRE18 was also simulated.Then, the six river discharge hydrographs different than the HRE18 formed ensemble averaged hydrographs used for validation, while the HRE18 was used for calibration.Here, intuitive expectation is that HRE18 will often have superior model performance than other six ensemble averaged events because the model parameters were optimized using the same rainfall data as in validation, which is not the case for the other six events where optimization was conducted using rainfall data from the particular event and validation was conducted using the HRE18 rainfall data.This process was described in very detail in Tro� selj et al. ( 2023), which is a predecessor of this study.Finally, the most important innovation of this study, compared to the predecessor study is the real-time meteorological input by two models (see below), with each 3-h lead-times used as input to each of these seven calibrated parameter sets, and showing maximal lead-times which have satisfactorily good predictive accuracy (NSE > 0.7).

Meteorological model
The Advanced Research WRF model version 4.0 (Skamarock et al. 2008) was configured with two-way nested two-domains at a resolution of 500-1000 m in the innermost domain and at a resolution of 5 km in the outer domain (Nayak and Takemi 2021).The initial and boundary conditions were forced on two ways, (1) from fifth generation of European Centre for Medium-Range Weather Forecasts (ECMWF) Atmospheric Reanalysis v5 (ERA5) at a 30 kilometres resolution and (2) from Japanese 55-year Reanalysis (JRA55, Kobayashi et al. 2015) at a 1.25 � (�55 km) resolution (Nayak and Takemi 2021).Six numerical experiments were conducted with deterministic approach, with initial times of 5 July 2018 at 3 pm Japan Standard Time (JST) and each subsequent 6 h interval until 7 July at 3 am JST.All meteorological experiments were conducted at least until 10 July 2018 at 00 am JST, so that their output would allow to be applied as input to the CDRM hydrological model for the entire analysed time span.The meteorological experiments are hereafter referred according to their initial time as 0515, 0521, 0603, 0609, 0615 and 0621, where the former two digits indicate the initial date (06 ¼ 6 July 2018) while the latter two digits indicate the initial hour (21 ¼ 9 pm) of the experiments.The meteorological forecasts were conducted in the Coordinated Universal Time (UTC) zone but converted to the JST zone in meteorological post-processing and used as JST throughout the whole study.The model physics used during these experiments includes the Kain-Fritsch cumulus scheme for the outer domain only, the WRF single moment six-class microphysics scheme, and the Yonsei University planetary boundary scheme.No cumulus convection scheme was used for the innermost domain with resolution of 500-1000 m.In addition, the spectral nudging technique was applied to incorporate the synoptic-scale influences for the outer domain.The rainfall amounts were produced for each experiment at every hour and applied as an input to the CDRM after validating the modelled results against the observations available over the flooded region, as described in more detail in Nayak and Takemi (2021).Every experiment results were modelled and analysed separately in the hydrometeorological framework to understand the uncertainty in the flood warning system.Only the 0521 experiment was discarded from the interpretation of results because its lead-times before peak of hydrographs were too long to produce accurate river discharge results.

Integrated hydrometeorological model
In Tro� selj et al. ( 2023), the observed hourly rainfall data were collected (JMA 2020) as point data from all rain gauges of the associated river basin with available published data.These data were then used for model calibrations, when model parameters were obtained using the rainfall from the same event, and mean ensemble river discharge validations, when parameterization was obtained using rainfall from six different events than HRE18.
In this study, the CDRM hydrological model, previously calibrated and validated with observed data, used rainfall forecasts data, obtained from the WRF meteorological model experiments.The WRF model was forced separately with ERA5 and JR55 datasets with identical 6 h intervals between six forecasts but different spatial resolution in the innermost of two domains.The meteorological forecasts were conducted with information which were possible to obtain real-time during the event, therefore similar forecasting approach may be used for future applications.The schematic diagram of combining the WRF and CDRM models into the integrated hydrometeorological real-time forecasting framework is shown in Figure 1.

Validation and verification metrics of simulated hydrographs
We expected that the physical characteristics of river runoff from the seven events of similar extreme scale are reproducible across each other (cross-validation) due to their similar rainfall magnitudes.To validate our expectations, the ensemble averages (hereafter: ensembles) of river discharges from six validation cases were compared.As proposed and described in very detail in Tro� selj et al. ( 2023), these ensembles were calculated as averaged values of the six validation cases of river discharges for every 168 hourly time steps (Equation ( 2)), which were computed using calibrated river basin parameter sets from the six designated historical events other than HRE18 and the observed rainfall data from HRE18.
where P t is the ensemble average at time t (t ¼ 1, … , 168), Q t s (i) is the simulated discharge at t for the i-th validation case, and n is the total number of validation cases (n ¼ 6).
This approach was applied for six initial times, as indicated in section 2.3, to evaluate ability of the integrated hydrometeorological framework to real-time forecast extreme river discharge hydrographs from the HRE18.Although we evaluate this event after it has already occurred, all the data which were used for conducting both meteorological and hydrological modelling is the data which can be readily available for future real-time forecasting.
The performances of the hydrological model for each individual simulated case and for the ensembles were evaluated by three measures (Sayama et al. 2020; taken from Tro� selj et al. 2023): NSE (Equation (3), Nash and Sutcliffe 1970), KGE (Equation (4), composed of Equations ( 5), ( 6) and ( 7), Gupta et al. 2009); and the relative Peak Error (PE) (Equation ( 8)), as the most applicable for our considered cases.NSE is widely used in the hydrological community; thus, most studies can be comparable with it.For this study, we considered NSE > 0.7 as a value representing satisfactory predictive accuracy of river discharge hydrographs while considering lead-times.
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Analysis of real-time meteorological rainfall forecasts
The WRF modelled results of experiments 0603, 0609, 0615 and 0621 forced by ERA5 and JRA55 are visualized in the following.Table 1 shows comparison of the observed and forecasted (a) cumulative rainfall amounts of all seven river basins for

Cumulative rainfall
Figure 2 shows cumulative basin-averaged rainfall amounts from all analysed rivers for both ERA5 and JRA55 meteorological forcing for all six experiments conducted.

Maximal hourly rainfall
Figure 3 shows mean domain-averaged rainfall of maximal hourly amounts from all analysed rivers for both ERA5 and JRA55 meteorological forcing for all six experiments conducted.

Validation of real-time hydrometeorological river discharge forecasts
Modelled results with reproducibility metrics of the calibration and the ensemble average validation cases for both 7-CPM and 5-CPM are visualized in Figure 4 for Ota River and Figure 5 for Takahashi River in the following subsections.Ota and Takahashi are hereafter selected as representative rivers for detailed discussion because they are the largest in Hiroshima and Okayama Prefecture, respectively.Identical presentation and figures for the other five analysed rivers are presented for reference in Supplementary Material C. The cumulative calibration and ensemble validation results for all seven analysed rivers are visualized in Figure 6.For all figures, four experiments of 6 h intervals preceding the peak time of the associated river hydrograph are shown.Therefore, for the westernmost Saba, Oze and Ota Rivers experiments 0521, 0603, 0609 and 0615, whereas for the other four rivers and for all rivers cumulatively, experiments 0603, 0609, 0615 and 0621 are shown.

Ota River
Figure 4 shows the Ota River real-time forecasted river discharge results for the HRE18 at Yaguchi Daiichi station, located 14.6 km upstream from the river mouth.Lead-times of 5, 11, 17 and 23 h before peak of the hydrograph were simulated using the ERA5 (Figure 4, left) and the JRA55 (Figure 4, right) forecasts.Ensemble averages of all 6 calibrated parameter sets with the 7-CPM and 5-CPM sets are compared with observed data.

Takahashi River
Figure 5 shows the Takahashi River real-time forecasted river discharge results for the HRE18 at Sakazu station, located 10.2 km upstream from the river mouth.Leadtimes of 4, 10, 16 and 22 h before peak of the hydrograph were simulated using the    ERA5 (Figure 5, left) and the JRA55 (Figure 5, right) forecasts.Ensemble averages of all 6 calibrated parameter sets with the 7-CPM and 5-CPM sets are compared with observed data.

All rivers cumulatively
Figure 6 shows cumulative real-time forecasted river mouth discharge results for the HRE18.Lead-times of 5, 11, 17, 23 and 29 h before peak of the hydrograph were simulated using the ERA5 (Figure 6, left) and the JRA55 (Figure 6, right) forecasts.
Cumulative ensemble averages of all 6 calibrated parameter sets with the 7-CPM and 5-CPM sets are compared with observed data.As the Figure 6 is the most important output of this study because of evaluating all rivers together, here we extended the visualization to five experiments preceding the timing of the associated hydrograph peak.

Evaluation of computed metrics for real-time forecasts lead-times
This study evaluates applicability of the proposed hydrometeorological methodology and approach in terms of the longest lead-times before the peak of the river discharge hydrograph, for which accurate verification metrics could be obtained.Generally, NSE � 0.7 represents a threshold for the satisfactory result.Table 2 summarizes the computed calibration and ensemble average validation reproducibility metrics for the 7-CPM and 5-CPM for Ota and Takahashi Rivers and all rivers cumulatively, while Table 3 shows the same but for the other five rivers.The summary is separated into two tables to distinguish the rivers shown in the main body of the article (Figures 4, 5, and 6), summarized in Table 2, and the ones shown in the Supplementary Material C, summarized in Table 3.

Validation of real-time hydrometeorological river discharge forecasts
Meteorological results are presented in as Figures 2 and 3, and their validation in Table 1.It can be concluded that both ERA5 and JRA55 forced meteorological forecasts are reproducing comparable cumulative and mean amount of rainfall for the associated peak hour with the JMA observed data.When the total amount of rainfall from all 6 meteorological experiments for all river basins are summarized and compared with the observed data for the same river basins and corresponding time ranges, forecasted cumulative rainfall amount accounted for 93% of the observed one for both ERA5 and JRA55 forcing.Mean amount of rainfall for the associated peak hour was also consistently reproduced across all experiments, from 8.3 to 12.2 mm/h.For comparison, the value of observed mean rainfall was 13.3 mm/h.However, the observed value accounts only for the area of river basins, whereas modelled values account for the entire rectangular domain of the meteorological modelling experiments, where the domain outermost edges correspond to outermost edges of the seven analysed river basins.Therefore, from meteorological prospective mean averaged and maximal hourly validation shows satisfactory accurate predictive accuracy Table 3. Summary of the computed calibration and ensemble average validation NSE, KGE and PE results for the 7-CPM and 5-CPM using the ERA5 (labelled as "River Name-E") and JRA55 (labelled as "River Name-J") forcing for Saba, Oze, Ashida, Asahi and Yoshii Rivers.The green colour indicates all the validation results with NSE ≥ 0.85 and 1.1 ≥ PE ≥ 0.9, whereas the yellow colour indicates 0.85 > NSE ≥ 0.7 as well as 1.2 ≥ PE >1.1 and 0.9 > PE ≥ 0.8.Although validation of the WRF meteorological real-time forecasts is crucially important to show its usage potential, we validate them in detail from the hydrometeorological perspective as a crucial part of this study.The methodologies applied to the WRF meteorological experiment were previously developed and validated in Nayak and Takemi (2021) for the JRA55 forcing.Then, the same meteorological methodology was reused in this study with additionally conducted experiments using ERA5 initial forcing data with finer spatial resolution than JRA55.Instead of validating them explicitly, meteorological results of this study were validated in terms of the integrated modelling hydrometeorological approach, by comparing computed and observed river mouth discharges for various initial times of meteorological forecasts.Our expectation is that it is nearly impossible to have a satisfactory accurate forecasted river mouth discharge results forced by a meteorological forecast, when the meteorological forecast is not well reproduced spatially and temporally.However, even when the meteorological forecast has satisfactorily well spatiotemporal accuracy, it is still possible to not be able to obtain accurate river discharge hydrograph results.This occurs when the associated hydrological model is not well constructed or insufficiently calibrated.An innovative ensemble parameter calibration approach and methodology for enhancing accuracy of flash flood hydrological modelling is proposed in Tro� selj et al. ( 2023), whereas this study shows its applicability for future development of EWS.This study integrates the hydrological modelling approach (Tro� selj et al. 2023) with two real-time meteorological forecasts, which can similarly be conducted ahead of future extreme flash flood events, thus it enables enhanced development of EWS.
In the following, the first particular question of this study is addressed: 'How accurately can our integrated hydrometeorological framework reproduce the river discharges from the HRE18, with various initial real-time forecasting lead-times?'.The systematic overview of computed NSE values for up to 24 h lead-times before peak discharge of the analysed river(s) event is shown in Tables 2 and 3 in terms of NSE, KGE and PE.Among them, NSE is often used in evaluation of river discharges, where values of NSE � 0.7 are generally accepted as a satisfactory reproducibility.Validation cases are more relevant for the discussion than calibration cases because they are calculated with hydrological model calibrations from preceding events and forecasted rainfall input from HRE18.Therefore, the validation approach can be used in the similar way for future development of EWS.
In the ERA5 experiment ensemble average validations, for all rivers cumulatively (Figure 4), NSE �0.7 was obtained in all 10 analysed cases of up to 29 h lead-times, with NSE �0.85 obtained in 5 cases.For the JRA55 experiment ensemble average validations, NSE �0.7 was obtained in all 6 cases up to 17 h lead-times, with NSE � 0.85 obtained in 3 cases.Generally, reproducibility metrics of the ERA5 forcing are higher than those of JRA55 forcing, which may be attributed to about twice finer modelling resolution of ERA5 (30 km) than JRA55 (55 km).
For Takahashi River (Figure 5), NSE �0.7 was obtained in 7 (6) of 8 analysed cases of up to 22 h lead-times, with NSE �0.85 obtained in 4 (2) cases for the ERA5 and JRA55 experiments, respectively.For Ota River (Figure 4), NSE �0.7 was obtained in 2 (2) of 4 analysed cases of up to 11 h lead-times for the ERA5 and JRA55 experiments, respectively.However, there are many results for Ota River slightly lower than 0.7, with the lowest value for both ERA5 and JRA55 being NSE ¼ 0.35 of up to 23 h lead-times.From Takahashi and Ota Rivers results separately, the occurrence of successful validations is comparable to the one of all rivers for Takahashi River but slightly lower for Ota River.In the hydrological modelling with observed rainfall from Tro� selj et al. ( 2023), the results from the two rivers are in similar range.Therefore, the reason for lower hydrometeorological results in Ota River might be in uncertainties in spatial distribution of meteorological forecasts.However, the finding that reproducibility metrics of results from all rivers together are large demonstrates that the approach and methodology introduced in this study is very robust in general.
As intuitively expected, the accuracy of the obtained reproducibility metrics for all river discharge hydrographs cumulatively gets decreased with increasing lead-times due to larger uncertainties in meteorological forecasting, but there were several exceptions to this expectation as well.For example, reproducibility metrics for ERA5 forcing of 22 h lead-times (NSE ¼ 0.89 for 7-CPM and 0.92 for 5-CPM) are higher than those of 16 h (NSE ¼ 0.85 for 7-CPM and 0.82 for 5-CPM) and 11 h (NSE ¼ 0.80 for 7-CPM and 0.77 for 5-CPM).Differences in results when using 7-CPM and 5-CPM for the CDRM model were minor, and underlying reasons for these findings were discussed and addressed in more details in Tro� selj et al. (2023).
A counterintuitive finding is that the reproducibility metrics from calibration cases do not significantly differ from the ones of validation cases in general (see Tables 2  and 3).This is a very important supportive finding which demonstrates the robustness of the introduced approach and methodology jointly from this study and from Tro� selj et al. (2023).Implications from these findings are that the proposed ensemble parameter calibration approach and methodology using several past extreme events are capable of producing similar results as the calibration of the same unprecedented rainfall event when using its own rainfall data.Thus, such approach can be reused and applied to accurate future real-time flood forecasting because it enables high reproducibility and forecasting metrics of river discharge hydrographs.

Evaluation of computed metrics for real-time forecasts lead-times
This study evaluates potential for application of the approach and methodology proposed in Tro� selj et al. ( 2023) to the development of flash flood EWS.In the following, the second particular question from the objectives is addressed: 'How long lead-times from our meteorological forecasts until the peak of a river discharge hydrograph can be reproduced with satisfactory accuracy?'.
From Figures 4, 5 and 6, summarized in Table 2, satisfactorily accurate reproducibility metrics (NSE � 0.7) were obtained for up to 29 h (all rivers cumulatively), 22 h (Takahashi River) and 11 h (Ota River) before peak of river discharge hydrographs for both applied meteorological forcings.As expected, obtained lead-times were longer for bigger rivers.Longer lead-times with more accurate river discharge hydrograph reproducibility metrics were obtained when using the finer spatial resolution ERA5 forcing than the coarser JRA55.Such long lead-times obtained in this study are huge step forward towards the development of EWS because they show that the approach and methodology introduced in this study and Tro� selj et al. ( 2023) can significantly extend lead-times of real-time flash floods forecasting frameworks.To put these long lead-times into proper context and comparison with present situation of real-time flood forecasting in Japan, we note that at present the lead-times of Japanese operational flood forecasting is typically from 3 to 6 h (Sayama et al. 2020).
Reproducibility metrics for the other five rivers, summarized in Table 3 and visualized in the Supplementary Material C, are following similar patterns than those of Takahashi and Ota Rivers.For the rivers located on the eastern side from Ota River (e.g.Ashida, Asahi and Yoshii), NSE � 0.7 was obtained for vast majority of analysed cases up to experiment 0609, which corresponds to lead-times of 15 or more hours.For Asahi and Yoshii Rivers, satisfactorily good results were obtained with lead-times of 23 or more hours.Saba and Oze Rivers, located on the western side of Ota River, are comparably smaller than other analysed rivers, with lower than 1000 m 3 /s peak observed discharge during the HRE18.Secondly, they are located on the outermost edge of the heavy rainfall front which more severely hit the other five rivers.Therefore, it is expected that their reproducibility metrics and satisfactorily accurate lead-times in this study will be comparably lower than for the other rivers.Still, NSE � 0.7 was obtained for lead-times of up to 8 h for Saba River, with a good reproducibility of the 0521 ERA5 experiment for both Saba River with 20 h lead-time, and Oze River with 21 h lead-time.A very useful finding is that ERA5 experiment with 20 or longer lead times (see each single river Figure, plot 'd') showed moderately good results of NSE � 0.6 for all seven rivers except Ashida River, which might be due to some local spatial uncertainties which affected the meteorological forecast.This indicate that very long lead-times of about one day or longer may be obtained with satisfactorily good real-time river discharge hydrograph forecasts.However, the meteorological forecasts sometimes did not reproduce spatiotemporal rainfall values accurate enough, which may then result in false warnings of EWS.Therefore, we recommend to develop and operate the EWS with multiple validated real-time meteorological forecasts at different spatiotemporal scales, to reduce the meteorological forecasting uncertainty.
For unbiased and objective comparison of our findings with other studies using proper context, there is not existing a single benchmark.This is because one study can be different from the other according to various crucial criteria, such as rainfall data availability to calibrate models should be in comparable range; rainfall data input should be based on observed data, not on predicted data; duration of time series and input-output data of river discharge results should be in comparable range; watershed sizes should be in comparable ranges; reproducibility metrics for results comparison should be identical (taken from Tro� selj et al. 2023); meteorological boundary conditions should be in comparable ranges; meteorological lead-times should not fluctuate much.To our knowledge, no other previous studies satisfy all of these conditions.However, comparisons with hydrometeorological forecast studies which satisfy most of aforementioned similarity conditions shows that Wijayarathne and Coulibaly (2020) obtained 0.42 � KGE � 0.75 and 0.32 � PNSE � 0.67 during the calibration period, 0.65 � KGE � 0.82 with 0.32 � PNSE � 0.44 for one-day lead times and 0.22 � KGE � 0.46 with 0.07 � PNSE � 0.28 for two-day lead times by applying deterministic meteorological forecasts.Liechti et al. (2013) obtained Nash-Sutcliffe efficiency values of 0.14 � NSE � 0.71 when forcing two deterministic forecasts and 0.29 � NSE � 0.83 when forcing three ensemble precipitation nowcasts on two event scales, while Alfieri et al. (2012) obtained 0.32 � NSE � 0.48 for the mean of ensemble discharge forecasts.These findings confirm expectations that the reproducibility of river discharge hydrograph results significantly decreases from the ensemble to the deterministic meteorological forcing data, because of increasing rainfall uncertainty levels.Therefore, obtaining the satisfactorily good reproducibility metrics with up to 29 h lead-times when using deterministic meteorological forcing is unexpectedly long and can be used for future developing of EWS.When reproducibility metrics from this study are compared with the hydrological study (Tro� selj et al. 2023), we observe their rapid decline from values of around NSE > 0.9 to NSE > 0.7.This indicates that meteorological uncertainty in flash flood forecasting is way bigger than hydrological, as it is intuitively expected due to bigger spatiotemporal sensitivity of meteorological forecasts.
The integrated hydrometeorological real-time forecasting framework and the associated development of EWS is also very important for coastal ocean modellers, because they need accurate real-time forecasts of a total freshwater budget supplied to the sea or ocean during extreme rainfall-induced events.As for each river separately, Takahashi River shows excellent forecasts for up to 4 h lead-time (NSE � 0.89) and satisfactory good forecasts for 10 and 16 h lead-times for both ERA5 and JRA55 forcing, whereas ERA5 also shows excellent forecast for 23 h lead-time (NSE � 0.86) but in that lead-time JRA55 underperforms (NSE � 0.44).For Ota River, no result is in an excellent range, but all results for up to 23 h lead-time are in range of NSE � 0.57 for ERA5 and NSE � 0.35 for JRA55 forcing.In existing operational real-time forecasting or nowcasting EWS, it is rarely possibly to obtain an accurate river discharge hydrographs prediction with lead-times longer than 3 h (Sayama et al. 2020).These high reproducibility metrics for such long lead-times obtained by using the proposed approach and methodology from Tro� selj et al. ( 2023) highly support our established hypothesis that combination of ensemble calibrated river basin parameters of hydrological models from several historical extreme discharge events of similar scale and forecasted meteorological data can accurately predict river discharge hydrographs of extreme rainfall-induced future events in real time with exceptionally long lead-times before the flood, most commonly of up to 24 h before the peak of the associated hydrograph.

Development of real-time flash flood discharge forecasting applications
This study introduces an innovative approach and methodology, which proposes how the integrated hydrological and meteorological modelling can be implemented into the development of operational flash flood EWS.In the following, the third particular question from the objectives is addressed: 'How can our findings be used for realtime forecasting a flash flood river discharges from extreme future rainfall events?'.
For more specific directions for the Chugoku Region of Japan, our operational recommendations for the intended development of EWS are summarized below.The system of rainfall observations stations from the Japan Meteorological Agency (i.e.JMA 2020) would need to readily provide real time observed hourly rainfall data, which should then be used as a real-time input to the CDRM or other equivalent hydrological models when a high rainfall event is expected to occur in upcoming several days.Then, the WRF model with ERA5 and JRA55 forcing or other equivalent meteorological models should be operated with a 3-hourly or 6-hourly deterministic meteorological forecasts, which should replace input of the observed rainfall data at every initial time step of every new available forecast, at the time of its release.
This study proposed that two meteorological forecasts can be usedtogether with two developed hydrological parameter calibration methodologies.This enables possibilities for total 4 simultaneous forecasting experiments which are expected to produce similar results for two hydrological methodologies, but more accurate results when using finer spatial resolution meteorological forecasts.For additional safety reasons, our recommendations are to utilize all 4 forecasting experiments at once and take the worst case scenario as relevant information to be communicated through EWS.Only in cases where one experiment has significantly different values than other three experiments, we may disregard its results as unreasonable and rely on the worst case scenario from the other three experiments.
Special consideration and highlight needs to be addressed to findings from Figure 6, where all seven river discharges are cumulatively shown for both observed data and modelled results.Such comprehensive cumulative freshwater budget estimations flowing into the Seto Inland Sea are useful information and potential input data for extension of the integrated hydrometeorological modelling framework into multidisciplinary real-time forecasting of the effect from the extreme river water levels on coastal sea dynamics and associated storm surge and pollution transport disasters (Ikeuchi et al. 2017;Troselj et al. 2017Troselj et al. , 2018Troselj et al. , 2019;;Kida and Yamazaki 2020;Tro� selj et al. 2021).Real-time forecasted total freshwater budget flowing to a coastal zone during a future extreme rainfall event should be one of crucial factors for coastal disaster Early Warning Systems, as in Wang et al. (2020).Therefore, developing an accurate real-time river discharge forecasts is a necessary basis towards developing enhanced land-river-ocean disaster prevention systems.
Developing a robust hydrometeorological framework which enables accurate forecasting of river discharge hydrographs in real time before a flood is desirable and useful for detecting future changes in the frequency of the largest class of floods.However, Mori et al. (2021) reported that the reliability of the future climatological river discharge hydrograph results depends on the reproducibility of extreme rainfall against historical events.Therefore, given the high reproducibility metrics of the river discharge results with long lead-times obtained in this study, we expect the approach and methodology jointly developed here and Tro� selj et al. ( 2023) can be readily reused and applied for predicting river discharges of extreme rainfall-induced floods from climatological studies as well.To calculate river discharge hydrographs of future climatological events, identical hydrological calibrated parameter sets as developed in Tro� selj et al. ( 2023) should be forced with a rainfall input data from various climatological datasets, instead of forecasted by the WRF model, as shown in this study.
We expect that the proposed methodology can be conveniently applied and replicated in gauged basins with enough historical rainfall data required for ensemble parameter calibrations of a hydrological model, but its applicability in partially gauged basins or ungauged basins is still questionable and should be further tested in the follow-up studies.Our expectation is that the proposed methodology cannot easily be replicated to study sites with much lower data availability than in Japan.However, we do not expect that the methodology from this study should be explicitly replicated because its reproducibility potential can differ depending on various rainfall data availability.Instead, we highlight that our proposed approach of ensemble parameterization of river basin parameters, whether the parameterization is conducted with a lot or a little of available rainfall data, is a promising direction for conducting realtime flash flood forecasts worldwide more accurately and on longer lead-times than how it is generally achieved nowadays.
In the follow-up studies, the river discharge hydrograph results obtained by these real-time forecasts can be further extended from forecasting rivers discharge hydrographs into inundation extent modelling.The Rainfall-Runoff-Inundation (RRI, Sayama et al. 2020) model is based on similar model structure as the CDRM, therefore it is expected that it can easily reproduce and extend the integrated hydrometeorological modelling framework developed in this study.This extension would also enable calculation of inundation extents and expand the applicability potential of the proposed approach and methodology into EWS.Also, the proposed approach and methodology can conveniently be reused and replicated not only in Japan but presumably worldwide.Additionally, the ensemble calibrated hydrological model parameters from Tro� selj et al. ( 2023) can be forced with projected future rainfall data of various climatological scenarios instead of the real-time forecasted data used in this study.This would allow climate impact assessment of high intensity but short duration rainfall events, which are expected to increase in the future climate.Furthermore, extension of the deterministic meteorological forecasts into ensemble forecasts, such as the Japanese regional model-based Mesoscale Ensemble Prediction System (MEPS, Ono et al. 2020) would additionally be a promising direction to enhance the spatiotemporal accuracy of meteorological modelling using probabilistic approach.

Conclusions
This study proposes an innovative approach and methodology for the development of flash flood Early Warning Systems and implementation of its operational usage.While Troselj et al. (2017) and Tro� selj and Lee (2021) established the initial tools and methodologies for developing real-time forecasting (nowcasting) models, the hydrological study Tro� selj et al. ( 2023) proposed a follow-up methodology which is conveniently applicable worldwide on any extreme-rainfall induced event.This EWS application framework is demonstrated here.
We showed that the CDRM model with seven ensemble calibrated parameter sets based on historical extreme rainfall events patterns of similar scales, using the SCE-UA optimization method with WRF model meteorological forecasts forced with ERA5 and JRA55 rainfall data, could have accurately real-time forecasted the river discharge hydrographs for the HRE18.The accurate lead-times (with NSE � 0.7) of up to 11 (Ota River) and 22 (Takahashi River) hours ahead of the associated river discharge hydrograph peak event were obtained.Similarly, the proposed approach and methodology can also accurately forecast river discharge hydrographs for extreme and unprecedented future rainfall events for the Chugoku region of Japan and presumably worldwide in real time before the flood.
The reproducibility metrics were particularly large when all river discharges were considered cumulatively, compared to those of each single river, as their accurate reproducibility metrics were obtained for up to 29 h lead-times.This finding particularly highlights robustness and wide applicability of the proposed approach and methodology.These results represent an important step towards the future development of real-time forecasts of river water levels and discharges for EWS and the reduction of associated flash flood disasters.Thus, introducing the approach and methodology which can greatly extend the flash flood forecasting lead-times in real time before the flood is a significant scientific and societal contribution of this study and confirms the expected applicability potential of our established hypothesis.
A limitation of this study is that the CDRM model calculates river discharge and water level, but cannot calculate inundation extents or determine weak points on river banks where flash floods are more likely to occur.Therefore, an integration of the CDRM model with another model which has similar structure but supports inundation calculations (e.g.RRI; FLDPLN and SRTM DEM from Bhatt et al. (2017) with different model structures) are recommended as possible extensions of its applicability potential for EWS.Another conditional limitation is that this study used a point rainfall observation stations to form Thiessen Polygons because point stations have generally the most readily availability worldwide.This enables convenient reuse and replication of the proposed approach and methodology anywhere and anytime.However, a more sophisticated rainfall input method, such as radar rainfall data and ensemble meteorological forecasts instead of deterministic, should be considered in follow-up studies because they are also increasingly available, as shown by Patel et al. (2022).Additionally, as ERA5 showed more accurate results than JRA55, we expect that a finer resolution meteorological forecasts would improve spatiotemporal reproducibility of real-time meteorological forecasts and associated nowcasting of flash floods river discharge hydrographs.
Our recommendations from this study and jointly supported with Tro� selj et al. ( 2023) summarize towards necessity of developing ensemble parameter calibration approaches and methodologies from the hydrological modelling perspective, based on similarity patterns of various past extreme rainfall events.This can enable development of robust integrated hydrometeorological real-time forecasting frameworks which should be implemented into flash flood EWS.
of July 2018.A part of this study was supported by the Collaborative Research fund by the Disaster Prevention Research Institute (DPRI) at Kyoto University (PIs: Lee and Mori).Jo� sko Tro� selj is grateful and appreciative to his current advisor Naota Hanasaki for inspiring guidance and to his former Kyoto University's Doctoral advisor Kaoru Takara and co-advisors Yosuke Yamashiki and Takahiro Sayama for providing source code and teaching methodology for proper usage of the CDRM model combined with the SCE-UA optimization method.Wahidullah Hussainzada developed an automatized Python script which enables faster modelling runs and can greatly reduce computational time when applied with multiple meteorological forecast simultaneously.Han Soo Lee, Syed Zeeshan Haider and Mahdi Khaleghi provided useful suggestions in the conceiving stage of the study.Kedar Otta discussed key parts of the study before submission and provided useful suggestions.Soumitra Pathak proofread English language corrections in main parts of the study.The Writing Center of Hiroshima University provided numerous useful suggestions to improve the quality of the writing and presentation of the contents.

Figure 4 .
Figure 4. Ota River real-time forecasted river discharge results for the HRE18 by WRF hourly rainfall forced with ERA5 (left) and JR55 (right) for experiments (a, e) 0615, (b, f) 0609, (c, g) 0603, and (d, h) 0521.Ensemble average validation of all six calibrated parameter sets with the 7-CPM (red -validation; orange -calibration) and the 5-CPM (green -validation; cyan -calibration) are compared with the observed river discharges (blue -MLIT 2020) at a site located 14.6 km upstream from the river mouth.

Figure 5 .
Figure 5. Takahashi River real-time forecasted river discharge results for the HRE18 by WRF hourly rainfall forced with ERA5 (left) and JR55 (right) for experiments (a, e) 0621, (b, f) 0615, (c, g) 0609, and (d, h) 0603.Ensemble average validation of all six calibrated parameter sets with the 7-CPM (red -validation; orange -calibration) and the 5-CPM (green -validation; cyan -calibration) are compared with the observed river discharges (blue -MLIT 2020) at a site located 10.2 km upstream from the river mouth.

Figure 6 .
Figure 6.Cumulative real-time forecasted river mouth discharge results for the HRE18 by WRF hourly rainfall forced with ERA5 (left) and JR55 (right) for experiments (a, f) 0621, (b, g) 0615, (c, h) 0609, (d, i) 0603, and (e, j) 0521.Cumulative ensemble average validation of all six calibrated parameter sets with the 7-CPM (red -validation; orange -calibration) and the 5-CPM (green -validation; cyan -calibration) are compared with the cumulative observed river discharges (blue -MLIT 2020) at sites located closely upstream from each river mouth.

Table 1 .
Comparison of the observed and forecasted (a) cumulative rainfall amounts from all seven river basins for each of six experiments from its initial time until 10 July 2018 at 00 am JST and (b) mean domain-averaged rainfall of maximal hourly amount, with indicated the maximal hour.
Note:The green colour indicates cases when difference between simulated and observed data is less than 10% and that maximal hour is 6 h from the observed one while yellow colour indicates the difference being between 10% and 20% and between 6 and 9 h.
each of six experiments from its initial time until 10 July 2018 at 00 am JST and (b) mean domain-averaged rainfall of maximal hourly amount.Findings from Table 1 are spatially visualized in Figure 2 (from Table 1(a)), and Figure 3 (from Table 1(b)).However, important to note is that Table 1(a) compares area of all river basins for both observed and forecasted data, whereas Table 1(b) compares observed data only in river basins but forecasted data in the entire simulated meteorological domain, where east, west, south and north edges corresponds with the extent of all seven river basins.

Table 2 .
Summary of the computed calibration and ensemble average validation NSE, KGE and PE results for the 7-CPM and 5-CPM using the ERA5 and JRA55 forcing for Ota and Takahashi Rivers and all rivers cumulatively.The green colour indicates all the validation results with NSE ≥ 0.85 and 1.1 ≥ PE ≥ 0.9, whereas the yellow colour indicates 0.85 > NSE ≥ 0.7 as well as 1.2 ≥ PE >1.1 and 0.9 > PE ≥ 0.8.
across various lead-times, but it is still open question how accurate is a predictive accuracy of their spatial distribution in real-time, which is out of scope of this study.