(2021) 8:58
P.C. and Sawazaki ﻿Prog Earth Planet Sci
https://doi.org/10.1186/s40645-021-00448-1

RESEARCH ARTICLE

Progress in Earth andPlanetary Science

Open AccessRiver discharge prediction for ungauged
mountainous river basins during heavy rain
events based on seismic noise data
Shakti P.C.*

and Kaoru Sawazaki

Abstract
Several mountainous river basins in Japan do not have a consistent hydrological record due to their complex environment and remoteness, as discharge measurements are not economically feasible. However, understanding the flowrate of rivers during extreme events is essential for preventing flood disasters around river basins. In this study, weused the high-sensitivity seismograph network (Hi-net) of Japan to identify the time and peak discharge of heavy rain
events. Hi-net seismograph stations are distributed almost uniformly at distance intervals of approximately 20 km,
while being available even in mountainous regions. The Mogami River Basin in Northeastern Japan was selected as atarget area to compare the seismic noise data of two Hi-net stations with the hydrological response of a nearby river.
These stations are not located near hydrological stations; therefore, direct comparison of seismic noise and observed
discharge was not possible. Therefore, discharge data simulated using a hydrological model were first validated with
gauging station data for two previous rain events (10–23 July 2004 and 7–16 September 2015). Then, the simulated
river discharge was compared with Hi-net seismic noise data for three recent events (10–23 July 2004, 7–16 September 2015, and 10–15 October 2019). The seismic noise data exhibited a similar trend to the time series of simulated discharge in a frequency range of 1–2 Hz for the selected events. Discharge values predicted from the noisedata effectively replicate the simulated discharge values in many cases, especially the timing and amount of peakdischarge.
Keywords: Discharge, Seismic noise, Hi-net, Hydrological simulation, Ungauged river basin, Heavy rain event, RRI,
Discharge prediction
1 Introduction
River discharge is defined as the total volume of waterflowing through a river at any given point; it is an important hydrological parameter for planning and decision
making of many water-based development activities.
River discharge cannot be measured directly but must be
computed by multiplying the area of water in a river crosssection with the average velocity of water in that crosssection (Herschy 1993). Different measurement methods
have been proposed to estimate river discharge, which is*Correspondence: shakti@bosai.go.jp
National Research Institute for Earth Science and Disaster Resilience, 3‑1
Tennodai, Tsukuba, Ibaraki 305‑0006, Japangenerally referred to as the observed discharge. For example, a current meter is typically used to measure the flow
velocity at various vertical locations at any point withina cross section. The flow velocity is then multiplied by
the corresponding area of each measurement, and thesum of these products gives the river discharge at that
selected point. Classical velocity-area methods are basedon the principle of the continuity of fluid flow (Buchanan
and Somers 1969) and provide instantaneous discharge
measurements to establish the stage-discharge relationship (Herschy 1998). This type of discharge measurement
is feasible for river basins with accessible topography(Dobriyal et al. 2017), as the discharge at any point along
a river should consider the size of the basin, amount of© The Author(s) 2021. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which
permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to theoriginal author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images orother third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line
to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory
regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of thislicence, visit http://​creat​iveco​mmons.​org/​licen​ses/​by/4.​0/.

P.C. and Sawazaki ﻿Prog Earth Planet Sci(2021) 8:58

rainfall, topographic features, etc. However, for numerous river basins located in mountainous regions, obtaining discharge measurements is highly challenging and
not economically feasible due to their remoteness andcomplex environments. Therefore, regular monitoring ofriver discharge is lacking for mountainous river basins,
which are also known as ungauged river basins.
Several studies have suggested that the frequencyof extreme weather events is increasing as the climate
continues to change (Kusunoki et al. 2008; Westra et al.
2014). Specifically, extreme rainfall can cause a sudden
increase in river discharge, which is extremely dangerous
for those living close to rivers (Georgakakos 2006; Oshikawa et al. 2008) and may result in the large-scale loss ofhuman life and infrastructural damage (Hirabayashi andKanae 2009; Dottori et al. 2018). To predict and prevent
water-related disasters in a river basin, regular measurement of river discharge is crucial, particularly during
extreme rain events; this is because it can determine theflow capacity of the river section in response to heavy
rainfall (Marchi et al. 2010). There are several river systems within ungauged river basins. A sudden increase in
the flow of any tributary of a basin may lead to a severe
disaster downstream of the basin in the form of flash
flooding, which may be more common in mountainous
regions. In some cases, the time lag between rainfall andflooding is short, especially in small river basins. In sucha situation, high temporal estimation of river discharge
is necessary for estimating the flood disaster level in adownstream section, and appropriate measures should
be taken in a timely fashion for disaster prevention andmanagement. Furthermore, information on the amountand timing of peak discharge is also important for assembling comprehensive flood data; however, this is hindered
by a lack of actual observations for ungauged river basins(Saharia et al. 2017). Hence, various indirect methods areavailable for quantifying and monitoring river discharge
at given points (Bjerklie et al. 2005; Marchi et al. 2010;
Dobriyal et al. 2017; Anthony et al. 2018; Kebede et al.
2020; Shi et al. 2020).
The most common indirect approach is rainfall-runoff
modeling, which has been employed to simulate riverdischarge in river basins around the world. Multiple typesof hydrological models are available globally, and there iscontinuous debate regarding which is the most suitablemodel for hydrological analysis of a river basin; however, this depends on the specific aims of the study. Currently available hydrological models include VIC (Lianget al. 1994), TOPMODEL (Beven et al. 1995), SWAT
(Arnold and Fohrer 2005), RRI (Sayama et al. 2012), andHEC-HMS (Scharffenberg 2016). However, such models are limited by their ability to validate simulated data,
especially over ungauged river basins (P.C. et al. 2018a,

Page 2 of 17

2018b). Another concern is the near real-time performance of simulation results. That is, hydrological simulations of river basins should be performed with highspatial and temporal resolution to achieve a high temporal discharge rate within river basins (Ochoa-Rodriguez
et al. 2015; Huang et al. 2019; P.C. et al. 2019).
In addition to discharge modeling, various approaches
have been developed to estimate river discharge in river
basins, particularly during flood disasters. For example,
non-contact measurements based on remote sensing
data are commonly adopted to estimate river discharge(Dobriyal et al. 2017; Anh and Aires 2019; Kebede et al.
2020; Shi et al. 2020). In a recent study, Bjerklie et al.
(2005) extracted river geometries and water velocity from
topographic maps and synthetic-aperture radar images,
respectively, to estimate the discharge of large rivers.
Although satellite observations can be useful for discharge estimates in large rivers, it is generally agreed that
additional analysis is required for small rivers in complex
topographies (Schumann et al. 2011; Huang et al. 2018).
Moreover, the presence of clouds and the temporal resolution of satellite observations can hinder remote sensing
observations, particularly during flood events (Clement
et al. 2018; P.C. et al. 2020a).
In some cases, hydrological measurements such as
those performed using gauging stations may either
destroy the channel course or alter the physical channel
during river flooding. Therefore, it may not be possible
to produce a comprehensive record using in situ measurement of flow under such conditions. To overcome
these issues, high-temporal-resolution seismic monitoring instruments have been used to infer hydrological data
and understand the timing of peak flow, thereby enabling
early flood warnings to be issued (Burtin et al. 2008;
Sawazaki et al. 2016; Anthony et al. 2018; Eibl et al. 2020).
For example, Burtin et al. (2008) and Sawazaki et al.
(2016) reported good correlations between seismic noisedata and the water level or discharge of mountainous rivers in Nepal and Japan, respectively, despite a substantial
distance between the seismic and hydrological stations.
There may be several independent river systems within arelatively small area of a given mountainous river basin.
Hence, uncertainties on the correlation may occur at
locations where there is a substantial distance between
the seismic and hydrological stations. Moreover, most ofthese studies focused on mountainous regions characterized by complex topography and river networks. Owing
to the steep and rugged topography in mountainous
regions, small streams with high flow velocity are common. In such situations, the relationship between seismicand hydrological data can only be determined accurately when observations points are close to each other.
Anthony et al. (2018) showed that seismic noise data canP.C. and Sawazaki ﻿Prog Earth Planet Sci(2021) 8:58

Page 3 of 17

Fig. 1 Topographic map showing the location and channel networks of the Mogami River Basin and its sub-basin. Blue triangles indicatehydrological stations. Purple stars and black dots indicate seismic stations and selected river points within the sub-basin, respectively

even be used to determine the discharge data of small
rivers when the seismological instrument is located very
close to a hydrological station. However, such co-locatedmeasurements are usually extremely difficult to perform
in mountainous regions. As hydrological (Mishra andCoulibaly 2009) and seismological (e.g., Aoi et al. 2020)
station networks are designed for very different purposes,
they are not typically located in the same places. Indeed,
seismic stations may often be located close to small andlarge rivers in mountainous regions where hydrological observations are rarely available. This is the typicalground truth situation in mountainous regions.
The National Research Institute for Earth Scienceand Disaster Resilience (NIED) deployed a dense andhigh-sensitivity seismograph network (Hi-net) (Obaraet al. 2005; Aoi et al. 2020) that covers several ungauged
mountainous river basins. This study employs Hinet to address the relationship between seismic noisedata and river discharge for hydrological and seismic

stations located far from each other, where a directcomparison of the two types of data is not typicallypossible. Seismological stations have been operating in
the mountainous regions of Japan for some time. It may
not be possible to fix or relocate these stations due toeconomical or technical issues. At the same time, discharge observations near existing Hi-net stations are
rarely available. Hence, there is a need to establish therelationship between the seismic noise data of installedstations and the discharge of nearby rivers. To do so, we
first perform hydrological simulations of a river basinand subsequently validate the simulation results using
gauging station discharge data at the catchment scale.
Then, the relationship between seismic noise data andsimulated discharge data is analyzed on the ungauged
sub-basin scale. This research selects Mogami River
Basin (Fig. 1), which is located in Yamagata prefecture,
Japan, as a case study. The aim of this study is to demonstrate the application of seismic data for predicting

P.C. and Sawazaki ﻿Prog Earth Planet Sci(2021) 8:58

the discharge in an ungauged river basin during a heavy
rain event.

2 Data and methods
Approximately, 80% of Japan is composed of hills andmountains. Most rivers in Japan originate in mountainous terrain, and have been serving as a backbone of Japanese life, culture, and agriculture for centuries. Many
urban areas in Japan, as well as forested nature reserves,
are located near rivers that flow from the mountains
where performing hydrological observations may not be
possible.
The Mogami River Basin is located in the northwestern region of Japan (Fig. 1) and is predominantly mountainous and forested, although there is also a small areaof urban and built-up land. The elevation varies fromapproximately sea level to more than 1500 m above sea
level. There are some hydrological stations in the main
channel of the basin but not in the upper part of thebasin. Hence, several sub-basins of the Mogami River
Basin do not have any hydrological stations for monitoring river discharge. Fortunately, there are some seismic
stations located in the mountainous region of the basin.
In this study, we selected a sub-basin of the Mogami
River Basin (Fig. 1) where two seismic stations (N.FGTH
and N. MGMH) are located. This sub-basin was selectedbased on its location (i.e., within a mountainous region),
its natural flow (i.e., a lack of hydraulic structures such as
dams or reservoirs), the presence of at least one Hi-net
station, and because it is far from human settlements.
We selected three previous significant heavy rain
events in the region: 10–23 July 2004, 7–16 September
2015, and 10–15 October 2019; the third event corresponds to Typhoon Hagibis, which caused heavy rainfall
and resulted in severe flooding, landslides, and inundation in several parts of Northern Japan (P.C. et al. 2020a).
The Ministry of Land, Infrastructure, Transport andTourism (MLIT) updates the river stage-discharge relationships each year and publishes discharge data throughthe MLIT website, which can then be downloaded freely.
However, the availability and continuity of discharge data
vary among stations. In the case of Mogami River Basin,
hourly discharge data for the first two events were collected from three stations within the basin (Fig. 1) that
stored long and continuous discharge data records:
Usugasawa (G01), Shimizu (G02), and Koide (G03). G01
represents the downstream boundary of the basin, G02
represents the middle of the basin and is close to selected
sub basin, and G03 represents the upstream boundary of
the basin. The maximum hourly discharge of the first two
events according to the G01 hydrological station, which
is located close to the outlet of the basin (Fig. 1), wasapproximately 5234 m­ 3/s and 2950 m­ 3/s, respectively.

Page 4 of 17

However, for the third event, discharge data were notavailable as of June 2021. Hourly radar rainfall data werecollected from the Japan Meteorological Agency (JMA)
for all the three events. The spatial and temporal resolutions of rainfall data were 1 km and 1 h, respectively.
An explanation of the other data required for hydrological modeling, such as topographic data, is provided in“Hydrological model” and “Seismogram data processing”
sections.
2.1 Hydrological model

Various types of hydrological models are available globally. Some models need to be purchased, while others
are open access for research purposes. There has been
continuous debate as to which model is most suitable forthe hydrological analysis of a river basin. However, theselection of a hydrological model depends on the specificaims of the study. We considered some important points
while choosing the model in this study. For example, theselected model should be conducive to the use of radar
rainfall data with very high temporal and spatial resolutions. The computation time should be as short as possible. The simulated discharge should possess a hightemporal resolution in gridded format, and the model
should be available freely for research purposes. To fulfill
the objective of the study, we adopted RRI for performing
the hydrological modeling of the Mogami River Basin inthis study.
The RRI is a two-dimensional model that has theadvantage of simultaneously modeling runoff and floodinundation (Sayama et al. 2012, 2020; P.C. et al. 2020a,
2020b; Nguyen et al. 2021). This model is applicable torainfall-runoff analysis and inundation profiling in eachgrid of a river basin. The flow in each grid cell is calculated with a 2D diffusive wave model, whereas channel flow is calculated with a 1D diffusive wave model.
Topography and meteorological data are the main data
inputs to the RRI model, and the outputs include discharge, river water level, and inundation level. Detailed
mathematical explanations of the RRI model have beenreported in several studies (Sayama et al. 2012; P.C. et al.
2020a; Nguyen et al. 2021).
Topographical features such as flow accumulation(ACC), flow direction (DIR), and digital elevation model(DEM) data are essential for implementing the hydrological model in a given river basin. Different types ofglobal topographic data are available free of charge; e.g.,
the multi-error-removed improved-terrain (MERIT)
DEM (Yamazaki et al. 2019) and HydroSHEDS (Lehneret al. 2013). However, each dataset contains uncertainties
regarding the topographic features. In this study, we used
MERIT DEM data, which is a global hydrography dataset developed based on the MERIT DEM and multiple

P.C. and Sawazaki ﻿Prog Earth Planet Sci(2021) 8:58

inland water maps. It contains DIR, ACC, and hydrologically adjusted DEM (Yamazaki et al. 2019). These data
cover a spatial resolution of three arcsecs (∼90 m) andexhibit fewer uncertainties than those offered by otherglobal topographic datasets.
The RRI model was set up to simulate discharge in eachgrid of the Mogami River Basin. It should be noted thatthe total area of the river basin depends upon the selection of the outlet point. The total area of the Mogami
River Basin according to the selected outlet is approximately 6930 ­km2. The RRI model is based on a grid system, and implementing a grid application with many cells
can result in a time-consuming simulation. Therefore,
to ensure rapid hydrological simulations of the selected
events in such a large river basin, the default grid size was
upscaled two times from the default topographic data
during model setup. Hence, the grid size after adjustment
for ACC, DIR, and DEM was approximately 180 m.
2.2 Seismogram data processing

NIED routinely examines the mechanical propertiesof the Hi-net instruments and performs quality checks
on Hi-net data (Obara et al. 2005; Aoi et al. 2020). The
objective of Hi-net is to detect the weak ground shaking
caused by micro-earthquakes and survey seismic activity, elucidate the mechanisms of earthquake generation,and determine the subsurface structure of Japan. For thispurpose, Hi-net seismic stations are distributed almost
uniformly in both plain and mountainous regions, withstation-to-station distance intervals of approximately
20 km. Furthermore, to avoid ambient seismic noise due
to social activity (e.g., traffic noise), Hi-net seismometers
are installed at the bottom of boreholes at depths exceeding 100 m. Hi-net ground motion data are continuously
recorded in 100-Hz sampling intervals, transferred to thedata center, and made openly available online in nearlyreal time. Hi-net has been operating since 2002; thus,
seismic noise data during the three target events arefreely available for research purposes.
We first collected the vertical component of seismograms (oscillation along the up-down direction) at two
Hi-net stations (N.FGTH and N.MGMH, Fig. 1) during
the target events. The power spectrum of the seismogram was computed using the Fast Fourier Transform
algorithm every 1 min, and the average power in the frequency range of 1–2 Hz was computed. The selectionof this frequency range is discussed in detail in “Comparison of simulated discharge with seismic noise data”
section. Then, we selected the minimum 1-min power
among continuous 10-min records from 5 min before
every hour to 5 min after every hour. Since the typicalduration of the signal from an earthquake or a landslide
is shorter than 10 min (e.g., Okuwaki et al. 2021), thisPage 5 of 17“clipping” procedure effectively removed the transient
signals that would otherwise interfere with the purpose ofthis research. In this way, the hourly noise power record
was obtained for the target time period. This record wasthen compared with nearby discharge records simulated
in an ungauged sub-basin.
2.3 Assessment tool

Assessment tools are very important for understanding
the difference between simulated and observed data andare often selected based on specific objective and goals.
The Nash–Sutcliffe efficiency (NSE, defined by Nash andSutcliffe 1970) is the most widely used tool for evaluating hydrological models using observed data. Mathematically, the NSE is given as

2ii− QobsQsim
NSE = 1 −  2 ,ii Qobs − Qobs
 
i

(1)

i , Qi , and Q
where Qsim
obs are the simulated discharge at
obs
time i, observed discharge at time i, and average of theobserved discharge over time, respectively. NSE varies
from − ∞ to 1, with NSE = 1 being the optimal value forthe evaluation test.
We also used the Kling-Gupta efficiency (KGE, Gupta
et al. 2009), which is based on the mean, standard deviation, and correlations of observed and simulated data;
KGE is being increasingly used for evaluations.



2 

2

Qsim
σsim

2
KGE = 1 − (r − 1) +
−1 +
−1 ,
σobs
Qobs

(2)
Here, r and σ are the correlation and standard deviation between the observation (obs) and simulation (sim),
respectively, and Qsim is the mean simulated discharge forthe given period. Like NSE, KGE = 1 indicates a perfectagreement between the simulations and observations.
The minimum thresholds of NSE and KGE for good performance depend upon the cases and research fields inquestion. From a hydrological perspective, if NSE andKGE values exceed 0.6, the modeling result is considered
to be ‘good’ (Moriasi et al. 2007; Towner et al. 2019).

3 Results
The first step of this study involved implementing thehydrological model for the entire Mogami River Basin.
Then, the simulated discharge was compared with theobserved discharge at several stations in the basin forprevious heavy rain events. After comparing the simulation results, our objectives were concentrated in an
ungauged sub-basin of the study area, where simulated discharge data and seismic data were comparedP.C. and Sawazaki ﻿Prog Earth Planet Sci(2021) 8:58

and analyzed. The results of each step are summarizedin “Hydrological simulation of Mogami River Basin”–“Discharge prediction from noise data.”
3.1 Hydrological simulation of Mogami River BasinFirst, hydrological simulations of Mogami River Basin
were performed for the selected events. Then, the simulated discharge values were extracted from nearby grid
points of the selected hydrological stations (Fig. 1) of
the Mogami River. Figure 2 shows the simulated andobserved discharge at gauging station points G01, G02,
and G03 along the Mogami River for the period of 10–23
July 2004 (first heavy rain event). The NSE values for theobserved and simulated data of all three stations were0.71, 0.65, and 0.69, respectively. Similarly, the KGE
values for the same stations were 0.82, 0.82, and 0.66,
respectively. Overall, a good correlation was observed
between simulated and observed discharge. However,certain biases were observed at some points throughout
the time period of each event, especially for the lower
discharge rate, which could have been caused by physicalDischarge (m3/s)

6000
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NSE: 0.71

Simulated

KGE: 0.82

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Discharge (m3/s)

properties and model uncertainties (Moges et al. 2021).
These uncertainties are not discussed in detail in thisstudy, as our target was to correlate the peak simulated
discharge results with the observed discharge data. The
NSE and KGE values were greater than 0.6 in all threestations for the first event, indicating that the model performed well and that the simulated results can be considered acceptable for the Mogami River Basin.
To further confirm the model performance, we performed hydrological modeling for the event of 07–16
September 2015 (second heavy rain event). The timeseries of simulated and observed discharge at the hydrological stations is shown in Fig. 3. The average values of
NSE and KGE for the three stations were 0.76 and 0.64,
respectively, which implies that the performance of thesimulation is as good as that observed for the first heavy
rain event. In terms of the timing and value of peak discharge, the simulated discharge data were comparable tothe observed discharge data. Therefore, it is confirmedthat the model performance of the simulated discharge
values for the Mogami River Basin was reliable. One of

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Page 6 of 17

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KGE: 0.66

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Fig. 2 Time-series profile of simulated discharge by RRI and observed discharge at three hydrological stations (G01, G02, and G03) for the event of
11–22 July 2004

P.C. and Sawazaki ﻿Prog Earth Planet Sci

Discharge (m3/s)

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Fig. 3 Time-series profile of simulated discharge by RRI and observed discharge at three hydrological stations (G01, G02, and G03) for the event of
7–16 September 2015

the benefits of the RRI model is that simulated discharge
can be extracted for any grid within the ungauged subbasin and used for further analysis.
3.2 Comparison of simulated discharge with seismic noise
dataFirst, we selected points on the main river channel of the
sub-basin that are close to each seismic station (Fig. 1).
The distance from the selected center points of theriver grid to N.FGTH and N.MGMH is approximately
240 m and 280 m, respectively. The extracted simulated
discharge for the selected two points was then compared with noise data from the seismic stations. For the
N.MGMH station, another small tributary is locatedcloser to the seismic station (Fig. 1), which may also
excite seismic noise. However, in this study, we considered that the contribution from the main channel
was more significant than that from the small tributary
because of the offset effect between the amount of discharge and distance to the seismic station.

Figures 4 and 5 depict the raw and clipped power
spectra of the seismogram recorded at N.FGTH and
N.MGMH for the event of September 2015, respectively,
where the clipped spectra were calculated using the procedure explained in “Seismogram data processing” section. Transit signals, which can be identified as verticallines in Figs. 4a and 5a, were effectively removed in theclipped running spectra (Figs. 4c, 5c). The spectral shapeshows clear differences among the time periods of daytime, midnight, and peak streamflow at both stations(Fig. 4b, d, 5b, d). For all the selected periods, the noise
power has the strongest peak around 0.2 to 0.3 Hz as secondary microseism excited the ocean waves (e.g., Ardhuin et al. 2019) at both stations. Although the energy
offered by the secondary microseism tends to decreaseas the frequency increases, this power is still high at frequencies lower than approximately 1 Hz. In the 1–2 Hz
range, an increase in noise power is identified only forthe period of peak streamflow (spectra shown by red),
especially at N.MGMH. At frequencies higher than 2 Hz,
although the noise power during peak streamflow isP.C. and Sawazaki ﻿Prog Earth Planet Sci(2021) 8:58

Page 8 of 17(a) 2015 N.FGTH running spectra(b) 2015 N.FGTH spectra
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Frequency (Hz)10−7 10−6 10−5 10−4 10−3 10−2 10−1

Noise power (nJ/m3)

Fig. 4 Spectrograms of seismic noise recorded at the N.FGTH station for the event of September 2015. a Running spectra of the raw seismogram.
b Spectra at the three time periods shown in (a), where black, blue, and red spectrum are obtained in the daytime, midnight, and peak streamflow
periods, respectively. c Running spectra of the seismogram after “clipping” transient peaks (e.g., earthquakes). d Spectra at the three time periods
shown in (c). The gray dashed lines in each panel represent the spectral window used for our analysis (1–2 Hz)

higher than that in other periods, the difference between
daytime (spectra drawn in black) and midnight (spectradrawn in blue) becomes significant. This difference arises
due to the cultural noise that reflects social activities
such as traffic and machinery, which is typically high inthe daytime and low at night (e.g., Mcnamara and Boaz2019). Considering these characteristics of the observed
spectra, we consider that the 1–2 Hz range is dominatedby streamflow. Therefore, using this frequency range is
optimal for our purpose, and is the main reason why theaverage power of this frequency range was selected forfurther analysis.
To elucidate the application of noise data to flood
events, the results for the events of July 2004, September 2015, and October 2019 are shown in Fig. 6, where
the last event was caused by Typhoon Hagibis. In these
events, the high-discharge peaks were highly synchronized with the 1–2 Hz noise peaks at both stations.

However, the noise power was not highly synchronizedwith the discharge peaks when the peak was relatively
low, especially for the 2004 event. One reason for this
could be that the simulated discharge did not always
closely fit the observed discharge. As shown in Fig. 2, thesimulated lower peaks tended to exceed the observed
lower peaks from 13–15 July 2004. It should be notedthat the noise power was compared to the simulated
discharge in this study, and not the observed discharge.
Contamination of the secondary microseism and culturalnoise in 1–2 Hz range may be another reason for thispoor synchronization.
3.3 Discharge prediction from noise data

A correlation was confirmed between the simulated discharge and noise power, especially for the maximum
peak discharge during the event period. As mentioned
in the previous section, this trend was not necessarily

P.C. and Sawazaki ﻿Prog Earth Planet Sci(2021) 8:58

Page 9 of 17(a) 2015 N.MGMH running spectra(b) 2015 N.MGMH spectra
10−2Noise power (nJ/m3)

Frequency (Hz)

40

30

20

10

0

09/08

09/09

09/10

09/11

09/12

09/13

10−3
10−4
10−5
10−6
10−7
10−8
0.1

09/14

09/08 15:00
09/09 01:00
09/11 01:00
0.2

0.5

Date

(c) 2015 N.MGMH running spectra (clipped)

5

10

20

(d) 2015 N.MGMH spectra (clipped)

Noise power (nJ/m3)

Frequency (Hz)

2

10−2

40

30

20

10

0

1

Frequency (Hz)

09/08

09/09

09/10

09/11

09/12

09/13

Date

09/14

10−3
10−4
10−5
10−6
10−7
10−8
0.1

09/08 15:00
09/09 01:00
09/11 01:00
0.2

0.5

1

2

5

10

20

Frequency (Hz)10−7 10−6 10−5 10−4 10−3 10−2 10−1

Noise power (nJ/m3)

Fig. 5 Spectrograms of seismic noise recorded at the N.MGMH station for the event of September 2015. a Running spectra of the raw seismogram.
b Spectra at the three time periods shown in (a), where black, blue, and red spectrum are obtained in the daytime, midnight, and peak streamflow
periods, respectively. c Running spectra of the seismogram after “clipping” transient peaks (e.g., earthquakes). d Spectra at the three time periods
shown in (c). The gray dashed lines in each panel represent the spectral window used for our analysis (1–2 Hz)

observed for cases of lower discharge. However, as thisstudy aims to understand the timing and peak discharge
in an ungauged river basin during heavy rain events, thisreduced correlation at lower discharge values is not aserious problem. Considering the observed correlation,
we modeled the predicted discharge, Qprd , and the noise
power, E, as follows:A(E − E0 )b (E > E0 ),Qprd =(3)0(E ≤ E0 )where A, b, and E0 are the control parameters. By fitting
Eq. (3) to the simulated discharge, we estimated theparameter set for each event and seismic station. We notethat Eq. (3) is derived empirically, and is not based onsolid physical background characteristics relevant tonoise excitation. The physical background of the noise
excitation process is discussed in “Seismic noise data forhydrological applications” section. We also note that E0
was fixed to the average noise power during the last twodays before each flood event. According to Eq. (3), E0
indicates the background noise power derived fromsources other than the streamflow. Since this value mayvary with time, a best-fit E0-value obtained for one event
is not necessarily applicable to another event. Therefore,
we optimized only the A and b values for each event andstation by maximizing the NSE value given by Eq. (1).
Moreover, it should be noted that the simulated discharge was considered as the reference data for the comii
parison; this implies that Qsim
and Qobs
of Eq. (1) wereirepresented as the predicted discharge ( Qprd
) and simui
lated discharge (Qsim), respectively, in the optimization
procedure.
Time seris data of observed noise density (1–2 Hz),simulated discharge, and predicted discharge at/near

1200

Noise power
Discharge (simulation)

800

0.004
400

0.002

0.010

0

07/1107/12 07/13 07/14 07/15 07/16 07/17 07/18 07/19 07/20 07/21 07/22

2004 N.MGMH 1−2 Hz

180

Noise power
Discharge (simulation)

Discharge (m3/s)

0.000

120

0.005
60
0.000

0.008
0.006

07/1107/12 07/13 07/14 07/15 07/16 07/17 07/18 07/19 07/20 07/21 07/22

2015 N.FGTH 1−2 Hz

0

1200

Noise power
Discharge (simulation)

800

0.004
400

0.002

0.025
0.020
0.015

09/07

09/08

09/09

09/10

09/11

09/12

09/13

2015 N.MGMH 1−2 Hz

180

Noise power
Discharge (simulation)

120

0.010

60

0.005
0.000

0.008
0.006

0

09/14

Discharge (m3/s)

0.000

09/07

09/08

09/09

09/10

09/11

09/12

09/13

09/14

2019 N.FGTH 1−2 Hz

0

1200

Noise power
Discharge (simulation)

800

0.004
400

0.002
0.000

0.010

10/10

10/11

10/12

10/13

0

10/14

2019 N.MGMH 1−2 Hz

180

Noise power
Discharge (simulation)

120

0.005
60
0.000

10/10

10/11

10/12

10/13

10/14

0

Discharge (m3/s)

2004 N.FGTH 1−2 Hz

Discharge (m3/s)

0.006

Page 10 of 17

Discharge (m3/s)

0.008(2021) 8:58

Discharge (m3/s)

Noise power (nJ/m3)

Noise power (nJ/m3)

Noise power (nJ/m3)

Noise power (nJ/m3)

Noise power (nJ/m3)

Noise power (nJ/m3)

P.C. and Sawazaki ﻿Prog Earth Planet Sci

Fig. 6 Time-series profile of simulated discharge at the main river channel close to the seismic stations N.FGTH and N.MGMH and the seismic noise
power of 1–2 Hz at these stations for the events of July 2004 (upper panels), September 2015 (middle panels), and October 2019 (lower panels)

P.C. and Sawazaki ﻿Prog Earth Planet Sci

Page 11 of 17

noise power–discharge relationship, significant event
dependence was observed for the fitting curves and theestimated A and b values due to the large scatter of thesimulated discharge.
To understand the uncertainty of the estimated parameters in this optimization, we visualized areas with relatively high NSE values (Fig. 8). The areas with high NSE
values exhibit very sharp and long peaks, and a strong
correlation between A and b values is observed. Even
though the best fit parameters differ by events, thesevalues seem to be indistinguishable when considering
their uncertainty ranges, especially for N.FGTH. Conversely, the difference between stations is distinguishable
because the background seismic noise level, topographyof river cross sections, and various other factors differ by
location.
To further examine the validity and predictability ofdischarge values, we computed Qprd using various combinations of estimated parameter sets and observed noise
energies. As there were three parameter sets and threenoise energies from the 2004, 2015, and 2019 events,
there were a total of nine combinations of Qprd for eachseismic station. Table 2 presents the NSE values for eachcase. Figure 9 provides a comparison of simulated andpredicted discharge using the parameter sets from all
three events.
The NSE values were generally high (> 0.70) for the2015 and 2019 events at the N.FGTH station. Notably,some predicted discharges exhibited high NSE values,
even when calculated using a parameter set estimatedfor a different event. For example, the 2019 discharge
data were predicted quite well using the 2004 and 2015
parameter sets (NSE is 0.86 and 0.84, respectively).
Regardless of the parameter sets used, discharge values predicted for the 2015 and 2019 events at N.FGTH
matched the simulated discharge closely, particularly thetiming and amount of peak discharge. This is because thethree parameter sets obtained for different events areindistinguishable when considering the uncertainty range(Fig. 8) for N.FGTH. These results confirm the good prediction performance of the model by using parameter
sets estimated for other events. An acceptable prediction
performance was also observed for N.MGMH when the

N.FGTH

1200

Discharge (m3/s)(2021) 8:58

800

400

2004
2015
2019
0
0.000

0.002

0.004

0.006

0.008

Noise power (nJ/m3)

N.MGMH

Discharge (m3/s)

180

120

60

2004
2015
2019
0
0.000

0.005

0.010

0.015

0.020

0.025

Noise power (nJ/m3)

Fig. 7 Relationship between simulated discharge and seismic noise
power data from the N.FGTH and N.MGMH stations for the events ofJuly 2004, September 2015, and October 2019. Regression curves are
estimated by fitting Eq. (3) to the data

F.FGTH and N.MGMH stations during the event of
10–23 July 2004, 7–16 September 2015, and 10–15
October 2019 are given in Additional file 1. In Fig. 7,
we show the results of fitting for each event and station. To assess the variation in the control parameters
for different events, distinct curves were fitted to each
event using different colors. The estimated parameters are summarized in Table 1. Overall, although
the fitting curves capture the general trend of theTable 1 Best fit A- and b-values for each event and station
Event

2004
2015
2019

N.FGTHN.MGMHA ­(m3/s) (nJ/m3)−bb

E0 (nJ/m3)

A ­(m3/s) (nJ/m3)−bb

E0 (nJ/m3)

1.26 × ­105

0.97

3.29 × ­10–4

3.55 × ­104

1.08

–4

3

0.65

8.42 × ­10–4

–4

5

1.69

5

1.12 × ­10

58.91 × ­10

0.90
1.28

6.82 × ­10
2.90 × ­10

2.24 × ­10
5.01 × ­10

E0 values are calculated from the average seismic noise level obtained two days prior to the flood for each event

1.44 × ­10–3
5.73 × ­10–4

P.C. and Sawazaki ﻿Prog Earth Planet Sci

2.5

Page 12 of 17

N.FGTH

2.5

2004 maxNSE=0.52
2015 maxNSE=0.78
2019 maxNSE=0.91
maxNSE−0.1
maxNSE−0.05
maxNSE−0.025

2.0

1.5

b

b

2.0

(2021) 8:58

2004 maxNSE=0.51
2015 maxNSE=0.75
2019 maxNSE=0.93
maxNSE−0.1
maxNSE−0.05
maxNSE−0.025

1.5

1.0

1.0

0.5
103

N.MGMH

104

105

106

107

108

0.5
103

104

105

106

107

108

A (m3/s)(nJ/m3)−b

A (m3/s)(nJ/m3)−bFig. 8 Best-fit A and b values and their uncertainty ranges. Stars show the best-fit values that maximize the NSE value. Colored areas represent
regions with relatively high NSE values; that is, NSE values are higher than the maximum NSE value minus 0.1 (yellow), 0.05 (orange), and 0.025(brown). Colored areas for different events partly overlap

Table 2 NSE values evaluated for each heavy rain event using parameters estimated for all heavy rain events
Event

N.FGTH
2004 parameters

N.MGMH
2015 parameters

2019 parameters

2004 parameters2015 parameters

2019
parameters

2004

0.52

0.40

0.48

0.51

0.42

0.18

2015

0.72

0.78

0.72

-1.1

0.75

-3.1

2019

0.86

0.84

0.91

0.37

0.61

0.93

parameter set estimated for the 2015 event was used to
predict discharge during the 2019 event (NSE = 0.61).
However, the prediction performance was much poorer
in some cases. For the 2004 event, even the predicted discharge values modeled by the parameter set of the same
event exhibited poor predictability (NSE of 0.52 and 0.51
for N.FGTH and N.MGMH, respectively). Nevertheless,the timing and amount of peak discharge were predicted
well by all parameter sets for the 2004 event at both stations (Fig. 9a) despite the low NSE values, which is useful for disaster response. It should be considered that thesimulated and observed discharge values do not match
perfectly (Figs. 2, 3). Therefore, it is possible that theobserved discharge near the stations differed significantly
from the simulated discharge for the 2004 event.
For the 2015 event at N.MGMH station, the timing of the peak was predicted well; however, the heightof the peak was considerably overestimated when using
the 2004 and 2019 parameter sets, and this resulted invery low NSE values (− 1.1 and − 3.1, respectively). The
cause of this overestimation was the spiky increase innoise power around 00:00 on 11 September (Fig. 6). We
checked the raw seismogram around this time and confirmed that it shows a gradual increase and decrease
within a few hours. Its appearance is very different tothat of earthquakes or landslides. The timing of this signal is almost midnight, and this fact negates the possibility of contamination from cultural noise because it must
be strong in daytime only. Therefore, only the possibility of human encroachment near the N.MGMH station(e.g., the release of a dam) remains. In fact, the peak of
N.FGTH was delayed than that of N.MGMH, and its
shape is smoother. Although we have no direct evidenceof human encroachment, the apparent behavior of noise
power gives us a hint of this possibility. Human encroachment is always challenging to address when simulating
entire periods using simplified hydrological models. Thisissue is discussed further in “Discussion.” Debris flow isalso a potential cause, but we did not find any evidence
that supports this possibility.

P.C. and Sawazaki ﻿Prog Earth Planet Sci

Page 13 of 17

2004 N.FGTH

1200

Discharge (m3/s)

a(2021) 8:58

Discharge (simulation)

800

Discharge (2004 parameters, NSE=0.52)
Discharge (2015 parameters, NSE=0.40)
Discharge (2019 parameters, NSE=0.48)400
007/1107/12

07/13

07/14

07/15

Discharge (m3/s)

120

07/19

07/20

07/21

07/22

07/19

07/20

07/21

07/22

Discharge (2004 parameters, NSE=0.51)
Discharge (2015 parameters, NSE=0.42)
Discharge (2019 parameters, NSE=0.18)60

07/1107/12

07/13

07/14

07/15

07/16

07/17

07/18

2015 N.FGTH

b 1200Discharge (m3/s)

07/18

Discharge (simulation)0

Discharge (simulation)

800

Discharge (2004 parameters, NSE=0.73)
Discharge (2015 parameters, NSE=0.78)
Discharge (2019 parameters, NSE=0.72)

400
0

09/07

09/08

09/09

09/10

09/11

09/12

09/13

09/14

09/12

09/13

09/14

2015 N.MGMH

300

Discharge (m3/s)

07/17

2004 N.MGMH

180

Discharge (simulation)

200

Discharge (2004 parameters, NSE=−1.1)
Discharge (2015 parameters, NSE=0.75)
Discharge (2019 parameters, NSE=−3.1)

100
0

09/07

09/08

09/09

09/10

09/11

2019 N.FGTH

c 1200Discharge (m3/s)

07/16

Discharge (simulation)

800

Discharge (2004 parameters, NSE=0.86)
Discharge (2015 parameters, NSE=0.84)
Discharge (2019 parameters, NSE=0.91)

400
0

10/10

10/11

10/12

10/13

10/14

10/13

10/14

Discharge (m3/s)

2019 N.MGMH
180
120

Discharge (simulation)
Discharge (2004 parameters, NSE=0.37)
Discharge (2015 parameters, NSE=0.61)
Discharge (2019 parameters, NSE=0.93)

60
0

10/10

10/11

10/12

Fig. 9 Simulated and predicted discharges for a July 2004 event, b September 2015 event, and c October 2019 event

P.C. and Sawazaki ﻿Prog Earth Planet Sci(2021) 8:58

4 Discussion
Several previous studies have reported a good correlation between observed discharge and seismic noise data
(Burtin et al. 2008; Sawazaki et al. 2016; Eibl et al. 2020).
However, hydrological and seismic stations are normally located far from each other. Therefore, this study
compared simulated river discharge data with the noisedata of nearby seismic stations in the frequency range of
1–2 Hz in the Mogami sub-basin. Here, we discuss thereliability of simulated discharge data and seismic noise
data, while elucidating the relationship between the two.
4.1 Reliability of simulated discharge data

Although global renowned hydrological models such as
HEC-HMS and SWAT have been applied to various typesof river basin, discharge is predominantly simulated at
the basin or sub-basin scale (Arnold and Fohrer 2005;
Beven et al. 1995; Liang et al. 1994; P.C. et al. 2018a).
The most important feature of the RRI model is that it isbased on a grid system so that simulated discharge canbe extracted at any grid point in the Mogami River Basin.
Hence, simulated discharge could be extracted for rivers
close to seismic stations in this study. Fully distributedhydrological models may also be applied to river basins
where various types of hydrometeorological data are
available; however, the performance of these models canbe poor in ungauged river basins due to a lack of input
variables and physical parameters (Tegegne et al. 2017;
P.C. et al. 2018a; Moges et al. 2021). Therefore, simplified hydrological models are more attractive as they areeasy to implement in a short time and require fewer
input data. However, each type of hydrological model
has its advantages and disadvantages. Therefore, a good
relationship may not always occur between observed
and simulated data. For example, the spiky noise peakobserved at N.MGMH for the 2015 event may reflect
such a discrepancy. Human encroachment on rivercourses, and undefined hydraulic properties of the river
may also cause discrepancies between observed and simulated discharge values. There are some river dams, especially in the middle and upstream parts of the basin, thatwere not included during the model setup and may produce some uncertainties in the simulated discharge data.
Observed discharge data are extremely limited for remoteand complex river basins; therefore, it may not be possible to compare model results for several sub-tributaries
within a basin. In this study, it is believed that reliable
discharge values were simulated from the RRI model for
sub-tributaries within the Mogami River Basin. Uncertainties in discharge values could have been derived fromuncertainties in the physiographic data (Yamazaki et al.
2019) or model properties (Gupta et al. 2012).

Page 14 of 17

In this study, JMA radar rainfall was used as the main
input in the simulation. To minimize the error associatedwith estimating rainfall, the JMA constantly updates theradar data with data available from Automated Meteorological Data Acquisition System (AMeDAS) rain
gauge stations. Therefore, we did not check the quality ofradar rainfall data in this study. The greatest advantage ofradar rainfall data is the high spatial resolution (P.C. et al.
2019). However, the quality of radar rainfall data may
be reduced over mountainous regions (P.C. et al. 2016),
which may increase the bias on simulated hydrological
data. Therefore, for proper flood disaster prevention andmanagement, the use of hydrological data with a hightemporal resolution may be the best option, particularly
during extreme events. However, hydrological simulationof ungauged river basins has been neglected for various
reasons, such as the unavailability of observed hydrological data and the time lag between rainfall and flooding, which is very short in small river basins. Meanwhile,simulated output data basically depend upon the input
data and model type. Physical distributed models requirevarious types of input data, which require a long computation time to produce output data. Even if one wants
to use high-resolution temporal and spatial inputs or
obtain output data in the same format from a simplifiedhydrological model, the computation time may increase.
Therefore, most hydrological models may not be suitable
for the consideration of input and output data with a hightemporal resolution for long timespans or near real-time
simulation.
The remote sensing approach may also be used to estimate river discharge. This is one of the more challenging
tasks, especially in mountainous regions during heavy
rain events. The effect of dense vegetation on the rivercourse, shadow and layover effect on an area of interest,
location presence of cloud coverage, and size of the rivercourse itself are extremely common phenomenon thatcan easily cause gaps in hydrological data collection during regular monitoring, particularly in heavy rain events(Schumann et al. 2011; Huang et al. 2018; Clement et al.
2018). To overcome such gaps, seismic noise data canbe a bridge not only for the regular monitoring of riverdischarge, but also for validating discharge data obtained
from remote sensing data.
4.2 Seismic noise data for hydrological applications

According to our analysis of seismic noise and river discharge data for a mountainous region of Japan, river discharge prediction using seismic noise data is a promisingtechnique. By estimating the parameter set used for predicting peak discharge from noise power, we may be able
to monitor real-time river discharge using seismic noise
recorded at nearby stations, even in locations where

P.C. and Sawazaki ﻿Prog Earth Planet Sci(2021) 8:58

performing direct discharge observations is practically
impossible.
Recorded seismic noise data filtered into the 1–2 Hz
frequency band were confirmed as the optimal band to
conduct a comparison with the flow of a nearby river inthis study. This frequency band contains relatively lower
power due to secondary microseisms and cultural noise.
These background noise properties are important toimprove the prediction performance of river discharge
in mountainous regions, where direct discharge data are
extremely limited.
However, we should note that the appropriate frequency range may depend on time and location. For
example, noise from secondary microseisms is particularly high during typhoons. Additionally, cultural noise
is very strong over a wider frequency range if the seismometer is installed closer to traffic. As such, the usable frequency range may depend on location and time.
In fact, Anthony et al. (2018) deployed a small array ofseismometers close to a river, with sensors emplaced at
depths of less than 1 m from the surface; consequently,
it was observed that seismograms at frequencies of lessthan 1 Hz closely matched the discharge trends for asmall river. Thus, the type of seismometer and installation conditions (Hi-net sensors are installed at depths ofmore than 100 m) also influence the dominant frequencyof seismic noise.
It is also important to consider the physical background on the streamflow noise excitation process. Thusfar, bedload transport and turbulent flow are considered
influential causes and have been modeled by Tsai et al.
(2012) and Gimbert et al. (2014), respectively; these models indicate different frequency dependencies in noise
excitation. Burtin et al. (2008) noted that the frequency
dependence of the noise excitation process may dependon the season or month of the year. However, in ourview, there is no decisive consensus regarding the dominant mechanism of the noise excitation process, and it
seems to be premature to apply the existing models toour observation without any consideration of diversity ofriver flow conditions. This is why we adopted the simple
empirical relationship given by Eq. (3) in this study. The
different conditions that we can apply using this empirical relationship will be researched in a future work.
To improve the proposed noise-based discharge prediction technique, two major factors should be considered. One is the discrepancy between the simulated andobserved discharge values, as discussed in “Reliability ofsimulated discharge data” section. Unless the discharge
record is obtained close to the seismic station, hydrological simulations are required to obtain discharge values
at a nearby point. As the simulated and real discharge
values do not always match sufficiently, it is necessary

Page 15 of 17

to develop more accurate and precise simulation methods. Another factor is the validity of the discharge-noise
relationship given by Eq. (3). This simple empirical model
assumes that the A and b values are constant and specificto the location. This assumption fails if there are changes
in factors such as the riverbed topography, sedimentconditions, and the installation environment of the seismometer. Variable model parameters indicate that theparameters estimated from past events cannot be applied
for prediction purposes.
Currently, our tentative conclusion is that a good prediction performance can be achieved on a case-by-casebasis, as shown in Fig. 9. Nevertheless, it is promisingthat the timing and size of high-discharge peaks could be
adequately predicted from seismic noise in many cases,
even though the parameters have not been robustly
estimated at this stage. Thus, further research should
continue to improve the prediction performance of thistechnique by examining multiple events in mountainous
ungauged river basins worldwide.

5 Conclusion
Discharge data for mountainous rivers are particularly
important for water resource management and relatedscientific research. Moreover, recent flood events inmountainous river basins in Japan have resulted in significant loss of life and damage to infrastructure. Therefore,
estimating the peak streamflow of rivers during flood
events is crucial for flood disaster prevention and management. Although performing direct observations is
the preferred method for estimating discharge data, it is
not practical due to the complex topography and remoteenvironment of mountainous regions. Therefore, the useof indirect approaches such as hydrological simulations
and remote sensing technology has been considered toestimate river discharge, especially during extreme rain
events. However, each approach has advantages anddisadvantages.
In this study, we proposed the use of Hi-net seismic
observations to predict the timing and amount of peakdischarge in a mountainous sub-basin of the Mogami
River Basin during heavy rain events. Hi-net has a good
network coverage throughout the mountainous regionsin Japan. Discharge data simulated by the RRI model was
validated using gauging station data for two independent
rain events, and then compared with seismic noise datafrom nearby stations for three heavy rain events. The
results indicated that seismic noise data in the frequency
range of 1–2 Hz exhibited a similar trend to the simulated discharge values.
We conclude that our study makes a significant contribution to the literature because performing direct observations of river discharge is often impossible in ungauged,

P.C. and Sawazaki ﻿Prog Earth Planet Sci(2021) 8:58

small, and mountainous river basins; however, Hi-net
exhibits a much better network coverage, even in themountainous regions of Japan. Therefore, the proposed
technique is promising for river discharge prediction inbasins far from hydrological stations. According to thiscase study, seismic data can be used to estimate river discharge time-series data, particularly the size and timing ofpeak discharge, within ungauged river basins in Japan. Suchmonitoring is crucial for flood disaster prevention andmanagement during heavy rain events in the mountainous regions of Japan. At this stage, the performance of thedischarge prediction differs on a case-by-case basis. Future
research should analyze more past rainfall events andexpand this approach to other seismic stations in mountainous river basins.
Abbreviations
ACC​: Flow accumulation; AMeDAS: Automated Meteorological Data Acquisition System; DEM: Digital elevation model; DIR: Flow direction; Hi-net:
High-sensitivity seismograph network; JMA: Japan Meteorological Agency;
KGE: Kling-Gupta efficiency; MERIT: Multi-error-removed improved-terrain;
MLIT: Ministry of Land, Infrastructure, Transport and Tourism; NIED: National
Research Institute for Earth Science and Disaster Resilience; NSE: Nash–Sutcliffe efficiency; RRI: Rainfall-runoff-inundation.

Supplementary Information
The online version contains supplementary material available at https://​doi.​
org/​10.​1186/​s40645-​021-​00448-1.
Additional file 1. An additional file for the observed noise density(1–2 Hz), simulated discharge, and predicted discharge at/near N.FGTH
and N.MGMH stations during the events of 10–23 July 2004, 7–16 September 2015, and 10–15 October 2019 is provided.
Acknowledgements
The authors are grateful to the Ministry of Land, Infrastructure, Transport, andTourism (MLIT), the Japan Meteorological Agency (JMA), and Dai Yamazaki’s
website for publishing and updating important information and related
datasets on their webpages. The authors would like to thank the anonymous
reviewers for their constructive comments on our paper.
Authors’ contributions
SPC proposed the topic, conceived and designed the research theme. KS and
SPC carried out the experimental study and analyzed the data to sum up theresults. KS collaborated with the corresponding author for the writing of themanuscript. All authors read and approved the final manuscript.
Funding
This study was funded by a Taisei Foundation 2020 research grant.
Availability of data and materials
Hi-net records are available from the data repositories of NIED (https://​doi.​org/​
10.​17598/​NIED.​0003). Observed discharge data are available from the Water
Information System webpage of MLIT (http://​www1.​river.​go.​jp/, in Japanese).
Physiographic data (MERIT DEM) are available at http://​hydro.​iis.u-​tokyo.​ac.​jp/​~yamad​ai/​MERIT_​DEM/. Radar rainfall data can be made available based onrequest.

Page 16 of 17

Declarations
Competing interests
The authors declare that they have no competing interest.
Received: 11 July 2021 Accepted: 22 September 2021

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