京都大学防災研究所年報 第 66 号 B
DPRI Annuals, No. 66 B, 2023

Characterization of Future Rainfall Prone to Sediment Hazards in a Changing
Climate Using Radial-Basis Function Network:
A Case Study of Rokko Mountain Area

Ying-Hsin WU, Akihiko YAMAJI and Eiichi NAKAKITA
Synopsis
This study, as a first attempt, aims to utilize the method of Radial-Basis Function
Network (RBFN) to examine hourly rainfall intensity and soil-water index obtained fromclimate projections for investigating features of future rainfall under climate change
influences. Our study area is focused on Rokko Mountain in Hyogo prefecture. The 1-km
MLIT 3rd-mesh system is adopted in our analysis. The 2-km and 5-km Non-Hydrostatic
Regional Climate Models (NHRCM) under RCP2.6 and RCP8.5 scenarios are used as
future climate projections. A transformation matrix is used to quantify geometricalchanges of RBFN contours. The characteristics of cumulative rainfall amount and rainfall
duration of hazardous rainfall events are also examined. The analysis results show thatsoil-water index is much enlarged while hourly rainfall is a bit enlarged under RCP2.6,
but, reversely, soil-water index remains unchanged while hourly rainfall is muchintensified on the mountain side facing Osaka Bay under RCP8.5 in 2-km NHRCM. The
hazardous rainfall events in 2-km NHRCM have shorter durations and smaller cumulative
amount comparing to the ones in 5-km NHRCM.
Keywords: climate change, NHRCM, Radar-AMeDAS, Radial Basis Function Network

1.

BackgroundIn the last decades, extreme climate becomes
more frequent to trigger considerable severe waterrelated disasters and has raised the great attention of
the government authorities and scientificcommunities. Recent extreme rainfall events show
obvious changes that rainfall was elongated in the
period and intensified in a much higher accumulated
amount and peak intensity that have broken newobservation records in many places, and havetriggered devastating floods, landslides, andsediment disasters beyond our experience. IPCC
report (IPCC, 2021) shows an increasing trend of
global temperature on earth-surface over the last 50
years, and this increasing trend is termed as global
warming phenomenon due to the huge amount ofemissions of greenhouse from human industrial

development in the last century. Under the
influences of global warming phenomenon in Japan,
long-term observation (JMA, 2020) has revealed anincreasing trend of occurrence frequency of extreme
rainfall of which the hourly precipitation is greaterthan 80 mm, and, meanwhile, a decreasing trend ofannual precipitation days. This implies that, in the
future, it would be more likely to occur muchintensified rainfall which is prone to amplify
occurrence of landslides and sediment hazards. To
achieve early warning practices for these kinds ofhazards, Ministry of Land, Infrastructure, Transport
and Tourism (abbreviated as MLIT) is currently
applying critical line (CL) method which utilizes twohydrometeorological indices, i.e., hourly rainfall
intensity (PREC hereafter) and soil-water index(SWI) (Osanai et al., 2010; MLIT 2020). The twohydrometeorological indices can reflect influences― 238 ―

Fig. 1Comparison among digital elevation models of MLIT 3rd-mesh (1-km), NHRCM02 (2-km), andNHRCM05 (5-km) in Subfigures a-c). Subfigure d) shows the study area of Rokko mountain. The elevation
variation relative to MLIT 3rd-mesh DEM are shown in e) and f). The target meshes are denoted by white
rectangles. The satellite photo is extracted from Google Map.

of short-term peak rainfall and long-term soil
moisture condition on landslide occurrence and canbe reasonably applied to assess potential risk of
sediment disasters (Saito and Matsuyama, 2015).
Also, we have explored the future changes ofdisastrous rainfall prone to sediment disasters (Wuet al., 2020; 2021; 2022). However, we only
considered the values of maximum PREC and SWI
without examining overall features of the two
rainfall indices. Therefore, we herein attempt toinvestigate future changes of PREC and SWI with afocus on the maximal geometric range of the two
indices. For future climate projection, we adopted
the 2-km and 5-km Non-Hydrostatic Regional
Climate Models, which is often called NHRCM(Murata et al., 2015; Murata et al., 2017; Kawase etal., 2021; Murata et al., 2022) and published byMeteorological Research Institute (MRI) of Japan
Meteorological Agency (JMA). Hereafter, the two
RCMs are abbreviated as RCM2 and RCM5,
respectively. The 1-km reanalyzed precipitation data
is used for verification. To reveal the geometricalchange of the two rainfall indices on each 1-km
MLIT 3rd-mesh, we utilize Radial Basis Function
Network (RBFN) (Osanai et al., 2010) to quantify
the geometric distribution of the two indices andexamine stretching of RBFN curves among
scenarios to interpret its relation to future changes ofrainfall prone to sediment disasters.
In this study, we select Rokko Mountain in
Hyogo prefecture as our study area, as is shown in
Fig. 1. In what follows, the introduction to data andmethodology we sued will be mentioned in Section
2, the analysis results will be discussed in Section 3.
The final part of Section 4 is concluding remarks.
2.

Data and Method

2.1 JMA Radar-AMeDAS
For verification and comparison, we utilized
high-resolution precipitation reanalyzed using
observations of 20 C-band radars and the AutomatedMeteorological
Data
Acquisition
System(abbreviated as AMeDAS) operating by JMA. The
data period is from 2006 to 2022 (17 years in total).
The resolutions are 30 minutes in time and 1 square
kilometer in space. As one of the major benefits, thecoordinate system used for Radar-AMeDAS is justthe MLIT 3rd-mesh system which is using for earlywarning of sediment disaster. This means that thedata on each 1-km mesh can well represent therainfall on that scale. For brevity, Radar-AMeDAS― 239 ―

dataset is herein abbreviated as JMARA.
2.2 Future climate projections NHRCM
The spatiotemporal resolutions of RCM5 are 5
km in space and 30 minutes in time, and RCM2 are
2 km in space and 1 hour in time. The differences ofdigital elevation models (DEM) among 1-km MLIT
3rd-mesh, 2-km RCM2, and 5-km RCM5 areillustrated in Fig. 1. The RCM2’s DEM is similar to
the real topographic, but the RCM5’s rather differsfrom the real topographic that the mountain peak issmoothed out. Some belief information of the two
RCM is listed in Table 1. Both have the sameensemble members, including one present climate
projection SPA, and four ensemble members of
future projections for the two scenarios ofRepresentative Concentration Pathway (RCP) 2.6
and 8.5 proposed in IPCC Fifth Assessment Reportin 2014 for representing human activities ofindustrial development. Each RCM is downscaled
from the simulation of a global climate model MRIAGCM3.2S by imposing sea-surface temperature(SST) of each scenario as the sea surface boundary
condition. The four future SST patterns are related
to El Niño phenomena. More technical details about
the two RCM can refer to the literature (Murata et al.,2015; Murata et al., 2017; Kawase et al., 2021;
Murata et al., 2022). The simulation period of each
RCM is 20 years with a one-year time slice and aspin-up period of 43 days. For the sake of brevity,
we shall take average of the four ensembles of
RCP2.6 and RCP8.5 to discuss their average features.
2.3 Extraction of rainfall events and indicesIn this study, the grid system of MLIT 3rd-meshwhose spatial resolution is 1 square kilometer isadopted for analysis. We processed JMARA dataset
continuously from 2006 to 2022 and processed the
20-year datasets of RCM5 and RCM2 in each oneyear time slice. The procedures of extraction of
rainfall events and indices are mentioned as follows.
The first step was to directly extract continuous timeseries of rainfall on the center of each 1-km meshwithout interpolation, and to convert the interval into
10-minute by uniformly distributing the original
rainfall series in the interval of 30 minute or one hour.
Then, the converted 10-minute rainfall series wasused for calculating continuous time series of SWI
by using the conventional method proposed by JMA.
Referring to MLIT’s definition of rainfall events(MLIT, 2020), we picked up all effective rainfall
events with a minimal rainfall threshold of 0.5
mm/hr. The two obtained time series of PREC and
SWI index were further analyzed to countoccurrence times of hazardous rainfall by checking
whether critical lines are passed as well as to identify
change features of hazardous rainfall using themethod of RBFN.
2.4 Radial-Basis Function Network (RBFN)In the current early-warning system, the criteria,
or called critical line on the parametric plane ofrainfall indices, for predicting occurrence of
sediment disaster are determined using the methodof Radial Basis Function Network, which is often
abbreviated as RBFN (MLIT, 2020; Osanai et al.,2010). For brevity, the RBFN theory is not detailed
here. By using radial basis function, such as
Gaussian basis function, RBFN is quite useful for
function approximation problems in many fields.
Therefore, the RBFN has been successfully used toquantify geometrical range of PREC and SWI of

Table 1 Brief information of all NHRCM members
Dataset
SPA

Scenario
N/A

SFA_C3
SFA_C0

Simulation Period
from 1980/09/01
to 2000/08/30

Less warm in East tropical Pacific

SFA_C1
SFA_C2

Boundary SST
Monthly observation(1979-2003)

RCP2.6&
RCP8.5Stronger El Niño
Warmer in Northwest Pacific
El NiñoSPA: present climate, SFA: future climate projection― 240 ―

from 2076/09/01
to 2095/08/30

Fig. 2 Contours of the response surfaces of rainfall indices (hourly precipitation and soil-water index) using
Radial Basis Function Network (RBFN) under the scenarios of (b, e) present climate, (c, f) RCP2.6, and (d,g) RCP8.5 as well as (a) historical observation at the mesh No. 52350137 where Kobe MeteorologicalObservatory is located. The analysis for RCP2.6 and RCP8.5 is performed by taking all the four members (C0,C1, C2, C3) into account.

non-occurrence rainfall events. To borrow thisbeneficial concept, as a first attempt, we utilize themethod of RBFN to the indices from climate
projections to examine future changes of rainfall
indices under climate change influence. In our
analysis, we follow the same theory and parametersettings to implement the RBFN model by referringto the official MLIT guideline (MLIT, 2020).
The input for training the RBFN model is pairsof rainfall indices, and the output of RBFN is a
response surface representing a probability density
function of non-occurrence rainfall. To gently remind, we only focus on investigating overall featuresof rainfall event on each mesh, but not on
determining criteria of disaster occurrence. So, we
consider all rainfall events are non-occurrence ones,
and used them to RBFN for finding out
corresponding response surfaces of rainfall events.
Finally, we examined geometrical stretch of
response surfaces among present and future
projections to evaluate the future change of rainfall
events.
2.5 Stretch of response surface of RBFN
After obtaining response surfaces using RBFN,
we then characterized the geometrical change of
response surface with a focus on examination ofcontours on the surface. Because sediment hazards

are usually triggered by extreme rainfall, ouranalysis tries to focus on this kind of rainfall which
may occurred in a lower probability. As a response
surface represent a probability density function of
non-occurrence rainfall, we choose to examine thecontour of= 0.1 which can be reasonably
considered as a boundary of extreme rainfall event.
To quantify the geometrical change between the
RBFN contours of present and future projections, we
assume a linear transformation mapping of two
contours,
=

(1)

,

where
= ,
respectively denotes thesequences of SWI and PREC of SPA with n pairs for= 1 ⋯ , and= ,denotes the ones of
future projections SFA. The transformation matrix J
is expressed as
=

=

! "
"
$%&'

−

$%&'

"
(, (2)! "where A, B, C, and D are the scaling component,
and $%&' the scaling factors in the directionsof SWI and PREC, respectively, and " denotes therotation angle with respect to the axes. In our
analysis which will be explained later, the rotation
angle " is generally too small to be ignored― 241 ―

Fig. 3 Comparison of the contours of= 0.1 under historical observation and the three climate
scenarios from a) NHRCM05 and b) NHRCM02 on the same mesh No. 52350137. The upper and rightsubfigures show the relative frequency of all events’ Soil-Water Index and Precipitation. Each circles denote
information from rainfall events.

hereafter. By comparing between contours of futureclimate with respect to the present climate, with thestretch ratios
and $%&' , a contour can beconsidered as being expanded in the positive SWI
direction if) 1, and shrunk in the negative
SWI direction when* 1. The similar manneris also applied to $%&' . Then, the least squares
method is then used to determine the four scaling
components of A, B, C, and D. The exact formulas
are listed in the appendix. With the obtained J,
further algebra gives the scaling factors ofand$%&' for quantification of the stretch or shrink of
the shape of RBFN contours.
3.

Analysis and Discussion

3.1 Comparison with Radar-AMeDAS
Fig. 2 illustrates comparison among thehistorical observation of JMARA, and climate
projections under different scenarios using RCM2
and RCM5 on the mesh of No. 52350137 where
Kobe Meteorological Observatory is located. The
contours in each dataset were obtained using
corresponding trained RBFN models. As a result, thecontour of SPA in RCM5 is similar to the JMARA

contour with a slight extension of SWI, but the oneof RCM2 has a higher PREC. The contours of
RCP2.6 in both RCMs show wider ranges of PREC
and SWI comparing to SPA. The contours of RCP8.5
in RCM5 have a slightly wider than RCP2.6, but theones of RCM2 are shrunk in the SWI axis. For better
comparison, Fig. 3 overlays all the contours of= 0.1 of all datasets from both RCMs withrelative frequency of SWI and PREC of rainfall
events. Clearly, we can see that the shape of= 0.1 contour is highly related to thefrequency of the two indices that the wider in the
direction of a rainfall index a wider frequency range
for the corresponding rainfall event, and vice versa.
Also, the RBFN contours could infer the
distributions with probability information.
3.2 Future changes of hourly rainfall and SoilWater Index
Fig. 4 illustrates the results of scaling ratios ofand $%&' of future climate projection withrespect to the present one. In the RCP2.6 scenario,
the range of SWI is much expanded as most of+ 1, and the PREC is also much extended in
RCM2 but slightly extended with some meshes― 242 ―

Fig. 4 The change ratios [%] of stretch of the contours of= 0.1, i.e., $%&' and, under the futurescenarios of RCP2.6 and RCP8.5 relative to the present climate member. The upper and lower rows show theresults using 5-km and 2-km NHRCM.

shrunk as* 1 in RCM5. This indicates therainfall pattern will tend to intensify the maximumof SWI in both RCMs but not to significantly change
the maximum of PREC in RCM5. Moreover, in the
RCP8.5 scenario, the contour feature is similar to the
RCP2.6 with a bit extension in RCM5. Particularly,
we find a reverse condition in RCM2 that the rangeof SWI is shrunk on the mountain side facing the
Osaka Bay. However, on the same side, the range of
PREC is much extended as) 1.2. From thiscondition, we could infer that the rainfall pattern will
be intensified to a higher hourly cumulative rainfall
amount but weakened to decline the maximum SWI.
Regarding the spatial distribution of RCP8.5 in
RCM2, we can observe that the stretch features are
divided well by the mountain ridge of the real
topography and the change of PREC is more obvious
on the side of Rokko Mountain facing the Osaka Bay
than the other side. This reason would be due to thatthe DEM of RCM2 matches better with the real
topography, as is shown in Fig. 1. As noticing this
opposite feature of the stretch of the ranges of SWI
and PREC under RCP2.6 and RCP8.5, we performed
further analysis to examine characteristics of rainfall
events prone to disaster and corresponding disasteroccurrence conditions, which will be explained in
the next subsection.

3.3 Features of hazardous rainfall events
To reveal the relation between stretch features ofcontours and possible disaster risk, we extracted alldisaster-prone rainfall events on each mesh by using
each specific critical line. With the extracted
hazardous events, we first examined the relation
between cumulative rainfall amount and rainfall
duration, as is shown in Fig. 5. Herein, all events are
extracted based on rainstorm system. We can see therainfall durations of RCM2 events are almost
concentrated within 72 hours and the cumulative
amount mainly ranges between 100 and 400 mm
with an average of maximum intensity > 60 mm/hr.
Then, the duration of RCM5 events lasts longer until
240 hours (10 days), and the cumulative amount
mainly ranges between around 150 and 600 mm witha maximum intensity < 20 mm/hr. Particularly, in
RCM5 there are totally 32 events with the maximum
hourly in-tensity < 20 mm/hr and the cumulative
amount > 500 mm. In these events the corresponding
critical line is passed because of much higher SWI.
On the other hand, the intensity of most RCM2
events is greater than 30 mm/hr, and there are fewer
events under RCP8.5. This condition reflects the
future climate events of RCM2 hold higher peakhourly rain rate, and the ones of RCM5 generally
possess weaker hourly intensity and longer durations.
Among influential factors, the major difference of― 243 ―

Fig. 5
Relation between cumulative rainfall and durations of the events passing CL and histograms withthe bin width of 12 hours. The colors denote variable datasets. The date period of Radar-AMeDAS is 17 years
and the others’ are 20 years. The symbol size denotes the peak hourly rain rate. The event number is quoted
after dataset item in the legend.

rainfall property between two RCMs could be
attributed to the grid resolution of which the effectcan also be seen from the stretch features, as isshown in Fig. 4.
Regarding the hazard occurrence condition, Fig.
6 shows the maps of hazardous rainfall event counts
and the monthly frequency. Without significant
difference of monthly frequency between two RCMs,
the maps of RCM2 show decreasing trends in future
projections, as are shown in Figs. 6e and 6f. Thisdecline trend can be verified by that the total numberof SPA event is 1.7 times of the RCP8.5 one, shownin Fig. 4. Meanwhile, it has been reported in theliterature (Murata et al., 2022) that in the area near
Osaka Bay the 20-yr mean maximum hourly
precipitation in July and August is higher in thepresent climate than the future one. This also verifies
that RCM2 holds decreasing future trends as higher
hourly precipitation will accompanies higher
possibility of hazard occurrence. More efforts will
be needed to clarify the mechanism of rainfall
generation in this area under present and futureclimate scenarios.

4.

Concluding remarks

In this study, we investigated future changes ofrainfall prone to sediment hazards by quantifying thegeometrical stretching of RBFN contours of rainfall
indices, i.e., soil-water index SWI and hourly
precipitation PREC, obtained from 5-km and 2-km
NHRCM. We also revealed the relation among thestretch features of RBFN contours, the basic
property of hazardous rainfall events, and possible
disaster risk. The characteristics of cumulative
rainfall amount and rainfall duration of hazardous
rainfall events are also examined. The analysis
results show that soil-water index is much enlarged
while hourly rainfall is a bit enlarged under RCP2.6,
but, reversely, soil-water index remains unchanged
while hourly rainfall is much intensified on themountain side facing Osaka Bay under RCP8.5 in 2km NHRCM. Regarding hazardous rainfall
characteristics, the hazardous rainfall events in 2-km
NHRCM have shorter durations and smaller
cumulative amount comparing to the ones in 5-km
NHRCM.
This study demonstrates the applicability of― 244 ―

Fig. 6 The spatial distribution and mesh-based monthly frequency of hazardous rainfall events under the
scenarios of SPA (a, d), RCP2.6 (b, e), and RCP8.5 (c, f). The values of SPA denote cumulative counts, andthe values of RCP2.6 and RCP8.5 denote variation relative to SPA. The upper and lower rows show the results
using 5-km and 2-km NHRCM.

RBFN with a Jacobian transformation matrix toassess the future change of rainfall events andprovide an alternative and objective way which cansystematically quantify characteristics of hazardous
rainfall in the future under climate change impact.
Furthermore, the quantified future changes of snake
line on each 3rd-mesh can help identify possible
hazardous rainfall pattern to assess future sedimenthazards.

Number 22K04331. We appreciate MLIT Sabo
Planning Division, Rokko Sabo Office, Hyogo
prefectural government, and Japan Weather
Association (JWA) for sharing valuable datasets.
The authors are grateful to the Publishing Committee
members who made the previous versions of this
instruction.

References
Acknowledgements
The datasets of 2-km and 5-km NHRCM areprovided by the Integrated Research Program for
Advancing Climate Models (TOUGOU) Grant
Number JPMX-D0717935498 from the Ministry of
Education, Culture, Sports, Science and Technology(MEXT), and by Research Funding from MLIT
Rokko Sabo Office, and by JSPS KAKENHI Grant

IPCC (2021): Climate Change: The PhysicalScience Basis. Contribution of Working Group I
to the Sixth Assessment Report of theIntergovernmental Panel on Climate Change.
Japan Meteorological Agency (2020): Climate
Change in Japan.
Kawase, H., Murata, A., Yamada, K., Nakaegawa,T., et al. (2021): Regional characteristics of future― 245 ―

changes in snowfall in Japan under RCP2.6 and
RCP8.5 scenarios, SOLA, Vol. 17, pp. 1–7.
MLIT (2020): Committee Discussions on
Technology and Evaluation of Sediment Disasters
under Climate Change. (in Japanese)
Murata, A., Sasaki, H., Kawase, H., Nosaka, M., etal. (2015): Projection of future climate changeover Japan in ensemble simulations with a highresolution regional climate model. SOLA, Vol.
11, pp. 90–94.
Murata, A., Sasaki, H., Kawase, H., Nosaka, M., etal. (2017): Projection of future climate changeover Japan in ensemble simulations using a
convection-permitting regional climate modelwith urban canopy. SOLA, Vol. 13, pp. 219–223.
Murata, A., Nosaka, M., Sasaki, H. and Kawase, H.
(2022): Dynamic and thermodynamic factors
involved in future changes in extreme
summertime precipitation in Japan projected byconvention-permitting regional climate model
simulations, JAMC, Vol. 61(9), pp.1221–1237.
Osanai, N., Shimizu, T., Kuramoto, K., Kojima, S.
and Noro, T. (2010): Japanese early-warning fordebris flows and slope failures using rainfall
indices with Radial Basis Function Network,
Landslides, Vol. 7, pp. 325–338.
Saito, H. and Matsuyama, H. (2015): Probable
Hourly Precipitation and Soil Water Index for 50yr Recurrence Interval over the JapaneseArchipelago, SOLA, Vol. 11, pp. 118–123.
Wu, Y.-H., Nakakita, E. and Yamaji, A. (2022):
Scaling of snake line change based on ClausiusClapeyron Relation. J. Jpn. Soc. Civ. Eng., Ser.

B1 (Hydraulic Eng.), 78(2), pp. I_97–I_102.
Wu, Y.-H., Nakakita, E. and Yamaji, A. (2021):
Future change of snake line pattern and its
relation to sediment disasters, J. Jpn. Soc. Civ.
Eng., Ser. B1 (Hydraulic Eng.), Vol. 77(2), pp.
I_193–I_198.
Wu, Y.-H., Nakakita, E. and Kunitomo, M. (2020):
Future change of rainfall-triggered landslide risk
using NHRCM05 based on critical line method, J.
Jpn. Soc. Civ. Eng., Ser. B1 (Hydraulic Eng.),Vol. 76(2), pp. I_67–I_72, 2020.
Appendix
Using the least-square method, the exact
equations for determining each component in J are
given as below,=∑ /0 0 ⋅∑ /0 20 3∑ 0 20 ⋅∑ /0 /0,∑ 20 /0 4 3∑ 20 20 ⋅∑ /0 /0(1)=∑ /0 0 ⋅∑ 20 20 3∑ 0 20 ⋅∑ 20 /0,∑ 20 20 ⋅∑ /0 /0 3 ∑ 20 /0 4

(2)

C=

∑ /0 $0 ⋅∑ /0 20 3∑ $0 20 ⋅∑ /0 /0

,

(3)

=

∑ /0 $0 ⋅∑ /0 20 3∑ $0 20 ⋅∑ /0 /0(4)∑ 20 /0 4 3∑ 20 20 ⋅∑ /0 /0∑ 20 20 ⋅∑ /0 /0 3 ∑ 20 /0 4,

where ∑ ∙ denotes the sequence summation of theseries of parameter.

― 246 ―

(Received August 31, 2023)