京都大学防災研究所年報 第 64 号 B
DPRI Annuals, No. 64 B, 2021

Analysis of Future Changes of Geometric Range of Snake Lines and its
Relation to Sediment Disasters in a Changing Climate

Ying-Hsin WU, Eiichi NAKAKITA and Akihiko YAMAJI
Synopsis
This study aims to investigate the future changes of sediment disasters with a focus on
investigating the patterns of snake line in a changing climate. Constituted by two parametersof hourly rainfall intensity and soil-water index, a snake line is a curve used for early-warning
on rainfall-triggered sediment disasters. For reasonably projecting future climate, we adopted
high-resolution future climate projections of 2-km and 5-km Non-Hydrostatic Regional
Climate Models under the scenarios of RCP2.6 and RCP8.5. Snake lines obtained by climate
projections were verified by the reanalyzed precipitation of Radar-AMeDAS. To quantify
snake line pattern, we focused on analyzing the geometric range of snake line in terms of the
maximal hourly rainfall and soil-water index. Obvious increasing trends for the twoparameters and corresponding distributions are revealed on each mesh. Based on six
stretching types of snake lines, we examined the spatial distributions and statistics of the
future change of snake line patterns under the two scenarios as well as their relation to rainfall
prone to sediment disasters. Based on the critical lines, we also demonstrate some statisticalfeatures of future hazardous rainfall.
Keywords: climate change, sediment disasters, snake line pattern, NHRCM, RadarAMeDAS

1.

Introduction

In this study, we attempt to quantitatively examine
the conditions of sediment disaster in a changing
climate. Extreme climate becomes more frequentworldwide to trigger considerable severe water-related
disasters, and has raised huge attention of
governmental sectors (MLIT, 2020) and scientificcommunities (Kawamiya et al. 2020; Mori et al.,2021). Recent extreme rainfall events show someobvious 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,
consequently, have triggered numerous devastating
floods, landslides and sediment disasters beyond ourpast experience. Among relevant reasons of extreme
weather, one influential factor could be attributed toclimate change accompanying increased average

earth-surface temperature due to the great amount ofgreenhouse gas emissions from human activities,
which is often termed as global warming phenomenon(Kawamiya et al., 2020 and references therein). As
global warming is a long-term heating of the earth’s
atmosphere, extreme weather would take place more
often in the future. Future extreme weather could bealtered to possibly amplify occurrence of landslides
and sediment hazards in the future.
To practice successful early-warning on landslides
and sediment disasters, Ministry of Land,
Infrastructure, Transport and Tourism (abbreviated as
MLIT) is currently applying the critical line method
which utilizes two parameters of hourly rainfall (HRhereafter) and soil-water index (SWI) (Osanai et al.,2010). To constitute a parametric curve of snake lines,
the two indices can reflect the influences of short-term
peak rainfall and the long-term condition of soil
wetness, and could be applied to efficiently assess the― 317 ―

potential occurrence of sediment disasters. Our
previous research has explored the future change ofdisastrous rainfall prone to sediment disasters (Wu etal., 2020). However, until now future characteristics ofsnake lines in a changing climate has not been
examined yet. So, the current study attempts toinvestigate future snake line patterns with a particularfocus on the maximal geometric range of snake lines
obtained by high-resolution climate projections. To
this end, we adopted the famous 2-km and 5-km NonHydrostatic Regional Climate Models (NHRCM,
hereafter RCM2 and RCM5, respectively), publishedby Japan Meteorological Agency (JMA). Also, the 1km reanalyzed precipitation was used to verify theapplicability of snake lines obtained from climate
projections. On each mesh, by examining the maximal
HR and SWI, we elaborate the future changes ofstretching types of snake line patterns as well as the
explicit relation to rainfall prone to sediment disasters.
Finally, we briefly summarize some statistical featuresof the hazardous rainfall events in terms of the monthly
frequency as well as prefectural future changes. On theother hands, as the hydrometeorological parameters ofinterest are used for early-warning, the current
research could be regarded as a quantitative reference
to understand the future status of early-warning alerts
for benefiting future disaster management as well as
making corresponding policies.
2.

Data and method

2.1 JMA Radar-AMeDAS
To confirm applicability of snake lines obtained byclimate simulation datasets, we utilized the highresolution precipitation reanalyzed using observationsof 20 C-band radars and the AutomatedMeteorological Data Acquisition System (AMeDAS)
operating by JMA. The dataset is often called RadarAMeDAS precipitation, and published by JMA
routinely. Here we only used the datasets in the periodof 2006 to 2020 (15 years in total). The resolutions are
30 minutes in time and 1 km in space. A major benefit
holds that the mesh system is exactly the one for all
critical lines. For brevity, in what follows RadarAMeDAS precipitation dataset is abbreviated as
JMARA.
2.2 Future projections: 2-km and 5-km NHRCM
The spatiotemporal resolutions are 5 km in spaceand 30 minutes in time for RCM5, and 2 km in spaceand 1 hour in time for RCM2. To cover the Japanesearchipelago, there are 527×804 grids in RCM5, and525×1721 grids in RCM2 in a narrower simulation
domain. Both have the same ensemble members, as arelisted in Table 1. SPA stands for present climate, andthe others (SFA_26, SFA_c1, SFA_c2, SFA_c3, andSFA_c0) for future climate. The domain boundary
conditions are derived from the simulations of MRIAGCM3.2S. The scenarios of future projections are set
according to Representative Concentration Pathway(RCP) 2.6 and 8.5, proposed in IPCC Fifth Assessment
Report in 2014 for representing human activities ofindustrial development. Four spatial patterns of seasurface temperature (SST) are imposed as the sea
surface boundary conditions in the future projectionsof RCP8.5. The simulation period of each dataset is 20
years with a one-year time slice and a spin-up period
from July 21 to September 1.
To focus on analyzing rainfall-triggered sedimenthazards, we directly extracted the parameter of surface

Table 1 Brief information of all NHRCM members (Both for RCM5 and RCM2)
DatasetScenario

Boundary SST

SPA-Monthly observation (1979-2003)

SFA_26

RCP2.6

El Niño

SFA_c1

RCP8.5Less warmer in East tropical Pacific

SFA_c2

RCP8.5Stronger El Niño

SFA_c3

RCP8.5

Warmer in Northwest Pacific

SFA_c0

RCP8.5

El Niño

― 318 ―

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

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

Fig. 1 An illustrative example of comparison among snake lines obtained by a) RCM5, b) RCM2, and RadarAMeDAS on the mesh of No. 50300668 in Asakura City, Fukuoka prefecture where occurred flooding andmassive shallow landslides during 2017 Northern Kyushu heavy rainfall. The definitions of kr and ks refer toEquation (1).

precipitation of liquid water (i.e., the parameters of
SMQR and RQ1 in RCM5 and RCM2, respectively)
without any interpolation. Some relating details of
NHRCM can refer to our previous research4).
Hereafter, for the RCP8.5 scenario, we shall focus on
discussing the average property of the four ensemble
members without further indication.
2.3 Extraction of parameters and rainfall events
In this study, the 1-km mesh coordinate system of
JMARA and for all critical lines is used for analyzing
NHRCMs. We processed 15-year JMARA dataset
continuously from 2006 to 2020, and processed alldatasets of RCM2 and RCM2 following the one-yeartime slice in the whole dataset period of 20 years. All
the processing steps are briefly mentioned as follows.
The first is to extract the continuous time series ofhourly rainfall on each mesh in each year slice, andthen to derive 10-minute rainfall by uniformly
extracting original data of one hour or 30 minutes. The
extracted 10-minute rainfall series was then used for
calculating the continuous time series of SWI by using
the conventional method proposed by JMA. To
prevent from duplicate counting of a single event, we
identified all effective rainfall events (MLIT, 2005;
Osanai et al., 2010) with a minimal threshold of 0.5
mm per one hour. Finally, we extracted the maximal
HR and SWI in the whole dataset period for examiningchanges of the geometric range of all snake lines oneach mesh. Fig. 1 shows an example on the mesh of
50300668 where is located at E130.85 and N33.39 in
Asakura City, Fukuoka prefecture (Takemi 2018;
Shakti et al. 2018). The geometric similarity of thesnake lines from RCM5 and RCM2 are confirmed withthe ones from JMARA. Obviously, we can observe theextension of the range of snake lines from both
NHRCMs. Therefore, in what follows we shall try tosystematically quantify the characteristics of thesegeometric changes and their relation to hazardous
rainfall prone to sediment disasters.
Besides, from all datasets of NHRCMs, the timeseries of HR and SWI were checked to judge whether
any pairs of the two parameters on each mesh passthrough the corresponding critical line of that mesh.
On each mesh, within one effective rainfall event, weonly counted one hazardous rainfall event no matter
how many times the critical line was crossed. The
event herein is not related to the one of any storm or
rainfall system from the viewpoint of meteorology.
3.

Results and discussion

3.1 Comparison with Radar-AMeDAS
To confirm the applicability of snake lines obtained
from NHRCMs, we compared them with the ones fromJMARA. Although the evolution of snake line could― 319 ―

Fig. 2 Comparison of the maximal hourly rainfall (HR) in a)-c) and soil-water index (SWI) in d)-f) among RadarAMeDAS and the present climate datasets of RCM5 and RCM2. The deviations are shown in b) and c) for the
maximal HR to Radar-AMeDAS, and e) and f) for the maximal SWI, respectively. Lower row shows thecorresponding histograms.

reflect some important features of sediment disasteroccurrence, we only focus on the maximal values of
HR and SWI to reveal the geometric range of a snakelines in the current analysis. Fig. 2 shows thedeviations of the maximal HR and SWI among
JMARA and the present climate datasets of RCM5 andRCM2. Obviously, as are shown in Fig. 2b and Fig. 2c,
the maximal HR from NHRCMs is much higher than
JMARA in almost all places, particularly in the Pacific
Ocean side. There are 82.2% of meshes with positive
deviation in RCM5 and 92.5% in RCM2. On the other
hand, in Fig. 2e and Fig. 2f, the maximal SWI does notdeviate much in RCM5, but slightly in the positive
direction in RCM2. Sharp rise can be seen in Mie,
Aichi, east Kyushu, and Tokai regions. Then, obvious
declines can be found in Wakayama, east Kumamoto,and Bandai-Asahi National Park from both NHRCMs.
So far, it has shown the deviations of the maximal
HR and SWI in the present climate datasets of
NHRCMs to JMARA. However, it is still unclear tostraightforwardly understand features of the futurechanges of the two parameters merely with respect totheir deviations to the present climate dataset. In what
follows, we turn to use relative ratios to explain futurechanges of the two hydrometeorological parameters of
HR and SWI.
3.2 Future changes of maximal hourly rainfall andSoil-Water Index
Before analyzing snake line patterns, we aim to
separately investigate future changes of the maximal
HR and SWI, as are illustrated in Fig. 3 and Fig. 4,
respectively. To express changes, the scale factors of
HR and SWI on each mesh are respectively given as

kr =

HRSFA
SWISFAand ks =,HRSPA
SWISPA(1)

where the subscripts of SPA and SFA denote thepresent and future climate datasets, and HR and SWI
hereafter denote the maximal values in the wholedataset periods. Based on the definition of Eq. (1),there would be no significant change if the scale factor
k → 1 , and there are 50% of decline or 2 times of― 320 ―

Fig. 3 Future changes of the maximal HR from RCM5 in a)-c) and RCM2 in d)-f). The scale factor kr denotes
the ratio of future projections under different scenarios to present climate (SPA). The lower row shows thecorresponding histograms.

increase when k → 0.5 and 2, respectively. To gently
remind, a higher value of the two scale factors does notguarantee a higher absolute value of the corresponding
parameter.
For the features of HR, Fig. 3 demonstrates that the
distributions of the scale factor kr under the RCP2.6
scenario show no obvious increasing trend along theJapanese archipelago, but the distributions under
RCP8.5 present clear rising trends everywhere except
some regions in west Japan (e.g., Mie, Aichi, south
Hyogo, east Shikoku, and north Kyushu). Significant
rises of kr ≈ 2.0 appear in Tohoku and Hokkaido
regions. The highest frequencies of the factor kr
under RCP2.6 and RCP8.5 reach around 1.1 and 1.3,
respectively. In contrast to HR, both in the NHRCMs
the scale factor k s of the maximal SWI shows that
58% of meshes have increasing trends under RCP2.6,
and 85% under RCP8.5. Particularly, the distributionsof k s under the same scenario are quite similar
between RCM5 and RCM2. Also, as is shown in Fig.
4, obvious decline trends of SWI can be found in Mie,
Aichi, Hyogo, and Fukuoka prefectures under RCP2.6.
For this results, it could be considered that the declineof SWI might represent the condition that soil may bedryer, but further investigation is required to verify thispossible condition of soil wetness which is one ofessential influential factors for occurrence oflandslides and sediment hazards.
To sum up, we have quantified the future changesof the maximal HR and SWI separately. It can be found
an obvious increasing future trends of the maximalHR, but just a mild one of the maximal SWI. Then, weshall examine features of the combination of the twoparameters.
3.3 Future changes of snake line patterns
To express geometric changes of the range of snakelines on the phase plane by the scale factors kr andk s , the six types of stretching of snake line are defined
as below― 321 ―

ks > 1.5
kr > 1.5,
Type-A:
1.05 < ks ≤ 1.5 
Type-B: 1.05 < kr ≤ 1.5,
Type-C:kr > 1.05,
ks ≤ 0.95  (2)Type-D:kr ≤ 0.95,
ks > 1.05
Type-E: 0.95 < kr ≤ 1.05, 0.95 < ks ≤ 1.05, 
Type-F:kr ≤ 0.95,
ks ≤ 0.95, Fig. 4 Future changes of the maximal SWI from RCM5 in a)-c) and RCM2 in d)-f) in terms of the scale factor
ks . The scale factor ks denotes the ratio of future projections under different scenarios to present climate (SPA).
The lower row shows the corresponding histograms.
with a given tolerance range of ±5% at unity. In theand RCM2 there are around 80% and 60% of meshes

practical sense, the stretching of Type-A and Type-B

under RCP8.5 and RCP2.6, respectively. The Type-C

represent that rainfall is intensified in the amount andand Type-D, representing partial enlargement of snake

extended in a longer duration; Type-C may reflect thatlines, would be declined more in the scenario of

rainfall is intensified in a shorter duration; Type-D

RCP8.5 than the one of RCP2.6. Particularly, for the

stands for a duration-prolonged rainfall in a higher

Type-D which may be prone to deep-seated landslides,

accumulated amount but with a lower peak intensity.

it can be found 4.9 and 2.6% of meshes under theThis rainfall type could be prone to deep-seatedscenario of RCP8.5 from RCM5 and RCM2,

landslides. Type-E represents no significant changes.

respectively, and 11.8 and 9.6% under RCP2.6. Then,

Finally, Type-F stands for rainfall weakened both inunder RCP2.6 and RCP8.5 there are respectively

intensity and duration. All these types are used foraround 28% and 16% of meshes having insufficient

simply categorizing future changes of the geometricchanges of snake line range. Finally, under both

range of snake lines, or says snake line patterns.

scenarios the distributions of the meshes in Type-F that

Fig.

5

demonstrates

thedistributions

andboth scale factors shrink are mainly in agreement withhistograms of the six stretch types. Both in thethe places with ks < 0.95 in Fig. 4. Another particular

NHRCMs, 30% of meshes are categorized as the Type-point is that, both in the RCM5 and RCM2, theA and Type-B representing obvious enlargement of

distributions and histograms under the same scenario

snake lines under RCP2.6, and 70% under RCP8.5.

coincide well with each other.

Also, the Type-A meshes (about 10%) are mostly

The future changes of the geometric range of snake

distributed in Shimane prefecture, Tohoku andline on each mesh have been quantitatively derived. In

Hokkaido regions under RCP8.5. For all of the

our limited understanding, as an additional advantage

conditions of enlargement of snake lines (Type-A,of the present analysis, it is believed that all these

Type-B, Type-C, and Type-D), from both of RCM5

features could help suggest the location of meshes for― 322 ―

Fig. 5 Future changes of snake line patterns categorized by six stretch types in terms of the maximal HR and
SWI. Schematic examples of the six stretch types are shown on the right. Subfigures a) and b) show the results of
RCM5; c) and d) the results of RCM2. The lower row on the left presents the ratios of the total number of themeshes of each stretch type to the total mesh number.

the re-examination or adjustment of the corresponding

difference in monthly frequency. These histograms

critical lines for better efficiency of early-warning.

clearly show that the occurrence of hazardous rainfall
events concentrates on the wet season from May to

3.4 Hazardous rainfall distribution

October, and is much intensified in the summer fromTo find the relation between the stretching of snake

July to September under RCP8.5. It can be observed aline with hazardous rainfall, the critical line on eachparticular condition that, under the scenario of RCP8.5

mesh was applied to the calculated time series of HR

in both NHRCMs, the error bars show low deviations

and SWI for counting rainfall events prone to sedimentof extracted hazardous rainfall events in July, but muchdisasters. Fig. 6 demonstrates the results of spatial

higher ones in August and September that would

distributions and the corresponding histograms insuggest further investigations to identify physicalterms of monthly frequency. To gently remind, theconditions of dominant rainfall as well as the relatinghazardous rainfall event is counted with respect to theambient atmospheric status.

mesh-based critical line method, not to any storm or

Although only analyzing the precipitation of liquid

rainfall system. By courtesy of MLIT and allwater, we can still observe very few hazardous rainfall

prefectural governments, all of the critical lines being

events in the winter season. In each dataset, the total

applying for the current early-warning practice arecounts from December to next year’s March are all lessobtained for our analysis. Despite the discrepancy ofthan 1.0% of total counts. Moreover, comparison

the spatial resolutions of NRCHMs, the distributions

between Fig. 5 and Fig. 6 reveals one particularof hazardous rainfall events are in good agreement

condition that the places with decreasing trends ofwith each other, but the histograms present slighthazardous rainfall events just satisfactorily match with

― 323 ―

Fig. 6 The count and deviation of hazardous rainfall prone to sediment disasters from RCM5 and RCM2: a) andd) show the total events in the present climate (SPA). b) and e) are the deviations of the RCP2.6 result to SPA ofeach model. c) and f) show the deviations of RCP8.5. The lower row demonstrates the corresponding total countsof hazardous rainfall event, and the error bars in c) and f) denote the maximum and minimum. The total counts in
RCM2 is around 21% more than RCM5.

the meshes in the stretch Type-F. But, the count of

results from both high-resolution NHRCMs could

hazardous rainfall event would not definitely beprovide more reliable assessment than the one in ourelevated at the meshes which are categorized as theprevious research (Wu et al., 2020).

stretch Type-A and Type-B, representing enlargement
in both directions on the phase plane of snake line. So

4.

Conclusions

far, it has been shown the spatial distribution of
hazardous rainfall.

This study investigates the future snake line

As we noticed the deviations from the histograms

patterns and their relation to sediment disasters in a

in Fig. 6, we further examine the temporal features inchanging climate by considering the geometric range

terms of monthly frequency. To link with the spatialon the phase plane of snake line constituted by the

distribution, Fig. 7 shows the monthly frequency

maximal hourly rainfall and soil-water index. With thenormalized by the mesh number of each geographicalapplication of the most current high-resolution future

region of Japan. The particular findings are that theprotections, the present analysis results reveal that theextracted hazardous rainfall are concentrated in July infuture change of the maximal hourly rainfall is

the regions of Japanese Sea Side, but uniformly

enlarged much higher than the maximal soil-water

distributed in the summer season from July toindex. Also, the soil-water index would decline in

September with a slight elevated normalized frequency

accompany with the declination of the count of

in September in the regions of Pacific Ocean Side. In

hazardous rainfall prone to sediment disasters. As thisOkinawa, it can be seen that the extracted events are

study only examined the maximal geometric range ofdistributed all year long except the winter season. On

snake lines, it is still open to answer temporal features

the other hand, we can also observe the obviousof snake line evolution in a changing climate.

increase of extracted events from the scenario ofLast, and the most importantly, it is believed that

RCP8.5 out of the one of RCP2.6. Compilation of thethis study could practically benefit understanding of― 324 ―

Fig. 7 The monthly frequency of hazardous rainfall normalized by the total number of 1-km mesh of graphicalregional: a) Hokuriku, b) Tohoku, c) Hokkaido, d) Kinki, e) Kanto, f) Chugoku, g) Chubu, h) Kyushu, i) Shikoku
regions, and j) Okinawa prefecture from RCM5 and RCM2. The numbers in the brackets denote the total numberof mesh in each region.

conditions of early-warning on rainfall-triggered“Projection and impact assessment of global

landslides and sediment disasters in a changing climate.

change,” Prog. Earth Planet. Sci., Vol. 8, 30.
MLIT (2005): Manual of Determining Rainfall

Acknowledgments

Threshold for Early-Warning of Sediment
Disasters.

This work was supported by the Integrated

MLIT (2020): Committee Discussions on Technology

Research Program for Advancing Climate Models

and Evaluation of Sediment Disasters under(TOUGOU) Grant Number JPMX-D0717935498

Climate Change.

from the Ministry of Education, Culture, Sports,

Mori, N., Takemi, T., Tachikawa, Y., Tatano, H.,

Science and Technology (MEXT), Japan. The authors

Shimura, T., Tanaka, T., Fujimi, T., Osakada, Y.,appreciate the valuable data of all the latest criticalWebb, A. and Nakakita, E. (2021): Recent

lines from MLIT Sabo Planning Division, JMA, andnationwide climate change impact assessments ofall prefectural governments.

natural hazards in Japan and East Asia. Weather
Clim. Extrem., Vol. 32, 100309.
Osanai, N., et al. (2010): Japanese early-warning for

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(Received August 31, 2021)