IMPACTS OF THE INCREASED RAIN DUE TO CLIMATE CHANGE ON SHALLOW LANDSLIDES AND SEDIMENT RUNOFFS IN KYUSHU
DISTRICT, JAPAN Tetsuya Kubota1*
ABSTRACT
Rain observation by pluviometers for 30 years were conducted in Fukuoka. Concurrently, shallow landslide analysis using aerial photographs for typical 3 periods and rain-sediment discharge monitoring at hydroelectric power dams were conducted in Miyazaki for 30 years.
Both of these areas are located in Kyushu district, western Japan where they often have severe landslide disasters. Theoretical analysis with geo-physical equation and statistical analysis are conducted with the data obtained in these areas. Consequently, following results were obtained. 1) Heavy rainfalls and their frequency are obviously increasing. Their increasing rate is almost up to 20mm/hr or 40mm/day in 30 years, and frequency of rain heavier than 40mm/hr is found to be 1.5 multiplied. 2) Sediment runoff discharge is expressed by the equation derived from hydraulic principle using slope element distribution model. This equation is substantiated with observed data in our research areas. 3) Observed sediment runoff increased definitely in last 30 years in accordance with the rainfall increment. 4) A prediction model for long-term sediment runoff with random-cycle combination model is proposed. This equation can describe the observed data with certain accuracy in the average from the ensemble prediction using various initial conditions.
Key Words: Climate change, Heavy rainfall, Shallow landslide, Sediment discharge, Kyushu
METHOD AND TARGET AREAS
Fig.1 The location of research areas
Rain observation by pluviometer for 30 years and periodical monitoring of the sediment discharge for 4 years with sediment trap facilities were conducted in Fukuoka (Northern Kyushu). On the other hand, rain and sediment discharge observation were conducted in Miyazaki (Southern Kyushu) for 30 years at hydroelectric power dams, while shallow landslide analysis using aerial photographs for recent typical 3 periods was concurrently conducted.
Both of these areas are located in Kyushu district, western Japan (Fig. 1), where severe landslides frequently occurred. The geological setting in research areas consists of Paleozoic and Mesozoic rocks such as schist, Phyllite, sand stone. Their vegetation consists of mainly Japanese cypress and
1 Forest Science Department, Faculty of Agriculture, Kyushu University, Fukuoka, Japan (*Corresponding Author; Tel: +81-92-642-3084 ; E-mail: kubot@agr.kyushu-u.ac.jp)
cedar.
Theoretical analysis with geophysical equation, statistic analysis with Kendall's rank correlation on both of the sediment runoff and the rainfall, the long-term cycle-frequency analysis of precipitation at the observatories which have record for 100 years, by standard method using self-correlation, are conducted with the data obtained in these areas (Fig.2).
RESULT AND CONSIDERATION
Increase of heavy rainfalls and their frequency observed
Heavy rainfalls are obviously increasing in every observatory for 30 years. In particular, extremes of daily and hourly rain often have clear tendency confirmed by Kendall's rank correlation analysis with statistic tests. Their increasing rate is almost up to 20mm/hr or 40mm/day in 30 years (Fig.3 (h ~ i)), and the frequency of extreme rain "Ri" heavier than 40mm/hr is found to be 1.5 multiplied. In addition to it, rain fluctuations have some specific cycle such of 3 or 6 year (Fig.3 (g)), judging from the power spectrum of the cycle analysis.
Concurrently, the interval of occurrence in daily rainfall which has the return period of more than 10 years tends to reduce (Fig.4).
Impact on shallow landslide density "N/A"
Shallow landslide density "N/A" is theoretically evaluated with following equation derived
(a) (b)
(c) (d)
(e) (f)
Fig.2 The observation sites (a)Fukuoka 2003~, (b)~(f) Miyazaki 1979~
from the analogy with thermodynamics (Yoshimatsu 1977).
C / A = ( ai · N ) / A = C0 · Re · C1 · ( R - Ro )C2 (1)
N: landslide frequency, ai: average scale of each landslide, A: watershed area, C1, C2: Constants related to precipitation pattern, Re: Relief energy of the basin, Ro: Rainfall loss.
The observed results clearly fit to the equation (Fig.3(f)) and we obtained next values for the sample area,
(a) Fluctuation of sedim ent runoff Q s(1000m3) at Iw ayato 0.0
100.0 200.0 300.0 400.0 500.0 600.0 700.0
1975 1980 1985 1990 1995 2000 2005 2010 Year
Qs(1000m3)
(b) Fluctuation of sedim ent runoff Q s(1000m3) at Tsukabaru 0.0
500.0 1000.0 1500.0 2000.0
1975 1980 1985 1990 1995 2000 2005 2010 Year
Qs(1000m3)
(c) Fluctuation of sedim ent runoff Q s(1000m3) at M orotsuka 0.0
50.0 100.0 150.0 200.0
1975 1980 1985 1990 1995 2000 2005 2010 Year
Qs(1000m3)
(d)
Fluctuation of sedim ent runoff Q s(1000m3) at Yam asubaru 0.0
50.0 100.0 150.0 200.0 250.0 300.0
1975 1980 1985 1990 1995 2000 2005 2010 Year
Qs(1000m3)
(e) Fluctuation of sedim ent runoff Q s(1000m3) at S aigou 0.0
50.0 100.0 150.0 200.0
1975 1980 1985 1990 1995 2000 2005 2010 Y ear
Qs(1000m3)
(f)
Relation betw een m axim um total rain R(m m ) and N /A(plot/km 2)
N /A = 9*10-22R7.5755 r2 = 0.9998
0 5 10 15 20
400 500 600 700 800 900 1000
R(m m )
N/A
(g)
Pow er spectrum of m axim um daily rain in M iyazam i 0
10000 20000 30000
2 4 6 8 10 12 14
C ycle (Year) Power(mm2/year)
(h)
The fluctuation of m axim um total rain Rm ax in the period in M orotsuka
R = 17.47ｔ - 34493
0 200 400 600 800 1000
1975 1980 1985 1990 1995 2000 2005 2010
Year
Rmax（ｍｍ）
(i)
The fluctuation of m axim um rain intensity R i in the period in M orotsuka R i = 1.06t - 2084
0 10 20 30 40 50 60 70
1975 1980 1985 1990 1995 2000 2005 2010
Year
Rimax(mm/hr)
(j)
Q s = 0.00530Ri・R ｒ＝0.911, r2 = 0.830
0.0 50.0 100.0 150.0 200.0
0 5000 10000 15000 20000 25000 30000 35000
Ri・R (m m2/hr) Qs(X103m3)
Fig.3 Fluctuation of sediment and rain : (a)~(e):Fluctuation of sediment runoff, (f)Relation between Rmax and N/A, (g)Power spectrum of maximum daily rain in Miyazaki, (h)~(i): Fluctuation of maximum total rain and hourly rain (increasing), (j)An example of the relation between Ri·R and Qs (Morozuka dam, Miyazaki).
C0 · Re · C1 / ai = 9 × 10-22, Ro = 0.0 and C2 = 7.58
Also, theoretically, sediment runoff discharge from landslides "Qsl" is proportional to N in way of next semi-empirical formula (Kaki 1983).
Qsl = f · vi · N, f = I0.4 / A0.2~0.3 (2)
vi: sediment volume of each landslide, f: runoff ratio, I: slope of the stream bed.
Therefore, sediment runoff is proportional to the number of shallow landslide.
In our study, sediment runoff "Qs" includes debris flows originated from streambed sediment.
Therefore, "Qs" is considered to be in direct proportional to "Ri · R", not to "R".
Impact on sediment runoff discharge "Qs"
Sediment runoff discharge is expressed by next equation derived from hydraulic principle (slope element distribution model, Hirano 1995).
Qs / A = M · Ri(t) ∫( Ra · cosθ )dt (3)
here, Qs: sediment runoff discharge, A: watershed area, M: a function concerning with sediment deposit features on the upstream torrent (porosity, cohesion, torrent bed slope gradient, sediment accumulation length and depth), t: time, θ: torrent bed slope gradient, Ri(t):
intensity of instant precipitation, Ra: instant precipitation.
If the time integral is made over the rainfall duration, then
∫(Ra·cosθ)dt = R·cosθ
here, R: total rainfall, Ri: rain intensity over 1 hour.
Therefore,
Qs = C ·Ri ·R, (C= A·M ·cosθ) (4)
Hence, theoretically "Qs" that has tight relation to shallow landslide occurrence rate can increase with increment of "Ri" and "R". This relationship is substantiated with observed data in our research areas, and the equation sufficiently describe the data with the constant C = 4.8~20.5 (Fig.3 (j): Kubota et. al. 2008)
Fluctuation of the interval in daily rainfalls over 10 years of return period in M orotsuka, M iyazaki
y = 9.0133T-0.9075 R=0.800, R2 = 0.6406
0 2 4 6 8 10 12 14 16
0 2 4 6 8 10
term s T
Interval (year)
Fluctuation of the interval in daily rainfalls over 10 years return period at Kam ishiiba, M iyazaki
y = 13.037T-1.3319 R =0.939, R2 = 0.881
0 5 10 15 20
0 1 2 3 4 5 6 7
term s
Interval (year)
Fig.4 Fluctuation of daily rain with 10 years of return period over 30years; Kamishiiba (altitude: z=420m) and Morotsuka (z=150m), Miyazaki prefecture, Kyushu district.
Increase of observed sediment runoff
Sediment runoffs in the area definitely increased with the rate of approximately 200,000 m3 in 30 years in accordance with the rainfall increment (Miyazaki area, Fig.3 (a) ~ (e)). This tendency is credited by Kendall's rank correlation analysis as a purposive increase.
Sediment Runoff Qs Calculated by Cycle-Random Model at Morotsuka Japan (10cases with different initial values) 0
50 100 150 200 250
1975 1980 1985 1990 1995 2000 2005 2010 Time
Qs(×1000m3)
Ensemble Prediction of Sediment Runoff Qs by Cycle- Random Combination Model and Observed Qs at Morotsuka 0
50 100 150 200
1975 1980 1985 1990 1995 2000 2005 2010 Time
Qs（×1000m3）
QspAverage QsObserved
Sediment Runoff Qs Prediction by Cycle-Random Model (Cases with 10 different initial condition) 0.0
50.0 100.0 150.0 200.0 250.0 300.0 350.0
2005 2010 2015 2020 2025 2030 2035
Time Qs (×1000m3)
Ensemble Prediction of Sediment Runoff by Cycle-Random Model at Morozuka, Miyazaki Japan 0.0
50.0 100.0 150.0 200.0 250.0 300.0 350.0
2005 2010 2015 2020 2025 2030 2035 Time
Qs（×1000m3）
Fig.5 Qs Calculation results by Semi-empirical Cycle-Random Combination Model
Qs Prediction by Semi-empirical Cycle-Random Combination Model
A prediction model for long-term sediment runoff fluctuation with the semi-empirical cycle-random combination model is proposed.
According to the power spectrum of the cycle analysis (Fig.3 (g)), the average of the power variation in the figure is almost flat and horizontal. It means that the long-term rain fluctuation has basically random behavior. Therefore, the sediment runoff which has tight correlation with precipitation has random characteristic in its long-term background fluctuation (Fig.5).
This model is basically a semi-empirical model that is comprised of random function with the long-term increment which corresponds to the back ground of the fluctuation (first and second terms in the equation (5)) and trigonometric function which expresses the extreme rain cycle (third term in the equation (5)).
3
Qs = ξ・RAND＋ｔ・｛ ∂Qs(Ri・R) / ∂ｔ ｝＋ Σ{ Ai・cos(ｎ・2πｔ/Ti) }－C (5) i=1
Here, RAND: Random function generating０～1 random numbers, ξ: Random function range= 38, ∂Qs(Ri・R)/∂ｔ＝3.34, n＝1, Ai: amplitude of the fluctuation = 38 (based on regression analysis in Fig.3 (c) ), T1: First fluctuation cycle of rain or sediment runoff = approximately 2.0 (Fig.3(g))、T2: one for second cycle = 6.0, T3: one for third cycle = 15.0 years.ｔ: time(year), C: constant obtained by regression analysis = 6598 (Fig.3 (c) ).
This equation can describe the observed data with certain accuracy (Fig.5) by the average from the ensemble prediction using various initial conditions. In Fig.5, the long-term predictions for next 20 years are also shown, implying another 100,000m3 increment of sediment runoff under the influence of the obvious cycle.
CONCLUSION
All things considered, following results were obtained. 1) Heavy rainfalls and their frequency are obviously increasing for last 30 years. In particular, extremes of daily and hourly rain often have clear tendency confirmed by Kendall's rank correlation analysis. Their increasing rate is almost up to 20mm/hr or 40mm/day in 30 years, and frequency of extreme rain heavier than 40mm/hr is found to be 1.5 multiplied. 2) Shallow landslide density is theoretically evaluated with the equation derived from the analogy with thermodynamics. Also, sediment runoff discharge from landslides is proportional to number of landslide in way of the semi-empirical formula. 3) Sediment runoff discharge is expressed by the equation with rain as the main factor derived from hydraulic principle using slope element distribution model.
Hence, theoretically, Qs that has tight relation to the rate of shallow landslide occurrence can increase with increment of rain. This relationship is substantiated with observed data in our research areas, and they sufficiently fit the equation. 4) Observed sediment runoff increased definitely with the rate of approximately 200,000m3 in 30 years in accordance with the rainfall increment. This tendency is credited by Kendall's rank correlation analysis as a purposive increase. The increase of rainfall due to climate change with the increasing rate mentioned above surely has strong impact on the rate of shallow landslide occurrence as well as sediment discharge. 5) A prediction model for long-term sediment runoff with random-cycle combination model is proposed. This model is basically a semi-empirical model that is comprised of the random function and the trigonometric functions that express the extreme rain cycle. This equation can describe the observed data with certain accuracy in the average from the ensemble prediction using various initial conditions.
Since the shallow landslide density in our sample area is directly proportional to rain "R", and the sediment runoff in torrents is directly proportional to "Ri · R", the increase of rainfall due to climate change showing the specific fluctuation cycle with the high increasing rate mentioned earlier can have strong impact on shallow landslide occurrence and sediment runoff discharge.
REFERENCES
M. Hirano, Characteristics of debris flow in Unzen Volcano, proceedings of the international Sabo symposium, Tokyo, Japan, 107-114 (1995).
T. Kaki, Erosion Control Planning, Japan Sabo Association, 35-74 (1983).
T. Kubota et. al., The warning standard rain of sediment runoff and shallow landslides along the mountainous torrent, Proc. the 1st world landslide forum Tokyo, International Consortium on Landslides, 325-328 (2008).
H. Yoshimatsu, Prediction of slope failures, J.JSECE. Vol.29, No.3, Ser. No.102, 1-9 (1977)
