The Journal of American Science, 2(2), 2006, Jiang, et al, Wavelet Characteristics of Hydrologic Time Series
Wavelet Characteristics of Hydrologic Time Series in upstream of
the Longchuan River
Shizhong Jiang 1, 2, Chuan Liang1
1.
College of Hydraulic Engineering, Sichuan University, Chengdu, Sichuan 610065, China,
jiangshizhong@126.com
2.College of Geography and Resources Science, Sichuan Normal University, Chengdu, Sichuan 610068, China
Abstract: Based on the theory of Morlet wavelet transform, the Multi-time-scale and jump characteristics of the
annual runoff volume, sediment discharge and precipitation time series in upstream of Longchuan River have been
studied. The results were verified that all of them demonstrate the multi-time-scale characteristics. The annual runoff
volume has about 6 years and 21 years major periods, the annual sediment discharge has about 4 years and 10 years
major periods, and the annual precipitation has about 2 years, 4.5 years and 9.5 years major periods. [The Journal of
American Science. 2006;2(2):82-87].
Keywords: the upstream of Longchuan River; dry and hot valley ecologic and hydrologic area; runoff volume;
sediment discharge; precipitation time series; wavelet transform; major period
Introduction
Surrounded by mountains east, west and south,
f（kt） can be described as follows:
Longchuan River has a close basin, comparative low
W f ( a, b)  a
elevation. While reaching, the warm and wet air-stream
has became a spent force with less vapor, sinks after

1
2
N
t  f (kt ) (
k 1
kt  b
)
a
cross the mountain, producing foehn effect. The
contradictory between water and heat is serious,
Where W f ( a, b) is a coefficient of wavelet
especially during spring and early summer, those make
transform; a and b are scale factor and time factor
it a typical frail area in China[1]. Therefore, through
respectively; △t is the intermission of sample time; N is
observed data of the runoff, sediment discharge and
（t） is
precipitation during 1958~1985 of Chuxiong Station
the sample number;
(drainage area 1788 km2), which is the control station
function of the Morlet wavelet function representing
on upstream of Longchuan River, the Multi-time-scale
（t）  e
and jump characteristics of the runoff, sediment
i 0t
e

t2
2
, constant
the compound conjugate
 0 =6[2].
discharge and precipitation in up Longchuan River
Canyon would be build. The proposed wavelet
1.2 Wavelet Variance Diagram
transform method is valuable for hydrologic forecast,
Square of wavelet coefficient integral in time area
simulation and decision analysis in dry and hot valley
is called Wavelet Variance Diagram Var (a ) [3]:
ecologic and hydrologic area.

2
Var (a )   W f (a, b) db
1 Methodology

1.1 Wavelet Transform
Generally, the separate hydrologic time series
2
82
Case Study
The Journal of American Science, 2(2), 2006, Jiang, et al, Wavelet Characteristics of Hydrologic Time Series
distribution of Morlet wavelet coefficient of annual
2.1 Studying basin
Being a tributary in JinSha River, the Longchuan
runoff time series in Chuxiong station, which is shows
River rises in Nanhua County Yunnan province. It pours
results of the runoff change stage texture and
into Longchuan River Canyon, extends more than 100
distribution of sudden change line: wavelet coefficient
km and joins into Jinsha River at Jiangbian in Yuanmou
zero isopleths corresponds with sudden change line;
County, which basin has a length of 257 km, average
while position isopleths corresponds with wet year;
slope 6.1‰, and drainage area is about 9187 km .
negative isopleths corresponds with dry year. By the
Dominant control stations are Xiao Huanggua Station,
way, plus period and minus period appear in turn, it is
Yuan Station Station, Chuxiong Station, and Duoke
clearly the domination by fluctuation with period 15~28
Station on primary tributary.
years, which centre time scale is about 21 years. The
2
wave with period 4~7 years display currently, thus
centre time scale is about 6 years.
2.2 Hydrologic characteristics
The
runoff
volume,
sediment discharge
and
Figure 3 figures out wavelet variance diagram of
precipitation curve are shown in Fig.1. The precipitation
annual runoff, sediment discharge and precipitation time
process appears single-hump with the peak in August,
series in Chuxiong Station. From Fig.3 (A), it could be
92.4% precipitation between May and November, in
seen both of 6 and 21 years major periods of time scale
which 72 ﹪ between June and September takes
throughout annual runoff series, especially the wave 21
precedence. There is a central distribution of sediment
years period had the strongest power.
discharge, which is corresponding with precipitation as
Figure 4 describes the two major period process of
well as the runoff. It takes 99.6﹪ between May and
wavelet transform of annual runoff time series both of 6
November, about 88.8﹪ in flood season.
and 21 years in Chuxiong Station. When the major
period is 6 years, the plus periods are 1959~1962,
1965~1968, 1971~1974, 1977~1980, which are wet
2.3 The Multi-time-scale and jump characteristics
years as well; while the minus periods are 1962~1965,
of Hydrologic time series
2.3.1
The
multi-time-scale
characteristics
1968~1971, 1974~1977, 1980~1983, with less runoff.
of
Similarly, when the major period is 21 years, the wet or
runoff volume
Firstly, standardize annual runoff from 1958 to
1985
in
Chuxiong
Station,
then
analysis
dry runoff, sudden change point and strong or weak
the
wave power exist in Figure 4.
standardized sample with Morlet Wavelet Transform,
and draw modulus and part time-frequency distribution
2.3.2
of wavelet coefficient, illus. in Figure 2.
Change period of precipitation time series
Figure 5 contains the square of modulus and part
Figure 2 (A) is about time frequency distribution of
time-frequency distribution of annual precipitation time
Morlet wavelet coefficient Modulus square of annual
series by Morlet wavelet transform from 1966 to 1985
runoff time series in Chuxiong station, which shows that
in Chuxiong Station.
wave signal with period 15~28 years are strong very
In Figure 5, during whole study time, the wave
much during whole study time. There is a strong centre
signal of 7~13 years time scale period are very strong,
in 1974 around; at the same time the wave signal with
and the wave centre appear around 1978, however the
period 4~7 years are strong yet, mostly appear around
centre time scale is about 9.5 years; while in 1971~1971
1959~1978, has a high centre in 1967 or so. Other
years the wave signal 4~6 time scale period are fairly
frequency signals are weak.
strong, but the wave centre appear around 1977, the
Figure
2
(B)
is about part time-frequency
centre time scale is about 4.5 years. During both of
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The Journal of American Science, 2(2), 2006, Jiang, et al, Wavelet Characteristics of Hydrologic Time Series
1966~1970
years
and
1981~1985
years,
the
1966 to 1985 in Chuxiong Station.
high-frequency wave signal with 1.5~3 years period are
Figure 6 shows the high-frequency wave of
strong too, the wave centre separately in1967 and 1984,
sediment discharge time series is about 3~6 years period.
the centre time scale is about 2 years, other frequency
The wave centre appears around 1976, and the centre
signal are rather weak. According to Figure 3(B), the
time scale is about 4 years. During whole study time,
wavelet variance diagram of precipitation time series in
the low-frequency wave signal with 8.5~14 years time
Chuxiong Station, there are 2, 4.5, 9.5 years three
scale are strong, the wave centre appears in 1977 around.
periods in annual precipitation time series.
The centre time scale is about 10 years; others
frequency signal are weak. From Figure 3(B) the
2.3.3
Change period of sediment discharge time
wavelet variance diagram of sediment discharge, it
series
could be seen 4 and 10 years two major periods of
Figure 6 shows the square of modulus and part
time-frequency
distribution
of
annual
sediment discharge time series in Chuxiong Station, but
sediment
the wave power are weak.
Precipitation(mm)
,Sediment
discharge(kg/s),
3
Runoff(m /s)
discharge time series by Morlet wavelet transform from
150
100
50
0
1
2
3
4
5
6
7
8
9
10 11 12
Runoff
Sediment discharge
Precipitation
Time(Month)
Figure 1. Runoff, Sediment Discharge and Precipitation Hydrograph at Chuxiong Station
28
26
24
22
20
a(Year)
18
16
14
12
10
8
6
4
2
1958
1963
1968
1973
b(Year)
(A)
84
1978
1983
The Journal of American Science, 2(2), 2006, Jiang, et al, Wavelet Characteristics of Hydrologic Time Series
28
26
24
22
a(Year)
20
18
16
14
12
10
8
6
4
2
1958
1963
1968
1973
b(Year)
1978
1983
(B)
Figure 2. Square of Modulus (A) and Part (B) Time-frequency Distribution of Morlet Wavelet Transform of Annual
120
80
40
0
1
5
9 13 17 21 25
Period(Year)
(A)
Wavelet variance
Wavelet variance
Runoff Time Series of Chuxiong Station
80
60
40
20
0
1
5
Period(Year)
(B)
9
13
17
Sediment discharge
Precipitation
Figure 3. Wavelet Variance Diagram of Annual Runoff (A), Sediment Discharge and Precipitation (B) Time Series at
Wf(a,b)
Chuxiong Station
a=6
a=21
2
-1
1958 1962 1966 1970 1974 1978 1982
-4
Time(Year)
Figure 4. Part of Morlet Wavelet Transform of Annual Runoff Time Series at Chuxiong station
85
The Journal of American Science, 2(2), 2006, Jiang, et al, Wavelet Characteristics of Hydrologic Time Series
20
20
18
18
16
16
a(Year)
a(Year)
14
12
14
12
10
10
8
8
6
6
4
4
2
2
1966
1971
1976
1981
1966
b(Year)
1971
1976
1981
b(Year)
(A)
(B)
Figure 5. Square of Modulus (A) and Part (B) Time-frequency Distribution of Morlet Wavelet Transform of Annual
Precipitation Time Series at Chuxiong station
20
18
16
14
a(Year)
12
10
8
6
4
2
1966
1971
1976
1981
b(Year)
(A)
20
18
16
a(Year)
14
12
10
8
6
4
2
1966
1971
1976
1981
b(Year)
(B)
Figure 6. Square of Modulus (A) and Part (B) Time-frequency Distribution of Wavelet Transform of Annual
Sediment discharge Time Series at Chuxiong station
3
change of precipitation condition affected, and little by
Conclusions
In Chuxiong Station, the change tendency of
man-made control. Runoff and sediment inner year are
runoff volume and sediment discharge depended on the
bad-distribution, mainly in summer and autumn. The
86
The Journal of American Science, 2(2), 2006, Jiang, et al, Wavelet Characteristics of Hydrologic Time Series
annual changes of runoff and sediment have the
Meteorology Press, 2001:61~69 (Ch).
multi-time-scale and jump characteristics. Upstream of
[2] Matlab S G. A Theory For Multi-Resolution Signal Decomposition:
Longchuan River is a topic plateau landforms in mid
Yunnan with a saying “three mountains encircle a
the Wavelet Representation. IEEE Trans PAMI, 1989(117):674～
flatland, middle a river” [4]. The agriculture in flatland is
693.
developed, dominated by paddy field, forest vegetation
[3] Wang Wen-Sheng, Ding Jing, Heng Tong. Study on the Periodicity
are thick in mountains zone, most are secondary
and Long-Time Forecast of the Annual Maximum Peak
evergreen broadleaf forest and Yunnan pine forest,
Discharge at Yichang Station of Yangtze River. Journal of
therefore the runoff is regulated greatly by the
Sichuan University (Engineering Science Edition), 2003(1):20～
vegetation.
23 (Ch).
Correspondence to:
Shizhong Jiang
College of Hydraulic Engineering
Sichuan University
Chengdu, Sichuan 610065, China,
jiangshizhong@126.com
[4] WEN An-bang, ZHANG Xin-bao, WANG Yu-kuan etc. Study on
Sedim entation Source Using Caesium-137 Technique in Yungui
Plateau Region of Upper Yangtze River. Journal of Soil and
Water Conservation, 2000(2):25～27,103(Ch).
References
[1] Chen Zhong-yu. General Exposition of Yunnan Climate, Beijing:
87