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Jurnal Kejuruteraan Awam 16(2): 56-65 (2004)
SYNTHETIC SIMULATION OF STREAMFLOW AND RAINFALL DATA
USING DISAGGREGATION MODELS
Nurul Adzura Ismail
1
,
Sobri Harun
1
, Zulkifli Yusop
2
1
Department of Hydraulics and Hydrology, Faculty of Civil Engineering,
Universiti Teknologi Malaysia, Skudai 81310, Johor, Malaysia.
2
Institute of Environmental and Water Resources Management, Faculty of Civil Engineering,
Universiti Teknologi Malaysia, Skudai 81310, Johor, Malaysia.
Abstract: Synthetic hydrological series is useful for evaluating water supply
management decision and reservoir design. This paper examines stochastic
disaggregation models that are capable of reproducing statistical characteristics
especially mean and standard deviation of historical data series. Simulation was
carried out on both transformed and untransformed streamflow and rainfall series of
Sungai Muar. The Synthetic Streamflow Generation Software Package (SPIGOT)
model was found to be the most robust for streamflow simulation. On the other hand,
the Valencia-Schaake (VLSH) model is more superior for generating rainfall series.
Keywords: Streamflow; Rainfall; Simulation; Disaggregation.
Abstrak: Siri hidrologi sintetik ialah satu kaedah yang berguna untuk menilai
keputusan dalam pengurusan bekalan air dan rekabentuk empangan. Kertas kerja ini
bertujuan menguji model disaggregasi stokastik yang berupaya menghasilkan semula
ciri-ciri statistik terutama min dan sisihan piawai ke atas siri bulanan aliran sungai
dan hujan. Simulasi telah dilakukan dengan kaedah transformasi dan tanpa
transformasi menggunakan data aliran sungai dan hujan tadahan Sungai Muar. Model
Synthetic Streamflow Generation Software Package (SPIGOT) dipilih sebagai model
yang paling baik untuk simulasi aliran sungai manakala model Valencia-Schaake
(VLSH) memberi keputusan yang terbaik dalam menjana siri hujan.
Katakunci: Aliran Sungai; Hujan; Simulasi; Disaggregasi.
Jurnal Kejuruteraan Awam 16(2): 56-65 (2004)
57
1. Introduction
The streamflow and rainfall sequences to be analyzed may be thought of as
one particular realisation, produced by underlying probability mechanism of
the phenomenon. In other words, in analysing streamflow and rainfall
sequences many hydrologists regard it as a realisation of a stochastic process.
The generated data sequences, particularly monthly time series such as
streamflow or rainfall are widely used in water resources planning and
management to understand the variability of future system performance.
Stochastic data generation aimed at generating synthetic data sequences that
are statistically similar to the observed data sequences. Therefore, the
generated data is important for more accurate solution of various complex
planning, design and operational problems in water resources development
(Yevjevich, 1989). Typically, stochastic simulation of hydrologic time series
such as streamflow and rainfall are based on mathematical models (Salas,
1993; Hipel and McLeod, 1994). Simulation methods for the hydrologic time
series can be classified into disaggregation and aggregation methods (Harun,
1999). Valencia and Schaake (1973) proposed the so-called disaggregation
model that subsequently becomes a major technique for modeling hydrologic
series. Further modification and applications of disaggregation model have led
to the development of other models such as Mejia - Rouselle, SPIGOT and
Lane.
The main objective of this study was to develop and test various stochastic
models capable of reproducing the historical statistical characteristics
especially mean and standard deviation of monthly streamflow and rainfall
series. The streamflow and rainfall records of Sungai Muar were obtained
from the Department of Irrigation and Drainage (DID), Malaysia. Ten data
sets were simulated from the historical records and each set consists of one
hundred years of flow and rainfall sequences. The model performance for
untransformed and transformed data series was compared.
2. Methodology
Several disaggregation models namely Valencia-Schaake model (Valencia and
Schaake, 1973), Mejia-Rouselle model (Mejia and Rouselle, 1976), Lane
(Lane, 1979) and Synthetic Streamflow Generation Software Package
(Grygier and Stedinger, 1991) were tested. The basic form of Valencia-
Schaake model (VLSH) can be written in a matrix form as:
ttt
BεAQY
(1)
for the case of disaggregating annual flows into seasonal flows, Y
t
,
y,.....y,y Y
m,t2,t1,t
i
t
is a column matrix containing the seasonal flow
values which sum to Q
t
, and for the same time Q and Y are referred as flow
Jurnal Kejuruteraan Awam 16(2): 56-65 (2004)
58
values. Q
t
is a 1 x 1 matrix of the annual streamflow value of year t, m is taken
as 12 month,
t
is the m x 1 matrix of independent standard normal deviates,
and A and B are the parameters matrices with dimensions of m x 1 and m x m,
respectively. The Mejia-Rouselle (MJRS) model takes the following form:
1tttt
Y C ε B Q AY
(2)
in which Y
t
, Q
t
,
t
, A and B are similar to the Valencia-Schaake model and C
is the additional (m x m ) parameter matrix. The Lane model (LANE) for a
single site can be written as:
(3)
in which Y
ν, t
is the seasonal streamflow vector; Q
v
is the annual streamflow
vector;
v,t
is the vector of normally distributed noise term with mean zero and
the identity matrix as its variance – covariance matrix. The noises
v, t
are
independent in time and space; v denotes the number of year and t is for
season (month). The condensed disaggregation procedures are based on
Synthetic Streamflow Generation Software Package (SPIGOT). The model
takes the following form:
(4)
where t is for month; ν is for year; Y
ν,t
is the seasonal streamflow vector;
tν,1tν, ttν,
ε E CE
is the normally distributed innovations of
v,t
, the
independent zero-mean normal random vectors; and Q
v,t
is the generated
annual streamflow vector.
For the case of rainfall simulation, the VLSH model can be written as:
ttt
ε B Z AX
(5)
where X
t
,
,
2,1,
,.....,
mt
tt
xxxX
i
t
is a column matrix containing the seasonal
rainfall values which sum to Z
t
, and for the same time Z and X represent
rainfall values. Z
t
is a 1 x 1 matrix of the annual rainfall value of year t, m is
taken as 12 month,
t
is the m x 1 matrix of independent standard normal
deviates, and A and B are the parameters matrices with dimensions m x 1 and
m x m, respectively. For the case of MJRS model, the rainfall series
simulation reads:
1tttt
XCε BZ AX
(6)
tν,tν,ttt ν,
E Q B AY
1tν, τtν,tνttν,
Y C ε B Q AY
Jurnal Kejuruteraan Awam 16(2): 56-65 (2004)
59
where the X
t
, Z
t
, A, B and
t
are similar with equation (5) and C is the
additional (m x m) parameter matrix. The LANE model for rainfall series can
be written as:
1tν,ttν,tν
t
tν,
XCε BZ
A
X
(7)
The development of streamflow and rainfall simulation model involves
three procedures; statistical analysis of data, fitting a stochastic model, and
generating a synthetic series. The simulation models used in this study are
based on work by Toa and Delleur (1976) and Grygier and Stedinger (1991).
The quality of the data was examined by performing time series plotting,
distribution plot and descriptive analyses. The statistical characteristics of the
observed data series are important factors in selecting the type of model.
Basically, a streamflow and rainfall series can be characterised by their mean,
standard deviation, skewness coefficient and season-to-season correlation
coefficient.
In the case of non-normally distributed monthly streamflow and rainfall
series the data was first transformed. Logarithmic, Box-Cox and power
transformation techniques were generally sufficient to obtain normal
distribution. The use of normally distributed series (after transformation) is
preferred because their statistical properties are well established compared to
the original series (non normal distribution). The generated series were then
compared with the historical records for the untransformed and transformed
cases. The normality of the data was tested using the skewness of normality
(Valencia and Schaake, 1973). The descriptive analysis consists of parameter
estimation and model testing to ensure that the model can fit the data well. The
parameter estimation step was done after the type of model(s) was selected.
The model parameters were estimated either by the method of moments
(MOM) or by the least squares methods (LSM).
The parameter estimations of the stochastic model were tested to ensure
that the model comply with the model requirement. The goodness of fit test
involved checking the residuals and comparing the model with the historical
properties. The basic assumptions about the residual are that they are normal
and independent. For testing whether the residuals are independent, two
approaches were used. The first compute the correlation coefficient and check
whether the values are statistically equal to zero. The second approach used
the Porte Manteau lack of fit test as described by Valencia and Schaake (1973)
and Grygier and Stedinger (1991).
Jurnal Kejuruteraan Awam 16(2): 56-65 (2004)
60
3. Results and Discussion
This analysis used 26 years of streamflow and 59 years of rainfall data of
Sungai Muar. The statistics of the historical and generated streamflow and
rainfall sequences were computed and compared. Figures 1 and 2 show that all
disaggregation candidate models can adequately preserve the historical mean
for transformed and untransformed streamflow. However, the SPIGOT model
preserves the historical standard deviation better than the other candidate
models (Figures 3 and 4). VLSH is obviously the best model for flow
simulation as it consistently preserve the statistical properties of most of the
mean monthly values for both untransformed and transformed flow series.
Nevertheless, all the tested models failed to preserve the skewness coefficient
for both untransformed and transformed streamflow and rainfall series.
In addidition, Box and Whisker plots of the annual flow for each model are
shown in Figures 5 and 6. The candidate models consistently demonstrate a
good reproduction of the historical properties (annual mean) for the
transformed flow sequences (Figure 5). The tested models, however, are less
promising in preserving the historical annual standard deviation except for the
VLSH model (Figure 6).
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
MONTH
0
20
40
60
80
100
120
140
MEAN (mcm)
HISTORICAL VLSH MJRS LANE SPIGOT
Figure 1: Mean monthly streamflow obtained by various
disaggregation models (transformed flow)
Jurnal Kejuruteraan Awam 16(2): 56-65 (2004)
61
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
MONTH
0
20
40
60
80
100
120
140
MEAN(mcm)
HISTORICAL VLSH MJRS LANE SPIGOT
Figure 2: Mean monthly streamflow obtained by various
disaggregation models (untransformed flow)
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
MONTH
0
20
40
60
80
STD DEVIATION
HISTORICAL VLSH MJRS LANE SPIGOT
Figure 3: Mean monthly standard deviation of streamflow obtained by
various disaggregation models (transformed flow)
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
MONTH
0
20
40
60
80
100
STD DEVIATION (mcm)
HISTORICAL VLSH MJRS LANE SPIGOT
Figure 4: Mean monthly standard deviation of streamflow obtained by
various disaggregation models (untransformed flow)
Jurnal Kejuruteraan Awam 16(2): 56-65 (2004)
62
VLSH MJRS LANE SPIGOT
450
550
650
750
MEAN (mcm)
Mean
±SD
±1.96*SD
Box & Whisker Plot
Historical mean = 518.61mcm
Figure 5: Annual mean streamflow obtained by various
disaggregation models (transformed flow)
VLSH MJRS LANE SPIGOT
300
500
700
STD. DEVIATION (mcm)
Mean
±SD
±1.96*SD
Box & Whisker Plot
Historical Std. Deviation = 322.35 mcm
Figure 6: Annual standard deviation of streamflow obtained by
various disaggregation models (transformed flow)
Similar comparisons were made for the rainfall simulation. In Figures 7 and
8, all the disaggregation models are able to produce very similar mean
monthly with the historical mean for both transformed and untransformed
rainfall series. Similar results were obtained for the preservation of mean
monthly standard deviation (Figure 9). As for the annual data, the candidate
models are successful in preserving the historical annual mean for transformed
rainfall series (Figure 10). However, the MJRS and LANE models slightly
underestimated the historical standard deviation (Figure 11). In overall, the
VLSH model is the most robust for preserving the historical annual standard
deviation for the transformed rainfall sequences.
Jurnal Kejuruteraan Awam 16(2): 56-65 (2004)
63
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
MONTH
50
100
150
200
250
300
MEAN (mm)
HISTORICAL VLSH MJRS LANE
Figure 7: Mean monthly rainfall generated by various
disaggregation models (transformed series)
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
MONTH
50
100
150
200
250
300
MEAN (mcm)
HISTORICAL VLSH MJRS LANE
Figure 8: Mean monthly of rainfall obtained by various
disaggregation models (untransformed series)
JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC
MONTH
0
40
80
120
160
200
STD.DEVIATION
(mm)
HISTORICAL VLSH MJRS LANE
Figure 9: Mean monthly standard deviation of rainfall obtained by
various disaggregation models (transformed series)
Jurnal Kejuruteraan Awam 16(2): 56-65 (2004)
64
VLSH MJRS LANE
1700
1900
2100
2300
2500
MEAN (mm)
Mean
±SD
±1.96*SD
HISTORICAL MEAN = 1806.92 mm
Box & Whisker Plot
Figure 10: Annual mean of rainfall obtained by various
disaggregation models (transformed series)
VLSH MJRS LANE
800
1000
1200
1400
1600
STD. DEVIATION (mm)
Mean
±SD
±1.96*SD
HISTORICAL STD. DEVIATION = 981.98 mm
Box & Whisker Plot
Figure 11: Annual standard deviation of rainfall obtained by various
disaggregation models (transformed series)
Jurnal Kejuruteraan Awam 16(2): 56-65 (2004)
65
4. Conclusion
The tested disaggregation models have successfully preserved the historical
mean and standard deviation of streamflow and rainfall series of Sungai Muar.
Nevertheless, the models failed to preserve the skewness coefficient. VLSH
model was found to be the best stochastic disaggregation technique as it
produces very similar properties to the historical streamflow and rainfall
series. These findings, however, must be considered preliminary as the models
were only tested on one site. Due to variability of hydrological data, this study
must be replicated to a number of rivers in Malaysia before any generalization
can be made.
Acknowledgements
This research has been supported by RMC-UTM Vote No 75034 and financial
support provided by NSF Ministry of Science and Technology. The
Department of Irrigation and Drainage (DID) is gratefully acknowledged for
providing the data.
References
Grygier, J.C.and Stedinger, J.R. (1991) SPIGOT: A Synthetic Streamflow Generation
Software Package User’s Manual V2.6, School of Civ. and Envir. Eng., Cornell
Unversity, Ithaca, N.Y.
Harun, S. (1999) Forecasting and Simulation of Net Inflows for Reservoir Operation
and Management. Ph.D. Thesis, University Teknologi Malaysia, 220 pp.
Hipel, K.W., and McLeod, A.I. (1994) Time Series Modeling of Water Resources and
Environmental Systems. Elsevier, Amsterdam.
Lane, W.L. (1979). Applied Stochastic Techniques (LAST computer package), User
Manual. Division of Planning Technical services, Bureau of Reclamation, Denver,
Colarado, USA.
Mejia, J.M., and Rouselle, J. (1976). Disaggregation models in hydrology revisited.
Water Resources Research, 12(2): 185-186.
Salas, J.D. (1993) Analysis and modeling of hydrologic time series. In Maidment, D.
(Ed.), Handbook of Hydrology, McGraw Hill, New York., p. 19.1-19.72.
Toa, P.C., and Delleur, J.W. (1976) Seasonal and nonseasonal ARMA models.
Journal of the Hydraulics Division, 102(HY10): 1541-1559.
Valencia, R.D. and Schaake, J.C. (1973) Disaggregation process in stochastic
hydrology. Water Resources Research, 9(3): 1295-1306.
Yevjevich, V. (1989) General introduction to application of stochastic hydrology in
water resources. Proceedings of the NATO Advanced Study Institute on
Stochastic Hydrology and its use in Water Resources Systems Simulation and
Optimization, Peñíscola, Spain. 18-29 September 1989
